dynamic light scattering studies of rod-like micelles in dilute and semi-dilute regime

Colloids and Surfaces A: Physicochem. Eng. Aspects 275 (2006) 161–167

Dynamic light scattering studies of rod-like micellesin dilute and semi-dilute regime

Gunjan Garg, P.A. Hassan∗, S.K. KulshreshthaNovel Materials and Structural Chemistry Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400085, India

Received 18 May 2005; received in revised form 12 September 2005; accepted 4 October 2005Available online 11 November 2005

Abstract

The effect of anionic hydrophobic salts, sodiump-toluenesulphonate (Na-PTS) and sodium salicylate (Na-Sal) on the growth behavior of cationicsurfactant micelles, cetyltrimethyl ammonium bromide (CTAB) has been investigated in the presence as well as absence of sodium chloride (NaCl)using dynamic light scattering measurements. In the absence of NaCl, a progressive decrease in the diffusion coefficient of CTAB (50 mM) micelleswas observed with increasing concentration of hydrophobic salts, Na-PTS and Na-Sal, suggesting an increase in the average dimension of themicelles. The micellar growth is explained in terms of a prolate ellipsoidal transition of the micelles. When the axial ratio of the micelles becomesl ribution ofr phobic saltc ards modelo©

K

1

itfsIswciltbmsw

trong

fntan-ilutely-s of

y-ntlychedv-theseclear

S)te

s-singdali-

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ong enough to drive the system into semi-dilute regime, a slow mode of long relaxation time begins to evolve and shows bimodal distelaxation time. In the presence of NaCl, the micellar growth is enhanced and the appearance of slow mode is evident at lower hydrooncentration than that is observed in the absence of NaCl. The onset of semi-dilute regime is consistent with the modified Doi–Edwf rod-like polymers. 2005 Elsevier B.V. All rights reserved.

eywords: Rod-like micelles; Dynamic light scattering; Sphere-to-rod transition; Living polymers; Semi-dilute regime

. Introduction

Surfactants are known to form thread-like or rod-like micellen dilute aqueous solutions containing suitable salts. The addi-ion of inorganic or organic salts to an ionic surfactant solutionacilitates the transition from spherical to rod-like micelles byhielding the repulsions between the charged headgroups[1–7].n recent years, considerable interest has been developed in theolution properties of the extended micellar structures formedhen salts are added to solutions of cationic surfactants such asetyl trimethyl ammonium bromide (CTAB). When the salt is annorganic electrolyte (e.g., NaBr, NaCl), long flexible, thread-ike micelles are formed with the molar ratio of salt to surfactantypically above 1, as inorganic counterions (e.g., Cl−, Br−)ind moderately to cationic micelles and thus lead to gradualicellar growth. In presence of organic salts, such as sodium

alicylate (Na-Sal) and sodiump-toluenesulphonate (Na-PTS),orm-like micellar structures are formed in cationic micelles at

∗ Corresponding author. Tel.: +91 22 25592327; fax: +91 22 25505151.

substantially lower concentrations of added salt due to the sbinding of hydrophobic counterions (salicylate andp-toluenesulphonate) to the micellar surface[8–10]. When the length othese micelles becomes sufficiently large, they become egled and are known to exhibit properties similar to semi-dpolymer solutions. The worm-like micelles are similar to pomers in that they are quite flexible and exhibit contour lengththe order of micrometers[11]. These so-called equilibrium polmers differ from classical polymers in that they are constabreaking and making and, therefore, do not exhibit a quencontour length distribution[12]. During the past few years, seeral groups have made efforts to explore the dynamics ofworm-like systems using various techniques such as numagnetic resonance (NMR) spectroscopy[13–15], dynamiclight scattering (DLS)[16–19], forced rayleigh scattering (FR[20], fluorescence spectroscopy[21–23], electrochemical rou[24–28]and dynamic viscoelastic (DVE)[29–32]techniques.

Nemoto and co-workers[16,17,20,33]have carried out sytematic studies on dynamics of the CTAB/Na-Sal micelles uDLS technique. According to their investigations, a bimodistribution of the decay rateΓ was observed over the sem

E-mail address: [email protected] (P.A. Hassan). dilute regime of thread-like micelles. Similar studies have been

927-7757/$ – see front matter © 2005 Elsevier B.V. All rights reserved.oi:10.1016/j.colsurfa.2005.10.001

162 G. Garg et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 275 (2006) 161–167

performed by Brown et al.[34] on CTAB and sodium naph-thalene sulphonate in aqueous solutions. Recently, Amin et al.[35] have reported a detailed dynamic light scattering study ofCTAB/Na-Sal solution over a wide range of CTAB concentra-tion and Na-Sal:CTAB mole ratio. According to their studies, thehydrodynamic correlation length, associated with the fast relax-ation mode is observed to depend on both the CTAB concentra-tion and Na-Sal:CTAB mole ratio. Previously, Magid et al. stud-ied the counterion-mediated micellar growth for cetyltrimethy-lammonium micelles in presence of 2,6-dichlorobenzoate andchloride counterions using small angle scattering techniques. Avariation in counterion composition at constant ionic strengthinduces large changes in micelle size. The aromatic ion 2,6-dichlorobenzoate increases the surfactant-packing parameterby increasing the average volume per surfactant monomer, acosurfactant-like effect, and decreasing the area per headgroup.Counterions such as chloride, which show only surface adsorp-tion, affect only headgroup area and are much less effective atdriving micellar growth[36,37].

Recent rheological studies on CTAB/Na-Sal system in pres-ence of added inorganic electrolytes revealed the occurrence of ashear-thickening behavior beyond a critical shear rate[38]. Thisphenomenon is ascribed to the formation of a shear-inducedstructure and is very sensitive to the concentration of inorganicelectrolytes. Thus, comparison of the microscopic structuralparameters of the CTAB/Na-Sal micelles in the presence andt f thiss

emi-q les inC iquea imeu lts oD ns ot entc ell aa

2

2

calsa useda em( eouss

2

per-f dig-i teda m-p( ure-m 0 to

130◦. All the measurements were taken at 25◦C. The measuredintensity correlation functions were analyzed by two methods: adouble exponential fit where bimodal distribution of relaxationtime is assumed and by the method of cumulants[39] whereunimodal distribution of relaxation time is considered.

3. Results and discussion

3.1. Effect of hydrophobic salts on micelle size

To understand the microstructure evolution in CTAB micelleswith addition of hydrophobic salts (Na-Sal and Na-PTS), DLSmeasurements were performed at different concentrations ofhydrophobic salts. The concentration of surfactant was kept con-stant (50 mM) and the concentration of hydrophobic salts (csalt)was varied from 10 to 50 mM.Fig. 1 shows a representativeplot of variation of the intensity correlation function,g2(τ), for50 mM CTAB with cNa-PTS= 10, 20 and 50 mM at a scatteringangle of 90◦. The solid line is a fit to the data by the method ofcumulants with a mean relaxation rate (Γ ) and polydispersityindex [P.I. = variance/(mean)2] as the fitted variables[39]. Atlow salt concentration for both the salts (Na-Sal and Na-PTS),the cumulants method gives a reasonably good fit to the data withthe correlation coefficient (r) greater than 0.999 and random dis-tribution of residuals. However, atcsalt= 50 mM, the cumulantsfi linei tiont t al.[ ofc uters them e thea do d ofc thod,C of

F TABw tt

he absence of NaCl is relevant for the understanding ohear-induced phenomenon.

The objective of the present study is to carry out a suantitative estimate of the parameters of the rod-like micelTAB/Na-Sal and CTAB/Na-PTS systems using DLS technnd compare the transitions from dilute to semi-dilute regsing models of rod-like polymers. Here we report the resuLS measurements made on dilute and semi-dilute solutio

hread-like micelles of (50 mM) CTAB in presence of differoncentrations of Na-PTS and Na-Sal, in presence as wbsence of 0.5 M NaCl.

. Experimental

.1. Chemicals

CTAB and Na-PTS were obtained from Sigma Chemind Na-Sal was obtained from Fluka. All chemicals weres received. Deionized water from a Millipore-MilliQ systresistivity∼18 M� cm) was used in all cases to prepare aquolutions.

.2. Dynamic light scattering

Dynamic light scattering (DLS) measurements wereormed using a Malvern 4800 Autosizer employing 7132tal correlator. The light source was Ar-ion laser operat 514.5 nm with maximum power output of 2 W. The sales of micellar solutions were filtered through 0.2-�m filtersAcrodisc) to avoid interference from dust particles. Measents were made at five different angles ranging from 5

ff

s

t slightly deviates from the data at larger times (see solidn Fig. 1), due to the evolution of a slow mode of long relaxaime. This is consistent with the earlier reports by Amin e35] and others[17,20,33,34]that show a bimodal relaxationorrelation function of polymer-like micelles in the semi-dilegime. The appearance of a slow mode atcsalt= 50 mM thoughmall in amplitude, is an indication of uniaxial growth oficelles thereby approaching the semi-dilute regime. Sincmplitude of the slow mode is very small (∼0.02) and is observenly at csalt= 50 mM, the data was analyzed by the methoumulants. Analysis using the constraint regularization meONTIN, [40,41] also revealed a unimodal distribution

ig. 1. Representative plot of the intensity correlation function for 50 mM Cith cNa-pts = 10, 20 and 50 mM at a scattering angle of 90◦. The solid line is fi

o the data using method of cumulants.

G. Garg et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 275 (2006) 161–167 163

Fig. 2. The variation of (a) apparent diffusion coefficient (Da) obtained from theslope of the plots ofΓ vs.q2 and (b) length (L) calculated from Perrin’s formulafor 50 mM CTAB at different concentrations of Na-PTS in presence as well asabsence of 0.5 M NaCl.

relaxation rate supporting the validity of cumulants results. Theshift of the correlation function to larger times with increase insalt concentration is an indication of the growth of the micelles.

The angular variation of the average decay rate (Γ ) of theintensity correlation function obtained from the fit at differentconcentrations of Na-PTS and Na-Sal was found to vary lin-early as a function ofq2 indicating translational diffusion of thescatterers and negligible contribution from rotational diffusionin case of anisotropic micelles. This is expected for micelles dueto very small dimension as compared to the wavelength of thelight.

The apparent diffusion coefficient (Da) of the micelleswas calculated from the slope ofΓ versus q2 plot. Thevariation of apparent diffusion coefficient,Da, of CTABmicelles at different concentrations of Na-PTS and Na-Sal isdepicted inFigs. 2(a) and 3(a), respectively. The open cir-cles in Figs. 2(a) and 3(a)show the data for CTAB/Na-PTSand CTAB/Na-Sal in presence of 0.5 M NaCl, which willbe discussed further. At very low concentration of the salts(csalt= 10 mM),Da and the corresponding hydrodynamic diam-eter, calculated using Stokes–Einstein relation, is in the samerange as that expected for small globular micelles. With suc-cessive addition of Na-PTS and Na-Sal,Da was found to dropsteeply reflecting a sudden increase in the average dimen-sion of the micelles. AtcNa-PTS= 15 mM, the Da value is63.4× 10−8 cm2/s corresponding to an equivalent sphere diam-e conc ic toh 7 nmf h of

Fig. 3. The variation of (a) apparent diffusion coefficient (Da) obtained from theslope of the plots ofΓ vs.q2 and (b) length (L) calculated from Perrin’s formulafor 50 mM CTAB at different concentrations of Na-Sal in presence as well asabsence of 0.5 M NaCl.

a dodecyl chain being only 2.17 nm[42]. Moreover, previousreports on CTAB micelles in the presence of hydrophobic saltsreveals the formation of long thread-like micelles[8–10,43–46].Thus, the observed drastic decrease inDa could be attributed tothe formation of prolate ellipsoidal micelles.

The DLS data at high salt concentration were analyzed interms of prolate ellipsoidal structure. To get a quantitative insightin to the growth of the micelles, the lengths of the micelleswere estimated using Perrin’s formula[47] that relates the aver-age diffusion coefficient to the axes of the ellipsoid. The minoraxis of the ellipsoid is taken as constant at 4.3 nm and onlythe semi-major axis is varied. Corrections to the measuredDa for possible hydrodynamic and thermodynamic contribu-tions were applied during the data analysis as reported ear-lier [52]. The average length (L) of the micelles as obtainedfrom the major axis of the ellipsoid for Na-PTS and Na-Salis depicted inFigs. 2(b) and 3(b), respectively. The open cir-cles inFigs. 2(b) and 3(b)show the length of the micelles forCTAB/Na-PTS and CTAB/Na-Sal in presence of 0.5 M NaCl,which will be discussed further. A marked increase in the lengthof the micelles was observed with increasing concentration ofhydrophobic salts, viz. from 11± 1 to 94± 9 nm for Na-PTSand 20± 2 to 93 +9 nm for Na-Sal.

It is true that when the micelles are sufficiently long, theybecome flexible beyond certain length scale; known as the per-sistence length,l , and the rigid-rod approximation is question-a canb staticl eena es of

ter of 7.7 nm, which increases further upon increasing theentration of the hydrophobic salts. However, it is unrealistave an isotropic spherical micelle having a diameter of 7.

or CTAB molecules, since the maximum extended lengt

-p

ble. The total persistence length for a polyelectrolyte chaine represented as the sum of an intrinsic and an electro

ength,lP,t+ lp,e [48]. In the past several years, there has bnumber of small angle neutron scattering (SANS) studi


worm-like micelles in which values oflp were estimated usingHoltzer (bending rod) plots[49]. Magid [50] made a survey onpersistence lengths determined for different micellar systemsusing analyses of light scattering and SANS data. The resultssuggest that micellar flexibility is apparently highly dependenton surfactant monomer structure, with values ranging from 100to 200A for nonionic surfactants to a few hundred nanometers.The lp’s reported for the penetrating counterion salicylate withC16TA and C16Py, suggest that its effect relative to a nonpene-trating counterion is to rigidify the micelles. For C16TA Sal/Na-Sal system, thelp was found to be 137 nm[51]. In the presentstudy, the flexibility of the micelles is not taken in to accountdue to the limited number of parameters that can be estimatedfrom DLS. However, the length calculated for CTAB/Na-Sal andCTAB/Na-PTS micelles, in the present study, is comparable orsmaller than the value oflp reported for C16TA Sal/Na-Sal sys-tem. Therefore, the rigid-rod model is a good approximation tobe used to analyze the data.

3.2. Effect of hydrophobic salts on micelle size in presenceof NaCl

As the micellar growth is very sensitive to the nature andthe amount of salt added to the solution, it is important toinvestigate the effect of electrolytes on rod-like micelles. Inor-ganic electrolytes such as NaCl, NaBr, NaNOand NaF cani ruc-t fs ear-t ng int owtho ure-m M)a ce of0 riedf

MC s of1 no ont ethodom entf ants( ntlyfo . Thed PTSa Cl it te isv NaCa -e rtantr

bics aClt ncen

Fig. 4. Representative plot of the intensity correlation function for 50 mM CTABwith cNa-pts = 10 and 20 mM in presence of 0.5 M NaCl at a scattering angle of90◦. The solid line is fit to the data using method of cumulants and the dottedline shows the fit to the data (20 mM Na-PTS) by biexponential decay.

tration of Na-PTS and Na-Sal. This is due to the shielding ofthe surface charge by the addition of NaCl. In addition to thehydrophobic as well as electrostatic interactions of hydrophobicsalts, the presence of NaCl helps in further reducing the electro-static repulsion and makes the aggregation easier. Due to which,the micelles grow faster and the topological interactions becomesignificant at lower concentrations of the hydrophobic salts.

Previous reports indicated that the slow mode of relaxationstarts evolving when the axial ratio of the micelles becomeslong enough to drive the system into semi-dilute regime[17,34].According to Nemoto et al.[17], the normalized time correlationfunction of intensity scattered from the samples exhibited thebimodal distribution of the decay rateΓ in a semi-dilute regimeof thread-like micelles. The fast mode,Γ f , was ascribed to thediffusion of micelles with a cooperative diffusion coefficient(Dc). On the other hand, the characteristic decay rate,Γ s, ofthe slow mode is related to the coupling between concentrationfluctuation and stress.

The existence of two characteristic decay times in presenceof NaCl is an indication of two dynamical processes. To accountfor the existence of two relaxation modes in the correlation func-tion for csalt≥ 15 mM, the data were analyzed by biexponentialdecay, given by the relation:

g2(τ) − 1 = Afe−Γfτ + Ase

−Γsτ (1)

w m-p rc r fitt them ram-e ei terso en-t nT

3nfluence significantly the formation of shear-induced stures in CTAB/Na-Sal micelles[38]. In particular, addition omall amounts of NaCl to CTAB/Na-Sal micelles imparts shhickening behavior to the fluid as opposed to shear thinnihe absence of NaCl. To envisage the effect of NaCl on the grf CTAB/Na-Sal and CTAB/Na-PTS systems, DLS measents were carried out on aqueous solution of CTAB (50 mt different concentrations of Na-PTS and Na-Sal in presen.5 M NaCl. The concentration of hydrophobic salts was va

rom 2 to 50 mM for Na-PTS and 2 to 30 mM for Na-Sal.Fig. 4 shows the intensity correlation function for 50 m

TAB in presence of 0.5 M NaCl at Na-PTS concentration0 and 20 mM at a scattering angle of 90◦. At small concentratiof Na-PTS (≤10 mM), a unimodal distribution of the relaxati

imes was observed and the data could be fitted by the mf cumulants (r > 0.999). However, forcsalt≥ 15 mM, the slowode of long relaxation time begins to evolve. This is evid

rom the poor quality of fit to the data by the method of cumulr < 0.999). The cumulants fit (solid line) deviates significarom the data at larger times (Fig. 4). A similar behavior isbserved for CTAB/Na-Sal system also in presence of NaClifference between the dynamical behavior of CTAB/Na-nd CTAB/Na-Sal micelles in absence and presence of Na

hat in absence of NaCl, the amplitude of slow relaxation raery small as compared to the one observed in presence oft the same concentration (Figs. 1 and 4). It indicates that presnce of NaCl in addition to hydrophobic salts plays an impoole in the growth behavior of CTAB micelles.

The growth of CTAB micelles in presence of hydrophoalts (Na-Sal and Na-PTS) is much faster with addition of Nhan that is observed in absence of NaCl for the same co

s

l

-

hereAf andAs are the amplitude of the fast and slow coonents with relaxation rates,Γ f and Γ s, respectively. Fosalt≥ 15 mM, biexponential decay function gives a betteo the data withr > 0.999 in comparison to that obtained byethod of cumulants and the incorporation of additional paters in the fit is validated from theF-test[53]. The dashed lin

n Fig. 4shows the fit with biexponential decay. The paramef the fit for CTAB/Na-PTS system obtained from biexpon

ial decay of the correlation function at 90◦ are summarized iable 1.


Table 1Parameters of intensity correlation function obtained from the fit by biexponential decay analysis for CTAB in presence of different concentrationsof Na-PTS and0.5 M NaCl at a of scattering angle 90◦: correlation coefficient (r), amplitude of fast mode (Af ), fast decay rate (Γ f ) and amplitude of slow mode (As), slow decayrate (Γ s)

Concentration (Na-PTS) (mM) r Af Γ f (�s−1) As Γ s (�s−1)

15 0.99996 0.774 (3) 0.0143 (1) 0.051 (3) 0.00098 (8)20 0.99992 0.764 (3) 0.0140 (1) 0.076 (3) 0.00065 (4)25 0.99990 0.764 (4) 0.0123 (1) 0.072 (4) 0.00063 (5)30 0.99983 0.806 (2) 0.0142 (2) 0.039 (2) 0.00008 (1)35 0.99983 0.799 (2) 0.0118 (1) 0.054 (2) 0.00016 (2)40 0.99990 0.757 (2) 0.0139 (1) 0.071 (2) 0.00018(1)45 0.99990 0.785 (4) 0.0139 (4) 0.056 (4) 0.00060 (6)50 0.99982 0.786 (2) 0.0144 (2) 0.049 (2) 0.00008 (1)

The variation of apparent diffusion coefficient,Da (obtainedfrom the slope ofΓ f versusq2 plot) of CTAB micelles (50 mM)at different concentrations of Na-PTS and Na-Sal in presence of0.5 M NaCl is shown inFigs. 2(a) and 3(a), respectively. As saltconcentration (cNa-PTSandcNa-Sal) increases,Da decreases ini-tially and then takes a more or less constant value. The observeddiffusion coefficient was used to calculate the apparent lengthof the micelles, assuming a prolate ellipsoid structure as dis-cussed earlier. The average length (L) of the micelles as obtainedfrom the major axis of the ellipsoid for Na-PTS and Na-Sal isdepicted inFigs. 2(b) and 3(b), respectively. Initially, the lengthof the micelles increases with increasingcNa-Sal and cNa-PTSuntil reaching a maximum value and then takes a nearly con-stant value of∼170 nm. It should be noted that this observedsaturation in the calculated length of the micelles does not indi-cate a limiting growth of the micelles. This is merely a reflectionof entering the semi-dilute regime of rod-like micelles. Beyondthe semi-dilute concentration, topological interactions becomesignificant and the diffusion of the micelles is severely hindered.This leads to an underestimation of the calculated length of themicelles.

Theoretical treatment by Doi and Edwards[54,55]providesthe basis for an understanding of dynamical behavior of a systemof strongly interacting rod-like polymers whose length (L) ismuch larger than the rod diameter (d). In the present study, weused Doi–Edwards model of rod-like polymers to compare thed

isi (tt nca

D

w n atw t al.[ so bire-f f1 withe es

The number density (ν) of the rod-like micelles having lengthL, and radiusr can be calculated with the equation:

ν = (c − cmc)Nav

πr2L(3)

wherec is the concentration of surfactant, cmc is the criticalmicelle concentration,Na is Avogadro’s number andv is thevolume of the surfactant monomer.

In the present study, knowing the volume fraction of themicelles, one can show that the conditionνL3 ∼ 30 is satisfiedwhen the axial ratio of the micelles becomes 42. This cor-responds to a length of the micelles of the order of 185 nm,considering the diameter of the micelle as 4.4 nm. The observedsaturated value of length 170 nm is close to the expected valueof 185 nm based on the molecular theory of entanglement ofrod-like polymers[58]. This further supports the fact that thebiexponential relaxation arises from a transition of the systemto semi-dilute regime.

A comparative study of lengths obtained for CTAB micellesin presence as well as absence of NaCl at different concentra-tions of Na-PTS and Na-Sal is given inTable 2. The micellarparameters reveal that, the striking difference in the rheology ofCTAB/Na-Sal in presence of NaCl and the formation of shear-induced structures[38] could be due to the strong growth andlonger length of the micelles as compared to that in absence ofN

f d tob salts.Ho func-t viora ands <1,a 0.1a thint therr steadoi tiono sl ationp

ynamics of rod-like micelles in semi-dilute regime.For rod-like polymers of length (L), the semi-dilute regime

dentified as the concentration at which the number densityν) ofhe polymer becomes much greater than 1/L3. According to theube model of Doi and Edwards[54–56], the rotational diffusioonstant in semi-dilute (Dr) and infinite dilute solutions (Dr,0)re related to the expression:

r = βDr,0(νL3)−2

(2)

hereβ is a numerical factor that indicates the concentratiohich topological interactions become significant. Mori e

57] measured theDr of rod-like polymers of different lengthver a wide range of concentration using dynamic electricringence and showed that the value ofβ is of the order o03. By a detailed study of tube statistics and comparisonxperimental results Hayakawa et al.[58] suggested that themi-dilute regime starts atνL3 ∼ 30.

aCl.In the present study, the amplitude of the slow modeAs is

airly small, typically less than 0.1 in all the cases and is foune almost independent of the concentration of hydrophobicowever, in the earlier studies by Amin et al.[35], the amplitudef the slow relaxation mode was observed to be a strong

ion of NaSal:CTAB mole ratios. This difference in the beharises from the limited range of concentration studied heremaller length of the micelles. At Na-Sal:CTAB molar ratiot CTAB concentration of 50 mM, the amplitude is less thannd almost independent of Na-Sal:CTAB molar ratio, wi

he experimental errors. Moreover, the amplitude will be fureduced when one considers the intensity correlation, inf electric field correlation. Due to very small amplitude, (As),

nherent polydispersity inΓ s and associated standard deviaf the measured data, the accuracy ofΓ s obtained from the fit i

imited. Thus, no attempts were made to extract stress relaxarameters of the micelles from the slow mode.


Table 2Comparison of the length of CTAB micelles in presence as well as absence of NaCl at different concentrations of the salts, Na-PTS and Na-Sal

csalt (mM) Length of CTAB micelles in presence of Na-PTS (nm) Length of CTAB micelles in presence of Na-Sal (nm)

CTAB/Na-PTS CTAB/Na-PTS/NaCl CTAB/Na-Sal CTAB/Na-Sal/NaCl

2 – 10± 1 – 10± 15 – 45± 4 – 58± 6

10 – 127± 13 – 153± 1515 11± 1 142± 14 20± 2 167± 1620 25± 2 161± 16 24± 2 169± 1725 40± 4 200± 20 34± 3 –30 42± 4 167± 17 40± 4 167± 1735 50± 5 195± 20 51± 5 –40 53± 5 167± 17 63± 6 –45 60± 6 167± 17 75± 7 –50 94± 9 163± 16 93± 9 –

4. Conclusion

This report investigates the growth behavior of CTABmicelles in presence as well as absence of NaCl on addition ofdifferent concentrations of hydrophobic salts like, Na-PTS andNa-Sal, by dynamic light scattering measurements. From DLSresults, it was found that the growth of the CTAB micelles ismuch more pronounced at the same concentration of hydropho-bic salts, Na-PTS and Na-Sal, when 0.5 M NaCl is added to thesolution. The length of the micelles was estimated assuming aprolate ellipsoid structure, ranging from dilute to semi-diluteregime. When the micelles become long enough to entangleeach other with addition of hydrophobic salt, the system reachesto semi-dilute regime and shows a biexponential decay behav-ior. In presence of NaCl, a faster growth of the micelles in thedilute regime and corresponding transition from dilute to semi-dilute regime at lower concentration of Na-Sal and Na-PTS isobserved. Comparison of the micellar lengths in the presence andabsence of NaCl in the dilute regime suggests that the biexponen-tial relaxation arises possibly from topological interaction of themicelles. This was confirmed by calculating the expected lengthof the micelles for topological interaction to occur based onDoi–Edwards model for rod-like polymers. It is indeed observedthat the length of the micelles at the transition from dilute tosemi-dilute regime is consistent with the Doi–Edward model.The transition point shift to lower hydrophobic salt concentra-t arei risesf oves of thC an bc d theg enceo avioo ior ina

A

tuteo arg

gratefully acknowledges Board of Research in Nuclear Science,DAE, India for the award of Dr. K.S. Krishnan Research Asso-ciateship.

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ion when the micellar growth is faster. All the evidencesn favor of the conjecture that the slow relaxation mode arom topological interaction of the micelles. Moreover, the abtudies suggest that the observed difference in the rheologyTAB-Na-Sal micelles in presence and absence of NaCl correlated to the difference in the length of the micelles anrowth behavior. The larger length of the micelles in presf NaCl could be responsible for the shear-thickening behf the micelles, as compared to the shear-thinning behavbsence of NaCl.

cknowledgements

The authors are thankful to Dr. C. Manohar of Indian Instif Technology, Mumbai for many fruitful discussions. G. G

ee

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