European Polymer Journal 45 (2009) 1748–1758

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European Polymer Journal

journal homepage: www.elsevier .com/locate /europol j

Combination of ‘‘living” nitroxide-mediated and photoiniferter-induced‘‘grafting from” free-radical polymerizations: From branched copolymersto unimolecular micelles and microgels

Daniel Gromadzki a,b,*, Sergey Filippov a, Miloš Netopilík a, Ricardas Makuška b,Alexander Jigounov a, Josef Pleštil a, Jirí Horsky a, Petr Št�epánek a

a Department of Supramolecular Polymer Systems, Institute of Macromolecular Chemistry, Academy of Sciences of the Czech Republic, Heyrovsky Square 2,162 06 Prague 6, Czech Republicb Department of Polymer Chemistry, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania

a r t i c l e i n f o a b s t r a c t

Article history:Received 8 February 2009Received in revised form 25 February 2009Accepted 25 February 2009Available online 5 March 2009

Keywords:Controlled/‘‘living” radical polymerizationBranched copolymersConformationMicrogelUnimolecular micelles

0014-3057/$ - see front matter � 2009 Elsevier Ltddoi:10.1016/j.eurpolymj.2009.02.022

* Corresponding author. Address: Department ofmer Systems, Institute of Macromolecular CheSciences of the Czech Republic, Heyrovsky SquareCzech Republic. Tel.: +420 296 809 269; fax: +420 2

E-mail address: d_grom@interia.pl (D. Gromadzk

We report on solution properties of lightly grafted copolymers composed of polystyrene(PS) backbone (degree of polymerization of PS backbone, Nb ¼ 95) and variable length ofpoly(tert-butyl methacrylate) P(tBuMA) side chains (degree of polymerization of sidechains, Nsc ¼ 14—222) at fixed number of grafting sites n = 11 and polydispersity index(Mw/Mn) ranging from 1.05 to 2.63. Synthesis of these graft copolymers is based on a novelsynthetic route [Gromadzki D, Makuška R, Netopilík M, Holler P, Lokaj J, Janata M, et al. EurPolym J 2008;44:59–71] involving two independent controlled/‘‘living” polymerizationmechanisms, namely nitroxide-mediated radical polymerization (NMP) for the synthesisof the backbone and photoinduced ‘‘grafting from” iniferter process for building ofP(tBuMA) branches. The viscosity-related contraction factors g0 < 1 confirmed high degreeof branching of the studied graft copolymers. Dilute solutions of graft copolymers in non-selective solvent (THF), examined by dynamic light scattering (DLS), small-angle X-rayscattering (SAXS) and viscometry, revealed a transition from comb-like conformationthrough wormlike-star to a microgel architecture under increasing number of monomericunits in side chains. These data were further supported by the structure factors Rg=Rh andRg=Rh obtained by independent measurements and extrapolated to infinite dilution. Persis-tence lengths of the samples exhibiting comb-like topology were larger compared to linearpolystyrene backbone and P(tBuMA) side chains in THF suggesting stiffening of the mainchain with increasing size of the attached side chains. Unimolecular micelles were detectedby DLS and SAXS in solvent selective for grafts, tert-amyl alcohol.

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1. Introduction A–B branched macromolecules are governed by the nature

Graft copolymers are macromolecules that in the sim-plest case consist of a backbone main chain made up froma monomer A and side chains (grafts or branches) made upfrom a monomer B attached to this backbone. Properties of

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Supramolecular Poly-mistry, Academy of2, 162 06 Prague 6,96 809 410.i).

of constituting segments, their length and grafting density[1]. A special case of a graft copolymers are molecularbrushes (cylindrical or bottle brushes), i.e. densely graftedmacromolecules in which every monomeric unit of themain chain contains a side chain while the main chain issignificantly longer than the side chains [2]. This paper isrestricted to investigation of solution properties of lightlygrafted copolymers with teeth randomly spaced alongthe backbone while solution properties of molecularbrushes will form a basis of a separate paper [3].

D. Gromadzki et al. / European Polymer Journal 45 (2009) 1748–1758 1749

There have been relatively few papers dealing with thetheory and simulation [4–12] and experimental character-ization of graft copolymers [13–18] with precisely con-trolled architectural parameters. Most of graftcopolymers were synthesized by ‘‘living” anionic polymer-ization and different coupling (‘‘grafting onto”) strategies[19]. This is a technique of choice for the preparation ofmodel graft copolymers because both the backbone andside chains are independently prepared and characterizedbefore the coupling step. However, the process requiresstringent reaction conditions, has low grafting efficiencyand difficult purification because of the excess of sidechains usually required for successful grafting. Notewor-thy, in contrast to chemical strategies one may constructa graft architecture applying a supramolecular ‘‘graftingonto” concept which utilizes physical interactions such ashydrogen and ionic bonding or coordination complexation[20,21].

The establishment of controlled/‘‘living” radical poly-merization (CRP/LRP) [22] techniques in the past decadeenabled synthetic polymer chemists to create a plethoraof macromolecular architectures, such as brush, star,hyperbranched, etc. [23]. In early eighties Otsu introducedthe concept of iniferter [24,25], i.e. a type of polymerizationthat operates under the mechanism of initiation-transfer-termination using thiurams and dithiocarbamates as chaintransfer agents. Although not truly ‘‘living”, this was thefirst example showing characteristics of a CRP/LRP process,i.e., the molecular weight increased with conversion whilethe polydispersity index (PDI) remained relatively lowthroughout the reaction. Nowadays, among the most effi-cient CRP/LRP systems are nitroxide-mediated radicalpolymerization (NMP) [26], atom transfer radical polymer-ization (ATRP) [27] and reversible addition-fragmentationchain transfer (RAFT) [28]. So far the most versatile tech-nique for the synthesis of graft or brush architecture wasATRP via ‘‘grafting through” (macromonomer method)[29] and ‘‘grafting from” [30] approaches.

The conformations of block and graft copolymers in di-lute solutions of non-selective solvents have recently re-ceived a great deal of attention. Yet, for the latter casethe influence of the length of both the backbone and theside chains on the conformational behavior is not fullyunderstood. Theoretical [31] and experimental [32–37] re-sults indicate a preferential ordering (segregation) ofchemically dissimilar segments in a diblock copolymerdue to unfavorable thermodynamic interactions governedby the Flory–Huggins segmental interaction parametervAB and the volume fraction (f ). In contrast, other work[38–43] suggest a model of a diblock copolymer consistingof two mutually interpenetrating random coils in an ex-panded conformational state. The core-shell like conforma-tion for graft copolymers having backbone A in the coreand branches B in the shell in dilute solution was con-cluded by Hadjichristidis and Roovers based on theirlight-scattering measurements in three thermodynami-cally good solvent for both parts but a different refractiveindex for each part [36]. Recently, Stepanyan et al. dis-cussed microphase separation behavior of A-B combcopolymers in the frame of mean field calculations andscaling arguments in solvents of different quality [44].

Under good solvent conditions, relevant to present study,the segregated state occurs at a critical pointv�ðgoodÞ

AB � N�3=8 and scales as v�ABN � N�5=8 with the decreas-ing value of the exponent from 5/8 to 0 when changing thequality of the solvent from good to poor conditions.

In a selective solvent, thermodynamically good for oneblock and bad for the other one, macromolecules undergoself-assembly into a variety of micellar aggregates depend-ing on the composition, solvent and solution concentration[45]. Micellization of block copolymers was a subject ofextensive investigations both from theoretical and experi-mental point of view [46–49]. In contrast, relatively fewstudies were focused on micellization of graft copolymers[13,14,50] prepared by CRP/LRP techniques. General obser-vations made by various authors indicate that graft copoly-mers in solvents selective for grafts form micelles with arelatively low aggregation number [51,52] or do not aggre-gate at all assuming a conformation of so-called unimolec-ular micelles [53–55].

We note that micellization studies of model graftcopolymers comprising polystyrene backbone and poly(-tert-butyl methacrylate) side chains were recently re-ported by Pitsikalis et al. [14]. However, systematicalstudies on conformation and micellization behavior oflightly grafted copolymers composed of the same mono-meric units prepared by CRP/LRP techniques as a functionof side chain length to authors’ knowledge have not yetbeen reported.

2. Experimental

2.1. Synthesis of graft copolymers by the combination ofnitroxide-mediated radical polymerization and photoinducediniferter process

Lightly grafted copolymers comprising polystyrenebackbone and poly(tert-butyl methacrylate) side chainswere synthesized employing two independent controlledradical polymerization processes, namely, nitroxide-medi-ated radical polymerization (NMP) and iniferter technique,as described in detail in our previous paper [56]. First,2,2,6,6-tetramethyl-piperidin-1-oxyl (TEMPO)-mediatedNMP was performed to synthesize poly(styrene-co-chlo-romethylstyrene) P(S-co-CMS) random copolymers. Mono-mer reactivity ratios of styrene and p-chloromethylstyrenein copolymerization are rS = 0.72 and rp-CMS = 1.08, respec-tively [57], which implies that the monomers are incorpo-rated into the resulting copolymer chain in a statisticalmanner. The p-chloromethylstyrene groups during nucleo-philic reaction with sodium N,N-diethyldithiocarbamateare subsequently quantitatively displaced giving polysty-rene bound dithiocarbamates as macroinitiators forphoto-induced ‘‘grafting from” iniferter polymerization.The chemical structure and schematic representation ofsynthesized comb molecules are shown in Fig. 1.

SEC eluograms (not shown) of both TEMPO-terminatedP(S-co-CMS) copolymers and the products of modification(macroinitiators) were unimodal indicating that the modi-fication proceeded smoothly without any cross-linking orside reactions. Degree of polymerization of the macroiniti-

SS

N

O O

CN

O Nm

n

Fig. 1. Chemical structure and schematic representation of synthesized graft copolymers.

1750 D. Gromadzki et al. / European Polymer Journal 45 (2009) 1748–1758

ator backbone and density of photo-initiating sites wereadjusted during the synthesis and modification of the mac-roinitiator while length of the side chains was set by vary-ing the molar concentration of the monomer to themacroinitiator and photopolymerization time. SEC eluo-grams and plots of molecular weight Mw, intrinsic viscosity[g] and mean square radius of gyration <s2> of a graftcopolymer prepared by a combination of NMP and photo-induced iniferter process is presented in Fig. 2.

The values of absolute number-average molecularweight Mn, weight-average molecular weight Mw, polydis-persity index Mw=Mn, and the degree of polymerization ofthe macro-iniferter backbone M2-DC and of the side chainsof the graft copolymers M2-1 to M2-8, N, obtained by tri-SEC measurements, are listed in Table 1.

Polystyrene backbone of the macroinitiator, M2-DC, hasthe degree of polymerization Nb = 95, carrying in average11 grafting sites to which PtBuMA side chains of variouslength are end-grafted. Side chains of the graft copolymersM2-1 to M2-4 are shorter than the backbone while the sidechains of the graft copolymer M2-8 are long exceeding thebackbone by about two times. Therefore, the former graftcopolymers can be referred to as the comb copolymerswhile the latter to as the starlike copolymer, respectively.

Fig. 2. Plots of Mw, intrinsic viscosity [g], mean square radius of gyration<s2> and normalized triple detector responses against elution volume ofthe graft copolymer M2-8 (see Table 1).

2.2. Characterization

2.2.1. Dynamic light scattering (DLS)Measurements were carried out on an ALV-6000 instru-

ment equipped with a 22 mW He–Ne laser in the angularrange 30�–150�. The obtained correlation functions havebeen analyzed by REPES [58] analytical software providinga hydrodynamic-radius distribution function, G(Rh). To ac-count for the logarithmic scale on the Rh axis, all DLS distri-bution diagrams are shown in the equal arearepresentation, RhG(Rh). For all polymers, the true valuesof Rh have been calculated from translational diffusioncoefficients D which have been measured well below thecross-over concentration (c*). This implies that the inter-particle interaction influencing D can be neglected.

2.2.2. Size exclusion chromatography (SEC)Polymer molecular weights were estimated using SEC

instrument: Deltachrom pump (Watrex Comp.), autosam-pler Midas (Spark Instruments, The Netherlands), two col-umns with PL gel MIXED-B LS (10 lm), separating in therange of molecular weights approximately 400–1 � 107 g mol�1. Tetrahydrofuran (THF) was used as a mo-bile phase at flow-rate 0.5 cm3min�1. The injection-loopvolume was 0.1 cm3. Measurements were performed withtriple viscosity/concentration/light-scattering detection.The set was connected to a light-scattering photometerDAWN DSP-F (Wyatt Technology Corp.), measuring at 18angles of observation, a modified differential viscometerViscotek model TDA 301 (without internal light scatteringand concentration detectors) and a differential refractome-ter Shodex RI 71. The data were accumulated and pro-cessed using the Astra and triSEC software. Theevaluation of the triple-detection data is described else-where [59].

2.2.3. Small-angle X-ray scattering (SAXS) on graft copolymersolutions

SAXS experiments were performed using a pinholecamera (Molecular Metrology SAXS System) attached to amicrofocused X-ray beam generator (Osmic MicroMax002) operating at 45 kV and 0.66 mA (30 W). The camerawas equipped with a multiwire, gas-filled area detectorwith an active area diameter of 20 cm (Gabriel design).Two experimental setups were used to cover the q rangeof 0.007–1.1 Å�1 (q ¼ ð4p=kÞ sinðh=2Þ), where k is thewavelength and h is the scattering angle). The scattering

Table 1Molecular and physical characteristics of the macroinitiator M2-DC and of the derived graft copolymers M2-1 to M2-8.

Polymer Mn � 10�3a (g/mol) Mw � 10�3b (g/mol) Mw/Mnc Nsc

d [g]e (cm3/g) Rgf

M2-DC 10.9 11.2 1.03 95 10.7 3.3g

M2-1 28.8 40.3 1.40 14 17.3 –M2-2 63.1 88.9 1.41 42 17.2 –M2-3 80.0 154 1.90 56 26.8 20.4h

M2-4 100 166 1.66 72 25.2 13.8h

M2-5 158 418 2.63 120 28.0 18.1h

M2-6 162 262 1.62 122 21.8 11.2h

M2-7 163 328 2.01 124 37.7 20.7h

M2-8 284 663 2.33 222 18.4 15.9h

a Number-average molecular weight.b Weight-average molecular weight.c Polydispersity index.d Degree of polymerization of macroinitiator backbone (Nb), M2-DC (first entry) and of the side chains (Nsc), (M2-1–M2-8).e Intrinsic viscosity.f Radius of gyration.g Rg from triSEC (viscosity plus light scattering, by Flory-Fox theory).h Rg from ASTRA (as an angular dependence of the scattered light).

D. Gromadzki et al. / European Polymer Journal 45 (2009) 1748–1758 1751

intensities were put on absolute scale using a glassy carbonstandard. Prior to fitting analysis the solvent scattering hadbeen subtracted.

2.2.4. Viscosity measurementsViscosity measurements were performed using Ubbe-

lohde dilution viscometers in a water bath at25 ± 0.01 �C. Intrinsic viscosity [g] was obtained usingHuggins equation

gsp=c ¼ ½g� þ kH½g�2c þ � � � ð1Þ

where kH is the Huggins coefficient, gsp ¼ ðgr � 1Þ is thespecific viscosity.

3. Results and discussion

3.1. Conformation of graft copolymers in a good non-selectivesolvent THF

To ensure that all experiments were performed in diluteconcentration regime intrinsic viscosity of the studied

Table 2Hydrodynamic parameters determined by DLS and viscometry.

Polymer D � 10�7a (cm2/s) Rhb (nm) c�g

c (%)

M2-DC 21.7 2.2 10M2-1 8.9 5.4 7.5M2-2 6.0 8.0 5.7M2-3 4.4 11.0 5.0M2-4 5.3 9.0 4.4M2-5 4.5 10.6 4.7M2-6 2.9 16.3 3.7M2-7 2.6 18.5 4.0M2-8 2.8 17.1 3.2

a Translational diffusion coefficient.b Hydrodynamic radius.c Viscosity-related overlap concentration.d Intrinsic viscosity measured by Ubbelohde viscometer.e Viscometric radius.f Generalized ratio.g Branching parameter.

polymers were measured and the viscosity-related overlapconcentration c�g ¼ 1=½g� [60] was estimated (Table 2).Fig. 3 shows plots of reduced viscosity of several graftcopolymers in THF at 25 �C as a function of concentration.

All dependences of the reduced viscosity on concentra-tion obey the Huggins equation. An error in estimating thevalue of intrinsic viscosity was in the range 0.1–0.3 cm3 g�1 for all samples.

Solutions of both macroinitiator, M2-DC, and the seriesof comb copolymers M2-1–M2-8 were examined by dy-namic light scattering in THF at 25 �C. Fig. 4 shows the dis-tribution of hydrodynamic radii for the macroinitiatorbackbone M2-DC and representative comb copolymers,M2-4 and M2-6.

All the copolymer samples exhibited single distribu-tions indicating that the polymers are fully dissolved inTHF. The translational diffusion coefficients D were ob-tained from angular dependence measurements at 12 an-gles in the range of 30�–150�, using the relation C = Dq2.The dependence of relaxation rate C on q2 is linear andpasses through the origin (Fig. 5), which implies that thepeaks are related to particles translational diffusion.

[g]d (cm3/g) Rge (nm) Rg/Rh

f g0g

10.1 2.6 1.17 0.98613.3 4.2 0.78 1.07417.6 6.2 0.78 0.75719.6 7.1 0.65 0.67922.7 7.4 0.83 0.78321.2 7.9 0.75 0.59827.0 11.8 0.72 0.38624.9 11.9 0.64 0.33231.7 13.0 0.76 0.409

0.000 0.00 2 0.,004 0.00 6 0.00 8 0.010 0.012

20

24

28

32

36

M2-4

M2-7

M2-3

M2-6

c (g cm-3)

sp/c

η

Fig. 3. Plots of reduced viscosity (gsp/c) versus concentration (c) forrepresentative graft copolymers.

10-1 100 101 102 103 1040.00

0.04

0.08

0.12

0.16

0.20

0.24

RhG

(Rh)

R h (nm)

Fig. 4. Distributions RhG(Rh) of hydrodynamic radii of the macroinitiator(D – M2-DC) and graft copolymers (d – M2-4; s – M2-6) in THF acquiredat scattering angle h ¼ 90� and c = 1 � 10�3 g cm�3 (dilute regime) at25 �C.

0 1 2 3 4 5 6 7 80

1

2

3

4

5

6

7

x 1

04(s

-1)

q2 x 1010 (cm-2 )

Fig. 5. Plots of the relaxation rate C versus q2 for grafts copolymers M2-1(D); M2-5 (d); and M2-8 (s). The diffusion coefficients, DT, wereobtained by least square fitting procedure (solid line).

1752 D. Gromadzki et al. / European Polymer Journal 45 (2009) 1748–1758

Then D is used to calculate hydrodynamic radii Rh bythe Stokes–Einstein relation:

D ¼ kBT=6pgRh ð2Þ

where g is the viscosity of the solvent (0.48 cP at 25 �C), kB

is the Boltzmann constant and T is the absolute tempera-ture. The acquired data are compiled in Table 2.

The measured Rh values (an error of the measurementsis about 3–5% for all samples) increased continuously withincreasing Nsc (see Table 2) reaching maximum at Nsc = 124(M2-7). The value of Rh for M2-8 (the longest side-chainlength) is, however, lower compared to that of M2-7. Gen-erally, macromolecule’s size (Rg or Rh) increases in parallelwith molecular weight by a power law with scaling expo-nent reflecting conformation of self-similar macromole-cules. The non-monotonous behavior of Rh suggestsconformational transition occurring with increasing lengthof the side-chains. Similar trend is observed for intrinsicviscosity as a function of a side-chain molecular weight(or Nsc). It increases with increasing Mw and reaches a pla-teau with some deviations at higher molecular weights.This situation can be explained as follows. At low and med-ium side chain length a polymer density q of the studiedgraft copolymers decreases with increasing molecularweight as it is common for linear chains in good solvents(qlin �M�0.8). This results in an increase of intrinsic viscos-ity due to expansion of the backbone by growing sidechains until P(tBuMA) side chains do not exceed the lengthof polystyrene backbone. After passing a threshold of crit-ical length, P(tBuMA) chains start to interact and formmore compact star-like architecture which naturally leadsto a larger segmental density. The effective repulsive inter-actions (excluded volume effect) between side chains arestrongly enhanced in THF due to a good solvating powerof the solvent towards P(tBuMA) grafts. Since conforma-tion of comb-like copolymers in dilute solutions is deter-mined by the solvent quality for the grafted chains, it canbe expected that sufficiently long grafts will impose stiff-ening of the bare backbone.

The hydrodynamic dimensions of the macroinitiatorand graft copolymers can be expressed as the viscometricradius Rg given by the equation for hard spheres [61]:

Rg ¼ ð3=10pNAÞ1=3ð½g�MwÞ1=3 ð3Þ

where NA is the Avogadro number. The values for Rg are in-cluded in Table 2. An important architectural parameterdescribing the inner density profile and conformation of amacromolecule in solution is the ratio of viscometric tohydrodynamic radius, Rg=Rh. According to Burchard [61]this generalized ratio is of special interest for establishingthe effect of branching. The value of Rg=Rh ¼ 1:17 for M2-DC macroinitiator is in accord with theoretical predictionsfor linear chains in a good solvent [61] while graduallydecreasing values spanning the range Rg=Rh ¼ 0:62—0:83for graft copolymers clearly illuminate the effect of increas-ing branching/compaction with growing side chains.

The conformational transition from comb-like to star-like macromolecules is further supported by the viscos-ity-related contraction factor g0 plotted on Fig. 6 as a func-tion of Nsc (for values of g0 see Table 2).

0 50 100 150 200 2500.2

0.4

0.6

0.8

1.0

1.2

g'

Nsc

Fig. 6. Dependence of viscosity-related contraction factor, g0 , on thedegree of polymerization of side chains, Nsc.

D. Gromadzki et al. / European Polymer Journal 45 (2009) 1748–1758 1753

The g0 values were calculated by

g0 ¼ ½g�br=½g�lin ð4Þ

where ½g�br is the intrinsic viscosity of the branched poly-mer and the subscript ‘lin’ denotes linear polymer of thesame molecular weight and composition. The referencevalues for linear chains of the same molecular weightand composition are not available in the literature there-fore intrinsic viscosity of linear polymers ½g�lin were esti-mated from Mark–Houwink–Sakurada (MHS) equation byassuming additivity of intrinsic viscosity of the copolymercomponents as

½g�lin ¼ w1K1Ma11 þw2K2Ma2

2 ð5Þ

where w1 and w2 are weight fractions of the PS backboneand P(tBuMA) grafts, respectively, calculated from molecu-lar weights of P(tBuMA) grafts and the molecular weight ofthe polystyrene backbone, M ¼ 1:07� 104 (Table 1). Theparameters of Eq. (7) are [56] K1 = 1.363 � 10�4 cm3 g�1,a1 = 0.714 and K2 = 1.520 � 10�4 cm3 g�1, a2 = 0.660. Thesize-related contraction factor g is given by

g ¼ hR2gibr=hR

2gilin ð6Þ

where hR2gi is mean-square radius of gyration, while g is re-

lated with g0 by g0 ¼ ge .Several values of the exponent e were suggested addi-

tionally to that of e ¼ 3=2 ensuing from volume consider-ations (Flory–Fox theory), e.g., e ¼ 1=2 [62] or e ¼ 1 forhighly branched polymers [63]. The values of g0 are there-fore only a qualitative description of the contraction insize, defined by g. The values of g0 << 1 suggest high de-gree of contraction and therefore of branching. The struc-ture of a short comb with long side-chains can beconsidered almost a star. The value of g ¼ 0:26, calculatedfrom the formula derived by Zimm and Stockmayer [64]

g ¼ ð3f � 2Þ=f 2 ð7Þ

for regular star, i.e., with all side-chains of the same lengthand functionality of f ¼ 11 is, however, lower compared tovalues of g0 for polymers with highest Mw. These resultsshow that the investigated copolymers exhibit lower seg-

mental density compared to true star-like architecture (lar-ger ½g�br) [65] which can be attributed to a sparse location ofP(tBuMA) arms on the backbone. This comparison is onlyquantitative and one has to bear in mind that the decreasein g0 indicates a compaction with respect to the referencechain which is an equivalent chain with a longer backbone(due to the side chains in the comb). The chain compactionis somewhat counterbalanced with the effect of actualchain stiffening due to excluded volume effect if comparedto the respective pure backbone without short side chainsattached to it. Other factors that additionally controlcopolymer’s segmental density, e.g. polydispersity, mayalso play a role. It is known that block and graft copolymersproduced by CRP/LRP techniques are characterized by a cer-tain polydispersity. The influence of the latter effect onsolution and phase behavior for block copolymers has re-cently been discussed [66] while for graft copolymers de-spite some theoretical treatments [67], a clear picturealong with experimental study are still missing.

3.2. SAXS analysis

The SAXS technique is commonly used to extract infor-mation about conformation and size of macromolecules insolution that can be performed by the analysis of Kratky orGuinier plots [68]. Scattering from macromolecules revealsthree regions in the dependence of scattered intensity onscattering vector, I � qa with behaviors characteristic forthe various length scales of the chain, namely the Guinierregime (qRg < 1), the regime characterizing coil behavior(self-avoiding random walk configuration) with a = �2 inH solvents and about a = �5/3 in good solvents, and finallythe region at higher q behaving as �q�1. At the latter regionlocal stiffness of the macromolecule can be revealed due toshorter length scales probed.

3.2.1. Low q rangeThe Rg value was extracted by applying Guinier approx-

imation IðqÞ ¼ Ið0Þ expð�R2g q2=3Þ to the initial region of

SAXS curves for all graft copolymers in THF solutions atconcentrations 5 � 10�3, 1 � 10�2 and 2 � 10�2 g cm�3.The advantage of this approach is that it can be usedregardless of the shape of the object involved. An extrapo-lation of 1=R2

g value to infinite dilution was subsequentlyperformed as shown in Fig. 7 for selected samples.

The SAXS-determined Rg values listed in Table 3 aregenerally smaller compared to Rg values obtained from tri-SEC. This is explained by the fact that the Flory parameterU1 in Flory–Fox equation exploited in TriSEC software forcalculation of Rg is dependent on the polymer structure.The ratio of the viscosity functions for the branched andlinear molecules with the same molecular weight,U1;b=U1;l, has limiting values of 2.71 for regular star-likepolymers, 1.9 for irregular stars, 2.41 for randomlybranched polymers and 1.00 for comb-like polymers. Theevalualtion of Rg using TsiSEC software, calibrated by linearpolystyrene standards, can be therefore done only for lin-ear-chain polymers (Sample M2-DC, Table 1).

The Flory radius [1] of the macroinitiator given by theequation RF ¼ l � N3=5 where l is the length of C–C bond(l � 2.5 Å) in a fully stretched cis–trans configuration

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.81/R

g2

x 10

4(Å

-2)

c (g/cm3 )

0.000 0.005 0.010 0.015 0.020

Fig. 7. Plots of 1=R2g versus concentration c of M2-4 in acetone (D), M2-8

in THF (s) and M2-8 in acetone (j).

Table 3Molecular and conformation parameters of graft copolymers determined bySAXS.

Sample Rga (nm) Rg/Rh

b f (±0.04)c vd lp (Å)e a (Å)f

M2-DC 4.0 1.82 0.33 0.67 8.3 ± 0.4 16.6M2-2 – – 0.18 0.59 14.1 ± 0.3 28.2M2-3 10.8 0.98 0.08 0.54 15.8 ± 0.4 31.6M2-4 6.8 0.76 0.25 0.63 18.7 ± 0.4 37.4M2-5 8.0 0.75 0.05 0.53 20.1 ± 0.8 40.2M2-6 10.3 0.68 0.00 0.50 18.0 ± 0.5 36M2-7 10.3 0.56 0.00 0.50 18.7 ± 0.3 37.4M2-8 8.0 0.47 �0.05 0.48 18.9 ± 0.4 37.8

a Radius of gyration determined by SAXS.b Structure factor obtained by combination of DLS and SAXS

techniques.c f – Excluded volume exponent.d v – Flory exponent calculated as v ¼ 1=a.e lp – Persistence length.f a – Kuhn segment length calculated as a ¼ 2 � lp .

0 50 100 150 200 250

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Rg/R

h

Nsc

hard spheres value

Fig. 8. Dependence of the ratio Rg/Rh parameter on the degree ofpolymerization of the side chains, Nsc.

1754 D. Gromadzki et al. / European Polymer Journal 45 (2009) 1748–1758

yields RF = 3.84 nm, not incompatible with values obtainedboth by triSEC and SAXS, Rg = 3.3 nm and Rg = 4.0 nm,respectively. Keeping in mind conformational changesestablished by the generalized ratio Rg=Rh and contractionfactor g0 in the previous section, we turn our attention toanother important ratio relating static and dynamic prop-erties defined as radius of gyration to hydrodynamic ra-dius, Rg=Rh. The dependence of Rg=Rh on Nsc is shown inFig. 8. Again, a decrease in Rg=Rh is observed with increas-ing length of P(tBuMA) arms for all graft copolymers. Thesamples M2-4 and M2-5 behave as hard spheres (Rg=Rh isclose to 0.778 as predicted [61] for this case) while thestructure factor of the copolymers M2-6–M2-8 is clearlybelow this theoretical value.

In the majority of reported cases the ratio Rg=Rh belowthe hard sphere value relates to particles with microgelarchitecture [61,69–71]. The branching effect is suspectedto be the main factor responsible for the ratio Rg=Rh ratiobelow the hard sphere limit. For dendrimers or hyper-branched polymers it approached 0.778 but never movedbelow this value [72]. This fact prompted us to assume amicrogel structure formed by intramolecular cross-linkingbetween growing chains. Indeed, this scenario is plausible,

since it is known that the dithiocarbamate species undergodecomposition during the grafting reaction. This effect [73]contributes to significant termination and radical recombi-nations leading eventually to cross-linked chains. To ouropinion, microgel hypothesis accounts for larger values ofa contraction factor in comparison with corresponding val-ues for true star-like polymers of the same molecularweight and justifies low values of the ratio Rg=Rh. The pres-ence of bridges prevents side chains from strong contrac-tion and as a consequence from further decrease ofintrinsic viscosity. The mechanism of the formation ofmicrogel architecture at various reaction conditions (ratioof the monomer to initiator, gel point conditions, etc.)and the detailed structural analysis is beyond the scopeof the present work.

3.2.2. Intermediate q rangeMacromolecular spherical architecture or branching is

easily detectable on a Kratky representation (I(q) q2 vs q)by a pronounced maximum followed by multiple scatter-ing peaks or a plateau in case of hard spheres of uniformsize and for branched polymers, respectively. Kratky plotsfor all investigated polymers in THF solutions are providedin Fig. 9. The changes of I(q) q2 with increasing side chainlength are clearly discernible in the middle q range. Themacroinitiator and graft copolymers with low side-chainlength (Nsc 6 72) show feature of a typical linear macro-molecule in a good solvent: I(q) q2 has a distinctive slopeas a function of q (Fig. 8a–e).

This is typical effect of excluded volume on the scatter-ing behavior. As the number of monomer units in the sidechains increases (curves f–h), the scattering peaks becomemore pronounced (see bump on Kratky plots of the sam-ples M2-6–M2-8). To quantitatively estimate the signifi-cance of an excluded volume effect we have calculatedan excluded volume exponent f given by the relation [68]

IðqÞ q�2=ð1þfÞ ð8Þ

The values of the excluded volume exponent f derivedfrom intermediate scattering region of the SAXS curvesshown in Fig. 10 are summarized in Table 3.

(a)

I(q)q

2

(b)

(c) (d)

(e) (f)

(g) (h)

q (Å-1

)

0.0 0.2 0.0 0.2

Fig. 9. Kratky plot for M2-DC (a); M2-2 (b); M2-3 (c); M2-4 (d); M2-5 (e);M2-6 (f); M2-7 (g); and M2-8 (h); c = 0.02 g cm�3.

D. Gromadzki et al. / European Polymer Journal 45 (2009) 1748–1758 1755

The value of f = 0.33 for the sample M2-DC is typical forlinear macromolecules in a good solvent [68]. An increasein graft’s length results in decrease of f up to merely zerofor the samples M2-5–M2-8 suggesting behavior of theideal chains in H-solvent [68]. Exponent values close toa = �2.0 (see Fig. 10) for the copolymers M2-5–M2-8 cor-relate well with their low structure parameters Rg=Rh;therefore we are inclined to think that such ‘‘ideal” behav-ior arises as a result of compensation of excluded volumeeffect by growing cross-linking between side chains. Fora copolymer with the longest side-chains (M2-8) the ex-cluded volume exponent f changes the sign from positiveto negative, remaining negative for the sample with thelongest side-chains. Negative sign of f is a proof of a certainmacromolecule contraction. As discussed in Ref. [68] theexcluded volume exponent f introduced in the power lawof I vs q is related to the scaling exponent v in MHS equa-tions. For example, the scaling law between radius of gyra-tions and molecular weight can be rewritten asRg ¼ K �Mv ¼ K �Mð1þfÞ=2. The calculated values of the Floryexponent v close to 0.6 for the macroinitiator and the graft

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

q-2.1

q-1.5

logI

(q)

logq-2.5 -2.0 -1.5 -1.0 -0.5 -0.0

Fig. 10. Log–log plot of scattered intensity I(q) as a function of thescattering vector q for the macroinitiator M2-DC (s) and graft copolymerM2-8 (h).

copolymers with low and moderate Nsc are characteristicfor chains in a good solvent while values of exponent v of0.5 for the samples M2-5–M2-8 suggest behavior of theideal chains in H-solvent (Table 3).

3.2.3. High q rangeAnother feature of investigated Kratky plots deserving

attention is that at high q range I(q) q2 follows a powerlaw q1 providing evidence for chains with wormlike parts(I � q�1) [68], except for the polystyrene based macroiniti-ator (Fig. 9a) obviously due to its flexibility. In other words,all studied graft copolymers behave as wormlike chainswith some persistence (Fig. 8b–h). Both this and other factsdiscussed in the previous sections allow us to apply aSharp–Bloomfield model [74] for chains with no excludedvolume interactions to extract quantitative informationabout studied polymers. The persistence length, lp, whichis the most important property of comb copolymers andthe contour length, L, were obtained by fitting the scatter-ing curves with equation (Fig. 11):

IðqÞ ¼ 2x2 expð�xÞ � 1þ xð Þ�

þ2lp

L4

15þ 7

15x� 11

15þ 7

15x

� �exp �xð Þ

� ��; ð9Þ

where x ¼ lpLq2=3.A continuous increase in lp from lp = 8.3 Å (macroiniti-

ator) to lp = 18.7 Å (the sample M2-4) with increasing sidechain length is seen for graft copolymers whose side chainsare shorter than length of the backbone. After this thresh-old (Nsc P 72 and longer) a plateau was reached suggestingthat further increase of side chains has no effect on lp. Sincethe polymers under investigation are assembled from twochemically distinctive entities PS and P(tBuMA), the exper-imental persistence length value obtained from Eq. (9) canbe an overlap of two independent lp. Because of largeweight fraction of P(tBuMA) chains (for the samples M2-3–M2-8 it exceeds 90%) we suppose that X-ray scatteringcomes mainly from the P(tBuMA) chains. It can be assumedthat increased stiffness is attributed exclusively to the ex-

0.01 0.1 1

10-3

10-2

10-1

I(q)

q (Å-1)

Fig. 11. The scattered intensity I(q) as a function of the scattering vector qfor the sample M2-3. The solid line represents best fit by a Sharp-Bloomfield model.

0 1 2 3 4 50.0

0.5

1.0

1.5

2.0

2.5

q2 x 10 10 (cm-2)

x10

4 (s

-1)

Fig. 13. Plots of the relaxation rate C as a function of q2 for M2-5 in THF(N); tert-amyl alcohol (j) and acetone (s). The translation diffusioncoefficients, DT, were obtained by straight line fitting (solid line).

Table 4Hydrodynamic and gyration radii of graft copolymer unimers M2-4 andM2-8 in THF and acetone in dilute concentration regime at 25 �C.

Polymer Rha Rg

b Rg/Rhc

THF Acetone THF Acetone THF Acetone

M2-4 9.0 9.7 6.8 7.3 0.76 0.75M2-8 17.1 14.4 8.0 8.0 0.46 0.56

a By DLS.b By SAXS.c By DLS and SAXS.

1756 D. Gromadzki et al. / European Polymer Journal 45 (2009) 1748–1758

cluded volume interactions and not to the nature of P(tBu-MA) grafts because both PS and P(tBuMA) chains beingprepared by radical polymerization are more flexible (tac-ticity effect) than their analogue species obtained by ionicpolymerization [75]. However, bearing in mind that tBuMA[76] with its bulky tert-butyl groups has much larger seg-mental volume compared to styrene monomer units im-plies that the contribution of steric mechanism to thestiffening of the backbone is significant and can not beneglected.

4. Micellization behavior in solvents selective forP(tBuMA) grafts

For the micellization studies we have selected the sam-ples M2-4 and M2-8 with the intermediate (Nsc = 72) andthe longest side chains (Nsc = 222). The solvents selectivefor the P(tBuMA) grafts were used, namely acetone andtert-amyl alcohol (TAA). First, DLS measurements wereperformed on solutions in a dilute concentration regime.As it is shown in Fig. 12, single distribution of hydrody-namic radii of the graft copolymers in acetone (solid line)indicates that the polymers are molecularly dissolved. Incontrast, size distribution in TAA was clearly bimodal(dashed line) suggesting the presence of single chainsand aggregates. Conversion from intensity weighted func-tion (Fig. 12) to volume weighted function shows thatthe volume of aggregates is negligible (�0.1%).

As shown in Fig. 13, dependence of relaxation rate C onq2 is linear in both solvents and passes through the origin,which implies that the peaks are related to particles trans-lational diffusion.

The hydrodynamic dimensions of M2-4 and M2-8 inacetone are slightly larger than the molecularly dissolvedchains in THF solutions (see Table 4). This fact is somehowsurprising since acetone is a non-solvent for PS and shouldforce the backbone to shrink resulting in a smaller size.Although the unimolecular state of graft copolymers inacetone was not attained, it is clear from these results thatthe surrounding P(tBuMA) branches act as efficient pro-tecting shell for PS forming hydrophobic core and that

10 -1 10 0 10 1 10 2 10 3 10 40.00

0.05

0.10

0.15

0.20

Rh (nm)

RhG

(Rh)

Fig. 12. Representative distribution RhG(Rh) of hydrodynamic radii of thegraft copolymer M2-8 dissolved in acetone (s) and tert-amyl alcohol (d)at the scattering angle h ¼ 90� .

the aggregation number is presumably very low. Thisremarkable behavior of graft copolymers is attributed totheir specific comb-like topology and the ‘‘solubilizingeffect” of the side chains, a phenomenon, which is cur-rently well documented in literature [14,45]. Unlike SAXSor static light scattering (SLS), DLS probes dynamics ofmacromolecules without providing information aboutshape of investigated objects. Nevertheless, combinationof these techniques permits construction of valuble struc-ture factors such as the Rg=Rh. The latter structure factorfor M2-4 in both THF (Rg=Rh = 0.76) and acetone(Rg=Rh = 0.75) corresponds roughly to what is predictedfor hard spheres (Rg=Rh = 0.776) while for M2-8 it is clearlybelow this limit with the values in THF and acetoneRg=Rh = 0.46 and Rg=Rh = 0.56, respectively, indicatingmicrogel architecture.

To get a better insight into the structure of micellaraggregates formed in acetone solutions we have performedSAXS experiments which are represented in Fig. 14 in formof a Kratky plots for the sample M2-8. For comparison pur-poses SAXS curve of the sample M2-8 in THF (unimer) isalso shown. A pronounced bump on a Kratky plot in ace-tone indicates a denser, more compact structure comparedwith the corresponding scattering pattern in THF in thesame q-range. The scattering behavior in higher q-rangeshows that the chain stiffness of the graft copolymer inacetone decreased as the I(q) q2 does not follow q1.

The studied graft copolymers formed unimolecular mi-celles in tert-amyl alcohol, a solvent which is even more

0.0 0.1 0.2 0.3 0.40

2

4

6

I(q)q

2x

104

q (Å-1 )

Fig. 14. Kratky plots for M2-8 in THF (s) and acetone (d), c = 0.02 g cm�3.

D. Gromadzki et al. / European Polymer Journal 45 (2009) 1748–1758 1757

selective towards P(tBuMA) grafts. In this case hydrody-namic radius of M2-4 and M2-8 was 6.6 and 10.6 nm,respectively, which was much lower compared to theirunimers in THF with the values 9.0 and 17.1 nm, and inacetone with the values 9.7 and 14.4 nm, respectively.

5. Conclusion

The conformational behavior of branched copolymerswith respect to the length of the side chains in diluteTHF solutions was thoroughly investigated in this work.It was demonstrated by experimental techniques (DLS,SAXS, viscometry) that progressive increasing of Nsc ledto conformational transition from combs through star-liketo a microgel architecture. The increasing size of tBuMAside chains induced stiffening of the backbone in diluteTHF due to elimination of an excluded volume effect.Accordingly, the Flory exponents with values close tov = 0.6 and 0.5 for graft copolymers with comb-like andstar-like topology, respectively, indicated bahavior ofchains in a good and H-solvent. The Kratky plots of inves-tigated graft copolymers in THF exhibited pronouncedmaxima indicating scattering from compact, branched ob-jects. The persistence lengths ranging from lp = 14.1–18.7 Åfor graft copolymers with comb-like topology were twotimes larger compared to the neat macroinitiator back-bone. The graft copolymers dissolved in tert-amyl alcoholformed unimolecular micelles as proved by DLS and SAXS.

Acknowledgement

The authors gratefully acknowledge the support by theCzech Academy of Sciences (IAA400500703), by the GrantAgency of the Czech Republic (202/09/2078) and the MarieCurie Research Training Network SOCON; Contract No.MRTNCT-2004-512331 (D.G.).

References

[1] Flory PJ. Principles of polymer chemistry. Ithaca, New York: CornellUniversity Press; 1953.

[2] Sheiko SS, Sumerlin BS, Matyjaszewski K. Prog Polym Sci2008;33:77–103.

[3] Gromadzki D et al., submitted for publication.[4] McCrackin FL, Mazur J. Macromolecules 1981;14:1214–20.[5] Lipson JEG. Macromolecules 1991;24:1327–33.[6] Fredrickson GH. Macromolecules 1993;26:2825–31.[7] Shinozaki A, Jasnow D, Balazs AC. Macromolecules 1994;27:

2496–502.[8] Foster DP, Jasnow D, Balazs AC. Macromolecules 1995;28:3450–62.[9] Rouault Y, Borisov OV. Macromolecules 1996;29:2605–11.

[10] Vasilevskaya VV, Klochkov AA, Khalatur PG, Khokhlov AR, ten BrinkeG. Macromol Theory Simul 2001;10:389–94.

[11] Wang R, Jiang Z, Hu J. Polymer 2005;46:6201–7.[12] Benoît H, Hadziioannou G. Macromolecules 1988;21:1449–64.[13] Pispas S, Hadjichristidis N, Mays JW. Macromolecules 1996;29:

7378–85.[14] Pitsikalis M, Woodward J, Mays JW, Hadjichristidis N.

Macromolecules 1997;30:5384–9.[15] Xenidou M, Beyer FL, Hadjichristidis N, Gido SP, Beck Tan N.

Macromolecules 1998;31:7659–67.[16] Beyer FL, Gido SP, Büschl C, Iatrou H, Uhrig D, Mays JW, et al.

Macromolecules 2000;33:2039–48.[17] Nakamura Y, Wan Y, Mays WJ, Iatrou H, Hadjichristidis N.

Macromolecules 2000;33:8323–8.[18] Terao K, Farmer BS, Nakamura Y, Iatrou H, Hong K, Mays JW.

Macromolecules 2005;38:1447–50.[19] Hadjichristidis N, Iatrou H, Pispas S, Pitsikalis M. J Polym Sci Part A:

Polym Chem 2000;38:3211–34.[20] Ruokolainen J, Mäkinen R, Torkkeli M, Mäkelä T, Serimaa R, ten

Brinke G, et al. Science 1998;280:557–60.[21] Ikalla O, ten Brinke G. Science 2002;295:2407–9.[22] Braunecker WA, Matyjaszewski K. Prog Polym Sci 2007;32:93–146.[23] Matyjaszewski K, Gnanou Y, Leibler L. Macromolecular engineering:

from precise macromolecular synthesis to macroscopic materialsproperties and applications. Wiley-VCH: Weinheim; 2007.

[24] Otsu T, Yoshida M. Makromol Rapid Commun 1982;3:127–32.[25] Otsu TJ. Polym Sci Part A: Polym Chem 2000;38:2121–36.[26] Hawker CJ, Bosman AW, Harth E. Chem Rev 2001;101:3661–88.[27] Tsarevsky NV, Matyjaszewski K. Chem Rev 2007;107:2270–99.[28] Moad G, Rizzardo E, Thang SH. Polymer 2008;49:1079–131.[29] Neugebauer D. Polym Int 2007;56:1469–98.[30] Pyun J, Kowalewski T, Matyjaszewski K. Macromol Rapid Commun

2003;24:1043–59.[31] Fredrickson GH, Leibler L. Macromolecules 1989;22:1238–50.[32] Zilliox G, Roovers JEL, Bywater S. Macromolecules 1975;85:573–8.[33] Prud’homme J, Bywater S. Macromolecules 1971;4:543–8.[34] Han CC, Mozer B. Macromolecules 1977;10:44–51.[35] Nguyen AB, Hadjichristidis N, Fetters LJ. Macromolecules

1986;19:768–73.[36] Hadjichristidis N, Roovers J. J Polym Sci Polym Phys Ed

1978;16:851–8.[37] Tsitsilianis C, Staikos G, Dondos A, Lutz P, Rempp P, Benoît H.

Macromol Chem 1990;191:2309–18.[38] Krause S. J Phys Chem 1964;68:1948–55.[39] Utracki LA, Simha R, Fetters LJ. J Polym Sci A-2: Polym Phys

1968;6:2051–66.[40] Utiyama H, Takenaka K, Mizumori M, Fukuda M, Tsunashima Y,

Kurata M. Macromolecules 1974;74:515–20.[41] Tanaka T, Omoto M, Inagaki H. Macromolecules 1979;12:146–52.[42] Ionescu L, Picot C, Duplessix R, Duval M, Benoît H, Lingelser JP, et al. J

Polym Sci Polym Phys Ed 1981;19:1033–46.[43] Matsusita Y, Shimizu K, Noda I, Chang T, Han CC. Polymer

1992;33:2412–5.[44] Stepanyan R, Subbotin A, ten Brinke G. Macromolecules

2002;35:5640–8.[45] Tuzar Z, Kratochvíl P. Adv Coll Interface Sci 1976;6:201–32.[46] Riess G. Prog Polym Sci 2003;28:1107–70.[47] Tuzar Z, Kratochvíl P. In: Matijevic E, editor. Surf Coll Sci, vol.

15. New York: Plenum Press; 1993.[48] Uchman M, Prochazka K, Štepánek M, Mountrichas G, Pispas S,

Špírkova M, et al. Langmuir 2008;24:12017–25.[49] Hadjichristidis N, Pispas S, Floudas G, editors. Block copolymers.

Synthetic strategies physical properties and applications. Wiley-Interscience; 2002.

[50] Tuzar Z, Kratochvíl P, Procházka K, Contractor K, Hadjichristidis N.Macromol Chem 1989;11:2967–73.

[51] Dondos A, Rempp P, Benoît H. J Polym Sci Polym Lett Ed1966;4:293–300.

[52] Price C, Woods D. Polymer 1974;15:389–92.[53] Selb J, Gallot Y. Macromol Chem 1981;182:1775–86.[54] Kikuchi A, Nose T. Polymer 1996;37:5889–96.

1758 D. Gromadzki et al. / European Polymer Journal 45 (2009) 1748–1758

[55] Kikuchi A, Nose T. Macromolecules 1996;29:6770–7.[56] Gromadzki D, Makuška R, Netopilík M, Holler P, Lokaj J, Janata M,

et al. Eur Polym J 2008;44:59–71.[57] Brandrup J, Immergut EH, Grulke EA, editors. Polymer

handbook. New York: Wiley; 1999.[58] Jakeš J. Collect Czech Chem Commun 1995;60:1781–97.[59] Netopilík M, Schallausky F, Reichelt S, Lederer A, Kratochvíl P. Int J

Polym Anal Charact 2007;12:273–84.[60] Bohdanecky M, Kovár J. Viscosity of polymer solutions. Elsevier;

1982.[61] Burchard W. Adv Polym Sci 1999;143:113–94.[62] Zimm BH, Kilb RW. J Polym Sci 1959;37:19–42.[63] Sheridan PF, Adolf DB, Lyulin AV, Neelov I, Davies GR. J Chem Phys

2002;17:7802–12.[64] Zimm BH, Stockmayer WH. J Chem Phys 1949;17:1301–14.[65] Ishizu K, Ono S, Uchida S. Macromol Chem Phys 1997;198:

3255–65.

[66] Gromadzki D et al. (and references therein), Polymer, accepted forpublication.

[67] Katzenstein A, Huber K. Langmuir 2002;18:7049–56.[68] Glatter O, Kratky O, editors. Small-angle X-ray

scattering. London: Academic Press; 1982.[69] Antonietti M. Angew Chem Int Ed 1988;27:1743–7.[70] Schmitz KS, Wang B, Kokufuta E. Macromolecules 2001;34:8370–7.[71] Pich A, Tessier A, Boyko V, Lu Y, Adler HJP. Macromolecules

2006;39:7701–7.[72] Boyko V, Richter S, Burchard W, Arnd KF. Langmuir 2007;23:776–84.[73] Lambrinos P, Tardi M, Polton A, Sigwalt P. Eur Polym J

1990;26:1125–35.[74] Sharp P, Bloomfield VA. Biopolymers 1968;6:1201–11.[75] Karandinos A, Nan S, Mays JW, Hadjichristidis N. Macromolecules

1991;24:2007–10.[76] Pochan DJ, Gido SP, Zhou J, Mays JW, Whitmore M, Ryan AJ. J Polym

Sci Part B Polym Phys 1997;35:2629–43.