Surfactant book Ch 7

7/25/2019 Surfactant book Ch 7

1/9

Chapter 7

Structure

of

ShearedCetyltrimethylammonium

TosylateSodium

Dodecylbenzenesulfonate

Rodlike

Micellar

Solutions

RichardD.KoehlerandEric W. Kaler

Center

forMolecular and

Engineering Thermodynamics,

Department

of Chemical

Engineering, University

ofDelaware,

Newark,

DE19716

The viscoelastic behavior observed inaqueous solutions of the

cationic/anionic

surfactant mixture cetyl trimethylammonium

tosylate(CTAT) and

sodium dodecyl benzyl sulfonate(SDBS)

provides evidence for the

presence

of rodlike micellar structures. In

particular, highly viscous andviscoelastic gels form at low total

surfactant concentrations. Sma l l angle neutron scattering

measurements reveal a strong interaction peak

that

becomes

anisotropic with increasing

shear rate.

This anisotropy indicates

an

increase in the order of the micelles in

a

preferential direction.

Mode l

fits

show

that

the rotational diffusion coefficients decrease with

increasing total surfactant concentration for samples inthemiddle of

the rodlike micellar region, but they increase on approach to the

phase

boundary. Thus micellesin thecenterof themicellarphasegrow

with increasing total surfactant concentration, whilethose

near

the

boundary remain shorter. The shorter micellesareprecursors to the

vesicle

and lamellarstructuresof nearby

phases.

Rodlikemicelles form in ionic surfactant solutionsathigh salt concentrations(7,2).

They also form

in

solutions containing strongly binding counterions such

as

salicylate(5-5)

or

tosylate(6). These ions contain

a

hydrophobicpart

that

prefers

to

remain in the nonpolar core of therodlike

micelle.

Ifthe counterion is replaced with

an oppositely charged surfactant, thereisvery strong counterion binding, and

rodlikemicelles,spontaneousvesicles, and lamellarstructurescan form(6). In the

C T A T / S D B S mixture (Figure 1)decreasing theC T A T / S D B S ratioat aconstant

total surfactant concentration shows

a

progression from

a

rodlike micellar

phase

on

the C T A T richside,to amicelle/vesicletwophasecoexistence region, and througha

CTAT - r i c h vesicle lobetothe equimolarline. Thephasebehavior is similar onthe

other side of the equimolarline. The current emphasis is ontheCT AT - r i ch micelle

phase.

Electron microscope images(6) and the viscoelastic response(7-5) of

moderately concentrated rodlike micellar solutions

suggests

that

they contain long

and entangled threadlike micelles.

Cates(7,


2/9

7.

K O E H L E R

&

K A L E R

ShearedCTT-SDBS Rodlike

Micellar

Solutions 111

the length distribution depend on the energy of formation of two micellar endcaps

during

the scission reaction(7,#). However, constant shear measurementsonthese

solutions suggest that the micelles act as

rigid

rods below a certain length

scale(9,70). These two different points of

view

are not inconsistent - the threadlike

micellescan be thought of as chains consisting of discrete rigid segmentsof afixed

persistence length (Figure 2). Since these segments are assumed to act

independently, the microstructure on small length scales can be modeled as a

collectionof

rigid

rods

with

length equal to the persistence length.

Smallangle neutron scattering ( SANS )provides useful information about the

structure and

shapes

ofmicellesin solution(77). However, for nonspherical particles

this technique cannot provide unambiguous information about particle shape(77,72).

Analysis

of particle structure can be

simplified

by alignment of the anisotropic

particles in electric(75), magnetic(73) orflow fields(9,70,73-76). Thedegreeof

alignmentdependson the axialratio of the particles, and alignment removes some

ambiguity in the determination of the particle

shape.

Measurements of scattering in

the presence of an external

field

also provides information about the rotational

diffusion coefficient of elongated particles(77).

S AN STheory

The measured intensity froma system of rodlikecolloidalparticles can be written

as(70,77),

^ ( q ) = exp( iq R

N M

) F

N

( q ) F

M

(q )^

(1)

T

\N

= M=

or,

f d

= S(FN,)

2

)

+

^( RNM=N(.F

d ~ ' / V ,

N = 1 M = 1

,

M

,

N

(2)

where

R

is a vector connecting the center of

mass

of particles and

M .

The

volume

of the rod is V

r

and Ap is the difference between the scattering length

density of the rod and the solvent, q is the difference between the incident and

scattered intensity vectors and has magnitude q=(47cA.)sin(e/2), where is the

neutron wavelength and is the scattering angle. The brackets indicateaverages

over the orientations of the rods.

F orcylindricalparticles F(q) is written(72)

sin

-V-cosa

L

T

, .

F(q) -F(q .)

= 4 r

(3)

where a is the angle between the rod axis, represented by a unit vector, u, and the

scattering vector, q (Figure 3). The amplitude functiondependson the radius R and

the length,L . Theformfactor is

DownloadedbyK

INGABDULLAHUNIVSCITECHLGYonAugust4,

2015|http://pubs.acs.org

PublicationDate:December9,

1994

|doi:10.1

021/bk-1994-0578.c

h007

In Structure and Flow in Surfactant Solutions; Herb, C., et al.;ACS Symposium Series; American Chemical Society: Washington, DC, 1994.


3/9

122

STRUCTUREAND FLOW IN SURFACTANT SOLUTIONS

1.5H

S

c

I

S

.

0.5H

(D

D

RodlikeMicelles

L

RodlikeMicelles

and

\fe

sides

1 1 1

100/0 98/2 96/4 94/6 92/8 90/10

weightratioCTAT/SDBS

Figure1: Schematic of the phase

diagram

ofCTAT/SDBSshowing the

progression

fromrodlike

micelle, throughamicelle/vesicle two phase region, to

a

vesicle

lobe on theC T A T

richside

of the

equimolar

line. Thecircles indicate

the samples studied with

SANS.

Figure2: Schematic showing the different lengthscalesforathreadlike

micelle.

Figure

3:

Scattering geometry for the shear flow experiment. Flow is in the x-

direction,the shear gradient,

and

the neutron beam are

in

thez-direction.The

azimuthal

and

polar

anglesare and .

DownloadedbyK




1994

|doi:10.1

021/bk-1994-0578.c

h007



4/9

7.

K O E H L E R K A L E R ShearedCTAT-SDBS RodlikeMicellar Solutions

123

(F

2

(q)) =

J

u

F

2

(q)f

(u)du =

J *

F

2

(q,a)f ,)8

(4)

The normalized orientational distribution function f(u)

represents

the probabilitythat

a rod is pointing between u and du and is a function of the azimuthal, () and polar,

) angles of the rod.

The second term in equation 2 can be simplified by neglecting any

correlation

between rod orientation and position. In this decoupling approximation

we have(70,7J)

| | ( q ) =(Ap)

2

OV

r

{(F

2

(q))+ n(F

q ))

2

cos q

r)[P(r) - l]drj.

(5)

where is the volume fraction of particles and P(r) is the angularly-dependent pair

distributionfunction. For spherical particles, P(r) is isotropic and

depends

only on

interparticle center-to-center distance.

G i v e n

an interparticle potential, integral

equations or Monte Carlo simulations can be used to obtain the pair distribution

function(77). For rods, the interaction potential, and so P(r),dependson both rod

orientation and interparticle distance. Spherical harmonic expansions of integral

equations have been used to

find

the angularlydependentpair distribution function

for uncharged elongated particles(79). R i g i dcharged rods have been modeled using

Monte

Carlo simulations and perturbation expansions around sphericalized reference

potentials(20).

I f

a

shear

f ield

aligns the rods, the Smoluchowski equation provides the

distribution function for the orientation of the rods. Doi and Edwards(27) and

Larson(22,25) write the time evolution equation for the orientational distribution

function

as

^ +

4-

f(uV v- uuu:V v ) f1- D

r

^ -

+ f i

3 u

+

3ulkT

= 0

(6)

where Vv is the velocity gradient tensor,D

r

is the rotational diffusion coefficient,

and V is the potential energy of interaction between rods. For the simple analysis

givenhere,V is set to zero and D

r

is assumed to be independent of orientation. Wi th

theseassumptions the distribution function of rods in ashear

flowdepends

on one

parameter, , which is the ratio of the shearrate to the rotational diffusion

coefficient, is ameasureof the ratio of strength of the

flow

thatorients the rods to

the strength of the restoring force of diffusionthatrandomizes them.

For calculation f(u) can be expanded in a series of spherical

harmonics(27,22)

f(u,t)= X b

m

\ m , where, |An)=

=0

m

=0

^even

Y? u)

for m = 0

- ^ ( Y 7( u )

+ (- l)

m

Y J

m

(u)) form*0

(7)

DownloadedbyK




1994

|doi:10.1

021/bk-1994-0578.c

h007



5/9

124

STRUCTUREANDF L O WINSURFACTANTSOLUTIONS

The particular

form

of

\m

combines the spherical harmonic functions, Y u ) ,so

that

the symmetry and boundary conditions of the problem are met.

This

expansion

is

then substituted into the

Smoluchowski

equation and the inner product is taken

with

respect to each member of the series.

Using

orthogonality and triple product

conditions yields a set of ordinary differential equations in time for the coefficients

b

/ m -

r t

A s a result of symmetry around the f low direction the maximum of the

distribution

function occurs at

=0

for any value of . The experimental geometry is

not symmetric in the plane perpendicular to the

vorticity,

so for low values of ,

when

diffusion

is important, the rods are pointed at 45 away

from

the f low

direction,

=

/ 4 .

At higher shear

rates,

(large ) the particles are aligned in the

flowdirectionwith =

/ 2 .

However, because this movement is out of the plane of

the detector, it is notvisiblein the scattering experiment.

For the experiments described

here

the second term in equation 5

tends

to

zero for q >

0.03A,

so a fit to higher q data perpendicular and parallel to the

f low

direction

provides information on the effective rotational

diffusion

coefficients of the

rodlikemicelles without the need for a detailed knowledge of the pair distribution

function.

Experimental

Section

Cety ltrimethyl ammonium tosylate C T A T )was obtainedfrom Sigma

Chemical

and

recrystallizedthree

times. Sodium dodecyl benzene sulfonate(SDBS) soft type was

used as supplied

from

TCI.

D O

was obtained

from

Cambridge Isotope

Laboratories

and also used as

supplied.

The

phase

diagram is reported elsewhere(o).

S A N S

samples were prepared by completely

mixing

stock solutions of

C T A T

and

S D B S

inD Oto the desired weight ratio. Two samples were in the center of the

one

phase

rodlike

micellarregion:

sample 1 containing

1.5wt

97/3

C T A T / S D B S

and sample 2 containing

1.0wt

97/3

C T A T / S D B S .

Two other samples were

prepared closer to the rodlike

micelle

phase

boundary, sample 3 containing

1.5wt

95/5

C T A T / S D B S

and sample 4 containing

1.0wt

94/6

C T A T / S D B S

(Figure 1).

S m al langle neutron scattering measurements were performed on the 30-meter

S A N S

spectrometer at the

National

Institute of Standards and Technology at Gaithersburg,

M D .

The sample to detector distance was 5.25m and a wavelength of 6

with

/=0.15 yielded

a q range between

0.005

- 1

and

0.08

1

.

The samples were

placed

in a concentric cylinder shear

ce l l

with

a 0.843mm gap width(24).

Measurements were made at

25

e

C

at steady shear

rates.

The samples were

presheared for 300 seconds before the measurements began.

The raw 2-D data was corrected by subtracting the appropriate experimental

background. Circular averages were made on shells 10 wide around a direction

perpendicular to the

flow

direction and parallel to the

flow

direction, and the data

was put on absolute scale

with

the use of a polystyrene standard. For

fitting,

the

experimental

data was

divided

by the prefactor in equation 5. The persistence length

or

effective rod length was estimated using Bragg's law, L= ^ / q

m a

x , where q

m a x

is

the q value of the peak in the scattering curve(70). The radius of the rod was found

byfitting

the

form

factor, equation 4, to the high q data at zero shear where the decay

of

the intensity curve

only

depends on the particle radius.

Effective diffusion

coefficients

at each shear

rate

were obtained by

fitting

equation 4 to data measured

for

q >

0.03

both parallel and perpendicular to the

flow

direction.

Results and

Discussion

Figure

4 shows representative scatteringpatternsat various shear

ratesfrom

1.0wt%

97/3 C T A T / S D B S inD2O(sample 2). At

rest,

the scattering

from thesemicellar

DownloadedbyK




1994

|doi:10.1

021/bk-1994-0578.c

h007



6/9

7. K O E H L E R & K A L E R Sheared

CTAT SDBS

odlike

Micellar Solutions

125

Figure4: Scattered neutron intensity, for

1.0wt

97/3CTAT/SDBSinD2O

showing

an

increase in anisotropy with shear rate, (a) shear rate 0 s

_1

, (b) shear

rate 10 s

-1

, (c) shear

rate

20 s

1

, (d) shear rate 40 sr

1

.

DownloadedbyK




1994

|doi:10.1

021/bk-1994-0578.c

h007



7/9

126

S T R U C T U R E ANDF L O WINS UR F A C T A N T SOLUTIONS

solutions is isotropic

and

displays a

single

strong correlation peak (Figure 4a).

This

indicates that the micellesarechargedandhighly interacting. The scattering patterns

become increasingly anisotropic with increasing shear rate, and

show

increasing

intensity in the directionperpendicularto the flow direction

and

decreasing intensity

in

the direction parallel to the flow direction.

This

change provides clear evidence

that the rodlike micelles are aligning. The increase in anisotropy implies the rods

align like the rungs on a ladder, thereby reinforcing the correlation peak in the

direction perpendicular to the flow and weakening it in the direction parallel to the

flow.

Figure

5

shows

scattering

from

sample 2 along

lines

perpendicular and

parallel

to the flow direction. The solid and dashed

lines

are the model

fits

of the

form

factor where the

effective

rotational diffusion coefficient is the only adjustable

parameter; the radius and length are determined

from

the zero shear data. The good

agreement

between

the shape of the experimental and fitted curves at high q

suggests

that the length estimatedfromthe q value of the intensity peak is a good

estimate

of

the persistence length of the micelles.

TableIshows

the results of

this

fit for the four

samples studied.

Table

I. Rotational Diffusion Coefficients as

a

Function

of

Shear

Rate

Shear Rotational Diffusion Coefficient D

r

(s

-1

)

Rate wt% surfactant, ratio of

C T A T / SD B S

(s-

1

)

1.5wt%,97/3

1.0 wt%, 97/3 1.5wt%,95/5 1.0wt%,94/6

5 1.7 1.0

1.7

0.7

10 1.0 1.3

1.7

1.3

20

0.4

2.0

1.7 2.7

50 0.6 2.0

1.2

6.7

100

1.0 2.0

8.3

10.0

Theeffective

rotational diffusion coefficient

decreases

with increasing total

surfactant concentration along the 97/3 C T A T / S D B Sline, which is in the middle of

the

rodlike

micelle region on the phase

diagram.

At higher

SDBS

ratios the

effective

diffusion coefficients increase with shear rate.

The

rotational diffusion coefficient, D

r o

, of

a rod

in dilute solution varies as

L

3

while in a semi-dilute solution Dr ~

D

r o

(cL

3

)-

2

.

The rotational diffusion

coefficient of the rodlike micelles depends strongly on the length of the rod. The

decreasing diffusion coefficient with increasing total surfactant concentration implies

an

increasing micelle length

or an

increase

in

entanglement.

Near

the phase boundary

(samples

3

and

4), the observation of

an

increasing

effective

rotational diffusion coefficient with increasing shear ratesuggeststhat the

micelles are short or mobile enough to remain unaligned

even

at very high shear

rates. The higher diffusion coefficient may be due tolessentanglement or may be

directly related to a

decrease

in

rod

length. The proximity of the phase boundary is

consistent

with the formation of shorter micelles and indicates that more endcaps can

form

near the phase boundary.

Conclusions

Rodlike

micelles that can be aligned in a shear flow are present on the

C T A T

rich

side

of the

CTAT/SDBSD2O

phase

diagram.

Modeling the neutron scattering data

provides information about theeffectiverotational diffusion coefficient ofthese

DownloadedbyK




1994

|doi:10.1

021/bk-1994-0578.c

h007



8/9

7. K O E H L E R & K A L E R ShearedCTATSDBS odlikeMicellar Solutions 127

DownloadedbyK




1994

|doi:10.1

021/bk-1994-0578.c

h007



9/9

128

STRUCTURE

AND

F L O W

IN

SURFACTANT

SOLUTIONS

rodlike

micelles. The

resultsindicate

that

longer,

moreentangled

micelles

are

formed

as thetotal surfactant concentrationisincreasedat aconstantratioof

C T A T / S D B S . Increasing

the

amount

of

SDBS

at a

constanttotal surfactant

concentration

leads

to

rodlike

micelles

which

are

muchshorter

and

more mobile.

Shorter

micelles

signala

change

in thestructures presentas thephasetransitionis

approached.

Acknowledgments

This

workwas

supported

byE.I.DuPontde

Nemours

Co.

The

authorsthankDr.

R.G.Larson forsupplying the

F O R T R A N

codeusedin thecalculationof the

orientationaldistributionfunction ofrodsin ashear flow. Theauthorsalso

acknowledge

G.Stratyand Dr. J.

Barkerfor theirhelpwiththe shear

cell

andSANS

measurements.

We

acknowledge

the

support

oftheNationalInstituteof

Standards

and

Technology, U.S. Department

of

Commerce,

in

providing

the

facilities used

in

thisexperiment. Thismaterialisbaseduponactivitiessupportedby the

National

Science

Foundation

underAgreement

No.

DMR-9122444.

LiteratureCited

1. Kern, R.;

Lemarechal,

P.;

Candau,

S.J.;

Cates,M . E .Langmuir,

1992,

8,

437.

2. Candeau,S.J.;

Hirsch,E .;Zana,

R.;

Adam,M .

J.Coll.InterfaceSci.,1988, 122,

430.

3. Hoffmann,H .;

Rehage,

H .;Rauscher,

A.

InStructureandDynamicsof

Strongly

InteractingColloidsandSupramolecular

Aggregates

inSolution;

Kluwer

Academic Publishers,

Amsterdam,

1992,

pp

493-510.

4. Kern

F.;Zana,

R.;Candau,S.J.Langmuir,1991, 7, 1344.

5.

Rehage,

H .;Hoffmann,H. J.

Phys.

Chem.,

1988,92,4712.

6. Kaler,E.W.;Herrington,

K .L . ;

Murthy,A . K .;Zadadzinski,J.A.N.

J.

Phys.

Chem.,

1992, 96, 6698.

7.

Turner,

M.S.;Cates,

M . E .

J.Phys.IIFrance,1992,2, 503.

8. Turner,

M.S.;

Cates,M . E .Langmuir,1991,7, 1590.

9. Herbst,

L .;

Hoffmann,

H .;Kalus,

J.;Thurn,

H .;Ibel,K .;

May, R.P.

Chem.

Phys.,

1986,

103,437.

10. Kalus,J.;Hoffmann,H. J.

Chem.

Phys.,1987,87,714.

11. Kaler,E.W.J.Appl.

Cryst.

1988, 21,729.

12. Guinier,

.;Fournet,G.

Small-AngleScattering ofX-Rays John Wiley

Sons,

Inc.,New

York,

1955, p19.

13. Kalus,

J.In

Structureand

Dynamicsof

StronglyInteractingColloidsand

SupramolecularAggregatesinSolution;KluwerAcademic Publishers,

Amsterdam,1992,

pp

463-492.

14. Hayter,J.B.;

Penfold,

J.

J.Phys.

Chem.,

1984,

88,

4589.

15.

Cummins,P.G.;Staples,

E .;

Hayter,

J.B.;

Penfold,

J.

J.

Chem.

Soc.,

Faraday

Trans.

1987,832773.

16. Cummins,P.G.;Hayter,J.B.;Penfold,J.;Staples,E.

Chem.

Lett. 1987,138,

436.

17.

Doi,

M .;

Edwards,S.F.TheTheory

of PolymerDynamics;Oxford

University

Press,

NewYork,1986;pp295,330.

19.

Perera,

.;

Kusalik,

P.G.;

Patey,

G.N.

J.

Chem.

Phys.,

1987,

87,

1295.

20. Canessa,E .; D'Aguanno,

B.;

Weyerich,

B.;

Klein,

R.

MolecularPhysics,1991,

73,

175.

21.

Doi,

M .;Edwards

S.F.J.

Chem.

Soc.,

Faraday Trans.

2, 1978,74,918.

22. Larson,

R.G.

Recent DevelopmentsinStructuredContinua;Longman:London,

1990;Vol2.

23. Larson,R.G.;

ttinger,R .G .

Macromolecules

1991,

24

6270.

24. Straty,G . C .

J.

Res.Natl.Inst Stand Technol. 1989,94 259.

R E C E I V E D

July

8, 1994

DownloadedbyK




1994

|doi:10.1

021/bk-1994-0578.c

h007

I St t d Fl i S f t t S l ti H b C t l

Surfactant book Ch 7

Documents

Transcript of Surfactant book Ch 7