Temperature-jump study of elongated micelles of cetyltrimethylammonium bromide

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1 Temperature-jump study of elongated micelles of cetyltrimethylammonium bromide S.J. Candau, F. Merikhi, G. Waton, P. Lemarechal To cite this version: S.J. Candau, F. Merikhi, G. Waton, P. Lemarechal. Temperature-jump study of elongated micelles of cetyltrimethylammonium bromide. Journal de Physique, 1990, 51 (10), pp < /jphys: >. <jpa > HAL Id: jpa Submitted on 1 Jan 1990 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2 82.70 A J. Phys. France 51 (1990) MAI 1990, 977 Classification Physics Abstracts D Temperature-jump study of elongated micelles of cetyltrimethylammonium bromide S. J. Candau, F. Merikhi, G. Waton and P. Lemarechal Laboratoire de Spectrométrie et d Imagerie Ultrasonores (*), Universite Louis Pasteur, 4 rue Blaise Pascal, Strasbourg Cedex, France (Reçu le 20 novembre 1989, accepté le 22 janvier 1990) Résumé Une étude de la cinétique de solutions aqueuses de micelles allongées de bromure de cetyltrimethylammonium en présence de bromure de potassium a été réalisée au moyen d une technique de saut de température utilisant la lumière diffusée comme moyen de detection. Le temps de relaxation a été mesuré en fonction de la concentration en tensio-actif et en sel et de la température. Les résultats obtenus, combinés à des mesures rhéologiques fournissent des informations sur le mécanisme de relaxation des contraintes dans ces systèmes Abstract. study of the kinetics of elongated micelles of cetyltrimethylammonium bromide in aqueous solutions containing potassium bromide has been performed by means of a T-Jump technique, using light scattering to probe the relaxation. The relaxation time has been measured as a function of the surfactant concentration, salt concentration and temperature. The T-Jump results combined with rheological measurements provide information on the stress-relaxation mechanism of these systems. Introduction. The temperature jump (T-Jump) technique has been widely used for the study of the micellar kinetics [1, 2]. A rapid and small change of temperature is generated in the solution. As a result, the micellar system shifts to a new state of equilibrium determined by the final value of the temperature. The evolution with time of the system is usually monitored by a change in an optical property such as absorption, scattering or fluorescence emission. Most of the studies performed up to now have dealt with highly dilute solutions, in the vicinity of the critical micellar concentration (CMC). The first successful attempt to describe theoretically the kinetics of micelle formation was published by Aniansson and Wall [3]. It was based on the assumption that the micelle formation-breakdown takes place through a series of stepwise reactions, the micelles growing by incorporation of monomer only. This model which was restricted to nonionic surfactants was subsequently extended by Kahlweit et al. [2, 4-5] to the case of ionic surfactants. However, the experimental results for ionic (*) Unité de Recherche Associée au CNRS n 851. Article published online by EDP Sciences and available at

3 978 surfactants could not be fitted by the theory except for a restricted range of concentration above the CMC. More specifically, in the high concentration range, the relaxation time was found to decrease as the surfactant concentration was increased, in contradiction with the theoretical predictions [1-2]. To interpret these results, Kahlweit et al. suggested that for systems where the intermicellar interactions are not too repulsive the stepwise reaction path is bypassed by a reversible coagulation process of submicellar aggregates [4, 5]. This process is likely to be the dominant one for the systems in which very long, flexible, wormlike micelles exist [6-17]. Recently, Turner and Cates [18] have studied theoretically the relaxation of a system of polymers or wormlike micelles that can break and recombine reversibly after a small perturbation. An important prediction of this model concerns the case of an initial perturbation corresponding to a shift in the mean chain length, as caused by a T- Jump. For this case, the entire perturbation is expected to decay exponentially with the characteristic time equal to twice the breaking time T b (the mean-waiting time for a chain of the average length to undergo a scission somewhere along its length). To monitor the relaxation, one needs to measure a physical quantity sensitive to a change in the mean length of the wormlike micelle. An obvious candidate is the light scattering which probes the weight average molecular weight in the dilute regime. In this paper we present results obtained by T-Jump in aqueous solutions of cetyltrimethylammonium bromide (CTAB) in the presence of KBr. The results are compared with the theoretical predictions of the model of Turner and Cates. Furthermore, the T-Jump data are used in conjunction with the results of previous rheological experiments to provide information on the mechanism of stress-relaxation and give an estimate of the scission energy of wormlike micelles. Theory. We recall below the main results of the theoretical models derived by Cates for the stress relaxation [16, 17] and the relaxation spectrum of micellar length distributions [18]. Static equilibrium properties. Mean-field models [16-20] predict that Co(L), the number density of wormlike micelles of length L is exponential with some mean L (L being expressed in monomer units) with where 0 is the surfactant volume fraction and Escis is the scission energy of the micelle that represents the excess free energy for a pair of spherical end-caps relative to the cylindrical interior regions [20, 21]. The above relationships have been derived for non ionic micelles or ionic micelles at large ionic strength. Indeed, dynamic measurements in semi-dilute CTAB solutions at high ionic strength (0.25 M KBr) gave results supporting the predicted 03A61/2 micellar growth [12, 13]. However, at low salt (0.1 M KBr) the strong dependence of the viscosity and self-diffusion constant on 03A6 could not be fitted by equations (2) [12, 13]. To explain these anomalies, a model calculation for semi-dilute elongated micelles solutions with no added salt was recently proposed [22]. This model suggests that Coulomb interactions result in an additional

4 979 contribution to the free energy of an end-cap that depends logarithmically on 03A6. This modifies the growth-law for L which now varies approximately, if we consider a relatively narrow range of 0 (about one decade), as 03A6 (1/2)(1 + A) where A> 0 depends on the renormalized Coulomb charge of an end-cap. The physical origin of the increased growth exponent is that the electrostatic free energy contributions favor the spherical end-caps over the cylindrical regions. This same effect leads to smaller micelle for a fixed 0. This was discussed by Porte [23] and more recently by Odijk [24]. Relaxation spectrum of micellar length distributions. Turner and Cates [18] have considered two types of chemical kinetics. i) The reversible unimolecular scission, characterized by a temperature dependent rate constant k per unit time per unit arc length, which is the same for all wormlike micelles and is independent of time and of the volume fraction. Such assumptions are strictly valid in the entangled regime when reaction rates are determined by the local motion of subsections of chain and not the diffusion of polymers over distances large compared to their gyration radii. ii) The end-interchange with conservation of micelle number. Within the framework of a model for reaction kinetics taking these two mechanisms into account, Turner and Cates found that the end-interchange reactions play no part in the relaxation after T-Jump whereas reversible scission leads to a single exponential decay with the characteristic time Equations (2) and (3) show that r T - J should decrease upon increasing the volume fraction as 03A6-1 /2 in the limit of high ionic strength The effect of added salt is more difficult to analyze. An increase of salt leads to an increase of Land therefore to a decrease of r T - j but k is likely to be also modified. Stress relaxation. In the semi-dilute range, i.e., at surfactant concentration large enough so that the elongated micelles overlap, the systems exhibit a viscoelastic behavior very reminiscent of that of transient polymeric networks [8-12, 14-17]. In the latter systems, the viscoelastic properties are described by a model based on the reptation theory [25]. However, the «living» character of the micelles provides additional pathways for disentanglement. Several regimes of behavior are predicted depending on the relative values of two characteristic times : (a) T r, reptation time of a polymeric micelle with a length equal to the average micellar length L and (b) T b the breaking time. When T b is long compared to T r, the theory of reptation of polydisperse polymers should apply, leading to a strongly non exponential form of the stress relaxation function. In the opposite case where Tb T r, the micelle breaking plays an important role in the viscous flow process as stressed first by Hoffmann et al. [8-10]. The Cates model predicts an almost pure exponential form of the stress relaxation function with the terminal time [ 16-17] : the

5 980 A single-exponential stress decay has been observed in solutions of several ionic surfactants [10-12, 14, 15] including the CTAB solutions studied here [10-12]. An interesting consequence of the relation (5) concerns the temperature effect. All three relaxation times are expected to follow arrhenian laws of the form exp (E/kB T), which leads to the following relationship between the activations energies ER, Eb and Er corresponding respectively to the temperature dependences of TR, Tb and T r According to the reptation theory [25] Tr ~ L3. This result combined to equation (2) yields : The above relation shows that independent measurements of ER by stress relaxation and of Eb by T-Jump (for the case of reversible scission) provide a determination of Esis. Materials and methods. The sample of CTAB was the same as in previous investigations [10-12]. The solutions were carefully degassed in order to avoid resonances of bubbles that would generate an important stray modulation of the light. The schematic diagram of the set-up is given in figure 1. Basically the set-up is similar to those described by Hoffmann et al. [26] and Strey and Pakusch [27]. The T-Jump is produced by Joule heating by means of the discharge of a capacitor. The rise time of the T-Jump is - 1 ps and the amplitude of the T-Jump calculated from the values of the stored electrical energy and the heat capacity of the sample can be varied between 0.1 and 2 C. The scattering cell is illuminated by an intense light beam obtained from a powerful (100 W) mercury source (OSRAM HBO) in conjunction with a large aperture condenser (ORIEL Aspherab). To avoid heating the solution, a shutter which is controlled electrically by computer, only permits the passage of light during the measurement. The cell is Fig Schematic diagram of the set-up.

6 thermostated at ± 0.1 C. The calibration of the temperature in the cell as a function of the temperature of the thermostat was realized using a thermistor. Interference filters allow to select the following wavelengths : 313, 365, 405, 436, 546, 577 nm. A fraction of the incident light beam is sent into a photodiode, which thus delivers a reference signal. An electronic device under control of the computer uses this signal to compensate the instabilities arising from the lamp power supply and the arc position. This device and the use of intense light beam allow one to improve the signal/noise ratio by a factor of the order of 100. The scattered signal is digitized and logged in the computer. For each measurement, about ten relaxation functions are added up in order to get an averaged curve which results in a further improvement of the signal/noise ratio. Figure 2 gives typical experimental curves. 981 Fig Typical relaxation curves for a CTAB solution at concentration C 10-2 M in = presence of 0.25 M KBr. The full lines are the best single exponential fits to the experimental curves. The relative variation of the scattered intensity is of the order of 1 %. Results and discussion. SHAPE OF THE T-JUMP RELAXATION FUNCTION. - Figure 2 shows that single exponential curves fit the experimental recordings of the T-Jump relaxation functions. In fact, for most measurements the best fits and the experimental curves are quite undistinguishable. This is in agreement with the prediction of equation (3) and allows one to determine Tb. EFFECT OF SURFACTANT CONCENTRATION. - Figure 3 shows the variations of 7-b as a function of CTAB concentration for 0.25 M KBr solutions at temperatures T = 30 C and T = 35 C. It is seen that Tb decreases steadily as the CTAB concentration is increased. However the results are not well fitted by the l/j - 1/2 dependence resulting from equations (2) and (3), but rather describe a sigmoïdal curve. This deviation can be understood from the following considerations.

7 Variations Fig. 3. of Tb and TR as a function of surfactant concentration in 0.25 M KBr solutions. The dotted lines have the theoretical slope - 1/2. i) The change of mean length L resulting from a T-Jump can be detected through the scattered intensity I, only in the dilute regime. In this range and if one neglects the intermicellar interactions, Is is given by : where II is the osmotic pressure, C the surfactant concentration, and P (K) the form factor that varies only slightly during the T-Jump. However, in the highly dilute range the rate constant k for reversible scission is likely to become concentration dependent as the micelles have to diffuse through the medium in order to recombine. In this case, equation (4) would no longer be valid. Moreover the contribution from the step-wise reaction path discussed in the introduction becomes non-negligible. This is presumably at the origin of the peak observed in the variation of the amplitude of the relaxation curve as a function of surfactant concentration (cf. Fig. 4). ii) On the opposite, in the high concentration range corresponding to semi-dilute solutions, the micelles are entangled and the scattered intensity does not probe any longer the length of the micelle. In this regime I, is given by [ 11 ] where e is the correlation length. As C increases, I, decreases. The cross-over between the regimes described by equations (8) and (9) respectively is quite broad because of the polydispersity of the micelles. At a scattering angle of 90 the maximum of 7g (C) occurs at C = 6 x 10-2 M for

8 Amplitudes Fig. 4. (per K) of the relaxation curves as a function of surfactant concentration in 0.25 M KBr solutions. The lines are guides for the eye. T 30 C. Beyond this concentration, the change of intensity is related to that of e and not = that of L which might introduce corrections to the law given by equation (4). At concentrations higher than those investigated here, 1 becomes nearly temperature independent. This explains the large decrease observed in figure (4) for the amplitude of the relaxation. This results in a quite poor accuracy for the data taken in the highest concentration range. An important conclusion to be drawn from the results of figure 3 is that the 7b(C) curves extrapolate in the high concentration range to values smaller than those of TR, the terminal time determined from stress-relaxation experiments [12]. Such crossing of the curves of 7-b(C) and TR(C) has also been observed by Hoffmann et al. [26]. This is in fact the very condition required for obtaining a single exponential stressrelaxation function, which is actually the experimental observation [12]. However it should be noted that in the low concentration side of the TR(C) curve the ratio Tb/TR is close to unity within experimental accuracy. Therefore, according to the theoretical calculation, the stress relaxation in this concentration range should show deviations from single exponential behavior in the short time range [16, 17]. Such deviations have not been observed in the experiments performed using the magneto-rheometer. On the other hand, they have been observed in experiments performed on other surfactant systems by means of dynamic viscoelastic measurements [28, 15]. The same result is found for aqueous solutions in presence of 0.1 M KBr as shown in figure 5. However, in that case, the ratio Tb/TR is much larger with an excess of salt. One observes also in figure 5 a maximum in the curve of T b ( C ). This maximum can be associated with the occurence at high dilution of the stepwise mechanism for the chemical kinetics. It also appears in the amplitude of the relaxation curves (cf. Fig. 6).

9 Variations Fig. 5. Of rb and TR as a function of surfactant concentration in M KBr solutions. The lines are guides for the eye. Fig Amplitude (per K) of the relaxation curves as a function of surfactant concentration in 0.1 M KBr solutions. The lines are guides for the eye.

10 Variations 985 EFFECT OF ADDED SALT. - According to the recent model of Safran, Cates and Pincus [22], the micellar growth is enhanced if Coulombic interactions are present (cf. theoretical section). As a result, one expects a larger variation of Tb with C when the amount of salt is decreased. This is what is observed in figure 5. However, it is difficult to draw quantitative conclusions, considering the different factors liable to affect the determination of Tb, as mentioned above. The effect of added salt at fixed volume fraction is illustrated in figures 7 and 8. The values of Th become smaller at high salt concentration. This behavior corresponds to a transition from the dilute regime at low salt to the semi-dilute one at high salt, the micelles growing under addition of salt. As expected, the larger the CTAB concentration, the smaller the salt content necessary to induce the transition. The decrease of T b upon increasing the concentration in KBr is accompanied by a large decrease of the amplitude of relaxation as shown in figure 8. Fig of Tb as a function of KBr concentration. The lines are guides for the eye. EFFECT OF TEMPERATURE. - The variations of log (rb) as a function of 11T are given in figures 9-11 for three KBr concentrations (0.1 M, M and 0.25) and different CTAB concentrations. The data are fitted by straight lines, indicative of an Arrhenian behavior. For a given salt concentration, the straight lines run parallel to each other within the experimental accuracy. From the slopes of these straight lines, one obtains the following values of the activation energy Increasing the salt content leads to larger micelles and therefore to a larger scission energy. This in turn would tend to increase Eb (cf. Eqs. (2) and (3)). Therefore the observed decrease of Eb when [KBr] is increased must be associated with the effect of added salt on k. The

11 Amplitude Fig. 8. (per K) of the relaxation curves as a function of KBr concentration. The lines are guides for the eye. Fig Variations of Tb as a function of 103/ T for CTAB solutions in 0.1 M KBr solutions. activation energies relative to the terminal time were previously measured for [KBr ] = 0.1 M and [KBr ] = 0.25 M [12]

12 987 Fig. 10. Variations of Tb as a function of 103/ T for CTAB solutions in M KBr solutions. Fig Variations of Tb as a function of 103/ T for CTAB solutions in 0.25 M KBr solutions. Combining the values of ER and Eb in equation (7) yields the following values of the scission energy The above values of the scission energy correspond to an energy of the order of kb T per surfactant molecule which appears reasonable.

13 988 Because of the micellar growth induced by an increase of the added salt, one would expect a smaller value of Escis for the sample with 0.1 M KBr. The experimental accuracy doesn t allow to draw such a conclusion. Conclusion. The results presented in this paper provide an experimental support to the theoretical model of Turner and Cates [18]. More specifically, we have verified that the perturbation of the distribution of lengths of wormlike micelles decays exponentially. The corresponding relaxation time, associated with the reversible scission kinetics, is a decreasing function of the surfactant concentration and becomes smaller than the terminal time of the stress relaxation function in the entangled regime. This is consistent with the observation of a single exponential decay of the stress relaxation. Combined T-Jump and stress relaxation experiments allowed us to determine the scission energy of the wormlike-micelles. Acknowledgments. The authors acknowledge the precious advices from M. Cates. They are also very grateful to P. Pincus, S. Safran and R. Zana for very useful discussions. This work was funded in part under EEC Grant Number SC 1 * 0288-C(EDB). References [1] LANG J., ZANA R., in «Surfactant Solutions», vol. 22, R. Zana, M. Dekker Eds. (New York, 1987) p [2] KAHLWEIT M., TEUBNER M., Adv. Colloid Interface Sci. 13 (1980) 1 and references therein. [3] ANIANSSON E. A. G., WALL S. N., J. Phys. Chem. 78 (1974) [4] LESSNER E., TEUBNER M., KAHLWEIT M., J. Phys. Chem. 85 (1981) 1529, [5] KAHLWEIT M., J. Colloid Interface Sci. 90 (1982) 92 ; Pure Appl. Chem. 53 (1981) [6] PORTE G., APPELL J. and POGGI Y., J. Phys. Chem. 84 (1980) 3105 ; PORTE G. and APPELL J., J. Phys. Chem. 85 (1981) 2511 ; APPELL J., PORTE G. and POGGI Y., J. Colloid Interface Sci. 87 (1982) 492. [7] PORTE G., J. Phys. Chem. 87 (1983) 3541 ; SAFRAN S. A., TURKEVICH L. and PINCUS P., J. Phys. Lett. France 45 (1984) L 69. [8] HOFFMANN H., LOEBL H., REHAGE H. and WUNDERLICH I., Tenside Detergents 22 (1985) 290. [9] WUNDERLICH I., HOFFMANN H. and REHAGE H., Rheol. Acta 26 (1987) 532. [10] REHAGE H. and HOFFMANN H., J. Phys. Chem. 92 (1988) [11] CANDAU S. J., HIRSCH E. and ZANA R., J. Colloid Interface Sci. 105 (1985) 521 ; CANDAU S. J., HIRSCH E. and ZANA R., J. Phys. France 45 (1984) 1263 ; CANDAU S. J., HIRSCH E. and ZANA R., Phys. Complex Supermol. Fluids, S. Safran and N. Clark Eds. (Wiley, New York) [12] CANDAU S. J., HIRSCH E., ZANA R. and DELSANTI M., Langmuir. 5 (1989) 1225 ; CANDAU S. J., HIRSCH E., ZANA R. and ADAM M., J. Colloid Interface Sci. 122 (1988) 430. [13] MESSAGER R., OTT A., CHATENAY D., URBACH W. and LANGEVIN D., Phys. Rev. Lett. 60 (1988) [14] SAKAIGUCHI Y., SHIKATA T., URAKAMI H., TAMURA A. and HIRATA H. J., Colloid Polym. Sci. 265 (1987) 750 ; SHIKATA T., HIRATA H. and KOTAKA T., Langmuir 4 (1988) 354. [15] SHIKATA T., HIRATA H., TAKATORI E. and OSAKI K., J. Non-Newtonian Fluid Mech. 28 (1988) 171. [16] CATES M. E., Macromolecules 20 (1987) 2289.

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