Langmuir 1991, 7, 1344-1351
1344
Rheological Properties of Semidilute and Concentrated Aqueous Solutions of Cetyltrimethylammonium Chloride in the Presence of Sodium Salicylate and Sodium Chloride F. Kern,+R. Zana,* and S. J. Candau*p+ Laboratoire de Spectromktrie et d’lmagerie Ultrasonores, Unit6 de Recherche Associke au CNRS No. 851, Universitk Louis Pasteur, 4, rue Blaise Pascal, 67070 Strasbourg Cedex, France, and Institut Charles Sadron, CRM-EAHP, CNRSIULP, 6,rue Boussingault, 67070 Strasbourg Cedex, France Received November 6,1990 The rheological behavior of the elongated flexible micelles present in aqueous solutions of cetyltrimethylammonium chloride (CTAC) in the presence of sodium salicylate (Nasal),at a mole ratio [Nasal]/ [CTAC] = 0.6, has been investigated as a function of the surfactant concentration C, temperature T, and NaCl content. The results show that the stress relaxation function characterizing the systems tends toward a single exponential as C increases and/or T decreases. These results are in agreement with the prediction of the theory of the rheological behavior of semidilute solutions of “living” polymer chains (polymer chains whose length varies on a time scale comparable to the reptation time). However, the quantitative analysis of the results (changesof terminal viscoelastic relaxation time TR,zero shear viscosity 9 , and time for reversible micelle breaking, with T ) on the basis of this theory reveals some inconsistencies. Also, the exponents of the power laws describing the changes of TRand 9 with C differ from those predicted by the model at high NaCl content and/or C. It is likely that these departures from the theoretical predictions arise from the nonuniform distribution of the bound chloride and salicylate counterionsin the hemispherical endcaps and cylindrical body of the elongated micelles present in the system.
Introduction Under appropriate conditions of concentration, salinity, temperature, presence of counterion, etc., small aqueous spherical micelles can undergo uniaxial growth and become rodlike.14 If the energy required to break a rodlike micelle into smaller parts (scission energy) is large enough, the length of the rods can become longer than their persistence length and they are then similar to semiflexible linear polymer chains. In particular, these flexible rodlike micelles can become entangled, even at fairly low surfactant concentration (or volume fraction). Strong evidence of such a behavior for several aqueous cationic surfactants in the presence of salt has been recently reported,lV4including spectacular electron micrographs visualizing entangled micelles.6 Recent papers have reported micellar growth and entanglements in reversed micellar systems617and in oil-swollenmicellar solutions of nonionic surfactants.8 The viscoelastic properties of systems of flexible and entangled micelleshave been extensively investigated both theoretically9 and e ~ p e r i m e n t a l l y ~ ~these ~ J +last ~ ~ years.
* To whom the correspondence should be addressed. f
Laboratoire de Spectrometrie e t d’Imagerie Ultrasonores.
t Institut Charles Sadron. (1) Makhloufi,R.; Hirsch, E.;Candau, S.J.;Binana-Limbele,W.; Zana, R. J . Phys. Chem. 1989,93,8095, and references therein. (2) Candau, S . J.; Hirsch, E.; Zana, R.; Delaanti, M. Langmuir 1989, 5 , 1225, and references therein. (3) Jindal, V.;Kalus, J.;Pilsi, H.; Hoffmann, H.; Lindner, P. J . Phys. Chem. 1990, 94, 3129, and references therein. (4) Porte, G.; Appell, J. Europhys. Lett. 1990, 12, 190. (5) Vinson, P.; Talmon, Y. J. Colloid Interface Sci. 1989, 133, 288. ( 6 ) Zhou, Z.; Chu, B. J . Colloid Interface Sci. 1989, 133, 348. (7) Scartazzini, R.; Luisi,P. L. J.Phys. Chem. 1988,92,829. Schurtenberger, P.; Scartazzini, R.; Magid, L. J.; Leser, M.; Luisi, P. L. J . Phys. Chem. 1990, 94, 3695. ( 8 ) Eshuis, A.; Mellema, J. Colloid Polym. Sci. 1984, 262, 159. (9) Cates, M. E. Macromolecules 1987,20,2289;Europhys.Lett. 1987, 4. 497: J . Phvs. (Paris) 1988. 49. 1593: J. Phvs. Chem. 1990.94. 371. ’ (10) Shikke,T.;Hirata, H.;Kotaka, T. L&gmuir 1987,3,1081;1988, 4, 354; 1989, 5 , 398.
0743-7463191 2407-1344$02.50/0
It is now recognized that the reversible breaking down of elongated micelles can have an important influence on the viscoelastic properties of these s y s t e m ~ . ~ J ~ J ~ J ~ Cates9has recently extended to “living” polymer chains (chains that undergo reversible breakdown processes and are thus good models for the elongated micelles) the reptation theory,20which describes the rheologicalproperties of unbreakable chains in the semidilute (entangled) regime. Cates’ model predicts several rheological regimes depending on the relative rates of diffusive polymer motion and reversible breakdown processes. In particular, a nearly single exponential stress decay function is predicted in the linear viscoelastic response, in the limit where the micelle breaking time is short compared to the reptation time of a micelle of length equal to the average micellar length. Recall that the micelle breaking time can be obtained from temperature-jump experiments.21*22 A thorough comparison between the theoretical predictions and the experimental results has been made recently in the case of the hexadecyltrimethylammonium bromide (CTAB) solutions in aqueous KBr.2J8J9 In the present paper we investigate the rheological behavior of ( 1 1 ) Shikata, T.; Hirata, H.; Takatori, E.; Oaaki, K. J . Noh-Newtonian Fluid Mech. 1988,28, 171. (12) Imae, T.; Abe, A.; Ikeda, S. J . Phys. Chem. 1988,92,1548. (13) Rehage, H.; Hoffmann, H. J . Phys. Chem. 1988,92,4712. (14) Hoffmann, H.; Ldbl, H.; Rehage, H.;WCmderlich, I. Tenside Deterg. 1985, 22, 290. (15) Thurn, H.;Ldbl, M.; Hoffmann, H. J . Phys. Chem. 1985,89,517. (16) Ldbl,M.;Thurn, H.;Hoffmann, H. Ber. Bunsen-Ges. Phys. Chem. 1984,88, 1102. (17) (a) Hoffmann, H.; Platz, G.;Rehage, H.; Schorr, W. Ber.BueenGes. Phys. Chem. 1981,25,877; (b) Adv. Colloid Interface Sci. 1982,17, 275. (18) Candau, S . J.; Hirsch, E.; Zana, R. In Physics of Complex and Supermolecular Fluids; Safran, S., Clark, N., Ede.; Wiley: New York, 1987; p 569. (19) Candau, S . J.; Hirsch, E.; Zana, R.; Adam, M. J. Colloid Interface Sci. 1988, 122, 430. (20) De Gennes, P. G. Macromolecules 1976,9, 587. ( 2 1 ) Turner, M . S.; Cates, M. E. Europhys. Lett. 1990,II, 681. (22) Candau, S . J.; Merikhi, F.; Waton, G.; Lemarechal, P. J . Phys. (Paris) 1990, 51, 977.
0 1991 American Chemical Society
Rheological Properties of CTAC in Nasal and NaCl
hexadecyltrimethylammoniumchloride (CTAC) micellar solutions in aqueous sodium salicylate (Nasal) at the fixed molar concentration ratio [NaSal]/ [CTAC] = 0.6, in the presence of NaC1. In this system the growth is induced by the binding of salicylate ions to the hexadecyltrimethylammonium micelles. Rheological studies of similar systems have been reported by Bayer et al.23(hexadecyltrimethylammonium salicylate in H2O + 0.01 M NaC1) and Shikata et al.lOJ1 (CTAB NaSal or salicylic acid, no swamping electrolyte). In particular, the effect of the ratio R = [NaSal]/[CTAB] on the rheological properties was fully investigated. A single exponential stress relaxation function was observed for R L 0.6, at sufficiently high surfactant concentration.1° At R > 1, a peculiar rheological behavior was notedlo and attributed2' to a charge reversal of the micelles resulting in a decrease of micelle length. However, this interpretation was recently questioned.I3 For our part we have investigated the CTAC NaSal system by time-resolvedfluorescencequenching and quasielastic light scattering (BELS).' CTAC rather than CTAB was selected for these studies because chloride counterions are more weakly bound to cationic micelles than bromide counterions.26*26 They are therefore easily displaced by the added salicylate ions, even at the fairly high sodium chloride content required in order to screen intermicellar interactions. This fact is important for some of the data referring to the effect of ionic strength in the present investigation. The QELS data showed that at R = 0.6, the system was fully entangled (the mesh size of the transient network formed by the entangled micelles remained constant at R 1 0.61.' So QELS measurements were performed at R = 0.6. The scattered intensity and the mutual diffusion coefficientwere found to obey power laws of the surfactant volume fraction CP, with exponents very close to those predicted for semidilute solutions of entangled polymer chains.' This paper reports a rheological investigation of the same system. The effects of the surfactant concentration, temperature, and concentration of added NaCl have been investigated in an attempt to check the predictions of the Cates model and to obtain a better insight on the mechanism responsible for the stress relaxation.
+
+
Theory We recall below the main equations derived by Cates. 1. EquilibriumProperties. Mean-field models931*2'7928 predict that Co(L),the number density of elongated micelles of length L, is exponential with some mean L (L being expressed in monomer units)
with
where CP is the surfactant volume fraction and E,i, is the scission energy of the micelle that represents the excess free energy for a pair of hemispherical endcaps relative to (23) Ba er, 0.;Hoffmann, H.; Ulbricht, W.; Thurn, H. Adv. Colloid Interface Jci. 1986, 26, 177. (24) Oleson, U.; SMerman, 0.;Guering, P. J. Phys. Chem. 1986,90,
----. 5999
(25) Verrall, R.; Milioto, S.;h a , R. J. Phys. Chem. 1988,92,3939. (26) Fabre, H.; Kamenka, N.;Khan, A.; Lindblom, G.; Lindman, B.; Tiddy, G. J. J. Phys. Chem. 1980,84,3428. (27) Blankachtein,D.;Thurston, G.;Benedek,G. J. Chem.Phys. 1986, 85,7268, and referencee therein. (28) Safran, S.; Turkevitch, L.; Pincue, P. J. Phys. Lett. 1984, 42, 1135.
Langmuir, Vol. 7, No. 7,1991 1346
a rodlike region containing an equal number of surfactants.28129 The above relationships have been derived for nonionic micelles or ionic micelles at large ionic strength. Indeed, dynamic measurements in semidilute CTAB solutions at high ionic strength (0.25 M KBr) gave results supporting the predicted @'I2 micellar gr0wth.~J9~30 However, at low salt concentration (0.1 M KBr) the strong dependence of the viscosity and self-diffusion coefficient on CP could not be fitted by eq 2.2J8J1A model calculation for semidilute elongated micellar solutions with no added salt was recently proposed31 to explain these anomalies. This model suggests that Coulomb interactions result in an additional contribution to the free energy of an endcap that depends lo arithmically on CP. This modifies the growth law for I ! which now varies approximately, if we consider a relatively narrow range of CP (about 1decade), as CP(1/2)(1+A) where A > 0 depends on the renormalized Coulomb charge of an endcap. The physical origin of the increased growth exponent is that the electrostatic free energy contributions favor hemispherical endcaps over the cylindrical regions. The same effect leads to smaller micelles for a fixed CP. This was discussed by and more recently by Odijk.33 2. Dynamic Properties. Cates et al.9*21 have considered two types of processes: (i) One process considered was 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 elongated micelles and is independent of time and of volume fraction. Such assumptions are strictlyvalid in the entangled regime when reaction rates are determined by the local motion of chain subsections and not the diffusion of polymers over distances large compared to their gyration radii. The micelle breaking time Tb is found to be given by
= (kL)-' (3) Equations 2 and 3 predict that T b should decrease upon increasing CP as W2in the limit of high ionic strength, according to Tb
-
Tb k-'CP-'/' eXp(-E,k/%,T) (4) The derivation of eq 4 assumed fully screened electrostatic effects and no excluded volume effect. Catess has accounted for excluded volume effect and obtained an equation identical with eq 4, where the CP-1/2 term is replaced by @-)'.e. This modified equation is used below. The effect of added salt is more difficult to analyze. An increase of salt leads to an increase of L and therefore to a decrease of Tb, but k is likely to be also modified. (ii) The other process considered was the bimolecular end interchange process where a free micellar end brings about the rupture of a micelle away from its ends and combines simultaneously with one of the two free ends resulting from the rupture, the other end remaining free. The associated breaking time is given by
= (k'CP)-' (5) where k' is the rate constant for the end interchange process. Within the framework of a kinetic model based on the above two processes, Turner and Cates21have shown that Tb
(29) Ieraelachvili,J. N.;Mitchell, D. J.; Ninham, B. W. J. Chem. SOC., Faraday Trans. 2 1976, 72, 1525. (30) Mewager, R.; Ott, A.; Chatenay, D.; Urbach, W.; Langevin, D. Phys. Rev. Lett. 1988,60,1410. (31) Safran, S.; Pincue, P. A.; Catea, M. E.; MacKintoeh, F. J. Phys. (Paris) 1990,51,503. (32) Porte, G. In Surfactants in Solution; Mittal, K. L., Lindman, B. Me.; Plenum: New York, 198& p 805. (33) Odijk, T. J. Phys. Chem. 1989,93, 3888.
1346 Langmuir, Vol. 7, No. 7,1991 the end interchange process is not active in the relaxation of the system following a temperature-jump, whereas reversible scission leads to a single exponential relaxation signal with a relaxation time
-
Kern et al.
L35*@-’
(11) where 5 is mesh size of the temporary network formed by the entangled polymer chains. The mesh size varies as the following power law of Tr
@38937
= 7 b / 2 = (2kL)-’
(6) 5 @477 (12) In systems where end interchange and reversible scission Equation 12 has been shown to hold for entangled miprocesses are simultaneously present, only the latter plays cellar systems formed by a variety of s ~ r f a c t a n t s l ~ ~ ~ ~ ~ ~ a role in T-jump relaxation. Thus the T-jump relaxation Combiningeqs 11and 12together with the 90.6dependence signal will be single exponential, with a time constant TTJ of L yields given by eq 4 or 6 even if end interchange reactions are faster than reversible scission. However, the micelle 7, N (13) breaking time, which is the quantity relevant in stress or eq term) Then, inserting eq 13 and eq 4 (with a relaxation experiments (see below), will be in this case 5 into eq 8 yields almost entirely controlled by end interchange. 3. Stress Relaxation. In the semidilute range, i.e., at for reversible scission surfactant concentration large enough so that the elongated micelles overlap,the systems exhibit a viscoelasticbehavior very reminiscent of that of transient polymeric netw o r k ~ . In polymeric * ~ ~ systems, ~ ~ the~viscoelas~ ~ ~ ~ ~ ~ ~ ~ ~ ~ for end interchange tic properties are described by a model based on the reptation theory.3s However, the “living” character of the micelles provides additional pathways for disentangleTR (14b) ment. Several regimes of behavior are predicted depending on the relative values of two characteristic times: Tr, repThe zero-shear viscosity q is related to the terminal time tation time of a polymeric micelle with a length equal to and the plateau modulus GOthrough the average micellar length L; Tb, breaking time. When 7 = GOT, (15) Tb is long compared to T r , the theory of reptation of polydisperse polymers should apply, leading to a strongly nonFor semidilute polymer solutions in good solvents, it has exponential stress relaxation function p(t) given by eq 7, been shown that40 where a is a constant TTJ
N
N
exP[-a(t/Tr)1’4] (7) In the opposite case where Tb
-i
Figure 3. Variation of f(w) with ~ ' ( w for ) a CTAC + NaSal system in the presence of 0.5 M NaCl, and a surfactant concentration 0.15 M,at temperatures ( 0 )30.5, ( 0 )35.3, ( 0 ) 39.6,(A)43.6,and (A)47.4 "C. The dashed line is the locus of the centers of the half-circles. (See text.)
00
3
G' (Pa) Figure 2. Cole-Cole plota for CTAC + NaSal systems at C = 0.15M: (a)0.1 M NaCl at temperatures30.1 "C (O),32.5 "C (O), 33.9 "C (A),36.2 "C (A),and 43.2 "C ( 0 ) ;(b) 0.25 M NaCl at temperatures 30.6 O C (O),35.4 "C (0),40.1"C (A),44.6 "C (A), and 60 "C ( 0 ) ;(c) 0.5 M NaCl at temperatures30.5 "C (0),35.3 "c (O), 39.6 (A),43.6 (A),and 47.4 (0). processes). This would again result in a decrease Of Tb and thus of T b / T r , and in more narrow relaxation spectra. The decrease of T b / T r as c or the NaCl content are increased explains the evolution of the shape of the Cole-Cole plots in Figures 1 and 2. Figure 2 shows that the nonexponentiality of the stress relaxation function increases slightly with T. It seems reasonable to attribute this change to an increase of q,/T,. It was found experimentally that q-,decteases upon increasing T.22 As for T ~it, is proportional to L3 (cf. eq 11) and therefore it also decreases as T increases. The results in Figure 2 suggest then that T b does not decrease as fast as 7 , and, therefore, that the activation energy, E b , of the breaking process is smaller than that of the reptation process E, = 3E,h/2. These activation energies are discussed further below. The nonexponentiality of the stress relaxation function can also be evidenced in a Cole-Cole representation of the imaginary part q"(o) of the complex viscosity as a function of the real part q'(w). The Maxwell model with one relaxation time is characterized by a semicircular plot centered on the q' axis. Systems with a distribution of relaxation times are characterized by a circular arc which is part of a circle having its center lying below the q' axis. The complex viscosity may then be written as q* = q / [ 1
+ GWT)'*]
(22) where the value of the constant CY is between 0 and 1and
3.1
3.2 3.3 Figure 4. Semilogarithmic representation of the variations of TR/m with l/Tfor CTAC + NaSal systems in the presence of 0.1 M NaCl at the surfactant concentrations (0)0.10 M,(m) 0.15 M,(e) 0.20 M, and (A)0.25 M. is a measure of the width of the distribution of relaxation times. The angle between the q' axis and the diameter of the circle going through the origin of the plot is given by aa/2. Figure 3 shows the evolution of the q"(o) vs q'(o) plots with T. The plots are semicircular but their centers are located below the q'(o) axis. It can be seen in Figure 3 that the centers of the half-circles are all located on the same straight line, which means that CY does not vary significantly with temperature. Notice that this result does not contradict the conclusion drawn from the G" vs G' Cole-Cole plots, that the nonexponentiality of the stress-relaxation function increases with T. Indeed, the high-frequencydata (mainly responsible for the deviation from single exponentiality) that are located in the right side of the G" vs G' plots become buried in the noise in the q" vs q' plots where they are located close to the origin. In any case, the above results show that the change of shape of the stress-relaxation function with Tis small. It must also be noted that the behavior shown in Figure 3 is similar to that observed for melts or semidilute solutions of polymers with narrow molecular weight distribution.@
Langmuir, Vola7, No. 7, 1991 1349
Rheological Properties of CTAC in NaSal and NaCl 3 2
1 o5
5
102
c
3 2
1 o4
0.1 0.15 0.2 0.25 Figure 6. log-log representation of the variations of q / q o and T ~ / qwith o surfactant concentration for CTAC + NaSal systems in the presence of 0.1 M NaCl at (A)30.0 OC, (e) 39.5 "C, and
5
( 0 )49.5
3
3.2
3.1
3.3
Figure 5. Semilogarithmicrepresentation of the variations of q / q o with 1/Tfor CTAC + NaSal systems in the presence of 0.1 M NaCl at the surfactant concentrations ( 0 )0.10M, (m) 0.15 M, (e)0.20 M,and (A)0.25 M. Table I. Activation Energies (in kcal/mol) for the Terminal Relaxation Time, & and Viscosity, E,, at Various Surfactant Concentrations. C,and Ionic Strengths (CN.CI) CN.C~,M C, M ER E, 0.1 0.15 0.20 0.25
42.2 39.0 39.4 39.7
42.0 39.0 39.0 40.0
0.25
0.07 0.10 0.15 0.20 0.25
45.6 40.6 38.0 41.0 35.0
45.3 41.0 37.6 40.7 38.0
0.5
0.05 0.07 0.10 0.15 0.20 0.25
34.4 40.9 41.5 39.5 32.0 34.0
39.0 40.7 40.4 36.8 32.1 32.2
0.1
2. Temperature Dependence of t h e Rheological Parameters. Semilogarithmic representations of the variations of T R / q o and q/qo as a function of 1/T are given in Figures 4 and 5 for a series of systems containing 0.1 M NaC1. Both TRand q have been divided by the solvent viscosity qo, in order to correct the observed changes for the temperature dependence of qo. The linear variations seen in Figures 4 and 5 and in other plots not shown indicate an Arrhenian behavior. The activation energies ER and E,,obtained from these results are listed in Table I. Within the experimental error ER and E,, are independent of the surfactant concentration and ionic strength, except for the systems a t high surfactant and ionic strength. Table I yields
E , N E,, = 39.0 f 3.5 kcal/mol Notice that we have also found ER N E,, in our previous (43) Marin, G. ThBee, Univereit.4 de Pau et dee Pays de l'hdour, 1977.
OC.
investigation of semidilute CTAB solutions in the presence of 0.25 M KBr.' However the values of the activation energies were much lower for this system, about 25.4 2 kcal/mol. The T-jump investigations of the (CTAB + NaSal) systems with 0.1 and 0.25 M NaCl revealed relaxation times too long to be measured with our apparatus, except in the high T-range. However, measurements could be performed in dilute systems with 0.5 M NaC1.l" The measured TTJ values showed an Arrhenian behavior with an activation energy
*
ETj
N
32
* 3 kcal/mol
This value is very close to that found for semidilute solutions of CTAB in 0.25 M KBr,2*2230 f 1.5 kcal/mol. If the breaking process is controlled by scissionrecombination ETJ= E b (see above) and the insertion of the rheology and T-jump data into eq 10 yields
E,
N
31 f 7 kcal/mol
This value is much larger than that found for CTAB in 0.25M KBr (14k ~ a l / m o land ) ~ appears to be unrealistically large for the scission-recombination process. Indeed its insertion in eq 2 yields physically unsound values of the micellar length. This leads to the conclusion that the breaking process and in turn the rheological properties may not be controlled by scission-recombination processes. A similar conclusion appears to hold for end-interchange processes. Indeed in the preceding paragraph it was concluded the Eb < E,. If eqs 8 and 9 are valid, this condition leads to
E, L E ,
N
39 kcal/mol
Such a large value of E, would also result in unrealistically long micelles, irrespective of the mechanism of micelle breaking: scission recombination or end interchange. Notice that at very high C and NaCl content (0.5 M), the ERvalues tend to decrease (Table I). A value of ER of 32 kcal/mol would yield more realistic micellar lengths. (44) Merikhi, F.; Waton, C.; Candau, S. J. Unpublished data.
Kern et al.
1350 Langmuir, Vol. 7, No. 7,1991
10'
Figure 7. log-log variations of T ~ / qand o ~ / r ) with o surfactant concentration for CTAC + Nasal systemsin the presence of 0.25 M NaCl at (A)30.0 O C , (e)39.5 "C, and (e)49.5 "C. However, other problems arise under such experimental conditions. A more detailed discussion of these various points is given in the next paragraph. Consider now the plateau modulus GO.Its value is given by the radius of the first quarter of circle fitting the data of the Cole-Cole plots of Figure 1. Figure 2 shows that Go is rather insensitive to temperature. This is in agreement with the model of semidilute solution of flexible polymer chains used to interpret the data. Indeed this model predicts that Go depends only on the mesh size or correlation length F4O (see eq 16). As T increases the micellar length decreases but the mesh size does not vary as the system is semidilute. Therefore Go remains nearly constant if we except the small effect due to the kBT term (see eq 16). 3. Effect of the Surfactant Concentration. Figures 6-8 show doubly logarithmic representations of the variations of the zero-shear viscosity q and terminal relaxation time TRwith the surfactant concentration C ( q and TRhave been corrected for the temperature dependence of the solvent viscosity, by plotting 1 / 9 0 and T R / q o against C) at the three ionic strengths investigated: 0.1, 0.25, and 0.5 M NaCl. Only those solutions with C high enough that the first half of the Cole-Cole plots could be fitted by a quarter-circle have been considered. The results in the presence of 0.1 M NaCl (Figure 6) obey the power laws
17
-
@3.4M.2
(24)
The exponents are consistent with the theoretical prediction on the basis of end-interchange micelle breaking (see eqs 14b and 17b). It must be realized however that this holds only in a restricted range of concentration of surfactant and NaC1. For systems with high C and NaCl content, the variations of v/vo and TR/TO with CP (Figures 7 and 8) become less pronounced and curved downward at 0.25 M NaCl and show a maximum at 0.5 M NaC1. These changes of behavior cannot be given a precise explanation in the present state of the theory dealing with
I
I
I
I
I
I
0.05 0.07 0.1 o.15 a2 0.25 Figure 8. log-log variations of TR/I)O and r)/r)o with surfactant concentration for CTAC + Nasal systems in the presence of 0.50 M NaCl at (A)30.0 OC, (e) 39.5 OC, and (e)49.5 "C.
such systems. We note that the theory predicts the occurrence of new relaxation regimes of the stress such as breathing modes when 7b/7r becomes very short, as is indeed the case a t high ionic ~ t r e n g t h .However ~ none of these regimes predicts maxima such as in Figure 8. Other possible breaking mechanisms have been suggested. One is the shedding of small micelles at the ends of a chain.9 This leads to pronounced departures from exponential .~ behavior in the stress relaxation function ~ ( t )Another mechanism is based on the bimolecular exchange of two interior bonds via a four-armed intermediate.1° However, if such reactions predominate, the treatment based on an underlying tube would probably be inapplicable and the stress-relaxation function nonexponential. At this point, it must be noted that the anomalous behavior discussed above seems to be linked with the presence of salicylate ions. Nonmonotonous variations of TR and q with surfactant and salt concentrations have also been reported for the CPyCl/NaSal systemx4and the CTAB/NaSal system.'O It was suggested that these variations may be specifically associated to the formation of a 1/1complex between salicylate ions and cationic surfactant head groups and the catalysis of the chain breaking reaction by the remaining uncomplexed Sal- ions.I0 One must also remark that the above systems contain two kinds of counterions Sal- and C1- (or Br-). Under such experimental conditions the counterions bound to the hemispherical endcaps may contain a larger proportion of C1- ions than the counterions bound to the micellar cylindrical body. Indeed it has been shown that C1- ions are less bound to micelles than the more lyotropic Salions.26126 On the other hand the packing parameter P = U / U M l (where u and 1 are the volume and length of the hydrophobic moiety and U M the optimal surface area per head groups) is larger for cylindrical than for spherical micel1es.s In the present case, aM must be thus larger in hemispherical endcaps than in the cylindrical body (u and 1 are constant), probably because of a larger ionization degree of the former. A larger proportion of C1- ions in the hemispherical endcaps would lead to such a situation.
Rheological Properties of CTAC in Nasal and NaCl A fluorescence quenching study of mixed micellar solutions of CTAB C T A W (therefore similar to the systems investigated here) concluded that the nonuniform binding of C1- and Br- ions results in a bimodal micellar distribution with a population of small spheroidal micelles binding more than average C1- ions coexisting with a population of elongated micelles binding more than average Br- ions. If the micellar distribution is also bimodal in the CTAC NaSal systems, the theoretical model used to interpret the rheological properties would not apply since it assumed an exponential distribution of micellar lengths. The conclusions reached above concerning the temperature and surfactant concentration dependences of the relaxation time would therefore be irrelevant. However, another more recent s t u d p involving cetyltrimethylammonium and cetylpyridinium micelles in the presence of two types of counterions (C1-/C103-, Cl-/N03and Cl-/Br-) showed no evidence for a bimodal distribution, and this possibility will not be further discussed in this paper. Nevertheless, the results did indicate a much stronger binding of NOS-, C103-, or Br- ions than of C1ions.& Recently it was suggested by Cates that, due to the presence of two types of counterions nonuniformly distributed in the elongated micelles, the scission energy should contain an entropy term associated with the rearrangement of counterions upon formation of an endcap.47 On this basis it becomes possible to explain the above results a t least qualitatively. Indeed the scission energy is now written as a free energy
Langmuir, Vol. 7, No. 7, 1991 1351
+
102-
+
and all equations carry over with E,i, replaced by F,. In particular this leads to
f,
N
@I12exp(E,i,/
2kBT) exp(-S,,/
2kB)
-
The Sa, term is independent of temperature, so the Arrhenius plots would still measure E,i, 32 kcal/mol. However, when calculating micellar lengths, a large positive S,iu may still lead to reasonable micellar lengths, thus resolving the apparent inconsistencynoted in the preceding paragraph. Likewise the problems noted in this section at high @ and/or C1- concentration may very well arise from the competitive bindings of C1-and Sal-. In particular, Porte and AppelP have clearly shown that the micelle length in solutions of, for instance, CPyB micelles in H20-0.2 M NaBr is reduced upon addition of 0.2 M NaCl. This result indicates that the overall ionic strength does not alone determine the micelle length and that the total amount of bound counterions (which is reduced upon addition of NaC1) is an equally if not more important parameter. Such problems are of course not present in CTAB-KBr systems where the Cates model was found to apply much better than for the CTAC-Nasal systems.2 Thisdifference provides a posteriori support to the above explanation of the peculiar results found for the CTAC-Nasal systems. (46)
Almeren, M.; Ufroth, J. E.; Rydholm, R. Chem. Phrs. Lett.
1979,63, 265:
(46) Porte, G.; Appell, J. Surfactants in Solution;Mittal, K. L.,Lindman,B. We.: Plenum Press: New York. 1982: Vol. 2.. D_ 804. (47) Cat&, M. Private communication. '
10
1
CtMI 1
I
a05 0.07
I
0.1
I
I
I
0.15 a2 a25
Figure 9. log-log representation of the variation of the plateau modulus Go with surfactant concentration in the presence of (A) 0.1 M NaCI, (D) 0.25 M NaC1, and ( 0 )0.5 M NaC1. Further investigationsshould be performed with systems where micellar growth occurs in the presence of only one type of counterion. In this respect CTASal-NaSal systems may show a less complex behavior than CTAC-Nasal systems. Figure 9 shows the variations of the plateau modulus Go with the surfactant concentration. The plots are linear at the three NaCl contents investigated. The exponent found at 0.1 M NaCl is 2.12, that is close to that predicted by the theory, on the basis of eq 16. However, lower exponent values are found at higher NaCl content: 2.07 and 1.83a t 0.25 and 0.50 M NaCl. These low values of the exponents parallel the abnormal behavior of TRand 7 a t such high NaCl content.
Conclusions We have investigated the rheological properties of semidilute solutions of elongated micelles of CTAC in the presence of sodium salicylate (mole ratio [NaSal] / [CTAC] = 0.6) in the presence of NaCl. The Cole-Cole plots show that the stress relaxation function tends to become single exponential as the surfactant concentration is increased or the temperature decreased. These observations are in agreement with the theory of Cates for the rheology of "living" polymer chains and correspond to systems where the micelle breaking time becomes shorter than the reptation time. However, the analysis of the temperature dependence of the zero shear viscosity 7 and terminal viscoelastic relaxation time TRyields a very high value of the activation energy of these two quantities, which results in unrealistic micelle lengths. Also, a t high NaCl and surfactant concentrations the changes of TRand 7 with @ do not follow power laws, contrary to the predictions of the Cates model. It is likely that this departure from the theoretical predictions arises from the nonuniform distribution of bound C1- and Sal- ions in the hemispherical endcaps and cylindrical body of the elongated micelles. This would result in the existence of an entropic term in the scission energy, associated with the formation of an endcap. Acknowledgment. We are indebted to Dr. M. Cates for his suggestions concerning the effect of the counterions on the micellar growth and for fruitful discussions in the framework of the EEC Grant Number SCI* 0288-C (EDB). We thank Dr. D. Collin for his help in setting up the rheology equipment.
