Effects of Protonation on the Viscoelastic Properties of

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J. Phys. Chem. B 2001, 105, 5411-5418

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Effects of Protonation on the Viscoelastic Properties of Tetradecyldimethylamine Oxide Micelles Hiroshi Maeda,*,† Atsushi Yamamoto,† Makoto Souda,† Hideya Kawasaki,† Khandker S. Hossain,‡ Norio Nemoto,‡ and Mats Almgren§ Department of Chemistry, Faculty of Sciences, Kyushu UniVersity, Fukuoka 812-8581, Japan, Department of Molecular and Material Sciences, IGSES, Kyushu UniVersity, Fukuoka 812-8581, Japan, and Department of Physical Chemistry, Uppsala UniVersity, Uppsala, S-751 21 Sweden ReceiVed: January 9, 2001; In Final Form: March 22, 2001

Marked effects of protonation (ionization) of tetradecyldimethylamine oxide on the viscoelastic properties of the micelle solutions were found. The effect strongly suggests the short-range attractive interaction between the headgroups of the nonionic (deprotonated) and the cationic (protonated) species. The zero shear viscosity reached a maximum at the half-ionized state (the degree of ionization R ) 0.5) and the value was larger than that of the nonionic species (R ) 0) or the cationic species (R ) 1) by more than 2 orders of magnitude. At a surfactant concentration C of 0.1 mol/kg, approximately single Maxwell behavior was observed as R approached 0.5 from either side. For the half-ionized micelles (R ) 0.5) in 0.1 mol/kg NaCl solutions, the steady-state compliance Je0 decreased with C with an exponent of 2.1 ( 0.2, suggesting the presence of an entangled network of flexible threadlike micelles. The relaxation time, on the other hand, exhibited a nonlinear dependence on C. It was about 0.1 s and remained nearly constant in the range C > 0.1 mol/kg (regime I), whereas it increased with C in the range of C < 0.09 mol/kg (regime II) with an exponent slightly larger than 1. The single Maxwell behavior was observed in regime I. The regime shift was not controlled by the ratio C/ms, ms representing the NaCl concentration. Effects of NaCl concentration and the temperature on the viscoelastic properties were also examined at R ) 0.5. Cryo-transmission electron micrographs clearly showed a highly entangled network in the solution for R ) 0.5, while much smaller micelles for R ) 0. Contrary to the expectation from the rheological results, a highly entangled network was also observed in the solution for R ) 1.

Introduction Viscoelastic surfactant solutions have been intensively studied over many years, both theoretically and experimentally.1-19 These solutions contain long flexible or semiflexible micelless often referred to as threadlike or wormlikesthat become entangled at high concentrations. The transient networks formed by entangled long threadlike micelles exhibit properties similar to those of semidilute and concentrated polymer solutions, with an important difference in that micelles can pass through each other, under certain conditions, by opening and reclosing (phantom network). It has been suggested that in some micelle solutions the networks are cross-linked. The micelle threads are branched and fused with one another. The joints are characterized by high fluidity.9,10 Strongly viscoelastic micelle solutions have been found to form on the interaction of cationic micelles with certain groups of counterions, mostly aromatic counterions such as salicylate,4,5,18,19 tosilate,14 and naphthalenesulfonates.17 In some systems, cosurfactants play an essential role for high viscoelasticity to appear.20 Viscoelastic properties of micelle solutions have been reviewed by Hoffmann20,21 and others.22 Theoretical aspects of the rheological properties of micelle solutions have been extensively developed by Cates and others.23-29 Evidence for entanglement and branching of threadlike micelles has also been obtained from self-diffusion measurements30-32 and cryo-electron microscopy. 33-34 * Author to whom correspondence should be addressed. E-mail: h. [email protected]. † Department of Chemistry, Faculty of Sciences, Kyushu University. ‡ Department of Molecular and Material Sciences, IGSES, Kyushu University. § Department of Physical Chemistry, Uppsala University.

Alkyldimethylamine oxide has been used mostly as a nonionic surfactant but it exists as either a nonionic or a cationic (protonated form) species, depending on the pH of the aqueous solution. The properties of the solution vary with pH. The effects of protonation have been extensively studied on dodecyldimethylamine oxide (C12DAO) and tetradecyldimethyamine oxide (C14DAO) and the results are summarized in a recent review.35 In the half-ionized or half-protonated state, a number of properties differ significantly from those expected as average properties of an 1:1 mixture of the nonionic and the cationic species. The aggregation number or micelle size exhibited a maximum36-40 and the critical micelle concentration (cmc) showed a minimum 40-42 around the half-ionized state (R ) 0.5). The degree of ionization (protonation) is denoted as R. The peculiar behavior observed at R ) 0.5 indicates that a strong attractive interaction occurs between the nonionic and the cationic headgroups, and this has led to the hypothesis of the hydrogen bonding between the nonionic and the cationic species at the surface of the micelles.37,43-44 This in turn indicates that protonation takes place more readily on the surface of nonionic micelles than for the monomeric state in solutions.45-47 The effects of protonation on the aqueous-phase behavior,48 on the solid-phase behavior,49,50 and the aggregate morphology formed on mica surfaces51 were also examined. Recently, a cooperative diffusion mode was observed in the dynamic light scattering of solutions of C14DAO at the half-ionized composition (R ) 0.5), indicative of the presence of entangled long micelles.40 Long threadlike micelles were also suggested from a SANS study.52 In the present study, viscoelastic properties of tetradecyldimethylamine oxide (C14DAO) solutions are examined with

10.1021/jp0101155 CCC: $20.00 © 2001 American Chemical Society Published on Web 05/18/2001

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Figure 2. Cole-Cole plots for C14DAO solutions with different R at C ) 0.1 mol kg-1, ms ) 0.1 mol kg-1. Symbols for R are (b) 0, (0) 0.24, (4) 0.4, (O) 0.5, (3) 0.6, (]) 0.75, (2) 1.

as functions of the degree of ionization of micelles in the range of frequency ω between 0.4 and 100 rad/s. For both the nonionic(R ) 0) and the cationic (R ) 1) micelles, viscoelasticities were very low. As the degree of ionization R approached 0.5 from either side, G′ and G′′ both increased and reached the respective maximum values at R ) 0.5. In Figure 2, the Cole-Cole plots of the data are shown. As clearly indicated by a hemicircle in this type of plot, single Maxwell type of relaxation is observed at R ) 0.5, whereas the behavior was non Maxwellian at R values smaller than 0.4 and greater than 0.6. In the case of the Maxwell behavior, G′ and G′′ are given as follows in terms of the relaxation time τΜ and the elastic modulus GM:

G′(ω) ) GMω2τM2/(1 + ω2τM2), G′′(ω) ) GM ωτM/(1 + ω2τM2) (1)

Figure 1. Angular frequency ω dependence of (A) storage shear modulus G′, and (B) loss shear modulus G′′ for C14DAO solutions with different degree of ionization R at C ) 0.1 mol kg-1, ms ) 0.1 mol kg-1. Symbols for R are (b) 0, (0) 0.24, (4) 0.4, (O) 0.5, (3) 0.6, (]) 0.75, (2) 1.

emphasis on the effect of protonation. The solutions were directly observed by CryoTEM. Experimental Section Material and Sample Preparation. C14DAO samples were prepared as reported previously.40 The surfactant concentration C and the NaCl concentration ms were in mol kg-1 or molal. The oscillatory shear, the shear flow, and shear creep measurement were performed with a stress-controlled rheometer (CarriMED CSL-100 England) with a cone plate (plate diameter 6 cm, 2° angle) and a parallel plate type geometry (plate diameter 4 cm). The storage modulus G′(ω) and the loss modulus G′′(ω) were measured as functions of angular frequency ω from 100 to 0.1 rad/s at temperatures varying from 25 to 55 °C. The dynamic measurements were made at strain amplitude levels where the dynamic moduli are strain independent. A solvent trap equipped with the rheometer was used to protect the sample from evaporation. Solutions were kept for at least 1 day before measurements. The temperature was controlled within 0.1 °C. Results Effects of Ionization. In Figure 1, the dynamic shear storage modulus G′(ω) and the loss modulus G′′(ω) of C14DAO solution (C ) 0.1 mol kg-1) in 0.1 mol kg-1 NaCl are shown

The viscosity η was given by η ) τMGM. The data exhibiting non-Maxwell behavior obtained at R values other than 0.5 were fitted to the following relations in the low-frequency range (the terminal relaxation region).

G′(ω) ) ητω2

(2)

G′′(ω) ) ηω

(3)

Viscosities were evaluated by eq 3. We evaluated the terminal relaxation time by eq 2 and the values are given in Figure 3B.The steady-state shear compliance Je0 was evaluated by eq 4 and is shown in Figure 3A.

Je0 ) τ/η

(4)

At R ) 0.5, τ exhibits a maximum and Je exhibits a minimum. We measured the viscosity of the solutions also by creep measurements and the flow measurements by a rotating viscometer. The viscosity showed reversible shear-thinning or thixotropy at R ) 0.5. Zero-shear viscosities η0 were evaluated by extrapolating the data to zero shear rate. Viscosities from the three different methods gave essentially identical results and they all showed the maximum at R ) 0.5. The data obtained from oscillatory shear method are shown in Figure 3C. It is notable that the viscosity increased by nearly 3 orders of magnitude for a change of R from either R ) 0 or 1 to R ) 0.5. Effects of the Surfactant Concentration. Effects of the surfactant concentration, C, were examined at R ) 0.5 in 0.1 mol kg-1 NaCl in the range of 0.04 and 0.5 mol kg-1, as shown in Figure 4. The corresponding Cole-Cole plots are shown in Figure 5 and we could discriminate two concentration regimes

Viscoelastic Properties of C14DAO Micelles

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Figure 3. The R dependence of (A) the steady shear compliance Je0, (B) the relaxation time τ, and (C) the zero shear viscosity η for C14DAO solutions at C ) 0.1 mol kg-1, ms ) 0.1 mol kg-1.

characterized of different relaxation mechanisms. In the concentrated solutions (regime I, C > 0.2 mol kg-1), single Maxwell relaxation behavior is found, while no such behavior is seen in the range of low concentrations (regime II, C < 0.09 mol kg-1). In regime I, the data were analyzed by eq 1 and τM and GM were evaluated. Zero-shear viscosity was evaluated by GMτM. In regime II, the data were analyzed by eqs 2-4. The Je0 and GM-1 decrease with C with an exponent 2.1 ( 0.2 over the whole range of C examined, as shown in Figure 6A.

Je0 or GM-1 ∝ C-2.1

(5)

This scaling relation indicates the presence of a network formed by the entanglement of long threadlike micelles in the solution. It is likely that this scaling holds over the whole range of C, irrespective of the concentration regimes. Accordingly, a transient network is expected to be present also in regime II. In regime II, however, there is a possibility that the observed exponent close to -2 might arise from the effect of polydispersity with respect to the micelle length. The relaxation time, on the other hand, exhibits a nonlinear behavior as shown in Figure 6B, different in the two regimes. The relaxation time in regime I, τM, was about 0.1 s and nearly constant independent of C. The data in regime II represent terminal relaxation times obtained by eq 2 and increase with C. The slopes of the two straight lines in this figure (d log τ)/(d log C) were 1.2 ( 0.1 for 0.04 < C/mol kg-1 < 0.1(regime II) and 0 ( 0.2 for 0.2 < C/mol kg-1 < 0.5(Regime I). The zero-shear viscosity also shows a nonlinear dependence in a double logarithmic plot, Figure 6C. The slope (d log η)/)d log C) changes from 3.2 ( 0.3 for the low C range (0.04 < C < 0.1) to 2.0 ( 0.3 for the high C range (0.2 < C/mol kg-1).

Effect of Ionic Strength at 25 °C. The effects of ionic strength were examined at three surfactant concentrations, 0.05, 0.10, and 0.20 mol kg-1, in the range of NaCl concentration ms between 0.05 and 0.3 mol kg-1. At ms ) 0.4 mol kg-1, phase separation took place. The steady-state shear compliance decreased monotonically with ms as shown in Figure 7A. Chain flexibility is expected to increase with ms due to a decrease of the electrostatic persistence length. Micelle growth with ms is also expected to contribute to the decrease of Je0. At C ) 0.1 mol kg-1, deviation from single Maxwell behavior became progressively large as ms either increased or decreased from 0.1 mol kg-1. We have seen above that the crossover concentration C* between the two regimes is around 0.1 mol kg-1 in 0.1 mol kg-1 NaCl. This does not imply, that the crossover is controlled by the condition that ratio C/ms ) 1, however, as shown below. We observed approximately single Maxwell type behavior for C ) 0.05 mol kg-1 at ms ) 0.2 mol kg-1. The relaxation times shown in Figure 7B suggest that the crossover takes place at C/ms ) 1/4-1/2, 1, and 2 for C ) 0.05, 0.1, and 0.2 mol kg-1, respectively. The data shown in Figure 7B suggest that the concentration-independent relaxation time in regime I only weakly depended on ms in the range ms < 0.1 mol kg-1, whereas it decreased with ms-2 in the range ms > 0.1 mol kg-1. We can summarize the ms dependence of the relaxation time in regime I as follows in a highly approximate way:

τ ∝ ms-2

(ms > 0.1 mol kg-1 : regime I)

(6)

τ ) constant independent of ms (ms < 0.1 mol kg-1 : regime I) In regime II, on the other hand, the relaxation time increased

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Figure 4. Angular frequency ω dependence of (A) the storage shear modulus G′ and (B) the loss shear modulus G′′ for C14DAO solutions with different md at R ) 0.5, ms ) 0.1 mol kg-1. Symbols for C are (×) 0.04, (4) 0.05, (1) 0.07, (0) 0.09, (+) 0.10, (]) 0.13, (b) 0.16, (O) 0.20, ([) 0.30, (3) 0.40, (O) 0.50 mol kg-1.

Figure 6. The C dependence of (A) the steady-state shear compliance Je0, (B) the relaxation time τ, and (C) the zero shear viscosity η of C14DAO solutions at R ) 0.5 in 0.1 mol kg-1 NaCl.

Figure 5. Cole-Cole plots for C14DAO solutions with different md at R ) 0.5, ms ) 0.1 mol kg-1. Symbols for C are (×) 0.04, (0) 0.05, (]) 0.07, (2) 0.09, (O) 0.10 (A), and (O) 0.10, (4) 0.20, (]) 0.30, (1) 0.40, (b) 0.50 mol kg-1 (B).

with ms and its power was between 1 and 2. The relaxation time at low C thus showed a maximum at about ms ) 0.1 mol

kg-1. In conclusion, the effect of NaCl concentration can be described with ms instead of the ratio C/ms. This is reasonable because no specific Cl- counterion binding has been suggested in the case of C14DAO. Effect of Temperature. The effects of the temperature T were examined in a range 25-55 °C on the solutions of 0.1 mol kg-1 NaCl for the half-ionized surfactant (R ) 0.5) at two concentrations C. Steady-state shear compliances were nearly constant, (2.5-3.5) × 10-3 Pa-1, in this range of T for C ) 0.5 mol kg-1, whereas they showed a tendency to increase with T at C ) 0.1 mol kg-1. The viscosity decreased with T according to η ∼ exp(-0.13T) for both concentrations (Figure 8A). At C ) 0.5 mol kg-1, the relaxation time decreased with T, and τ/ηsolv

Viscoelastic Properties of C14DAO Micelles

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Figure 8. The temperature dependence of (A) the zero shear viscosity η and (B) τΜ/ηsolv for C14DAO solutions in 0.1 M NaCl at R ) 0.5. (O) C ) 0.1 mol kg-1,(b) C ) 0.5 mol kg-1, and ηsolv represents the solvent viscosity.

Figure 7. Effects of NaCl concentration ms on (A) the steady-state shear compliance Je0, (B) the relaxation time τ, and (C) the zero shear viscosity η for C14DAO solutions (R ) 0.5) at different surfactant concentrations. C (mol kg-1): (O) 0.05, (b) 0.10, and (4) 0.20.

vs 1/T plot gives a straight line (Figure 8B).

τ/ηsolv ∝ exp[E/RT]

(7)

We obtained the activation energy E of 21.2 ( 2 kcal mol-1. In comparison, a value of 25-30 kcal mol-1 was reported for cetyltrimethylammonium bromide (CTAB) in 0.25 M KBr.7 Hence, the relaxation mechanism in regime I is not expected to differ much from that of CTAB insofar as the activation energy is concerned. Cryo-transmission Electron Micrography (CryoTEM). Figure 9 (A-C) presents cryoTEM micrographs obtained from 0.1 mol kg-1 NaCl solutions of R ) 0 (A), 0.5 (B), and 1(C). To understand what is shown in these micrographs, we must first consider some aspects of the cryoTEM technique. The aqueous samples are rapidly vitrified in the form of very thin films spanning holes in a polymer support. The vitrified films are directly examined in transmission mode at liquid nitrogen

temperature. The thickness of the films varies over the holes, from maybe about 500 nm close to the support to a few nm in the middle of the hole. The thickness must not be much larger than 500 nm for anything to be observed, scattering of electrons from the vitrified water is otherwise excessive. The variation of the thickness results in that the middle portions of the micrographs often are void of structures whereas the projections from thick parts show a multitude of overlapping structures that in reality may be present at different heights and cannot be distinguished from true entanglements. When long threadlike micelles (or polymers) are observed parts of film that are thinner than the radius of gyration of the coiling threads will be avoided, and those threads that enter the thin part will be spread mainly laterally in the film. In the thicker parts, segments that are pointing in the direction normal to the film, and thus in the direction parallel to the electron beam, will be more frequent, and imaged as dark spots on the micrographs. In Figure 9A-C, the thin part of the films are at the top, where in all cases an area without any micelles is found, whereas long threadlike micelles are found with increasing density further down. In Figure 9A, at R ) 0 (pH ) 10), the micelles are much shorter than in Figure 9B,C, where the first very long micelles bordering to the empty thin area are displayed particularly clear. It is obvious that these micelles form both branches and loops, but few loose ends. The branching is not abundant, but several 100 nm separate the junctions. That the micelles are shorter in Figure 9A is seen both from the large number of open ends, and from the abundance of black dots, indicating segments

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Figure 9. Cryoscopic transmission electron micrographs of 0.1 mol kg-1 C14DAO solutions in 0.1 mol kg-1 NaCl. (A) R ) 0, (B) R ) 0.5, and (C) R ) 1.

normal to the film, found also rather close to the void area, where the film must still be quite thin. The images thus indicate clearly a difference between the micelle structure at R ) 0 on one hand, and at R ) 0.5 and 1 on the other. The micrographs in Figure 9B,C do not reveal any structural difference between the half-protonated and fully protonated micelles, although the dynamic properties change very substantially from the protonated to the half protonated form. This may suggest rapid breaking of fully protonated chains. Similar observations were made already by Clausen et al.53 for CTAC-NaSal.) In some other images from R ) 0.5, bilayer structures appeared (not shown). We are not sure about the interpretation of these findings, but the fact that bilayer structures were found only in the samples of R ) 0.5 (pH ) 5) indicates that this composition is one where the headgroups attract each other to

make structures with little curvature possible. It should be added that examples of coexisting threadlike micelles and bilayers have been found earlier,54 and in some cases just in samples displaying viscoelasticity.54 Discussion Relaxation Mechanism. An important feature of regime I is that the relaxation is of single-exponential type. According to Cates,23,24 single-exponential behavior is expected in the fastbreaking limit of the micelles and the relaxation time τ2 is then given as the geometric mean of the reptation time τrep and the breaking time τbreak:τ2 ) (τrepτbreak)1/2. However, this model predicts the relaxation time to have a concentration dependence with a power of 1.5:τ2 ∼ C1.5. This prediction is inconsistent with the observed independence of concentration in regime I:τM

Viscoelastic Properties of C14DAO Micelles ∼ C0. We have to look for a relaxation mechanism other than the fast-breaking limit of the reptation mode. We tentatively assume that the single-exponential behavior in regime I is a manifestation of a single dominating mechanism in the transient network irrespective of polydispersity with respect to the micelle length. The most probable candidate for this process is a chemorheological process involving the breaking/formation of entanglement points or cross-links.5 For micelles, the entanglements or cross-links can be broken and formed with respective rate constants k- and k+. The number of those entanglements pertaining to the residual stress n(t) decays exponentially with time, n(t) ) 〈n〉 exp(- k-t), since newly formed chains are free from strain. In this way, the relaxation time τ1 is given by τ1 ) 1/k-. As a mechanism of the stress relaxation of the network, entanglements are supposed to vanish by the crossing of two chains. For this to occur, first the two chains should merge at the entangled point and then this four-way crossing should disappear leaving two chains. The breaking rate constant of an entanglement k- will thus be written as k- ) exp(∆G*/kT) in terms of the activation free energy ∆G*, which is independent of the surfactant concentration C. This is consistent with the present result τ ∼ C0 in regime I. The argument is in line with that of Shikata et al.5 Another possible relaxation mechanism will be sliding of the entanglement point.9 This idea is in line with the observed branches and loops in TEM picture (Figure 9B). In this case, ∆G* will correspond the activation free energy for sliding the branching point along the micelle. In regime II, an approximate relation τ ∼ C is found. We expect in this concentration regime a relaxation process to hold that is similar to that in slightly entangled semidilute solutions. We expect then, τ ∼ M2 where M denotes the average molecular weight of micelles.55 According to the classic argument on the micelle growth,56 it is shown that M increases with C0.5. This simple argument proposes τ ∼ M2 ∼ C in regime II. The observed exponent of unity is consistent with this expectation. On the other hand, the above assumed Rouse-type mechanism would predict a different scaling exponent (-0.5) of Je0. But this inconsistency might be compromised by taking into account the effect of polydispersity. When the concentration increases, micelles grow and the number of micelles also increases. This will increase the number of entanglements per micelle and hence the relaxation process through the diffusional motion of micelle chains becomes more and more inefficient. Eventually, the relaxation path through the chain crossing becomes more effective. In this way, we can expect a change of the relaxation mechanism with the concentration as observed in the present study. It is to be stated here that our interpretation of the data in the present study in terms of the two regimes is just a possibility among others. Conclusion Protonation (ionization) of tetradecyldimethylamine oxide was found to have marked effects on the viscoelastic properties of the micelle solutions were found. The zero shear viscosity,the shear modulus and the relaxation time all reached the maximum values at the half-ionized state (the degree of ionization R ) 0.5). For the half-ionized micelles (R ) 0.5) in 0.1 mol/kg NaCl solutions, the steady-state compliance Je0 decreased with C with an exponent of 2.1 ( 0.2, suggesting the presence of an entangled network of flexible threadlike micelles. Two concentration regimes were discriminated in the concentration dependence of the relaxation time. A single Maxwell behavior was observed in the high concentration regime I (C > 0.1 mol/

J. Phys. Chem. B, Vol. 105, No. 23, 2001 5417 kg) and the relaxation time was about 0.1 s and nearly independent of C. At low concentrations, regime II (C < 0.09 mol/kg), the relaxation time increased with C with an exponent slightly larger than 1. This change in the relaxation mechanism with concentration can be understood from the increase of both the number of micelles and the micelle length at low concentrations, resulting in that the diffusional movement of the micelles becomes increasingly hindered, whereas at high concentrations a relaxation mechanism involving merging and break up at micelle crossings becomes more effective. Effects of NaCl concentration ms showed that the elastic modulus increased with ms and the regime shift took place at different ratios C/ms. From the temperature dependence of the viscoelasticity at R ) 0.5 in 0.1 mol/kg NaCl solutions, a value of 21.2 ( 2 kcal mol-1 was obtained as the activation energy. Cryo-transmission electron micrographs clearly showed a highly entangled network in the solution for R ) 0.5, while much smaller micelles for R ) 0. Contrary to the expectation from the rheological results, a highly entangled network was also observed in the solution for R ) 1. The present results strongly suggest the short-range attractive interaction between the headgroups of the nonionic (deprotonated) and the cationic (protonated) species of amine oxides. Acknowledgment. This research is supported partly by the Grant-in-Aid for Scientific Research (B) (No. 12440200) from Monbu-kagaku-sho, Japan References and Notes (1) Rehage, H.; Hoffmann, H. Faraday Discuss. Chem. Soc. 1983, 76, 363. (2) Rehage, H.; Hoffmann, H. Rheol. Acta 1982, 21, 561. (3) Candau, S. J. J. Colloid Interface Sci. 1985, 105, 521. (4) Shikata, T.; Hirata, H.; Kotaka, T. Langmuir 1987, 3, 1081. (5) Shikata, T.; Hirata, H; Kotaka, T. Langmuir 1988, 4, 354. (6) Candau, S. J.; Hirsch, E.; Zana, R.; Adam, M. J. Colloid Interface Sci. 1988, 122, 430. (7) Candau, S. J.; Hirsch, E.; Zana, R.; Delsanti, M. Langmuir 1989, 5, 1225. (8) Kern, F.; Lemarechal, P.; Candau, S. J.; Cates, M. E. Langmuir 1992, 8, 437. (9) Appell, J.; Porte, G.; Khatory, A.; Kern, F.; Candau, S. J. J. Phys. II France 1992, 2, 1045. (10) Khatory, A.; Kern, F.; Lequeux, F.; Appell, J.; Porte, G. N.; Morie, N.; Ott, A.; Urbach, W. Langmuir 1993, 9, 933. (11) Khatory, A.; Lequeux, F.; Kern, F.; Candau, S. J. Langmuir 1993, 9, 1456. (12) Kern, F.; Lequeux, F.; Zana, R.; Candau, S. J. Langmuir 1994, 10, 1714. (13) Carver, M.; Smith, T. L.; Gee, J. C.; Delichere, A.; Caponetti, E.; Magid, L. J. Langmuir 1996, 12, 691. (14) Soltero, J. F. A.; Puig, J. E.; Manero, O. Langmuir 1996, 12, 2654. (15) Hassan, P. A.; Valaulikar, B. S.; Manohar, C.; Kern, F.; Bourdieu, L.; Candau, S. J. Langmuir 1996, 12, 4350. (16) Oda, R.; Narayanan, J. N.; Hassan, P. A.; Mandrar, C.; Salkar, R. A.; Kern, F.; Candau, S. J. Langmuir 1998, 14, 4364. (17) Brown, W.; Johansson, K.; Almgren, M. J. Phys. Chem. 1989, 93, 5888. (18) Nemoto, N.; Kuwahara, M. Colloid Polym. Sci. 1994, 272, 846. (19) Nemoto, N.; Kuwahara, M.; Yao, M.-L.; Osaki, K. Langmuir 1995, 11, 36. (20) Hoffmann, H. ACS Symposium 578, Chapter 1 “Viscoelastic surfactant solutions”. (21) Rehage, H.; Hoffmann, H. Mol. Phys. 1991, 74, 933. (22) Magid, L. J. J. Phys. Chem. B 1998, 102, 4064. (23) Cates, M. E. Macromolecules 1987, 20, 2289. (24) Cates, M. E. J. Phys. France 1998, 49, 1593. (25) Messager, R.; Ott, A.; Chatenay, D.; Urabach, W.; Langevin, D. Phys. ReV. Lett. 1988, 60, 1410. (26) Cates, M. E. J. Phys. Condens. Matter 1990, 2, 6869. (27) Turner, M. S.; Cates, M. E. J. Phys. II France 1992, 2, 503. (28) Drye, T. J.; Cates, M. E. J. Chem. Phys. 1992, 96, 1367. (29) Lequeux, F. Europhys. Lett. 1992, 19, 675. (30) Kato, T.; Anzai, S.; Seimiya, T. J. Phys. Chem. 1987, 91, 4655. (31) Kato, T.; Anzai, S.; Seimiya, T. J. Phys. Chem. 1990, 94, 7255. (32) Kato, T.; Terao, T.; Seimiya, T. Langmuir 1994, 10, 4468.

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