Langmuir 1994,10, 4027-4030
4027
Phase Transitions in Entanglement Networks of Wormlike Micelles Toshiyuki Shikata*?? and Dale S. Pearson*?# Department of Macromolecular Science, Osaka University, Toyonaka, Osaka 560, Japan, and Department of Chemical and Nuclear Engineering, and Materials Department, University of California, Santa Barbara, California 93106 Received April 19, 1993. In Final Form: August 10, 1994@ The condition of isotopic to liquid crystalline phase transitions in entanglement networks of a wormlike micellar system was examined. The system was aqueous solutions of cetyltrimethylammonium bromide and sodium salicylate and showed profound viscoelastic behavior. The plateau modulus, h0, was proportional to C D ~where ~ , CDis the concentration of the surfactant, like semidilute polymer solutions. However, at CD = 0.6 M the system showed a phase transition to liquid crystalline phase, and the proportionality in GNO did not hold any more above CD 5;: 0.4 M. CD dependence of the contour length between entanglement points, Le (= CD-'.~),was also quite similar to that of semidilute polymer solutions below CDa 0.4M. At the concentrationof phase transition, Le was shorter than the size of an equivalent random flight (Kuhn) segment of the micelle. When the micellar portion between entanglement points becomes shorter and loses characters of the random flight chains, the whole system exhibits a phase transition to the liquid crystalline state.
Introduction Entanglement networks formed by wormlike or threadlike or rodlike micelles of surfactant molecules have very unique proper tie^.'-^ They show profound viscoelastic behavior as well as entangling polymer systems.6 Since the concentration dependence of the high-frequency plateau modulus is qui,tesimilar to that of a concentrated flexible polymers system, the elasticity of the wormlike micellar system essentially results from an entanglement effect among micelles. However, it is also well known that the slowest relaxation mechanism of the wormlike micellar system is quite different from that of the polymer system and is likely controlled by mechanisms of scission and reformation of the m i ~ e l l e . ~Some ,~ theoretical models7,*had been proposed to explain the relaxation mechanism, whereas the mechanism is still not fully understood. Recently, we elucidated that the stress-optical law held well in the wormlike micellar system consisting of cetyltrimethylammonium bromide (CTAB) and sodium salicylate (NaSalLg This means that origin of elasticity of the micellar system is excess entropy caused by orientation of some portions of wormlike micelles between entanglement points as the rubber elasticity in the polymer system.6 Therefore, the only difference in dynamic processes between the micellar and the polymer system should be the slowest relaxation mechanism to release entanglements, whereas other features in short-time behavior should have the same characters in both system^.^ The portion of wormlike micelle between t Osaka University. University of California. 8 Deceased. Abstract published inAdvance ACSAbstructs, October 1,1994. (1)Gravsholt, S.J. Colloid ZnteTface Sci. 1976,57, 575. (2)Candau, S.J.;Hirsh, E.; Zana, R.; Delsani, M. Langmuir 1989, 5,1225. (3)Rehage, H.; Hoffmann, H. Mol. Phys. 1989,5,1225. (4) Shikata, T.; Hirata, H.; Kotaka, T. Langmuir 1988,4 , 354. (5)Shikata, T.; Kotaka, T. J.Non-cryst. Solids 1991,131-133,831. (6) Ferry, J. D. Viscoelastic Properties of Polymers, 3rd ed.; Wiley: New York,1980. (7) Cates, M. E. Macromolecules 1987,20,2289. ( 8 )Cates, M.E. Macromolecules 1988,21,256. (9)Shikata, T.; Dahman, S. J.; Pearson, D. S. Langmuir 1904,10, 3470.
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entanglement points would behave as the Gaussian chain with a certain equivalent random flight step segment at a concentration below the phase transition concentration to liquid crystalline state just like the flexible polymer system. In a flexible polymer system, the size of the random flight step segment (Kuhn length) is so short that one could not reach such a condition in which the distance between entanglement points is less than the Kuhn length even in bulk or in the undiluted state. On the other hand, in the wormlike micellar system, the Kuhn length has been estimated as 52 nm by means of a flow-birefringence t e ~ h n i q u e .Therefore, ~ one could easily reach the condition where the distance between entanglement points is comparable to the Kuhn length by making moderately concentrated systems. This situation would be quite similar to that of semiflexible polymer solutions. Various kinds of semiflexible polymer solutions with Kuhn lengths comparable to that ofthe wormlike micellar system show a phase transition to the liquid crystalline phase at a certain concentration, and the transition concentration is a strong function ofthe persistence length and the diameter of the semiflexible polymer, but it is not a function of molecular weight ifthe polymer is sufficiently 1 0 n g . l ~ -Thus, ~ ~ one might expect that rheological properties and phase transition phenomena observed in the wormlike micellar system essentially correspond to those observed in the semiflexible polymer system. A shear flow induced phase transition from the isotropic to liquid crystalline phase in a certain aqueous wormlike micellar system has been observed at a concentration which is close to the phase transition concentration. l6 This suggests that there would be strong and special orientational correlations among the wormlike micelles even below the phase transition concentration. In this paper, we report the phase transition phenomena of the wormlike micellar system from the isotropic to liquid (10)Werbowyj, R. S.;Gray, D. G. Macromolecules 1980,13,69. (11)Itou, T.; Teramoto, A. Macromolecules l9-i 21,2225. (12)Itou, T.; Teramoto, A. Polym. J. 1984,16,779. (13)Kubo, K. Mol. Cryst. Liq. Cryst. 1981,74, 71. (14)Conio, G.; Bianchi, E.; Cifferi, A.; Teald, A.; Aden, M. A. Macromolecules 1983,16,1264. (15)Laivins, G.; Gray, G. D. Macromolecules 1986,18,1753. (16)Schmitt,V.;Lequeux, F.; Pousse, A.; Roux,D. Langmuir 1994, 10,955.
0 1994 American Chemical Society
Shikata and Pearson
4028 Langmuir, Vol. 10, No. 11, 1994 S l O p . 2 . I5
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Figure 1. Concentration, CD,dependence of plateau modulus, Go.CD*means the phase transition concentration.
crystalline state. The phase transition condition will be compared with that of semiflexible polymer systems and, moreover, will be discussed in relation to the contour length between entanglement points, the distance between entanglement points, and the Kuhn length or the persistence length of the wormlike micelle. Experimental Section The system examined contains aqueous solutions, CTAB: NaSaW, of CTAB and Nasal. "he range of concentration, CD, of CTAB was from 0.006 to 1.0 M, and the concentration, CS,of Nasal was kept as CS = CD + 0.2 M. According to previous r e p ~ r t s the , ~ , longest ~ relaxation time of this micellar system is controlled by the concentration of free salicylate ions, CS*,which could be estimated as CS* = CS - CD;therefore, the longest relaxation times of all tested solutions were 2-3 s and were independent of cD.495The phase transition concentration, CD*, from the isotropic to liquid crystalline phase was determined by use of a polarizing microscope (Microphoto-FX,Nikon). Dynamic viscoelastic measurements were carried out with a conventional rheometer (RMS800 Rheometrics) equipped with cone and plate fixtures. The tested frequency range was from 0.1 to 100rad s-l, and the measuring temperature was about 25 "C. All the systemsexcept for CD> 0.6 M showed obvious plateau values, G O , in the storage modulus, G , at the high-frequency side. G of solutions at CD > 0.6 M increased gradually with frequency and did not show a plateau value, so that we accepted the highest G value as Gofor these solutions. Results and Discussion Concentration, CD, dependence of plateau modulus, Go, is plotted in Figure 1,and phase transition concentration, CD*,is also pointed out in the same figure. A nice power law relation between h0and CD holds with a slope of U 4 v 5 until CD = 0.4 M, and above that Goshowed a maximum, followed by a decrease, and consequently the system showed the phase transition at CD*.Because the slope of2.2 is exactly the same as that of semidilute flexible polymer solutions,6it is likely that the dynamic features of entangling wormlike micelles up to CD = 0.4 M are quite similar to those of flexible polymer molecules. The type of observed liquid crystalline phase is a so called hexagonal phase, HI, which has two-dimensional hexagonal periodicity of extended very long wormlike micelles. The same liquid crystalline phase of HI has been also observed in an aqueous system of cetylpyridinium bromide with Nasal at similar temperature and concentration ~0nditions.l~ Recently, we reported the applicability of the stressoptical law in the same wormlike micellar system.9 This means that the origin of the elasticity of this micellar system is excessive entropy caused by the orientation of some micellar portions between entanglement points and is exactly the same mechanism in the concentrated ~
~
~~~
(17) Monduzzi,M.; Olsson, U.; Sodeman, 0.Langmuir 1993,9,2914.
Figure 2. CDdependence of the molecular weight,Me,between entanglement points and the entanglement spacing, 5, for the wormlike micellar system.
polymer systems or rubber systems. Thus, we could estimate well-defined rheological parameters, such as the molecular weight, Me, between entanglement points and the entanglement spacing, 6, with standard methods6 in polymer rheology as shown below
Me = cRT GNO
where c is concentration of the micelle in weight (g ~ m - ~ ) , R is the gas constant, T i s the absolute temperature, and kg is Boltzmann's constant, respectively.
The dependence ofMeand 6 on CDare plotted in Figure 2. Both ofMeand 6 have a power law relation of CDbelow CD = 0.4 M, and their slopes are -1.1 and -0.71, respectively, and these slopes are again exactly the same as those uf semidilute flexible polymer solutions in good solvent.18 From these, we can conclude that below CD= 0.4 M there exists an entanglement network consisting of wormlike micelles behaving as flexible random flight (Gaussian) chains between entanglement points like the polymer system. Because Me is a decreasing function of Co, increasing CDreduces Me to a certain limiting value at which the micellar portion between entanglement points loses the character ofthe Gaussian chain due to the rigidity of the micelle; consequently, the system would show deviation from the viscoelastic behavior of the semidilute flexible polymer solution in good solvent. The Me at C D = 0.4 M must be the smallest one at which the micellar portion could behave as the Gaussian chains. Even from CD= 0.4to 0.6 M, the system keeps isotropic phase from judgement on optical observation, so that the micellar portion between entanglement points would still have dynamic processes to release its own excessiveorientation but would no longer behave as Gaussian chains. In this concentration range, there would be strong orientational correlation among the micelles as observed in an aqueous system of cetylpyridinium chlorate with sodium chlorate.16 Because the micellar portion at the entanglement point is not cross-linked permanently and has the ability to migrate in the restricted area of entanglement spacing, it can release the orientation of the micellar portion between entanglement points. The phase transition from the isotropic to the liquid crystalline phase is controlled by the total free energy of the system, so that one needs to calculate the total free (18)Daud, M.; Cotton,J. P.; Farnoux, B.; Jannik, G.; Sarma,G.; Benito, H.; Duplessix, R.; Picot, C.; De Gennes, P. G. Macromolecules 1976, 8 , 804.
Phase Transitions in Entanglement Networks
Langmuir, Vol. 10,No. 11, 1994 4029
Figure 3. CDdependence of the contour length, Le,between entanglement points and the distance, (rez)m,between the entanglement points of the same micellar portion. The solid and broken lines are calculated by the wormlike chain model (eq 4).18 energy to predict the phase transition concentration. However, in this study we are concerned with the relationship among contour length between entanglement points, Le, the distance between entanglement points, (re2)1/2, ofthe micellar portion, and the persistence length, q, of the wormlike micelle. According to our previous r e p ~ r tthe , ~ monomer of the wormlike micelle consists of about 18 CTA+Sal- (molar mass = 421) complexes and has a length and diameter of A RZ 0.85 nm and d % 4.8 nm, respectively, so that we obtain a relation of Le = Ag; g G MJ(421 x 18). The persistence length of the wormlike micelle in the entanglement state was evaluated as q = 26 nm through flow birefringence data, assuming the unperturbed state described by eq 3 (r3 -- 2q = 1,
(3)
Le
where 1~ is the Kuhn length for the equivalent random flight ~ e g m e n t . ~ Figure 3 shows the relationship between Le and (re2)1/2 as functions of CDat CD < 0.4. Solid and broken lines in this figure show the contour length, L,and the end-to-end evaluated by the Porod-Kratky wormlike distance, (r2)1/2, chain (WC) modellQ(eq 41, assuming that L has the same power law relation of CDas Le does for the micellar system even above CD = 0.4 M and also the same q = 26 nm as the wormlike micelles. (r2> = 2q[1 -
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1 - exp((4) L In the entangling wormlike micellar system, (re2)u2 should be a little bit more extended than (r2)l12of WC with the same L as the Le for the micelles, because the micelle has sequential parts on both entanglement points and would of the not shrink easily. Therefore, we expect that (re2)1/2 micellar system above CD= 0.4M could be approximately estimated by extrapolating straight as the dotted line in Figure 3, the upper limit ofestimation. The crossing point, C,(=0.5 M), between the solid and dotted lines represents the concentration where the micellar portions between entanglement points start to behave as rigid rods because (re2)l12 = Le, and it is very close to the obtained phase transition concentration, CD*.Moreover, C, is also the concentration where the size of portions between entanglement points becomes equal to the Kuhn segment. Because the Kuhn segment is hypothetically the smallest size monomer sequence which can behave as the random flight chain, the fact that Goof the wormlike micellar ~~
(19) Kratky, 0.;Porod, G.RecZ.Trau. Chem.Roys-Bas 1949,68,1106.
system corresponds well to the behavior of a semidilute flexible polymer solution up to CD = 0.4 M (very close to C,)is quite comprehensible. Since above C,the micellar portion between entanglements points would lose bending or folding motion to release its own orientation generated incidentally, therefore, the ability to increase entropy due to randomization of reorientation of the micellar portions would be weak a t least for the longest relaxation time, 2-3 s i n this system. Thus, C,should be one of the most convincing thresholds of phase transition to the liquid crystalline phase from the viewpoint of dynamic features. Comparison with Semiflexible Polymer Systems and Theoretical Models. The tested wormlike micellar system was prepared to have the longest relaxation time of 2-3 s and gave CD*= 0.6 M, and it was also reported that the same micellar system with much longer relaxation time showed the phase transition a t CD*= 0.6 M.20 This means that the phase transition concentration for the tested wormlike system almost reached the value independent of the relaxation time of the system or of a time scale of global motion of the wormlike micelle. Thus, the phase transition concentration of the micellar system should be compared with that of semiflexible polymer systems with infinite molecular weight. Khokhlov and Semenov's (KS)mode121had been one of the most reliable theoretical predictions for the phase transition concentration for semiflexiblepolymer systems. The KS model is a sophisticated modification of Onsager's mode1t2which can predict 4* successfullyonly for a system with short rigid rods or chains, taking account of the flexibility of the chains. Itou and Teramoto" reported that the phase transition concentration of a solution of poly(hexy1 isocyanate), PHIC, which is a typical semiflexible polymer, showed rather good agreement with the KS model prediction. According to the KS model, we could estimate the phase transition volume fraction, +* = 0.96 (or CD*G 1.7 M) for our micellar system, assuming that the molecular weight of the wormlike micelle is infinite. However, this 4* value is almost unity and means no existence of phase transition. This discrepancy might be coming from a limitation of the KS model that their model could predict the phase transition concentration only in a restricted condition in which a ratio d/(2q), which is a measure of flexibility, is less than 0.092. The ratio for the wormlike micelle is only 0.088 and is so close to the limit value that their model is no longer applicable in our system. In an aqueous solution of (hydroxypropyl)cellulose,14HPC, and a diAPC, butylphthalate solution of (acetoxypropyl)cellulo~e,~~ which have the ratios of 0.09 and 0.10, respectively, the KS model also does not predict plausible 4*.11 However, PHICll has the ratio 0.016-0.02, much smaller than 0.092, so that the KS mode121 predicts the phase transition concentration quite successfully for the PHIC system. Recently, Sat0 and T e r a m ~ t oimproved ~~ the KS model with the scaled particle theory24and got better prediction of 4* for rather flexible HPC and APC systems. Figure 4 shows the relationship between the phase transition volume fraction 4* and the ratio of d42q) for systems for which persistence lengths were well evaluated and which possess enough molecular weight to show molecular weight independent 4* except for schizophillan12 (20) Nemoto, N.; Yamamura, T.; Osakai, K.; Shikata, T. Langmuir 1991, 7, 2607. (21) Khokhlov, A. R.; Semenov,A. N. Physica A: (Amsterdam)1981, 108A, 546; l982,112A, 605. (22) Onsager, L. Ann. N.Y.Acad. Sci. 1949,51, 627. (23) Sato, T.; Teramoto, A. Mol. Cryst. Liq. Cryst. 1990, 178, 143. (24) Cotter, M. A. J. Chem. Phys. 1977, 66, 1098.
4030 Langmuir, Vol. 10,No. 11, 1994
Shikata and Pearson entanglement points, (re2)1/2, as follows:
‘
Le(d/2)2n
3L,d2 --
= (4n/3){(r,2)1/2/2]3 2(r,2)3’2
(5)
With eq 3 and the condition (re2)v2 = 2q,we obtain a critical volume fraction, &*,at which the chain portion between the entanglement points has the same length as the Kuhn length.
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d/(W Figure 4. Relationship between the phase transition volume fraction &* and the ratio of dl(2q) for systems with enough molecular weight to show molecular weight independent +*: ( 0 ) schizophillane/water,12(0) poly(y-benzyl L-glutamate)/ (a) polfin-hexyl isocyanate)/toluene,’l dimethylf~rmamide,’~ (A) poly(n-hexyl isocyanate)/dichloromethane,ll(El) (hydroxypropyl)cell~~lose/watr,~~ ).( (acetoxypropyl)cellulose/dibutylphthalate,15(E31p0lfil-phenyl-l-propyne)/toluene,2~ and (e)this
study. Solid,broken, dotted, and chain lines mean predictions of the KS model,21ST eq 7, and Onsager’s &*,22 respectively.
and poly(y-benzyl ~-glutamate)l~ systems; the data of the highest molecular weight samples are plotted for these two systems in this figure. This figure also contains data of the wormlike micellar system, and it is obvious that the micellar system has a relationship between dl(2q)and #* quite similar to that for semiflexible polymer systems. Solid and broken lines in this figure represent predictions of the KS modelz1and Sat0 and Teramoto’s (ST)modelz3 for the case of infinite molecular weight. It seems that the ST model could predict +* quite correctly not only for semiflexible polymer systems but also for our micellar system. However, the ST model could not predict #* = 1for ordinary flexible polymer systems: the d/(2q)value is 0.14 for a typically flexible poly(1-phenyl-1-propyne) which never shows the phase t r a n s i t i ~ n .It~ seems ~ that the ST model could not work well in the region of semiflexible to flexible chains (0.1 < d/(2q)< 0.15),and thermodynamical theories such as the KS and ST models fail in the region. The reason for this discrepancy would be that the KS and ST models take account of only the second virial coeffi~ient.~~ From these, there must be a new mechanism that controls the phase transition for the semiflexible to flexible chains. We propose that the phase transition concentration or volume fraction of the region is governed by a function of the ratio of d42q) and the condition of (re2)v2 = Le (= 2q or Zk). Crude Modeling for the Phase Transition in the Semiflexible to Flexible Chains with Infinite Molecular Weight. First of all, we assume an isotropic and unperturbed state of an entanglement network and introduce a hypothetical volume fraction &, of the semiflexible chain portion with a diameter d and contour length Le in a sphere with a radius equal to the distance between (25) Hirao, T.; Teramoto, A.; Sato,T.; Norisuye,T.; Masuda, T.PoZym.
J. 1991,23,925.
Here, we convert the hypothetical critical volume fraction, &,*, to the real critical volume fraction, &*, of the chain, which should be calculated from the entanglementspacing, 5, not from 5 is always smaller than (re2)v2and around the condition of (re2)y2 = 2q in about V3 of (re2)1/2 the case of the wormlike micellar system, so that the relation below could be obtained.
(7) A dotted line in Figure 4 shows the relation of eq 7. In an isotropic system consisting of chains with infinite molecular weight, translational motion of the chains along their contour is strongly depressed and essentially could be neglected; therefore, the portion of the chain between entanglement points could move only in a small restricted area with the entanglement spacing. At the concentration #* where the condition (re2)v2= 2q is satisfied, the effective motion of chain portions within the restricted area with the entanglement spacing 29 would be approximately regarded as free rotational motion of rigid rods with an equivalent length of 2q, because the average size of the chain portion between entanglement points would be the same as the Kuhn segment size and the chain portion would almost lose flexibility and behave like a rod at this condition; moreover, there would be no correlation among the orientational motion of the individual chain portions. At the condition (re2)uz= 2q, we assume applicability of the simplest Onsager’s theoretical modelz2of the phase transition in the chain system considered above with chain diameter d and the equivalent length 2q: the relationship between Onsager’s #* and d/(2q) is plotted in Figure 4 with a chain line. In a condition in which the ratio dl(2q) is larger than 0.08, &* is always larger than Onsager’s #*, so that the system at # = &* would satisfy the condition (re2)1/2 = 2q and also # greater than Onsager’s +* simultaneously and, therefore, would show the phase transition. However, when # is less than #r*, the portion between entanglement points has several Kuhn segments and does not behave like a rod within the entanglement spacing; therefore, even at Onsager’s &* the system does not show the phase transition. On the other hand, in a condition in which the ratio d/(2q)is smaller than 0.08, the phase transition would be observed neither at the concentration of &* nor at Onsager’s +*. At Onsager’s #* in the condition of d/(2q) 0.08, of course, the average spacing between entanglement points would be shorter than 2q, and the condition we argued above would not be satisfied. In this regime, obviously the KS or the ST model would be much more successful.
