Shape and Size of Highly Concentrated Micelles in CTAB/NaSalSolutions by Small Angle Neutron Scattering (SANS)Narayan Ch. Das,*,† Hu Cao,† Helmut Kaiser,† Garfield T. Warren,§ Joseph R. Gladden,‡

and Paul E. Sokol*,†,§

†Low Energy Neutron Source (LENS), Center for the Exploration of Energy and Matter, Indiana University, Bloomington, Indiana47408, United States‡Department of Physics and Astronomy & National Center for Physical Acoustics University of Mississippi, University, Mississippi38677, United States§Department of Physics, Indiana University, Bloomington, Indiana 47405, United States

ABSTRACT: Highly concentrated micelles in CTAB/NaSal solutions with a fixed salt/surfactant ratio of 0.6 have been studied using Small Angle Neutron Scattering (SANS) as afunction of temperature and concentration. A worm-like chain model analysis of the SANSdata using a combination of a cylindrical form factors for the polydisperse micellar length,circular cross-sectional radius with Gaussian polydispersity, and the structure factor based ona random phase approximation (RPA) suggests that these micelle solutions have a worm-likemicellar structure that is independent of the concentration and temperature. The size of themicelle decreases monotonically with increasing temperature and increases withconcentration. These observations indicate that large micelles are formed at low temperatureand begin to break up to form smaller micelles with increasing temperature.

1. INTRODUCTION

Surfactants are amphiphilic molecules with both a bulkyhydrophilic head, which is often charged, and a relativelyshort and slender hydrophobic tail. Above their critical micelleconcentration (CMC), surfactant molecules spontaneously self-assemble into aggregates to form micelles in aqueous solutions.Depending on the size of the headgroup, length of tails, chargeof the surfactant, temperature, concentration and even the flowcondition, these large aggregates can form into a number ofdifferent shapes, including spherical and wormlike micelles,vesicles, and lipid bilayers.1 When micelles grow and becomewormlike, these aggregates are much like polymers andentangle in three-dimensional networks above the CMC.Wormlike micelles (WLMs) are long, flexible threadlikesurfactant aggregates exhibiting a hierarchy of length scaleand striking viscoelastic behavior.2−6 The viscoelastic wormlikemicelles are already extensively used in consumer and personalcare products.7,8

Micelles are well studied structural fluids in which macro-molecular structures in an aqueous solution have dramaticeffects on rheological properties.9 Cetyltrimethylammoniumbromide (CTAB) is one of the surfactants extensively studiedin micelle solutions during the last two decades.10−14 The largemajority of these studies have been confined to the low tomedium surfactant concentration range (0−100 mM).Comparatively little work has been done on high concentrationsolutions despite the fact that concentrations of up to 1 Msurfactant are accessible and the structure at such high

concentrations is still an open question. There are also practicalapplications for these solutions in the high concentration rangethat motivate a better understanding of these unique materials.For instance, above several hundred mM, these solutions beginto mimic a soft gel rather than a fluid, flowing for slow shearstresses and tearing for faster shears, and thus probe theboundary between fluid and solid.15 Additionally, they arebirefringent with stress optic coefficients that scale withconcentration so that ever smaller stresses can be visualizedthrough crossed polarizing filters in ever increasing concen-tration micelle solutions. It is well-known that CTAB growsfrom globular to wormlike shapes when salts, such as KBr,NaSal (sodium salicylate), NaNO3, etc., are added. Theassociation of halide anions (Cl− and Br−) with surfactantcations (CTA+) is moderate, and thus the growth of micelles isgradual.16 However, with the association of strongly bindingcounterions, such as Sal−, these surfactants immediately forminto wormlike micelles even at low concentrations, withoutpassing through an intermediate spherical morphology, whichwas exemplified in the CPCL (cetylpyridinium chloride) +NaSal system.17−19

Small Angle Neutron Scattering (SANS) is a powerful toolfor studying surfactant polymorphism because of the largescattering contrast between the hydrogenated surfactants and

Received: June 15, 2011Revised: June 12, 2012Published: July 24, 2012

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deuterated water (D2O) as the solvent. In addition, thestructural parameters, like the length and radius of micelles fallin the wave-vector range covered by the SANS technique (Q ≈10−3 to 0.4 Å−1). This technique can provide importantinformation about the shapes, sizes, and even parameters ofinteraction between micelles. So far, most of the SANS studieson CTAB/NaSal micelle solutions have been reported only onlow surfactant and salt concentrations. In the concentrationrange of about 1−30 mM CTAB and salt/surfactant ratio of0.6, it is known that the surfactant molecules self-assemble intolong tubular (wormlike) structures with diameters on the orderof ∼22 Å and lengths that can be tens of micrometers at roomtemperature16 (and shorter at higher temperatures). However,CTAB/NaSal micelle solutions at high concentrations (100 −800 mM/L) and their temperature dependence have not beenstudied as well and little structural information exists in theliterature, although nematic and hexagonal phases have beenobserved.12 Therefore, the micelle solutions of interest in thisstudy are highly concentrated CTAB (100, 200, 400, 600, 800mM) with a fixed ratio of CTAB/NaSal = 0.6 in D2O as afunction of temperature from 20 to 60 °C. Our SANS studiesclearly illustrate that highly concentrated CTAB/NaSal micelleshave a wormlike structure. Second, there is no structuraltransition observed in the studied temperature range andconcentrations. These wormlike micelles shrink linearly inparticle size with increasing temperature and increases withconcentrations.

2. EXPERIMENTAL SECTIONThe SANS experiments were performed at the Low Energy NeutronSource (LENS) located at the Center for Exploration of Energy andMatter (CEEM), Indiana University. LENS is a novel, university-basedpulsed neutron source based on a high-current, variable-pulse-widthproton accelerator to produce either short or long neutron pulses.LENS utilizes a low energy p-n reaction in Be, a water reflector and asolid methane moderator to produce a high flux of low energyneutrons. The SANS Instrument at LENS is a conventional neutron“time-of-flight” instrument. The incident flight path is 8.6 m and usespinhole collimation to provide a beam with a divergence of 7 mrad atthe sample position. A cooled Beryllium filter is used to reduce fastneutron backgrounds and limits the shortest wavelength available to 4Å. The sample-to-detector distance is variable, from 1.1−4.2 m and, forthese measurements, 2.2 m was used allowing us to cover a Q-range of0.008−0.3 Å−1 utilizing λ = 4−18 Å neutrons. For these measure-ments, the accelerator was operated at 13 MeV with a peak current of20 mA, pulse width of 600 μS and repetition rate of 20 Hz yielding anaverage power on target of 3 kW.CTAB (99%, ρ = 0.39 g/cm3) and NaSal (99%, ρ = 0.32 g/cm3)

were obtained from Sigma-Aldrich. Micelle solutions with fiveconcentrations (100/60, 200/120, 400/240, 600/320, 800/480 mM/L) were prepared in D2O, which provides a better neutron scatteringcontrast between the micelle solution and the solvent. The micellesolutions were held in a quartz banjo cell with a thickness of 2 mm.The raw data were circularly averaged after background correction dueto sample cell and detector noise and then converted into absoluteunits by comparison with a water standard, taking into account thetransmission of the samples. The data were collected in the Q-range of0.008 to 0.25 Å−1 for the temperature range of 20 to 60 °C.Imaging of the samples using a CryoTEM was also attempted but

the high viscosity of the samples frustrated these efforts. A VitrobotMark III freezing robot was used to prepare the samples which allowedthe entire freezing chamber to be heated to 50 °C. However, even atthese elevated temperatures, the viscosity of the sample remained highenough that standard techniques (pipetting followed by blotting)failed to produce an appropriate thin film. A free-standing film within awire loop was produced but upon freeing, by submersion in liquid-

nitrogen-cooled liquid ethane, only crystalline samples were produced.Extensive efforts to produce vitrified samples suitable for imaging wereunsuccessful.

3. THEORETICAL MODEL AND DATA ANALYSISMETHODS

CTAB/NaSal solutions generally form in two basic shapes,ellipsoidal and rodlike (or wormlike) micelles. Their scatteringprofiles are quite different, especially in the low-Q range. Inpractice, the data analysis of the scattering spectrum providesinformation on the structural parameter, such as the shape, sizeof the particles, and its size distribution. Specifically, thescattering intensity from wormlike micelles provides informa-tion about three lengths in direct space: contour length, Lc,persistence length, lp, and the cross sectional radius, rcs, with itssize distribution. The modeling and data analysis of thescattering spectrum for the micelles sample is extremely difficultdue to intermicellar interactions. Meanwhile, in the presence ofcorrelations between the micelles, the scattered intensity, I(Q)is no longer simply expressed by a single-particle form factor,F(Q). Hence for micelles in general, the total I(Q) can beexpressed as follows:20−22

= +I Q n F Q S Q I( ) ( ) ( )m bkg (1)

where nm is the normalization factor, which includes thenumber density of micelles, F(Q) is the form factor, connectedwith the intramicellar particle resulting from the size and shapeof the micelle, S(Q) is the interparticle structure factor, whichspecifies the correlation between the centers of neighboringmicelles, and Ibkg is the incoherent background intensity, mainlydue to the hydrogen in the sample, where it is assumed that theeffect of polydispersity in F(Q) and S(Q) can be separated. Theform factor was modeled for semiflexible self-avoiding cylinderswith a circular cross-section, as described by the wormlike chainmodel with excluded volume interactions developed byPedersen and Schurtenberger.23 It depends on three parame-ters: Lc, lp (or the Kuhn length b = 2lp), and rcs. Since themicelles are expected to have polydispersity of the length andcross-section, the form factor with the polydispersity is definedby the following:

ρ= ΔF Q L F Q F Q( ) ( ) ( ) ( )2c2

L cs (2)

where Δρ (= ρm − ρs) is the difference in scattering lengthdensity between the micelles and the solvent, ρm and ρs are thescattering length density of the micelles and solvent,respectively, and FL(Q) and Fcs(Q) are the polydisperse formfactor for the length and cross-section.The longitudinal polydisperse form factor is expressed by the

following:

∫

∫=

∞

∞F Qf L F q L dL

f L dL( )

( ) ( , )

( )r

r

L2 L

2

c

c (3)

with a polydispersity given by an exponential distribution6

=⎛⎝⎜

⎞⎠⎟f L L

LL

( , ) expcc (4)

Assuming that the micelles have a cyclindrical cross-sectionwith Gaussian polydispersity in the cross-sectional radius, rc.,the cross-sectional form factor can be expressed by thefollowing:

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∫∫

=

∞

∞F Qf r F q r dr

f r dr( )

( ) ( , )

( )CS

0 cs c cs cs cs

0 cs cs cs (5)

and the cross-section scattering function for micelles with acircular section of radius, rc is as follows:

π=⎛⎝⎜

⎞⎠⎟F Q r

J Qr

Qr( ) ( )

2 ( )cs c

2 2 1 c

c (6)

where J1(x) = (sinx − x cosx)/x2 is the first-order sphericalBessel function and Gaussian distribution of the cross-sectionalradius is as follows:

πσ σ= −

−⎛⎝⎜

⎞⎠⎟f r

r r( )

1

2exp

( )2c 2

c2

2(7)

where r and σ are the average and dispersity index of the cross-sectional radius, respectively.Worm-like micelles are open coil-like structures that interact

with each other in the solvent, even at low concentrations.Those intermicellar interactions not only influence high q-data,they also influence the corresponding scattering data at lower q-values and consequently the inferred overall size of the micelles.Thus, it is important that the structure factor, which representsintermicellar interactions, adequately incorporates these inter-

actions to accurately determine structural parameters such as

the contour length, Kuhn length, and cross-sectional radius of

the micelles. Several scattering experiments and Monte Carlo

simulations have demonstrated the importance of including

intermicellar interactions when determining structural param-

eters.24,25 The structure factor, S(Q) in the presence of

intermicellar interactions can be expressed using a random

phase approximation (RPA) and PRISM type interactions.26,27

β=

+S Q

F Q L( )

11 ( , )L (8)

where FL(Q,L) is the longitudinal length form factor and β = [1

− S(0)]/S(0) is a parameter representing the strength of the

intermicellar interaction, where S(0) is the forward contribu-

tion to the structure factor.An explicit functional form of S(0) has been formulated

using a renormalization-group method28 originally developed

for semidilute polymer solution for analyzing the measured

apparent molar mass of the micelles. Later, several authors

successfully employed the following functional form:22,26,29

Figure 1. Neutron scattering intensity versus Q as a function of temperature for CTAB/NaSal micelle solutions with a molar ratio of CTAB/NaSal =0.6, (a) 100/60 mM, (b) 200/120 mM, (c) 400/240 mM, and (d) 600/360 mM. Symbols indicate experiential data. The solid curves throughsymbols represent best fit of WLM model.

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= + − + +

+ − +⎜ ⎟

⎛⎝⎜

⎞⎠⎟

⎧⎨⎩⎡⎣⎢

⎛⎝

⎞⎠

⎤⎦⎥⎫⎬⎭

S XX

X

X XX

(0) 118

9 22ln(1 )

exp 0.251

11

ln(1 )2(9)

where X = 42.1 ϕeff. The effective volume fraction, ϕeff of chainscan determined by the following:

φ φ=+ −⎛

⎝⎜⎞⎠⎟⎛⎝⎜⎜

⎞⎠⎟⎟

r kr

r

reffcs

1

cs

g

g,u (10)

where ϕ is the volume fraction of micelles, rcs is the cross-sectional radius, k−1 (= √lp) is the Debye length, and r and rg,uare the theoretical radius of gyration of a completely charge anduncharged chain, respectively. The relationship between r andrg,u for a given contour length can be estimated using theempirical relationship as presented by Pedersen.23,26 Latter,Helgeson et al. also successfully employed the same empiricalrelationship to calculate r and rg,u.

22 The SANS data obtainedfor highly concentrated micelles containing CTAB/NaSal in theD2O were analyzed with the WLM model in eqs 1−10. Thefitting routine written in Mathcad was used to fit the SANS datain which the average contour length, polydispersity index, andcross-sectional radius are adjusted to minimize the averageaggregate squared normalized standard error.

4. RESULTS AND DISCUSSION

SANS measurement were performed on CTAB/NaSal micelleswith varying surfactant concentration at fixed of 0.6 CTAB/NaSal and temperature to directly measure micelles shape andsize. Figure 1 shows the measured SANS data for four CTAB/NaSal micelle solutions as a function of temperature from 20 to60 °C. The symbols represent the experimental data, and thecurves are the best fit using WLM model according to eqs1−10. No abnormal changes in scattering intensities werefound in these micelle solutions. At each of the concentrations,it was found that the scattering intensity at large Q > 0.08 Å−1 isindependent of the temperature, whereas the scatteringintensity monotonically decreases at low Q < 0.08 Å−1 onheating. The observed scattering behaviors in these foursolutions suggest that the cross-sectional radius of the micelles,which is reflected in the large Q behavior, is not significantlyaffected, whereas the contour length, which is reflected in thesmall Q behavior, actually becomes shorter with increasingtemperature.Figure 2 shows scattering profiles of five micelle solutions at

20.5 °C. With increasing concentration as shown Figure 2, theoverall scattering intensity increases. Increase in the scatteringintensity at low q-range is due to the concentration inducemicellear growth and number density of micelles. However, thescattering intensity of 600/360 mM micelle is very close to thatof 800/480 mM micelle, indicating that micelles have reachedthe limit in the size and number of micelles at such highconcentrations. In addition, the interference effects of scatteringfrom different micelles at higher concentration due tointermicellar interaction decrease the scattering intensity atlow scattering.29 The combination of these opposing effects ofintermicellar interactions and concentration induced growth athigh concentration, resulting in a marginal increase of scatteringintensity or decrease in the relative change of scatteringintensity.

The scattering intensity from wormlike micelles typicallydisplay three spectral regions containing information aboutthree length in direct Q space: the contour length, Lc, thepersistence length lp, and the cross sectional radius rcs asdiscussed earlier. In the case of long wormlike aggregates, thecross section is generally well separated in the q space from thecontour or persistence length. In very small Q region, the decayof I(Q) follows the Guinier law (I(Q) ≈ e−(Q2Rg

2/3)) allowingthe determination of radius of gyration, or equivalent ofcontour length (⟨Rg

2⟩ ≈ (bL/6)). The power law decay of I(Q)with Q represent the chain flexibility and parametrized by theKuhn length. The region at higher Q is followed by decay ofI(Q) contains information regarding the micellar radial crosssection. The model fitting of scattering function containing L, b,r, and Q over full range of scattering curve can providequantitative structural informations.Figure 3 shows a representative SANS spectrum for a sample

of 200/120 mM CTAB/NaSal in D2O at 20.5 °C. The absolutescattering intensity was fitted using the Schurtenberger WLMmodel as described in the previous section. The scatteringlength density of the surfactant and solvent were estimatedusing standard methods.30 The volume of micelles wasestimated based on the total volume fraction of surfactant insolution from the solid density of CTAB. The remainingparameters of contour length, Kuhn length, the micellar radius,and radius polydispersity were fitted to SANS data usingcombination of eqs 1−10. The solid line through symbols inFigure 3 indicates the fitting result of representative data. TheWLM model gives a good fit to the data over the entire q-range,providing an excellent description of the experimental results.The best fit parameters Lc, b, rcs, and σ for 200/120 mMCTAB/NaSal micelle at 20.5 °C are 6, 5, 2, and 0.035,respectively. In this study, the solvent (D2O) scattering lengthdensity is ρs = 5.76 × 10−6 Å−2 and the 800/480 mM micellescattering density is calculated to be ρm ≈ 1.1 × 10−7 Å−2

(smaller for 600/360 mM and lower concentrations), whichcould be neglected compared to ρs. The inset in Figure 3presents the structure factor, S(Q) and form factor F(Q) withpolydisperse contour length and cross-sectional radius with Lc =69 nm, b = 5 nm, rcs = 2 nm, and σ = 0.035, indicating amarginal contribution of intermicellar interaction. Thesewormlike micelles are similar to polymers in that they arequite flexible with typical persistence length 2−2.5 nm (Kunh

Figure 2. Neutron scattering intensity versus Q as a function ofconcentration at room temperature 20.5 °C for CTAB/NaSal micellesolutions. The solid lines through experimental data represent themodel scattering intensity for wormlike micelles.

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length = 4−5 nm),31,32 and this persistence length isindependent of temperature and concentration at a fixedsurfactant and salt ratio.22,33 This persistence length representsthe distance over which the micelle shows rigidity ornonflexibility. In other words, a wormlike micelle behaves asa rigid rod when its length Lc ≤ lp and a flexible when Lc > lp.The cross section radius obtained from WLM model fitting ofour studies is close agreement with previous measurement forCTAB/NaSal micelles assuming ellipsoidal micellar34 orCTAB/NaNO3 wormlike micelles structures.22

The best fit results, the solid curve through the symbol ofexperimental data, of WLM model to experimental SANS dataat different temperatures 20−60 °C and different concen-trations of 100/60, 200/120, 400/240, and 600/360 mMCTAB/NaSal at fixed ratio = 0.6 are shown in Figure 1a−d .Overall, the fits to the WML model describe the experimentaldata remarkably well. Small deviations from the model at low qvalues are observed in some samples, which may be due toneglect of electrostatic interaction between micellar segments.26

The fit values of Lc over temperature range of 20 to 60 °C forfive different concentrations 100/60, 200/120, 400/240, 600/360, and 800/480 mM of CTAB/NaSal from WML modelfitting is shown in Figure 4. Specifically, the contour lengthincreases significantly with surfactant concentration anddecreases with increasing temperature at a fixed CTAB/NaSalratio, as shown in Figures 4 and 5. The Lc values obtained fromWML model fitting for 100 mM and 800 mM CTAB micellesare ∼600 and 760 Å at 20 °C, respectively. The contour lengthof these highly concentrated micelles shows similar behavior asseen very low concentrated micelles22 for CTAB/NaNO3 andCTAB/NaSal.35 Since the total volume fraction of the micelleremain unchanged with an increase in temperature, the rodlikeor wormlike micelles probably break along the growth directionto form shorter ones upon heating. The similar observation hasalso been reported in CTAB/NaSal 100/20 mM micelles.35

A recent rheology and SANS study of CTAB and sodiumnitrate (NaNO3) has revealed wormlike micelles from 40 mM

up to 100 mM of CTAB concentration. It is well-known thatwormlike micelles can be easily formed at the lowconcentration of CTAB with the addition of strongly bondingsalt, following a transition from spherical or ellipsoidal to longrodlike or wormlike micelles. However, as concentration ofCTAB increases with a fixed ratio (=1.0) of surfactant/salt, thecontour length of wormlike micelles exponentially increase,reaching ∼192 nm in CTAB 100 mM and ∼118 nm in 40 mM.However, our study of highly concentrated CTAB/NaSalmicelles from 100/60 mM up to 800/480 mM is notinconsistent with low concentrated CTAB/NaNO3 wormlikemicelles.22 In addition, the high q behavior which representscross sectional of our data appears to be independent ofsurfactant concentration at fixed surfactant/salt ration isconsistent with CTAB/NaNO2 micelles system.

22

Figure 6 shows the temperature dependence on the contourlength (Lc) of micelles for five concentrations. The dashed lines

Figure 3. Neutron scattering intensity versus Q for 200 mM CTAB with 120 mM NaSal micelle at 20.5 °C. Curve gives best fit to the WLMscattering model as described in section 3. The inset shows the wormlike micelle form factor F(Q) and structure factor S(Q) based on random phaseapproximation (RPA).

Figure 4. Contour length versus temperature as a function ofconcentration for CTAB/NaSal micelle solutions.

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present the fitted Arrhenius behavior (L ≈ exp(Es/kbT)) whereEs is typically associated with the scission energy of the micelle,kb is Boltzmann’s constant, and T is absolute temperature. Thetemperature dependence of micelle length has been the subjectof many studies in the literature. An often cited theoreticalwork by Cates and Candau presents a mean field approach tothe problem which results in an Arrhenius type scaling of lengthwith temperature.6 This type of scaling has been verifiedexperimentally through linear rheology,22,36,37 however certaintypes of micelle structures have been shown to exhibit oppositetemperature trends (e.g., lengthening).38 The linear depend-ence of the ln(L) vs 1/RT plots in Figure 6 for eachconcentration and over all temperatures strongly suggest thatthere are no structural transitions for these micelles over thistemperature range. The scission energy is often found from theslope of the fitted lines and can vary widely depending on thetype of micelle and surfactant to salt ratio. Our values rangefrom Es = 3.3 to 4.0 kbT, which is lower than other commonlyreported values (∼10−20 kbT) for lower concentrations.

22,37 Itshould be noted however that because of the small contourlength of our micelles, the length range spans only a partialdecade between 20 and 55 °C and thus resulting scissionenergies may lack accuracy.

5. CONCLUSIONS

In summary, highly concentrated CTAB/NaSal micelles with afixed salt/surfactant ratio of 0.6 have been studied by SANS as afunction of temperature and concentration. The modelinganalysis results of the SANS data suggest that these studiedmicelle based on CTAB/NaSal solutions form wormlike micellestructures and the micelle structural parameters, like contourlength, varies with concentration and temperature, whereas theKunh length and cross-sectional radius are independent ofconcentration and temperature. The contour length decreasesmonotonically with increasing temperature or increases withconcentration and reaches the limit at high concentrations of600/360 and 800/480 mM micelle solutions. Since the totalvolume of wormlike micelles stays unchanged, these observa-tions indicate that long micelles start to break up as thetemperature increases, and those broken surfactant moleculescoalesce again to form more micelles.

■ AUTHOR INFORMATION

Corresponding Author*Email: ncdas@indiana.edu (N.Ch.D.); pesokol@indiana.edu(P.E.S.).

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

This report was prepared by Indiana University under AwardNo. 70NANB10H255 from the National Institute of Standardsand Technology, U.S. Department of Commerce. Thestatements, findings, conclusions, and recommendations arethose of the authors and do not necessarily reflect the views ofthe National Institute of Standards and Technology or the U.S.Department of Commerce. Construction of LENS wassupported by the National Science Foundation Grants Nos.DMR-0220560 and DMR-0320627, the 21st Century Scienceand Technology fund of Indiana, Indiana University, and theDepartment of Defense. Operation of LENS is supported bythe Office of the Vice Provost for Research at IndianaUniversity.

■ REFERENCES(1) Belmonte, A. Self-oscillation of a cusped bubble rising through amicellar solution. Rheol. Acta 2009, 39 (6), 554−559.(2) Schubert, B. A.; Kaler, E. W.; Wagner, N. J. The microstructureand rheology of mixed cationic/anionic wormlike micelles. Langmuir2003, 19, 4079−4089.(3) Shikata, T.; Hirata, H.; Kotaka, T. Micelle formation of detergentmolecules in aqueous media: viscoelastic proerties of aqueouscetyltrimethylammonium bromide solutions. Langmuir 1987, 3,1081−086.(4) Candau, S. J.; Hirsch, E.; Zana, R.; Delsanti, M. Rheologicalproperties of semidilute and concentrated aqueous solutions ofcetyltrimethylammonium bromide in the presence of potassiumbromide. Langmuir 1989, 5, 1225−1229.(5) Sasaki, M.; Imae, T.; Ikeda, S. Aqueous sodium halide solutions ofcationic sufactants with consolute phase boundary. Viscosity behaviorin semidilute regime. Langmuir 1989, 5, 211−215.(6) Gates, M. E.; Candau, S. J. Statics and dynamics of worm-likesurfactant micelles. J. Phys.: Condens. Matter 1990, 2, 6869−6892.(7) Yang, J. Rheology and structure of worm-like micelles. Curr. Opin.Colloid Interface Sci. 2001, 6, 451−456.(8) Rosen, M. J.; Dahanayake, M. Industrial Utilization of Surfactant:Principle and Practice; AOCS Press: Champaign, IL, 2000.

Figure 5. Contour length as a function of concentration for CTAB/NaSal micelle solutions at 20 and 60 °C.

Figure 6. Micelle length (contour length, Lc) as a function oftemperature. The dashed lines represent the fitted Arrhenius behaviorof Lc ≈ exp(E/kbT).

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Langmuir Article

dx.doi.org/10.1021/la2022598 | Langmuir 2012, 28, 11962−1196811968