Langmuir 1994,10, 4468-4474
Intermicellar Migration of Surfactant Molecules in Entangled Micellar Solutions Tadashi Kato,* Toshiaki Terao, and Tsutomu Seimiya Department of Chemistry, Faculty of Science, Tokyo Metropolitan University, Minamiohsawa, Hachioji, Tokyo 192-03, Japan Received April 11, 1994. I n Final Form: July 6,1994@ Surfactant self-diffusion coefficients (D)have been measured on semidilute solutions of nonionic surfactants (C16E7, c1&, and C14E6) at different temperatures by using the pulsed-gradient spin echo method. The self-diffusion coefficient of these surfactants first decreases with increasing concentration (c) and then increases. Above about 10%by weight, the log D-log c plot gives a straight line whose slope is in good agreement with the theoretical prediction (2/3)of the previously reported model which takes into account intermicellar migration of surfactant molecules. In order to simulate the observed diffusion coefficient in the whole concentration range, this model has been modified by taking into account the micellar diffusion. The activation energy for the molecular diffusion processes in the higher concentration range has been obtained from the simulation results at different temperatures. The observed activation energy is anomalouslylarge (110-160 kJ*mol-l)and increases as the hydrophobicity of surfactant molecules is increased, which can also be explained by the above model. Concentrationdependence of the viscosity systems. The slope of the double logarithmic plot decreases has been measured on C&7, C14E6, and with increasing temperature. The plot of the slope vs T - Tc(Tc,the lower critical solution temperature) for different systems falls into a smooth line. Transition from an entangled network to a multiconnected network is discussed.
Introduction In recent years, much attention has been paid to the structure and dynamics of semidilute solutions of wormlike micelles. 1-27 Static properties such as osmotic compress-
* Abstract published in Advance A C S Abstracts, November 15, 1994. (1)Cates, M. E.; Candau, S. J. J. Phys.: Condens. Mutter 1990,2, 6869. therein ...., and references .~.. . ~ ._ . ~ . . . . (2)Kern, F.; Zana, R.; Candau, S. J. Langmuir 1991,7, 1344. (3)Imae, T. J.Phys. Chem. 1988,92,5721; 1989,93,6720; 1990,94, 5953;Colloid Polvm. Sci. 1989,267,707. (4)Hashimoto; K.; Imae, T. iangmuir 1991,7,1734. (5)Kato, T.; Anzai, S.; Seimiya, T. J. Phys. Chem. 1987,91,4655. (6)Kato, T.; Anzai, S.; Seimiya, T. J . Phys. Chem. 1990,94,7255. (7)Kato, T.; Terao, T.; Tsukada, M.; Seimiya, T. J.Phys. Chem. 1993, 97,3910. (8)Drye, T. J.;Cates, M. E. J. Chem. Phys. 1992,96,1367. (9)Granek, R.;Cates, M. E. J. Chem. Phys. 1992,96,4758. (10)Turner, M. S.;Marques, C.; Cates, M. E.Lungmuir 1993,9,695. (11)Hoffmann, H. Proceedings of the ACS Symposium; American Chemical Society: Washington, DC, 1994. (12)Hoffman, H.; Oetter, G.; Schwander, B. Prog. Colloid Polym. Sci. 1987,73,95. (13)Hoffmann, H.; Rauscher, A.; Gradzielski, M.; Schulz, S. F. Langmuir 1992,8,2140. (14)Shikata, T.; Hirata, H.; Kotaka, T. Langmuir 1987,3, 1081; 1988,4,354;1989,5,398. (15)Ott, A.; Urbach, W.; Langevin, D.; Schurtenberger, P.; Scartazzini, R.;Luisi, P. L. J. Phys.: Condens. Matter 1990,2,5907. (16)Bouchaud, J. P.; Ott, A,; Langevin, D.; Urbach, W. J.Phys. 11 1991,1 , 1465. (17)Schurtenberger, P.; Magid, L. J.; King, S. M.; Lindner, P. J. Phys. Chem. 1991,95,4173. (18)Phillies, G. D. J. Langmuir 1991,7, 2072. (19)Appell, J.;Porte, G . ;Khatory, A.; Kern, F.; Candau, S. J . Phys. 111992,2,1045. (20) Khatory,A.; Kern, F.; Lequeux, Appell, J.; Porte, G.; Morie, N.; Ott, A.; Urbach, W. Lungmuir 1993,9,933. (21)Khatory, A.; Lequeux, F.; Kern, F.; Candau, S. J. Langmuir 1993,9,1456. (22)Berret, J.; Appell, J.; Porte, G. Langmuir 1993,9, 2851. (23)Clausen, T. M.;Vinson, P. K.; Minter, J. R.; Davis, H. T.; Talmon, Y.; Miller, W. G. J. Phys. Chem. 1992,96,474. (24)Brown, W.; Johansson, K.; Almgren, M. J. Phys. Chem. 1989, 93,5888. ( 2 5 ) Olsson, U.; Soderman, 0.;Guering, P. J . Phys. Chem. 1986,90, 5223. (26)Monduzzi, M.; Olsson, U.; Soderman, 0.Langmuir 1993,9,2914. (27)Nemoto, N.;Kuwahara, M. Langmuir 1993,9,419. ~
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0743-7463/94/2410-4468$04.50/0
ibility show similar behaviors as observed in semidilute solutions of flexible polymers and can be explained by the scaling theory of entangled polymer^.^*-^^ On the other hand, dynamical properties such as viscoelasticities and self-diffusion behaviors are different from those of polymers. The difference has been discussed by several investigators on the basis of the dynamics of network structures formed by wormlike micelles. In the previous s t ~ d ywe , ~ have measured light scattering intensities and the surfactant self-diffusion coefficient (D)on semidilute solutions of a nonionic surfactant C16E7.31 It has been shown that the light scattering results can be explained by the scalingtheory for flexible polymers proposed by Daoud and Jannink32,33which takes into account the existence of the critical solution t e m p e r a t ~ r e . ~ ~ On the other hand, the surfactant self-diffusion coefficient first decreases with increasing concentration (c), goes through a minimum, and then increases. These results cannot be explained by the theories for polymers and even for “living p 0 1 y m e r s ” ~ which ~ ~ ~ takes into account chain breakage and recombination. Moreover, the activation energy for diffusion processes in the higher concentration range has been found to be anomalously large. In order to explain these results, we have proposed a simple model which takes into account the intermicellar migration of surfactant molecules. This model predicts a power law D = c2I3which is in good agreement with the experimental results in the higher concentration range. (28)De Gennes, P. G. Scaling Concepts in Polymer Physics; Cornel University Press: Ithaca, N Y , 1979. (29)Doi, M.; Edwards, S. F. The Theory ofpolymer Dynamics; Oxford Science Publications: Oxford, 1986. (30)Fujita, H. Polymer Solutions; Elsevier: Amsterdam, 1990. (31)In this paper, n-alkyl poly(oxyethy1ene) surfactants, CnHzn+t(OCzH&OH, are denoted as C,E,. (32)Daoud, M.; Jannink, G. J. Phys. (Paris) 1976,37,973. (33)Cotton, J. P.: Nierlich, M.: Boue. F.: Daoud. M.: Farnoux. B.: Jannink, G.; Duplessix, R.; Picot,’ C. J. ‘Chem. Phys. 1986,65,1101: (34)Similar results have been obtained in our previous study on the C I Z Esystem.6 ~
0 1994 American Chemical Society
Intermicellar Migration of Surfactant Molecules
Langmuir, Vol. 10, No. 12, 1994 4469
In the present study, we have performed PGSE measurements on semidilute solutions of C14E7 and C14E6 as well as C&7 a t different temperatures with the aim of confirming the generality of our model. These systems have been chosen because their lower critical solution temperatures (T,) are not far from that ofthe C16E7 system. At the same time, the above model has been modified to simulate the observed self-diffusion coefficients in the whole concentration range. We have also measured viscosities on C16E7, C14E6, and C12E5 systems to obtain further information on dynamics of entangled micelles.
Table 1. Lower Critical Solution Temperature TCand Critical Concentration cc for D20 Solutions of CI&, c14%CME~, and Cl2E5 surfactant
Tc/”C
cclgdm-3
C16E7 C14E7 C14E6 C12E5
51.0 f 0.5 56.5 i 0.5 41.0 i 0.5 30.5 f 0.5
12f4 18 f 6 8 f 4 15 f 8
where x = -2.85 and -4 for Y = 0.588 and v = 0.5, respectively (for a = 0.5). On the other hand, the zero-shear viscosity for entangled polymers follows the power law
length, the “end interchange’’ reactions occur. They have calculated the scaling of the stress relaxation time, the zero-shear viscosity, and the monomer diffusion coefficient with the concentration in three regimes, Le., unbreakable chains, reptative regime, and breathing regime. For the bond interchange reactions, the exponent for the diffusion coeficientx is -1.4 and -0.8 in the reptative regime and the breathing regime, respectively. For the end interchange reactions, on the other hand, x = -1.6 and -1.2 in the reptative regime and the breathing regime, respectively. The exponent for the zero-shear viscosity y is 4.0 and 2.6 for the bond-interchange reactions in reptative regime and breathing regime, respectively. For reversible scission and end-interchange reactions, y takes values between 2.9 and 3.7. Diffusion Model Taking into Account Intermicellar Migration. In a previous paper,7 we have proposed a diffusion model in the higher concentration range (> 10 wt % >> the overlap concentration) taking into account the intermicellar migration of surfactant molecules. In this model, it is assumed that (1)a surfactant molecule diffuses in a micelle along its contour during the time tmig and then migrates to adjacent micelles, (2) tmig satisfies the condition R , ~ I D L
