Brine-Rich Corner of the Phase Diagram of the Ternary System

Institute of Physical Optics, Ministry of Education of Ukraine, 23, vul. ... L1−liquid crystal lamellar Lα−isotropic sponge L3−multiphasic stat...
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Langmuir 1996, 12, 5011-5015

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Brine-Rich Corner of the Phase Diagram of the Ternary System Cetylpyridinium Chloride-Hexanol-Brine Yu. A. Nastishin* Institute of Physical Optics, Ministry of Education of Ukraine, 23, vul. Dragomanova, Lviv, 290005, Ukraine, Laboratoire de Physique des Solides, Bat. no. 510, Universite´ Paris-Sud, 91405 Orsay Cedex, France, and Universites Paris VI et Paris VII, Laboratoire de Mineralogie et Cristallography, tour 16-4, place Jussieu, 75252 Paris Cedex 05, France Received January 2, 1996. In Final Form: June 7, 1996X The brine-rich side (mass fraction of brine is 0.75 < Φ < 0.98) of the phase diagram of the ternary system cetylpyridinium chloride-hexanol-brine (1% NaCl by weight) is studied. The hexanol-to-surfactant ratios η at which the isotropic micellar L1-liquid crystal lamellar LR-isotropic sponge L3-multiphasic state phase transitions occur on the η versus (1 - Φ) orthogonal phase diagram vary like a hyperbola with dilution. The solubility of hexanol in brine is found to be responsible for the variation of η values with dilution. An expression which well describes the experimental phase boundaries is found taking into account the hexanol solubility in brine. The hexanol mass fraction β in brine outside the surfactant aggregates is deduced from the experimental phase boundaries. The β value is somewhat lower than the hexanol solubility in brine. The hexanol-to-surfactant ratio η0 which describes the bilayer composition is found to be constant with dilution at the LR-L3 phase transition but varies at the L1-LR phase transition. The presence of hexanol molecules in brine as well as in the surfactant aggregates implies that the surfactant aggregate has to be considered as an open system. We predict that the composition of the bilayer can be changed upon external influence.

1. Introduction The ternary system cetylpyridinium chloride (CPCl)hexanol-brine displays a large variety of physical phenomena upon varying the composition of the mixture and temperature.1-3 Three classical phases: an isotropic micellar phase L1, a birefringent lamellar liquid crystal LR, and an optically isotropic phase which scatters light and exhibits streaming birefringence, the so-called sponge phase L3, appear on the brine-rich side of the phase diagram.1,2 The studied system contains four components: a solvent (water), the salt (NaCl), surfactant (CPCl), and cosurfactant (hexanol). The phase diagram of this system should have four corners. Assuming that brine is a single component the authors of refs 1 and 2 present the phase diagram of this system with three corners: brine, CPCl, and hexanol. The phase boundaries in this diagram approximately look like straight lines converging to the brine corner. Such a peculiarity of the phase diagram as was mentioned in ref 2 implies that the stability of the phases and hence the general shape of the micellar primary structures are determined by the hexanol-to-surfactant ratio (η ) h/c) in the solution only and hardly depend on the mass fraction of the solvent (Φ). One can thus define at each point of the diagram two orthogonal directions Φ and η. For such a reason the concentration phase diagram is often presented in the η-Φ coordinates. The phase boundaries in the η(Φ) orthogonal coordinate system in accordance with ref 2 should be straight lines parallel to the Φ-axes. Our careful study of the phase diagram shows that in the vicinity of the brine corner the phase boundaries are not straight lines and that far away from the brine corner they are essentially tilted to the Φ-axes (Figure 1). The result of the experiment shows the necessity of a careful revision of the assumptions which were used above. * Address for correspondence: Institute of Physical Optics, 23, vul. Dragomanova, Lviv, 290005, Ukraine. X Abstract published in Advance ACS Abstracts, August 1, 1996. (1) Gomati, R.; Appel, J.; Bassereau, P.; Marignan, J.; Porte, G. J. Phys. Chem. 1987, 91, 6203-6210. (2) Porte, G.; Gomati, R.; Haitamy, O. El.; Appel, J.; Marignan, J. J. Phys. Chem. 1986, 90, 5746-5751. (3) Nastishin, Yu.; Lambert, E.; Boltenhagen, Ph. C. R. Acad. Sci. Paris, Ser. IIb 1995, 321, 205-210.

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Figure 1. Concentration phase diagram of the system cetylpyridinium chloride-hexanol-brine at room temperature.

The most important assumption which was implied but not mentioned is the absence of hexanol molecules in brine outside the surfactant aggregates. However it is known4 that hexanol is slightly soluble in water. The critical concentration of the solubility of hexanol in water is βw ) 0.59% by weight.4 There is no evident interdiction for hexanol molecules to be present in brine outside surfactant aggregates as well as inside them. Hence the actual ratio η0 which describes the surfactants’ aggregate composition is lower than the total ratio η which describes the system and which is measured in the experiment. Here and below, the index 0 corresponds to the surfactant aggregates. Therefore the parameter η in Figure 1 describes the whole system but not the surfactant aggregates. An expression which describes well the experimental phase boundaries is found in the present paper, taking into account the hexanol solubility in brine. 2. Experiment CPCl and hexanol were obtained from Sigma and used with no further purification. NaCl was obtained from Aldrich, and (4) Handbook of Chemistry and Physics, 39th ed.; Chemical Rubber Publishing Co.: Cleveland, OH, 1957-1958; p 977.

© 1996 American Chemical Society

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Figure 2. Fitting (dashed lines) of the experimental phase boundaries (solid lines) by expression 2, using eqs 7 and 8. LR-L3 boundaries: (a) R ) 0, β ) 0.0035, η0 ) 1.05 for the lower boundary and β ) 0.0034, η0 ) 1.07 for the upper one. L1-LR boundaries: (b) R ) 0, β ) 0.0033, η0 ) 0.37 for the lower boundary, and β ) 0.0029, η0 ) 0.49 for the upper one; (c) R ) 0.239, η0* ) 0.16, Ω ) 130 for the lower boundary and R ) 0.130, η0* ) 0.38, Ω ) 194 for the upper one. (d) L3-multiphasic state phase boundary: R ) -0.205, η0* ) 1.30, Ω ) 302. water was distilled prior to the preparation of brine (φ ) 1% NaCl by weight). Samples were introduced in hermetic test tubes, weighted, heated, and then twice stirred and centrifuged. The phase behavior is determined by direct polarized light observation and by polarizing microscopy. The obtained phase diagram for the brine-rich side (75% < Φ < 98%) at room temperature is given in Figure 1. The phase diagram is presented in the η(1 Φ) orthogonal coordinate system. The L1 isotropic micellar phase occurs at low hexanol-to-surfactant η ratios. For higher values of η , the birefringent LR phase is stable. The LR phase is separated from the L1 phase in the diagram by a well-defined biphasic region. At still higher η the L3 phase exists in a thin region. The L3 phase is well separated from the LR phase by a thin biphasic region. The phase boundaries L1-LR-L3-multiphasic state in the η(1 - Φ) orthogonal coordinate system look like hyperbolas (Figures 1 and 2). In the vicinity of the brine corner the phase boundaries are not straight lines, and far away from the brine corner they are essentially tilted to the (1 - Φ)-axes.

3. Expression for the Description of the Phase Boundaries It is well established now that the addition of hexanol induces transformations of the surfactant aggregates with a change of the Gaussian curvature of the surfactant aggregate surfaces from a positive one in L1 across a zero in LR to a negative value in the L3 phase, respectively.2 Very little is known on the microscopic scales. However the role of hexanol in the surfactant aggregate transformations implies that hexanol molecules are inside the surfactant aggregates. As was mentioned above hexanol is slightly soluble in water. We have measured the critical mass ratio βb ) mhb/mb of the solubility of hexanol in brine,

i.e. the hexanol-to-brine mass ratio in the system brine + hexanol at which two single domains (a water solution of hexanol and a hexanol solution of water) appear rather than one. Here mhb is the hexanol mass in brine of mass mb. It was found that βb ) 0.0039. Let us take into account the fact that some mass mhb of hexanol is in the brine outside the surfactant aggregates. If the total hexanol mass is mh, the mass of hexanol inside the surfactant aggregates is mha ) mh - mhb. The ratio η0 which describes the surfactant aggregate composition is then

η0 ) (mh - mhb)/mc

(1)

where mc is the total mass of the surfactant in the system. Using the balance equation, we obtain that the total ratio η ) mh/mc which describes the composition of the whole system, i.e. the parameter which we obtain in the experiment weighting the components of the system, is of the form

η ) [η0 + βΦ/(1 - Φ)]/[1 - βΦ/(1 - Φ)]

(2)

where Φ ) mb/m is the brine mass fraction in the system, m ) mc + mh + mb is the total mass of the system, and β ) mhb/mb is the ratio of the hexanol mass in brine-to-the brine mass mb. In fact, hexanol can be considered as a solute, which is present in two immiscible solvents: brine and surfactant aggregates. Since the critical hexanol solubility in brine

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satisfies the condition βb ) 0.0039 , 1, the solution of hexanol in brine can be considered as a weak one. Then the chemical potential µhb of hexanol in brine is of the form5

µhb ) Ψb + kT ln β′

(3)

where Ψb is an unknown function of the temperature T and of the pressure, k is the Boltzman’s constant, and β′ is the β ratio in molar units. Let us express the Ψ function in the form Ψb ) µ0h - kT ln yb. Here µ0h is the chemical potential of pure hexanol and yb is some unknown function of the temperature and pressure. Substituting Ψ in eq 3 gives

µhb ) µ0h + kT ln(β/yb)

(4)

One can see from eq 4 that the chemical potential of hexanol in brine becomes higher than the chemical potential of pure hexanol if β > yb. Therefore the condition β ) yb describes the limit of the solubility of hexanol in brine. Since yb is not dependent on β the parameter yb is the critical solubility of hexanol in brine yb ) βb ) 0.0039. The molar fraction of hexanol in the surfactant aggregates approximately is 0.6 at the phase boundary L1LR and 0.7 at the phase boundary LR-L3. The surfactant aggregate cannot be considered as a weak solution. Also hexanol cannot be considered as a solvent for surfactant molecules. Indeed the form of the chemical potential of a solvent given in ref 5 implies that in a weak solution the chemical potential of the solvent decreases when the solute amount increases. For the surfactant aggregates it is strictly not so. The topology of the phase diagram (Figure 1) shows that the system exists in the multiphasic state if the hexanol-to-surfactant ratio is higher than some critical value ηc. The ηc parameter which describes the phase boundary L3-multiphasic state is the critical solubility of hexanol in the surfactant aggregates. The fact that at the small surfactant amount in the surfactant aggregates (high η0) the system exists in the multiphasic state means that the chemical potential of hexanol in the surfactant aggregates at η0 > ηc becomes higher than the chemical potential of pure hexanol. Hence there is no reason to consider hexanol as a solvent for surfactant molecules. One can consider hexanol in the surfactant aggregates as a partially miscible solute. However the solution can not be considered as a weak one. To take into account a possible deviation of the surfactant aggregates from the ideal behavior following refs 5 and 6 the chemical potential of hexanol molecules in the surfactant aggregates can be expressed in the form

µha ) µ0h + kT ln[η′0f(η′0,β′)/ya]

(5)

Here ya is an unknown function of the temperature and pressure, f(η′0,β′) is the two-dimensional analog of the fugacity which describes the deviation of hexanol in the surfactant aggregates from the ideal behavior, and η′0 is the ratio η0 in molar units. One can see from eq 5 that the chemical potential of hexanol in the surfactant aggregates becomes higher than the chemical potential of pure hexanol when η′0 > ya/f(η′0,β′). Therefore at first approximation one can consider the parameter ηc ) ya/ f(η′0,β′) as the critical solubility of hexanol in a given (5) Landau, L. D.; Lifshitz, F. M.; Statistical Physics; Nauka: Moscow, 1976; p 90. (6) Dogra, S. K.; Dogra, S. Physical Chemistry through Problems; Wiley Eastern Limited: New Dehli, 1984; Chapters 17 and 18, pp 510587.

surfactant aggregate. One can expect that the parameter ηc has different values for the different surfactant aggregates. Since at equilibrium the chemical potentials µhb and µha of hexanol molecules in brine and in the surfactant aggregates are equal, we obtain

η0/β ) ηc/βb

(6)

Expression 6 describes the distribution of hexanol between brine and surfactant aggregates. The parameter Ω ) ηc/ βb is the partition coefficient. Let us suppose that the given phase transition occurs at the given Φ-independent η0 parameter. At present this assumption is accepted in the literature1,2 and is often used7,8 at least for not very high dilution, although it is not exactly proved. A reason for the constancy of η0 along the dilution is considered in ref 9. To verify the possibility to describe the phase boundaries by expression 2, we fit the experimental phase diagram at the Φ-independent η0 parameters. From eq 6 one can see that β is constant when η0 is constant. 4. Fitting of the Experimental Phase Boundaries 4a. Lr-L3 Phase Boundaries. A good fitting of the experimental LR-L3 phase boundaries by expression 2 in the studied dilution range is at β ) 0.0035, η0 ) 1.05 for the lower boundary and β ) 0.0034, η0 ) 1.07 for the upper one (Figure 2a). Note that small deviations from the fitting lines are of the same order as the accuracy of the experiment. The phase transition LR-L3 occurs when the hexanol-to-surfactant ratio which describes the bilayer composition is η0 ) 1.05. It corresponds approximately to seven hexanol molecules per two surfactant molecules in the bilayer. Since expression 2 well fits the experimental LR-L3 phase boundaries with the fitting parameters β which are less than the solubility of hexanol in brine, βb ) 0.0039, we conclude that the parameter η0 is the hexanol-to-surfactant ratio which describes the bilayer composition. η0 is independent of Φ. Hence in the whole investigated dilution region the composition of the bilayers at the LR-L3 phase boundaries is constant with dilution. 4b. L1-Lr Phase Boundaries. However expression 2 describes the experimental L1-LR phase boundaries only in the high dilution region (Figure 2b). One can expect that some of the surfactant molecules are in the water outside the surfactant aggregates. Taking into account this contribution to the function η(Φ) leads to the renormalization of the β coefficient in eq 2. The β parameter has to be replaced by the expression [β - γη0]. Here γ is the surfactant mass fraction in brine outside the surfactant aggregates. The γ parameter cannot be larger than the critical micellar concentration (cmc). In accordance with ref 10 the cmc of CPCl in water is 0.0003 by weight. Since γ , β, the renormalization of β leads to very small changes. For such a reason we omit this contribution in our calculations. The deviation from the distribution law (eq 6), i.e. the possibility of the β parameter being dependent on Φ at constant η0, also has to be analyzed. This deviation can occur when the fugacity f in eq 5 is a function of Φ. Then the parameter β can be a function of Φ even if the η0 parameter is constant. Supposing that β ) β0 + RβΦ (β0 (7) Porte, G.; Appel, J.; Basssereau, P.; Marignan, J. J. Phys. II 1989, 50, 1335-1347. (8) Boltenhagen, Ph.; Lavrentovich, O.; Kleman, M. C. R. Acad. Sci., Ser. II 1992, 315, 931-935. (9) Coleman, B.; Kleman, M. To be published. (10) Reactifs biochimiques et organiques pour la recherche et diagnostic.; Sigma Chemie: Paris, 1995; p 1692.

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and Rβ are fitting parameters) at constant η0, one can obtain good fitting of the L1-LR phase boundaries by expression 2. However the obtained parameters β in the whole studied dilution range are essentially higher than the solubility of hexanol in brine. Hence one can consider the distribution law (eq 6) to be valid along the L1-LR phase boundaries. Therefore the deviation of expression 2 from the experimental L1-LR phase boundaries shows that the parameter η0 at which the L1-LR phase transition occurs is not constant with dilution. It is well established now1,2,11 that the primary micelles from which the L1-LR phase transition occurs have the shape of a wormlike cylinder. The cylinders are more and more entangled when the brine fraction decreases. The close packing of the micelles at low dilution leads to the orientational prenematic ordering of the micellar cylinders.12 At still lower Φ the hexagonal and nematic phases exist. The dependency η0(Φ) can be a result of the increase of the interaction of the primary micellar structures when the dilution decreases. For such a reason the η0 parameter in eq 2 is replaced by the function

η0(Φ) ) η0* + RΦ

(7)

where R and η0* are fitting parameters. If η0 is described by eq 7, the parameter β in eq 2 changes with the dilution in accordance with the distribution law eq 6. From Figure 2b we see that the deviation of the experimental results from the fitting line (eq 2) is small. Since the variation of the parameter η0 along the dilution is small in order to determine the variation of β with the variation of η0, we use at first approximation the distribution law (eq 6) with a Ω ) constant. Then

β ) η0* + RΦ/Ω

(8)

Substituting eqs 7 and 8 in eq 2, we obtain the expression which fits well the experimental L1-LR phase boundaries at R ) 0.239, η0* ) 0.16, Ω ) 130 for the lower boundary and R ) 0.130, η0* ) 0.38, Ω ) 194 for the upper one (Figure 2c). The dependencies η0(1 - Φ) and β(1 - Φ) are given in parts a and b of Figure 3, respectively. The β parameter is lower than βb in the whole studied dilution range. 4c. L3-Multiphasic State Phase Boundary. Expression 2 does not fit well the L3-multiphasic state phase boundary. Since the phase transition L3-multiphasic state leads to the decomposition of the system but not to a morphological transformation of the surfactant aggregate one can expect the different behaviors of the LRL3 and L3-multiphasic state phase boundaries as a result of the deviation from the distribution law (eq 6) at the decomposition of the system. The best fitting of the L3multiphasic state phase boundary by expression 2 for β(Φ) ) β0 + RβΦ (β0 and Rβ are fitting parameters) at constant η0 is for negative β values. Hence the dependency β(Φ) does not describe the deviation of expression 2 from the experimental phase boundary, and one can consider the distribution law (eq 6) to be valid along the dilution. The best fitting of the L3-multiphasic state phase boundary by expression 2 using eqs 7 and 8 is at R ) -0.205, η0* ) 1.30, Ω ) 302 (Figure 2d). The β(1 - Φ) dependency deduced from the L3-multiphasic state phase boundary is shown in Figure 3b. (11) Gomati, R.; Appel, J.; Bassereau, P.; Marignan, J.; Porte, G. J. Phys. Chem. 1987, 91, 6203-6209. (12) Berret, J.-F.; Roux, D. C.; Porte, G. J. Phys. II 1994, 4, 12611279.

Figure 3. (a) Concentration phase diagram of the system cetylpyridinium chloride-hexanol-brine at room temperature in the η0 versus (1 - Φ) coordinates. (b) β parameters versus (1 - Φ) at phase boundaries: (1) lower L1-LR boundary; (2) upper L1-LR boundary; (3) lower LR-L3 boundary; (4) upper LR-L3 boundary; (5) L3-multiphasic state boundary.

5. Discussion The phase diagram obtained from the fitting results in the η0 versus (1 - Φ) coordinates is shown in Figure 3a. The η0 parameters describe the surfactant aggregate composition at the phase boundaries. For all phase boundaries the β parameters are somewhat lower than the mass ratio βb ) 0.0039 of the hexanol solubility in brine (see Figure 3b). This fact confirms that the proposed description of the phase boundaries is plausible. Here we present clear evidence that hexanol molecules are in brine as well as inside the surfactant aggregates. In fact, surfactant aggregates can be considered as a twodimensional surfactant solution of hexanol. Surfactant molecules in the surfactant aggregates play the role of a two-dimensional solvent for hexanol molecules. Hence the η0 parameter has the same sense for the surfactant aggregate composition as the β parameter has for the brine solution of hexanol. Both the β and η0 parameters are hexanol-to-solvent mass ratios in the brine solution and in the two-dimensional surfactant solution, respectively. The partition of hexanol between a bilayer and brine implies that the bilayer is an open system. Since the chemical potential µha of a strained monolayer of the bilayer is a function of its principal curvatures c1 and c2,13 µha can be expressed as

µha ) µ0h + kT ln[eµ/kTη0/ηc]

(9)

(13) Petrov, A. G.; Bivas, I. Prog. Surf. Sci. 1984, 16, 389-512.

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where µ is the elastic energy per hexanol molecule in a strained monolayer. At equilibrium the chemical potential of the hexanol molecules in brine, µb, is equal to the chemical potential, µha of the hexanol molecules in a strained monolayer of the bilayer. From µha ) µb we obtain that the chemical potential of the hexanol molecules in brine should be changed if the bilayer curvature is changed. The chemical potential of the hexanol molecules in brine can be changed only at the expense of a change in β; i.e., the hexanol amount in brine is a function of the bilayer curvature. Let β0, η0 and βd, ηd be the values of the β and η0 parameters of a given monolayer of the bilayer at zero- and nonzero µ, respectively. The variations of β and η0 at the increase (decrease) of the hexanol amount in brine on the value ∆Φh ) +(-)∆mh/m at the expense of the migration of some portion of the hexanol molecules of the mass ∆mh from the given monolayer of the bilayer into brine (from brine into the monolayer) are of the form

βd ) β0 + (∆Φh/Φ)

(10)

ηd ) η0 - (η0 + 1)∆Φh/(1 - Φ)

(11)

From the equilibrium condition one can obtain

ηd ) η0[1 + (β0 + Ω-1)Φ/(1 - Φ)]/[1 + eµ/kT(β0 + Ω-1)Φ/(1 - Φ)] (12) Since the elastic energy µ is a function of the principal bilayer curvatures, the ηd ratio which describes the bilayer composition is a function of the bilayer curvature. The view of the µ function can be obtained following ref 13. From eq 12 it follows that the variation of ηd will be more significant with the increase of the dilution. Since the bilayer composition is a function of the bilayer curvature and the elastic moduli of the LR phase are functions of the bilayer composition, one can conclude that the elastic moduli of the LR phase are functions of the bilayer curvature. Therefore one can expect that the studied system has nonlinear elastic properties. The situation is similar to that is for the exchange of molecules between two monolayers of the bilayer (free flip-flop) considered in ref 13, but in our case the exchange of hexanol molecules is between the strained bilayer and brine. We do not develop this problem in this paper. We shall do it in a future one. We would like to point out only that since the chemical potential of the bilayer is a function of the curvature of the bilayer, we predict a change of the

partition coefficient under an external influence (shearing, compressive or tensile stress, macromolecules inducing a deformation of the bilayer, etc.). One can expect a change of the partition coefficient at the increase of the external pressure, for example at the centrifugation of the sample. A change of the partition coefficient at an external influence implies the possibility of the existence of a new large class of exchange phenomena induced by external influence in the lyotropic systems in which the partition of the cosurfactant between a solvent and surfactant aggregates exists. 6. Conclusion The brine-rich corner of the phase diagram of the system cetylpyridinium chloride-hexanol-brine is studied. The phase boundaries L1-LR-L3-multiphasic state in the vicinity of the brine corner in the η(1 - Φ) orthogonal coordinate system are not straight lines, and far away from the brine corner they are essentially tilted to the (1 - Φ) axes. The solubility of hexanol in brine is responsible for the variation of the hexanol-to-surfactant ratios at which phase transitions occur on the η(1 - Φ) phase diagram. The hexanol-to-surfactant ratios η0 which describe the surfactant aggregate compositions are lower than the total hexanol-to-surfactant ratios which describe the whole system and which are usually measured in the experiment. The η0 parameter at which the phase transitions LR-L3 occurs is constant with dilution. The η0 parameter at which the L1-LR phase transition occurs varies along the dilution. The presence of hexanol molecules in brine as well as in the surfactant aggregates implies that the surfactant aggregate has to be considered as an open system. We predict that the composition of the bilayer can be changed upon an external influence. Cosurfactant exchange between the strained surfactant aggregate and the solvent is possible. Acknowledgment. I am very grateful to Professor M. Kleman for a critical reading of the manuscript and for helpful suggestions. I would like to thank Eric Lambert, Mukta Singh, and Catherine Quilliet for everyday collaboration. I thank the Laboratory of MineralogyCrystallography of Pierre and Marie Curie University (Paris VI) for hospitality while this work was in progress. This research was supported by Ministry of Education of France and by Ministry of Education of Ukraine. LA960013J