istina.msu.ru · J. Costamagna, F. M. Rabagliati, B. L. Rivas Macromolecular Complexes Vol. 304 J....

Macromolecular Symposia | 316

Molecular Mobility and Order inPolymer Systems

Selected Contributions from:The 7th International Symposiumon Molecular Mobility and Order inPolymer SystemsSt. Petersburg, RussiaJune 6 – 10, 2011

Symposium Editors:Anatoly Darinskii(Russian Academy of Science,St. Petersburg, Russia)

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Macromolecular Symposia Vol. 316

Molecular Mobility and OrderinPolymerSystems

Selected Contributions from:The 7th International Symposiumon Molecular Mobility and Order inPolymer SystemsSt. Petersburg, RussiaJune 6 – 10, 2011

Symposium Editors:Anatoly Darinskii(Russian Academy of Science,St. Petersburg, Russia)

� 2012 WILEY-VCH Verlag GmbH & Co. KGaA

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Table of Contents | v

MacromolecularSymposia:Vol. 316

Articles published on the web will appear

through:

wileyonlinelibrary.com

Cover: The 7th International Symposium

on Molecular Mobility and Order in Poly-

mer Systems was held in St. Petersburg,

Russia, from June 6–10, 2011. The cover is

selected from the article by P. Pakhomov

et. al. and shows characteristic forms of

filament-like aggregates.

Molecular Mobility and Order in Polymer SystemsSt. Petersburg, Russia

Preface Anatoly Darinskii

Semiflexibility Highlights the Polymers’

Topology: Monte Carlo Studies

� 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Ganna Berezovska,*

Maxim Dolgushev,

Alexander Blumen

www.ms-j

| 1

Theory of Light-Induced Deformation of

Azobenzene Elastomers

V. P. Toshchevikov,*

M. Saphiannikova,

G. Heinrich

| 10

Effect of Chemical Structure and

Charge Distribution on Behavior of

Polyzwitterions in Solution

A. A. Lezov, P. S. Vlasov,

G. E. Polushina,

A. V. Lezov*

| 17

Diblock Copolymer Micelles with Ionic

Amphiphilic Corona

Evgeny A. Lysenko,*

Alevtina I. Kulebyakina,

Pavel S. Chelushkin,

Alexander B. Zezin

| 25

ournal.de

vi | Table of Contents

Synthesis and Solution Properties of Loose

Polymer Brushes Having Polyimide

Backbone and Methylmethacrylate Side

Chains


Anna Krasova,

Elena Belyaeva,

Elena Tarabukina,

Alexander Filippov,*

Tamara Meleshko,

Dmitry Ilgach,

Natalia Bogorad,

Alexander Yakimansky

www.ms-j

| 32

Hydrodynamic Properties of ‘‘Pseudo-

Dendrimer’’

Alexander P. Filippov,*

Alina I. Amirova,

Elena V. Belyaeva,

Elena B. Tarabukina,

Natalia A. Sheremetyeva,

Aziz M. Muzafarov

| 43

Modeling of Structure and Nonlinear

Optical Activity of Epoxy-Based

Oligomers with Dendritic

Multichromophore Fragments

Olga D. Fominykh,

Marina Yu. Balakina*

| 52

A New Approach to the Determination of

Adhesion Properties of Polymer Networks

Yulia G. Bogdanova,*

Valentina D. Dolzhikova,

Ilya M. Karzov,

Alexander Yu. Alentiev

| 63

Autoadhesion of Glassy Polymers
Yuri M. Boiko* | 71
2D Diffusion of Macromolecules Adsorbed

on Glass Microspheres

A. S. Malinin,*

A. A. Rakhnyanskaya,

A. A. Yaroslavov

| 79

Dynamic Mechanical Analysis and

Molecular Mobility of the R-BAPB Type

Polyimide

V. P. Toshchevikov,*

V. E. Smirnova,

V. E. Yudin,

V. M. Svetlichnyi

| 83

Thermostable Polycyanurate-Polyhedral

Oligomeric Silsesquioxane Hybrid

Networks: Synthesis, Dynamics and

Thermal Behavior

Olga Starostenko,

Vladimir Bershtein,*

Alexander Fainleib,

Larisa Egorova,

Olga Grigoryeva,

Alfred Sinani,

Pavel Yakushev

| 90

Supramolecular Hydrogels Based on Silver

Mercaptide. Self-Organization and

Practical Application

Pavel Pakhomov,*

Svetlana Khizhnyak,

Maxim Ovchinnikov,

Pavel Komarov

| 97

ournal.de

Table of Contents | vii

Comparative Study of the Quantity of

Volatile Organic Compounds in Water-

Based Paint and Solvent-Based Applied

Polyurethane


Ailton R. da Conceicao,*

Ednilson A. R. Pimenta,

Ronaldo S. Fujisawa,

Evandro L. Nohara

www.ms-j

| 108

Thermal Degradation of Adsorbed Bottle-

Brush Macromolecules: When Do Strong

Covalent Bonds Break Easily?

Jaroslaw Paturej,

Lukasz Kuban,

Andrey Milchev,

Vakhtang G. Rostiashvili,

Thomas A. Vilgis

| 112

ournal.de

ix | Preface

The International Symposium on ‘‘Mole-

cular Mobility and Order in Polymer

Systems’’ was the seventh one in the

series of similar St. Petersburg IUPAC

meetings on macromolecules held in

1994, 1996, 1999, 2002, 2005 and 2008,

and organized by the Institute of Macro-

molecular Compounds of the Russian

Academy of Sciences (RAS). Symposiums

1996, 2002 and 2008 had a slightly title

‘‘Molecular Order and Mobility in Polymer

Systems’’ and were devoted mainly to

equilibrium properties of polymer systems.

The present Symposium was dedicated to

the International Year of the Chemistry

Co-organizers of the Symposium were

the Department of Chemistry and Material

Science of Russian Academy of Sciences

and the Polymer Council of Russian Acad-

emy of Sciences. The symposium was spon-

sored by the International Union of Pure and

Applied Chemistry (IUPAC) and sup-

ported by the Russian Foundation for Basic

Research (RFBR), St. Petersburg Scientific

Center of RAS, Intertech Corporation,

Bruker Company and L’Oreal Company.

21 plenary lectures, 69 oral communica-

tions and 216 posters were presented at the

Symposium. The overall number of authors

is 766 from 19 countries. Abstracts of all

presentations can be found in the Book of

Abstracts.

Among the Symposiums participants

were prominent scientists, in particular,

M. Ballauf, A. Blumen, A.H.E. Muller,

W. Paul (Germany) J. Klein (Israel), G. J.

Fleer, F.A.M. Leermakers (Netherlands),

H.-A. Klok and M. Textor (Switzerland),

F. Svec and S. Nazarenko (USA), C. M.

Marques (France), H. Tenhu (Finland),

A. Milchev (Bulgaria), T. Birshtein,

Yu. Gotlieb, A. Khokhlov, A. Lezov,

A. Ozerin (Russia) etc.

For many young scientists from Russia

the symposium was the unique possibility

to present their results for the international

community and to communicate with their

foreign colleagues.

This issue contains 15 papers written by

authors of some plenary and oral presenta-


tions at the Symposium which cover a

rather broad range of problems of modern

polymer science.

The issue starts with the theoretical

paper of G. Berezovska et al. Semiflex-

ibility Highlights the Polymers’ Topology:

Monte Carlo Studies where authors in the

framework of the bond fluctuation model

show that under semiflexible conditions the

topology is more pronounced for general

and local properties of polymers.

Authors of the paper of V. P. Toshche-

vikov et al. Theory of light-induced defor-

mation of azobenzene elastomers present

the theory predicting the dependence of

the response to the light of the polymer

network with chromophores on their

orientation distribution around the main

chains.

Two papers are devoted to ionizable

polymers in solution.

A. A. Lezov et al. Effect of Chemical

Structure and Charge Distribution on

Behavior of Polyzwitterions in Solution

consider the conformation of the interest-

ing type of polyzwitterions, namely, poly-

betaine where the anionic and cationic

groups are on the same monomer unit.

E. A. Lysenko et al., Diblock Copolymer

Micelles with Ionic Amphiphilic Corona

have presented results of the study of diblock

copolymer micelles with homogeneous

hydrophobic core and heterogeneous amphi-

philic corona.

Results for branched polymers are pre-

sented in three papers.

The subject of the paper of A. Krasova

et al. Synthesis and Solution Properties of

Loose Polymer Brushes Having Polyimide

Backbone and Methylmethacrylate Side

Chains is the solution behavior of a cylindrical

polymer brush where backbone and side

chains differ considerably in chemical nature

and, hence, thermodynamic properties.

In the paper of A. P. Filippov et al,

Hydrodynamic Properties of ‘‘Pseudo-den-

drimer’’ the conformation of nonregular

hyperbranched polymers in the solution is

compared with that of regular dendrimer of

the same chemical nature.

www.ms-journal.de

Preface | x

In the theoretical paper of O. D. Fomi-

nykh et al. Modeling of structure and

nonlinear optical activity of epoxy-based

oligomers with dendritic multichromo-

phore fragments the relationship between

structure and NLO activity is studied by the

computer simulation.

Two papers are devoted to adhesive

properties of polymers.

Authors of the paper of Yu. G. Bogda-

nova et al. New Approach to the Determi-

nation of Adhesion Properties of Polymer

Networks suggest to use the works of

adhesion of polymer to liquids simulating

polar or non-polar phases for prediction of

adhesive properties of network (binder,

coupling agent) and for the choice of

network provided the best tensile strength

of composite material.

In the paper of Yu. M. Boiko Autoadhe-

sion of Glassy Polymers.

The autoadhesion and adhesion (bonding

of one and the same material and of two

different materials, respectively) of two con-

tacting polymer pieces is related with the

mobility in the surface layers of polymers.

The paper of A. S. Malinin et al. 2D

diffusion of macromolecules adsorbed on

glass microspheres also concerns surface

phenomena. Authors have demonstrated

an example of 2D diffusion of macromole-

cules when adsorbed polycations migrate

from one colloidal particle to another

without desorption into the solution.

Two papers are devoted to mechanical

properties of polymers in bulk.

V. P. Toshchevikov et al. Dynamic

Mechanical Analysis and Molecular

Mobility of the R-BAPB Type Polyimide

present results of the dynamic mechanical

analysis of one of potential candidates

as high-performance thermoplastic matrix

for thermally stable fiber reinforced com-

posites as well as nanocomposites.

Olga Starostenko et al. Thermostable

Polycyanurate-Polyhedral Oligomeric Sil-

sesquioxane Hybrid Networks: Synthesis,

Dynamics and Thermal Behavior discuss

an unusually strong influence of low con-

tent of molecularly dispersed inorganic

nanoparticles (polyhedral oligomeric sil-

sesquioxane) on the glass transition char-

acteristics of the hybrid nanocomposite.

An example of a pseudo-polymeric system

is discussed in the paper of P. Pakhomov et al.

Supramolecular hydrogels based on silver

mercaptide. Self-organization and practical

application Authors demonstrate a novel

supramolecular system which is able to form

thixotropic hydrogels at very low concen-

trations of initial components.

The paper of A. R. da Conceicao et al.

Comparative Study of the Quantity of

Volatile Organic Compounds in Water-

Based Paint and Solvent-Based Applied

Polyurethane is an example of the work in

the applied polymer science. Authors

compare the VOC results and combust-

ibility of the paint based on solvents with

water-based paint.

Anatoly Darinskii

Macromol. Symp. 2012, 316, 1–9 DOI: 10.1002/masy.201250601 1

The

Her

E-m

Cop

Semiflexibility Highlights the Polymers’ Topology:

Monte Carlo Studies

Ganna Berezovska,* Maxim Dolgushev, Alexander Blumen

Summary: In this article we analyze in how far semiflexible behavior enhances the

differences in the properties of classes of polymers whose topological structure

varies. We focus on three pairs of macromolecular classes: stars vs. chains, unknotted

rings vs. rings with one knot (trefoils), and stars vs. unknotted rings. For this we

determine the mean-square radii of gyration and the bond-bond correlation func-

tions through Monte Carlo simulations which use the bond fluctuation model. We

show that introducing semiflexibility magnifies the differences between experimen-

tally measurable quantities and may even lead to qualitative changes. Our simulation

results are supported by theoretical studies which make use of the maximum entropy

principle.

Keywords: branched; Monte Carlo simulations; ring polymers; stiffness; theory

Introduction

The properties of polymers are influenced

both by their topology and also by the

degree of semiflexibility of their segments.

While recent analytical extensions of the

generalized Gaussian structures picture

(GGS)[1] to the case of semiflexible branched

polymers[2–5] and rings[5,6] give qualitative

clues to the behavior of polymers, numerical

simulation techniques allow to investigate the

role of the excluded volume and thus provide

a more realistic approach. For this we present

here a simulation study of different topolo-

gical structures by means of the bond

fluctuation model (BFM),[7,8] which allows

to account both for branching and/or pre-

sence of loops and also for semiflexible

behavior. In the analysis of our results we

focus on the mean square radius of gyration

(as a general static property of polymers) and

on the bond vector correlation function (as an

example of local properties). We compare

the simulation data with the theoretical

predictions based on the extended GGS

oretische Polymerphysik, Universitat Freiburg,

mann-Herder-Str. 3, D-79104 Freiburg, Germany

ail: [email protected]

yright � 2012 WILEY-VCH Verlag GmbH & Co. KGaA

approach[2–4] and on the maximum-entropy

principle (MEP).[5,6]

Now, a theoretical approach which was

recently shown to be very well suitable for

the description of semiflexible tree-like

polymers (STPs) as well as of semiflexible

rings is the MEP.[9,10] Being initially

applied to semiflexible chains in a dis-

crete[11] and in a continuous[12] framework,

it was implemented to STPs[2] and general-

ized to semiflexible rings.[5,6] An important

feature of the MEP method is that it

introduces constraints only on adjacent

bonds. Moreover, the treatment of STPs

with MEP was shown to be equivalent, and

hence an alternative, to the recently devel-

oped approach for STPs[2] done in the spirit

of Bixon and Zwanzig.[13]

An example where the theoretical

approaches mentioned above as well as

the numerical investigations turn out to be

helpful is the study of so-called cospectral

polymer (CP) structures.[14,15] These struc-

tures are important, since in the GGS

picture they have the same Laplacian

spectrum although being topologically dif-

ferent. Hence, in GGS, flexible polymers

whose structures are cospectral graphs are

predicted to be indistinguishable under the

usual static and dynamical measurements.

, Weinheim wileyonlinelibrary.com

Macromol. Symp. 2012, 316, 1–92

Taking into account that large tree-like

structures have (at least) one cospectral

counterpart,[16,17] the problem becomes of

much importance. Our recent mathemati-

cal-analytical study[18] shows that when the

polymers are semiflexible one can distin-

guish between cospectral structures. This is

qualitatively confirmed by our simulation

results on the smallest tree-like cospectral

pair.[18]

Discrete semiflexible rings provide

another example of analytical results

obtainable through MEP.[5,6] It turns out

that in the rigid limit, besides solutions

pertaining to unknotted rings, one obtains

other solutions related to knotted rings.[5,6]

To have a check of the theory, Monte Carlo

(MC) simulations are very helpful, and here

especially the BFM, which in its standard

form conserves the topology of the objects

but also permits to turn off and on the

excluded volume interactions.[5,6]

Having noticed that under semiflexible

conditions the topology is more pro-

nounced (as in the case of CP and of the

rings described above) and motivated by

recent achievements in theory based on the

MEP, we decided to study in detail the

influence of the semiflexibility on different

topologies. For this we start with simula-

tions on star polymers with functionality

f¼ 3 and f¼ 4, and continue by considering

unknotted rings and rings with one knot

(known as trefoils).

Our paper is structured as follows: In the

next section we describe the simulation

technique and present the quantities under

study. Then we proceed to present simula-

tion results on stars and rings, by focusing

on the role of semiflexibility; for this we

compare the behaviors of stars vs. chains, of

unknotted rings vs. trefoils and finally of

stars vs. rings. We end up our paper with

conclusions.

Simulation Method

We investigate here the properties of

semiflexible polymers in the framework

of the bond fluctuation model (BFM).[7,8] In

Copyright � 2012 WILEY-VCH Verlag GmbH & Co. KGaA

the BFM each monomer of a coarse-grained

polymer is represented by a cube of unit

length on the simple cubic lattice. The

excluded volume property is introduced by

requiring that each lattice site belongs to one

cube at most. Although the lengths of the

bonds are allowed to fluctuate, they have to

belong to the set of lengths 2,ffiffiffi5p

,ffiffiffi6p

, 3 orffiffiffiffiffi10p

. All spatial distances are measured in

units of the lattice spacing. Altogether, the

three-dimensional BFM allows 108 different

bond vectors and 87 different angles

between them. Applying the cubic point

group operations to the set of vectors {(2, 0,

0), (2, 1, 0), (2, 1, 1), (2, 2, 1), (3, 0, 0), (3, 1, 0)}

one obtains the complete set of allowed

bond vectors.

Starting from an initial configuration one

creates a new one through one local move:

First, one chooses at random a unit cube;

then one attempts to move it randomly by a

unit length in one of the six lattice

directions. The attempt is rejected if at

least one of the eight sites of the unit cube in

the new position lands on an occupied site

or if the new bond does not belong to the

allowed set. The restrictions on the bond

lengths are topology-preserving, since they

prevent the crossing of segments. One

Monte Carlo step (MCS) is achieved when

in average each bead has attempted one

trial move. The BFM scheme was originally

applied to chain-like structures, but it now

encompasses a large number of polymer

structures.[19–25] In Figure 1 we represent

schematically a branched polymer and some

of the allowed BFM moves.

Since we want to model semiflexible

objects we introduce an energy penalty for

moves which are allowed under the above

scheme, but which involve an energy change

of DU. For this we use the Metropolis

algorithm[26] to determine the transition

probability w

w ¼ min 1; exp � DU

kBT

� �� (1)

for accepting an allowed local move.

Now, to be in line with the theoretical

calculations for semiflexible tree-like struc-

, Weinheim www.ms-journal.de

Figure 1.

Realization of a branched polymer in the bond-

fluctuation model (BFM) (N¼ 7 elements are dis-

played). The bond vectors di are indicated by black

arrows; the gray arrows show allowed elementary

moves, see text for details.

Macromol. Symp. 2012, 316, 1–9 3

tures[2] and using the fact that the sum of

the cosines of all the angles between the

bond vectors at each junction point i is

bounded,[27] we assume the bending energy

Ui corresponding to the junction i with

functionality fi to be:

Ui

kBT¼ Bi

fi

2�Xfða;bÞg

ð�1Þscosuab

0@

1A: (2)

Here Bi is the stiffness parameter

corresponding to the junction i (Bi being

0 in the flexible case), the sum {. . .} runs

over all the distinct pairs (a, b) of bond

vectors involving junction i, and uab is the

angle between the bond vectors a and b.

The parameter s is either 0 (for bond

vectors in a head to tail configuration) or

1 otherwise.

The total energy of a configuration is the

sum of energies of every junction point. But

being interested in the energy difference

DU it is enough to calculate only the

contributions from the junctions which

are affected by the trial motion. If for

example a junction (say i) experiences a

trial move, then one has to take into

account only contributions to the energy

change DU from all pairs of adjacent bonds

of which at least one is attached to i. Thus,

using Equation (2), the energy difference


DU to be used in Equation (1) is:

DU

kBT¼ �

X½ða;bÞ�

ð�1ÞsBj cosunewab � cosuold

ab

� �:

(3)

In Equation (3) the sum [. . .] runs over

all distinct pairs of adjacent bond vectors

(a, b), of which at least one involves

junction i, and j denotes the junction of

the (a, b)-pair. The unewab (uold

ab ) stand for the

new (old) angles.

A remark on the form of the potential

given by Equation (2) is in order.

Obviously, in it the term fi/2 is irrelevant.

It is introduced in order to have for fi¼ 2, in

a head to tail orientation of the bond

vectors, from Equation (2):

Ui

kBT¼ Bið1� cosuÞ: (4)

With Bi��B Equation (4) is one of the

classical potentials used in simulations of

semiflexible chains[28,29] and of rings.[21,22]

In our study we focus on the normalized

mean-square radius of gyration hR2gi=hl2

biand on the normalized bond-bond correla-

tion functions hdi � dji=hl2bi, where di is

the ith bond of the structure. The value

offfiffiffiffiffiffiffiffihl2

biq

is around 2.7 lattice units, which is

typical for the BFM.[20,22] We use the

following expression to determine hR2gi

from the MC data[30]

hR2gi ¼

1

N

XN

i¼1

hðri �RCÞ2i; (5)

where RC is the center of mass. From the

STP model one has a theoretical expression

for hR2gi, namely

hR2gi ¼

l2

N

XN

k¼2

1

lk: (6)

Here l2 is the mean-square length of

each bond and {lk} are the non-vanishing

eigenvalues of the matrix ASTP, which

determines the Langevin equations in the

semiflexible case.[2,5] Alternatively, for

stars and chains hR2gi can be obtained using

explicit expressions from ref.[5,31]. A few


Macromol. Symp. 2012, 316, 1–94

remarks concerning the stiffness parameters

used in simulations (namely Bi) and in the

theoretical studies (namely ti[5]) are now

required. In the simulations we will let

the semiflexibility parameter Bi to be the

same for all junction types, Bi��B, and

we will use B¼ 0 in the flexible case and

B¼ 6 in the semiflexible case. Given that in

the theoretical framework the mean-square

lengths of all bonds are equal, hl2bitheory ¼ l2,

the theoretical stiffness parameter ti can be

introduced through[2,5,6]

hda � dbi ¼ ð�1Þshl2biti; (7)

where da and db are adjacent bond vectors

connected through the bead i and s is the

same as in Equation 2. For chains and rings

we consider homogeneous situations, in

which all the bonds are connected head to

tail and ti�� t for all i. In the case of stars the

bonds have a head to tail orientation in the

arms and also for them we will set ti�� t.

Only the bonds directly attached to the

core have tail to tail orientations and, in

principle, another stiffness coefficient,

namely q ¼ t=ðf � 1Þ, where f is the func-

tionality of the core of the star. Based on

Equation (7) one can now readily connect

t to B. For chains and stars we can relate

in this way B¼ 0 and B¼ 6 to the values

t¼ 0.19 and t¼ 0.84, respectively. These

values are almost independent of the chain

or of the arm length.[5] For rings the t-values

for several N and for B¼ 0 and B¼ 6

are presented in Table 1.[5,6] One can

notice that in the case of rings the t-values

depend on the ring length; this is due to the

closure condition.[6] For ring lengths suffi-

ciently large the values of t are almost

constant.

Table 1.Theoretical stiffness parameters t for unknotted rings obtfor details. Data from ref.[5,6]

N¼ 16 N¼ 32 N¼ 64

B¼ 0 0.159 0.176 0.182B¼ 6 0.764 0.807 0.816


Objects of Investigation

Linear Chains and Stars

We start by investigating the role of a single

branching point. For this we consider stars

of functionality f¼ 3 and 4 and molecular

weight N ¼ fnþ 1, where n is the number of

beads in each arm. We will compare the

results for them with those for chains of size

N ¼ 2nþ 1 (these can be viewed as ‘‘two-

arm’’ stars, f¼ 2, with arm length 2n). In the

BFM-simulations we take n up to n¼ 50 and

for the chains we go with N up to N¼ 320.

As stiffness parameters we use B¼ 0 and

B¼ 6. The size of the simulation box varies

with the size of the object considered and

for the largest stars or chains it contains

700� 700� 700 lattice units. Each object is

equilibrated for some 109 MCS, after which

the conformations are saved every 1000

MCS. The averages are then taken over at

least 106 realizations. The radius of gyration

is obtained from the simulation data using

Equation (5).

Figure 2 presents in double-logarithmic

scales hR2gi=hl2

bi as a function of N for chains

and for stars for B¼ 0 (upper figure) and for

B¼ 6 (lower figure). The theoretical curves

are evaluated based on Equation 6 using

t¼ 0.19 and t¼ 0.84 as stiffness parameters.

Comparing the simulation data for

hR2gi=hl2

bi as a function of N one can

immediately see that hR2gif¼2 > hR2

gif¼3 >

hR2gif¼4 holds for both B¼ 0 and B¼ 6.

However, for the semiflexible case, B¼ 6,

the differences between the gyration radii

for chains and for stars get much more

pronounced. In line with this observation,

for B¼ 6 and increasing N the objects start

to be more flexible and the distance

between the different curves is getting

smaller. Now, due to the fact that the

ained from the simulations using Equation (7), see text

N¼ 128 N¼ 256 N¼ 512

0.185 0.185 0.1860.819 0.821 0.821


Figure 2.

Double-logarithmic plots of hR2gi=hl2bi versus N for

chains ( f¼ 2) and for stars ( f¼ 3 and f¼ 4). The

symbols indicate the simulation results and the stiff-

ness parameter is B¼ 0 in the upper part and B¼ 6 in

the lower part of the figure. The lines depict the

theoretical results for the corresponding t, t¼ 0.19

and 0.84, see text for details. Data from ref.[5]

Figure 3.

Initial configuration of a knotted ring with N¼ 32

beads (each bead represents a BFM cube), see text for

details.

Macromol. Symp. 2012, 316, 1–9 5

BFM accounts for excluded volume inter-

actions which are not included in the

theory, the agreement between the simula-

tion data and the theoretical curves is rather

qualitative for B¼ 0, while being rather

reasonable for B¼ 6. Paying attention for

B¼ 0 to the smallest values of N (these

being N¼ 5, 16, and 21 for f¼ 2, 3, and 4,

respectively) one can notice that the

deviations from the theory increase with

growing f. This happens due to the growing

density of monomers in the vicinity of the

core and hence due to the more pro-

nounced excluded volume interactions. For

B¼ 6 and small N the agreement between

simulations and theory is rather good; the

effect of the excluded volume decreases


due to the local stiffness. With increasing N

the excluded volume interactions become

more important, which leads to stronger

deviations from the theory. For a more

extensive study of the influence of the

excluded volume on the static properties of

stars and chains we address the reader to

ref.[5]

Rings and Trefoils

In this subsection we study the influence of

stiffness on unknotted rings and on rings

with one knot (the so-called trefoils). Here

we focus not only on the normalized mean

square radius of gyration hR2gi=hl2

bi but also

on the bond-bond correlation functions.

For this we simulate unknotted rings and

trefoils of lengths up to N¼ 512 and

stiffness parameters B¼ 0 and B¼ 6. As

simulation volumes we take cubes, for

N� 64 of 200, for N� 256 of 400 and for

N¼ 512 of 800 lattice units side-length, and

implement periodic boundary conditions.

Depending on the parameters, we equili-

brate both kinds of rings between 109 and

3 � 109 Monte Carlo steps (MCS). Then the

conformations are stored in intervals of

1000 MCS, and the averages are performed

over 106 to 2 � 106 realizations. We take a

square as initial configuration of the

unknotted rings; for the trefoils we sketch

an initial configuration in Figure 3.

Starting with the local properties of

unknotted rings and trefoils we consider the

bond-bond correlation functions hdi � dji.


Figure 4.

Bond-bond correlation functions of semiflexible

unknotted rings obtained from BFM simulations

(symbols) and compared to the theory (lines) for

B¼ 0, upper figure, and B¼ 6, lower figure, see text

for details. Data partly from ref.[5,6]

Figure 5.

Bond-bond correlation functions of semiflexible tre-

foils obtained from BFM simulations (symbols) for

B¼ 0, upper figure, and B¼ 6, lower figure, see text

for details. Data partly from ref.[6]

Macromol. Symp. 2012, 316, 1–96

We report our findings for unknotted rings

in Figure 4 and for trefoils in Figure 5. We

display hd1 � dji=hl2bi as a function of

ðj� 1ÞN, where j numbers the bonds con-

secutively. The upper parts of Figure 4

and 5 show the data for B¼ 0 and the lower

parts the data for B¼ 6. In both figures the

symbols stand for the simulation data; the

lines in Figure 4 show theoretical results for

unknotted rings obtained in refs.[5,6]

Comparing the simulation data for

unknotted rings with those for trefoils

(Figure 4 and Figure 5) we observe that

the data of Figure 4 show minima around

N/2, while in Figure 5 there are maxima

around N/2 and minima around N/4 and

around 3N/4. With growing B these features

get more pronounced, both for the

unknotted rings and for the trefoils. Hence

for quite stiff unknotted rings the bonds d1


and dN/2 are almost antiparallel, whereas for

trefoils that pair is parallel, the antiparallel

pairs being, say, d1 and dN/4 as well as dN/2

and d3N/4. Thus, accounting for the sym-

metry of the ring, hd1þk � djþki ¼ hd1 � dji, in

quite stiff situations one minimum implies a

steady rotation of consecutive angles by a

total amount of 2p, whereas for trefoils this

amount is 4p. These findings are intuitively

clear and are, furthermore, supported by

the theoretical analysis.[6] For larger N and

fixed B the polymers become more flexible

and the extrema get washed out; then it is

more difficult to distinguish between

unknotted rings and trefoils. This again

emphasizes the main idea of this article:

Topological differences are better seen

when considering quite stiff objects. We

also note that the agreement between the

theory and the simulations gets much better

in stiffer situations, B¼ 6, see the lower part

of Figure 4.


100010010

N1

10

100

1000

<R

g2 >/<

l b2 >

ring; B=0ring; B=6trefoil; B=0trefoil; B=6

~N1.20

~N1.27

Figure 6.


unknotted rings (empty symbols) and for trefoil (filled

symbols) for B¼ 0 and B¼ 6. The straight lines cor-

respond to fitting with power laws with indicated

exponents, see text for details.

Figure 7.


unknotted rings and for stars ( f¼ 3 and f¼ 4). The

symbols are obtained from simulations with the

stiffness coefficients being B¼ 0 (upper) and B¼ 6

(lower part of the figure). The lines depict the theor-

etical results for the corresponding t, see text for

details. Data partly from ref.[5]

Macromol. Symp. 2012, 316, 1–9 7

We proceed further by investigating

the mean-square radius of gyration of

unknotted rings and of trefoils for the

stiffness parameters B¼ 0 and B¼ 6. The

results are presented in Figure 6. The values

obtained from simulations are computed

using Equation 5, and are presented through

open symbols for the unknotted rings and

through solid ones for the trefoils. The solid

and dashed lines in Figure 6 show fits to the

simulation data by power laws, where

the scaling exponents equal 1.20� 0.01 for

the flexible unknotted rings and 1.27� 0.01

for the trefoils. These values are in good

agreement with the scaling exponents

reported in,[32] which are 1.176 for the

unknotted rings and 1.266 for the trefoils.

Now, as a function of N we always find that

hR2gitrefoil < hR2

giring, given that the trefoil is a

more compact object than the correspond-

ing unknotted ring. As in the case of chains

and stars discussed above, for moderate

values of N the stiffness considerably

increases the differences in the hR2gi=hl2

bivalues between the unknotted rings and the

trefoils. For large N we get again a more

flexible situation and the hR2gi-values of the

trefoils approach the ones of the correspond-

ing unknotted rings.

Rings and Stars

As a last example we compare the situa-

tions encountered for unknotted rings and


for stars of core functionalities f¼ 3 and

f¼ 4. We again study the influence of

stiffness on the normalized mean-square

radius of gyration hR2gi=hl2

bi. For fully

flexible, phantom stars and rings,

Zimm et. al. found[33,34] hR2gistar=hR2

gichain ¼ð3f � 2Þ=f 2, see Equation (32) and (39) of

ref.,[33] and hR2giring=hR2

gichain ¼ 1=2, as can

be readily inferred from Equation (52a) of

ref.[34] For fixed N one has thus for flexible,

phantom objects:

hR2giring < hR2

gif¼4 < hR2gif¼3: (8)

The situation changes when the struc-

tures get stiff. Thus, for rigid, maximally

extended, unknotted rings and stars geo-

metric arguments lead in the limit of

very large N to hR2gif¼4 : hR2

giring : hR2gif¼3 ¼


Macromol. Symp. 2012, 316, 1–98

14 : 3

p2 : 49 and hence to

hR2gif¼4 < hR2

giring < hR2gif¼3; (9)

i.e. to a change in the order of the radii of

gyration.

For a more realistic picture we again

perform BFM-simulations and find a very

satisfactory agreement with the theory. To

show this we plot in Figure 7 the gyration

radii both for stars and for unknotted rings

for B¼ 0 (upper part) and B¼ 6 (lower part

of Figure 7). Here again the symbols

correspond to the simulation data and the

curves are the theoretical results. For stars

the values of hR2gi=hl2

bi were obtained using

Equation 6 with t¼ 0.19 and t¼ 0.84 for

B¼ 0 and for B¼ 6, respectively. The values

of t for rings are taken from Table 1. For

B¼ 0 we find for all N that Equation (8)

holds. Going to a more stiff situation, B¼ 6,

the behavior changes, and for N964 the

order of the radii of gyration is that of

Equation (9). Thus, we indeed find in the

simulations a crossover between fully

flexible and fully rigid situations; hence

by varying the stiffness coefficient one can

pinpoint the underlying topologies even on

a qualitative level.

Conclusion

We devoted this article to investigate how

changes in flexibility help in highlighting

the topology of polymers. For some

structures, such as CP, this question

becomes of major importance since fully

flexible, ideal CP are indistinguishable.[18]

We were encouraged by recent achieve-

ments in theory, namely by the ease with

which stiffness parameters can be taken

into account, for both in the MEP frame-

work[2,5,6] as well as in the GGS picture.[5]

Here we confronted the theoretical results

to findings from MC simulation studies, in

which the BFM technique was used. This

allowed us to investigate the influence of

semiflexibility under realistic conditions, by

also accounting for the excluded volume

interactions which are not taken into


account in the theoretical studies men-

tioned above.

In our study we focused on two groups of

topologies: simple branched structures such

as stars and chains (the latter can be viewed

as two-arm stars) and simple loop structures

such as unknotted rings and trefoils. By

comparisons within each of the groups (stars

vs. chains, unknotted rings vs. trefoils) and

between the groups (stars vs. unknotted

rings) we could investigate the influence of

semiflexibility on the static properties of

polymers, namely on the mean-square radii

of gyration and the bond-bond correlation

functions. For not-too-large N, both for stars

and chains, and for unknotted rings and

trefoils the differences between the mean-

square radii of gyration increase when the

semiflexibility parameter B gets larger. This

allows a differentiation between these poly-

mers within each of the groups. For

unknotted rings and trefoils the differences

in topologies manifest themselves even

stronger in their bond-bond correlation

functions: With growing B the extrema in

the bond-bond correlation functions become

more pronounced. Comparing different

stars vs. unknotted rings we observe quali-

tative changes: The simulations for B¼ 0

support the theoretical ordering hR2giring <

hR2gif¼4 < hR2

gif¼3 whereas for B¼ 6 and

small N the order is hR2gif¼4 < hR2

giring <

hR2gif¼3. Thus the simulation results are

in good agreement with the theoretical

findings.

Acknowledgements: The authors acknowledgethe support of the Deutsche Forschungsge-meinschaft (Bl 142/11-1) and of the Fonds derChemischen Industrie.

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Macromol. Symp. 2012, 316, 10–16 DOI: 10.1002/masy.20125060210

1 Le

H2 In

31

E-3 Te

sto

G

Cop

Theory of Light-Induced Deformation of Azobenzene

Elastomers

V.P. Toshchevikov,*1,2 M. Saphiannikova,1 G. Heinrich1,3

Summary: A microscopic theory is proposed to describe light-induced deformation of

photo-sensitive elastomers bearing azobenzene chromophores in their strands. We

use an orientation approach in which it is assumed that the light-induced defor-

mation is caused by reorientation of azobenzene chromophores with respect to the

electric vector of the linearly polarized light, E, due to the trans-cis-trans photo-

isomerizaion process whose efficiency depends on the orientation of the chromo-

phores with respect to the vector E. In the framework of the Gaussian approximation

for elasticity of network strands it is shown that the value of the light-induced

deformation depends on the chemical structure of network strands, namely, on the

orientation distribution of chromophores around the main chains which is related

to the length and elasticity of spacers. Depending on the chemical structure,

azobenzene elastomers can demonstrate expansion or uniaxial contraction along

the vector E, as well as non-monotonic deformation with increasing light intensity

(expansion at small light intensities and contraction at high ones).

Keywords: azobenzene elastomers; networks; photo-deformable polymers; statistical

mechanics; theory

Introduction

Azobenzene elastomers represent crosslinked

polymer systems containing photosensitive

azo-moieties in their chemical structure.[1–13]

These compounds belong to a class of smart

materials which are able to transform the light

energy into mechanical stress. Since the

deformation driven by the light can be

controlled rapidly, precisely and remotely,

azobenzene elastomers have a fascinating

potential for micro- and nano-technologies

serving as artificial muscles, sensors, micro-

robots, micropumps, actuators, etc.[1–13]

Light-induced deformation of azoben-

zene polymers is initiated by the photo-

isomerization process of azobenzene chro-

ibniz Institute of Polymer Research Dresden,

ohe Str. 6, 01069 Dresden, Germany

stitute of Macromolecular Compounds, Bolshoi pr.

, 199004 Saint-Petersburg, Russia

mail: [email protected]

chnische Universitat Dresden, Institut fur Werk-

ffwissenschaft, Helmholtz Str. 7, D-01069 Dresden,

ermany


mophores. The chromophores affected by

the light of a proper wavelength are able to

change their shape from the rod-like trans-

state to the bent cis-state.[14–16] One can

distinguish two types of photo-deformable

azobenzene elastomers. The systems of the

first type[3–10] are based on anisotropic

liquid crystalline nematic elastomers with

dispersed azobenzene chromophores in a

network matrix. The rod-like trans-isomers

of the chromophores stabilize the LC

phase, whereas the bent cis-isomers desta-

bilize it. Consequently, trans-cis photoi-

somerization caused by an ultraviolet

illumination induces a transition of the

LC-elastomer from the nematic to isotropic

state, this transition being accompanied by

a uniaxial deformation of a sample with

respect to the LC-director. Theoretical

description of the light-induced deforma-

tion in the materials of such a kind is based

on a modification of the theory of phase

transitions in nematic elastomers, with the

nematic-to-isotropic phase transition being

dependent now on the light intensity.[4,5]


Macromol. Symp. 2012, 316, 10–16 11

Photo-deformable azobenzene elasto-

mers of the second type are based on

elastomeric matrices which are macroscopi-

cally isotropic.[8,11–13] Under influence of the

linearly polarized light, azobenzene elasto-

mers of this type are deformed along the

electric vector of the light E. Thus, in

contrast to azobenzene polymers based on

nematic elastomers whose direction of

deformation is restricted by the LC-direc-

tor,[3–10] the direction of deformation in

azobenzene elastomers based on isotropic

matrix can be varied by rotating the

polarization vector of the light.[8,11–13] Thus,

investigation of photo-deformable elasto-

mers with variable direction of deformation

is of a special interest. To our knowledge,

there are no theories in the literature which

describe light-induced deformation of iso-

tropic azobenzene elastomers with variable

direction of deformation.

In the present paper we propose a

microscopic statistical theory of light-

induced deformation of isotropic azoben-

zene elastomers affected by uniform linearly

polarized light. The theory is based on the

orientation approach[17–19] which was pro-

posed recently to describe photo-mechanical

properties of isotropic low-molecular-

weight glassy azobenzene polymers built

from short molecules (oligomers) bearing

azobenzene chromophores in side chains.

According to this approach, the light-

induced mechanical stress originates from

reorientation of chromophores with respect

to the polarization vector of the light E. This

reorientation is caused by an anisotropic

character of the trans-cis-trans photoisome-

rization process: maximal probability of the

transition from the rod-like trans-state to the

bent cis-state is achieved at such orientation

of the rod-like chromophore, when its long

axis is parallel to the electric vector of the

light E.[14–16] As a result, after multiple

trans-cis-trans photoisomerization cycles

the number of rod-like chromophores,

which are arranged parallel to the vector

E, becomes lower than the number of

chromophores which are oriented in per-

pendicular direction, i.e. orientation aniso-

tropy appears. The light-induced orientation


anisotropy can be described by introducing

an effective orientation potential acting on

each chromophore.[20] Recently, we have

shown[17–19] that orientation potential intro-

duced in ref.[20] provides the values of the

light-induced stress, s, higher than the

values of the yield stress typical for glassy

polymers sY � 50MPa at the light intensi-

ties Ip � 1W=cm2 which are usually used in

experiments. At stresses s > sY a polymer

demonstrates an irreversible deformation.

Irreversible light-induced deformation

of glassy azobenzene polymers opens up

the possibility for inscription of surface

relief gratings onto these materials.[21–26]

To explain this possibility some authors

have proposed a concept of the light-

induced softening.[27–33] In this concept it

is assumed that the light of intensity

Ip � 1W=cm2 is able to melt locally a glassy

azobenzene polymer and such a ‘‘molten’’

polymer can be then irreversibly deformed.

However, it was shown recently with the

help of three different experimental tech-

niques[23–26] that illumination with a visible

light does not affect material properties of

an azobenzene polymer such as bulk

compliance, Young modulus and viscosity,

i.e. an azobenzene polymer remains in the

glassy state. Hence, the theories which need

a concept of light-induced softening are not

able to describe correctly the phenomenon.

The orientation approach developed in

refs.[17–19] allowed us to explain for the first

time the possibility of inscription of surface

relief gratings onto glassy azobenzene

polymers avoiding a concept of the light-

induced softening. Moreover, the orienta-

tion approach[17–19] has illustrated that

photo-elastic behavior of azobenzene poly-

mers is very sensitive to their chemical

structure, namely, to orientation distribution

of chromophores around the main chains.

Depending on it, a sample can demonstrate

either expansion or uniaxial contraction

along the polarization direction of the

light. These results are in a qualitative

agreement with experiments[34–37] and com-

puter simulations[38–40] and demonstrate a

great potential strength of the orientation

approach[17–19] for describing the photo-


Macromol. Symp. 2012, 316, 10–1612

mechanical properties of azobenzene poly-

mers of different chemical structure. In

the present paper, we extend the orienta-

tion approach developed in refs.[17–19]

for glassy uncross-linked azobenzene poly-

mers to cross-linked azobenzene polymers

(elastomers).

Model of an Azobenzene Elastomer and

Main Equations

An azobenzene elastomer is modeled as an

ensemble of polymer chains between net-

work junctions (network strands). Each

network strand consists of N freely-jointed

rod-like Kuhn segments, see Figure 1a.

Each Kuhn segment contains Nch azoben-

zene chromophores which are chemically

attached to the main chain of the segment

(Figure 1b). Orientation structure of chro-

mophores inside the Kuhn segments is

characterized by the orientation distribu-

tion function, Wða; bÞ. Here a is the angle

between the long axis of a chromophore

and the main chain; the angle b charac-

terizes an azimuthal rotation of chromo-

phores around the main chain (Figure 1b).

Short fragments of azobenzene molecules

possess, as a rule, a planar symmetry.[38–40]

Thus, the azimuthal angle b is introduced as

the angle between the plane of symmetry of

the Kuhn segment and the plane formed by

the long axis of the chromophore and the

main chain. The function Wða;bÞ is defined

by the potentials of internal rotations and

by the length of spacers connecting the

Figure 1.

(a) Model of an azobenzene elastomer. Each network stra

bearing Nch azobenzene chromophores in side chains. (b

inside a Kuhn segment.


chromophores with the main chain. As a

rule, one uses the spacers with symmetrical

potentials of internal rotation, e.g. poly-

ethylene’s spacers.[3,4,34–37] Due to the

symmetry of the spacers the orientation

distribution of chromophores inside the

Kuhn segments is symmetrical and obeys

the following relations: Wða;bÞ ¼Wða;�bÞand Wða; bÞ ¼Wð180� � a;bÞ.

According to the orientation appro-

ach[17–20] a photo-induced deformation of

azobenzene polymers is initiated by the

orientation anisotropy of azobenzene chro-

mophores which appears after multiple

trans-cis-trans isomerization cycles of the

chromophores under illumination with the

linearly polarized light. The light-induced

orientation anisotropy of azobenzene chro-

mophores is described by means of an

effective orientation potential acting on

each chromophore:[17–20]

VðQÞ ¼ V0cos2Q; (1)

where Q is the angle between the long axis

of the chromophore and the polarization

vector of the light E; V0 is the strength of

the potential. The value of V0 is determined

by the intensity of the light Ip and can be

estimated as:[20,41]

V0 ¼1

2ayt Ip � C � Ip; (2)

where a is the absorption coefficient, y

is the volume of azobenzene and t is

the effective transition time between two

nd consists of N freely-jointed rod-like Kuhn segments

) Orientation structure of azobenzene chromophores


Macromol. Symp. 2012, 316, 10–16 13

isomer states. The value of the proportion-

ality constant C at the room temperature

has been estimated in previous works

as C � 10�19J � cm2=W.[20,41]

Under illumination with the linearly

polarized light each Kuhn segment reori-

ents due to the interaction of the chromo-

phores with the light wave. Thus, under

light illumination the network strands

change their conformations, and each

end-to-end vector b is transformed into a

new vector b(. As in a classical theory of

rubber elasticity,[42] we assume that net-

work strands deform affinely with the bulk

deformation of the elastomer because of

the constraints of the crosslinks. Taking

into account the incompressibility for

elastomers, one can write the condition of

affinity of deformation in the following

form:

b0x ¼ bxl; b0y ¼ by=ffiffiffilp

; and

b0z ¼ bz=ffiffiffilp

:(3)

We assume that the electric vector of the

light E is directed along the x-axis, see

Figure 1. Due to the axial symmetry with

respect to the vector E an azobenzene

elastomer demonstrates a uniaxial defor-

mation along the x-axis and l in Eq. (3) is

the elongation ratio of a sample along this

axis. We calculate the light-induced elonga-

tion l using the Gaussian approach for the

statistics of network strands. The distribu-

tion of the end-to-end vectors b0 of network

strands in a deformed elastomer can be

written in the framework of the Gaussian

approach as follows:

Pðb0Þ ¼ Cexp

"� ðb0xÞ

2

2hðb0xÞ2i

þðb0yÞ

2

2hðb0yÞ2iþðb0zÞ

2

2hðb0zÞ2i

!#;

(4)

where C is a normalization constant, and

hðb0xÞ2i; hðb0yÞ

2i and hðb0zÞ2i are the mean-

square projections of the network strands

on the x, y, and z-axes. Their values can be

expressed in terms of the averaged projec-


tions of the Kuhn segments on these

axes, hl2ai:

hðb0aÞ2i ¼ Nhl2

ai for a ¼ x; y; z: (5)

Now, it is a simple matter to find the

light-induced elongation l as a function of

the light intensity using the equation for the

free energy F (per a network strand):

FðlÞ ¼ �kT lnPðb0Þh i; (6)

where the averaging is performed over all

strands. Substituting Eq. (4) into Eq. (6)

and using the relationship between vectors

b and b( given by Eq. (3) we obtain the

following expression for FðlÞ:

FðlÞ ¼ kT

6

l2l2

hl2xiþ 2l2l�1

hl2yi

" #: (7)

Here we have used the axial symmetry

of an elastomer with respect to the vector

E: hl2yi ¼ hl2

zi, as well as the equality

hb2xi ¼ hb2

yi ¼ hb2zi ¼ Nl2=3 for an isotropic

elastomer at the absence of external fields.

The equilibrium value of the light-induced

elongation l is determined from the mini-

mum of the free energy, @F=@l ¼ 0, that

gives from Eq. (7):

l ¼ hl2xihl2

yi

!1=3

: (8)

Using Eq. (8) we have calculated the

value of l as a function of the strength of

the potential V0 which is proportional to

the light intensity, see Eq. (2). The aver-

aging in the right-hand side of Eq. 8

is performed over all orientations of the

rod-like Kuhn segments and takes into

account the contribution of the orientation

potential (1) acting on all chromophores

inside the Kuhn segments, as it was

calculated in refs.[17–19] for short rod-like

azobenzene oligomers. Below we show that

the photo-mechanical behavior depends

on the orientation distribution of the

chromophores inside the Kuhn segments

Wða;bÞ.


Macromol. Symp. 2012, 316, 10–1614

Photo-Mechanical Behavior of Azobenzene

Elastomers Depending on Their Chemical

Structure

Depending on the chemical structure, which

is defined in our approach by the orientation

distribution function of chromophores inside

the Kuhn segments Wða;bÞ, azobenzene

elastomers can demonstrate three types of

photo-mechanical behavior.

I. If 3 sin2a� �

W�2 < 0, the chromo-

phores lie preferably along the main chains.

Orientation of the chromophores perpen-

dicular to the electric field E of the light

results in the orientation of the Kuhn

segments also perpendicular to the vector

E and is accompanied by a uniaxial

contraction of an azobenzene elastomer

with respect to the vector E: l < 1. In this

case the function lðV0Þ decreases mono-

tonically.

II. If 3 sin2a� �

W�2 > sin2acos2b

� �W

�� ,the chromophores are arranged preferably

perpendicular to the main chains. Orienta-

tion of the chromophores perpendicular to

the electric vector E under light illumina-

tion leads in this case to the orientation of

the Kuhn segments parallel to the vector E

and is accompanied by a uniaxial expansion

of an azobenzene elastomer along the

vector E: l > 1. In this case the function

lðV0Þ increases monotonically.

III. The intermediate case 0 < 3

sin2a� �

W�2 < sin2acos2b

� �W

�� corresponds

to the structures with non-monotonic

Figure 2.

Dependences of the elongation ratio l on the reduced str

the structural angles a� and b�: (a) b� ¼ 65� is fixed and a

is varied.


dependence of the light-induced elongation

as a function of the strength of the potential

V0: lðV0Þ increases at small values of V0

and decreases at large values of V0.

To illustrate these three types of photo-

mechanical behavior of azobenzene elasto-

mers, we have calculated the dependences

lðV0Þ for elastomers, whose structural angles

a and b are fixed at equiprobable values

b ¼ �b� and a ¼ a�; 180� � a�, the values

a� and b� being variables. The dependences

lðV0Þ have been calculated numerically by

means of Eq. (8). Figure 2a and 2b illustrate

the dependences lðV0Þ for different values

of a� and b�. The results of numerical

calculations show three types of photo-

mechanical behavior of azobenzene elasto-

mers in accordance with qualitative con-

siderations presented above:

I uniaxial contraction, l < 1 (open

symbols in Figure 2), II uniaxial expansion,

l > 1 (filled symbols in Figure 2) and III

non-monotonic dependence of l on V0

(semi-open symbols in Figure 2). Thus,

azobenzene elastomers, as low-molecular-

weight glassy azobenzene polymers,[17–19]

can demonstrate different signs of light-

induced deformation (expansion/contraction/

non-monotonical behavior). Conclusion

about different signs of light-induced defor-

mation of low-molecular-weight glassy

azobenzene polymers has been confirmed

experimentally[34–37] and by means of com-

puter simulations.[38–40]

ength of the potential, NchV0=kT, at different values of

� is varied, (b) a� ¼ 50� and a� ¼ 70� are fixed and b�


Macromol. Symp. 2012, 316, 10–16 15

We conclude by noting that at very large

degrees of deformation the finite extensi-

bility of network strands can strongly

influence the photo-mechanical behavior

of azobenzene elastomers. One can expect

that at high light intensities the elongation ltends to its limiting value which depends on

the length of network strands: the shorter

are the chains between junctions, the

smaller is the elongation l at the same

light intensity. The Gaussian approach used

here is not able to describe the effects of

finite extensibility of network strands.

More detailed analysis of the effects of

finite extensibility of network strands on

the photo-mechanical behavior of azoben-

zene elastomers can be a topic of further

generalizations.

Conclusion

Thus, we have proposed a theory of light-

induced deformation of azobenzene elasto-

mers under illumination with uniform and

linearly polarized light. The theory is based

on the orientation statistical approach, acco-

rding to which the photo-induced mechanical

stress originates from the preferable reor-

ientation of the azobenzene chromophores

perpendicular to the electric vector of the

light. Using the Gaussian approximation for

elasticity of network strands the light-induced

elongation has been calculated as a function

of the light intensity for elastomers of

different chemical structure, which is defined

in our model by the orientation distribution

of the chromophores around the main chains.

It is shown that depending on the chemical

structure azobenzene elastomers can demon-

strate either uniaxial contraction or expan-

sion along the polarization vector of the

light. For some chemical structures, elonga-

tion of a sample displays a non-monotonic

behavior with the light intensity and can even

change its sign: a stretched sample starts

to be uniaxially compressed. Thus, we have

extended the orientation approach devel-

oped in refs.[17–19] for uncrosslinked glassy

azobenzene polymer to crosslinked azoben-

zene elastomers.


Acknowledgements: The financial support ofthe DFG grant GR 3725/2-1 is gratefullyacknowledged.

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Phys

Ulya

Fax:

E-m

Cop

Effect of Chemical Structure and Charge Distribution

on Behavior of Polyzwitterions in Solution

A. A. Lezov, P. S. Vlasov, G. E. Polushina, A. V. Lezov*

Summary: The hydrodynamic and conformational properties of polyelectrolyte

poly(N,N-diallyl-N,N-dimethylammonium chloride) and its corresponding polybetaine

poly(2-diallyl(methyl)ammonio)acetate) molecules in aqueous solutions with various

ionic strength and pH, were studied by viscometry, static and dynamic light

scattering methods. It was established that a 1 M NaCl solution is a thermo-

dynamically good solvent for poly(N,N-diallyl-N,N-dimethylammonium chloride). In

water solutions conformation of poly(2-diallyl(methyl)ammonio)acetate) molecules

corresponds to polymer coil under u–conditions. An increase in the concentration of

NaCl in water and 0.1M NaOH solutions from 0 to 1 mol/l brings about a sharp gain in

the intrinsic viscosity of the polymer and in the hydrodynamic radius of molecules.

This effect results from the decomposition of zwitterion pairs responsible for the

compact conformation of polymer molecules in water and 0.1 M NaOH. The Kuhn

segment length for poly(2-diallyl(methyl)ammonio)acetate) molecules A¼ 6.3 nm

determined in water and in 0.1 M NaOH solutions practically coincided with A value

6.6 nm, received in 1 M NaCl and in 0.1 M NaOH/1M NaCl. For poly(N,N-diallyl-N,N-

dimethylammonium chloride) molecules in 1 M NaCl solutions A¼ 3.9 nm.

Keywords: conformation; macromolecule; polyelectrolyte; polyzwitterion

Introduction

Ionic macromolecules have an ability to

change conformation as a response to

variations in the ionic strength and pH of

solution. Polymers containing ionic groups

may be divided into two classes, polyelec-

trolytes and polyzwitterions.[1–8] Polyelec-

trolytes contain anionic or cationic groups,

while polyzwitterions contain both anionic

and cationic groups.

Polyzwitterions includes both polyam-

pholytes and polybetaines.[1] Polyampho-

lyte contain the charged groups on different

monomer units, while polybetaine refers to

those polymers with the anionic and

cationic groups on the same monomer unit.

While the polyelectrolytes are usually

soluble in water, many from polyzwitter-

ical Faculty of Saint-Petersburg State University,

novskaya 1, 198504 Saint-Petersburg, Russia

(þ7)8124287598;



ions to be insoluble in water due to the

strong electrostatic attraction between the

oppositely charged monomers that leads to

the collapsed coil conformation of the

molecules. The range of solubility in

different solvents is greater for phospho-

and carboxybetaines than it is for sulfobe-

taines. Polycarboxybetaines exhibit more

varied aqueous solution behavior because

of the weak acid nature of the carboxylic

acid group.[1,9,10]

The presence of an inorganic salt, which

screens the interactions and weakens

attractions, causes the dissolution of the

polymer. Thus, the solution behavior of

polyzwitterions is opposite that of poly-

electrolytes, exhibiting the so-called ‘‘anti-

polyelectrolyte’’ effect.[6,7] Polyzwitterions

have found applications in various fields

that include biosensors, ion exchange,

model for understanding the complex

behavior of proteins.

Recently a new type of pH- responsive

polymers containing amino acid residues


Macromol. Symp. 2012, 316, 17–2418

was synthesized. These polycarboxibe-

taines are soluble in water solution.[9–11]

In the present paper the molecular

properties of the polyelectrolyte poly

N,N-diallyl-N,N-dimethylammoniumchlor-

ide (PD) and its corresponding polybetaine

poly(2-diallyl(methyl)ammonio)acetate)

(PB) in aqueous solutions with different pH

and ionic strength were studied. To deter-

mine the macromolecular parameters and

thermodynamic quantities of PD and PB in

solution viscometry, dynamic and static

light scattering techniques were used.

Experimental Part

Poly(N,N-diallyl_N,N_dimethylammonium

chloride) was prepared as described in.[8,11]

Monomer 2-(diallyl(methyl)ammonio)ace-

tate was received from diallylamine (Fluka)

as 67% aqueous solution.[12] Polycarbox-

ibetaine (PB) poly(2-diallyl(methyl)ammo-

nio)acetate) was synthesized by radical

polymerization in water solvent.[13]

Solutions of PD and PB in water (a

refractive index of n0¼ 1.3423 and a

viscosity of h0¼ 0.89 cP), in 0.1M NaOH

and in salt containing solvents were pre-

pared at room temperature. The viscosities

of PD and PB solutions were measured on

Ubbelohde and Ostwald viscometers at

25 8C.

The dynamic and static light scattering

measurements were performed at

25.0� 0.1 8C in the range of scattering

angles u¼ 258–1308 on a PhotoCor Com-

plex setup (Russia) equipped with a

PhotoCor-FC real-time correlator (288

channels, 20 ns) operating in the multiple-

t mode and a single-mode He-Ne laser

(l0¼ 632.8 nm). The autocorrelation func-

tions of scattered light intensity were

processed with DynaLS software to obtain


functions of the distribution over relaxation

times t. The dependences of reciprocal

relaxation time 1/t on the square of

scattering vector Sin q ¼ 4pn0l0

Sin u2 for all

the polymers were approximated by

straight lines passing through the origin,

indicating the diffusion character of the

processes under study.[14,15] Transitional

diffusion coefficient D was calculated from

the slope of these dependences according

to the relationship[14]

1

t¼ Dq2 (1)

Hydrodynamic radius Rh was estimated

via the Stokes–Einstein equation:[16]

Rh ¼kT

6ph0D(2)

The setup was calibrated relative to

benzene and toluene. Refractive index

increment Dn=Dc of PD and PB was

determined on an IRF-23 refractometer

at 25 8C.

Results and Discussion

The PD homopolymer belongs to the

family of cationic polyelectrolytes. The

study of its hydrodynamic and conforma-

tional properties was performed in a 1 M

NaCl solution, where electrostatic interac-

tions between monomer units were sup-

pressed.[8] The molecular properties of PB

samples were studied in aqueous solutions

with different pH, containing different

amounts of a low-molecular-mass salt.

Static light scattering measurements

make it possible to estimate weight-average

molecular mass Mw and second virial

coefficient A2 for PD and PB samples.[14,15]

Figure 1 a, b shows the experimental

dependences of contrast factor H � c=Ru,

where H ¼ 4p2n20

NAl4DnDc

� �2and Ru is the Ray-

leigh ratio of the scattering intensity on the

concentration of PD and PB in a 1M NaCl

and water solutions. The value of

Mw ¼ H�cRu

� ��1

c!0was determined from the

ordinate intercept, while the value of A2 was


c, g/dl

510×⋅

θRcH

1.0

0.5

0.50 1.0

1

2

3

4

a)

(Hc/Rθ)

θ=0 x105

0.50 1.0

cx102, g/сm3

1

2

1

2

3

4

5

6

b)

Figure 1.

a, b. H�cRu

values vs solution concentration c for PD1 (&),

PD3 (*), PD5 (~), PD6 (~) in 1 M NaCl.(a), for PB2 (�),PB3 (~), PB4 (!), PB5 (&).in 1M NaCl as well as for

PB4 (*) and PB5 (&) in water (b).

Macromol. Symp. 2012, 316, 17–24 19

calculated from the slope of this depen-

dence in accordance with the following

equation:[14,15]

H � cRu

� �u!0

¼ 1

MWþ 2A2 � c (3)

Table 1.Molecular-mass and hydrodynamic characteristics of PD

Sample [h], dl/g k0 D� 107, cm

PD1 0.97 0.29 1.59PD2 0.93 0.28 1.56PD3 0.80 0.31 1.89PD4 0.68 0.31 2.50PD5 0.38 0.42 2.91PD6 0.34 0.42 3.20


The refractive index increment Dn=Dc

for PD and PB solutions in 1M NaCl was

equal to 0.22� 0.02 cm3/g. Table 1 and 2

lists the values of Mw and A2 along with

degree of polymerization Z ¼MW=M0,

where the molecular mass of the repeating

unit Mo¼ 162 for PD and 169 for PB. Note

that the values of A2¼ 2.9� 10�4 ml �mol/g2

for PD correlate with those derived from

the light scattering data recently.[8] Second

virial coefficient A2> 0 for PB in 1 M NaCl

and is near to zero in water solutions

(Table 2).

The concentration dependences of

reduced viscosity for all PD samples in

1M NaCl were approximated by straight

lines, and their extrapolation to infinite

dilution made it possible to estimate

intrinsic viscosity [h] of the polymer,

whereas Huggins constant k0 was deter-

mined from the slopes of these depen-

dences. The relevant data on [h] and k0 are

summarized in Table 1. The values of k0 for

PD lie in the interval between theoretical

values for polymers in good (0.25) and ideal

(0.5) solvents.[16]

Viscosity data for PB samples are shown

in Figure 2. In the absence of added salt, the

viscosity plots are linear. The addition of

strong electrolyte, like sodium chloride,

leads to change in reduced viscosity values.

By increasing the ionic strength, while the

viscosity of the PB in 0.1M HCl decreases,

as expected, the viscosity of PB in water

as well as in 0.1 M NaOH solutions

increases due to ‘‘antipolyelectrolyte’’

behavior (Figure 2). This implies the

zwitterionic character of the PB because

of full deprotonation of the strongly acidic

ammonioacetate moiety.[9,10]

samples in 1M NaCl solutions.

2/s Mw� 10�3 Z� 10�3 Rh, nm

385 2.39 15.5378 2.35 15.7330 2.05 13.0163 1.01 9.8134 0.83 8.4118 0.73 7.7


Table 2.Molecular-mass and hydrodynamic characteristics of PB samples in solutions.

Sample Solvent [h], dl/g D� 107,cm2/s

Mw� 10�3 Z Rh, nm A2� 104,mol �ml/g2

PB1 H2O 6.4 3.81M NaCl 0.19 6.1 22 130 4.0 2.8

0.1 MNaOH 6.4 3.8PB2 H20 0.37 3.8 6.4

1M NaCl 0.45 3.6 60 355 6.8 3.20.1M NaOH 3.9 6.3

0.1M NaOH/1M NaCl 3.7 6.6PB3 H2O 0.59 3.0 8.1

1M NaCl 0.79 2.8 104 598 8.7 3.50.1M NaOH 0.60 3.1 7.9

0.1M NaOH/1M NaCl 0.72 2.9 8.40.1M HCl 0.87 2.6 9.4

0.1M HCl/1M NaCl 0.50 3.2 7.6PB4 H2O 2.8 8.7

1M NaCl 0.85 2.3 112 639 10.6 2.5PB5 H2O 0.71 2.3 10.6

1M NaCl 1.23 1.9 178 1050 12.8 2.10.1M NaOH 2.2 11.1

0.1M NaOH/1M NaCl 1.9 12.8

Macromol. Symp. 2012, 316, 17–2420

Figure 3a depicts the autocorrelation

functions of scattered light for PB4 in 1M

NaCl. The distribution of the scattered light

intensity for PD and PB shows one main

peak, which characterizes the dimensions

of the molecules in solution (Figure 3b).

Translational diffusion coefficient D of

polymer molecules was calculated from

the slope of the linear dependence of

reciprocal relaxation time 1/t on the square

of scattering vector q in accordance with

Equation (1). The concentration depen-

1.51.00.5

0.4

0.6

0.8

1.0

7

8

6

54

3

c, г/дл

ηr, dl/g

0

1

2

Figure 2.

Concentration dependences of reduced viscosity hr

for PB3 in 0.1M HCl (�); 1M NaCl (&); 0.1M NaOH/1M

NaCl (~); water (*); 0.1M NaOH (^); 0.1M HCl/1M

NaCl (&); for PB5 (~) and PB2 (r) in water.


dences of translational diffusion coefficient

D were approximated by straight lines. The

extrapolation of the concentration depen-

dences of translational diffusion coefficient

D to infinite dilution made it possible to

determine the value of D0 for PD and PB

molecules (Figure 4, Table 1, 2). Hydro-

dynamic radius Rh of macromolecules, as

Figure 3.

Autocorrelation functions of (a) scattered light and (b)

the scattered-light intensity distribution for PB4 in 1M

NaCl.


3

4

5

6

0 0.5 1.0 c, g/dl

Dx107, сm2/s1

2

3

45

6

7

Figure 4.

Translational diffusion coefficient D vs solution con-

centration c for PB1 in 1M NaCl (*), PB2 in 0.1M NaOH

(~) and 0.1M NaOH/1M NaCl (~), PB3 in 0.1M NaOH

(&); 0.1M NaOH/1M NaCl (^); PB4 in water (&) and in

1M NaCl (�).

5.04.5

-6.5

0

-6.5

01

2

3 4

logMw

log[η] logD

Figure 5.

log½h� - logMW and logD0 - logMW relations for PB in

1M NaCl (&, ~) and in water (&, ~).

Macromol. Symp. 2012, 316, 17–24 21

estimated from D0 values by using

Equation (2), is given in Table 1 and 2.

Figure 5 shows the dependences of log D

and log½h� on logMw for PD and PB in

different solvents. From analysis of these

Table 3.Coefficients Kh, KD and exponent a and b values in thdifferent solvents.

Sample Solvent Kh � 10

PD 1M NaCl 5.52PB water 51.4PB 0.1M NaOH –PB 1M NaCl 5.82PB 0.1M NaOH/1M NaCl –


dependences, the Mark–Kuhn–Houwink

equations ½h� ¼ KhMa and D ¼ KDMb

were obtained (Table 3).[16]

These dependences were used to deter-

mine exponent n value relating the gyration

radius of molecules or their hydrodynamic

radius Rh to the molecular mass MW of a

polymer: Rh �MnW . The values of n¼ 0.55

and 0.59 calculated from the translational

diffusion and viscometry data for PD,

respectively, turned out to be higher than

the theoretically predicted value of 0.5 for

polymers under u - conditions.[16,17] This

fact, along with a relatively high value of

second virial coefficient A2, shows that a 1M

NaCl solution is a thermodynamically good

solvent for PD. The obtained value of n

agrees with that received for PD in the

same solvent recently.[2,8]

The values of n¼ 0.5 for PB in water

solutions practically coincides with that for

ideal polymer coil. In 1M NaCl and in 0.1M

NaOH containing 1M NaCl solutions

exponent value n corresponds to the

theoretically predicted value of 0.58 for

polymers in ‘‘good’’ solvents.[17] This fact

along with a positive value of second virial

coefficient A2 shows that a 1M NaCl and

0.1M NaOH/1M NaCl solutions are a

thermodynamically ‘‘good’’ solvents for

PB. Thus in salt-free water solution intra-

chain attraction leads to highly compact

conformation, the polymer coil is expanded

in 1M NaCl.

The size of molecular coil depends on

both long-range and short-range intrachain

interactions. Long-range interactions

between monomer units leads to change

in second virial coefficient A2 and exponent

n value while equilibrium rigidity or Kuhn

segment length A depends on short-range

e Mark–Kuhn–Houwink equations for PD and PB in

5 a KD � 104 b

0.77 2.02 �0.550.6 0.94 �0.5– 0.82 �0.48

0.82 1.87 �0.58– 3.36 �0.6


4002000 2)(1 ε−M

(η0DM/kT)x10-10

0.5

1.0

Figure 6.

Plot of h0DMkT

vs. Mð1�"Þ=2 for PD in a 1 M NaCl solution (�)and for PB in water (~), 0.1 M NaOH (~), 1 M NaCl (&)

and 0.1M NaOH/1 M NaCl (*).

Macromol. Symp. 2012, 316, 17–2422

interactions between neighbouring mono-

mers in macromolecule.[16,17]

Kuhn segment length A for PD and PB

macromolecules was estimated in terms of

the theory of translational friction of a

wormlike necklace with allowance for

excluded-volume effects:[18]

ho

DM

kT¼ P�1

1 ½ð1�"Þð1�"

3Þ��1Mð1�"Þ=2Að"�1Þ=2

�MLð"þ1Þ=2 þML

3p½ln A

dþ 1þCð"Þ�

(4)

Here, constant P1 ¼ 5.11, ML¼5.77� 109 and 6.04� 109 Da/cm is the

molecular mass of the chain unit length

for PD and PB, which is equal to the ratio of

the molecular mass of the repeating unit of

a chain M0 to the length of its projection in

the chain direction, l and d is the hydro-

dynamic diameter of a chain. The value of

exponent " ¼ 2n� 1 was estimated from

the experimental value of n (Table 3).

Function Cð"Þwas tabulated in.[18]

Figure 6 demonstrate the dependence ofh0DM

kT on Mð1�"Þ=2 for PD and PB. The Kuhn

segment length of the molecules A was

determined from the slope of the straight

line in Figure 6 in accordance with

Equation (4). The Kuhn segment length

A¼ 3.9 nm for PD molecules is less than

that for PB molecules A¼ 6.3 nm deter-

mined for water and 0.1M NaOH solutions

as well as A¼ 6.6 nm, received for PB in

1M NaCl and in 0.1 M NaOH/1M NaCl.

From the ordinate intercept, the hydro-

dynamic diameter of the chain, d¼ 0.5 and

0.8 nm for PD and PB, correspondingly,

was found. These values of d conform to

the chemical structure of PD and PB

macromolecules.

To gain insight into the effect of the

solution pH on the behavior of PB

molecules, the hydrodynamic characteris-

tics of PB3 sample in water - saline

solutions were measured.

Rh � 1þ 4

3

N1=2

A3B

264

8><>:


The concentration dependences of the

reduced viscosity for PB3 in water solution

can be described by straight lines

(Figure 3). This fact shows that the

polyelectrolyte expansion no effect on the

hydrodynamic characteristics of the PB3

molecules. It is suggested that this effect

results from deprotonation of COOH

groups in an alkaline solution, a phenom-

enon that increases the number of negative

charges on a macromolecule, thereby

moving this value closer to the number of

positive charges. Table 2 represents intrin-

sic viscosity [h] and hydrodynamic radius

Rh of PB3 in water solutions. The addition

of NaCl to the solution up to a concentra-

tion of 1 mol/l causes an increase in the

values of [h] and Rh (Table 2).

Such an antipolyelectrolyte effect was

theoretically analyzed in.[19–22] On the basis

of the data from,[20,22] it may be shown that

the dependence of the hydrodynamic radius

of polyzwitterionic molecules Rh with close

amounts of positively and negatively

charged groups on the overall concentra-

tion of the low-molecular mass salt in

solution, c0, may be determined through

the relationship (4)

þ ðp� nÞ2

2c0� l

3=2B p

1=2ðpþ nÞ2

2ffiffiffiffiffiffiffi2c0

p

3759>=>;

1=2

(5)


Macromol. Symp. 2012, 316, 17–24 23

where lB is the Bjerrum length, B is

the second virial coefficient of excluded

volume interaction in polymer chain.[17]

The screening of the attractive polyzwitter-

ion interactions is described by the third

term of Equation 4, and the screening of the

repulsive effects is described by the second

term. When charges are perfectly balanced,

f � g ¼ 0, and only the attractive term need

be considered. When, f � g 6¼ 0, the beha-

vior of the polymer coil in solution depends

on the relative magnitude of the two terms.

At low ionic strength the second term

dominates, and the resulting positive

electrostatic excluded volume causes the

stretching of the polymer chain. At inter-

mediate ionic strength, the second term

diminishes rapidly and the third term

dominates, resulting in a negative electro-

static excluded volume and a collapsed

polymer chain. At high ionic strength,

both terms become unimportant, and the

electrostatic contribution to the coil size

becomes unimportant.

The general behavior predicted by

Equation 4 was observed experimentally

by measuring the viscosity of PB3 solutions

as a function of sodium chloride concentra-

tion (Figure 8). The dependence of

½h�=½h�H2O ¼ ðRh

.RH2OÞ3 on c0 calculated

1.0

1.1

1.2

1.3

0 0.5 1.0c0, mol/l

[η]/[η]H2O

Figure 7.

The dependence of ½h�.½h�H2O ratio on NaCl concen-

tration c0 in PB3 solution. Points – experimental

data, line – theoretical dependence, calculated by

using Equation 4 for A2¼ 3.5� 10�4 mol �ml/g2

A¼ 6.6 nm.


in accordance to the Equation (4) for

electroneutral polybetaine (f¼ g), is repre-

sented on Figure 7.

Conclusion

It was established that behavior of PB

corresponds to polyelectrolytes or polybe-

taines in dependence on pH and ionic

strength. In acidic solutions PB demon-

strate behavior typical for polyelectrolytes.

In solutions with pH 6–13, when 1M NaCl

is added to the solution, there is an

antipolyelectrolyte effect that manifests

itself as an increase in the intrinsic viscosity

and hydrodynamic radius of the polyzwit-

terion molecules. The increase in low-

molecular – mass salt concentration in

water solution leads to transition of the

polymer coil from collapsed conformation

to expanded state that corresponds to the

change in exponent a value from 0.5 to 0.58.

Thus, in an alkaline solution, PB molecules

practically behave as electroneutral poly-

betaines, for which the dimensions of

molecules typically increase with the ionic

strength of solution. Equilibrium rigidity of

polyzwitterion molecules does not depend

on low-molecular-mass salt concentration

in solution. A higher value of A for PB

molecules relative to that of the PD may be

explained by the presence of bulky side

groups in the repeating unit of polymeric

betaine. These groups enhance hindrance

to rotation around main-chain bonds.

[1] A. B. Lowe, C. L. McCormick, Chem. Rev. 2002,

102(11), 4177.

[2] S. Kudaibergenov, W. Jaeger, A. Laschewsky, Adv.

Polym. Sci. 2006. 201, 157.

[3] J. Bohrisch, C. Eisenbach, W. Jaeger, H. Mori,

A. Muller, C. Schaller, S. Traser, P. Wittmeyer, Adv.

Polym. Sci. 2004, 165, 1.

[4] A. Thunemann, M. Muller, H. Dautzenberg, J.-F.

Joanny, H. Luwen, Adv. Polym. Sci. 2004, 166, 113.

[5] C. Wandrey, J. Hermindez-Barajas, D. Hunkeler,

Adv. Polym. Sci. 1999, 145, 125.

[6] D. B. Thomas, Yu. A. Vasilieva, R. S. Armentrout,

C. L. McCormick, Macromolecules 2003, 36(26), 9710.


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[7] G. S. Georgiev, E. B. Kamenska, E. D. Vassilieva, I. P.

Kamenova, V. T. Georgieva, S. B. Iliev, I. A. Ivanov,

Biomacromolecules 2006, 7(4), 1329.

[8] H. Dautzenberg, E. Gornitz, W. Jaeger, Macromol.

Chem. Phys. 1998, 199(8), 1561.

[9] Sk. Asrof Ali, Aal-e-Ali Polymer. 2001, 42, 7961.

[10] H. A. Al-Muallem, M. I. M. Wazeek, Sk. Asrof Ali,

Polymer 2002, 43, 4285.

[11] P. S. Vlasov, S. N. Cherniy, N. S. Domnina, Russ. J.

Gen. Chem. 2010, 80(7), 1314.

[12] Ph. Favresse, A. Laschewsky, Macromol. Chem.

Phys. 1999, 200(4), 887.

[13] A. V. Lezov, P. S. Vlasov, A. A. Lezov, N. S. Domnina,

G. E. Polushina, Polymer Sci. 2011, 53(11), P.

[14] R. Pecora, Dynamic Light Scattering, Academic

Press, New York 1976.


[15] B. Chu, Laser Light Scattering, Plenum Press, New

York 1976.

[16] V. N. Tsvetkov, Rigid-Chain Polymers, Consultants

Bureau, New York 1989.

[17] A. Yu. Grosberg, A. R. Khokhlov, Statistical Physics

of Macromolecules (Nauka, Moscow 1989; American

Institute of Physics, Ithaca 1994).

[18] H. B. Gray, V. A. Bloomfield, J. E. Hearst, J. Chem.

Phys. 1967, 46(4), 1493.

[19] Y. Kantor, M. Kardar, Phys. Rev. E. 1995, 51(2), 1299.

[20] P. Higgs, J.-F. Joanny, J. Chem. Phys. 1991, 94(2),

1543.

[21] A. R. Khokhlov, S. G. Starodubtzev, V. V. Vasilevs-

kaya, Adv. Polym. Sci. 1993, 109, 125.

[22] A. V. Lezov, G. E. Polushina, A. A. Lezov, P. S.

Vlasov, N. S. Domnina, Polymer. Sci. A. 2011, 53(2), 93.



1 D

St

11

Fa

E-2 Ru

Ku3 In

A

19

Cop

Diblock Copolymer Micelles with Ionic Amphiphilic

Corona

Evgeny A. Lysenko,*1 Alevtina I. Kulebyakina,2 Pavel S. Chelushkin,3

Alexander B. Zezin1

Summary: Aqueous dispersions of diblock copolymer micelles with homogeneous

hydrophobic core (polystyrene) and heterogeneous amphiphilic corona from ionic

N-ethyl-4-vinylpyridinium bromide (EVP) and hydrophobic 4-vinylpyridine (4VP) units

have been prepared at pH 9. The structure and dispersion stability of micelles as

function of the ratio and distribution pattern of ionic and hydrophobic units in corona

have been systematically studied by means of transmission electron microscopy,

static and dynamic light scattering, UV-spectrophotometry techniques. It was shown

that gradual decrease of the quantity of EVP-units in corona had no impact on micelle

structure until its fraction was above 0.7. When EVP-fraction dropped below this point

noticeable changes in micelle mass and dimensions were observed. In the case of

random distribution of 4VP and EVP units these changes were moderate in value and

jump-like in character. In the case of mictoarm (starlike) distribution of 4VP and EVP

blocks changes were large in value and monotonous in character. The presented

results may be of certain use for design of polymer micelles with nanosegregated

corona.

Keywords: amphiphilic; diblock copolymers; micelles; polyelectrolytes; self-assembly

Introduction

Self-assembly is a process of spontaneous

reversible formation of organized struc-

tures via non-covalent interactions of the

system components. Ionic amphiphilic

diblock copolymers belong to self-assem-

bling polymers. In aqueous media they

spontaneously form micelles with insoluble

hydrophobic core and lyophilizing ionic

corona.[1] These micelles are regarded as

promising drug delivery vehicles and

nanoreactors for synthesis and stabilization

epartment of Chemistry, M.V. Lomonosov Moscow

ate University, Leninskie Gory 1/3, Moscow,

9991 Russia

x: (þ7) 495 9390174;


ssian Research Center Kurchatov Institute, pl.

rchatova 1, Moscow, 123182 Russia

stitute of Macromolecular Compounds, Russian

cademy of Science, Bolshoi pr. 31, St. Petersburg,

9004 Russia


of various nanoparticles because of their

remarkable binding and solubilizing prop-

erties as well as enhanced disintegration

resistance towards dilution.[2,3]

In the simplest case polymer micelles

consist from chemically uniform core and

chemically uniform corona.[1,2] A challen-

ging task for polymer chemistry is creation

of hierarchically organized polymer micelles,

i.e. micelles with compartmentalized core

and/or corona consisting of smaller structural

units that differ in composition and proper-

ties. Such micelles would resemble globules

of natural proteins with their microheter-

ogeneous structure and may pave the way for

design of smart multifunctional nanostruc-

tures.[3] First examples of polymer micelles

with segregated core or corona can be found

in literature.[4–9] Three ways of creation

such micelles can be distinguished: synth-

esis of multiblock (primarily triblock)

copolymers,[4,5] synthesis of amphiphilic

copolymers with a mixed (static and block)


Macromol. Symp. 2012, 316, 25–3126

distribution of units of various polarity[6,7]

and joint micellization (hybridization) of

several diblock copolymers with different

chemical nature.[8,9]

The present paper deals with two types

of polymer micelles in aqueous media.

Both types consist from hydrophobic

homogeneous polystyrene (PS) core and

heterogeneous corona formed by nonpolar

4-vinylpyridine (4VP) and charged N-ethyl-

4-vinylpyridinium bromide (EVP) units.

The first variable in our investigation is

mole fraction of EVP units in corona,

b¼ [EVP]/([EVP]þ [4VP])¼ 0� 1. The sec-

ond variable is distribution pattern of

charged and nonpolar units within corona.

The first type of micelles consists from

PS-block-poly(4-vinylpyridine-stat-N-ethyl-4-

vinylpyridinium bromide) (PS-P(EVP/

4VP)-b) block copolymers with random

distribution of EVP and 4VP units along

corona-forming block. Therefore, block

copolymer micelles of the first type possess

random distribution of EVP and 4VP units

in corona. The second type includes hybrid

(mixed) micelles from PS-block-poly(4-

vinylpyridine) (PS-P4VP[0]) and PS-block-

poly(N-ethyl-4-vinylpyridinium bromide)

(PS-PEVP) diblock copolymers. Here and

below such micelles will be designated as

PS-PEVP/PS-P4VP-b. Block copolymer

micelles of the second type possess mic-

toarm (starlike) distribution of PEVP and

P4VP blocks within corona. The purpose of

the investigation is to find the influence of

composition and distribution pattern of

ionic and hydrophobic units in corona on

micellar structure and properties. Micelle

characteristics (mass, dimensions and

aggregation stability) as a function of their

composition b and distribution pattern

have been systematically studied to find

such correlations.

Experimental Part

Polymers

Diblock copolymers of PS-P4VP, PS-PEVP

and PS-P(EVP/4VP)-b have been synthe-

sized as described elsewhere.[10] The


lengths of PS, P4VP, PEVP and P(EVP/

4VP) blocks were equal 100 units, the

polydispersity index for all diblock copoly-

mers was 1.12. For PS-P(EVP/4VP)-b

copolymers b¼ 0.3� 1.0. The initial PS-

P4VP sample was synthesized and gener-

ously provided to us by Prof. Adi Eisenberg

from McGill University, Montreal, Quebec,

Canada.

Preparation of Micelle Dispersions

Aqueous dispersions of individual PS-

P(EVP/4VP)-b micelles were prepared

using the dialysis technique. Initially, PS-

P(EVP/4VP)-b copolymers were dissolved

in a mixed DMF/methanol (80/20 v/v)

solvent and stirred for one day. After that,

water was added to the mixture dropwise

under vigorous stirring. When water con-

tent was 33 vol. %, the mixture was left for

one day to reach the equilibrium. Another

portion of water was added until it content

was 67 vol. %. The mixture was stirred

additionally for one day. Finally, the water-

organic mixture was dialyzed against

pure water during one week using mem-

brane tubing to remove organic solvents.

The concentration of PS-P(EVP/4VP)-b in

final dispersion was determined from

UV-spectrophotometry measurements at

l¼ 257 nm.[10]

To prepare aqueous dispersions of

PS-PEVP/PS-P4VP-b micelles, individual

PS-PEVP and PS-P4VP copolymers were

initially dissolved in DMF/methanol (80/

20 v/v) solvent and mixed at appropriate

ratio b¼ 0.05� 1.0. All other steps were

identical to that described above for PS-

P(EVP/4VP)-b micelles. In our recent

publication we have demonstrated the

formation of hybrid micelles with joint

PS-core and mixed PEVP/P4VP corona

upon addition of water into above men-

tioned diblock copolymers mixture in DMF/

methanol solvent. We have found that the

micelle composition coincided or appro-

ached closely to the composition of the

copolymer mixture.[11] The PS-core of hybrid

micelles ‘‘freezes’’ during the dialysis proce-

dure thus fixing the micelle aggregation

number and the structure of the core.[12]


Macromol. Symp. 2012, 316, 25–31 27

All experiments were performed at

room temperature (25 8C) in TRIS buffer

solution (0.01 M, pH 9) to keep the 4VP

units completely uncharged and hydropho-

bic.[13] To evaluate aggregation stability of

micelles in saline media the micelle disper-

sions were mixed with NaCl aqueous

solutions of appropriate concentration

and vigorously stirred for one day. In

the case of precipitation the insoluble

phase was separated from the supernatant

via ultracentrifugation during 15 min at

13000 rpm. The concentration of block

copolymer micelles in supernatant was

determined by UV-spectrophotometry

technique at l¼ 257 nm.

Measurements

Spectrophotometer measurements were per-

formed at UV-VIS Lambda-25 spectrophot-

ometer (Perkin-Elmer, USA) in 10 mm

quartz cells. Static and dynamic light scatter-

ing measurements were performed using

PhotoCorr-M light scattering spectrometer

(PhotoCorr, Russia). A 25-mW He-Ne laser

operating at 633 nm wavelength was used as

a light source. Light scattering angles varied

within 30� 150o. Refractive index incre-

ments were measured by a KMX-16 differ-

ential refractometer (Milton Roy, USA)

with a 2-mW He-Ne laser as a light source,

l¼ 633 nm. All solutions were filtered two

times through Millipore GS 0.45 mm prior to

all light scattering measurements. Static light

scattering data were treated by Zimm

Figure 1.

TEM microphotographs of PS-PEVP (a), PS-P(EVP/4VP)-0.17

dispersions.


method, extrapolating the obtained values

of reduced intensity of scattered light to

zero scattering angle. The negative staining

technique was used for the transmission

electron microscopy (TEM) studies. Sam-

ples were studied by use of Hitachi H-7000

microscope (Hitachi, Japan) using uranyl

acetate as contrasting agent.


Chosen TEM microphotographs of PS-

PEVP, PS-P(EVP/4VP)-0.17 and PS-PEVP/

PS-P4VP-0.2 micelles are presented in

Figure 1. One can easily notice the spherical

morphology of all micelles. This result is

expected since spherical morphology is

characteristic for diblock copolymers when

the core and corona forming blocks are of

comparable lengths.[14] One can found

micelles in Figure 1a, 1b and 1c are of

different size. This observation may reflect

the strong influence of micelle composition

and distribution pattern of ionic and non-

ionic units in corona on micelle mass and

dimensions. To follow this influence, meth-

ods of static and dynamic light scattering

were applied.

Figure 2 shows the dependencies of

weight-average molecular masses (Mw) and

hydrodynamic radii (Rh) of PS-P(EVP/

4VP)-b micelles as a function of b.

(Note that values of Mw and Rh were

obtained by extrapolation of corresponding

(b) and PS-PEVP/PS-P4VP-0.2 (c) from salt-free aqueous


Figure 2.

Weight-average molecular weight Mw (�) and hydro-

dynamic radius Rh (&) of PS-P(EVP/4VP)-b micelles in

0.05 M NaCl aqueous dispersions as a function of b.

Macromol. Symp. 2012, 316, 25–3128

experimental data to zero concentration.)

One can easily notice that mass and

hydrodynamic radius of micelles change

in a jump-like manner near b � 0.6� 0.7,

while below and above this narrow region

micelle characteristics change insignifi-

cantly.

Using the obtained data we have

estimated other structural characteristics

of the micelles: their weight-average aggre-

gation number Nw, the radius of the PS-core

(RC) and the dimensions of the P(EVP/

4VP)-corona (D). Aggregation number was

calculated as Nw¼Mw/M0, where M0 is a

molecular mass of a single macromolecule.

To calculate RC we use the following

equation:

RðnmÞ ¼ 3MPSPPSNw � 1021

4pNArPS

� �1=3

Here MPS¼ 104 g/mol– molar mass of PS

unit, PPS¼ 100–polymerization degree of

PS-block, rPS¼ 1.04 g/cm3–density of amor-

phous PS in a solid state (it is supposed that

Table 1.Structural characteristics of PS-P(EVP/4VP)-b micellesin 0.05 M NaCl aqueous dispersions.

b Nw RC (nm) D (nm)

0.29 180 9 90.48 190 9 120.56 180 9 120.62 180 9 110.74 100 7 181.0 100 7 16


PS-core of micelles does not contain water)

and NA – Avogadro’s number. The corona

dimensions were calculated as D¼Rh – RC.

The results of calculations are summarized

in Table 1 and their general qualitative

interpretation is presented in Scheme 1

below.

When b< 0.6 micelles possess higher

aggregation number (larger PS-core) and

contracted corona. When b> 0.7 micelles

possess lower aggregation number (smaller

PS-core) and expanded corona (Table 1

and Scheme 1). We believe the reason of a

jump is the reversion in the balance

between nonpolar interactions of 4VP units

and electrostatic interactions of EVP units

in corona. At low b the structure of a

micelle is determined by hydrophobic

attraction of dominating 4VP-units. Such

attraction manifests itself in local associa-

tion of 4VP units in corona, which in turn, is

accompanied by contraction of the corona

and increase in micelle aggregation number

(left micelle in Scheme 1). At high b the

fraction of 4VP-units is low and the micelle

structure is determined by the electrostatic

repulsion of charged EVP units. The

micelle ‘‘tries’’ to alleviate unfavorable

electrostatic repulsion in corona. This is

achieved by unfolding of P(4VP/EVP)

chains (i.e. by expanding the corona) and

decrease the aggregation number (right

micelle in Scheme 1).

In the case of hybrid PS-PEVP/PS-

P4VP-b micelles 4VP and EVP units are

chemically bound into blocks per 100 units.

These blocks are planted from joint PS-core

in a star-like fashion. Because P4VP blocks

are insoluble in water at pH 9 the hybrid

micelles must have three-layered structure

Scheme 1.

Structural organization of PS-P(EVP/4VP)-b micelles in



Figure 3.

Weight-average molecular weight Mw (�) and hydro-

dynamic radius Rh (&) of PS-PEVP/PS-P4VP-b micelles

in 0.05 M NaCl aqueous dispersions as a function of b.

Table 2.Structural characteristics of PS-PEVP/PS-P4VP-bmicelles in 0.05 M NaCl aqueous dispersions.

b Nwa) RC (nm) D (nm)

0.2 1200 17 240.3 700 14 230.4 230 10 200.5 110 8 200.6 90 7 180.7 110 8 141.0 100 7 15

a)For hybrid micelles M0¼bM0(PS-PEVP)þ (1-b)M0(PS-

P4VP), where M0(PS-PEVP) and M0(PS-P4VP) are molecularmasses of individual diblock copolymers.

Macromol. Symp. 2012, 316, 25–31 29

from the PS-core, intermediate shell form

contracted P4VP blocks and the outer

lyophilizing layer from charged PEVP

blocks.[9] For hybrid micelles the depen-

dencies of Mw and Rh upon corona

composition b are quite different from that

for PS-P(EVP/4VP)-b micelles. As can be

seen from Figure 3 both Rh and Mw values

are constant at high b (b� 0.7 for Rh and

b� 0.5 for Mw), while essentially and

monotonously changing at low b (b< 0.7

for Rh and b< 0.5 for Mw). The calculated

values of Nw, RC and D are presented in

Table 2, while the overall influence of b on

structural characteristics of hybrid micelles

is visualized in Scheme 2.

When b� 0.7 micelle characteristics are

similar to that of pure PS-PEVP. The

reason of micelle structural stability lies

in domination of electrostatic repulsions of

Scheme 2.

Structural organization of PS-PEVP/PS-P4VP-b micelles in


PEVP units over hydrophobic attraction of

PS and P4VP units. Nevertheless due to the

collapse of P4VP blocks onto PS-core the

specific area of core-corona interface per

one PEVP-chain does increase. To shield

the baring interface PEVP-chains start to

elongate, this means the growth of D. The

effect becomes noticeable at b< 0.7

(Table 2). When b drops below 0.5, the

PS core also grows to diminish the specific

area of the core-corona interface (Table 2).

The growth of PS-core means the elonga-

tion of PS chains. Elongation of PS-chains

amplifies the effect of PEVP elongation and

enables to sustain micelle aggregation

stability despite decreasing the ‘‘lyophiliz-

ing potential’’ of the corona. Contour

lengths (25 nm) of PS and PEVP-chains

define their elongation limit. From Table 2

one can see that when b¼ 0.2 the RC and D



Macromol. Symp. 2012, 316, 25–3130

values are close to the limit. This point

means the boundary of micelle phase

stability. When b drops below 0.2, micelles

precipitate.

Scheme 1 and 2 demonstrate the role of

distribution pattern of ionic and hydro-

phobic units in corona on micelle structure

as a function of corona composition. In the

case of statistical distribution of 4VP and

EVP units structural changes are moderate

in values and jump-like in character

(Scheme 1). In the case of mictoarm

distribution of P4VP and PEVP blocks

changes are large in values and monoto-

nous in character. The origins of this

difference lie in spatial segregation of ionic

and nonionic units in the case of hybrid

micelles. To prove this statement theore-

tical consideration of micelle structure is

necessary. Such consideration is in progress

now and its discussion will be presented in

our nearest publications.

The micelle structure must determine

the micelle properties. To illustrate this

correlation we have examined the aggrega-

tion stability of micelles towards increasing

the ionic strength of the solution. Figure 4

presents the diagram of micelle aggregation

stability upon addition of NaCl. Here

[NaCl]� is a threshold concentration, below

it micelles are stable, and above it micelles

quantitatively precipitate. So the area left

and above the curve [NaCl]� - b corre-

sponds to micelle precipitation (salting

out), while the area right and below the

0.80.60.40.20.00.0

0.4

0.8

1.2

β*(1)precipitation

precipitation

β*(2)

β

[NaC

l]*, M

Figure 4.

Diagrams of dispersion stability of PS-P(EVP/4VP)-b

(~) and PS-PEVP/PS-P4VP-b (�) micelles in aqueous

media in the presence of NaCl.


curve designates the micelle aggregation

stability. As can be seen from Figure 4 for

both types of micelles the value of [NaCl]�

monotonously increases with increase of b.

Above some threshold composition (b�)

micelles do not precipitate even at satu-

rated NaCl concentrations, ca 5.5 M.

For PS-P(EVP/4VP)-b micelles 0.6<

b�(1)< 0.7, i.e. fits the region of micelle

structural transformation. For hybrid PS-

PEVP/PS-P4VP-b micelles 0.2<b�(2)<

0.3, i.e. lies near the boundary of maximal

core and corona chains elongation. Here we

see the evident correlation between micelle

structure and its ability to persist against

salting out. Due to spatial segregation of

ionic and nonpolar blocks in their corona

hybrid micelles persist more efficiently

against precipitation impact of adding salt.

Conclusion

We have systematically studied the influ-

ence of corona composition on structure

and dispersion stability of diblock copoly-

mer micelles with ionic amphiphilic corona

in aqueous media. We have found that

micelle structure is quite insensitive to

variation of its composition within the

range of b¼ 0.7�1.0. When the fraction

of charged units drops below this range the

structural reorganization of micelles is

observed. The reorganization allows to

sustain micelle aggregation stability despite

decreasing the lyophilizing capacity of the

corona. The character of micelle structural

reorganization depends upon the distribu-

tion pattern of ionic and hydrophobic units

in corona and can be qualitatively

explained by the interplay of electrostatic

and hydrophobic interactions of polymer

units within the micelle. We believe

that our findings may be of certain

importance for design of multifunctional

polymeric micelles with heterogeneous

microstructure.

Acknowledgements: Authors thank Russian Ba-sic Research Foundation for financial support(Grant No 10-03-00392a).


Macromol. Symp. 2012, 316, 25–31 31

[1] S. Forster, V. Abetz, A. H. B. Muller, Adv. Polym. Sci.

2004, 166, 173.

[2] M. Ballauff, Prog. Polym. Sci. 2007, 32, 1135.

[3] S. Forster, T. Plantenberg, Angew Chem. Int. Ed.

2002, 41, 688.

[4] C.-A. Fustin, V. Abetz, J.-F. Gohy, Eur. Phys. J. E 2005,

16, 291.

[5] F. Schacher, A. Walther, A. H. E. Muller, Langmuir

2009, 25, 10962.

[6] M. A. Crichton, S. R. Bhatia, J. Appl. Polym. Sci.

2004, 93, 490.

[7] D. D. Bendejacq, V. Ponsinet, M. Joanicot, Langmuir

2005, 21, 1712.

[8] M. Stepanek, K. Podhajecka, E. Tesarova,

K. Prochazka, Z. Tuzar, W. Brown, Langmuir 2001, 17,

4240.


[9] A. B. E. Attia, Z. Y. Ong, J. L. Hedrick, P. P. Lee, P. L. R.

Ee, P. T. Hammond, Y.-Y. Yang, Curr. Opin. Colloid

Interface Sci. 2011, 16, 182.

[10] A. I. Kulebyakina, E. A. Lysenko, P. S. Chelushkin,

A. V. Kabanov, A. B. Zezin, Polymer Science, Ser. A 2010,

52, 574.

[11] E. A. Lysenko, A. I. Kulebyakina, P. S. Chelushkin,

A. B. Zezin, Doklady Physical Chemistry 2011, 440,

187.

[12] K. Prochazka, D. Kiserow, C. Ramireddy, Z. Tuzar,

P. Munk, S. E. Webber, Macromolecules 1992, 25,

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[13] T. J. Martin, K. Prochazka, P. Munk, S. E. Webber,


[14] O. V. Borisov, E. B. Zhulina, Macromolecules 2003,

36, 10029.



Inst

Aca

1990

Fax:

E-m

Cop

Synthesis and Solution Properties of Loose Polymer

Brushes Having Polyimide Backbone and

Methylmethacrylate Side Chains

Anna Krasova, Elena Belyaeva, Elena Tarabukina, Alexander Filippov,*

Tamara Meleshko, Dmitry Ilgach, Natalia Bogorad, Alexander Yakimansky

Summary: Graft-copolymers with polyimide backbone and PMMA side chains are

synthesized by ATRP of methylmethacrylate on the polyimide macroinitiator. The

obtained copolymers, macroinitiator, and cleaved side chains are investigated by1H NMR, SEC, static and dynamic light scattering, sedimentation, and viscosimetry

in solutions. The synthesized copolymer is relatively loose polymer brushes: the

average distance between grafted PMMA chains is �11 nm (4 repeat units of

the backbone). The hydrodynamic and conformational characteristics of graft-

copolymers change on passage from ethylacetate to chloroform due to difference

in the thermodynamic quality of the solvents with respect to the copolymer

components. The backbone is characterized more extended conformation than

individual polyimide macromolecule.

Keywords: atom transfer radical polymerization; conformational analysis; graft copolymers;

polyimide macroinitiator; solution properties

Introduction

In the last decade, intensive theoretical and

experimental studies of the properties of

cylindrical polymer brushes in solutions

were performed. Their regular multi-

branched structure leads to a significant

difference in solution behavior of comb-

like copolymers with densely grafted side

chains and the corresponding linear poly-

mers.[1–15] Cylindrical brushes have a high

density of polymer substance in the volume

occupied by macromolecules in solution,

this feature being indicative of their

relatively compact structure. In the case

of a long backbone, the conformation of

their macromolecules is extended wormlike

chain due to steric repulsion between

side chains, Kuhn segment length, A, being

itute of Macromolecular Compounds of Russian

demy of Sciences, Bolshoy pr., 31, Saint-Petersburg

04, Russia

(þ7) 812 3286869;



one order of magnitude larger compared to

that of a linear chain with similar chemical

structure. If lengths of the backbone and

side chains are close, the conformational

and hydrodynamic properties of the den-

sely grafted copolymers are similar to those

of macromolecular stars. The longer are

side chains and the better is the solvent for

the side chains, the higher is the rigidity of

the backbone. Usually, temperature depen-

dence of the second virial coefficient, A2, for

cylindrical brushes is much weaker than

that for linear analogs and the magnitude of

dA2/dT at Q-point decreases with side chain

lengthening (T is temperature).

It should be emphasized that practically

all investigations mentioned above were

devoted to grafted copolymers with both

the backbone and side chains represented

by vinyl polymers, such as poly(meth)acryl-

ates, polystyrene, etc. It is interesting to

analyze the properties of regular grafted

copolymers having the backbone and

side chains which would differ considerably

in chemical nature and, hence, thermo-


Macromol. Symp. 2012, 316, 32–42 33

dynamic properties. Depending on thermo-

dynamic quality of a solvent for the back-

bone and side chains of the graft-copoly-

mers, their macromolecules may adopt

different conformations in solution. As

conformation types do not usually change

from solution to bulk state, it becomes

possible to tune the supermolecular struc-

ture and morphology of graft-copolymer

films by an appropriate choice of the

solvent for film casting.

In this respect, polymer brushes with

polyvinyl side chains grafted to a poly-

imide backbone are rather perspective.

Polyimides present a class of highly

thermally stable polymers with a unique

complex of properties.[16] For example,

during the past decade, a careful attention

was paid to functional polyimide deriva-

tives for applications in optoelectronics.[17]

For these applications, modifications of

polyimides with regularly grafted side

chains of different structure by controlled

radical polymerization methods are rather

promising.

The aims of the present work are to

synthesize the polymer brushes with poly-

imide (PI) backbone and poly(methyl

methacrylate)s (PMMA) side chains and

to study their conformational properties in

dilute solutions.

O

O

* N

OO

Br

O

Br

O

N

OO

O

*

Scheme 1.

Synthesis of the polyimide macroinitiator.


One of the most promising synthetic

approaches in synthesis of polymer

brushes is the so-called ‘‘grafting from’’

method based on the growth of side

chains from the polymeric backbone-bound

initiating groups, i.e. on the use of multi-

center macroinitiators.[18] In the present

work, a novel multi-center polyimide

ATRP macroinitiator was synthesized

from a soluble polyimide with side OH-

groups, and 2-bromo-isobutyroyl bromide

(Scheme 1). Using atom transfer radical

polymerization (ATRP) from side chain

2-Br-isobutyrate groups of polyimide multi-

functional macroinitiators in the presence

of Cu(I) halide complexes, polyimide-graft-

polymethylmethacrylate copolymers (PI-g-

PMMA) are synthesized (Scheme 2). The

polyimide macroinitiator and side chains

cleaved from the backbone by alkaline

hydrolysis of the polymer brush (Scheme 3)

were investigated too.

Experimental Section

Preparation of Solvents, Reagents, and

Monomers

N-methyl-2-pyrrolidone (N-MP) and

toluene were dried by vacuum distillation

from calcium hydride. THF was boiled with

KI, N(C2H5)3

OOBrBr

OOO

O

*N

OHHOO

O

*N

n

n


(bpy)2CuCl, N-MPO

O

Br(Cl)H3CO

OCH2

O

Br(Cl) OCH3

OCH2

O

OO

O

O

O

* *N N

OO

OOBrBr

OO

O

O

O

* *N N

OO

O

O

m m

n

n

Scheme 2.

Synthesis of PI-g-PMMA.

Macromol. Symp. 2012, 316, 32–4234

potassium hydroxide and then distilled

from calcium hydride. Triethylamine was

distilled twice, first after boiling with dry

acetic anhydride and then after boiling

with potassium hydroxide. CuCl was pur-

ified from Cu(II) impurities with glacial

acetic acid according to the standard

H2C

OCH3OH

O

O

* N

OO

O

O

m

KOH

HO

Scheme 3.

Cleavage of PMMA side chains from the polyimide bac


procedure.[18b] Potassium iodide was dried

in vacuum at 140 8C. 2-Br-isobutyroyl-

bromide was used without a preliminary

purification.

3,30-dihydroxybenzidine was heated in

vacuum at 100 8C for 10 hours. Dianhydride

of 3,30,4,40-(1,3-diphenoxybenzene)-tetra-

OOO

O

*N

Br(Cl) OCH3

OCH2

O

Br(Cl)H3CO

OCH2

O

m m

n

kbone.


Macromol. Symp. 2012, 316, 32–42 35

carboxylic acid was heated in vacuum at

140 8C for 10 hours. Methylmethacrylate

(MMA) was twice distilled in vacuum.

Synthesis of Multicenter Polyimide

Macroinitiator

In the first stage of the synthesis of the

initial polyimide, room temperature poly-

condensation between 3,30-dihydroxyben-

zidine and dianhydride of 3,30,4,40-(1,3-

diphenoxybenzene)-tetracarboxylic acid

was performed in NMP solution, producing

20 wt.% solution of the corresponding

polyamic acid. In the second stage, the

polyamic acid was cyclodehydrated in

solution at 170–180 8C, distilling off water

byproduct as its azeotropic mixture with

toluene.

3 g of thus obtained 20 wt.% polyimide

solution in N-MP was diluted with N-MP to

the concentration of 3 wt.%. Then, into this

diluted solution, 1.4 mL of triethylamine

and 0.8 g of KI were added. The reaction

mixture was cooled down on ice bath and

then solution of 0.6 mL of 2-Br-isobutyroyl-

bromide solution in 6 mL of THF was

slowly dropped. The reaction solution was

stirred under cooling for 4 hours, then it

was heated up to room temperature and

stirred for more 20 hours. The precipitated

salt Et3N �HBr was filtered off, and the

polymeric product was precipitated from

the filtrate into methanol. The polymeric

product was washed by ethanol until it

became colorless, and then several times

with warm water (40 8C). The multicenter

polyimide macroinitiator was finally repre-

cipitated from chloroform into petroleum-

ether, filtered off and dried at 50 8C at a

reduced pressure.

Synthesis of Polyimide-graft-PMMA

Atom transfer radical polymerization

(ATRP) of MMA from the multicenter

polyimide macroinitiator was carried out in

N-MP solution. 0.078 g of the macroinitia-

tor was dissolved in 13 mL of N-MP, and

then 2,20-bipyridine (0.0568 g) and CuCl

(0.012 g) were added. The obtained solution

was placed into a glass tube, then, MMA

was added into the tube. The reaction


solution was deoxygenated by triple freez-

ing and evacuation, then, the tube was

sealed and place in a thermostat at 80 8C for

20 hours. Then, in order to terminate the

ATRP process, the reaction solution was

quickly cooled down, open to air, and 50%

diluted with THF. After chromatographic

purification from the catalyst on an alumina

column, the solution was concentrated on a

rotary evaporator, and the polymer pro-

duct, polyimide-graft-PMMA, was precipi-

tated into methanol. The precipitate was

filtered off and dried at 50 8C at a reduced

pressure.

Cleavage of Side Chains of

Polyimide-graft-PMMA

0.1 g of polyimide-graft-PMMA was dis-

solved in 15 mL of THF, and 10 mL of KOH

solution in methanol (5 wt.%) was added.

The solution was kept in a round-bottom

flask with reflux condenser for 16 hours at

70 8C. Then, the solution was concentrated

on a rotary evaporator, and water was

added for complete polymer precipitation.

The polymer was filtered off and washed

with water until neutral pH. The isolated

polymer was dried at 50 8C at a reduced

pressure.

Polymer Characterization by 1H

NMR-Spectroscopy1H NMR-spectra were recorded on a

Bruker AC-400 (400.1 MHz) device, using

DMSO-d6 as the solvent.

Characterization of Cleaved PMMA Side

Chains by GPC

Gel permeation chromatography (GPC) of

cleaved PMMA side chains was performed

on an HPLC – Tower (vacuum degasser,

isocratic pump, autosampler, UV- and

RI-detector) from Agilent 1200 Series.

THF was used as the eluent at a flow rate

of 1 mL/min at 40 8C. PMMA standards

were used as the references.

Methods of Molecular Optics and

Hydrodynamics

The prepared samples were studied by the

methods of molecular optics and hydro-


0.0120.0090.0060.003

1

2

3

cH/R×105, mol/g

c, g/cm3

Figure 1.

Dependence of the inverse scattered light intensity

cH/I90 on concentration c for PI in DMFA.

0.90.60.3

0.5

1.0

1.5

sin2θ/2 + kc

cH/I, mol/g

Figure 2.

Zimm diagrams for PI-g-PMMA in chloroform.

Macromol. Symp. 2012, 316, 32–4236

dynamics in dilute solutions in the following

solvents: PI-g-PMMA in ethylacetate

(dynamic viscosity h0¼ 0.43 cP, density

r0¼ 0.900 g � cm�3, and refractive index

n0¼ 1.370) and chloroform (h0¼ 0.57 cP,

r0¼ 1.489 g � cm�3, and n0¼ 1.443), PI in

chloroform and N,N-dimethylformamide

(DMFA) (h0¼ 0.80 cP, r0¼ 0.94 g � cm�3,

and n0¼ 1.428), and PMMA in ethyl-

acetate. All measurements were performed

at 21.0 8C. CHROMAFIL filters (Macherey-

Nagel GmbH&Co KG, Germany) made of

PTFE with pore sizes of 0.23 or 0.45 mm

were used for filtration of solutions and

solvents.

The static and dynamic light scatterings

were investigated on a Photocor apparatus

(Russia), its optical part being equipped

with a Photocor goniometer. A Spectra-

Physics helium-neon laser with the wave-

length of l¼ 632.8 nm and a power of

�10 mV was employed as a light source.

The correlation function of scattered light

intensity was derived with the aid of a

Photocor-FC correlator with 288 channels.

The data were treated by the cumulant

method and Tikhonov regularization pro-

cedure. The refractive index increment

dn/dc was measured, using a Rayleigh

interferometer LIR-2 (Russia): for PI

dn/dc¼ 0.158 and 0.169 cm3 � g�1 in

chloroform and DMFA, respectively;

for PI-g-PMMA dn/dc¼ 0.069 and 0.103

cm3 � g�1in chloroform and ethylacetate,

respectively.

The molar masses, Mw, second virial

coefficients, A2, and gyration, Rg, and

hydrodynamic, Rh, radii of macromolecules

were measured as described in detail in

monographs.[19,20] Figure 1 and 2 demon-

strate Debay plot and Zimm diagram for

the macroinitiator PI and grafted PI-g-

PMMA copolymers.

Two modes were found for PI in

chloroform. In all other cases, only one

mode was observed. The diffusion coeffi-

cient D corresponding to this mode and

consequently the hydrodynamic radius

Rh(c) do not depend on concentration

and scattering angle. The similar behavior

was fixed for the fast mode of macro-


initiator PI solution. Therefore the average

experimental values of Rh(c) were taken as

the magnitudes of hydrodynamic radii Rh of

macromolecules.

Analytical ultracentrifugation was

carried out on a Beckman-Coulter Proteo-

melab XL-I ultracentrifuge at 258 in a

double-sector cell using interference

optical system. Rotor rotation speed was

40000 rpm. Sedimentation coefficients s

were calculated from the displacements of

the maxima of differential distributions

obtained as derivatives of integral distribu-

tions available from the ultracentrifuge.

Sedimentation coefficient at infinite dilu-

tion s0, was calculated by means of fitting

procedure in accordance with the Gralen

equation 1/s¼ 1/s0(1þ ksc), where ks is

the concentration coefficient and c is the

solution concentration. We have obtained

s0¼ 3.2 Sv for PI macroinitiator in DMFA

solution.


Table 1.Molar mass and hydrodynamic characteristics of investigated polymers.

Polymer Solvent [h][cm3 � g�1]

Mw �10�3

[g �mol�1]A2� 104

[cm3 �mol � g�2]Rg

[nm]Rh

[nm]Rg/Rh

PI chloroform 57 1040 �0.1 76 9.5/77a) –DMFA 49 70/66 b) 10 – 8.9 –

PMMA chloroform 31 – – – – –ethylacetate 14 33/27 c) – – – –

PI-g-PMMA chloroform 54 550 3.6 34 12 2.8ethylacetate 22 590 1.4 24 12.5 1.9

a)The first and second values are the hydrodynamic radii Rh,f and Rh,s corresponding to the fast and slowmodes;b)the first and second values are Mw and MSD;c)the first and second values are Mw obtained by SEC andviscosity molar mass.

Figure 3.1H NMR spectra of the (1) initial polyimide, (2) poly-

imide macroinitiator and (3) polyimide-graft-PMMA

copolymer.

Macromol. Symp. 2012, 316, 32–42 37

The hydrodynamic molecular masses

MSD of macroinitiator was calculated via

the Svedberg equation

MSD ¼RT

1� r0v

s0

D0(1)

Here, R is the universal gas constant and

T is the absolute temperature. The specific

partial volume v¼ 0.639 cm3 � g�1 was

measured pycnometrically by a glass den-

simeter with a volume of 2.038 cm3. The

diffusion constant D0¼ 3.0� 10�7 cm2 � s�1

was obtained by dynamic light scattering

method.

Intrinsic viscosity, [h], was measured

with an Ostwald capillary viscometer.

The efflux times of solvents t0 were 73.3

(ethylacetate), 69.9 (chloroform), and

155.4 s (DMFA). The values of [h] and

Huggins constant k’ were estimated via

the Huggins equation hsp/c¼ [h]þ k0[h]2c,

where k’ characterizes the polymer-solvent

hydrodynamic interaction and the

hydrodynamic behavior of solutions.[21–23]

Based on intrinsic viscosity value and

using ratios Kuhn-Mark–Houwink equa-

tions [h]¼ 0.0096M0.78 in chloroform[24a]

and [h]¼ 0.021M0.64 in ethylacetate[24b] we

estimated the viscosity molar mass Mh of

PMMA side chain. The calculated values

Mh¼ 31000 (chloroform) and 27000 (ethy-

lacetate) are in a good agreement with Mw

measured by SEC.

All obtained molecular and hydro-

dynamic characteristics are listed in

Table 1.



A necessary prerequisite for preparation of

regular graft-copolymers by the ‘‘grafting

from’’ ATRP method is a complete func-

tionalization of the corresponding multi-

center macroinitiator, i.e. the presence of

groups, initiating ATRP, in every monomer

unit of the macroinitiator. Polyimide multi-

center macroinitiator was obtained by

esterification of OH-groups of the initial

polyimide by 2-Br-isobutyroyl bromide in

the presence of catalytic amounts of KI,

according to the published procedure.[25]

As seen from Figure 3, 1H NMR spectrum

of the macroinitiator (curve 2) does not

contain the signal of phenol hydroxyls

(10 ppm) which is present in the initial

polyimide spectrum (curve 1). Instead, the


Macromol. Symp. 2012, 316, 32–4238

signal of initiating 2-Br-isobutyrate groups

appears at 1.9 ppm. Comparing its integral

intensity with the integral intensity of

aromatic protons at 6.0–8.5 ppm, the func-

tionalization of the macroinitiator is esti-

mated to be nearly complete.

The obtained polyimide macroinitiator

is insoluble in MMA. Therefore, ATRP of

MMA from this macroinitiator cannot be

carried out in bulk monomer. The most

effective solvents for polyimides are aprotic

amide solvents like N,N-dimethylforma-

mide, N,N-dimethylacetamide, and N-MP.

Earlier, we found that ATRP of MMA

from a polyimide macroinitiator effectively

proceeds in N-MP at 80 8C in the presence

of the complex of CuCl and 2,20-bipyridine.

The same conditions were used here for the

synthesis of the polyimide-graft-PMMA

copolymer. It is seen from Figure 3 that

in its 1H NMR spectrum (curve 3) there is

practically no signal of 2-Br-isobutyrate

groups at 1.9 ppm, but signals of �OCH3

(3.9 ppm) and�CH3 (0.9 ppm) groups of

MMA units are present.

In order to determine the molecular

weight characteristics of the grafted

PMMA side chains, they were cleaved

from the polyimide backbone by complete

degradation of the latter under alkaline

hydrolysis (Scheme 3). Sufficiently mild

conditions of this process were found in

which ester groups of PMMA side chains

are not hydrolyzed, as is evidenced by the

absence of vibration bands of carboxylic

groups (2800–3600 cm�1, 1700 cm�1, 1560–

1600 cm�1) in FTIR spectra of thus cleaved

PMMA side chains. The complete degrada-

tion of the polyimide backbone is also

proved by the absence of aromatic UV-

absorption at 260 nm in UV-spectra of the

cleaved PMMA side chains. Also, 1H NMR

spectrum of the cleaved PMMA side chains

does not contain signals of aromatic pro-

tons. Therefore, one may conclude that the

isolated polymer product of the alkaline

hydrolysis of polyimide-graft-PMMA is

indeed its PMMA side chains. Molar mass

characteristics of the cleaved PMAA side

chains were determined by SEC method,

using THF eluent and PMMA standards.


One can see from Table 1 that there is

a good agreement between molar masses

of grafted copolymers PI-g-PMMA deter-

mined in different solvents. The situation is

different for the macroinitiator PI. The

molar masses of PI estimated by static light

scattering in chloroform are more than an

order of magnitude higher than Mw in

DMFA. On the other hand, the Mw and

MSD values of PI determined in DMFA

practically coincide. The reason for such a

remarkable difference in the Mw values can

be ascertained by dynamic light scattering.

As was noted above, PI in chloroform

solutions is characterized by a bimodal

particle size distribution. In this case, the

hydrodynamic radii, Rh,s, corresponding to

the slow mode is more than six times higher

than the Rh,f values of species responsible

for the fast mode (Table 1). The Rh,f values

are close to the hydrodynamic radius Rh

measured in DMFA. These data lead us to

assume that species responsible for the fast

mode in chloroform are individual macro-

molecules of the macroinitiator PI. It is

large species responsible for the slow mode

that contribute mostly to Mw and radius of

gyration Rg obtained by static light scatter-

ing. These data could be explained by the

fact that chloroform, unlike DMFA, is not a

good solvent for polyimides. The macro-

initiator PI becomes soluble in chloroform

due to a-Br-isobutyrate side groups

attached to the polyimide backbone. How-

ever, obviously, supramolecular aggregates

of PI chains still do form in chloroform. It

should be noted here that although almost

every repeating unit of PI contains two

2-Br-isobutyrate side groups, unsubstituted

OH-groups of the original polyimide can

still be present in PI macromolecules,

enhancing aggregation in chloroform,

which, unlike DMFA, does not breaks

H-bonds effectively.

We estimated the rigidity of the macro-

initiator PI chains, using the values of

hydrodynamic radius Rh of its macromole-

cules in DMFA and chloroform. It is known

that for linear polydisperse polymers in a

good solvent the ratio r of gyration radius

Rg to hydrodynamic radius Rh is close to


Macromol. Symp. 2012, 316, 32–42 39

2.05.[26] Therefore, for PI chains in DMFA

(a good solvent) we obtained Rg� 18 nm.

In Q-solvent r¼ 1.73,[26] then Rg¼rRh,f� 16 nm in chloroform which is a poor

solvent for PI. If the macroinitiator is

modeled by the wormlike chain, its Rg

may be expressed by

R2g ¼

LA

6�A2

4þ A3

4L� A4

8L2ð1-e�2L=AÞ (2)

where L is the contour length of the chain

and A is the Kuhn statistical segment

length. For the investigated PI sample,

L¼ l0M/M0� 210 nm, where l0 and M0 are

length and molecular weight of monomer

units. Then, in accordance with relation (2),

A� 10 and 8.2 nm in DMFA and chloro-

form, respectively. Thus, we may conclude

that the PI macroinitiator is a semiflexible

polymer. This is why the values of Kuhn

segment length in the used solvents are

close. As it is known, the excluded volume

effect is weakly pronounced for rigid chain

polymers.[21]

The molar mass of PI-PMMA is higher

by about 8–9 times than that of PI. Never-

theless, the intrinsic viscosities of grafted

copolymer in chloroform and macroinitia-

tor in dimethylformamide are close and the

[h] value for PI-PMMA in ethylacetate is

less than that of PI. Such behavior is caused

by the difference in conformation of

PI-PMMA and PI macromolecules. For

sufficiently rigid macroinitiator molecules,

the conformations of swollen draining

coil are realized in solutions. The macro-

molecular brushes, as it is known are

characterized by the compact sizes and

the dense structure.[12–14] Probably the

similar situation takes place for investi-

gated comblike copolymers. Besides the

conformations of PI-PMMA molecules in

chloroform and ethylacetate are different.

As it is seen from the Table 1, the intrinsic

viscosities, radius of gyration, and ratio

Rg/Rh change on passage from one solvent

to another. The highest values of [h], Rg,

and Rg/Rh are obtained in chloroform.

In ethylacetate the reduction in Rg was

about 10–20%. In this solvent intrinsic

viscosity was lower by a factor of �2.3


than that in chloroform. The Rg/Rh value

decreases from 2.8 to 1.9. A reduction

in [h], Rg, and Rg/Rh may be due to

changes in the shape and density of

macromolecules.

In order to explain these experimental

facts and to make more strict conclusions

about conformational changes we will

consider the structure of PI-g-PMMA

molecules. The density of side-chain graft-

ing to the backbone was estimated using the

molar masses M obtained for copolymer,

macroinitiator, and side chains. In this

calculation the average values of molar

masses for each polymer investigated

were used: MPI-PMMA¼ 570000 for co-

polymer, MPI¼ 68000 for poly(imide), and

MPMMA¼ 30000. The summary number

NPMMA of side chains in of PI-g-PMMA

macromolecules may be expressed as

NPMMA¼ (MPI-PMMA�Mmc)/MPMMA. The

molar mass of main chain is Mmi¼MPI�M0-mi/M0-PI� 40000. Here, M0-mi¼548 and M0-PI¼ 880 are molar masses of

monomer units of copolymer backbone and

PI macroinitiator, correspondingly. Conse-

quently, NPMMA� 18, that is each macro-

molecule of copolymer investigated con-

tains only 18 PMMA side chains. The

distance hL between two neighboring

PMMA is close to 11 nm (or about 4

monomer units of the PI), i.e. the synthe-

sized PI-g-PMMA can be considered as

loose polymer brushes, in contrast to the

dense cylindrical macromolecular brushes

reported in numerous papers.[1–5,12–15]

Moreover both main and side chains are

sufficiently long and their contour lengths

distinguish not so strongly: Lbb� 255 nm for

PI and Lsc� 75 nm for PMMA. If PMMA is

modeled by Kuhn statistical segment chain,

the longitudinal H and transversal Q

sizeof their macromolecules in the unper-

turbed state may be defined by H¼ 1.4

ð6R2gÞ

1=2¼ 1.4 (LA)1/2� 17 nm and Q¼ 0.7

ð6R2gÞ

1=2¼ 0.7 (LA)1/2 1/2H� 9 nm. It is clear

that in chloroform and ethylacetate which

are good solvents for PMMA, the sizes H

and Q will increase. However in any case

the H and Q values will not differ strongly

from distance between two neighboring


Macromol. Symp. 2012, 316, 32–4240

side chains. Hence there are hollows for

PMMA chains in macromolecules of copo-

lymer investigated. The opposite situation

takes place in densely brushed polymers in

which the backbone and side chains are

stiffened considerably by enhancement of

repulsion between the neighboring side

chains. These repulsion interactions in

PI-PMMA will be weaker and it may

assume that the chain conformation will

change not very strongly.

Taking into account the close lengths of

backbone and side chains and low density

of grafting, it is seemed reasonable to

model the macromolecules of copolymer

investigated by rigid prolate rotational

ellipsoid with semimajor La and semiminor

Lb axes (Figure 4).

This model is the rough approximation

but it allows us to make the important

qualitative conclusions. The translational

friction coefficient f and the diffusion

constant D0 of such particles in solutions

can be expressed as (see, for example, [21])

f ¼ kT

D0¼ 6ph0 La

ðp2 � 1Þ1=2

plnpþ ðp2 � 1Þ1=2

p� ðp2 � 1Þ1=2

(3)

Here, k is Boltzmann’s constant and

p¼ La/Lb is axis ratio. The radius of gyration

of rotational ellipsoid with constant density

Figure 4.

The structure of PI-g-PMMA molecules in ethylacetate

and chloroform.


can be written as

Rg ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðLa

2 þ 2Lb2Þ=5

q(4)

By substituting values of D0 and Rg

into equations (3) and (4) we may easily

estimate the parameters of model ellipsoid

which are presented in Table 2. (The

experimental values of diffusion constant

were obtained by the dynamic light scatter-

ing method: Rh¼ kT/6ph0D0).

The ellipsoid has more extend shape in

chloroform in comparison with that in

ethylacetate. This result is in agreement

with change in experimental values of [h]

and Rg/Rh on passage from chloroform

to ethylacetate, since the increase of

the geometrical asymmetry (axes ratio)

of macromolecules leads to the growth

of intrinsic viscosity and shape factor

Rg/Rh.[21,26]

Using obtained characteristics we may

make some assumptions about inner

structure of PI-PMMA macromolecules

in investigated solutions. First of all, we

note, that the ethylacetate and chloroform

are good solvents for side PMMA chains.

The macroinitiator does not dissolve in

ethylacetate; the chloroform is a poor

solvent for the polyimide backbone. In

ethylacetate solution, the backbone tends

to be hidden from the solvent inside

PMMA coils. Correspondingly, the PI

chain is folded and the loops and ‘‘shuttle’’

packet form (Figure 4).

As a result of backbone contraction, the

free volume per one PMMA side chain

decreases and the repulsive interaction of

side chains increases. On the one hand, this

growing repulsion balances the forces

promoted to coiling of main chain and

prevents to its collapse. On the other side,

Table 2.Parameters of model ellipsoid in chloroform andethylacetate.

Solvent La

[nm]Lb

[nm]p

chloroform 75 7 10ethylacetate 50 15 3.4


Macromol. Symp. 2012, 316, 32–42 41

the excluded-volume interaction between

the side chains leads to their straightening

and some increase in PI-PMMA macro-

molecule dimensions.

The investigated copolymers may be

considered as polymer brushes with the

chemical nature of the backbone and

side chains. The solution properties of

such systems are rather complicated. In

particular in solvent that is good for

the backbone and bad for side chain, the

macromolecules may have the pearl-

necklace structure.[3,27,28] However the

probability of similar configuration for

PI-PMMA molecules is not enough since

they are characterized by the low grafting

density and have relatively long side chains

in comparison with backbone. For realiza-

tion of the pearl-necklace structure it is

needed that length of backbone must be

much more than that of side chain.[27,28]

The shape and dimensions of the

PI-PMMA molecules in chloroform is

caused by the repulsive interaction of side

chains. The chloroform is thermodynami-

cally very good solvent for PMMA, and the

side chains rush to occupy the large volume

straightening backbone and increasing

the form asymmetry of comblike macro-

molecules. Correspondingly, the semimajor

axis length La of model ellipsoid in chloro-

form is higher by a factor of 1.5 than that in

ethylacetate.

In conclusion we note that in both

chloroform and ethylacetate the PI back-

bone is sufficiently strongly stretched. The

end to end distance h for PI individual

molecules in Q-solvent is equal to about

45 nm, because for long chain macromole-

cules �6 R2g and Rg� 18 nm for PI macro-

initiator. In the case of PI-PMMA, the

highest possible value hmax of the end

to end distance of PI backbone coincides

with length of model ellipsoid major axes.

Correspondingly, hmax� 150 nm in chloro-

form and 100 nm in ethylacetate. The

minimum value hmin may be estimated

using formula h¼ 2(La�H), where H is

longitudinal size of PMMA molecules.

Such situation takes place when the PMMA

molecules are situated on each end of


backbone. Taking into account the thermo-

dynamical quality of used solvents it will

not be serious mistake to assume that H

does not exceed 25 nm. Consequently, for

minimum end to end distance for backbone

we obtain hmin� 50 nm in ethylacetate and

hmin� 100 nm in chloroform. Thus, even in

the case of collapsed backbone in ethyl-

acetate, their linear dimensions are

comparable with those for individual PI

molecules due to the side chain interaction.

Conclusion

It was shown that ATRP of methylmetha-

crylate on the polyimide macroinitiator

may be used for the synthesis of relatively

loose polymer brushes with the strongly

different chemical natures of the backbone

and side chains. This difference is respon-

sible for their conformational and hydro-

dynamic properties. The rotation ellipsoid

model is used for the description of their

solution behavior. Size and shape of the

macromolecules depend on the thermody-

namic quality of the solvent with respect to

the backbone and side chains. The obtained

data make it possible to conclude that the

backbone of PI-g-PMMA is always more

extended than the PI macromolecule of the

same molar mass.

Acknowledgements: Work was supported by theRussian Foundation for Basic Researches (pro-ject 11-03-00353) and the Program No 3 ofDepartment of Chemistry and Material Scienceof Russian Academy of Sciences ‘‘Creation andstudy of macromolecules and macromolecularstructures of a new generation’’.

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1 In

A

bu

Fa

E-2 N.

M

so

Cop

Hydrodynamic Properties of ‘‘Pseudo-Dendrimer’’

Alexander P. Filippov,*1 Alina I. Amirova,1 Elena V. Belyaeva,1

Elena B. Tarabukina,1 Natalia A. Sheremetyeva,2 Aziz M. Muzafarov2

Summary: Hyperbranched polycarbosilane with terminal butyl groups is obtained by

chemical modification of hyperbranched polyallylcarbosilane using the reaction of

hydrosilylation with methyldichlorosilane, followed by treatment of the polychlor-

osilyl derivative with butyllithium. Its hydrodynamic and conformational properties

are studied by the methods of light scattering, sedimentation-diffusion analysis, and

viscosimetry in dilute solutions of methyl-tert-butyl ether, hexane, THF, chloroform,

and toluene. The results obtained are compared with the data for the initial

polyallylcarbosilane and carbosilane dendrimer with butyl terminal groups. It is

demonstrated that branching regularity is the decisive factor determining the

solution properties at fixed degree of the branching.

Keywords: hyperbranched polymers; light scattering; regularity of branching; solution

properties; viscosity

Introduction

The properties of hyperbranched polymers

at fixed chemical structure of monomer

units and molar mass (MM) are determined

by a number of structural parameters such

as the degree of branching DB,[1,2] the

Wiener index W,[3] and the regularity of

their structure. Variation in these para-

meters leads to change in molecular con-

formation which is responsible for the

essential difference in hydrodynamic beha-

vior of polymer in solution.

The degree of branching characterizes

the ratio of different types of monomer

units in macromolecule. Usually either

J.M.J. Frechet equation[1]

DB ¼ ðND þNTÞ=ðND þNL þNTÞ (1)

or H. Frey relation[2]

DB ¼ 2ND=ð2ND þNLÞ (2)

stitute of Macromolecular Compounds of Russian

cademy of Sciences, Bolshoy pr., 31, Saint-Peters-

rg 199004, Russia

x: (þ7) 812 3286869;


S. Enikolopov Institute of Synthetic Polymeric

aterials of Russian Academy of Sciences, Prof-

yuznaya st., 70, Moscow 117393, Russia


are used for quantitative estimation of DB

of hyperbranched polymers synthesized

from AB2-type monomers, where NL, ND,

and NT are the number of linear, dendritic,

and terminal units, correspondingly. In

practice DB is controlled by the synthesis

conditions. In some cases reliable monitor-

ing of the process can be carried out based

on the data, e.g., of the NMR methods.[4–6]

Increase in the degree of branching leads to

decrease in the asymmetry of macromole-

cular shape and growth of the fraction of

polymer substance in the volume which the

macromolecule occupies in the solution. It

is accompanied by changes in hydrody-

namic properties. In particular, the expo-

nent a in the Mark-Kuhn equation for

intrinsic viscosity [h] increases from (0.1–

0.2) to a¼ 0.5 and even more.[7–9]

The Wiener index describes the spatial

arrangement of atoms of the macromole-

cule. Its value is determined as

W ¼ 1

2

XN

j

XN

i

dij (3)

where N is the number of monomer units

in the macromolecule (polymerization

degree) and dij is the number of bonds

separating i- and j-element (unit) of the


Macromol. Symp. 2012, 316, 43–5144

structure along the shortest chain contour

between them. The Wiener index is a direct

measure of macromolecule compact-

ness.[10] In the case of the hyperbranched

macromolecule the W value is minimal

when the dendritic units are mainly located

in its center, to be more precise - near the

growth point (focal point), while at the

periphery mainly linear chains prevail. The

W index is maximal for hyperbranched

macromolecules with the ‘‘core’’ built

mainly from linear fragments and branch-

ing units concentrated in the ‘‘shell’’.

Theory predicts that conformational and

hydrodynamic properties of hyperbranched

polymers depend strongly on W.[11–16] For

example, at fixed MM intrinsic viscosity [h]

� Wa, with exponent a increasing with the

growth of polymerization degree. At pre-

sent it appears to be difficult to perform

controlled changing of the Wiener index

during the synthesis of hyperbranched

polymers and experimentally estimate the

W value. Though there are several works in

which polymers obtained by grafting of

hyperbranched blocks to ends of either star

arm[17,18] or linear chain,[19–22] it does not

seem quite correct to consider such systems

as hyperbranched polymers.

The regularity of branching means the

presence of certain patterns in the distribu-

tion of dendritic monomer units in macro-

molecule. Such patterns are a characteristic

feature of dendrimers, therefore they are

often called regular hyperbranched poly-

mers. In dendrimers the centers of branch-

ing are located at fixed distances from the

focal point. Moving from the growth center

along the chain contour in any direction, the

same set of structural elements at the same

distance can be found. It is the absence of

such branching pattern that is the main

differential feature of the hyperbranched

polymer as opposed to the dendrimer.

It seems difficult, if at all possible, to

synthesize a hyperbranched macromole-

cule with the degree of branching not equal

to 1, which is also characterized by regular

structure. On the other hand, as early as in

1998 H Fray reported synthesizing hyper-

branched polycarbosilane with DB � 1[23]


based on AB3-type monomer, though

detailed studies of its properties were not

made.

The important question is how the

behavior of hyperbranched systems with

DB¼ 1 differs from that observed for

dendrimers, on the one hand, and from

hyperbranched polymers with DB 6¼ 1, on

the other hand. Which of the factors,

branching regularity or branching degree,

is decisive in the formation of the branched

macromolecule properties? To answer this

question, we studied hyperbranched poly-

carbosilane with butyl terminal groups (PCS-

3-Bu) by the methods of molecular hydro-

dynamics and optics in dilute solutions.

The results obtained for PCS-3-Bu were

compared with the similar data for the

carbosilane dendrimers of sixth generation

with butyl groups in the surface layer of

their molecular structure (G6(Bu)) studied

earlier[24] and hyperbranched polymethy-

lallylcarbosilane (PCS-3-All)[25,26] modi-

fied into PCS-3-Bu.

Experimental Part

Preparation of Hyperbranched

Polymethylallylcarbosilane with

Methylchlorosilyl Groups

The mixture of 13.30 g (0.115 mol) of

methydichlorosilane, 8 cm3 of dry hexane,

4.5 g (0.036 mol) of polymethylallylcarbosi-

lane, and 30 ml of PC-072 catalyst was kept

in a sealed vessel under argon at ambient

temperature for 4 days, until, according to

the 1H NMR data, CH¼CH2 bonds com-

pletely disappeared. The reaction mixture

was maintained in vacuo for 2 hours to

obtain a transparent dense polymer used in

further reactions. 1H NMR spectrum

(250 MHz, CDCl3, d): -0.09 (m, 3H,

Si(CH3)), 0.59 (m, 6H, Si(CH3)CH2�),

0.80 (s, 3H, Si(CH3)Cl2), 1.29 (m, 4H,

�CH2�), 1.50 (m, 2H, �CH2Si(CH3)Cl2).

Synthesis of Hyperbranched Polymer with

Butyl groups

17 cm3 of dry THF was added to 86 cm3 of

2.5 mol butyllithium in hexane cooled


Figure 1.

Dependence of a reverse coefficient of sedimentation

1/s on the concentration c for the solutions of PCS-3-

Bu in hexane and chloroform.

Macromol. Symp. 2012, 316, 43–51 45

to �12 8C. With the temperature main-

tained at maximum �108C, 4.3 g

(0.018 mol) of polymer with methyldichlor-

osilyl groups in 5 cm3 of dry hexane was

added dropwise into the reaction mixture.

The reaction mixture was stirred at �108Cfor 30 min, followed by heating up to the

ambient temperature. After the reaction

was complete, the excess of butyllithium

was decomposed by ethyl alcohol. The

reaction mixture was washed with distilled

water until the neutral reaction of the

washing liquid was reached and dried over

Na2SO4. The solvent was then removed,

and 4.5 g (89%) of polymer was prepared.1H NMR spectrum (250 MHz, CDCl3, d):

�0.09 (m, 6H, Si(CH3)), 0.59 (m, 12H,

SiCH2�), 0.86 (m, 6H, CH3), 1.38 (m, 12H,

�CH2�).

Methods of Investigation

Molar-mass and hydrodynamic character-

istics of PCS-3-Bu were determined by the

methods of the static and dynamic light

scattering (SLS and DLS, respectively),

sedimentation-diffusion method, and visco-

metric analysis in the following solvents:

methyl-tert-butyl ether (MtBE, dynamic

viscosity h0¼ 0.77 cP, density r0¼0.758 g cm�3, refraction index n0¼ 1.376),

THF (h0¼ 0.46 cP, r0¼ 0.890 g cm�3, n0¼1.405), hexane (h0¼ 0.31 cP, r0¼0.667 g cm�3, n0¼ 1.375), toluene (h0¼ 0.55

cP, r0¼ 0.870 g cm�3, n0¼ 1.494) and chloro-

form (h0¼ 0.57 cP, r0¼ 1.489 g cm�3,

n0¼ 1.443). Light scattering, sedimentation

velocity, and translation diffusion were

studied in hexane and chloroform, while

intrinsic viscosity was measured in all above

solvents. All experiments were carried out

at 21 8C.

Sedimentation was studied using the

analytical ultracentrifuge MOM-3180

(Hungary) with the Philpot-Svensson

refractometric system. Rotation frequency

of rotor v¼ 45000 rpm. Sedimentation

boundary was formed by the method of

stratifying the less dense liquid over the

denser one. Flotation was observed in

chloroform, while sedimentation was found

in hexane. Sedimentation coefficient s was


estimated based on the movement rate of

sedimentation boundary.[27,28] The depen-

dence of s on concentration c was described

well by the Gralen equation 1/s¼ 1/s0�(1þ ksc), where ks is a concentration

sedimentation coefficient (Figure 1). Extra-

polation of s�1 to c! 0 gives the magnitude

of sedimentation constant s0 presented in

the Table 1.

Diffusion was studied on Tsvetkov

diffusometer, provided with Lebedev inter-

ferometer.[28] Diffusion coefficient D of

solution of c concentration was estimated

based on the method of squares and

maximum ordinate. Dependence of disper-

sion s2 of diffusion boundary on the time t is

approximated well with straight lines. The

line slope was used for estimating the value

of D¼s2/4t. Measurements were carried

out within c� 10�3 g � cm�3 concentration

range, where D usually does not depend on

c.[27,28] Hence, the value of the D coefficient

obtained at finite concentrations was taken

as a constant of translational diffusion D0

(Table 1).

Hydrodynamic molar masses MSD were

calculated using Svedberg equation

MSD ¼RT

1� r0v

S0

D0(4)

where R is a universal gas constant and T is

absolute temperature. A partial specific

volume v was found by the picnometer

method using densimeter with the volume

of 2.038 cm3. The value of v¼ (1.10� 0.02)


Table 1.Molecular and hydrodynamic characteristics of PCS-3-Bu.

solventa) [h] s0 D0� 107 MSD� 10�3 Mw� 10�3 A2� 103 Rh-Da)

cm3/g Sv cm2/s cm3 mol/g2 nm

hexane 7.7 6.7 16.6 44 49 0.4 4.2/4.9chloroform 7.6 �10.7 8.8b) 46 44 �0 �/4.3MtBE 8.3 – – – – – –toluene 7.2 – – – – – –THF 8.0 – – – – – –

a)Determined by translation diffusion and DLS methods, respectively.b)The value of D0 is calculated based onRh-D, found by the dynamic light scattering in chloroform.

Macromol. Symp. 2012, 316, 43–5146

cm3 � g�1 for PCS-3-Bu matches

v¼ (1.09� 0.03) cm3 � g�1 for the initial

PCS-3-All within the experimental

error.[25,26] It should be noted that the

specific partial volume for dendrimer

G6(Bu) is likely to be close to 1.14 cm3 � g�1

as its density r� 1/v¼ 0.88 g � cm�3.[24]

Intrinsic viscosity [h] was measured in

Ostwald capillary viscometer. The flow

time t0 of solvents was within the range

from 67.0 to 105.6 s. The value of [h] and

Huggins constant k0 were estimated based

on the Huggins’ equation (Figure 2)

hsp

�c ¼ h½ � þ k0 h½ �2c (5)

The [h] values are given in Table 1. The

Huggins constants are rather high, lying in

the range from k0 ¼ 0.76 (THF) to k0 ¼ 1.1

(MtBE). The increased values for k0 were

Figure 2.

Dependence of the reduced viscosity hsp/c on the

concentration c for the solutions of PCS-3-Bu in MtBE,

hexane, chloroform, and toluene.


obtained earlier for hyperbranched and

star polymers.[25,26,29–33] This seems to be

typical compact symmetrical macromole-

cule solutions.

Light scattering was studied on Photocor

setup (Ltd. ‘‘Antek-97’’, Russia). The

correlation function of the intensity of

the light scattered was obtained using

Photocor-FC correlator with 288 channels.

The data were processed by the cumulant

method and the Tikhonov regularization

procedure. Toluene was used as a

calibration liquid, whose absolute scatter-

ing intensity Rv is 1.38� 10�5 cm�1.

The solution and solvent were filtered

into cells previously dust-freed with ben-

zene. Chromafil filters (‘‘Macherey-Nagel

GmbH&Co. KG’’, Germany) with 0.45 mm

pores were used.

Weight-average molar masses Mw were

found by the standard method[27,34,35] and

calculated using equation

cH

I90¼ 1

Pð90oÞMwþ 2A2c (6)

where H is the optical constant

H ¼4p2n2

0ðdn=dcÞ2

NAl4(7)

Here I90 is the excess intensity of the

light scattered at an angle of 90o, P(90o) is

Debye scattering factor at an angle of 90o,

A2 is the second virial coefficient, NA is

Avogadro’s number, l¼ 632.8 nm is the

wavelength. A refractive index increment

dn/dc was measured using a Relay inter-

ferometer LIR-2 (Russia). Concentration

dependence cH/I90 in Figure 3 is typical for


Figure 3.

Dependence of cH/I90 and Rh-DLS on the concentration

c for PCS-3-Bu in chloroform.

Macromol. Symp. 2012, 316, 43–51 47

dilute polymer solutions. The values of Mw

and A2 calculated through Equation (6) are

given in Table 1. A relatively high positive

value of the second virial coefficient was

obtained in hexane, which means that this

solvent is thermodynamically good for

PCS-3-Bu while chloroform is a Q-solvent

(A2¼ 0). Notably, the MM values found by

different methods and in various solvents

coincide within the experimental error

margin (Table 1).

A single mode was found by the method

of DLS for PCS-3-Bu solutions. The

diffusion coefficient D corresponding to

the mode and consequently the hydrody-

namic radius Rh-DLS(c) do not depend on c

(Figure 3) in the concentration range

studied. Therefore the average experimen-

tal value of Rh-DLS(c) was taken as a

magnitude of hydrodynamic radius Rh-DLS

of macromolecule.


Hyperbranched polymer PCS-3-Bu was

synthesized by two-step modification of

polymethylallylcarbosilane PCS-3-All. A

polymer derivative was obtained by the

reaction of hydrosilylation with methyldi-

chlorosilane followed by treatment with

butyllithium. Due to such procedure,

PCS-3-Bu differs notably from PCS-3-All

in the set of monomer units. Macromole-


cules of polymethylallylcarbosilane contain

linear

-Si

CH3

CH2-CH CH2

CH2-CH2-CH2-

--

dendritic

-Si

CH3

CH2-CH2-CH2-

CH2-CH2-CH2-

and terminal

-Si

CH3

CH2-CH CH2--

CH2-CH CH2--

units. Based on the synthesizing conditions

and the data of NMR spectroscopy[36,37]

their ratio is NL: ND: NT¼ 0.50: 0.25: 0.25.

So the branching degree of polycarbosilane

with allyl groups is DB¼ 0.5. In PCS-3-Bu

there are no linear units, with its macro-

molecules containing 50% of dendritic and

terminal units.

-Si

CH3

CH2-CH2-CH2-CH3

CH2-CH2-CH2-CH3

Therefore, using Equation (1 and 2), DB

value can be estimated as DB¼ 1. It should

be noted that the composition of monomer

units is the same for both PCS-3-Bu and the

G6(Bu) carbosilane dendrimer with term-

inal butyl groups in the surface layer.[24]

Hence, it is reasonable to compare the

properties of PCS-3-Bu studied in this work

with those of dendrimer G6(Bu) and the

initial hyperbranched PCS-3-All.

As seen from the Table 1, PCS-3-Bu is

characterized by a rather high value of

MM� 46000, which corresponds to the

degree of polymerization N� 320. Such

magnitudes of MM and N are between the

values of the corresponding parameters for

sixth (calculated M¼ 36120.7) and seventh


Figure 4.

Values of [h] in dependence on a number of monomer

units N for hyperbranched PCS-3-Bu, PCS-3-All[25,26] in

hexane, chloroform, MtBE, THF, and toluene, dendri-

mer G6(Bu),[24] and lin-PCS.[43]

Figure 5.

Values of viscosity hydrodynamic radius Rh-h of

macromolecules in dependence on a number of

monomer units N for the hyperbranched PCS-3-Bu

in hexane, chloroform, MtBE, THF, toluene, PCS-3-

All,[25,26] dendrimer G6(Bu),[24] and lin-PCS.[43]

Macromol. Symp. 2012, 316, 43–5148

(M¼ 72554.1) generations of polycarbosi-

lane dendrimers. For hyperbranched PCS-

3-All characterized by the same MM, the

degree of polymerization is a little higher

(N� 360), as MM of its terminal monomer

units is notably lower than in the case of

PCS-3-Bu and G6(Bu). So the comparison

will be made for polymers with high, but not

olygomer MM.

Intrinsic viscosity of PCS-3-Bu does not

depend on the solvent (Table 1). Remark-

ably, the [h] values are the same for good

and Q-solvents. A similar phenomenon was

observed for the initial PCS-3-All.[25] It

should be noted, that PCS are able to

change essentially their hydrodynamic

parameters when the thermodynamic qua-

lities of the solvent are remarkable worse.

For example, the [h] decrease was found in

bad solvents compared to good and Q-

solvents in the case of PCS with fluorine

terminal groups.[33]

As for the absolute values of intrinsic

viscosity of PCS-3-Bu, they are not big and

lie in the range of [h] values typical for

hyperbranched polymers with high degree

of branching.[8,9,25,26,30,33] The small mag-

nitudes of [h] for PCS-3-Bu point to the

comparably high density of the polymer

substance in the volume occupied by the

macromolecule in the solution. This fact is

the evidence of their compact structure. On

the other hand, the intrinsic viscosity values

of PCS-3-Bu are notably higher than [h]

values obtained for dendrimers,[38–42] par-

ticularly for G6(Bu).

The Figure 4 demonstrates the depen-

dence of [h] on a number of monomer units

N for PCS-3-Bu, the starting PCS-3-All[25,26] and dendrimer G6(Bu) [24] is pre-

sented. Here the Mark-Kuhn-Houwink

relation for linear polyallylcarbosilane

�CH2�CH2�CH2�Si(CH3)2�,[43] a struc-

tural analogue of PCS-3-All, is given. It is

seen that experimental data for PCS-3-All

lie directly under the straight line related to

the relationship between log [h] and log N

for PCS-3-All and essentially higher the

analogous line obtained for G6(Bu). There-

fore the values of [h] for PCS-3-Bu are close

to those of the intrinsic viscosity of PCS-3-


All and notably bigger than analogous

magnitudes for the dendrimer at the same

degree of polymerization.

It is obvious that such dependence will

also hold true for the size of hydrodynamic

equivalent spheres, or viscometric hydro-

dynamic radii Rh-h, of macromolecules of

the polymers compared. The value of Rh-h is

estimated based on intrinsic viscosity cal-

culated via the Einstein equation

h½ � ¼ 2:5NAV

M

� �¼ 10p

3

NAR3h�h

M(8)

where V is a volume of hydrodynamically

equivalent sphere. The dependence of Rh-h

on N is given in Figure 5. At the fixed


Macromol. Symp. 2012, 316, 43–51 49

number of monomer units the values of Rh-h

for hyperbranched polymers PCS-3-Bu and

PCS-3-All differs by less than for 8%, while

the a hydrodynamic radius of the dendri-

mer molecule is 1.3 times lower than Rh-h of

PCS-3-Bu. Therefore the increase of intrin-

sic viscosity from the dendrimer to the

hyperbranched polymer with DB¼ 1, is

caused by the growth of macromolecular

size.

In the translational friction phenomenon

the hydrodynamic radii of macromolecules

PCS-3-Bu and PCS-3-All differ insignif-

icantly. The corresponding diffusion radius

Rh-D was calculated based on Stokes

equation

f ¼ kT=D0 ¼ 6ph0Rh-D (9)

using the values of diffusion coefficients D0

measured by the methods of DLS and

translational diffusion. In the Equation (9) f

is a coefficient of translational friction of

spherical particle, k is Boltzmann constant.

As seen in Figure 6, the points correspond-

ing to Rh-D for PCS-3-Bu lie a little below

the straight line representing the depen-

dence of log Rh-D on log N for the initial

PCS. However, this difference is about

10%, which is within the experimental error

margin of the determination of a diffusion

coefficient D0 by the methods of DLS and

translation diffusion.

It should be noted that for the polymer

studied the diffusion hydrodynamic radius

Figure 6.

The values of the diffusion hydrodynamic radius Rh-D

of macromolecules in dependence on a number of

monomer units N for hyperbranched PCS-3-Bu in

hexane and chloroform, PCS-3-All.[26]


Rh-D is larger about 1.2 times than visco-

metric one Rh-h. Similar difference is

marked rather often both for linear sys-

tems[28] and for polymers with complex

architecture.[30,32] The reason of this phe-

nomenon is that the law of size equivalency

is not complied strictly at the translational

and rotational movement of macromole-

cule. Roughly speaking, the molecule

‘‘flows’’ differently in the processes of

diffusion and viscosity.

The values of hydrodynamic invariant

A0[28,44,45]

A0 h0ðD0

TÞ2=3 ½h�S0R

100ð1� vr0Þ

� �1=3

; (10)

obtained for PCS-3-Bu (Table 1) are in a

favor of this conclusion. They are lower not

only than the theoretical and average

experimental magnitudes for linear flex-

ible-chain polymers (A0¼ 3.2� 10�10

erg �K�1 �mol�1/3),[27,44] but also less than

the theoretical meaning of A0¼ 2.88�10�10 erg �K�1 �mol�1/3 for hard spheres.

The decreased A0 were observed earlier for

hyperbranched PCS,[25,26,32] polyamino

acids,[29] carbosilane dendrimers[46] and

lactodendrimers.[47] The reasons of the

decreased magnitudes of hydrodynamic

invariant for the above systems are still

unclear. One of the important factors

influencing the value of A0 can be none-

quivalence of the viscometric and diffusion

hydrodynamic radii of macromolecules.

The difference observed in the hydro-

dynamic behavior of PCS-3-Bu and G6(Bu)

is caused by the conformational change on

passage from dendrimer to hyperbranched

polymer with DB¼ 1. Taking into account

high values of [h] and Rh of PCS-3-Bu

compared to those of G6(Bu), the conclu-

sion can be made about the looser structure

of PCS-3-Bu molecules, which means that

they are characterized by smaller fraction

of the polymer substance in the volume

occupied by the macromolecule in the

solution. According to these parameters,

PCS-3-Bu is close to the starting PCS-3-All.

The same can be said about the shape of

macromolecules PCS-3-Bu which geome-

trical asymmetry is more pronounced than


Macromol. Symp. 2012, 316, 43–5150

that of molecules of dendrimer G6(Bu).

However, additional studies such as the

Mark-Kuhn dependence for the hydrody-

namic parameters are required to make

more valid conclusions about the shapes of

PCS-3-Bu macromolecules.

Conclusion

Analysis of the data obtained allows us to

conclude that, in terms of its hydrodynamic

and conformational behavior, the hyper-

branched PCS with the degree of branching

DB¼ 1 is closer to hyperbranched poly-

mers with DB¼ 0.5 than to dendrimers.

Hence, the statistical distribution of

branching points even at maximal DB¼ 1

results in a significant difference between

the hydrodynamic properties of such poly-

mer and those of the branched polymer

with regular structure (dendrimer).

Correspondingly, other conditions being

equal (the chemical composition and the set

of monomer units, MM, and the degree of

branching), hydrodynamic properties of

branched polymers are defined for the

most part by the regularity of branching.

Moreover, taking into account the obtained

values for hydrodynamic parameters for

PCS, an assumption can be made that the

behavior of hyperbranched polymers at the

high degrees of branching (DB 0.5) is

more sensitive to the change of the

regularity of their structure than to the

DB increase.

Acknowledgements: The work was supported bythe Russian Foundation for Basic Research(project 11-03-00353) and the Program No 3 ofDepartment of Chemistry and Material Scienceof the Russian Academy of Sciences ‘‘Creationand study of macromolecules and macromole-cular structures of a new generation’’.

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Inst

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Cop

Modeling of Structure and Nonlinear Optical

Activity of Epoxy-Based Oligomers with Dendritic

Multichromophore Fragments

Olga D. Fominykh, Marina Yu. Balakina*

Summary: Epoxy-based oligomers having length up to four units with dendritic

chromophore-containing fragments covalently attached through spacers to the

bearing chain are studied. The structure of the oligomers was obtained in the course

of conformational search by Monte-Carlo method, the distribution of the torsion

angles values in the dendritic fragment was examined by molecular dynamics. The

nonlinear-optical response of the studied oligomers and dendritic chromophore

fragments was calculated by the TDHF method at AM1 level. Intradendron cross-

linking of chromophore groups is investigated, diphenylmethandiisocyanate used as

hardening agent. Cross-linking is shown to decrease the angles between the

chromophores in the dendron, thus providing enhanced nonlinear-optical charac-

teristics of the oligomer. Stacking-like arrangement of chromophore groups,

observed in variety of oligomers, is investigated in the framework of topological

analysis of electron charge density, and Van-der-Waals interactions are found to be

responsible for the stacking effect.

Keywords: dendritic multichromophore fragments; epoxy-based oligomers; molecular

modeling; nonlinear optical characteristics; quantum-chemical calculations

Introduction

The translation of microscopic optical

nonlinearity of organic chromophores to

macroscopic nonlinear optical (NLO)

activity of material is recognized as one

of the key problems of the design of new

polymer materials for photonic and opto-

electronic applications.[1–3] Conventionally

conjugated molecules with large dipole

moment are used as NLO chromophores,

as a result the increase of the chromophore

number density in the material leads to

the increase of energetically favorable

antiparallel dipole-dipole interactions

causing chromophores aggregation.[2,4]

itution of Russian Academy of Sciences A.E.

uzov Institute of Organic and Physical Chemistry

azan Scientific Centre of RAS, Arbuzov str. 8,

88, Kazan, Russia

(þ007) 843 273 22 53;



To prevent these undesirable electrostatic

intermolecular interactions the new strat-

egy was introduced recently. It consists in

the incorporation of NLO chromophores

into the dendritic or hyperbranched poly-

mers;[4–14] in particular, chromophores are

arranged in dendritic fragments, which are

used either as guest molecules in polymer

composites,[8,14] or are attached to the

polymer bearing chain.[11,12] The specific

structure of such fragments results in a forced

chromophore separation realized through

steric interactions, thus decreasing the

detrimental intermolecular interactions. This

reduction of intermolecular electrostatic

interactions allows for increased chromo-

phore number density in the formation of

a polymer NLO material, thus enhancing

electro-optic response.

Dendritic architectures of dipolar

chromophores have been shown to be

superior in NLO activities compared to

the corresponding single-strand dipolar


Macromol. Symp. 2012, 316, 52–62 53

chromophores.[9,10,15,16] Dendritic structure

of molecular systems was shown to demon-

strate enhanced electro-optic activity,

in special cases, for example, when

the aromatic-perfluoroaromatic substituted

dendron chromophores are used, this

enhancement becomes really dramatic:

electro-optic coefficient was measured to

be 10 times the value for the LiNbO3, the

traditional inorganic NLO material.[12] The

important feature of the dendritic materials

consists in the cooperativity of the NLO

response:[16,17] in[16] it was shown that

azobenzene dendron with 15 chromophore

groups exhibites first hyperpolarizability

nearly � 20 times higher than that of a

single chromophore; each chromophore

contributed coherently to the macroscopic

NLO activity of the material.

Various structures of dendritic multi-

chromophore fragments are designed differ-

ing by the attachment geometry (end-on

relative to side-on attachment of chromo-

phore groups is realized[8]), by the core

nature, by the nature and length of chro-

mophore-to-dendritic core tether groups.[8]

The specific structure of dendritic mole-

cules favors the efficient poling in the

process of creation of polymer materials

with quadratic NLO activity, when the

orientation of the chromophore groups

occurs in the electric field applied to the

material heated to the temperature close to

the Tg; further cooling of the material in the

electric field results in the conservation of

the macroscopic polarization of the mate-

rial.[1–3] A special task is the achievement of

relaxation stability of the materials NLO

response, which is solved by the cross-

linking of polymer chains resulting in the

retention of the established chromophore

orientation. The cross-linking is conven-

tionally realized either due to available

reactive groups or the introduction of

additional reagents as hardening agents.

In the polymers with dendritic structure

the retention of the orientation order is

achieved both by cross-linking of bearing

polymer chains and by additional curing

of chromophore-containing fragments.[7–9]

The effect of cross-linking on the NLO


activity of the dendritic structures is

essential: cross-linked dendrimer has

NLO coefficient d33 doubled in comparison

with the composite material, while d33 of

non cross-linked dendrimer is lower than

that of a composite material.[9] Dendritic

structures also appear optimum for

improving intrinsic photochemical stability

and controlling the solubility; they are

shown to have improved thermostability

(the decay of electro-optic activity with

temperature[7,8]).

Computer simulations allow detailed

examinations of molecular conformations

that can not be achieved by experimental

means, and may be useful for estimating

the relationship between the structural

features of the molecular system under

study and its NLO activity. Atomistic

simulation of dendritic systems was carried

out to predict order parameter achieved

in the course of poling and the value

of electro-optic coefficient.[14,18,19] Tri-

chromophore dendrimer was studied[17]

by united-atom Monte-Carlo calculation,

multi-chromophore dendrimers were

examined in.[14] The possibility to exploit

internal electrostatic interactions to form

the structures exhibiting the enhanced

poling-induced order was examined in.[19]

The dynamics of the process of chro-

mophores orientation in polymer matrix

was studied in.[20–22] No significant differ-

ence in conformational properties was

observed for poled and unpoled systems:[20]

the distributions of backbone torsion angles

were found to be similar for these two cases,

what was demonstrated by the example

of PMMA doped with N,N-dimethyl-p-

nitroaniline chromophores.

Our goal here is to establish the relation-

ship between structure and NLO activity

of epoxy-based oligomers with dendritic

azochromophore fragments. The structure

of the oligomers based on Bisphenol A

Diglycidyl Ether studied here is presented

(Figure 1); 4-dimethylamino-40-nitroazo-

benzene chromophores are used as NLO-

phores. Each unit contains two-branched

dendritic fragment with azochromophore in

each branch. Here we study the structure


NCH3

CH3

OHO O

OH

nOO

O O

NN

NO2

NN

NO2

N N

αβ

γ

τ

NCH3

CH3

OHO O

OH

nOO

O O

NN

NO2

NN

NO2

N N

αβ

γ

τ

b) a)

Figure 1.

Epoxy-based oligomer unit with short (a) and long (b) tether groups in dendritic fragment.

Macromol. Symp. 2012, 316, 52–6254

and conformations of oligomers with a

number of units from two to four, those

with two units being analyzed in detail.

Quadratic NLO responses of the studied

oligomers, as well as definite dendritic

fragments, are calculated quantum-

chemically. The effect of intra-dendritic

cross-linking of chromophore fragments on

the NLO response of the system is analyzed

by the example of dimer. Stacking-like

structures of chromophore groups, detected

in various oligomers, are analyzed.

N

I

a)

ϕ ϕ

N

OO

chromophore groups

bearing chain

spacer group

core

tether groups

Figure 2.

The schematic structure of the dendritic NLO unit (a);

spacer and chromophore moieties in the dendritic frag


Molecular modeling of such systems is of

particular importance, since it can help in

the optimization of electric characteristics

of the material and planning the synthesis

of polymers.

Computational Details

The structure of the model chromophore-

containing dendritic fragment (NLO unit)

is shown on Figure 2(a); dendritic fragment

II III

NN

b)

conformations with possible relative orientations of

ment (b).


Macromol. Symp. 2012, 316, 52–62 55

is attached to the bearing chain through

N,N-dimethylaminobenzoate group, 1,3-

dioxypropane is used as a core, and either

ethylene or hexamethylene groups are used

as chromophore-core tether groups. The

spacer group has non-zero hyperpolariz-

ability, which is essentially smaller than that

of a chromophore group but still noticeable.

Special attention was paid to the planarity

of the chromophore fragment, what is

essential for the effective NLO response.

The structures of the studied oligomers

were established in the course of conforma-

tional search. The available conformational

space was determined by Monte–Carlo

calculation[23] with MMFF94S force field[24]

in the presence of the solvent with low

dielectric constant (chloroform with per-

mittivity 4,8). The GB/SA continuum

model was used for the account of solvent

effect.[25] The Molecular dynamics (MD)

calculation in chloroform at room tempera-

ture was performed for the chosen char-

acteristic conformations of the oligomers

under study to obtain the distribution of

torsion angles values in the dendritic

branches. The notation of relevant torsion

angles is given in Figure 1. For MD

calculation the following set of parameters

was used: time step, 1.0 fs; equilibration

time, 5 ps; simulation time, 1 ns. All calcu-

lations were performed with MacroModel

program package.[26] The structures of

multichromophore NLO fragments were

optimized by the semiempirical AM1

technique.

The calculation of the electric properties

of chosen conformers and NLO dendritic

fragments was carried out within the

framework of the time-dependent Hartree-

Fock (TDHF) method[27] at the TDHF/

AM1 level using Firefly QC package,[28]

which is partially based on the GAMESS

(US)[29] source code.

We estimated the experimentally mean-

ingful characteristics:[30] the mean polariz-

ability, calculated as

a avð Þ ¼ 1

3axx þ ayy þ azz

� �


and projection of the vector part of hyper-

polarizability on the dipole moment vector:

bjj ¼3

5

Xi

mibi

mk k:

To study the formation of stacking-like

arrangement of chromophore groups in the

dendritic fragment the Atoms in molecules

(AIM) topological analysis[31,32] was per-

formed. This approach allows characteriza-

tion of the peculiarities of intermolecular

interactions in the molecular system basing

on the analysis of its electron charge density

distribution. The topological properties of

the molecular charge distribution are

characterized by the number and type of

charge density r(r) critical points, where the

gradient of charge density,5r(r), vanishes.

The critical points, classified according to

their rank and signature, can be of four

types: (3;�3), (3;�1), (3;þ1) (3;þ3), corre-

sponding to the nuclei positions, the bond

between atoms, cyclic or cage elements in

the molecule, respectively. Signature of a

critical point is equal to the difference

between the number of the Hessian positive

and negative eigenvalues (l1< l2< l3),

having the meaning of charge density

curvatures in the directions of Hessian

eigen-vectors. The additional derived quan-

tity is the Laplacian of the charge density,

r2rb, at bond critical point. The topology of

Laplacian of r(r) is more complicated than

that of r(r) itself; it determines where the

field is locally concentrated or depleted. For

closed-shell interactions, as found in ionic

bonds, hydrogen bonds, and van der Waals

molecules, r2rb should be positive and

rb low.[31,33] The topological analysis was

carried out using AIM2000 programme.[34]

Results and Discussions

Dendritic Fragment

The structure of the chromophore-containing

fragment (NLO unit) shown on Figure 2a was

obtained in the course of conformational

search and geometry optimization by the

AM1 technique. The distinguishing feature of


Macromol. Symp. 2012, 316, 52–6256

the obtained conformations is the difference

in relative arrangement of chromophores and

the spacer group through which they are

attached to the bearing chain; the possible

structures belong to three main types

(Figure 2b). Of course, this representation

is to much extent schematic and the attribu-

tion of a conformation to a definite type is

somewhat arbitrary.

When the projections of the dipole

moment vectors, ~m, of the spacer group

and those of both chromophore groups on

the chosen direction are of the same sign,

the structure of the type I is realized;

corresponding arrangement of moieties

favors the enhancement of the NLO

response of the system. If the projections

of dipole moment vectors of the chromo-

phore groups are of one sign, and that

of the space group of the opposite sign,

the structure of the type III is realized;

in this case NLO response is a little bit

smaller than that in case I. The most

unfavorable for the NLO response is

the arrangement of moieties giving the

structure of type II, where the projections

of two chromophore vectors are of the

opposite sign.

We have studied the structures with

different length of the chromophore-core

tether groups. The angle between the

chromophore groups, w, was chosen to

characterize the obtained structures. The

calculated values of molecular polarizabil-

ities are presented in Table 1.

Molecular polarizabilities of the frag-

ment are determined by its structure,

Table 1.Electric properties of chromophore group (Ch), spacer (Spand long (L) tether along with angles between the chro

Ch Sp I

S

1 2 1

m 9.0 4.1 13.15 16.48 13.8a(av) 30.33 14.65 90.30 89.36 99.71b(x) 3.83 �0.32 61.36 89.26 97.74b(y) 4.35 0.08 47.14 �4.67 �16.7b(z) �67.09 �14.61 �62.8 �51.8 �28.3bjj 40.24 8.09 59.29 61.98 61.76w 88.1 67.4 79.2


polarizability, a, being somewhat less

sensitive while the value of first hyper-

polarizability, bjj, reflects the subtle

changes in the structure. The higher bjjvalue characterizes the structures with

smaller angle between the chromophore

dipoles; the longer tether group allows

the conformations with smaller angles,

favorable for the optimal NLO properties,

to be realized. For the systems with short

tether group the structure of the type III

was shown to be most probable, while for

the systems with long tether group all

the structures are found. Long tether

separates chromophore groups, thus

reducing the probability of unfavorable

dipole-dipole interaction of the spacer and

chromophore groups. The values for bjjconfirm the above-made statement: with

the hyperpolarizability of the spacer

group having bjj value much smaller than

that of a chromophore but still significant

the structures of the type I seem to be most

favorable, while structure III is a little bit

worse for the realization of the optimal

NLO activity. The value of bjj for the

structure II is the smallest, what is in

agreement with mutual arrangement of

chromophore groups in this structure.

Thus, for the study of the epoxyamine

oligomers NLO response we have chosen

such conformers in which the dendritic

fragments have minimum angle between

the chromophore groups, and the projec-

tions of ~mof different dendritic fragments

on the definite direction are mainly of the

same sign.

) and typical conformations of NLO unit with short (S)mophore groups in one dendron (w).

II III

L S L S L

2 1 2

6 21.94 5.55 4.29 15.53 13.8199.33 83.58 90.98 87.60 89.5724.31 �21.61 �15.41 �7.61 �33.76�16.4 �30.73 21.15 33.61 �11.20�129.26 24.40 10.30 85.58 �103.72

79.04 26.19 14.94 53.66 64.5632.8 158.5 173.8 43.7 9.1


Macromol. Symp. 2012, 316, 52–62 57

Epoxy-Based Oligomers with Dendritic

Chromophore Fragments

The number of stable unique conforma-

tions within 5 kcal/mol relative to the global

minimum were established in the course

of the conformational search. Analyzing

the results of the search we observed that

longer tether groups allow much more

number of confirmations to be realized.

Dimers (O2S and O2L)

In molecular systems with long tether

groups (O2L) the conformations of the

NLO fragments belonging to all three types

mentioned above are realized. However,

only a few conformations may be found

with the structure I of each NLO unit,

beneficial for a large NLO response; more

frequent is the case when one unit has type I

structure, and the other one – type III

(Iþ III case); the conformations with

appropriate mutual orientation of chromo-

phore groups are observed among them.

Figure 3.

Chosen conformers of dimers O2S (a) and O2L (b) with


In a large number of conformations the

structures with the stacking-like arrange-

ment of chromophore groups are observed

(stacking-like structures are assumed

to have almost parallel arrangement of

chromophore group dipole moment vec-

tors). Various stacking arrangements are

found: chromophore groups belong either

to the same dendritic fragment or to the

neighboring fragments.

As for the structures with short tether

group (O2S) most frequent are the con-

formers with IIIþ III structures of the

dendritic fragments, the structures with

stacking-like chromophores arrangement

being very rare.

We have selected the conformers with

short and long tether groups with dendritic

fragments of Iþ III type with the arrange-

ment of NLO chromophore groups favor-

able for NLO response; they are shown on

Figure 3. In Table 2 the electric properties

for these dimers are presented along with

(Iþ III)-type structures of dendritic fragments.


Table 2.Electric characteristics of the oligomers in chloroform.

Ch O2 O3 O4

S L S L L

m, D 9.44 25.82 37.88 47.40 37.15 52.27a(av),10�24 esu 30.46 217.22 242.35 316.01 350.32 473.87bjj, 10�30 esu 50.45 166.20 168.98 173.59 199.37 184.64wxp1-xp2 42.5 44.4 88.0 112.7 98.1wxp3-xp4 103.0 47.6 78.3 87.5 40.9wxp5-xp6 30.4 33.8 19.8wxp7-xp8 9.9

Q1-2 43.7 48.8 40.3 16.9 46.0Q1-3 34.9 41.4 55.3Q1-4 10.7

Macromol. Symp. 2012, 316, 52–6258

those for separate chromophore group. In

dimer O2L the angles between the chro-

mophore groups in the first and second

dendritic fragment, w12 and w34 respec-

tively, have close values, while w12 and w34

in O2S are essentially different. We intro-

duced the angle u to characterize mutual

arrangement of dendritic fragments. The

angle u12 between the NLO fragments have

close values for O2S and O2L, u12 for O2L

being slightly larger than that for O2S. It

can be seen from Table 2, that hyperpolar-

izability bjj for O2L is higher than that for

O2S, what is in agreement with the values

w12 and w34. This gives evidence to the

preference of long tether group.

Earlier we have investigated the torsion

angles along the epoxy-based bearing chain

by molecular dynamics and found out

the fragments responsible for the chain

flexibility.[35] So we can assume that the

bearing chain is flexible enough not to

prevent the orientation of the dendritic

fragments in the applied electric field.

The analysis of denoted on Figure 1 torsion

angles in dendritic fragment was carried out

for O2S and O2L. Molecular modeling was

performed by molecular dynamics method

in chloroform at 300 K. The obtained

distributions for values of torsion angles

are presented on the graphs in Figure 4. The

graphs for a, b, and g angles for O2L and

O2S look quite similar, the only difference

is in angle t: in the case of O2L the graph

has two maxima, thus demonstrating the

possiblity of the chromophore group to


rotate, while in the case of O2S the graph

has a unique maximum, giving the evidence

of preferable planarity of the chromophore

group, resulting in more rigid structure of

the fragment compared to that in the case of

O2L. The presence of several maxima on

the graphs (a)-(d) allows to conclude that

the dendritic fragment has flexible regions,

what gives hope that these fragments can be

efficiently oriented in the applied electric

field.

We have examined the stacking-like

structures in terms of ‘‘Atoms in mole-

cules’’ topological analysis of electron

charge density distribution.[31] The distance

between the planes containing the chro-

mophores is about 3.8 A. In the stacking-

like structure the chromophores are shifted

one relative to another, the angles between

the chromophore dipole moments is about

208. A set of critical points, corresponding

to interchromophore interaction, was

detected. Values of topological character-

istics of electron charge density distribution

r(rcr) and r2rðrcrÞ in critical points of

(3;-1)-type are within the range typical for

van der Waals interactions: 0.002–0.005 a.u.

and 0.008–0.01 a.u., correspondingly.[33]

The stacking arrangement of the chromo-

pohres results in hyperpolarizability bjjincrease 1.4 times compared to that of one.

Trimer and Tetramer

The above conclusions were tested by the

example of trimer with short and long

tether groups, O3S and O3L (Figure 5a).


angle

200150100500-50-100-150-200

frequ

ency

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

angle

150100500-50-100-150

frequ

ency

0

5000

10000

15000

20000

25000

a) b)

angle

200150100500-50-100-150-200

frequ

ency

0

2000

4000

6000

8000

10000

12000

angle

200150100500-50-100-150-200

frequ

ency

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

d) c)

angle

200150100500-50-100-150-200

frequ

ency

0

1000

2000

3000

4000

5000

6000

angle

100806040200-20-40-60-80-100-120

frequ

ency

0

2000

4000

6000

8000

10000

12000

f) e)

Figure 4.

Torsion angles in the tether group of O2L: a (a), b (b), g (c), d (d), and the angle of the chromophore group

torsion t (e); and the the angle of the chromophore group torsion t in O2S (f).

Macromol. Symp. 2012, 316, 52–62 59

For the estimation of electric properties we

have chosen the conformers with short and

long tethers with the structures of the

dendritic fragments, which may be attrib-

uted to Iþ Iþ III. In this case similar to

the case of the dimers the stacking-like

arrangement of chromophore groups is


often realized, mainly the chromophores

belonging to different dendrons participat-

ing in this arrangement for the conformers

with short tethers. The data of Table 2

demonstrate that in this case the structure

with long tether has a higher value of

bjj. However, the angles between the


Figure 5.

The structures of trimer O3L (a) and tetramer O4L (b).

Figure 6.

2 units with long tether cross-linked with MDI.

Macromol. Symp. 2012, 316, 52–6260

chromophore groups in the branches of

dendron have rather close values in the

structures with short and long tether

groups, while the angles between the

dendrons are smaller in the structure with

long tethers.

We have examined the effect of the

bearing chain elongation on the values of bjjby the example of corresponding tetramer

O4L (Figure 5b). For this case the chosen

conformer has the Iþ Iþ Iþ III structures

of the dendritic fragments with intra-

dendron stacking of chromophore groups

in two neighboring dendrons, thus ordering

of four chromophore groups takes place.

However the mutual arrangement of den-

dritic fragments results in such architecture

which does not provide the enhancement of

the hyperpolarizability in comparison with

the O3L case (Table 2).

Cross-Linking

It is known that cross-linking of the

dendron branches in the course of the

chromophores alignment process allows to

fix the orientation order,[9] so we studied

the role of intradendron cross-linking of the


chromophore fragments by the example

of O2L with a modified chromophore

(4-dimethylamino-30-oxymethyl-40-nitro)azo-

benzene, containing hydroxymethyl group

in the second benzene ring. Diphenyl-

methandiisocyanate (MDI) was used as a

hardening agent (Figure 6). According to

the data of Table 3, the cross-linking results

in the essential increase of the bjj values due

to both the decrease of the angles between

the chromophore groups in the dendronds


Table 3.Electric properties of non-cross-linked O2L and cross-linked O2L_cl dimers.

O2L O2L_cl

m, D 37.88 44.50a(av),10�24 esu 242.35 299.00bjj, 10�30 esu 168.98 202.66wxp1-xp2 44.4 22.0wxp3-xp4 47.6 6.8Q1-2 48.8 18.0

Macromol. Symp. 2012, 316, 52–62 61

and the small angle between them. Inter-

dendron stacking-like arrangement of chro-

mophore groups is realized in this dimer,

the angle between the chromophores dipole

moments vectors being 7.28, what is much

less than that in the stacking-arranged

chromophores without cross-linking. It

should be mentioned that MDI fragment

was found to be a good cross-linking agent

as its structure and tether group length

provided a good combination favoring the

appropriate arrangement of chromophore

groups, resulting in promising NLO

response value of the studied molecular

system. To study the case of the interden-

dron cross-linking it is reasonable to choose

the oligomer with more number of units.

Conclusion

Characteristic conformations of dendritic

NLO fragment are established and the

following structural factors, responsible for

the NLO activity are revealed: mutual

arrangement of the spacer and chromo-

phore groups and tether group length. The

use of long tether was shown to decrease

the probability of undesirable antiferro-

electric orientation of chromophore and

spacer groups. The angle between chromo-

phore groups in dendritic fragment was

demonstrated to be a relevant parameter

characterizing its structure.

The study of the epoxy-based oligomers

with dendritic azochromophore-containing

fragments has shown that the bearing chain

is rather flexible and does not prevent

orientation of dendritic fragments; flexibil-

ity and length of tether plays significant


role, allowing for small angles between

the chromophore groups, resulting in the

enhanced NLO activity.

The analysis of the cross-linking of

dendron branches has demonstrated that

intra-dendron cross-linking allows realizing

structures with smaller angles between the

chromophore groups. It can fix the orienta-

tion order thus providing the relaxation

stability of NLO response.

Stacking-like arrangement of chromo-

phores was observed in the oligomers

with different number of units. Topological

analysis of electron charge density distribu-

tion in such stacking structures allowed one

to explain their origin by the van der Waals

interactions between the chromophore

groups.

To conclude, it is worth mentioning, that

the suggested theoretical models are to

much extent schematic; experimentally

studied bulk material systems are expected

to contain broad distributions of complex

geometries. Clearly, a statistical distribu-

tion of interactions exists, and we focus on

only one important type of interactions.

Obviously, this work should be continued.

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A New Approach to the Determination of Adhesion

Properties of Polymer Networks

Yulia G. Bogdanova,* Valentina D. Dolzhikova, Ilya M. Karzov,

Alexander Yu. Alentiev

Summary: A new approach for the determination and comparison of adhesion

properties of polymer networks was proposed. One permits to optimize the choice

of polymers for composite materials with inorganic fibers (at the absence of binder

diffusion to the fiber). For the first time the works of adhesion of polymer to liquids

simulating polar or non-polar phases were used for prediction of adhesive properties

of network (binder, coupling agent) and for the choice of network provided the best

tensile strength of composite material. The correctness of proposed approach was

experimentally proved by measuring of tensile strength micro plastics.

Keywords: adhesion; contact angle; micro plastic

Introduction

The regularities of support of polymer

composites strength are being investigated

in different fields of science. The phenom-

enon of adhesion occupies a central place in

these researches. The age of adhesion

problem is more than one hundred years

but the perspective of creation of unified

theory which describes this phenomenon

appears still rather shadowy. So, the

development of principals permitting to

optimize the choice of components for

creation of material with the best strength

characteristics, particulary, the choice of

matrix (binder, coupling agent) for definite

fiber, seems more real. Adhesion is tradi-

tional object of colloid chemistry. So the

colloid-chemical approach for composite

materials in terms of surface energy

characteristics is quite reasonable because

the interface between the solid substrate

and polymer network should be considered

as a full-fledged component of composite

material.[1]

onosov Moscow State University, Department

hemistry, Leninskie Gory 1/3, 119991, Moscow,

sia

(þ7) 495 9328846;



Theory

It is commonly known that strength of

plastics (P) depends on adhesion strength

(to) on its low-level cell.[2] The general view

of the dependence P¼ f(to) for plastics

reinforced with fibers is presented at the

Figure 1. The situation when plastic

strength value is monotonic increasing with

adhesion strength increase (area I at the

P¼ f(to)) is in field of interest of present

investigation. The parameters for predic-

tion of the strength of plastics are usually

experimental values which were founded

from micro mechanical tests such as adhe-

sion strength of corresponding micro plastic

or critical fiber length.[3,4] In spite of the

statistical character of these values its

thermo dynamical echo is the work of

adhesion which is determined in terms of

surface energy characteristics of composite

components in micro plastics:

Wa ¼ gSð1Þ þ gSð2Þ � gð12Þ;

where gS(1) and gS(2) are the specific free

surface energy values of network/air and

fiber/air interfaces, g (12) is specific free

surface energy value of fiber/network inter-

face (interfacial free energy).[5] It is gen-

erally known that energetic characteristics

of surfaces can be successfully determined


Figure 1.

The general view of the dependence of composite

material strength from «fiber-matrix» adhesion

strength.[1]

Figure 2.

Scheme of determination of advancing contact angle.

Macromol. Symp. 2012, 316, 63–7064

using the testing of surfaces with contact

angle of liquids with the definite surface

tension.[6] Such possibility is consequence

of Young equation for equilibrium contact

angle u:

cos u ¼ gSV � gSL

gLV

where gSV, gSL, gLV are specific free surface

energies of solid/vapor, solid/liquid and

liquid/vapor interfaces accordingly.[5,6] So,

the wetting method is very promising for

the adhesion prediction in the number of

systems «definite fiber-various matrix» and

one permits to optimize the choice of

polymer binders or its compositions pro-

vided the best adhesion and, as conse-

quence, highest strength of final material.

As a rule, the work of adhesion is

determined using the Young-Dupre equa-

tion:[5]

Wa ¼ gLð1Þð1þ cos uÞ;

where u is equilibrium contact angle of a

droplet of liquid binder with surface tension

gL(1) at the fiber surface (advancing contact

angle, Figure 2). But some shortcomings

exist in such approach. First, this technique

is not quite correct for application to high-

viscosity liquid binders because in this

case effective non-equilibrium u is used for

calculation of Wa. Therefore such experi-

ments are hard for standardizing when

binders with different viscosity are investi-

gated. Second, this approach doesn’t take


into account the alteration of the work of

adhesion under the hardening of binder in

the issue of temperature decrease, solvent

evaporation or chemical reaction proceeding.

Another way of Wa determination is

calculation of its value in accordance to

Girifalco-Good-Fowkes molecular theory

of wetting[5,6] using equation:

Wa¼ 2ðgdSð1Þg

dSð2ÞÞ

1=2 þ 2ðgpSð1Þg

pSð2ÞÞ

1=2;

(1)

where indexes (d) and ( p) correspond to

dispersive (non-polar) and polar compo-

nents of free surface energy solid matrix

and fiber. This approach is very convenient

for search pointed modifying ways of

matrix or of the fiber surface to provide

the high adhesion. But experimental deter-

mination of the surface energy components

is not always possible for polar fibers

because of in case of polar surfaces thin

advance film on the front of liquid droplet

existence must be taken to account.[6]

The acid-base method permits to esti-

mate and to compare the adhesion in

different systems «fiber-network». The

prediction parameter in such approach is

coerced acidity parameter:[7]

DD ¼ DðnetworkÞ �DðfiberÞ;

where D are acidity parameters of network

and fiber surfaces calculated using Berger

method:

D ¼ 2½ðgabSV=L1 þ gab

SV=L2Þ1=2

� ðgabSV=L3 þ gab

SV=L4Þ1=2�;

where gabSV/L is acid-base component of

interfacial energy of «network or fiber-test


Figure 3.

Scheme of experimental determination of polymer

work of adhesion to model liquids. Contact angles are

marked iv accordance to.[11]

Macromol. Symp. 2012, 316, 63–70 65

liquid» interface which can be determined

using wetting method,[8,9] L1, L2 and L3, L4

are test liquids – Lewis bases (aniline and

formamide) and acids (liquefied phenol and

glycerol). In accordance to acid-base

method, the most adhesion occurs in system

with maximal difference of network and

fiber surface acidity DD. But too often DD

values are near to experimental error of D

determination.

To take into account the difficulties

mentioned earlier, to optimize the choice of

network with the best adhesion properties it

would be reasonably to apply the model

systems. We propose using water and

octane as a model liquids to simulate polar

and non-polar phases and using the work of

adhesion of polymers to the model liquids

to predict the best adhesive from set of

solid networks to polar (Wpp), non-polar

(Wdd) phases and to polar and non-polar

phases (Wdp) both. The corresponding

equations for calculation are:

Wpp ¼ gSð1Þ þ gW � gSðWÞW (2)

Wdd ¼ gSð1Þ þ gO � gSOð1Þ (3)

Wdp ¼ gSOð1Þ þ gW � gSðOÞW ; (4)

where gS(W)W and gSO(1) are free surface

energy values of interfaces «polymer(equa-

lized with water)-water» and «polymer-

(equalized with octane)-octane»,

gW¼ 72.6 mJ/m2 and gO¼ 21.8 mJ/m2 are

water and octane surface tension values at

208C.[10]

So, the surface energy of solid matrix, its

dispersive and polar components gS(1)¼gd

S(1)þ gpS(1) and the interfacial energy of

«polymer-model liquid» interface gSL

(gS(W)W or gSO(1)) ought to be determined.

Many approaches and techniques exist for

gS(1) determination using contact angles.[6,8]

But the gSL value determination is rather

complex.

The simplest way is using of Antonov

rule: gSL ¼ g1 � gLVj j, where gLV is the

surface tension of model liquid (water or

octane). But this way is correct not always.

To take into account the possible mobility

of polymer contacting with model liquid the

special technique developed by Rucken-


stein[11] were used. The essence of one is the

measuring of contact angles at the surface

after the long-time contact with the model

liquid. Scheme of such experiment is

presented at the Figure 3.

The calculations of equilibrium values of

interfacial energy were performed as follows:

gSðWÞW ¼ fðgpSWÞ

1=2 � ðgpWÞ

1=2g2

þ fðgdSWÞ

1=2 � ðgdWÞ

1=2g2;

where gpSW and gd

SW are the polar

and dispersive components of gS(W)W,

gpW¼ 50.8 mJ/m2, gd

W¼ 21.8 mJ/m2 are

the polar and dispersive components of

water surface tension, respectively.[10,11]

The following equations were used for

calculation gpSW and gd

SW:

gpSW ¼ ðgW � gO � gOW � cos uOÞ2=4g

pW ;

where gOW¼ 50.8 mJ/m2 is «water-octane»

interfacial tension,

gdSW ¼ ðgOWcosuO � gW � cos uV

þ gOÞ2=4gO;

where uO uV – contact angles of octane

droplets and air bubbles, respectively

brought to the polymer surfaces placed in

water (Figure 3).

For calculation of gSO(1) the following

equation was used:

gSOð1Þ ¼ gdSOð1Þ þ g

pSOð1Þ þ gO

� 2ðgdSOð1ÞgOÞ1=2;


Macromol. Symp. 2012, 316, 63–7066

where polar component of interfacial

energy of «polymer(equalized with octane-

octane» gpSOð1Þ ¼ ðgOW � cos uWO þ gW �

gOÞ2=4gpW and its dispersive component

gdSOð1Þ � gd

Sð1Þ ; uWO is contact angle of water

droplet placed to the polymer surface in

octane media (Figure 3).

The calculation of gS(O)W were per-

formed usind equation:

gSðOÞW ¼ gpSW þ fðgd

SOÞ1=2 � ðgd

WÞ1=2g2:

The aim of this work was experimental

checking of correctness of Wa application in

model systems «polymer-liquid» (Eqs. 2-4)

for prediction of strength properties of

composite materials.

Experimental Part

In this work our new approach was applied

for two types of systems. First was complex

Figure 4.

Structural formulae of monomers of ER (a) and PAA (b)

Figure 5.

Structural formulae of POKs monomer unit; R¼ CH3 fo


grid polymer – epoxynovolac resin (ER)

modidfied with polyamidoacid (PAA)

which can co-curing with resin (Figure 4).

Second were polyolefinketones (POKs)

which are the linear partially crystallizable

strictly alternating copolymers of carbon

monoxide and ethylene with propylene

(PECO) or butene-1 (BECO)[12]

(Figure 5).

Polymer films were layered at the solid

carrier (Alumina plate) by watering with

subsequent drying in air atmosphere. ER/

PAA-films were layered from mixed solu-

tions of ER (ethanol, acetone) and PAA

(dimethylformamide) with subsequent

heating at 1608C during 6h.[13] PAA con-

tent was varied in interval v¼ (0�10)wt %.

POK-films were layered from 0.5wt %

solutions of POK in chloroform with

subsequent drying 24h at the room tem-

perature.

The work of adhesion values of polymer

films to model liquids were determined

.

r PECO and R¼ C2H5 for BECO.


Figure 6.

Scheme of the checking of correspondence between the work of adhesion in model «polymer-liquid» systems

and the tensile strength of composites.

Table 1.Characteristics of micro plastics with ER/PAA network.

Fiber Resin ER/PAA content Porosity Maximal strength Extention

wt% % GPa %

Glass 42� 4 2� 5 2.4� 0.1 2.8� 3.7Basalt 35� 3 3� 5 2.3� 0.1 2.8� 3.5UKN 45� 3 3� 6 3.4� 0.2 1.4� 1.9Torayca 33� 3 4� 9 4.7� 0.2 2.4� 3.5

Figure 7.

Photo of meniscus of water between the filaments of

«Torayca» x 200, «OLYMPUS BX51».

Macromol. Symp. 2012, 316, 63–70 67

using Ruckenstein technique[11] and the

obtained values were compared with tensile

strength of corresponding micro plastics

(Figure 6).

For POKs the literature data about

tensile strength of single-layer glass tissue

micro plastics were used.[14] POKs were

applied as coupling agent at the combina-

tion of polar glass fiber with polar poly-

amide (PA) matrix. To compare its adhe-

sive properties the values of the work of

adhesion of POKs to water Wpp must be

used. When it is interesting to compare the

efficiency of POKs as coupling agent at the

combination of polar glass fiber and non

polar polyethylene (PE) matrix, the work of

adhesion of polymers equilibrated with

octane to water Wdp must be compared.

For modified epoxynovolac resin (ER/

PAA) the comparison of the work of

adhesion to water Wpp or to octane Wdd

with experimentally determined tensile

strength of yarn-like micro plastics was

performed to estimate the influence of

PAA additives on adhesive properties of

resin to different fibers. In case of carbon


fibers it was possible to determine the gS(2)

(the specific free energy of fiber/air inter-

face), to calculate the Wa (Eq. 1) and to

compare the dependencies the adhesive

properties of ER/PAA network with dif-

ferent PAA content in the real and the

model systems: Wa¼ f(v), Wpp¼ f(v) and

Wdd¼ f(v).

The yarn-like micro plastics were

prepared and ones tensile strength was

determined using ISO standard.[13] The

characteristics of micro plastics are pre-

sented at the Table 1.


Figure 8.

The dependencies of the work of adhesion of ER/PAA network to model liquids (on the left) and carbon fibers (on

the right) from PAA content.

Figure 9.

The dependencies of micro plastics tensile strength P from PAA content in network v.

Macromol. Symp. 2012, 316, 63–7068

Specific free surface energy of polymer

films gS(1) as well as its dispersive gdS(1) and

polar gpS(1) components were determined

by two-liquid method of Owens-Wendt-

Kaelble.[6] The calculations were per-

formed by solving of equation set:

ð1þcosuL1ÞgL1¼2ðgdL1 gd

SÞ1=2þ2ðgp

L1 gpSÞ

1=2

ð1þcosuL2ÞgL2¼2ðgdL2 gd

SÞ1=2þ2ðgp

L2 gpSÞ

1=2;

(

where uL1 and uL2 are contact angles of the

droplets of test liquids at the polymer

surface (Figure 2), gpL1, gp

L2, gdL1, gd

L2–

polar and dispersive components of

the surface tension1 of test liquids[10,12] ;

gS(1) ¼gdS(1)þ gp

S(1).

For carbon fibers the gS(2) was deter-

mined by the similar way. The contact angles

1Redistilled water and ethylene glycol with a purity

grade of at least 99,8%and water content of no higher

than 0,005% were used as test liquids.


of test liquids at the fiber surface were

determined using photo of meniscus of test

liquid between its filaments (Figure 7).

The accuracy of measurements was

DgS¼� (0,5 – 0,7) mJ/m2. All measure-

ments were performed at 208C.

Results

The dependencies of work of adhesion of

ER/PAA network to the model liquids

from the PAA content Wpp¼ f(v) and

Wdd¼ f(v) are symbate to ones calculated

for carbon fibers Wa¼ f(v) (Figure 8). All

dependencies have maximums at the

v¼ 3% of PAA content in ER/RAA

network. So, the work of adhesion of

polymer to model liquids Wpp and Wdd

does correlate with the work of adhesion

Wa in real systems.


1,5

2

2,5

3

3,5

4

4,5

5

110100908070605040

Wdd, mJ/m 2 Wpp, mJ/m 2

P(1)

(2)

(3)

(4)

R2=0,9874

R2=0,9548

R2=0,8550

R2=0,9912

R2=0,9935

R2=0,8851

R2=0,7669

R2=0,9462

Figure 10.

The correlation dependencies of the work of adhesion

of ER/PAA network to model liquids with tensile

strength of yarn-like micro plastics with Torayca (1),

UKN (2), Glass (3) and Basalt (4) fibers at PAA content

v � 3%.

Table 2.The POKs work of adhesion values in model systems«polymer-liquid» and tensile strength values ofsingle-layer glass tissue micro plastics with polyethy-lene and polyamide networks and with POKs ascoupling agents of fiberglass.

Polymer Wdp P�(PE) [14] Wpp P�(PA) [14]

mJ/m2 MPa mJ/m2 MPa

PECO 55 124� 14 107 109� 10BECO 41 113� 10 112 156� 14

�Tensile strength of initial networks P(PE)¼ 26� 2,P(PA)¼ 56� 4; without coupling agent P(PE)¼ 60�8 MPa, P(PA)¼ 103� 6 MPa.[14]

Macromol. Symp. 2012, 316, 63–70 69

The tensile strength of all micro plastics

also depends extremely from PAA

content in ER/PAA network and one is

maximal at v¼ 3% of PAA in the network

(Figure 9).

Earlier it was shown that the maximum

existence is related with peculiarities of co-

curing of ER in presence of different

amounts of PAA which provides the best

adhesive properties of finish network at

v¼ 3%.[15] The PAA content determines

the hot-sealing reactions path and the phase

state of solid network. At v � 3% the co-

curing occurs with participation of amide

groups of PAA and epoxy groups of ER

and ensures the maximal conversion extend

of epoxy groups at v¼ 3%. At v> 3% the

co-curing occurs with participation of

amide and carboxylic groups both and also

parallel reaction with polyimide formation

takes place. Due to difference of reactions

provided the PAA content the ER/PAA

network homogeneous at v � 3% and

heterogeneous at v> 3%.

For homogeneous network a good

correlation between strength of micro plastic

and the work of adhesion of matrix to the

model liquids was observed (Figure 10).

The work of adhesion of POKs to model

liquids also is in a good agreement with

literature data about tensile strength of

single-layer glass tissue micro plastics with

polyethylene and polyamide networks and


with POKs as coupling agents of fiberglass

(Table 2).

The higher is the Wdp of polymer, the

better one is as coupling agent for combi-

nation of polar glass fiber with non-polar

PE network. The higher is the Wpp, the

better polymer is as coupling agent for

combination of polar glass fiber with polar

PA network. The experimental fact that

the BECO with more long side group

is better coupling agent for combination

of glass fiber with PA matrix than PECO

is explained with the higher content of

polar -(ethylene-CO)- co-monomers in

BECO polymer chain in comparison to

PECO one.[12]

Conclusion

Good correlations of the work of adhesion

of polymer films to liquids simulating polar

and non-polar phases with tensile strength

of micro plastics with inorganic fibers and

investigated polymers as networks and

coupling agents prove the correctness of

the new approach presented in this article.

The advantages of application of the work

of adhesion of polymers to model liquids

are follows:

– u

, W

sing of solid network, so, the accounting

of change of adhesion properties of bin-

der at the liquid-solid transition;

– th
e possibility of prediction of efficiency
of polymer as a network (binder,

coupling agent) for hybrid composites;

einheim www.ms-journal.de

Macromol. Symp. 2012, 316, 63–7070

– c
hance of prediction of adhesion of poly-
mer to filler of any nature and form.

Of course, the case of tensile character-

istics prediction for plastics is more

complicated. But nevertheless, the thermo-

dynamic principals of choice of polymer

which provides the best adhesion to sub-

strate must be reflected even when the

complex of factors influences. That is why

the experimental evidence of choice the

best adhesive provided the best strength

properties of composite material was

obtained.

Acknowledgements: Dr. J.V. Kostina, TopchievInstitute of Petrochemical Synthesis, Moscow,Russia for IR-spectroscopy investigation of hot-co-sealing of ER and PAA, Dr. A.V. Shapagin,Frumkin Institute of Physical Chemistry andElectrochemistry, Moscow, Russia for the ASMphotos of ER/PAA surfaces, Prof. G.P. Belov,Institute of Problems of Physical Chemistry,Ghernogolovka, Russia for the synthetic sam-ples of POK, Russian Foundation for Basicresearch, project N 10-08-01303a for financialsupport.

[1] A. J. Kinloch, Adhesion and Adhesives Science and

Technology, London - New York Chapman and Hall,

1987, 441p.

1Redistilled water and ethylene glycol with a purity

grade of at least 99,8%and water content of no higher

than 0,005% were used as test liquids.


[2] Yu. A. Gorbatkina, Mechanics of Composite

Materials, 2000, 36(3), 29.

[3] M. L. Kerber, V. M. Vinogradov, G. S. Golovkin, et al.

Polymer Composites: Structure, Properties and Techno-

logy: Training Manual (Ed., A. A. Berlin, St. -Petersburg

Professiya, 2008, 556p. [in Russian].

[4] V. E. Yudin, V. M. Svetlichnyi, A. N. Shumakov,

R. Schechter, H. Harel, G. Marom, Composites: Part A,

2008, 39, 85.

[5] A. W. Adamson, Physical Chemistry of Surfaces, New

York John Wiley and Sons, 1976, 551p.

[6] J. Vojtechovska, L. Kvitek, Acta Univ. Palacki. Olo-

muc, 2005, Chemica 44, 25.

[7] I. A. Starostina, Y. I. Aleeva, E. V. Sechko, O. V.

Stoyanov, Encyclopedia of Polymer Composites: Proper-

ties, Performance and Applications, New York Nova

Publisers, 2009, 681–704

[8] C. J. Van Oss, M. K. Chaudhury, R. G. Good, Chem.

Rev., 1988, 88, 927.

[9] E. J. Berger, Acid-Base Interaction: Relevance to

Adhesion Science and Technology (Ed., K. L. Mittal,,

H. R. Anderson, Jr. Utrecht VSP, 1991, 207.

[10] L. H. Lee, Langmuir, 1996, 12, 1681.

[11] E. Ruckenstein, S. H. Lee, J. of Colloid and Int. Sci.,

1987, 120, 153.

[12] Yu. G. Bogdanova, V. D. Dolzhikova, A. G. Maguga,

Polymer Sci., Series D, 2011, 4(1), 8.

[13] ISO 10618, Carbon Fibre – Determination propertes

of resin-impregnated yarn, 2004.

[14] Yu. N. Smirnov, O. N. Golodkov, Yu. A. Ol’khov,

G. P. Belov, Polymer Sci., Series B, 2007, 49, 91.

[15] I. M. Karzov, A. Yu. Alentiev, Yu. G. Bogdanova,

Yu. V. Kostina, A. V. Shapagin, Moscow Univ. Chem.

Bul., 2010, 65(6), 384.



A.F

ches

E-m

Cop

Autoadhesion of Glassy Polymers

Yuri M. Boiko*

Summary: Thick bulk films of linear amorphous polymers with different chain

architecture and molecular weight were brought into contact with themselves in

a lap-shear joint geometry at bonding temperatures (T) below the glass transition

temperatures of their bulk (Tbulkg ), at a small contact pressure, in order to form

autoadhesive joints. As-bonded joints were shear-fractured in tension at ambient

temperature, and their lap-shear strength was measured as a function of T, bonding

time and molecular weight. The kinetics of the process of the development of the

lap-shear strength at T< Tbulkg was investigated, and the molecular mechanisms

governing this process were discussed. The quasi-equilibrium surface glass transition

temperatures of the investigated polymers were estimated and compared with the

corresponding values of Tbulkg .

Keywords: autoadhesion; glass transition temperature; glassy polymers

Introduction

The study of the molecular dynamics at

polymer surfaces and interfaces has

received great attention over the two last

decades.[1–18] This interest is caused by a

significant difference in the molecular

mobility revealed in those layers with

respect to the interior bulk regions of the

polymer sample. More specifically, an

enhanced molecular motion in the near-

surface layer in comparison with that in the

polymer bulk, at a constant sample tem-

perature that is lower than the glass

transition temperature of the sample bulk

(Tbulkg ), is predicted both theoretically and

from the simulation studies.[9,10] It means

that the long-range segmental motions that

are frozen in the glassy bulk may be

accomplished at free polymer surfaces over

a temperature interval of some tens degrees

of Kelvin. In the literature, there is the

experimental evidence of the existence of

such an effect (mainly, for thin films having

the thickness of the order of some random

coil sizes, i.e. tens-hundreds nm).[9–14,16–18]

. Ioffe Physico-Technical Institute, 26 Politekhni-

kaya, St. Petersburg 194021, Russia



However, there are also some studies

reported that this effect has not been

observed.[19,20] So, the issue of the differ-

ence between the surface glass transition

temperature (T surfaceg ) and Tbulk

g still needs

further clarification.

The molecular mobility at free polymer

surfaces is directly related to autoadhesion

and adhesion (bonding of one and the same

material and of two different materials,

respectively) of two contacting polymer

pieces. Actually, the interaction between

the surfaces of non-polar polymers results

only in the physical attraction of the

molecular groups of the chain segments

located on the contacting surfaces provid-

ing the build-up of weak van-der-Waals

bonds at the interface. For this reason, such

interfaces are very weak mechanically since

their fracture energy (G) corresponds to the

thermodynamic work of autoadhesion or

adhesion (Wa) which should be accom-

plished to reversibly separate the contact-

ing surfaces. For amorphous polymers, the

values of Wa are very small (< 0.1 J/m2) in

comparison with the values of G for the

interdiffused interfaces (1-103 J/m2),[21,22]

first, due to a larger number of van-der-

Waals bonds per unit of the contact area

formed by the segments diffused from one


Table 1.Some characteristics of the investigated polymers.

Polymer(designation)

Mw,kg/mol

Mn,kg/mol

Tbulkg ,

8C

PS (PS-230) 230 81 103(PS-225) 225 75 97(PS-1111) 1,110.5 965.6 106(PS-103) 102.5 97 105

PMMA 87 43.5 109PPO 44 23 216

Macromol. Symp. 2012, 316, 71–7872

sample into another one, and second, due to

the formation of topological entangle-

ments. In its turn, the diffusion of chain

segments is not feasible in the glassy state of

the polymer. Therefore, it is of principal

significance as whether the contact zone is

in the glassy (when the long-range seg-

mental motions are frozen) or viscoelastic

state (when those are activated). So, the

lowest temperature (Talowest) at which the

autoadhesion of a polymer is still observed

may correspond to Tsurfaceg . This approach

has been proposed recently to measure the

Tsurfaceg of polymers by analyzing the lap-

shear strength (s) at symmetric polymer-

polymer interfaces as a function of bonding

temperature.[2,4] However, the problem in

determining Talowest appearing in this case is

imposed by very weak intermolecular

interaction at the interface resulting in its

fracture prior to mechanical testing. To put

it differently, as-measured T surfaceg may be

overestimated. Another possibility to char-

acterize Tsurfaceg in the frameworks of the

adhesion approach is to estimate the quasi-

equilibrium Tsurfaceg (T surface

g -equil), the low-

temperature limit of T surfaceg , i.e. the highest

temperature at which the mechanically

resistant joint cannot be formed.

In principle, the diffusion nature of the

development of s at the contact zone of the

two polymer bulk samples with vitrified

(glassy) bulk has already been demon-

strated.[1–8,16–18] However, a better under-

standing of the mechanisms governing this

process is still needed, in particular, con-

cerning a key molecular property and an

elementary kinetic unit of motion govern-

ing it. In this respect, the influence of

bonding (or healing) time (t) and tempera-

ture (T), and of the molecular weight (M) on

the interface strength may provide with

useful information. Thus, the goal of this

work is two-fold: (i) to investigate the

kinetics of the strength development at the

contact zone of the amorphous polymers

with glassy bulk and (ii) to estimate the

low-temperature limit of the Tsurfaceg of

amorphous polymers. For this purpose,

the lap-shear strength of a number of

symmetric amorphous polymer-polymer


interfaces healed at T< Tbulkg , measured at

ambient temperature, was analyzed as a

function of t, T and M, and T surfaceg -equil was

estimated by the extrapolation of the curves

s x (T) to s¼ 0, where x is the power law at

which those curves become of a linear

shape.

Experimental

Polymers

Linear amorphous non-crystallizable atac-

tic polymers of three types of chain

architecture were selected in this study:

polystyrene (PS), poly(2,6-dimethyl-1,4-

phenylene oxide) (PPO) and poly(methyl

methacrylate) (PMMA). The values of

weight-average (Mw) and number-average

molecular weights (Mn), and of Tbulkg ’s

measured at a heating rate of 10 K/min

and estimated as a middle point of the

corresponding heat capacity jump are listed

in Table 1. All these polymers are the high-

molecular weight polymers since their M’s

are lager that the corresponding entangle-

ment molecular weight (Ment).

Samples

Samples with smooth surfaces and a thick-

ness (d) of 100 mm were prepared by

extrusion or compression molding between

the plates of silica glass. The investigated

samples are considered as monolithic bulk

samples, since the thickness of their near-

surface layers, when taken as the size of

a statistical coil of an unperturbed chain

(two radii of gyration� 2Rg), is smaller

than 10�3d. Hence, the chain confinement

effects which are characteristic of ultrathin


Figure 1.

Lap-shear joint geometry used in the present work.

Contact area is shown by hatching.

Macromol. Symp. 2012, 316, 71–78 73

polymer films (d< 2Rg) and result in a

significant depletion in their Tg’s with

respect to Tbulkg of some tens degrees of

Kelvin[23,24] are not relevant to the bulk

regions of the investigated samples.

Bonding Step

The samples were bonded in the lap-shear

joint geometry at a small contact pressure

of 0.2 MPa applied to the contact area of

5 mm� 5 mm (see Figure 1). Healing (or

bonding) time t varied from 10 min to 24 h.

Healing temperatures were from 34 to

948C (PS�PS interfaces), 34 to 1048C(PMMA�PMMA interface) and 113 to

1568C (PPO�PPO interface).

Fracture Tests

As-bonded autoadhesive joints were shear-

fractured in tension on an Instron tensile

tester at room temperature and a crosshead

speed of 5 mm/min. The distance between

the clamps of the tester was set at 5 cm. Lap-

shear strength s was calculated as fracture

Figure 2.

Lap-shear strength of a symmetric PS-PS interface with M

healing temperature of 648C (¼ Tbulkg – 33) and (b) as a fu

Solid lines are drawn as a guide to the eye; error bars


load divided by the contact area averaged

from at least 10 measurements. More

details of the experimental procedures

can be found elsewhere.[1–8]


In Figures 2a and 2b, the lap-shear strength

of a symmetric PS-225–PS-225 interface is

plotted as a function of healing time (at a

healing temperature of 648C that corre-

sponds to Tbulkg – 33) and healing tempera-

ture (at a healing time of 1 h), respectively.

As seen, the two curves shown in Figs. 2a

and 2b have non-linear shapes, which raises

the question concerning the molecular

mechanisms governing the process of

strength development and finding the

proper scaling laws describing it. Since

the diffusion of chain segments plays a key

role in the autoadhesion and adhesion

between the two contacting polymer pieces,

the data sets presented in Figs. 2a and 2b

should be analyzed on their correspon-

dence to the diffusion mechanisms that are

characteristic of random-coil polymers.

First, let us investigate the kinetics of this

process. For this purpose, reptation models

which have been proposed for the viscoe-

lastic state of the polymer bulk and inter-

face may be employed.[21,25] On the one

hand, the minor chain reptation model[21]

predict an increase in the interface strength

as a function of the interpenetration depth

(X) as s � X.

w¼ 225 000 g/mol (a) as a function of healing time at a

nction of healing temperature at a healing time of 1 h.

show the standard deviation of the mean.


Macromol. Symp. 2012, 316, 71–7874

On the other hand, at times shorter than

the reptation time (trept), i.e. when the

displacement of a chain is smaller than its

coil size, four main molecular mechanisms

should be taken into consideration:[21,25] (1)

the diffusion of a statistical segment

(X � t1/2), (2) the diffusion of an entangle-

ment segment (X � t1/4), (3) the diffusion

due to restricted Rouse relaxation of the

chain (X � t1/8) and (4) reptation (X � t1/4).

Therefore, depending on the molecular

mechanism, one may expect the following

kinetics laws for the evolution of the

interface strength: s � t1/2, s � t1/4 and

s � t1/8. For finding a proper scaling law for

the data presented in Fig. 2a, let us analyze

s as a function of t1/2, t1/4 and t1/8 (see

Figures 3a, 3b and 3c, respectively). It

follows from Figs. 3a, 3b and 3c that the best

linear fit is observed in the coordinates

s – t1/4, meaning that the molecular

mechanism of the strength development

is not governed by the diffusion of Kuhn

segments or Rouse relaxation of the chain.

However, further clarification of this

mechanism is still needed since that scaling

law corresponds both to the diffusion of the

entanglement segment and to the chain

reptation along its contour within a tube.

For this purpose, the effect of M on s may

provide with useful information. Actually, s

should not depend on M in the first case

while it should do in the second one, though

this dependence, at t< trept, is rather weak:

s � 1/M1/4.[21] The latter is in accordance

with the following With an increase in Mw of

PS from 103 to 1,111 kg/mol, a decrease in s

Figure 3.

Lap-shear strength of a symmetric PS–PS interface with M

of 648C (¼ Tbulkg – 33) as a function of (a) the square root

and (c) one-eighth power. Solid lines correspond to a le


from 0.27 to 0.16 MPa and from 0.30 to

0.23 MPa at T¼ Tbulkg – 33 and T¼ Tbulk

g – 23,

respectively, has been observed at

t¼ 24 h.[6]

These differences between the corre-

sponding values of s for PS-103 and PS-

1111 seem not to be very large, being

roughly 20–40%, in view of a significant

difference in the molecular weight (by one

order of magnitude). However, since D� 1/

M [26] (D is the curvilinear one-dimensional

reptation diffusion coefficient along the

chain contour at t< trept), s � X and X �(D � t)1/4,[21] one may conclude that this

behavior, semi-quantitatively, is in good

accordance with the mechanism of the

reptative chain motions when the displace-

ment of chain ends plays a key role in the

chain diffusion. More specifically, the

following kinetics law is predicted for this

process if it is governed by the interpene-

tration depth: s � t1/4/M1/4.[21] In order to

investigate the validity of this scaling law at

T< Tbulkg , consider the data for the sym-

metric PS-103–PS-103 and PS-1111–PS-

1111 interfaces as s (t1/4/M1/4) (see

Figures 4a and 4b). As a result of this

procedure, one obtains linear-shaped mas-

ter curves characterizing with rather high

values of the correlation coefficient (k) of

0.95–0.96 (for a perfect fit, k¼ 1) both at

T¼ Tbulkg – 33 and T¼ Tbulk

g – 23. Therefore,

it may be concluded that the molecular

property governing the kinetics of the

development of the interface strength at

the contact zone of the two PS samples with

glassy bulk, at T� Tbulkg – 33, is the

w¼ 225 000 g/mol developed at a healing temperature

of healing time and healing time to the (b) one-fourth

ast-square analysis.


Figure 4.

Lap-shear strength of symmetric PS-103–PS-103 and PS-1111–PS-1111 interfaces developed at (a) T¼ Tbulkg – 33 and

(b) T¼ Tbulkg – 23 as a function of t1/4/M1/4. Solid lines correspond to a least-square analysis.

Figure 5.

Lap-shear strength of a symmetric PS-PS interface

with Mw¼ 225 000 g/mol as a function of reciprocal

healing temperature in semi-logarithmic coordinates,

at a healing time of 1 h. A solid line corresponds to a

least-square analysis.

Macromol. Symp. 2012, 316, 71–78 75

interdiffusion depth of the reptative chains.

Actually, if such a molecular property

would be, for instance, the number of

chains crossing the interface, much stronger

dependence of s on M, i.e. s � 1/M 5/4,

should be observed,[21] which is not the case

for the experimental data presented in

Figs. 4a and 4b. It should also be noted that

the theoretical scaling laws s� t1/4 and, to a

lesser extent, s � 1/M1/4 have already

been shown to be valid at T> Tbulkg as

well.[21,27–29] These behaviors imply that the

process of the reptative motions of chain

segments in the two distinct regions of T

with respect to Tbulkg (T< Tbulk

g and

T> Tbulkg ) is not sensitive to the physical

state of the bulk, and that it governs the

evolution of the interface strength until the

viscoelastic state at the contact zone is

preserved.

Since any diffusion process is generally

believed to follow an Arrhenius-like ther-

mally activated behavior[21,27–29] the data

presented in Fig. 2b should be analyzed as

logs (1/T). The result of this procedure is

shown in Figure 5.

It is clearly seen that the constructed

graph has a linear shape, indicating that

this process is actually an Arrhenius-like

process. From the slope to the curve

drawn through the experimental data

points of Fig. 5 as a solid line, one may

estimate the activation energy of autoadhe-

sion (Eaa) using the following relationship:


s¼ s0 � exp[�Eaa/(RT)], where s0 and R are a

constant and the universal gas constant,

respectively. As-calculated value of Eaa is

65 kJ/mol. However, in order to compare

correctly this value of Eaa with the activation

energy of the diffusion process (Eda), the

former one should be ‘‘converted’’ to Eda as

Eda ¼ 4Ea

a.[7] Taking into consideration that,

at t< trept, s � X � D1/4,[21] one obtains

Eda ¼ 260 kJ/mol. This value of Ed

a (at t <<

trept and T< Tbulkg ) compares with the values

of Eda ¼ 250-360 kJ/mol at t> trept and

T> Tbulkg for the PS�PS interfaces.[30] It

indicates, first, that an elementary kinetic

unit of the diffusion process in the two

interval of T located on both sides of Tbulkg is


Macromol. Symp. 2012, 316, 71–7876

the same, and, second, that the physical

state of the interior bulk regions does not

influence the scenario of the development

of the molecular events at the interface,

until it is in the viscoelastic state. Besides,

the values of Eda indicated above are close to

the values of Ea of the process of alpha-

relaxation in the near-surface layer (Ea�surfa )

of PS of 210 to 320 kJ/mol.[1,12–14] Therefore,

one may conjecture that an elementary act

of interdiffusion at the interfaces of two

PS pieces with glassy bulk is controlled by

alpha-relaxation.

Let us now turn to the question of

Tsurfaceg . Recently, it has been shown[2,4] that

the Tsurfaceg of an amorphous polymer can be

measured as the lowest T (T lowest) at which

the diffusion-governed autoadhesion

occurs. However, in order to properly

estimate T lowest using this approach, one

should perform the bonding experiments

with a rather narrow T step, which is not

always an easy task because of rather small

loads measured upon fracture of such

joints. As an alternative, another possibility

to characterize Tsurfaceg in the frameworks of

the adhesion approach is to estimate

Tsurfaceg -equil, i.e. the low-temperature limit

of Tsurfaceg , by the extrapolation of the curves

s (T) to s¼ 0. At first sight, non-linear

shape of those curves[2] makes it difficult to

estimate s¼ 0. Nevertheless, after a

detailed analysis of those curves, it was

found that they become linear when plotted

as the square root of s as a function of T (see

Figure 6.

Square root of lap-shear strength as a function of (a) hea

to Tbulkg for various symmetric polymer-polymer interface

square analysis while dashed lines are their extrapolati


Figure 6a). As-estimated values of T surfaceg -

equil for all the symmetric interfaces

investigated fall into a rather narrow

interval of T between 30 and 608C, though

the Tbulkg ’s of the polymers involved differ

by 1208C. However, when the abscissa of

Fig. 6a is reduced to Tbulkg , one may estimate

the effect of the reduction in Tsurfaceg -equil

with respect to Tbulkg (see Figure 6b).

As seen, this effect turned out to be very

strong in all the cases considered, being

between �60 and �140 degrees and

depending significantly on the chain archi-

tecture. For the carbon-chain polymers

under investigation, PSs and PMMA, the

values of the effect are rather close, �60

and �808C, respectively. The strongest

effect is observed for PPO (�1408C). This

behavior might be explained, first, by more

rapid conformational transitions in PPO

provided by the presence of the oxygen

atoms in the chain backbone[31] and, second,

by a smaller number of repeat units per

Kuhn segment in PPO (3-4) as compared to

those in PMMA (6) and PS (9).[32] As far as

the influence of the molecular weight and

polydispersity on the difference between

Tsurfaceg -equil and Tbulk

g is concerned, it does

not almost depend on these two molecular

properties for the four PSs investigated.

Hence, these two factors seem not to be

important for the molecular dynamics in the

near-surface and interface layers of the high-

molecular weight amorphous polymers with

glassy bulk.

ling temperature and (b) healing temperature reduced

s; healing time is 1 h. Solid lines correspond to a least-

ons.


Macromol. Symp. 2012, 316, 71–78 77

One of the important fundamental

questions of the contemporary physics of

polymers is the question of the existence of

the enhanced molecular mobility at poly-

mer-polymer interfaces in comparison with

that in the polymer bulk. For instance, it has

been suggested by Sharp and Forrest[11]

that the effect of the lowering of T surfaceg

with respect to Tbulkg should vanish after the

surfaces are brought into contact. To put it

differently, according to this point of view,

the presence of the free polymer surface is a

necessary condition for this effect to show

up. However, the results reported in the

present study indicate that the long-range

segmental motions do exist at the contact

zone of the two polymer pieces with glassy

bulk, as it do at the contact zone of the two

polymer pieces with the viscoelastic state of

the bulk. This behavior may be explained as

follows. A decreased mass density and a

decreased concentration in the entangle-

ments at polymer surfaces and interfaces in

comparison with those in the polymer bulk

are believed to be the important factors of

the manifestation of this effect.[2,15] It is

obvious that these molecular properties

cannot immediately, upon the contact,

attain those that are characteristic of the

bulk, even at early stages of healing, though

a steady slowdown of this effect is expected

as healing progresses. Seemingly, that is

why the effect of the enhanced molecular

mobility existing on the free polymer

surface continues to exist at the early stages

of healing of polymer-polymer interfaces as

well.

Conclusion

It has been shown that the molecular

property governing the process of the

evolution of the strength at the contact

zone of the two amorphous polymer pieces

with glassy bulk is the interpenetration

depth of the reptating chains. The elemen-

tary kinetic unit of motion of this process is

Kuhn segment. The realization of this

molecular mechanism of the interface

healing is provided by the viscoelastic state


of the contact zone over a certain interval of

bonding temperatures wherein the long-

range segmental motions is activated,

despite the glassy state of the bulk wherein

this mode of the molecular motion is

frozen. The proposed adhesion approach

has been shown to be useful to estimate the

quasi-equilibrium surface glass transition

temperature of an amorphous polymer by

the extrapolation of the corresponding

curves ‘‘square root of lap-shear strength

versus bonding temperature’’ to zero

strength. It has been found that the effect

of the lowering of the quasi-equilibrium

Tsurfaceg with respect to Tbulk

g is characteristic

of non-crystallizable polymers. For the

high-molecular weight amorphous poly-

mers (M>Ment), this effect depends

strongly on the chain architecture and

weakly on the molecular weight and

polydispersity.

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[13] T. Kajiyama, K. Tanaka, N. Satomi, A. Takahara,


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Dep

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E-m

Cop

2D Diffusion of Macromolecules Adsorbed on Glass

Microspheres

A. S. Malinin,* A. A. Rakhnyanskaya, A. A. Yaroslavov

Summary: It has been demonstrated that diffusion of polycation adsorbed on glass

microspheres occurs without desorption of the macromolecules into the solution

and, therefore, can be characterizerd as 2D-diffusion. The diffusion coefficint is

estimated to be 1.4� 10�12 cm2/s.

Keywords: adsorption; diffusion; monolayers; polyelectrolyte; surfaces

Introduction

Despite the fact that it is possible to predict

the behavior of polymers in 3D systems in

solution due to the scaling method which

was proposed for the description of poly-

mer dynamics in solution by de Gennes,[1]

only a few studies considering 2D-diffusion

of polymers can be found. Firstly polymer

dynamics on surfaces has been presented as

a mathematical model[2,3] and only recently

some papers reporting experimental facts on

this phenomenon for polyelectrolytes and,

especially, biopolymers have appeared.[4]

The aim of the present study was to

provide experimental investigation of 2D-

diffusion of synthetic polyelectrolytes on a

surface of adsorbent and to make a

quantitative estimation of the parameters

of this process.

Materials and Reagents

The adsorbent used for the study were glass

microspheres (GMs) with average diameter

of 10� 1 mm and 5� 0.5 mm (Figure 1).

The polymer under consideration was

cationic poly-4-vinylpyridine (average

polymerization degree 600, 90% alkylated

with ethyl bromide and 10% alkylated with

bromacetic acid). In addition, this copoly-

mer was labeled with FITC (1 label per 1

artment of Polymers, Chemistry Department,

onosov Moscow State University, 119991 Moscow,

sia



macromolecule) in order to enable fluor-

escent registration of the diffusion process

(Figure 2).

Diffusion Studies

In order to study the nature of the

migration of the polycation on the surface

of the glass microspheres, we adsorbed the

polymer with fluorescent label onto 5-mm

glass microspheres (the adsorption was

demonstrated to be irreversible since there

was no polymer detected in solution after

rinsing) and mixed the latter with the same

amount of polymer-free 10-mm micro-

spheres. As Figure 3 shows, two types of

fluorescent particles were found in the

system after 24 h and, consequently, both

5-mm and 10-mm particles contained the

polycation on their surface. Such result

demonstrated that some migration process

had occurred in the system; however, it was

not clear whether the migration featured

desorption of the polymer from the surface

into the solution or it proceeded as 2D-

difussion of the whole polymer macromo-

lecule from the particle to its neighbor.

On one hand, there are evidences in

literature[5] that adsorption of polymers is

equilibrium process so some small amount

of polymer should be present in solution in

any case. On the other hand, equilibrium

constant could be extremely small and

equilibrium could be almost totally shifted

to adsorption.[6] Some further studies were

made to clarify this point. Two pieces of

mirror were taken and one of them was


Figure 1.

TEM image of glass microspheres.

Figure 2.

Chemical formula of polycation F-PEVP.

Macromol. Symp. 2012, 316, 79–8280

treated the same way as glass microspheres

providing F-PEVP adsorption onto the

surface. The intensity of fluorescence was

measured by fluorometer. The other one

was cleaned and left without polymer. Both

mirrors were put into buffer solution at the

same reservoir. The distance between them

was about 1 mm. Two weeks later the

mirrors were taken off from the buffer

solution. The intensity of fluorescence of

both mirrors was measured. The fluores-

cence intensity of mirror without polymer

was still zero while mirror with polymer had

the initial fluorescence intensity. Therefore,

Figure 3.

Image from fluorescent microscope of mixture two types

of fluorescent and visible images.


there is no polymer migration through the

solution and, consequently, the migration

of strong adsorbed polymers could occur

only as 2D diffusion without desorption.

For the further investigation and quan-

titative description of the observed process

of 2d diffusion we mixed glass microspheres

of one size (5 mm), half of them contained

F-PEVP and the other half being empty.

Just after mixing we detected fluorescent

and non-fluorescent particles (Figure 4a)

but 24 hours later all particles contained

fluorescent polymer on their surface

(Figure 4b). Therefore, total redistribution

of the polycation between the particles was

observed.

Using Carl Zeiss software (Axiovision

4.8.1), we could measure intensity of

of glass microspheres; a) fluorescence, b) combination


Figure 4.

Image from fluorescent microscope of mixture two types of glass microspheres; a) mixture of fluorescent and

non-fluorescent glass microspheres just right after mixing, b) same mixture 24 hours later.

Macromol. Symp. 2012, 316, 79–82 81

fluorescence of each particle. In the initial

system shown in the Figure 4a the intensity

of fluorescent particles was taken as 1, the

intensity of non-fluorescing particles was

taken as 0. Similar estimation for the

resultant system shown in Figure 4b showed

that intensity of fluorescence of all particles

was 0.5 (the particles were mixed in equal

ratio). The same situation was obtained for

mixtures with different ratios (2:1, 1:1, 1:2)

of fluorescent and non-fluorescent particles.

As Figure 5 demonstrates, resultant fluor-

Figure 5.

Histogram of dependence of relative intensity of fluores

of fluorescent: non-fluorescent particles in 24 hours af


escence intensity was a linear function of

ratio.

Therefore, migration of polycation

could be considered as a quasi-equilibrium

process. Since the adsorbed polycation was

distributed uniformly, we suppose that this

process is has enthropic nature. As soon as

some empty space for polymer appeared in

the system, the polycation started to diffuse

until distribution of polymer became uni-

form. The nature of 2D polymer diffusion

is the same as the nature of Brownian

cence of glass microspheres mixture on different ratio

ter mixing.


Figure 6.

Decrease of fluorescence of GMs from time.

Macromol. Symp. 2012, 316, 79–8282

motion []. We made an experiment to check

this assumption. We mixed equal amount of

glass microspheres filled with F-PEVP and

glass microspheres filled with the same

polymer but without fluorescent label so

that there were no empty spots on the

surface of glass microspheres. As a result,

we did not observe redistribution of poly-

cation nor in 24 hours nor in a 7 days. So the

non-labeled polycation could be used as

stop-reagent for registration of the kinetic

curve of the process.

For the kinetic studies we mixed GMs

with F-PEVP and GMs without polymer in

ratio 1:1 and an excess of the stop-reagent

(PEVP) was added to the samples in certain

time moments so that 9 samples presenting

the system development over a 24 h period.

The decrease of fluorescence in time is

demonstrated in Figure 6. The analysis of

this kinetic curve employing Fick’s second

equation provided the value of the diffusion

coefficient in the considered system which

appeared to be 1.4� 10�12 cm2/s. This value

is much lower than diffusion coefficient for

adsorbed DNA in work.[4]

Similar experiments made for other

conditions showed that temperature increase

(to 608C) and presence of low-molecular


electrolyte (3 M NaCl) lead to the growth of

the diffusion coefficient (4.2� 10�12 cm2/s

and 3.2� 10�12 cm2/s, respectively).

Conclusion

It has been demonstrated that adsorbed

synthetic polycation is able to migrate from

one colloidal particle to another without

desorption. It is an example of 2D-diffu-

sion.

Acknowledgements: This work was supported byCarl Zeiss AG (grant for young scientists ofleading universities of Russian Federation).

[1] P. G. De Gennes, ‘‘Scaling concepts in polymer

physics’’, Cornell University Press, Cornell 1979.

[2] J. Cloizeaux, G. Jannik, ‘‘Polymers in solution’’,

Clarendon Press, Oxford 1990.

[3] I. Carmesin, K. Kremer, J. Phys. 1990, 51, 915.

[4] V. Kahl, M. Hennig, B. Maier, J. O. Raedler, Electro-

phoresis 2009, 30, 1276.

[5] T. Radeva, V. Milkova, I. Petkanchin, Colloid and

Surfaces A. 2002, 209, 227.

[6] A. Voronov, S. Minko, A. Shulga, E. Pefferkorn,

Colloid Polym Sci. 2004, 282, 1000.



1 In

31

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Cop

Dynamic Mechanical Analysis and Molecular Mobility

of the R-BAPB Type Polyimide

V. P. Toshchevikov,*1,2 V. E. Smirnova,1 V. E. Yudin,1 V. M. Svetlichnyi1

Summary: Dynamic mechanical experiments are performed to study molecular

mobility of the R-BAPB type polyimide based on 1,3-bis-(3,30,4,40-dicarboxyphenoxy)-

benzene (R) and 4,40-bis-(4-aminophenoxy)biphenyl (BAPB) with a molecular weight

Mw � 80 000 g/mol. Frequency dependences of the storage and the loss tensile

moduli are measured within the temperature domain 1998C� T� 2118C that includes

the glass transition temperature of the compound, Tg¼ 2068C. It is shown that the

time-temperature superposition principle holds for the R-BAPB type polyimide. A

theoretical analysis of the master curves constructed at Tref¼ 2048C is performed on

the basis of the piecewise-power-type distribution function of the relaxation times.

Relaxation times for typical scales of motion inside polyimide macromolecules are

calculated and the molecular weights of the characteristic kinetic units (the Kuhn

segment and the chain fragment between entanglements) are estimated.

Keywords: dynamic modulus; mechanical properties; polyimides; theory

Introduction

Polyimides (PIs) are considered to be one of

the most important engineering plastics

which have a fascinating potential for

technical applications due to their excellent

thermal stability, mechanical properties, and

chemical resistance.[1–4] Nowadays, one of

the perspective topics is a design of the

PI-based nanocomposites which exhibit

increased modulus and strength, high heat

distortion temperature, decreased thermal

expansion coefficient, reduced gas perme-

ability, and increased solvent resistance

compared to pristine polymers.[5–11] For

understanding the physical mechanisms

which determine the practically important

properties of these compounds one needs to

know their molecular features, in particular,

the conformations and mobility of macro-

molecules that compose these materials.

One of the widely-used methods for inves-

stitute of Macromolecular Compounds, Bolshoi pr.

, 199004 Saint-Petersburg, Russia


ibniz Institute of Polymer Research Dresden,

ohe Str. 6, 01069 Dresden, Germany


tigating the structure and molecular mobility

of polymers is the dynamic mechanical

analysis.[12–14]

The present paper is devoted to the

dynamic mechanical analysis of the R-

BAPB type PI (Figure 1) which can be a

potential candidate as high-performance

thermoplastic matrix for thermally stable

fiber reinforced composites as well as

nanocomposites.[9–11] The frequency and

temperature dependences of the dynamic

tensile moduli for the R-BAPB type PI are

measured and analyzed by means of a

theoretical method which allows us to

describe the molecular mobility within a

wide range of scale of motions.

Experimental Part

Poly(amic acid) (PAA) was obtained

by polycondensation of 1,3-bis(3,30,4,40-

dicarboxyphenoxy)benzene (R) and 4,40-

bis-(4-aminophenoxy)biphenyl (BAPB)

supplied by Wakayama Seika Co., Ltd.

(Japan) in a 20% solution of N-methyl-2-

pyrrolidone (NMP) at 258C. The average

molecular weight of R-BAPB type PAA,


CN

C

O

O n

O OOO C

NC

O

O

Figure 1.

Chemical structure of the R-BAPB type polyimide.

Macromol. Symp. 2012, 316, 83–8984

Mw � 80 000 g/mol, was estimated by GPC

method. PI films (40 mm thick) were

prepared from the PAA by casting on soda

lime glass plates and subsequent drying in

an oven at 608C for 20 hr under air

atmosphere. Imidization was achieved by

placing the films in an air oven for curing at

1008C for 1hr, 2008C for 1 hr, 3008C for 1 hr,

and 3508C for 10 min. Subsequently, the

cast films were removed after complete

imidization from the glass plates by soaking

in water. The glass transition temperature

of the polyimide Tg¼ 2068C was deter-

mined by the DSC method (DSC 204

F1 Phoenix, NETZSCH).

The equipment DMA 242 C, NETZSCH

was used to measure the frequency depen-

dences of the storage, E0, and the loss, E00,

tensile moduli of R-BAPB films of base

dimension 5� 10 mm2. The measurements

were performed at the temperatures

T¼ 1998C, 2028C, 2048C, 2088C, and

2118C. The equipment uses a method in

which a small oscillating tensile strain is

applied to a statically pre-strained sample

at normal force of 0.1 N. The amplitude of

the oscillating strain was chosen to be small

enough (e¼ 0.1%) to insure that the

deformations of samples were absolutely

Figure 2.

Frequency dependences of the storage (a) and loss (b) m


elastic and reversible. It was possible to

conduct experiments with reversible defor-

mation for the amorphous R-BAPB type PI

until T¼ 2118C, i.e. higher than the glass

transition temperature, Tg¼ 2068C. We

relate this possibility with the presence of

entanglements between macromolecules

which prevent the translational movements

of the macromolecules and suppress the

irreversible deformation.

Figures 2a and 2b show the experimental

dependences of the dynamic moduli E0 and

E00 on the frequency F for PI films within the

frequency range from 10�1 Hz to 102 Hz at

different temperatures. To extend the

frequency sweep we use the method of

master-curves.[12–14]

Master Curves for the R-BAPB Type PI

The method of master-curves is based on

the time-temperature superposition princi-

ple,[12] according to which the dependence

of the tensile relaxation modulus, E, on

the time, t, and the temperature, T, can be

presented in the following form:

EðtÞ ¼ nkT � f ðt=t0ðTÞÞ; (1)

where n is the polymer density (number of

monomers in the unit volume), k is the

oduli for the R-BAPB type PI at different temperatures.


Macromol. Symp. 2012, 316, 83–89 85

Boltzmann constant, f(x) is a certain dimen-

sionless function and t0 is a certain char-

acteristic relaxation time of the polymer

(e.g., t0 can be the time of the rotational

diffusion of a monomer), which is known to

be a function of temperature. Note that the

most theoretical dynamic models, which

describe the molecular mobility of polymers

on different scales (the Rouse model,

dynamic models of semiflexible chains, the

tube model for entangled macromolecules,

etc.), predict the dependence E(t) in the form

of Equation (1).[12–14] In these models, all

relaxation times are related to the relaxation

time t0 through dimensionless multipliers

which depend on the scale of motion but

are independent of temperature. Thus, the

temperature dependence of all relaxation

times are expressed in terms of the unique

function t0(T). Now, the storage E0 and loss

E00 moduli,

E0ðvÞ ¼ Re iv

Z1

0

EðtÞe�ivtdt

0@

1A and

E00ðvÞ ¼ Im iv

Z1

0

EðtÞe�ivtdt

0@

1A;

(2)

can be rewritten with the use of

Equation (1) in the following form:

E0ðvÞ ¼ nkT � f1ðvt0ðTÞÞ and

E00ðvÞ ¼ nkT � f2ðvt0ðTÞÞ:(3)

Here v¼ 2pF is the angular frequency, and

f1(x) and f2(x) are new dimensionless

Figure 3.

Dependences of tan d on the angular frequency v¼ 2pF

temperatures.


functions which are determined by the real

and imaginary parts of the Fourier trans-

form of the function f(x) in Equation (1).

Hence, the phase angle tan d¼E00/E0 can be

written as:

tandðvÞ ¼ f2ðvt0ðTÞÞ=f1ðvt0ðTÞÞ: (4)

Thus, the change of temperature from a

certain value Tref to a current value T is

equivalent to a horizontal shift of tan d

along the frequency axis in the logarithmic

scale by the factor log aT¼ log[t0(T)/

t0(Tref)]. Moreover, the moduli E0 and E00

demonstrate under change of temperature

not only the horizontal shift but also the

vertical shift due to the factor nkT, see

Equation (3). Therefore, the procedure of

constructing the master curves for E0 and E00

consists of two steps: (1) calculation of the

horizontal shift factor aT from the fre-

quency dependences of tan d and (2)

calculation of the vertical shift factor for

E0 and E00.

Figure 3a shows the dependences of tan

d on v¼ 2pF plotted in the logarithmic

scale at different temperatures. One can

see that the profiles of the dependences

tan d(v) at different temperatures look

identical and differ only by the hori-

zontal shifts, as it was mentioned above.

Keeping the data for Tref¼ 2048C to be

unchangeable and applying the horizontal

shifts to the curves for other temperatures it

is possible to obtain a relatively smooth

dependence for tan d(aT v), see Figure 3b.

(a) and on the reduced frequency aT v (b) at different


Figure 4.

Horizontal (a) and vertical (b) shift factors as functions of temperature.

Macromol. Symp. 2012, 316, 83–8986

The values of the shift factor aT as a

function of temperature are given in

Figure 4a. Furthermore, applying the

horizontal shift with the factor log(aT) to

E0(v) and E00(v) at different temperatures,

we have found that the dependences E0(aT

v) and E00(aT v) are characterized by small

gaps at the points where the experimental

data for different temperatures are coupled

to each other. These gaps are caused by the

temperature-dependent factor nkT. Apply-

ing the same vertical shift to both depen-

dences E0(aT v) and E00(aT v) plotted in the

double-logarithmic scale it was possible

to obtain simultaneously a good matching

of both curves E0(aT v) and E00(aT v).

Figure 4b shows the temperature depen-

dence of the vertical shift factor bT which is

necessary to obtain continuous functions

bTE0(aT v) and bTE00(aT v).

Figure 5.

Master-curves for the storage (a) and loss moduli (b).

method of the distribution function of the relaxation t


Figures 5a and 5b illustrate the master

curves for the storage and loss moduli, i.e.

the dependences bTE0(aT v) and bTE00

(aT v). The master curves are characterised

by smooth dependences after horizontal

and vertical shifts which are found to be the

same for the storage and loss moduli. This

means that the method of master curves

works well for the R-BAPB type PI. This

method allows us to extend the frequency

sweep for E0 and E00 from 3 to 5 decades.

Below we present a theoretical analysis of

the master curves.

Theoretical Analysis of the Molecular

Mobility of the R-BAPB Type PI

To analyze the dynamic mechanical beha-

vior of the R-BAPB type PI we develop a

method based on the distribution function

of the relaxation times, H(t).[12] In terms of

Thick lines show the fitting results by means of the

imes.


Macromol. Symp. 2012, 316, 83–89 87

H(t) the relaxation and dynamic moduli can

be rewritten in the following form:[12]

EðtÞ ¼Z1

0

d lnt �HðtÞexpð�t=tÞ; (5)

E0ðvÞ ¼Z1

0

d lnt �HðtÞ ðvtÞ2

1þ ðvtÞ2;

and

E00ðvÞ ¼Z1

0

d lnt �HðtÞ vt

1þ ðvtÞ2:

(6)

We construct the distribution function

H(t) using the asymptotic behavior of the

shear modulus G for different scales of

motions[12–16] as well as the approximate

relation E¼ 3G.

One can see from Figures 5a,b that in

the intermediate frequency domain the

dynamic moduli obey the power-type

frequency behavior, E0/E00/v1/2, typical

for the Rouse-like regime. In this regime

the distribution function H(t) obeys an

asymptotic behavior:[12–14]

HRouseðtÞ ffi 3nkT1

2

t

t1

� ��1=2

; (7)

where n is the number of chains in the unit

volume and t1 is the maximal Rouse-

type relaxation time of a polymer chain

which can be written in the form (cf. with

refs. 12-14):

t1 ¼zhR2i6p2kT

: (8)

Here z is the total friction coefficient of a

polymer chain and hR2i is the mean-square

end-to-end distance of the chain. Further-

more, in the frequency domain, which

is slightly above the Rouse-like regime

(E0/E00/v1/2), the moduli increase more

rapidly than the 1/2-power of the frequency,

see Figures 5a,b. This effect is caused by the

bending rigidity of polymer chains which

can be described by the worm-like dynamic

model.[14,15] This model provides the fol-

lowing relation for the dynamic modulus,


see Equation (35) in ref. 15:

E�bendðvÞ � E0ðvÞ þ iE00ðvÞ ffi 323=4

15

nkTL

Lpiv

jL3p

kT

!3=4

;

(9)

where L is the chain length, Lp is the

persistence length, and j is the friction

coefficient per chain length. The distribu-

tion function H(t) for Ebend can be written

in the following form:

HbendðtÞ ¼25=4

5pckT t

kT

jLp

� ��3=4

; (10)

where c¼ nL/2Lp is the number of Kuhn

segments in the unit volume. We recall that

the Kuhn segment is twice longer that the

persistent fragment.[12–14] The crossover

between the Rouse-like dynamics and the

bending motions of chain fragments is

determined by a characteristic relaxation

time tp which satisfies the equality

HRouse(tp)¼Hbend(tp). Using Equations (7)

and (10) as well as the relationships j¼ z/L

and hR2i¼ 2LpL we have found the value of

tp in the following form:

tp ¼25

3254

jL3p

kT: (11)

One can show using ref. 15 that tp is the

maximal bending relaxation time of the

persistent fragment. Thus, we can approx-

imate the distribution function H(t) by

Equation (10) at tb< t< tp and by

Equation (7) at tp< t< t�. Here we have

introduced two characteristic relaxation

times: tb is the relaxation time for a minimal

chain fragment which is able to demon-

strate a bending motion, while the relaxa-

tion time t� defines the scale of motion

where the entanglement effects start to

influence the polymer dynamics.

At t< tb Equation (10) does not hold

anymore, and the dynamics in this relaxa-

tion domain has a character of small high-

frequency longitudinal vibrations of chain

fragments. For simplicity we approximate

the relaxation spectrum at 0 <t< tb by

the power-type function H(t) / tb, where


Macromol. Symp. 2012, 316, 83–8988

the index b> 0 is a phenomenological

parameter.

At t> t� the polymer dynamics is

influenced by the entanglement effects that

can be described by the tube model which

provides the following equation for the

modulus:[12–14]

EtubeðtÞ ¼ Ee8

p2

Xp:odd

p�2expð�p2t=tdÞ:

(12)

Here Ee is the plateau modulus, which is

defined by the elasticity of chain fragments

between entanglements, and td is the disen-

tanglement time of a chain from the tube. The

sum in Equation (12) can be approximated

by an integral over the index p. Changing

the integration variable p by a new variable

t¼ td/p2, we can rewrite Equation (12) in the

form of Equation (5) where the distribution

function H(t) takes the following form:

HtubeðtÞ ¼ Ee2

p2t=tdð Þ1=2 at t� � t � td;

and HðtÞ ¼ 0 at t > td:

(13)

Now, we define the characteristic relaxa-

tion time t� as a crossover between the

Rouse-like regime and the chain dynamics

inside the tube: HRouse(t�)¼Htube(t�). The

last equality and Equations (7),(8),(11) and

(13) provide the following value for t�:

t� ¼75p

ffiffiffi6p

16� ckT

Eetptd

� �1=2: (14)

Summarizing the results for the four

relaxation regimes one can write H(t) as

follows:

HðtÞ ¼

a1ckT � ðt=tbÞb � ðtb=tpÞ�3=4 ; t � tb

a1ckT � ðt=tpÞ�3=4 ; tb � t � tp

a1ckT � ðt=tpÞ�1=2 ; tp � t � t�

ð2Ee=p2Þ � ðt=tdÞ1=2 ; t� � t � td

0 ; t > td

8>>>>>>><>>>>>>>:

: (15)

The coefficients are determined by

continuity of the function H(t) and by

exact asymptotic dependences given by

Equations (7), (10)-(14): a1¼ 75 � 61/2/


8p 7.31. We have fitted the master-curves

(see Figure 5) using Equation (15), the

factors ckT, b, tb, tp, Ee, and td being used as

the fitting parameters. The values of the

fitting parameters are given in Table 1.

Now, the molecular weights of the Kuhn

segment, MK, and of a chain fragment

between entanglements, Me, can be esti-

mated. For this we associate the minimal

bending relaxation time tb with a chain

fragment which contains two aromatic rings

(one of them includes the amino-group, see

Figure 1), whose molecular weight is

M0 236 g/mol. In the relaxation domain

tb< t< tp the relaxation times are propor-

tional to the 1/4 power of the length of a

chain fragment.[14,15] Therefore, we can write

tp/tb¼ (MK/2M0)4, since the persistent frag-

ment is twice shorter than the Kuhn segment.

Thus, MK¼ 2M0(tp/tb)1/4 1000 g/mol. The

value Me can be found as: Me¼Ne MK, where

Ne is the number of Kuhn segments

between entanglements. The value Ne is

related to the plateau modulus Ee as

follows:[16]

Ee ¼ ckT 1þ 2=ð1�N�1e Þ�2

� �=Ne: (16)

The last equation holds both for

Gaussian chains (Ee!3nkT at Ne!1)

and for very short chains (Ee!1 at

Ne!1). From Equation (16) and using the

data of Table 1 we find Ne 2 and, hence,

Me¼NeMK 2000 g/mol. Thus, we can

expect that the reptation regime should

start at the value Mcr ffi 2Me 4000 g/mol,

since in this case each chain is entangled ‘‘at

both ends’’. The value Mcr 4000 g/mol is

close to the number-averaged molecular

weight Mcr estimated in ref. 8 for polyimides.

Furthermore, one can now estimate the mass

density of the compound: r¼ c �MK/NA 1.26 g/cm3. Here NA¼ 6.022� 1023 mol�1 is


Table 1.Values of the fitting parameters at T¼ Tref¼ 2048C.

Parameter: b ckT tb tp Ee, MPa td

Value: 0.55 5 MPa 1.5� 10�3 s. 2.8� 10�2 s. 20 MPa �2� 103 s.

Macromol. Symp. 2012, 316, 83–89 89

the Avogadro constant. The value r1.26 g/cm3 is close to the value r¼ 1.3 g/cm3

measured for the polyimide R-BAPB.[10,11]

The agreement of the fitting results with

experimental data demonstrates a great

potential strength of the proposed theoretical

method.

Conclusion

We have performed a dynamic mechanical

analysis of the R-BAPB type PI. It has been

shown that the time-temperature super-

position principle holds for the R-BAPB

type PI, and the master curves for the

frequency dependences of the tensile

storage and loss moduli have been con-

structed. Using a theoretical model based

on the piecewise-power-type distribution

function of the relaxation times we have

calculated the molecular weights of the

Kuhn segment (MK 1000 g/mol) and of

the chain fragment between entanglements

(Me 2000 g/mol) for the R-BAPB type PI.

The model allows to estimate the mass

density of the polymer: r 1.26 g/cm3 that

is close to other experimental data.[10,11]

The agreement of the theoretical results

with experimental data demonstrates a

great potential strength of the proposed

theoretical method which can be used in the

future for investigation of other complex

effects: molecular weight distribution, pre-

sence of included particles, etc.

Acknowledgements: The financial support of theRussian Foundation for Basic Research (the


project 11-03-00944) is gratefully acknowledged.The authors cordially thank Prof. Yulii Ya.Gotlib for the helpful discussions.

[1] M. I. Bessonov, M. M. Koton, V. V. Kudryavtsev, L. A.

Laius, Polyimides - Thermally Stable Polymers, New York

Plenum Publishing Corp, 1987.

[2] D. Wilson, H. D. Stengenberger, P. M. Hergenrother,

Polyimides, New York Chapman and Hall, 1990.

[3] C. E. Sroog, In: M. K. Ghosh,, K. L. Mittal, Polyimide,

fundamentals and applications, New York Marcel Dek-

ker, 1996.

[4] V. M. Svetlichnyi, V. V. Kudryavtsev, Polymer

Science, Series B 2003, 45(5-6), 140.

[5] J.-C. Huang, Z. Zhu, J. Yin, X. Qian, Y.-Y. Sun,

Polymer 2001, 42, 873.

[6] H.-L. Tyan, C.-M. Leu, K.-H. Wei, Chem. Mater. 2001,

13, 222.

[7] S. Campbell, D. Scheiman, High Perform. Polym.

2002, 14, 17.

[8] V. E. Yudin, G. M. Divoux, J. U. Otaigbe, V. M.

Svetlichnyi, Polymer 2005, 46, 10866.

[9] V. E. Yudin, V. M. Svetlichnyi, A. N. Shumakov, D. G.

Letenko, A. Y. Feldman, G. Marom, Macromol. Rapid

Commun. 2005, 26, 885.

[10] V. E. Yudin, J. U. Otaigbe, L. T. Drzal, V. M.

Svetlichnyi, Advanced Composites Letters 2006, 15,

137.

[11] V. E. Yudin, V. M. Svetlichnyi, A. N. Shumakov,

R. Schechter, H. Harel, G. Marom, Composites: Part A

2008, 39, 85.

[12] J. Ferry, ‘‘Viscoelastic Properties of Polymers’’, 3rd

Ed. New York Wiley, 1980, p. 668.

[13] M. Doi, S. F. Edwards, ‘‘The Theory of Polymer

Dynamics’’, Clarendon, Oxford 1986, p. 391.

[14] M. Rubinstein, R. H. Colby, ‘‘Polymer physics’’,

Oxford University Press, Oxford 2003, p. 454.

[15] D. C. Morse, Macromolecules 1998, 31, 7044.

[16] A. V. Dobrynin, J.-M. Y. Carrillo, Macromolecules

2011, 44, 140.



1 In

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Thermostable Polycyanurate-Polyhedral Oligomeric

Silsesquioxane Hybrid Networks: Synthesis,

Dynamics and Thermal Behavior

Olga Starostenko,1 Vladimir Bershtein,*2 Alexander Fainleib,1 Larisa Egorova,2

Olga Grigoryeva,1 Alfred Sinani,2 Pavel Yakushev2

Summary: A series of hybrid polycyanurate - epoxy cyclohexyl-functionalized poly-

hedral oligomeric silsesquioxane (PCN/ECH-POSS) nanocomposite networks with

ECH-POSS content varying from 0.025 to 10 wt. % were synthesized and characterized

using FTIR, DSC, DMA and CRS techniques. It was revealed that already as low as

0.025 wt. % POSS cardinally changed PCN glass transition characteristics including

the strong shift of the transition onset to higher temperatures and manifesting a

second, higher-temperature glass transition characterizing interfacial dynamics;

additionally, enhancing creep resistance and thermal stability at the earlier stage

of degradation were observed.

Keywords: glass transition; nanocomposites; polycyanurates; POSS

Introduction

Densely cross-linked polycyanurates (PCN)

synthesized from cyanate ester resins have

attracted much interest in recent years

because of their excellent thermal and good

mechanical properties, which commend

them for use in high performance technology

(e.g., as matrices for composites for high-

speed electronic circuitry and transpor-

tation).[1,2] Additionally, cyanate/epoxy

composites provide superior performance

through the co-reaction between cyanate

and epoxy groups of blend components; as a

result, fine properties of the final composite

are reached.[3] Further enhancing PCN and/

or overcoming their drawbacks could be

attained in PCN hybrids and nanocompo-

sites.[4]

Last years the great attention has been

paid to preparing and characterization of

hybrid polymer/inorganic nanocomposites

stitute of Macromolecular Chemistry, NAS, 02160

yiv, Ukraine

ffe Physical-Technical Institute, RAS, 194021

.-Petersburg, Russia



containing 3D molecules (particles) of poly-

hedral oligomeric silsesquioxane (POSS) of

about 1 nm in size.[5] POSS compounds have

the cage structures with the common formula

(RSiO1.5)8, 10, or 12, which are called as T8, T10

and T12 cages, respectively. Typically, an

each cage silicone atom in POSS is bonded

to three oxygen atoms and to a single R

substituent. The functional groups of POSS

may react, via grafting, copolymerization or

other reaction, with monomer or polymer,

and hence POSS cages can be covalently

incorporated into a polymer matrix. Thus,

POSS offers a chance to prepare hybrid

nanocomposites with molecularly dispersed

inorganic structural units where POSS

cages may be considered, to a certain

extent, as�1 nm silica inclusions or clusters

chemically bound with a polymer matrix.

Just the ability of POSS to be dispersed as

unassociated units covalently bound to a

matrix is the key to impact POSS on

polymer dynamics and properties. The

numerous studies (see, e.g.,[5–9]) showed

that different polymer-POSS nanocompo-

sites can exhibit dramatic improvements in

polymer matrix properties such as thermal

stability, oxidation resistance, mechanical


Macromol. Symp. 2012, 316, 90–96 91

behavior, surface hardness as well as

reduction in flammability and so on.

Recently, amine- or cyan-, or hydroxyl-

functionalized POSS molecules were intro-

duced into cyanate ester resin in the

amounts from 1 to 15 wt. %.[10,11] Thus,

octaaminophenyl-POSS additive provided

formation of the hybrid PCN/POSS nano-

composites with the substantially changed

properties, in particular Tg shift to both

higher and lower temperatures.

In the present study, the nanocomposites

based on PCN with different doping levels

by epoxy cyclohexyl-POSS, starting from

0.025 wt. %, were studied. The chemical

structure and final properties of the nano-

composites were investigated by means of

Fourier-transform infra-red spectroscopy

(FTIR), differential scanning calorimetry

(DSC), dynamic mechanical analysis (DMA)

and laser-interferometric creep rate spec-

troscopy (CRS).

Experimental Part

1,1’-bis(4-cyanatophenyl) ethane (dicya-

nate ester of bisphenol E, DCBE), under

the trade name PRIMASET1 LECy L-10

(from Lonza Group Ltd., Switzerland), and

epoxy cyclohexyl POSS1 Cage Mixture

(ECH-POSS, from Hybrid Plastics Inc.,

Hattiesburg, MS, USA) were used as

received. The formulas for this monomer

and ECH-POSS (T8 cage) are shown

below. The polymer nanocomposites

from DCBE and ECH-POSS with ECH-

POSS content c¼ 0.025, 0.05, 0.1, 0.5, 1.0,

2.0, 5.0, and 10.0 wt. % were synthesized.

The initial mixtures were first stirred

at 1708C during 2 hrs for pre-polymeriza-

tion of DCBE and chemical grafting of

ECH-


POSS to the growing PCN network

through the reaction between cyanate and

epoxy groups. Then the filled pre-polymer

was step-by-step cured and sequentially

post-cured at 170-3008C for 6 hrs.

At monitoring the curing process, FTIR

spectra were recorded between 4000 and

600 cm�1 using a Bruker Tensor 37 spectro-

meter. For each spectrum, 32 consecutive

scans with a resolution of 4 cm�1 were

averaged. The IR band at 2968 cm�1 was

used as an internal standard. The dynamics,

thermal behavior and elastic properties

of the PCN/ECH-POSS hybrids were

characterized using the combined DSC

(Perkin-Elmer DSC-2 apparatus), DMA

(DMS 6100 Seiko Instruments, 1 Hz), and

CRS[12] approach.

Results and discussion

Figure 1 shows how decreasing the inten-

sities of the absorption bands at 2237 and

2266 cm�1 characterizing cyanate groups is

accompanied with appearing the bands at

1369 and 1564 cm�1 of the cyanurate ring

vibration in the spectra during the poly-

merization of initial DCBE/POSS mixture,

as a consequence of the basic process

of polycyclotrimerization of cyanate

groups with formation of triazine cycles.

Meantime, the slight absorption band at

1738 cm�1 appears also in the nanocompo-

site spectra which confirms the presence of

oxazolidinone rings formed owing to co-

reaction between cyanate groups of DCBE

and epoxy groups of ECH-POSS.[3] This

provides the evidence of chemical hybridi-

zation between both constituents in these

systems. A simplified scheme of molecular

structure of the hybrid network formed is

presented in Fig. 2.


Figure 1.

FTIR spectra of model initial PCN/ECH-POSS reactive blend (a), and heated at 1708C for 2 hrs (b) or 3 hrs (c). The

composition of the blend was cyanate/epoxy groups¼ 1:1.

Macromol. Symp. 2012, 316, 90–9692

It was revealed that POSS additives

substantially changed PCN glass transition

characteristics, as estimated by DSC

(Figs. 3 and 4). Unlike a single glass

transition (Tg¼ 2448C) in neat PCN, DSC

Figure 2.

A scheme of PCN/ECH-POSS molecular structure fragme


curves of the hybrids exhibit two transi-

tions, the main one with Tg1 varying,

depending on a composition, from 243 to

2758C, and the weaker transition with Tg2�3758C followed by the hybrid degradation.

nt.


Figure 4.

Main glass transition temperatures of the PCN/ECH-

POSS nanocomposites as a function of POSS content.

Figure 3.

DSC curves of neat PCN and three PCN/ECH-POSS

nanocomposites at heating up to 4008C with the

rate 208C min�1 (scans I and II, cooling rate

3208C min�1).

Macromol. Symp. 2012, 316, 90–96 93

The latter transition may be assigned to

dynamics in the interfacial layers (a strong

‘‘constrained dynamics’’ effect [12,13]).

TGA control showed that thermal

degradation with mass loss started from

� 4208C for neat PCN and low-POSS

content composites, however, degradation

of interfacial bonds started, obviously,

already at T � 4008C since the second glass

transition disappeared in the DSC curves

obtained at scan II (Fig. 3). The largest, by

�300, increasing Tg1 was recorded for the

hybrids with c¼ 0.025 or 0.1% only;

essentially, the temperature of glass transi-

tion onset, Tg1’, increased from 209 to


2618C, and main glass transition became

more narrow in these hybrids (from 540 for

neat PCN to 20-258C for the hybrids,

Fig. 4). The opposite tendency of decreas-

ing Tg1, especially Tg1’, and broadening

glass transition was observed at high POSS

contents, obviously, due to decreasing

locally PCN cross-linking because of DCBE

expense for co-reaction with ECH-POSS.

Enhancing thermal stability of PCN-

POSS hybrids compared with neat PCN at

the earlier stage of degradation was

revealed also by DSC: after scanning to

4008C in nitrogen atmosphere, the tem-

peratures of the transition onset Tg1’ at

scanning II equaled 1878C for neat PCN,

1618C for the hybrid with c¼ 10% but

2498C for the hybrid with c¼ 0.025%.

Similarly, unlike DMA peak with

Tmax¼ 2488C in neat PCN, the main peak

with Tmax varying from 246 to 2658C(the latter at c¼ 0.025%), as well as the


Macromol. Symp. 2012, 316, 90–9694

overlapping peaks at �370–390 and 4308C,

associated with the interfacial dynamics

and degradation process respectively, were

observed for the hybrids. Dynamic modulus

E’ over the 20–2008C range increased for

the hybrids regarding neat PCN, maximum

by 30–40% at c¼ 0.5% (Fig. 5).

At last, the discrete creep rate spectra,

including a few overlapping peaks and

demonstrating the pronounced dynamic

heterogeneity around main Tg, were obtained

(Fig. 6). The constrained dynamics effect

manifests itself here in the displacement of

the spectra by 10-208C to higher tempera-

tures regarding the PCN spectrum, enhan-

cing creep resistance and increasing the

temperature of the sharp creep acceleration

and fracture of the nanocomposites regard-

Figure 5.

DMA data (above - Tand, below – dynamic modulus E’ vs

ECH-POSS hybrids.


ing neat PCN, e.g., from 270 to 3308C at

c¼ 0.1 wt.%.

Thus, the most remarkable result in this

study is the strong impact on polymer

dynamics of very low 3D nanofiller content,

viz., as low as 0.025 wt. %. Really, for linear

polymer matrix with 3D nanofiller additive,

a totally nanoscopically-confined state of a

matrix is usually suggested in case an

average inter-particle distance, L, is close

to or less than the unperturbed dimensions

of macromolecular random coil, as esti-

mated by radius of gyration Rg, typically of

an order of 10 nm in size for many

polymers.[12,13] Therefore, a few percent

loading was typically required for attaining

the substantial constraining dynamics by

3D particles of 10-20 nm size. Meantime, in

. temperature plots) obtained for PCN and three PCN/


Figure 6.

Creep rate spectra obtained at tensile stress 0.5 MPa for neat PCN and two hybrids.

Macromol. Symp. 2012, 316, 90–96 95

the case of semi-interpenetrating networks

such effect was strongly pronounced at

0.25 wt. % nanodiamonds only when L >>

Rg; this was explained by the double

covalent bonding (hybridization) between

the matrix components and of the matrix

with nanofiller.[14]

The unusually large impact of 0.025%

POSS on PCN glass transition dynamics

may be explained, obviously, by the

combined action of a few factors. First,

separated (unassociated) 1-nm size ECH-

POSS molecules of cage structure play the

role of nanofiller particles (silica nano-

blocks) with extraordinarily high specific

surface area of a few thousands m2g�1; that

provides the enormous surface of inter-

facial boundaries in the hybrid nanocom-

posites under study and �10 nm average

inter-particle distances at c¼ 0.025 wt. %

POSS. Secondly, strong interfacial interac-

tions due to covalent bonding of POSS with

the polymer matrix are of importance.

Meantime, however, the amounts of 1-

10 wt. % POSS have earlier been used

typically as the blocks at preparing poly-

mer-inorganic hybrids.[5] Therefore, we

suppose that unusually strong influence of


low POSS loading on dynamics may be

treated also as a consequence of more long-

range impact of rigid 3D nanoparticles

within the densely cross-linked PCN matrix

than in linear or loosely cross-linked

matrices.

Thus, under the optimal conditions the

nanocomposites studied behave, to a cer-

tain extent, as ‘‘interphase controlled

materials’’ containing mainly the nanodo-

mains with exclusively strongly (directly at

interfaces, glass transition at �370–3908C)

and substantially suppressed dynamics

(main glass transition at � 260–2808C).

[1] Chemistry and Technology of Cyanate Ester Resins, I.

Hamerton, Ed., Chapman & Hall Glasgow 1994.

[2] Thermostable Polycyanurates. Synthesis, Modifi-

cation, Structure and Properties, A. Fainleib, Ed., Nova

Sci. Publ., New York, 2010.

[3] G. Seminovych, A. Fainleib, E. Slinchenko,

A. Brovko, L. Sergeeva, V. Dubkova, React. Funct.

Polym. 1999, 40, 281.

[4] V. A. Bershtein, A. M. Fainleib, P. N. Yakushev, In

Thermostable Polycyanurates. Synthesis, Modification,

Structure and Properties, A. Fainleib, Ed., Chapter 7

Nova Sci. Publ., New York 2010, pp. 195–245.


Macromol. Symp. 2012, 316, 90–9696

[5] K. Pielichowski, J. Njuguna, B. Janowski,

J. Pielichowski. Adv. Polym. Sci. 2006, 201, 225.

[6] S. H. Phillips, T. S. Haddad, S. J. Tomczak, Current

Opinion in Solid State and Mater. Sci. 2004, 8, 21.

[7] M. Sanchez-Soto, S. Illescas, H. Milliman, D. A.

Schiraldi, A. Arostegui, Macromol. Mater. and Eng.

2010, 295, 846.

[8] J. K. Kim, K. H. Yoon, D. S. Bang, Y.-B. Park, H.-U.

Kim, Y.-H. Bang, J. Appl. Polym. Sci. 2008, 107, 272.

[9] T. F. Baumann, T. V. Jones, T. Wilson, A. P. Saab, R. S.

J. Polym. Sci. Part A: Polym. Chem. 2009, 47, 2589.


[10] K. Liang, H. Toghiani, G. Li, Jr., C. U. Pittman,

J. Polym. Sci., Part A : Polym. Chem. 2005, 43, 3887.

[11] K. Liang, G. Li, H. Toghiani, J. H. Koo, Jr. Chem.

Mater. 2006, 18, 301.

[12] V. A. Bershtein, P. N. Yakushev, Adv. Polym. Sci.

2010, 230, 73.

[13] E. P. Giannelis, R. Krishnamoorti, E. Manias, Adv.

Polym. Sci. 1999, 138, 107.

[14] V. A. Bershtein, L. V. Karabanova, T. E. Sukhanova,

P. N. Yakushev, L. M. Egorova, E. Lutsyk, A. V. Svyatyna,

M. E. Vylegzhanina, Polymer 2008, 49, 836.



1 Ph

sit

E-2 Re

So

Cop

Supramolecular Hydrogels Based on Silver Mercaptide.

Self-Organization and Practical Application

Pavel Pakhomov,*1,2 Svetlana Khizhnyak,1 Maxim Ovchinnikov,2 Pavel Komarov1

Summary: A novel supramolecular thixotropic hydrogel based on low-concentrated

solutions of L-cysteine and silver nitrate is synthesized. Self-organization and

gelation in the system are studied experimentally by means of UV-vis and FTIR

spectroscopy, dynamic light scattering, rotational viscometry, transmission electron

microscopy, as well as theoretically by quantum mechanics and molecular dynamics.

A mechanism of the formation of the supramolecular hydrogel is suggested,

potential application for medicinal purposes is considered.

Keywords: cluster; fractal; gel-network; hydrogel; L-cysteine; self-organization; silver

nitrate; supramolecular

Introduction

Problem of simultaneous organization of

polymolecular structures in solutions is

very important for interpreting the forma-

tion of many physico-chemical and biolo-

gical objects such as clusters, micelles,

liposomes, polyelectrolyte complexes and

supramolecular ensembles.[1,2] Special

interest is focused on the solutions having

ability to gelation at very low concentra-

tions of the dispersed phase. In the nature

such systems are extremely rare and attract

great attention. Authors have discovered

a novel supramolecular system based

on aqueous solutions of the amino acid

L-cysteine and silver nitrate, which is able

to form thixotropic hydrogels at low

concentrations of the initial components

(�0.01%).[3,4] Moreover, the L-cysteine

hydrogel is a unique modeling system to

study the processes of self-organization and

gelation in nanostructured aqueous solu-

tions of low molecular weight compounds,

though cysteine is used to capping the silver

and gold colloidal particles and the self-

ysical Chemistry Department, Tver State Univer-

y, Sadovy per. 35, 170002 Tver, Russia


search Centre, Tver State Medicinal Academy,

vetskaya 4, 170642 Tver, Russia


assembly of the nanoparticles is investi-

gated.[5,6] Practical importance of the novel

gel-system consisting of the biologically

active components is connected with an

opportunity to apply it as a matrix for

producing highly efficient pharmaceutical

formulations.

Samples and Technique

Chemicals. L-cysteine (‘‘Across’’, 99%),

AgNO3 («Lancaster», 99%) and Na2SO4

(analytical grade) were used as received,

cysteine-silver solutions (CSS) and hydro-

gels were prepared as described in.[7,8]

Figure 1 demonstrates preparation of

the hydrogels from aqueous solutions of

L-cysteine and AgNO3.

It is seen that pouring together of the

two aqueous solutions leads to the forma-

tion of the turbid sample (Figure 1a), which

allowed to stand becomes transparent and

slightly yellow colored, so called aging

(Figure 1b). Various substances, for exam-

ple, an electrolyte added to the aged

CSS can initiate gelation. The hydrogel

obtained is stable in an overturned test

tube. Rheological studies of the hydrogels

were performed on a Carry-Med rotational

viscometer between two plates at a

fixed oscillation regime (1Hz). To avoid


Figure 1.

Preparation of the L-cysteine based hydrogel: (a) L-cysteine-silver solution immediately after mixing of the

initial components, (b) the CSS after aging, (c) the gel after addition of an electrolyte (Na2SO4) to the aged CSS.

20

40

60

80

G',

Pa

Macromol. Symp. 2012, 316, 97–10798

evaporation the sample was covered by

paraffin oil. The FTIR spectra of the

samples were recorded on ‘‘Equinox 55’’

(‘‘Bruker’’) spectrometer. Hydrogel sample

for the spectroscopic measurement was

dried by liquid nitrogen and pressed with

KBr into a pellet. UV-vis spectra were

recorded on a ‘‘Specord M-40’’ spectro-

photometer (‘‘Carl Zeiss’’), with a thick-

ness of the quartz cuvettes of 2 and 10 mm.

Transmission electron microscopy mea-

surements were performed on a LEO 912

AB OMEGA (‘‘Carl Zeiss’’) instrument. The

samples for TEM studies were placed on a

standard copper grid with a polymer

substrate from poly(vinyl formal) with a

thickness of about 100 nm. Aggregation of

the clusters formed in the CSS solutions was

studied by dynamic light scattering (DLS)

on an instrument with Al-Sp 81 goniometer,

digital photon correlator ALV-5000, the

light source He-Ne laser (632.8 nm), power

36 mW; scattering angle was 908. Before the

DLS measurements the samples were

centrifuged for 20 minutes at a rate of

10000 rpm. The distribution of aggregates

over the diffusion coefficient was deter-

mined as described in.[9,10] The antibacter-

ial properties of the L-cysteine based

solutions and hydrogels were studied in

accordance with.[7]

4030201000

t, h

Figure 2.

Storage modulus G’ as a function of time at 258C,

an oscillation frequency 1 Hz; concentration of

L-cysteine, AgNO3, Na2SO4–3.0, 3.75, 0.4 mM, respect-

ively.


The main feature of the L-cysteine based

hydrogels is thixotropy, they can easily be

destroyed due to vigorous shaking and


recovered being left for a while. Figure 2

shows a result of rheological investigation

of a freshly prepared gel sample at a fixed

oscillation frequency. It is seen from the

figure that the storage modulus of the gel

system grows very slowly with a time,

but after a certain critical value of t (ca.

30 hours) a sharp increase and a drop in the

modulus value occur. Keeping of the

sample at the weakly oscillating mode leads

to the next dramatic increase and drop in

G’. Such rheological behavior is character-

istic of thixotropic systems.[11] It is assumed

that after the addition of the electrolyte to

the CSS, a three-dimensional network is

formed. However, the gel-network is weak

due to non-covalent interactions between

structural units of the dispersed phase. It

should be noted that rheological investiga-

tions of the L-cysteine based hydrogels is


Table 1.Degree of a sample’s deformation

Points Degree of deformation

5 The gel sample is kept practicallyundestroyed after overturn of thetest tube

4 The gel sample deforms strongly andforms a cupola-like meniscus, but doesnot flow down

3 The gel sample is deformed and fallsdown slowly

2 The gel sample falls down1 The gel is very weak and falls down easily0 The gel is not formed

Macromol. Symp. 2012, 316, 97–107 99

rather difficult because of mechanical stress

leads to its destruction.

In order to estimate the stability and

hardness of the L-cysteine based hydrogels

after addition of various electrolytes at

different concentrations of the initial com-

ponents, a five point scale was used.[7] This

scale was developed to describe different

complex processes, for example, magni-

tudes of earthquakes, wind force. In our

case the main idea of this approach is the

following: the test tube with a gel sample is

overturned rapidly and degree of deforma-

tion of the sample under the action of its

own weight is estimated by appropriate

points according to the Table 1.

This approach demonstrated in Figure 3

is very effective to get information on the

concentration ranges of all components of

the system for the preparation of the most

stable hydrogels. The optimal concentra-

tion of the electrolyte (Na2SO4) during

gelation is nearly one order lower than the

0,50,40,30,20,1

1

2

3

4

5

Deg

ree

of d

efor

mat

ion,

poi

nts

CAgNO3, mM

a)

Figure 3.

Gel hardness as a function of (a) Na2SO4 content and (b)

L-cysteine are 3.85 and 3.08 mM, respectively; (b) the c

0.25 mM, respectively.


concentrations of L-cysteine and AgNO3

(Figure 3a) and the optimal concentration

of AgNO3 is somewhat higher than the

concentration of L-cysteine (Figure 3b).

To characterize self-organization and

mechanism of gelation in the L-cysteine

based systems various techniques are

applied.

FTIR Spectroscopy has shown that

immediately after mixing of the aqueous

solutions of L-cysteine and AgNO3 silver

mercaptide (SM) is formed according to the

following reaction:[3]

HS� CH2CHðNH2ÞCOOHþAgþ

! AgS� CH2CHðNH2ÞCOOHþHþ:

The absorption band of the stretching

vibrations of the thiol groups, n(SH), at

2544 cm�1 is observed in the spectrum of

cysteine powder (Figure 4, curve 1), but

disappears in the gel spectrum (curve 2).

Moreover, the pH of the initial L-cysteine

solution (3mM) is about 5.1, after addition

of silver nitrate pH decreases till 2.5. Thus,

the formation of SM molecules in CSS

explains its turbidity after mixing

(Figure 1a). However, the solution gradu-

ally becomes transparent (Figure 1b) and

the very transparent solution is a precursor

of gelation.

UV-Vis Spectroscopic Studies of the

cysteine–silver solutions at various concen-

trations and molar ratio of the components

have shown (Figure 5) that the aging

process, which corresponds to transition

4,34,24,14,03,93,83,7

1

2

3

4

5

Deg

ree

of d

efor

mat

ion,

poi

nts

CNa2SO4, mM

b)

AgNO3 content. (a) The concentrations of AgNO3 and

oncentrations of L-cysteine and Na2SO4 are 3.02 and


20002250250027503000325035003750Wavenumber cm-1

0.1

0.2

0.3

0.4

0.5

0.6

Abs

orba

nce

Uni

ts

νSH 2544 сm-1

2

1

Figure 4.

FTIR spectra of (1) L-cysteine powder and (2) gel sample dried by liquid nitrogen.

Macromol. Symp. 2012, 316, 97–107100

of the solution from turbid to transparent

state, is accompanied by the appearance

and further growth of the absorption bands

at 310 and 390 nm. It is obvious from the

Figure 5 that immediately after mixing of

the initial components there is no any

absorption bands in the spectrum (curve –

0 min). It is found out that the both

absorption bands can be detected in the

spectra some minutes late and rate of their

growth depends on concentrations and

molar ratio of L-cysteine and AgNO3 and

in a great scale on temperature. The aging

4003503000,0

0,4

0,8

1,2

A

λ, nm

0 min 30 min 60 min 90 min 120 min

Figure 5.

UV-vis spectra of cysteine–silver solution as a func-

tion of time at T¼ 258C.


of CSS occurs in the definite temperature

range of 10–458C and lasts from several

minutes at high temperatures to several

hours at low. Another required condition

for the successful aging of the CSS is excess

of silver nitrate. The hydrogels can be

obtained, if content of silver ions 1.2–1.5

times greater than the amount of L-cysteine

molecules.

On the basis of these data, it is assumed

that the two absorption bands (310 and

390 nm) associated with the charge transfer

from donor sulfur atoms to acceptor silver

atoms correspond to the formation of

supramolecular oligomeric chains consist-

ing of SM molecules of the following types:

� � �Ag� SR � � �Ag� SR � � �Ag� SR � � � ;

� � �Ag� SR � � �Agþ � � � SR�Ag � � � ;

where R¼CH2CH(NH2)COOH. The for-

mation of the oligomeric chains from SM

molecules in CSS was mentioned in.[12] In

fact, a SM molecule in aqueous solution is

in zwitterionic form [HS-CH2-CH(NHþ3 )-

COO�], that is a dipole with oppositely

charged ends.[13] Due to the electrostatic

interaction of these dipoles, supramolecu-

lar oligomeric chains are formed in the CSS

and, moreover, they are associated via the


SAg

RSAg

RSR

Ag AgR

S AgR

S Ag SR

........

S RAg

........

........SAg

R

S RAg

........

........SAg

R

S AgR

........

........

S RAg........SAg

R S AgR

SR

Ag SR

Ag................S R

Ag........SAg

R

................

........Ag+........ ........ ........ ........ ........ ........Ag+........

Ag+

........Ag+........

Ag+

........Ag+........ ........ ........ ........

Ag+

........

Figure 7.

Schematic presentation of the fractal cluster.

Macromol. Symp. 2012, 316, 97–107 101

excess silver ions. It is found out that

dilution of the CSS leads to decreasing of

the absorption of the bands (310 and

390 nm) that is an evidence of dissociation

of the linked oligomeric chains. Thus, the

band 390 nm in UV-vis spectra of the aged

solutions cannot be directly related to the

plasmon resonance in silver nanoparticles,

because of, as was shown in,[14] silver

nanoparticles are absent in CSS and CSS-

based hydrogels, and the plasmon reso-

nance peak in silver nanoparticles is

observed at 400 nm or above, depending

on their shape and size.[15–18]

DLS, which is a powerful tool to

investigate self-organization phenomena,

has shown that CSS is composed of

aggregates of various sizes including nuclei

(1–2 nm) and clusters (Figure 6). With an

increase of the CSS aging time, the

dimensions of the aggregates are grown

significantly. It is important to remark that

the clusters formed from SM molecules

have most likely fractal (branched) struc-

ture, because only in this case small amount

of the dissolved substance (�0.01%) is able

to the gel formation.[19–20] Schematic pre-

sentation of the fractal cluster is given in

Figure 7.

These suggestions have been confirmed

by TEM study of the L-cysteine based

solutions and gels. Figure 8 depicts electron

micrographs of the solutions obtained at

various concentrations of the components

and the hydrogel induced by addition of the

a)

1010,10,0

0,4

0,8

D, µm2/s

W(D) 389 nm73 nm

12 nm

1 nm

Figure 6.

Diffusion coefficient distribution for cysteine–AgNO3 solu

concentrations of L-cysteine and AgNO3 are 2.7 and 3.3


salt at various magnifications. Clusters

appeared in the cysteine–silver solutions

immediately after mixing of the initial

components according to DLS data can

be formed at very low concentrations. In

the case of low concentrations of the

dispersed phase (highly diluted solutions)

only separated chains consisting of the

clusters (dark dots distinguished on the

electron images) are observed in CS

solution (Figure 8a), at higher concentra-

tions the spatial network is formed and sizes

of the clusters are enlarged (Figure 8b).

We have found that density of the three-

dimensional network depends on the

concentrations of the components in the

samples.

Such CSS network structures can parti-

cipate in further self-assembling and form

continuous three-dimensional network, if

b)

1010,10,0

0,4

0,8

D, µm2/s

W(D) 644 nm

89 nm

18 nm

2 nm

tion at different time of aging: a – 30, b – 122 min. The

mM, respectively.


Figure 8.

Electron micrographs of (a–b) CSS a – Ccys¼ 0,3 mM, CAgNO3¼ 0,375 mM; b –Ccys¼ 0,75 mM,

CAgNO3¼ 0,9375 mM; (c–d) hydrogel at different magnifications, Ccys¼ 0,75 mM, CAgNO3¼ 0,9375 mM;

CNa2SO4¼ 0,375 mM.

Macromol. Symp. 2012, 316, 97–107102

an initiator of the gelation is added to the

system. It is obvious from the Figure 8c that

Na2SO4 induces the association of the

cluster chains and the formation of fibrillar

structures. Sulfate-anions link the posi-

tively charged oligomeric chains composed

of SM molecules[21] or clusters acting as

stickers and thus forming the three-dimen-

sional gel network (Figure 8d). It is

established that depending on the type of

the electrolyte used, the character of the

three-dimensional network of the gel

is varied significantly.[14] For example,

Figure 8d shows the image of the nanofi-

ber-like network induced by Na2SO4.

On the basis of all experimental results

processes of aggregation and self-organiza-

tion in the CSS and hydrogel were studied

also theoretically by quantum mechanics[22]

and molecular dynamics.[23]


We constructed the full-atom model of

the solution with explicit account of both

the solvent molecules and Agþ, NO�3 , Naþ,

SO2�4 and H3Oþ low molecular weight ions

taking into consideration the CSS composi-

tion. The SM was considered in the

zwitterionic form with dissociated carboxyl

and protonated amino groups. In our model

sulfur-silver interactions were explicitly

taken into account. To calculate the intra-

an intermolecular forces, the total potential

in the functional representation employed

in AMBER force field (FF) was used.[24]

The values of some force constants which is

absent in AMBER force field in case Agþ,

NO�3 , SO2�4 ions was taken from PCFF.[25]

All other force constants missing in

AMBER FF were calculated using

semi-empirical molecular orbital method

ZINDO/1.[26] All simulations were per-


Macromol. Symp. 2012, 316, 97–107 103

formed with using DL POLY 2.20 soft-

ware.[27]

Three different types of initial state (IS)

models, i.e., (1) chaotic (disordered), (2)

cluster, and (3) filament-like one row of SM

molecules, were used to study the gelation

in CSS. These states correspond presum-

ably to different experimental phases of

CSS self-organization i.e., to the comple-

tion of the formation of SM molecules, the

phase of solution aging, and gel-like state.

To build models of CSS we use the cubic

simulation box with the edge L¼ 53 A. The

total number, N, of silver mercaptide

particles is taken 15. The number of silver

nitrate molecules is 20. Numbers of low-

molecular ions were taken on the basis of

concentration ratios at which the gel is

formed from CSS. In the case of the

selected cell size and the number of silver

mercaptide particles the number of Agþ is

5, NO�3 – 20, Naþ – 2, SO2�4 –1 and H3Oþ –

15. 4662 water molecules were placed into

the cell so that the total density of substance

was equal to �1.1 g/cm3. For each of first

two types of IS (chaotics and clusters), three

statistically independent systems and, for

the IS of the third type (filament-like), six

systems were generated to exclude the

influence of initial configuration on the final

state. The primary relaxation of prepared

models of the CSS solution were performed

under conditions of NVE ensemble at

T¼ 300 K for 100 ps. In this case, the

velocities of molecules were renormalized

at each step of the calculations. Then, we

studied the evolution of the CSS model

under the conditions of an NVT ensemble

over 5 ns for the disordered and cluster

initial states and over 10 ns in the case of

filament-like ISs. Coordinates of atoms that

form all subsystems of the model were

stored in trajectory files with intervals of

100 ps for the subsequent visual analysis of

the evolution of the solution.

In the final states of the prepared

systems (when the total energy of systems

remains nearly unchanged), aggregates

with elongated and branched shapes are

observed, see examples of instantaneous

states in Figure 10 (a, b). Visual analysis


demonstrates that the mutual ordering of

SM particles in aggregates, which are

formed due to the evolution of chaotic

ISs, are similar to the ordering of SMs

arising as a result of the evolution of cluster

ISs. As a rule, two types of structures are

formed, i.e., clusters in which silver and

sulfur atoms form compact nuclei, and

band-shaped aggregates, in which neigh-

boring SM particles are bonded by virtue of

interaction of their dissociated carboxyl

and protonated amino groups, as well as

sulfur–silver bonds.

The study of the evolution of filament-like

initial states (which, presumably, should

correspond to the final state of CSS model)

showed that, out of six prepared systems,

three aggregates retained their initial order-

ing (examples are given in Figure 9, c and d);

one aggregate was transformed into an

aggregate with a thin neck composed of

low-molecular-weight ions (Figure 9e); and

two remaining aggregates were ruptured over

1 and 1.8 ns to form elongated aggregates,

whose structure remained almost unchanged

during further simulation (Figure 9f).

The analysis of trajectory files makes it

possible to monitor the step-by-step evolu-

tion of filament-like aggregates with time.

The decomposition of two (out of six)

prepared aggregates proceeds according to

the identical scheme. Cations and SM

zwitterions are gradually drawn together

into compact elongated groups connected

by the neck composed of low-molecular-

weight ions, which gradually ruptured due

to thermal motion. The final state

(Figure 9e) is characterized by the neck

composed of ions, which was formed in

filament-like aggregate prior to its rupture.

Thus, we can conclude that, although

filament-like aggregates are stabilized by

sulfur–silver interactions, which are expli-

citly taken into account, chains composed

of one row of SM molecules (N¼ 15) are

generally unstable. In other words, it is

possible that aggregates that retain their

filament-like state can be spontaneously

ruptured over a long period of time.

An analysis of the internal structure of

aggregates formed due to evolution from


Figure 10.

Characteristic forms of filament-like aggregates: (a) magnified instantaneous photomicrograph of molecular

aggregate (SM molecules, H3Oþ, Agþ, and Naþ ions are shown); (b) the model representation of filaments

composed of SM clusters linked by hydrogen bonds between (1) and –C(O)O� functional groups and (2) ionic

cross-links.

Figure 9.

Final states of systems which (a) did not have initial ordering, (b) contained the group of clusters in the initial

state, and (c) – (f) are characterized by filament-like ordering. Water molecules are not presented in the figure for

clearness. N¼ 15, T¼ 300 K.

Copyright � 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.ms-journal.de

Macromol. Symp. 2012, 316, 97–107104

Macromol. Symp. 2012, 316, 97–107 105

the initial disordered state, cluster state,

and after the rupture of filament-like state

demonstrates that SM molecules form

cluster structures due to numerous adjacent

sulfur–silver bonds and bonds between –

NHþ3 and –C(O)O� groups (Figure 10a).

The scheme of the structure of the formed

chains of clusters is shown in Figure 10b.

These chains represent a supramolecular

chain aggregates formed by clusters of SM

particles, which are linked by the adjacent

bonds formed between neighbor clusters

with the participation of (I) dissociated

carboxyl and protonated amino groups and

(II) low-molecular-weight ions coordinated

with –NHþ3 and –C(O)O� groups. Due to

the fact that –NHþ3 and –C(O)O� func-

tional groups are located primarily on the

surface of the aggregate, both chain and

branched structures can be formed in the

bulk of solution.

Because of the centers of clusters

formed by SM contain silver atoms

(Figure 10a), it can be assumed that the

filaments of the gel network (in real CSS)

can have a similar structure. Indeed, the

black dots on the electron micrographs

(Figure 8) are silver nanoparticles and

silver sulfide crystals, which emerged under

the action of the electron beam. The latter

event can occur, if SM particles are grouped

into the filaments of the gel network so that

silver atoms that comprise filaments form

compact structures. The presence of

absorption band at 390 nm in CSS confirms

this hypothesis because its appearance can

be associated with the presence of compact

clusters of silver atoms.[28]

Structures analogous to that shown in

Figure 9f (their average diameter is 16A)

demonstrate the tendency internal rearran-

gement over the long period of time. The

concentration of SM molecules in the unit

volume of such aggregates is two-fold

higher than that of filament-like aggregates

shown in Figure 9 (c and d). This analysis

suggests that aggregates constructed using a

doubled amount of SM molecules will be

stable. To verify this hypothesis, we con-

structed aggregates based on two parallel

chains composed of SM molecules. The


total number of zwitterions and SM cations,

N, is equal to 30 and; the size of simulation

cell L¼ 53 A. Four new variants of the

mutual ordering of SM molecules were

generated for performing calculations.

According to the completed simulation,

all constructed aggregates are stable at

the achieved simulation times 20 ns. An

increase in the temperature of the ensemble

above 340 K resulted in the fairly fast (for

2–3 ns) gradual rupture of filaments to form

several disordered clusters. The average

diameter of these filaments in the final state

is approximately 15.5 A, i.e., it corresponds

to the largest diameter of aggregates in

Figures 8 (a, b, and f). In the final state, all

filament-like aggregates compose of the

chain of clusters formed by SM particles,

which are connected to one another via the

interaction between –NHþ3 and –C(O)O�

groups of SM particles that belong to

neighboring clusters (Figure 9b, variant I

of clusters interaction). These clusters, in

turn, are formed due to noncovalent

interactions between sulfur and silver

atoms of neighboring silver mercaptide

zwitterions. A similar principle of self-

assembly at the expense of amino and

carboxyl groups was also described for

other systems[29] that evidences about the

universal character of the observed

mechanism of self-organization in CSS.

Thus, the theoretical investigations have

shown that the system involved show a

tendency toward self-assembling and the

formation of threadlike structures and

three-dimensional networks.

It should be remarked that the CSS and

hydrogels are attractive objects not only for

the study of mechanism of self-assembling

and gelation in diluted solutions, but also

for their potential applications. Its practical

importance is connected with an opportu-

nity to apply these systems consisting of

biologically active components as a matrix

for producing highly efficient pharmaceu-

tical formulations. In experiments it is

established that the matrix itself has

possessed not only antimicrobial proper-

ties, but has stimulated the cell division.

The data on the antibacterial activity of the


Table 2.Antibacterial activity of the CSS (numerator) and the hydrogel (denominator) at different dilution

Test cultures Antibacterial activity of CSS/hydrogel samples at various dilution

1: 10 1: 20 1: 50 1: 100

Bacillus cereus þ/� þ/þ þ/þ þ/þBacillus subtillis þ/� þ/þ þ/þ þ/þEscherichia coli �/� þ/þ þ/þ þ/þSalmonella abony �/� �/� þ/� þ/�Pseudomonas aeruginosa �/� �/� þ/þ þ/þStaphylococcus aureus þ/� þ/þ þ/þ þ/þ

Note: The plus sign denotes the growth of bacteria in a nutritive environment; the minus sign, the absence ofsuch growth.

Macromol. Symp. 2012, 316, 97–107106

L-cysteine based solutions and hydrogels

are given in the Table 2. It is seen that even

after ten-fold dilution, the hydrogel inhibits

all the tested bacteria and has a more

pronounced effect than that of the CSS.

Additional introducing of the biologically

active compounds (medications, liposomes,

micelles[7]) or water soluble polymers

(PVA, poly(acrylic acid), poly(ethylene

oxide), poly(vinylpyrrolidone) into the

systems will increase their efficiency. Appli-

cation of the novel pharmaceutical pro-

ducts is particular perspective in the treat-

ment of patients with radiation injuries,

burns and wounds, because of ionizing

radiation mostly damages the cells during

division cycle.

Conclusion

Complex investigations including experi-

mental (FTIR and UV-vis spectroscopy,

DLS, TEM, rheometry) and theoretical

(quantum mechanics and molecular

dynamics) allowed us to elucidate the ability

to self-organization and gelation at low

content of the dispersed phase (<0.01%)

in supramolecular systems based on L-

cysteine and silver ions. Such nanostructured

systems containing the amino acid and silver

ions and compatible with many bioactive

substances can serve as a matrix of pharma-

ceutical preparations for treatment of radia-

tion injuries, burns and wounds.

Acknowledgements: We are grateful to S.S.Abramchuk (Moscow State University) for


providing us with electron micrographs of CSSand hydrogels and V.M. Chervinetz (Tver StateMedical Academy) for studies of antibacterialactivity of the samples. We thank the ResearchComputer Center at Moscow State Universityfor providing computational resources of the«Lomonosov» cluster to perform time-consum-ing computations.

This work was financially supported by thespecial federal program ‘‘Development of theScientific Potential of the Higher School for2009–2011’’, grant no. 2.1.1.10767.

[1] J.-M. Lehn, ‘‘Supramolecular Chemistry. Concepts

and Perspectives’’, VCH, New York 1995.

[2] A. Ciferri, ‘‘Supramolecular Polymers’’, Dekker, N.Y

2000.

[3] P. M. Pakhomov, M. M. Ovchinnikov, S. D. Khizh-

nyak, M. V. Lavrienko, W. Nierling, M. D. Lechner,

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[4] M. M. Ovchinnikov, S. D. Khizhnyak, M. V. Lav-

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Journal of Physical Chemistry, 2005, 79 (Suppl 1), S51.

[5] S. Mandal, A. Gole, N. Lala, R. Gonnade, etc.,

Langmuir, 2001, 17, 6262.

[6] K. M. Mayya, A. Gole, N. Jain, S. Phadtare,

D. Langevin, etc., Langmuir, 2003, 19, 9147.

[7] M. M. Ovchinnikov, P. M. Pakhomov, S. D. Khizh-

nyak, Patent (Russia), 2008, N. 2317305.

[8] P. M. Pakhomov, M. M. Ovchinnikov, S. D. Khizh-

nyak, O. A. Roshchina, P. V. Komarov, Polymer Science

(Russia), Ser. A, 2011, 53, 820.

[9] S. Provencher, Comput. Phys. Commun., 1992, 27,

213.

[10] W. Burchard, Macromol. Symp., 1996, 101, 103.

[11] G. Schramm, ‘‘A Practical Approach to Rheology and

Rheometry’’, Haake, Karlsruhe 1994.

[12] L. O. Andersson, J. Polym. Sci., Part A1, 1972, 10,

1963.

[13] P. V. Komarov, I. P. Sannikov, S. D. Khizhnyak,

M. M. Ovchinnikov, P. M. Pakhomov, Nanotechnologies

in Russia, 2008, 3, 716.


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[14] P. M. Pakhomov, S. S. Abramchuk, S. D. Khizhnyak,

M. M. Ovchinnikov, V. M. Spiridonova, Nanotechnol-

ogies in Russia, 2010, 5, 209.

[15] Y. Sun, Y. Xia, Analyst, 2003, 128, 686.

[16] Q. Wang, H. Yu, L. Zhong, et al., Chem. Mater.,

2006, 18, 1988.

[17] Y. M. Mohan, Th. Premkumar, K. Lee, K. E. Gecke-

ler, Macromol. Rapid Commun., 2006, 27, 1346.

[18] P. Billaud, J. R. Hautzinger, E. Cottancin, et al., Eur.

Phys. J., D, 2007, 43, 271.

[19] B. M. Smirnov, ‘‘Physics of fractal clusters’’,

Nauka, M., 1991.

[20] B. M. Smirnov, ‘‘Advances in physical sciences’’,

1992, 162, 43.

[21] M. M. Ovchinnikov, S. D. Khizhnyak, P. M. Pakho-

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[22] P. V. Komarov, V. G. Alekseev, S. D. Khizhnyak,

M. M. Ovchinnikov, P. M. Pakhomov, Nanotechnologies

in Russia, 2010, 5, 165.

[23] P. V. Komarov, I. V. Mikhailov, V. G. Alekseev, S. D.

Khizhnyak, P. M. Pakhomov, Colloid Journal (Russia),

2011, 73, 482.

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Chem. Soc., 1995, 117, 5179.

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[29] A. Yu. Men’shikova, Nanotechnologies in Russia,

2010, 5, 52.



1 D

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Comparative Study of the Quantity of Volatile

Organic Compounds in Water-Based Paint and

Solvent-Based Applied Polyurethane

Ailton R. da Conceicao,*1,2 Ednilson A. R. Pimenta,1,2 Ronaldo S. Fujisawa,1,2

Evandro L. Nohara1

Summary: The concern about the environmental impacts generated in the production

of goods and services has increased last decades. The industry has used paints and

varnishes in the manufacturing process have been pressed to improve air pollution

prevention. Thus, the present work aims to identify the quantitative differences of

VOC’s and analyze the effect of VOC’s in the burning rate, in a solvent and water-based

paint, applied in the manufacture of automotive steering wheels. The results has

showed that the solvent-based paint contains nine times more VOC’s in your

formulation in relation to water-based paint, when compared liquid and volatile

organic compounds present in the solvent-based paint increase the speed of combus-

tion of the polyurethanes samples. These data indicate that a discussion on the subject

must be initiated in order to reduce these emissions that can harm society.

Keywords: combustibility; paint; polyurethane; volatile organic compound

Introduction

PUs are produced by the polycondensation

of an isocyanate reaction with a polyol

(several functions polymers with terminal

hydroxyl groups) and other reagents such

as: healing agents or chain extensors,

containing two or more reactive groups:

catalysts; expansion agents; surfactants and

loads.[1] Many of the additives change and

interfere the essential properties of fire

formation, as heat, fuel and oxygen.[2]

According to research about polymeric

materials combustion it is defined as physics

and chemical reactions in which the sub-

stances react with the oxygen releasing heat

and producing water and carbon dioxide.

Usually in the polyurethane steering-

wheels production it is applied the ‘‘in mold

coating’’ process of painting which consists in

epartamento de Engenharia Mecanica, Universi-

de de Taubate – UNITAU, Rua Daniel Danelli

, Jardim Morumbi, Taubate- SP


utoliv do Brasil Ltda – Av. Roberto Bertoletti,

551, Taubate – SP


placing the paint over the mold surface that

is transferred to the part through a heat

transfer. The paints used are liquid, viscous,

consisting of one or more pigments dispersed

in a liquid binder which forms an opaque film

and adherent to the substrate when suffering

a healing process to an extended thin film.[5]

In a way the paints typically have volatile

organic compounds, also known by the

acronym VOC (Volatile Organic Com-

pound). The hydrocarbons of low molecular

weight are also important pollutants from

burning fossil fuel. These compounds are

known as volatile organic compounds

(VOC’s).[6] The VOC is defined by the

standard ASTM D 3960,[7] ‘‘Standard Practice

for Determining Volatile Organic Compound

(VOC) Content of Paints and Related Coat-

ings, ’’as any compound of carbon that joins in

atmospheric photochemical reactions.[8]

The term volatile organic compound is

used to describe materials in the organic

phase excluding steam methane.[9] Manu-

facturers of coatings (including paints) are

part of a strategy to reduce emissions of

VOC’s in many countries. Some alterna-


Macromol. Symp. 2012, 316, 108–111 109

tives are high solids coatings, water-based

paints to replace solvents, powder paints

and healing with UV radiation.

Because of this, several technologies are

being successfully adopted, as the formula-

tion of products with less odor and no VOC,

or even exempt from this type of issue.

The effects of volatile organic compounds

(VOC’s) to the environment have motivated

this research which achieves to develop a

new water-based paint for application in the

manufacture of automotive steering-wheels,

comparing the VOC results and combust-

ibility of the current paint, based on solvents

with water-based paint.

Experimental Part

For the manufacture of the samples we used

polyurethane obtained from the reaction of

polyol (OH group) and isocyanate (NCO

group). In the process of painting the

wheels which was done at room tempera-

ture, we used two types of paint: 1 - water-

based paint (single component), 2 – sol-

vents-based paint (toluene and xylene)

composed of three components with the

following ratio: 1000 g of paint, 150 g of

catalyst and 1200 g of diluents.

The paint was manually applied by

conventional spray to 708C preheated mold

in which the paint was transferred from the

mold surface to the part through heat transfer.

VOC Test in the Paint

The VOC test is to determine the amount of

volatile organic compoundsfound in the

paint. The method used was based on

ASTM D3960.[7]

Calculation of VOC in the Paints

For solvent-based paint, the VOC is

calculated according to Equation 1:

VOC ¼ ð100� SpÞ �Me� 10 (1)

For water-based paint, the VOC is

calculated according to Equation 2:

VOC ¼ ðA�WÞ �Me� 10 (2)


VOC¼Volatile organic content (g/L) in

paints

Sp¼ solids by weight (%), Me¼ density

of liquid paint (g/cm3), A¼mass of all the

volatile ready paint, including water,

W¼mass of water in 100 g of ready paint,

10¼ factor to convert (%) and (g/cm3) in g/L.

Flammability Test

The flammability test was based on the

CONTRAN 675/86 standard, which con-

sists of burning the material end with a

Bunsen burner. A reference mark was done

on each specimen with a distance of 38 mm

from the edge and a second mark with a

distance of 254 mm from the first stroke.

The specimens were obtained by a poly-

urethane injection in a high-pressure

machine (200 bar), injecting 1 second of

foam into a 500 ml plastic cup and imme-

diately dumping them into the mold with

dimensions of 350 mm X 100 mm X 12 mm

(length x width x thickness). The burning

rate was determined based on the following

types:

– N

, W

on- inflammable (type A): The material

refuses to burn or just go out, after

removing the contact with the Bunsen

burner.

– S
elf-extinguishing (type B): The material
burns and combustion ends just before

the flame has reached the first mark.

– T
ype C: The material stops burning
within 60 seconds and does not burn

more than 50 mm.

– T
ype D: The material burns and the
flame extinguishes between the reference

marks.

– T
ype E (combustible): Combustion con-
tinues until the second mark.

For types D and E, the burning rate is

calculated in mm/min.


The Table 1 presents the VOC measuring

results of solvent-based paints and water-

based paints.


Table 1.Results of tests for VOC paints.

Tests Solvent-based paints Water-based paints

Solids by weight (Sp) 23,14% 31,28%Specific density (Me) 0,950 g/cm3 1,075 g/cm3

Mass of all solvents included water (A) –— 68,72%Water density (W) –— 61,27%VOC 730,2 g/L 80,1 g/L

Macromol. Symp. 2012, 316, 108–111110

The solvent-based paint and the water-

based paint have a density of 0,950 g/cm3

and 1,075 g/cm3, respectively. The highest

density of water-based paint is due to the

it’s higher percentage of solids by weight

(31,28%) compared to solvent-based paint

(23,14%). Manufacturers of water-based

paint typically use percentages of solids

weight in relation to solvent-based paint in

order to obtain the same mechanical

properties or higher compared to solvent-

based paints. Based on values in Table 1,

the VOC value found in the water-based

paint presents a nine fold lower amount

(80,1 g/L), obtained from Equation 2, in

relation to the sample of solvent-based

paint (730,2 g/L), and resulted from

Equation 1. The difference can be seen in

Figure 1.

Figure 1.

Comparison of VOC solvent-based paint and water-bas

Figure 2.

Combustibility test in solvent-based paint.


Figure 2 shows the combustibility test of

three samples of solvent-based paint in which

the samples 1, 2 and 3 showed the same type

of burning D. In this case, the samples

presented their burning rate: sample 1 of

11,95 mm/min, sample 2 of 11,73 mm/min

and sample 3 of 10,35 mm/min.

Figure 3 shows the combustibility test of

three samples of water-based paint, in

which sample 1 was burning type C and

samples 2 and 3 were both a burning type B.

The burning rate in water-based paint

was lower, probably because it has a smaller

amount of solvent in the formulation;

however the amount of solvents found in

the solvent-based paint is 10 times greater

than in the water-based paint, which did

not show the same proportionality in the

increase of the burning rate. It was then

ed paint.


Figure 3.

Combustibility test in water-based paint.

Macromol. Symp. 2012, 316, 108–111 111

observed that the flame in the solvent and

water-based paints samples spread slowly

in the PU substrate, but the samples

of solvent-based paint released a greater

amount of gas (smoke).

Conclusion

The amount of VOC found in the water-

based paint is less than in the solvent-based

paint because the water acts as solvent. The

sample of water-based paint showed 7,45%

of solvents and a VOC of 80,1 g/L, that is,

nine times lower if compared to the sample

of the solvent-based paint, which showed

78,86% of solvents and a VOC of 730,2 g/L.

The solvent-based paint had a higher

burning rate due to the fact of consisting

of a larger quantity of solvents in its

formulation. The presence of solvents in

the solidified paint concerning the PU

samples affects the speed of combustion,


although not in the same proportionality

when compared to the liquid state.

[1] Walter. Vilar, Quımica e tecnologia dos poliuretanos,

3a ed. Rio de Janeiro Vilar Consultoria, 2005, 400 p.

[2] R. C. Trombini, Desenvolvimento e Caracterizacao

de Composicoes Polipropileno/Cargas retardantes de

chamas. p. 233, 2006.

[3] M. S. Rabello, Aditivacao de Polımeros, Sao Paulo

Artliber Editora, p. 242, 2000.

[4] J. M. Davies, Y. C. Wang, P. M. H. Wang, Polymer

Composites in fire. Part A, p. 1131. 2006.

[5] Fazenda, Jorge M.R. (Coord.) Tintas & Vernizes:

Ciencia e Tecnologia. 3a edicao, Sao Paulo, Eggard

Blucher, 2005.

[6] Colin. Baird, Environmental Chemistry. 2a edicao,

New York W.H. Freeman and Company, 1998.

[7] ASTM D 3960 -98 Standard Practice Determining

Volatile Organic Compound (VOC) Content of Paints

and Related Coatings.

[8] T. Helms, W. Johnson, S. Tong, EPA’s photochemi-

cal reactivity policy – overview.

[9] R. M. Harrison, (Ed.). Understanding Our Environ-

ment: An Introduction to Environmental, 2a edicao, The

Royal Society of Chemistry, Inglaterra, 1992.



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Thermal Degradation of Adsorbed Bottle-Brush

Macromolecules: When Do Strong Covalent Bonds

Break Easily?

Jaroslaw Paturej,1,2 Lukasz Kuban,3 Andrey Milchev,1,4 Vakhtang G. Rostiashvili,1

Thomas A. Vilgis1

The scission kinetics of bottle-brush molecules in solution and on an adhesive

substrate is modeled by means of Molecular Dynamics simulation with Langevin

thermostat. Our macromolecules comprise a long flexible polymer backbone with L

segments, consisting of breakable bonds, along with two side chains of length N,

tethered to segments of the backbone with grafting density sg. In agreement with

recent experiments and theoretical predictions, we find that bond cleavage is

significantly enhanced on a strongly attractive substrate even though the chemical

nature of the bonds remains thereby unchanged. Our simulation results indicate

that the mean life time hti of covalent bonds decreases by more than an order of

magnitude upon adsorption even for brush molecules with comparatively short

side chains N ¼ 1� 4. The distribution of scission probability along the bonds of

the backbone is found to change significantly when the length and/or the grafting

density of the side chains are varied. The tension, experienced by the covalent

bonds is found to grow steadily with increasing sg. The mean life time hti declines

with growing contour length L as hti/L�0:17, and also with growing side chain

length N. The probability distribution of fragment lengths at different times is

compatible with experimental observations and reveals a two-stage (initially fast,

then slow) process with different rates. The variation of the mean length L(t) of the

fragments with elapsed time characterizes the thermal degradation process as a

first order reaction.

Keywords: bottle-brush molecules; degradation and stabilization of polymers

Introduction

The study of degradation and stabilization

of polymers is important both from prac-

tical and theoretical viewpoints.[1] Disposal

of plastic wastes has grown rapidly to a

world problem so that increasing environ-

mental concerns have prompted researchers

ax Planck Institute for Polymer Research

ckermannweg 10, 55128 Mainz, Germany

stitute of Physics, University of Szczecin, Wielko-

lska 15, 70451 Szczecin, Poland

estochowa University of Technology, Institute of

ermal Machinery, Armii Krajowej 21, 42200

estochowa, Poland

stitute for Physical Chemistry, Bulgarian Academy

Science, 1113 Sofia, Bulgaria


to investigate plastics recycling by degrada-

tion as an alternative.[2] On the other hand,

degradation of polymers in different envir-

onment is a major limiting factor in their

application. Recently, with the advent of

exploiting biopolymers as functional materi-

als,[3,4] the stability of such materials has

become an issue of primary concern.

Most theoretical investigations of poly-

mer degradation have focused so far on

determining the rate of change of average

molecular weight.[5–14] The main assump-

tions of the theory are that each link in a

long chain molecule has equal tensile

strength and accessibility, that they break

at random, and that the probability of

rupture to happen within certain time


Macromol. Symp. 2012, 316, 112–122 113

interval is proportional to the number of

links present. Experimental studies of

polystyrene, however, have revealed dis-

crepancies[6] with the theory[5] so, for

example, the thermal degradation stops

completely or slows down markedly when a

certain chain length is reached. Only few

theoretic studies[15,16] have recently

explored how does the single polymer chain

dynamics affect the resulting bond rupture

probability. In both studies,[15,16] however,

for the sake of theoretical tractability one

has worked with a model of a Gaussian

chain bonded by linear (harmonic) forces

whereby the anharmonic (non-linear) nature

of the bonding interactions was not taken

into account. One could claim that the

process of thermal degradation still remains

insufficiently studied and understood.

Recently it was found experimen-

tally[17,18,19] that the tension in covalent

bonds may reach orders of magnitude

higher values upon adsorption of brush-

like macromolecules onto a substrate. One

studied brushes consisting of a poly(2-

hydroxyethyl metacrylate) backbone and

a poly(N-butyl acrylate) (PAB) side

chains with degrees of polymerization

L¼ 2150� 100 and N¼ 140� 5, and found

spontaneous rupture of covalent bonds

(which are otherwise hard to break) upon

adsorption of these molecules on mica,

graphite, or water-propanol interfaces.[17]

Indeed, as the densely grafted side chains

adsorb, they experience steric repulsion

due to monomer crowding which creates

tension in the backbone. This tension,

which depends on the grafting density,

the side chain length, and the extent of

substrate attraction, effectively lowers the

energy barrier for dissociation, decreasing

the bond life time.[20] Thus, one may observe

amplification of bond tension from the pico-

newton to nano-newton range which facil-

itates thermal degradation considerably.

Meanwhile, in several works Panyukov

and collaborators[21,22] predicted and the-

oretically described the effect of tension

amplification in branched macromolecules.

They argued that the brush-like architec-

ture allows focusing of the side chain


tension to the backbone whereby at given

temperature T the tension in the backbone

becomes proportional to the length N of the

side chain, f � f0N.[21,22] The maximum

tension in the side chains is f0 � kBT=b with

kB -being the Boltzmann constant, and b -

the Kuhn length (or, the monomer dia-

meter for absolutely flexible chains).

The effect of adsorption-induced bond

scission might have important implication

for surface chemistry, in general, and for

specific applications of new macro- and

supramolecular materials, in particular, for

example, by steering the course of chemical

reactions. One may use adsorption as a

convenient way to exceed the strength of

covalent bonds and invoke irreversible

fracture of macromolecules, holding the

key to making molecular (DNA) architec-

tures that undergo well-defined fragmenta-

tion upon adsorption.

In the present talk we report on our

studies of chain fragmentation in desorbed

and adsorbed bottle-brush macromolecules

by means of a coarse-grained bead-spring

model and Langevin dynamics. In addition

to our initial investigation[23] which was

carried out at maximal grafting density

sg¼ 1.0 we report new simulation results in

which we examine the effect of varying

sg¼ 1.0 on the resulting rupture rate

distribution along the chain backbone. In

Section 2 we describe briefly our model and

then present our simulation results in

Section 3. A summary of our results and

conclusions is presented in Section 4.

Anticipating, one might claim that the

reported results appear in good agreement

with observations and theoretical predic-

tions.

The Model

We consider a 3D coarse-grained model of

a polymer chain which consists of L repea-

table units (monomers) connected by bonds,

whereby each bond of length b is described

by a Morse potential,

UMðrÞ ¼ Df1� exp½�aðr � bÞg2 (1)


Macromol. Symp. 2012, 316, 112–122114

with a parameter a � 1. The dissociation

energy of such bonds is D, measured in units

of kBT, where kB denotes the Boltzmann

constant and T is the temperature. The

maximum restoring force of the Morse

potential, fmax ¼ �dUM=dr ¼ aD=2, is

reached at the inflection point,

r ¼ bþ a�1lnð2Þ. This force fmax determines

the tensile strength of the chain. Since the

bond extension r – b between nearest-

neighbor monomers along the polymer

backbone in our 3D-model is always

positive, the Morse potential Eq. (1) is

only weakly repulsive and segments could

partially penetrate one another at r< b.

Therefore, in order to allow properly for

the excluded volume interactions between

bonded monomers, we take the bond

potential as a sum of UM(r) and the so

called Weeks-Chandler-Anderson (WCA)

potential, UWCA(r), (i.e., the shifted and

truncated repulsive branch of the Lennard-

Jones potential);

UWCAðrÞ

¼ 4"s

r

� �12� s

r

� �6þ 1

4

� �Qð21=6s� rÞÞ

(2)

with Q(x)¼ 0 or 1 for x< 0 or x� 0, and

" ¼ 1. The non-bonded interactions

between monomers are also taken into

account by means of the WCA potential,

Eq. (2). Thus the interactions in our model

correspond to good solvent conditions. The

length scale is set by the parameter s¼ 1

whereby the monomer diameter

b ¼ 21=6s � 1:12s.

In our MD simulation we use a Langevin

equation, which describes the Brownian

motion of a set of interacting particles

whereby the action of the solvent is split

into slowly evolving viscous force and a

rapidly fluctuating stochastic force:

m _v

iðtÞ ¼ �z~vi þ ~Fi

MðtÞ þ ~Fi

WCAðtÞ þ ~RiðtÞ:(3)

The random force which represents the

incessant collisions of the monomers with

the solvent molecules satisfy the fluctua-

tion-dissipation theorem hRigðtÞR

jdðt0Þi ¼

2zkBTdijdgddðt � t0Þ. The friction coefficient


z of the Langevin thermostat, used for

equilibration, has been set at 0.25. The

integration step is 0.002 time units (t.u.) and

time is measured in units offfiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffims2=D

pwhere m denotes the mass of the beads,

m¼ 1. We emphasize at this point that in

our coarse-grained modeling no explicit

solvent particles are included.

Two side chains of length N are grafted

to every s�1g -th repeatable unit of the

backbone (except for the terminal beads

of the polymer backbone where there are

three side chains anchored). In this way

a grafting density sg, which gives the

number of side chain pairs per unit length

is defined. Thus the total number of

monomers in the bottle-brush macro-

molecule is M ¼ Lþ 2N½ðL� 1Þsg þ 2�.Because of the high grafting density, we

use rather short side chains N ¼ 1� 4 in

our simulations - Figure 1.

For the bonded interaction in the side

chains we take the frequently used Kremer-

Grest potential, UKGðrÞ ¼ UWCAðrÞþUFENEðrÞ, with the so-called ‘finitely-exten-

sible non-linear elastic’ (FENE) potential,

UFENEðrÞ ¼ �1

2kr2

0ln 1� r

r0

� �2" #

: (4)

In Eq. (4) k¼ 30, r0¼ 1.5, so that the

total potential UKG(r) has a minimum at

bond length rbond � 0.96. Thus, the bonded

interaction, UKG(r), makes the bonds of the

side chains in our model unbreakable

whereas those of the backbone may and

do undergo scission.

The substrate in the present study is

considered simply as a structureless adsorb-

ing plane, with a Lennard-Jones potential

acting with strength "s in the perpendicular

z–direction, ULJðzÞ ¼ 4"ssz

� �12� s

z

� �6� �

.

In our simulations we consider as a rule

the case of strong adsorption,

"s=kBT ¼ 5:0� 10:0.

The initially created configurations,

Figure 1 (left panel), are equilibrated by

MD for a period of time so that the mean

square displacement of the polymer center-

of-mass moves a distance several (3� 5)


Figure 1.

(left) Staring configuration of a bottle-brush molecule (a ‘‘centipede’’) with L¼ 13 (backbone) and N¼ 3 (side

chain), so that for grafting density sg¼ 1 the total number of segments M¼ 97, and for sg¼ 1/4 one has

M ¼ Lþ 2N½ðL� 1Þsg þ 2� ¼ 43. (right) A snapshot of a thermalized ‘‘centipede’’ with L¼ 20 backbone

monomers (blue) and 42 side chains (red) of length N¼ 4. The total number of beads is M¼ 188. Here kBT¼ 1

1 and the strength of adsorption "s ¼ 9:5. Side chains which are too strongly squeezed by the neighbors when

the backbone bends are seen occasionally to get off the substrate in order to minimize free energy.

Macromol. Symp. 2012, 316, 112–122 115

times larger than the polymer size (i.e.,

larger than the radius of gyration Rg).

During this period no scission of backbone

bonds may take place. We then start the

simulation with a well equilibrated con-

formation of the chain and allow thermal

scission of the bonds. We measure the mean

life time t until the first bond rupture

occurs, and average these times over more

than 2� 104 events so as to determine the

mean hti which is also referred to as Mean

First Breakage Time (MFBT). In the course

of the simulation we also sample the

probability distribution of bond breaking

regarding their position in the chain (a

rupture probability histogram), the prob-

ability distribution of the First Breakage

Time, t, as well as other quantities of

interest like the strain (and the tension) of

individual bonds. At periodic intervals we

analyze the length distribution of backbone

fragments and establish the Probability

Distribution Function (PDF) of fragment

sizes, Pðn; tÞ, which also yields the time

evolution of the mean fragment length L(t).

One should point out that we perform

our computer experiment in a somewhat

more idealized way that in a laboratory. It is

possible that in the latter case the chains

begin to break even during the process of

adsorption so that the lower bound of life


time t becomes difficult to determine under

well defined conditions. Therefore, in our

computer experiment we work at suffi-

ciently low temperature T so that the first

scissions occur after reasonably large wait-

ing time.

Since in the problem of thermal degra-

dation there is no external force acting on

the chain ends, a well defined activation

barrier for a bond scission is actually

missing, in contrast to the case of applied

tensile force. Therefore, a definition of an

unambiguous criterion for bond breakage is

not self-evident. Moreover, depending on

the degree of stretching, bonds may break

and then recombine again. Therefore, in

our numeric experiments we use a suffi-

ciently large expansion of the bond, rh¼ 5b,

as a threshold to a broken state of the bond.

This convention is based on our checks that

the probability for recombination of bonds,

stretched beyond rh, is sufficiently small.

Simulation Results

Equilibrium Properties

We have checked some typical properties

of the strongly adsorbed brush molecules as

the scaling of the mean end-to-end distance

between terminal points on the polymer


10 100L

102

103

104

Re2 (L

)

Re

2(N=1)

Re

2(N=2)

Re

2(N=3)

Re

2(N=4)

43210 5N

10

15

20

25

30

Re

2

43210 5N

0.94

0.96

0.98

1.00

b2

a) b)

L3/2

102 103

M10-3

10-2

10-1

D

N=1N=2N=3N=4M

-1

Figure 2.

(a) Variation of the the end-to-end distance R2e with chain length L in a bottle-brush molecule with side chains of

length N. Lines denote a scaling relationship R2e/L2n. The (asymptotically) exact scaling in 2d, R2

e/L3=2, is

indicated by a bold dashed line for comparison. Insets show the increase of R2e and the mean squared bond

length b2 with changing side chain length N for L¼ 30. Here and in (b), T¼ 1.0 and "s ¼ 9:5. (b) Diffusion

coefficient D vs total number of beads M ¼ Lþ 2N½ðL� 1Þsg þ 2� for bottle-brush molecules of different length

L. The dashed straight line indicates the D/M�1 power law, expected for Rouse dynamics.

Macromol. Symp. 2012, 316, 112–122116

backbone, R2e , with backbone length L for

several lengths of the side chains, N - see

Figure 2a. One can easily verify from

Figure 2a, that the structure of the bottle-

brush macromolecules indicates a typical

quasi-2d behavior, as one would expect for

the case of strong adsorption. One observes

a scaling behavior R2e /L2n where the

power-law Flory exponent attains a value

n¼ 0.77� 0.02 that is close to the asympto-

tically exact one, n2d¼ 3/4.[24] However, the

observed values of n appear systematically

somewhat higher than n2d¼ 3/4 (the latter is

indicated in Figure 2a by a thick dashed

line). A closer inspection of the displayed

scaling behavior reveals even a small yet

systematic increase in the R2e vs L-slope as

the length N of the side chains grows.

From the insets in Figure 2a, on the

other hand, one can see that the end-to-end

distance of the backbone, R2e , itself steadily

increases with growing length N of the side

chains. The same applies for the mean bond

length b2 between segments along the

backbone as function of N. Evidently, due

to the high grafting density the side chains

progressively repel and stretch each other

into an extended conformation as they

get longer. Naturally, the steric repulsion

between side chains is strongly enhanced

when the macromolecule is adsorbed and

attains a quasi-twodimensional conforma-


tion.[21] As a result, both its contour and

persistent lengths are increased, that is, with

growing N the polymer becomes stiffer. Since

the studied lengths L are not very large, the

macromolecules do not accommodate suffi-

ciently many persistent lengths and manifest

a scaling behavior in between that of

entirely flexible polymer chains with

n¼ 3/4, and rigid rods with n¼ 1.0.

Similar to the static properties, discussed

above, the diffusion coefficient D¼ kBT/z

of adsorbed bottle-brush molecules -

Figure 2b - reveals a typical Rouse-like

behavior, representative of the so-called

‘free draining limit’ when the friction z of a

M-bead polymer coil in the solvent is simply

M times larger that the friction of an

individual bead z0, that is z ¼Mz0. This is

indeed manifested in the inset in Figure 2b.

As far as the present computer experi-

ment employs Langevin dynamics where

the solvent is only implicitly taken into

account, one might wonder, if our results

would change in a system with explicit

solvent being present. It is known, however,

that the long-range effect of a planar wall

on the mobility of a particle decays as 1/h,

where h is the distance from the wall.[25]

Therefore, at least for strongly adsorbed

bottle-brush molecules we believe that

hydrodynamic interactions will have

virtually no effect on polymer dynamics.


Macromol. Symp. 2012, 316, 112–122 117

Distribution of Scission Rates and Tension

along the Chain

We examine here in more detail

the distribution of scission probability (the

probability of bond rupture) along the

polymer backbone for the case of a strong

adsorption, T¼ 0.125, "s ¼ 0:5 in Figure 3.

One can readily verify from Figure 3a that

for a given contour length L the shape of the

probability histogram changes qualitatively

as the length of side chains N and the

grafting density sg are varied. While for

N¼ 1, sg¼ 1.0 the scission probability is

uniformly distributed along the backbone

(being significantly diminished only in the

vicinity of both terminal bonds), for N¼ 4,

sg¼ 1.0, in contrast, one observes a well

expressed minimum in the probability in

the middle of the chain in between the two

pronounced maxima (‘‘horns’’) close to the

chain ends. Evidently, at the highest

grafting density the side chains for N> 1

become mutually strongly squeezed

whereby their mobility is suppressed and

no additional tension in the respective

bonds of the backbone is induced. Such

mutual blocking of side chains is absent for

N¼ 1, of course, since they are too short to

block one another. Thus, it appears that

there should exist some necessary free

volume around the side chains which would

enable their motion and, therefore, permit

the generation of increased tension that

would ultimately lead to bond rupture. In

0 10 403020 50 600

0.01

0.02

0.03

Rup

ture

PD

F

4842363024181260 54 60Consecutive Bond Number

0

0.01

0.02

0.03

Rup

ture

PD

F

0 10 403020 50 600

0.01

0.02

0.03

Rup

ture

PD

F

60565248444036322824201612840

Consecutive Bond Number0

0.01

0.02

0.03

Rup

ture

PD

F

σg = 1 σg = 1/2

σg = 1/3 σg = 1/4a)

Figure 3.

(a) Scission probability histogram for a polymer backb

different grafting density 0:25 sg 1:0. (b) Variation

density sg for brush molecules with fixed side chain le


very long bottle-brush molecules such areas

of enhanced mobility would exists in the

vicinity of the macromolecule ends as well

as around bends and kinks in the con-

formation.

As the grafting density sg is decreased,

the mutual blocking is relieved and the

shape of the scission probability histogram

becomes uniformly distributed along the

backbone of the bottle-brush macromole-

cule - Figure 3. For sg< 0.5 one observes

alternatively high and low average scission

rates, cf. Figure 3, whereby the high rates

appear always in pairs because the induced

large tension is transmitted to the bonds

immediately connected to each grafting

site.

In the course of our MD simulation one

has also the possibility to measure directly

the tension f induced by the steric repulsion

of side chains on the covalent bonds that

comprise the macromolecule backbone. It

is interesting to see how this tension is

distributed along the backbone of the

macromolecule and whether it correlates

with the distribution of scission rates,

Figure 3. In Figure 4a we show the

distribution of the mean tension fn along

the bonds with consecutive number n along

the backbone of adsorbed bottle-brush

macromolecule. Evidently, away from both

terminal bonds the tension is uniformly

distributed along the inner bonds for

sg� 0.5. In fact, such a distribution is

0 10 403020 50 600

0.02

0.04

0.06

0.08

Rup

ture

PD

F

60565248444036322824201612840


0.02

0.04

0.06

0.08

Rup

ture

PD

F

0 10 403020 50 600

0.02

0.04

0.06

0.08

Rup

ture

PD

F

0 18126 3024 36 4842 54 60Consecutive Bond Number

0

0.02

0.04

0.06

0.08

Rup

ture

PD

F

σg = 1 σg = 1/2

σg = 1/4 σg = 1/6

b)

one with L¼ 61, length of the side chains N¼ 1, and

of the scission probability histogram with grafting

ngth N¼ 4.


0 10 403020 50 601

1.5

2

2.5

3

Ten

sion

fn

60565248444036322824201612840


1.5

2

2.5

3

Ten

sion

fn

0 10 403020 50 601

1.5

2

2.5

3

Ten

sion

fn

0 18126 3024 36 4842 54 60Consecutive Bond Number

1

1.5

2

2.5

3

Ten

sion

fn

σg = 1σg = 1/2

σg = 1/4 σg = 1/6

a)

0.40.2 0.6 10.8

σg

1

1.5

2

2.5

3

Ten

sion

<f>

L = 61N = 4

b)

Figure 4.

(a) Mean tension fn in the bonds with consecutive number n of an adsorbed macromolecules with L¼ 61 beads at

T¼ 0.125, g ¼ 0.25 and "s ¼ 0:5. The respective grafting density is indicated in the graphs. The length of the side

chains here is N¼ 4. (b) Variation of the mean tension averaged over all bonds of the bottle-brush backbone

with changing grafting density sg.

Macromol. Symp. 2012, 316, 112–122118

assumed in the interpretation of all experi-

mental observations.[18,19] For smaller

grafting density the tension is seen to

alternate in compliance with the bond

scission distribution, shown in Figure 3 so

that one can prove the existence of direct

relationship between fn and and the ensuing

probability of bond rupture. In Figure 4b

we show the general increase of the mean

tension hf i in the bonds with growing sg for

side chains of length N¼ 4. Evidently,

within the interval 1=6 sg 1:0 one

observes an increase by a factor �2.5. It

is to be expected that this increase of

tension force depends on the interplay of

4030 60 100

L

30

40

50

60

70

80

90

100

<τ>

<τ><τ> ~ L

-0.17

a)

Figure 5.

(a) Variation of the MFBT htiwith contour length L and wi

(inset) for length of the side chains N¼ 2. Here kBT¼ 0

desorbed (free) and adsorbed brush molecule with L¼


both sg and N. Indeed, it is conceivable that

at any grafting density one may consider

sufficiently long side chains when the steric

repulsion eventually saturates so that the

increase of tensile force f reaches some

upper bound. Therefore, it is clear that

more investigations are needed before this

question is comprehensively explored.

Dependence of hti on L

In Figure 5a we show the dependence of the

mean time hti elapsed before any of the

backbone bonds breaks on the contour

length L and on the total number of

segments in the bottle-brush molecule

43210 65

N0

2e+03

4e+03

<τ>

adsorbedfree

b)

th total number of monomers M of the brush molecule

.10 and "s ¼ 0:50. (b) Mean life time hti vs N for a

30.


Macromol. Symp. 2012, 316, 112–122 119

M ¼ Lþ 2N½ðL� 1Þsg þ 2�. The mean life

time hti of the macromolecule was obtained

as a first moment of the probability

distribution of life times, W(t), (not shown)

which strongly resembles a Gaussian dis-

tribution with a slight asymmetry (a some-

what longer tail at the large times).

Evidently, in Figure 5a one observes a well

expressed power law, hti/L�b with expo-

nent b � 0.17. Since for large L one has

M/L, the variation of hti with the total

number of segments M is the same.

This finding is important because it

indicates that hti depends rather weakly

on the total number of bonds that might

break, in clear contrast to thermal degrada-

tion of polymers without side chains[26]

where b¼ 1. Indeed, when bonds break

entirely at random, the probability that any

of the L bonds may undergo scission within

a certain time interval should be propor-

tional to the total number of bonds, and

therefore hti/ � 1=L. In cases of chain

scission when a constant external force

pulls at the ends of the polymer, however,

one finds typically b< 1[27,28] whereby the

value of b steadily decreases as the force

strength grows. This suggests a gradual

crossover from a predominantly individual

to a more concerted mechanism of bond

Figure 6.

Snapshots of an adsorbed bottle-brush macromolecule

length N¼ 4, sg¼ 1.0 at T¼ 0.125 and "s ¼ 0:50 before (

nearly completed at t¼ 600 t.u.


scission. In adsorbed bottle-brush mole-

cules it is the side chains that induce tension

in the polymer backbone and thus lead to

rupture behavior similar to that with

external force.

In Figure 5b we compare the depen-

dence of hti on length N of the side chains

for the case of non-adsorbed (free) and

adsorbed brush molecules of length L¼ 30.

Generally, adsorption alone is found to

diminish the mean rupture time by more

than an order of magnitude, at least for

N> 1. As mentioned before, the case N¼ 1

where neighboring side chains almost do

not overlap is qualitatively different so,

upon adsorption, the MFBT shortens by a

factor of three only.

Fragment Size Distribution

We studied the fragmentation kinetics and

the resulting molecular weight distribution,

Pðn; tÞ, of strongly adsorbed bottle-brush

molecules for the shortest side chains N¼ 1,

2, 4, at sg¼ 1.0 - see Figure 6. As usual,

Pðn; tÞ denotes the probability to find a

fragment of size n at time t after the onset of

the degradation process. As discussed

above, for N¼ 1 the side chains do not

overlap very strongly and produce a scis-

sion probability distribution for the bonds

(a ‘‘centipede’’) with backbone length L¼ 61 and side

above) and after (below) the fragmentation process is


Macromol. Symp. 2012, 316, 112–122120

along the polymer backbone that matches

the one, inferred from experiment.[17] In

contrast, the case N¼ 2 leads to bond rate

histogram which qualitatively resembles

that for N¼ 4, s¼ 1.0.

One can easily derive an expression for

the time evolution of the mean backbone

length, LðtÞ ¼R

nPðn; tÞdn, provided some

basic assumption is made in regard of the

bond scission kinetics. If one assumes that

the scission kinetics is described by a first-

order reaction, then for irreversibly break-

ing bonds one may describe the rate of

scission as

dmðtÞdt¼ �kðmðtÞ �m1Þ; (5)

where the number of intact bonds in the

system at time t is m(t), and k denotes the

relevant kinetic constant. In Eq. (5) m1is the number of intact bonds at late times,

t ! 1. Eq. (5) is then easily solved to

mðtÞ ¼ ðm0 �m1Þe�kt þm1; (6)

where m0 ¼ mðt ¼ 0Þ. If the total number

of bonds in the system is M, then the

average contour length L(t) of all fragments

at time t will be

LðtÞ ¼ M

M �mðtÞ ; (7)

20 40

60 80

100

0

0.04

0.08

0.12

0.16

Fragment size - n

P(n

,t)

0.2 0.40.6

0.81.0

1929

Time

a)

Figure 7.

(a) Probability distribution of fragment sizes Pðn; tÞ at dif

the fragmentation process for a brush molecule on a s

Variation of the mean fragment length, taken as 1� LðtÞ�and N¼ 2 - (triangles) in semi-logarithmic coordinates

legend. Solid lines denote the theoretical results, Eq. (8


since the number of fragments in the

system is given by the number of broken

bonds. For the mean contour length L(t)

one then gets an expression, derived 1939

by Wolfrom et al.[29]

1

LðtÞ �1

L1

� �¼ 1

L0� 1

L1

� �e�kt; (8)

where L0 ¼M=ðM �m0Þ is the initial

contour length at t¼ 0, and

L1 ¼M=ðM �m1Þ is the mean contour

length of backbone fragments at infinite

time t!1. In fact, L1 denotes the minimal

size of a cluster that does not disintegrate

any further. This lower limit of the chain

length of fractured molecules can be

ascribed to reduction, or even vanishing

of the backbone tension.

In Figure 7a we show the length

distributions of the degradation products

at different times after the onset of the

scission process. The shapes of Pðn; tÞ are

found to agree well with the experimentally

observed ones[18] even though our species

are about an order of magnitude smaller

than in the laboratory experiment, and the

side chains - even more. In the beginning of

the degradation, t ¼ 0:2� 0:4, one can still

observe a d–function-like peak at the initial

length L0¼ 100 of the backbone. Later, for

t� 0.4, the distribution goes over into a

20100

Time t [x 20 t.u.]

1

1-1/

L(t

)

~e -0.0025 t

~ e-0.012 t

b)

ferent times t (in units of 20 MD t.u.) after beginning of

ubstrate with L¼ 100, N¼ 1 at T¼ 0.12, "s ¼ 0:5. (b)1, for a brush molecule with side chains N¼ 1 (circles),

with the respective kinetic constants indicated in the

), with L1¼ 1.


Macromol. Symp. 2012, 316, 112–122 121

rather flat one with a maximum around size

n � 20. Eventually, one ends up with a

rather sharply peaked Pðn; t ¼ 29Þ which

yields Lðt ¼ 600Þ � 7:5. At late times,

t> 600, the process goes steadily on until

finally the limit of L1¼ 1 is reached.

In Figure 7b we plot the evolution of the

mean fragment length L(t) by using the

quantity 1� LðtÞ�1 which is more appro-

priate in order to expose the true kinetics of

the fragmentation process. It is immedi-

ately seen from Figure 7b that the bottle-

brush fragmentation comprises a two-stage

process whereby an initial very short and

steep decay is followed by a much longer,

albeit slower, one.

In view of Figure 7b one might assume

that the maximum tension along the brush

backbone, f � f0N,[21] depends implicitly

on L too. The tension is quickly relaxed

below a threshold fthðL;NÞ when the

backbone fragments get short enough so

that below a critical length Lth the side

chains experience much weaker steric

repulsion. In our computer experiments

with an initial length L0¼ 100 this happens

at Lth=L0 � 20% when N¼ 1, and at

Lth=L0 � 10% when N¼ 2. As expected,

Lth steadily decreases when the length of the

side chains grows, as our data on N¼ 3, 4

(not shown) suggest. For L Lth, the

fragmentation proceeds with a significantly

smaller kinetic constant. Such an effect has

not been reported in the laboratory experi-

ments[18,17] but it cannot be ruled out that

the observations there refer to the lengthy

secondary fragmentation whereas the

initial quick drop of the mean length L(t)

lasts too short so as to be detected.

One should note, however, that the

initial and the secondary fragmentation

processes can be represented as nearly

perfect straight lines in both normal

and semi-log coordinates. It appears, there-

fore, that the observed fragmentation

kinetics cannot be unambiguously qualified

as a first-order chemical reaction. As

expected, the rate of fragmentation is, of

course, much higher for the longer side

chains with N¼ 2. Moreover, one may

conclude that recombination of bonds


plays a negligible role during the degrada-

tion process.

Conclusion

In this work we have used a Langevin MD

simulation to model the process of thermal

degradation in strongly adsorbed bottle-

brush molecules. Our results confirm the

strong effect of adsorption on chain scis-

sion, due to strong increase in backbone

tension, predicted recently theoretically.[21]

This has been indeed observed in recent

experiments.[17–19] Since the chemical nat-

ure of the bonding interactions remains

unchanged, the observed adsorption-

induced bond cleavage is of purely mechan-

ical origin and is due to the conformational

changes which a branched molecule under-

goes when the energy gain by contact with

the surface confines the molecule in a quasi-

2D shape.

Among the main results of our investi-

gation one should note

s

, W

tatic (R2g;R

2e) and dynamics (diffusion

coefficient D) properties of strongly

adsorbed bottle-brush molecules on a

substrate reveal a typical behavior of

quasi-2D objects with scaling exponent

n¼ 3/4, characteristic for the Rouse

behavior of a polymer.

T
he mean life time of a bond htidecreases by more than an order of mag-
nitude upon adsorption of a free bottle-

brush molecules on an adhesive surface.

T
he mean time hti before a bond breaks
decreases weakly with growing contour

length L of the backbone, hti/L�0:17,

and faster with the length of the side

chains, N. However, the studied lengths

N of the side chains are too short for a

definite scaling law to be established.

T
he probability distribution for rupture
depends on both grafting density sg and

length of the side chains N. It is sensitive

to the degree of steric repulsion of the

side chains - the shape of the scission

probability distribution resembles the

experimentally established one only for


Co

Macromol. Symp. 2012, 316, 112–122122

weaker repulsion when the side chains do

not mutually block one another.

T
he length distribution Pðn; tÞ and the
average length of fragments, L(t), during

the degradation process are found to

agree well with the experimentally

observed albeit the accumulated tension

in the backbone is released in two stages.

A very short interval of fast breakage

down is to about 20% of the initial mean

length of the molecule is followed by a

considerably slower process which lasts

until the chain breaks down to fragments

of the size of individual repeat units.

T
he measured variation of the mean
fragment size with time appears compa-

tible with first-order reaction kinetics.

Generally, the reported results may be

regarded as a first attempt to get a deeper

insight in the fascinating behavior of

adsorbed brush molecules during fragmen-

tation. Of course, many aspects of the

adsorption-induced thermal degradation

may and should be explored in much more

detail than in the present study. We plan to

report on such investigations in a future

work.

Acknowledgements: One of us, A. M., appreci-ates support by the Max-Planck Institute forPolymer Research, Mainz, during the time of thepresent investigation. We acknowledge supportfrom the Deutsche Forschungsgemeinschaft(DFG), Grant No. SFB 625-B4, BI 314/23 andFOR 597.

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