J. Phys. Chem. 1986,90, 5746-5751
5746
Morphological Transformations of the Primary Surfactant Structures in Brine-Rich Mixtures of Ternary Systems (Surfactant/Alcohol/Brlne) G. Porte,* R. Gomati, 0. El Haitdmy, J. Appell, and J. Marignan Groupe de Dynamique des Phases Condens5es (CNRS-UA 233) and GRECO McroCmulsions, U.S.T.L., 34060 Montpellier Cedex, France (Received: July 23, 1985; In Final Form: April 25, 1986)
We investigate the brine-rich side (volume fraction of brine >0.8) of the phase diagram of a quasi-ternary system: Cetylpyridinium chloride/hexanol/brine (0.2 M NaCI). The three classical phases LI, lamellar, and L2 appear on this side of the diagram. Their respective stabilities are mainly determined by the alcohol-to-surfactant ratio in the solution and only slightly depend on the dilution. We try to understand the phase behavior in terms of morphological transformations of the elementary objects (micelles, bilayers) induced by the variations of the alcohol/surfactant ratio. The analysis is based on the idea that adding alcohol induces a monotonic variation of the spontaneous curvature of the surfactant film. The simple model proposed by McMullen et al. (McMuIlen, E. W., Ben-Shaul, A.; Gelbart, W. M. J. Colloid Interface Sci. 1984, 98, 523) is used in order to investigate the morphology sequence which arises from this simple analysis: spheres, small disks, long capped cylinders, branched cylinders, bilayers perforated by a large density of pores, smooth bilayers, loose network of connected bilayers (foamlike structure). This shape sequence agrees (at least qualitatively) with the phase behavior of the system. And also, the model is able to reproduce adequately several otherwise reported phenomena, which are the second cmc at the “sphere to rod” transition in binary mixtures, the LI/LI phase separation in dilute binary mixtures of ionic surfactants, and the formation of lamellar phases perforated by “structural defects”.
Introduction When dealing with surfactants in solutions, one may meet two ideally opposite situations. The f m t one is the case of concentrated microemulsions where there is much water, much oil, and a moderate amount of the surfactant mixture (surfactant alcohol). In such a situation the hydrophilic and hydrophobic media play a symmetrical role and are not submitted to local constraints except the density constraints. They are separated by the surfactant film which has its own mechanical propertiessponta,neouscurvature and elastic resistance to extra bending-and which incorporates most of the surfactant and alcohol m o l e c ~ l e s . ~ -Closely ~ related to this quite loose set of constraints, the details of the morphology (curvature of the film) of the mixture a t a local scale fluctuate strongly. The contribution of the entropy of the folded film is predominant in the free energy of the solution, while the morphology has little incidence. According to these general features, concentrated microemulsions are often pictured (for calculation purposes) as an array of microscopic cells with an arbitrary - ~ an convenient shape filled a t random with oil or ~ a t e r . ~Such approach indeed forgets about the morphology (arbitrary shape of the cells) and provides, in principle, an appropriate estimation of the important entropic contribution. The situation is very different with systems with no oil, that is, binary systems (surfactant/(salted) water) or ternary systems (surfactant/alcohol/(salted) water). In such cases, the hydrophilic and hydrophobic media are no more in symmetrical positions. In particular, the hydrophobic medium is submitted to a strict geometrical constraint: its local thickness must not exceed twice the length (I-) of the all trans paraffinic chain of the surfactant molecule.6 This is a local constraint, and it must be fulfilled everywhere in the solution. Large micellar objects of finite size (with one dimension at least >> I,) exhibit different curvatures according to which part of the object is concerned (ends effects as discussed in ref 6 ) . These curvature heterogeneities are not induced by transient, thermally induced, fluctuations but are steadily prescribed by the geometrical constraint: they define the actual shape of the micellar object. Associated with each particular shape, standard contributions to the free energy of the solution will arise? An examination of the phase diagram of many ternary systems’ indicates that, often, these standard contributions heavily dominate the contribution of the entropy of mixing to determine the stability of the different phases. We are thus driven to a situation opposite to the situation of concentrated microemulsions: the morphology of the elementary
+
*To whom correspondence should be addressed.
object is essential, while the contribution of the entropy of mixing is, in a first approximation, almost inconsequential. The aim of the present study is to investigate a situation of the second type. The experimental work is performed with a quasi-ternary system: cetylpyridinium chloride (CPCl) hexanol brine (0.2 M NaCl salted water). We focus our attention on the brine-rich side of the diagram (C$w> 0.8, where C$w is the volume fraction of the brine). The geometry of the diagram indicates that, in this range, the morphology of the objects is essentially determined by intramicellar features and hardly affected by the interactions between objects. This renders the analysis easier indeed. One of the expected consequences of using brine rather than pure water is actually to screen the long-range electrostatic repulsions. In the first section, the general physical properties of the three lamellar, L2) that appear in the brine-rich side of the phases (L1, phase diagram of this system are briefly described. The radial geometry of the diagram can be understood straightforwardly, and the phase behavior is interpreted in terms of morphological transformation of the primary surfactant structures. In section 11, we then use a very crude simple model’ which takes into account the tunable optimum local curvature and also the essential geometrical constraint. It is actually able to simulate a rich polymorphism for the elementary objects, and the morphology diagram calculated on the basis of this model agrees (qualitatively) with the general phase pattern of the present system. This morphological approach has some special consequences which interestingly parallel experimental observations reported in the current litterature. These points are discussed in the last section.
+
+
I. Experimental Section a. Materials. CPCl is obtained from Fluka (purum grade) and further purified by two recrystallizations in water and one in wet acetone (2 g of water in 100 cm3 of acetone). Hexanol is also obtained from Fluka (puriss. grade; >99% controlled by gas chromatography) and used with no further purification. NaCl (1) McMuUen, E.W.; Ben-Shad, A.; Gelbart, W. M. J. Colloid Interface Sci. 1984, 98, 523. (2) De Gennes, P. G.; Taupin, C. J . Phys. Chem. 1982, 86, 2294. (3) Talmon,Y.;Prager, S.J . Chem. Phys. 1978, 69, 2984. (4) Jouffroy, J.; Levinson, P.; De Gennes, P. G. J. Phys. 1982,43, 1241. (5) Widom, B. J. Chem. Phys. 1984, 81, 1030. (6) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. J . Chem. SOC., Faraday Trans. 2 1976. 72. 1525. (7) Ekwall, P. In Advances in Liquid Crystals; Brown, G., Ed.; Academic: New York, 1971; Vol. 1, p 1.
0022-3654/86/2090-5746$01.50/00 1986 American Chemical Society
The Journal of Physical Chemistry, Vol. 90, No. 22, 1986 5747
Surfactant Structures in Brine-Rich Mixtures
a
20,
1.5-
10
H,O t Na
CI
0.1
c PCI
I
0
Figure 1. Brine-rich side (+w > 0.8) of the phase diagram of the system cetylpyridinium chloride/hexanol/brine (0.2 M NaCl).
is obtained from Merck (pro analysis grade; >99.5%), and water is doubly distilled prior to the preparation of the brine (0.2 M NaC1). The samples are then prepared by weight, heated, stirred, and sonicated first at 70 OC and then at 30 OC. Some biphasic samples (especially lamellar/Ll) separate very slowly, and 2 weeks of equilibration is necessary for an accurate determination of the phase boundaries at 30 OC. The phase behavior is determined by direct optical observation and by polarized light observation. Some apparently monophasic samples are opalescent; phase contrast microscopy is used in order to differentiate them from eventual multiphasic stable emulsions. b. General Phase Behavior. In what follows, we use the notations c$S, 4A,and 4w to represent the volume fractions of respectively the surfactant, the alcohol, and the brine. The obtained phase diagram for the water-rich side is given in Figure 1. The general pattern of this diagram is analogous to that found for other systems by Benton and Miller.* Three different monophasic domains are observed. The classical L1 isotropic micellar phase occurs at low alcohol-to-surfactant ratio (dA/dS). For the binary system (c$~/& = 0), we know from previous experimentalstudies that the micelles are small and globular in shape up to $s = 0.1 at least.9 When alcohol is added, the apparent viscosity (Figure 2a)of the L1 phase increases very steeply as does also the apparent turbidity of the mixture, indicating that the size and shape of the micelles undergo very strong transformations. The variations of the apparent hydrodynamic radius RH of the micelles as measured by means of quasi-elastic light scattering confirm this size evolution (Figure 2b). As these variations are smooth although very large, we conclude that the addition of alcohol induces the progressive shape transformation from small globules to very long cylinders (as discussed at length in ref 6, 10, and 1 1.) A more complete set of experimental results and detailed discussion of this point will be given in a forthcoming paper. For higher values of the alcohol-to-surfactant ratio, an optically birefringent phase is stable. It is separated from the L1 phase on the diagram by a well-defined biphasic region. The birefringent phase extends very far toward high concentrations of active matter (up to 0.51 at least) for similar values of +A/&. At high concentration, it can be unambiguously characterized by X-ray scattering; this is a classical lamellar phase (Figure 3a). It is (8) Benton, W. J., Miller, C. A. J . Phys. Chem. 1983, 87, 4981. (9) Porte, G.; Poggi, Y.; Appell, J.; Maret, G.J . Phys. Chem. 198488,
5716. (10) Missel, P. J.; Mazer, N. A.; Benedek, G. B.; Young, C. Y.; Carey, M. C. J. Phys. Chem. 1980,84, 1044. (11) Porte, G. J . Phys. Chem. 1983, 87, 3541.
0
I
I
0.5
1
I 1.5
J
L
,
1.75 1.90 ___c
% hex.
0
I
I
I
I
0
0.1
0.2
0.3
-
% hex.
Figure 2. (a) Viscosity of a solution with 50 mg/cm3 CPCl in brine as a function of the amount of added hexanol (L,phase). (b) Apparent hydrodynamic radius (RH)of the micelles in a solution with 2.5 mg/cm3 CPCl in brine as a function of the amount of added hexanol (L,phase).
possible to follow the evolution of the Bragg peak spacing sB as a function of 4w at constant 4 A / & ratio up to about & = 0.88. The plot of sB vs. 4w is linear and extrapolates to SB = 0 for +W = 1 (Figure 3b). This behavior is typical of a lamellar phase that swells with constant hydrophobic lamellae thickness, that is, constant expanding lamellar phase according to the terminology
574% The Journal of Physical Chemistry, Vol. 90, No. 22, 1986
Porte et al. junction line
b
Figure 4. Foamlike plausible structure for the isotropic L2*phase.
0
05
1
%v
Figure 3. (a) X-ray scattering pattern of a concentrated sample of the
lamellar phase. with the weight composition 0.34 CPC1/0.17 hexanol/0.49 brine. The pattern is typical of a regular lamellar phase. (b) Evolution of the Bragg peak spacing sB as function of the dilution. It reveals a simple swelling behavior. The constant thickness of the lamellae is 24
A.
of Ekwall et al.Iz For higher dilutions (+w > 0.88),the main Bragg peak melts into the broadening central scattering and cannot be accurately identified with our standard X-ray diffraction apparatus. Nevertheless, there is no apparent phase separation up to &.= 0.98 at least, and the phase remains definitely birefringent at rest even a t very high dilution. We therefore admit by continuity that the phase still consists of infinite lamellae with long-range orientational order for the proper value of +A/+S at high +w. At still higher +A/+S there is a very thin monophasic region; this phase is well separated from the lamellar phase by a very thin but clearly defined biphasic region. It is isotropic at rest but exhibits strong transient streaming birefringence upon gently stirring, especially at high dilution. It scatters light more and more as +w increases. This thin monophasic domain is continuously connected to the large domain of stability of the Lz phase which classically spreads toward the alcohol corner of the diagram. For (12) Ekwall, P.; Mandell, L.; Fontell, K. Acta Chem. Scand. 1968, 22,
1543.
this reason, we have noted as L2* the streaming birefringent phase in Figure 1. At still higher 4 A / + ~no , homogeneous phase is stable in the dilute regime. We enter into multiphasic domains, first L,/L2*, then L,/L2*/Lz, and last L1/L2. c. Qualitative Analysis. To a good approximation, the phases boundaries in Figure 1 are straight lines converging to the brine corner of the diagram. This situation is especially convenient. It implies that the stability of the phases and hence the general shape of the micellar primary structures are determined by one composition variable (+A/+S) only and hardly depend on the dilution (&). Or, as above stated, the +w-independent (+A/ +s-dependent) standard terms in the free energy of the mixture largely dominate the +w-dependent contribution of the entropy of mixing in determining the general shape of the objects. We can thus define at each point P of the diagram (Figure 1) two orthogonal directions D and p. D corresponds to dilution at constant morphology (+w varies at constant +A/+s), and p corresponds to morphological transformations at constant net concentration of active matter (+*/& varies at constant 4w). Very generally, lower curvature (Le., a smaller ratio of the head-group area to the volume of the lipophilic tails) structures are stabilized by added cosurfactant. Actually, convincing experimental evidence has been obtained in the case of concentrated m e s o p h a ~ e s l ~in- 'ternary ~ systems that, among others, one role of the added cosurfactant is to reduce the preferred curvature of the surfactant p a ~ k i n g . ' ~ JQualitatively, ~ this also applies adequately in our diluted mixtures at least in the L1 and lamellar cylinder lamella). phases (globule By continuity, we thus expect the structure of the Lz* phase to be such that, on the average at least, the local curvature of the interface is negative (directed toward the brine rather than toward the aliphatic medium). In the absence of solid structural data (which anyway will be very difficult to obtain owing to the degree of dilution of L2* and to its disordered character), we can imagine at least two possible structures for Lz*.The first one is the random foamlike structure schematized in Figure 4: most active matter stands in portions of bilayers (site A in Figure 4) where the local curvature is zero. The pieces of bilayers are connected to each other by a line of junctions (site B in Figure 4) where the local curvature is strongly negative. This structure exhibits a true L2 topological character (disconnected brine domains separated by a continuous aliphatic medium). It thus differs from the bicon-
- -
(1 3) Hendrilor, Y.; Charvolin, J.; Raviso, M. J. Colloid Interface Sci. 1984, 100, 591.
(14) Alperine, S.;Hendrikx, Y.;Charvolin, J. J. Phys., Lett. 1985,46, L27. (15) Gelbart, W. M.; McMullen, W. E.; Masters, A.; Ben-Shaul, A. Langmuir 1985, 1, 101. (16) Mather, D. E. J. Colloid Interface Sci. 1976, 57, 240.
The Journal of Physical Chemistry, Vol. 90, No. 22, 1986 5749
Surfactant Structures in Brine-Rich Mixtures
m bilayered body
I
locally
bi layered
lo 1
cap
cylindrical body
Figure 5. Specifications of the model: (a) spherical micelle; (b) cylindrical micelle; (c) discoidal micelle, general sketch and cut view.
tinuous structure generally proposed for middle-phase microemulsions. An alternative structure would be obtained starting with a plane bilayer and imposing everywhere on the bilayer a constant saddle splay deformation. One so obtains a surface that regularly fills the space. As analyzed in ref 17, the local curvature is everywhere negative a t both surfaces of the deformed bilayer (although it is indeed zero in between). Both structures are expected to shrink spontaneously and to expel excess brine upon further addition of alcohol, and this accounts properly for the very thin domain of existence of L2* in Figure 1. 11. The Model To have some consistency with the experimental situation, the model should involve the two essential ingredients: (1) one control parameter related to the experimentally tunable optimum curvature of the surfactant film and (2) the geometric constraint of maximum thickness ( 1 < /,,,ax). The model proposed by McMullen, Ben-Shaul, and Gelbart' for similar purposes meets these requirements. We use here a simplified version of this model. The local curvature is represented by the local area over volume ratio ( / A / V ) , 6where I is the local thickness of the surfactantalcohol film, A is the local area occupied by the polar heads, and Vis the corresponding volume of the hydrophobic core. The local standard free energy Ago is set
is the standard free energy of an elementary portion Au of the object where the local (IA/V) is equal to its optimum value (IA/ W0. The second term is the excess energy due to the deviations from this optimum value. Since is shapeindependent, it is inconsequential for the morphological problem. We forget about it in what follows. The coefficient k , which is here phenomenologically introduced, represents the tendency of the local ( l A / V ) to restore back to its optimum value ( l A / f i 0 . It is reminiscent of the interfacial tension y in McMullen et a1.k model. We do not try to estimate its magnitude and guess that it depends on the system under consideration. The suitability of expression 1 in the case of ternary systems is discussed in the Appendix. Following again McMullen et al.,' we introduce the geometrical constraint by setting I everywhere constant and independent of 4A/4S.This is indeed a drastic simplification compared to what most probably occurs in reality. Having set the two local ingredients of the model, we should derive the stable shapes using variational procedures. The intrinsic difficulty here is that the mathematical solutions will often involve nonanalytical curvature distributions. The standard procedure to skirt around the difficulty is much less systematic: it is to specify a priori the largest set of shapes that are plausible candidates and then select which of these involve the lower free energy for the mixture as a function of the control parameter. The following set of shapes has been considered: sphere (Figure 5a); finite cylinder with hemispherical caps (Figure 5b); flat disks T O ( ~ ~ / ~ ~ ) A U
(17) Charvolin, J. J . Phys. (Lees Ulis, Fr.) 1985, 46, C3-173
Figure 6. Specificationsof the model: branched cylinders.
locally bilayered
N
locally hemitoro'idal hole
Figure 7. Specificationsof the model: perforated lamella (a) cut view of one hole and (b) hexagond arrangement of the holes (overview).
with a hemitoroidal rim (Figure 5c); infinite flat ribbon with hemicylindrical edges, infinite cluster of branched cylinders (Figure 6 ) ; infinite bilayers perforated by a dense array of circular holes (Figure 7); infinite smooth bilayer, spherical vesicle, infinite microtubule. As discussed in ref 11, we a priori discard the cylindrical closed rings which are unstable due to unfavorable configurational entropy. The summing operation of Ago in order to calculate go (size, shape) is straightforward. In the following expressions, we have introduced x and y. x is a measure of the size of the objects; it is the ratio of the volume of the hydrophobic core of the object over that of the minimum size sphere (uo = 4 / 3 d 3 ) . y is McMullen et al.'s parameter:
0,> -1)
(2)
g,'(sphere) = '/2kuo(y- 2)2
(3)
y = ( l A / q 0- 1 We get
gxo(cylinder) = '/,ku0[x(y- 1)2
+ (3 - 2y)l
+
(4)
+
gxo(disk) = 1/2kuo[xy2 1.85(1.081x - 0.081)1/2(1- 2y) (1.15 - 0 . 3 ~ + ) 1/[1.85(1.081~- 0.081)'/2 - 0.8511 (5) gxo(vesicle) = '/&u0[ xy2
+ 2(3 - 4y) + small terms
(91
(6)
lim gxD(microtube)/x = '/kuo(y2 + F ( R ) )
x-c-
(7)
where F(R) is a strictly positive function of the microtube's radius R and does not depend on the control parameter y. lim gxo(smooth bilayer)/x = '/2kvg2
(8)
p-
and lim gX0(perf.bilayer, x3 = F-
'/*
+
kuo[x'y2 + 17(1.12 0 . 1 2 ~ ' ) ' / ~ (-1 2 y) - (20 3 8 ~+ ) 1/[-18 + 17(1.12 + 0.12x')'/2]] (9)
5750 The Journal of Physical Chemistry, Vol. 90, No. 22, 1986
Porte et al.
benzenesulfonate/pentanol/water. And this system apparently provides a typical example of a situation with small k . SPH~RES
SMALL D I S K S
(A’
LONG C Y L I N D E R S
\ = 0’75 1
BRANCHED
CYLINDERS
B I L A Y E R S PERFORATED B Y SMALL H O L E S
-
- - ....- - - ..-
..... ..
SMOOTH B I L A Y E R S
yx
-0.25
RULT I PHAS I c
DOMA I N
Figure 8. Morphology diagram in the limiting case of very large k . (A) Size of the largest disk here corresponds to a ratio of diameter to thickness (21)of 1.4. (B) Equilibrium size of the holes corresponds to the minimum possible radius r (Figure 7). This minimum radius is here
arbitrarily set to 0.51. where, here, x’is the volume of the elementary cell (surrounded by the thick line in Figure 6) in units of the volume uo (x’is thus a measure of the size of the holes). The go for the cluster of branched cylinders is omitted since it involves uninteresting heavy notations. It can be derived straightforwardly from (4)and (9) when we consider Figure 6 , where the structure of a pair of junction points is identical with the piece of perforated lamella drawn in Figure 7. Also the go of the flat ribbon is trivially derived from (4) and (8). In the general case, deriving the actual size and shape distribution in the mixture is a tremendous work owing to the contribution of the entropy of mixinge6 Two limiting cases can, however, be straightforwardly analyzed. a. Case for Very Large k. This corresponds to phase diagrams with a radial structure like ours. The standard terms dominate. The effects of the entropy of mixing can be forgotten in a first approximation, and the stable morphology is that for which go(shape)/x is minimum. Comparing the go(shape) as a function of y provides the artificial morphology diagram given in Figure 8. The general phase behavior is indeed reproduced. On the other hand, it here appears associated to an unexpectedly rich polymorphism. b. Case for Very Small k . The opposite case is even simpler to analyze. For all values of y , the influence of the standard terms is dominated by the term of the entropy of dilution. Only objects of small size are allowed. The series of morphological transformations is drastically simplified: spheres for y > 2 and small disks for y < 2. As a consequence, LIshould be the only stable phase in the dilute regime. These features actually meet nicely the experimental results (phase diagram and X-ray determination of shapes)’*J9 obtained in the dilute regime (#w > 0.8) for the system sodium octyl(18) Larche, F. C.; Dussossoy, J. L.;Marignan, J.; Rouviere, J. J . Colloid InterfaceSci. 1983, 94. Marignan, J.; Delichere, A.; Larche, F. C. J . Phys., Lett. 1983, 44, L-609. (19) Marignan, J.; Bassereau, P.; Delord, P. J . Phys. Chem. 1986, 90, 645.
111. Applications to Other Situations It is well-known that micellar polymorphism also occurs in dilute systems without alcohol (in particular the sphere-to-rod transition in binary or quasibinary If the model has some physical pertinency, it should also apply to such situations. In this section, we briefly discuss some points where the morphology diagram in Figure 8 can be tested against the observations of the current literature dealing with micellar polymorphism in binary and ternary systems. a. “2nd cmc” at the “Sphere-to-Rod Transition”. Generally, when the elongation of initially small micelles in binary mixture is induced by increasing the surfactant c o n c e n t r a t i ~ n , ~it* ~takes *~~ place only once a particular concentration (the second cmc) is passed. As analyzed in ref 9, the unexpected existence of a particular concentration involved in the elongation process can be understood by assuming that the small micelles which are stable at low concentration (4s < 2nd cmc) are not spherical but disklike with a moderate axis ratio (as suggested by the magnetic birefringence results). The domain of existence of small disklike micelles (1.4 < y < 2) between spheres and long cylinders in Figure 8 reproduces adequately this feature. We have checked that working out the model in the conditions investigated in ref 9 actually provides a well-defined second cmc at the globule to rod transition. b. L , / L , Phase Separation. L, over L1 phase separations with critical behavior at particular temperature, and concentration have been observed in ionic surfactant/brine mixture^^^-^^ where the micelles are khown to be long flexible rods. The question arises about what “attractive forces” are large enough to overcome the electrostatic repulsion between like-charged micelles and to determine the phase separation. In the frame of the present model, we expect that for low enough y 0, 0.75) mutual branching of the flexible micelles takes place. The density of “junction points” in the obtained infinite cluster of branched cylinders depends very sensitively on y : upon further decrease of y , the cluster will spontaneously shrink and expel excess brine, a process which could induce the Ll/LI phase separation. The model thus suggests a purely morphological interpretation for the phase separation in the case of ionic surfactant quasibinary solutions. c. Lamellae wirh Holes. In ref 26 and 27, the special physical properties (conductivity) and the X-ray scattering patterns of the lamellar phase of the system decylammonium chloride/ NH4Cl/H20 have been investigated. They were interpreted in terms of structural defects in the lamellae allowing the passage of the brine across the hydrophobic layers. The holes in the lamellae which are here found stable in the range 0.34 < y < 0.75 could be evidence of such structural defects. d . Absence of Ribbons and Biaxial Micelles. These are particular points where the model meets the experimental observations. On the other hand, flat infinite ribbons and consequently anisometric biaxial micelles (finite ribbons) are found unstable for all values of y in the frame of the present approach. This expectation is contradicted by the experimental evidence of such shapes in well-ordered concentrated ternary mixtures (re(20) Corkill, J. M.; Herrmann, K. W. J . Chem. Phys. 1963, 67, 934. (21) Reiss-Husson, F.;Luzatti, V . J . Phys. Chem. 1964, 88, 3904. (22) Hoffmann, H.; Platz, G.; Rehage, H.; Schorr, W.; Ulbrich, W. Ber. Bunsenges. Phys. Chem. 1981,85, 255. (23) Blankschtein, D.; Thurston, G. M.; Benedeck, G. B. Phys. Reu. Lett. 1985, 54, 955. (24) Dorshow, R. B.;Nicoli, D. F., presented at the 5th International Symposium on Surfactants in Solutions, Bordeaux, July 9-13, 1984. (25) Appell, J.; Porte, G. J. Phys., Lett. 1983,44, L-689.Porte, G.;Appell, J. In International School of Physics “Em’coFermi“;Physics of Amphiphiles: Micelles, Vesicles and Microemulsions; Degiorgio, V . , Corti, M., Eds.; North-Holland: Amsterdam, 1985;p 461. (26) Radley, K.;Saupe, A. Mol. Crysr. Liq. Crysr. 1978, 44, 227. Haven, T.;Armitage, D.; Saupe, A. J . Chem. Phys. 1981, 75, 352. (27) Holmes, M. C.;Charvolin, J. J . Phys. Chem. 1984, 88, 810.
Surfactant Structures in Brine-Rich Mixtures spectively rectangular and nematic phases of the system SdS/ d e c a n ~ l / w a t e r ~ ~ *This ’ ~ ) .failure of the model underlines its overly crude character. Note, however, that the model involves intramicellar requirements only, while intermicellar interactions are also probably determinant for the morphology in concentrated and well-ordered solutions.
Conclusion In this paper, we tried to understand the phase behavior of diluted solutions of ternary systems in terms of morphological transformations of the elementary objects. The analysis is based on the assumption that the spontaneous curvature of the surfactant film is the leading parameter, just as it has been done in ref 28 for the case of microemulsions. A model, which involves the optimum curvature as the only control parameter and which accounts for the essential geometric constraint, was used in order to investigate the consecutive morphology sequence. The morphologies expected to take place successively when the amount of alcohol is increased are the following: spheres, small disks, long flexible cylinders, branched cylinders, lamellae perforated with a dense array of holes, lamellae perforated with a looser and looser array of holes, smooth lamellae, and finally the L2 disordered structure schematized in Figure 4. The complexity of the polymorphism apparently contrasts with the extreme simplicity of the model. Although oversimplified, it accounts for one essential fact: in systems with no oil, the geometrical constraint and the criterion of minimum local free energy conflict with each other. The obtained morphology is the result of a compromise. The interesting feature of this model is that it indicates that the complex polymorphism probably originates from this situation of compromise rather than from the more or less sophisticated and realistic expression chosen for the local standard free energy. The model involves the phenomenological coefficient k which measures the tendency of the system to restore the local curvature back to its optimum value. Examination of the phase diagrams of two systems (CPCl/hexanol/brine and OBS/pentanol/ water18J9)suggests that the phase diagrams could be interestingly classified according to their relative situation compared to the two limiting cases, large k and small k. However, although such a comparison suggests large differences from one system to another, we presently do not know what mechanisms, at the molecular level, determine a larger or smaller magnitude for k. As it is described in section 11, the model has some artificialities. In particular the surfactant-alcohol film is specified as having a constant thickness independent of the local composition and curvature, a picture which is certainly overly crude. The quadratic expression 1 for the excess local standard free energy due to deviations from the optimum (lA/V)?,is certainly very much arbitrary when large deviations are involved. As a matter of fact, (28) Safran, S. A.; Turkevich, L. A. Phys. Rev. Lett. 1983, 50, 1930. Safran, S.A.; Turkevich, L. A,; Pincus, P. A. J . Phys., Lett. 1984, 45, L-69. Safran, S.A. In Statisiical Thermodynamics of Micelles and Microemulsions; Chen, S. H., Ed.; Springer-Verlag: Berlin, in press.
The Journal of Physical Chemistry, Vol. 90, No. 22, 1986 5751 these simplifications are probably not inconsequential; they might alter the guesses derived from the model to an uncontrollable extent. More serious even are the limitations due to the impossibility to predict, in an unequivocal way, the expected morphology by means of classical variational procedures. The obtained morphology sequence closely depends on how large and complete is the a priori stated series of candidate shapes. We certainly cannot conclude that all the morphologies, which are consistent with the specifications of the model, belong to the diagram of Figure 8. In that sense, the approach is not predictive but only helps to make reasonable guesses. Despite the model’s limitations and artificialities, its direct consequences actually meet several experimentally evidenced phenomena previously reported and discussed, and the agreement is encouraging.
Acknowledgment. This research has received partial financial support from PIRSEM (CNRS) under AIP 2004.
Appendix Expression 1 for the local standard free energy is well suited to the case of binary systems. Since the object consists of surfactant molecules only, there is no coupling between the local curvature and the local composition. It may seem inappropriate in the case of ternary systems. The objects consist of an assembly of surfactant molecules and of alcohol molecules. In this situation, the inhomogeneous distribution of the alcohol in a given object may relax the excess free energy due to the inhomogeneous curvature. However, the observed existence of very large objects in the dilute regime (long cylinders in L,, infinite lamellae in the lamellar phase), while the entropy of mixing would prefer small globules, clearly indicates that this relaxation is far from being complete. The effect of alcohol partitioning in micelles with inhomogeneous curvature has been considered in ref 15. The treatment in ref 15 is based on the assumption that the globalexperimentally bed-value of I$*/& is respected at the individual micelle level, Le., that every aggregate has the same alcohol-tesoap ratio independent of its size and shape. This simplification is not inconsequential; it implies paradoxically that, at given T, 4A,and salinity, the local value of I$*/I$s in both the cylindrical body and the end caps strongly depends on the size of cylindrical micelles. The basic assumption which underlies expression 1 is different. We here suppose that, at given temperature and salinity, the local composition of a given part of a micellar object is determined unequivocally by the chemical potential of the alcohol in the mixture (a field variable) and by the local area-to-volume ratio. But it does not depend on semilocal features such as the size of the micelle. Since Ago in (1) involves explicitly the local feature ( l A / V )and also implicitly the chemical potential of the alcohol via (lA/V),,, there is no basic objection to its application to a three-component situation. Registry NO. NaCI, 7647-14-5; cetylpyridinium chloride, 123-03-5; hexanol, 1 1 1-27-3.
