J. Phys. Chem. 1991,95, 5344-5352
5344
1
2
3
4
5
6
DEUTERON N'
Figure 15. Computed dependence of the deuteron longitudinal relaxation on the molecular ordering for Lorentzian spectral densities. The parameters of these calculations are given in Table IV for the lamellar phase. attenuated with the distance to the polar head for larger values of this order parameter. Conclusion
This work reports the dynamical and conformational behavior of an anionic surfactant with organic counterion in hexagonal and lyotropic mesophases. In these phases the surfactant behaves as
a quite rigid entity undergoing a very anisotropic motion about a privileged axis nearly coincident with that of the all-trans conformer. The analysis of the 13C-'H splittings as well as the 'F relaxation reveals unexpectedly high probabilities for the trans rotamer about the C-C and 0-C bonds, without striking differences between the hexagonal and lamellar phases. The enhancement of the probabilities of the most elongated conformers mmt likely results from confinement effects due to intermolecular interactions, which we did not attempt to analyze. They indeed not only correspond to the potential of mean torque as in nonionic surfactant^^^ but also to the Coulombic interactions between the polar heads. Owing possibly to the moderate ordering of the surfactant (&, zz -2F2hcx= 0.34-0.37), there is no evidence of an ODF contribution to the I F or 2H longitudinal relaxation in the 2-1 I-T range of magnetic field strengths used here. Calculations based on experimental data show that, for Lorentzian spectral densities, the influence of the molecular ordering on the longitudinal relaxation at the usual NMR frequencies becomes very small below F2 = 0.4 in a lamellar phase. This observation could be helpful to introduce some simplifications in the calculations of relaxation rates in liquid crystals.
Acknowledgment. We are greatly indebted to Dr. B. Gallot (Laboratoire des Materiaux Organiques, CNRS, Vernaison) for X-ray experiments as well as to Drs. J.-P.Korb (Laboratoire de Physique de la MatiEre CondensEe, Ecole Polytechnique, Palaiseau) and J. R. C. van der Maarel (Gorlaeus Laboratories, University of Leiden) for stimulating discussions. Registry NO. OCPT, 117826-62-7.
Effect of Alcohols on the Phase Behavior of Microemulsions M.Kablweit,* R. Strey, and G . Busse Max-Planck-Institut fir Biophysikalische Chemie, Postfach 2841, 0-3400, Catringen, FRG (Received: November 9, 1990)
In the literature, medium-chain alcohols are frequently considered as cosurfactants that act mainly on the properties of the amphiphilic monolayer at the water/oil interface in microemulsions. In this paper it is suggested that alcohols should rather be considered as cosolvents that distribute between the aqueous and the oil-rich bulk phases, and the interfacial layer, thereby decreasing the effective hydrophilicity of the amphiphile as well as the effective hydrophobicityof the oil. This is supported by the fact that alcohols adsorb rather weakly at the waterloil interface in amphiphile-free H2D-oil mixtures. Experiments on the effect of nonionic amphiphiles on the mutual solubility between water and alcohols, furthermore, give no indication for the formation of (inverse) micelles in the alcohol-rich phase. Finally, it is demonstrated that the effect of alcohols on the phase behavior and, accordingly, on the interfacial tension uabbetween the water-rich and the oil-rich phases depends on the position of the experimental temperature Tapwith respect to the mean temperature T of the three-phase body of the ternary water-ail-amphiphile mixture. With nonionic amphiphiles, Orb increases upon the addition of alcohol if Tap > but decreases (at first) if Tcxp< With ionic amphiphiles, one finds the reverse.
r,
r.
I. Introduction Consider a mixture of water (A), an oil (B), and a nonionic amphiphile (C). Within a welldefmed temperature interval AT, such a mixture may separate into three coexisting liquid phases, a water-rich (a), an oil-rich (b), and an amphiphile-rich (c) phase. At the mean temperature T of AT one finds a maximum of the mutual solubility between water and oil, and a minimum of the interfacial tension crab between phases a and b, both properties being the basis for applying such mixtures in research and industry. The separation of the mixture into three phases arises from the interplay between the miscibility gaps of the three corresponding binary mixtures A-B, B-C, and A-C. Because the features of these phase diagrams, in particular, those of the two latter mixtures, depend sensitively on the chemical nature of the oil (that is, its hydrophobicity), as well as that of the amphiphile (that is,
the hydrophilicity of its head group in relation to the hydrophobicity of its tail), this also holds for the dependences of T,AT, and b,b on the natures of the oil and the amphiphile. As a consequence, all three properties change systematically as one varies either the oil or the amphiphile within a homologous series. The qualitative rules of this dependence were summarized in a recently published review article.' Consider now the effect of an added fourth component. The Gibbs-Duhem relation between the variations of the field variables in the bulk phases 0 = s6T + &6fii Sp = Q (1.1) states that, at constant external pressure, the chemical potentials ( I ) Kahlweit, hi.; Strey, R.;Busse, G . J . Phys. Chem. 1990, 91, 3881.
0022-3654191 /2Q95-5344$Q2.5Q/Q 0 1991 American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 13, 1991 5345
Effect of Alcohols on Phase Behavior of Microemulsions of the three components may be varied either by changing the temperature at fixed mean composition, or by adding an appropriate fourth component at fmed T. Accordingly, T,AT, and 0.b may be varied by adding either a second oil, a second amphiphile, or an inorganic salt. Qualitatively, the effects of the additives can be predicted by studying their effects on the phase diagrams of the B-C and A-C mixtures. Consider a simple example: Experiment shows that in ternary H20-n-alkane (Bk)-nonionic C,E, mixtures with a given C,E,, T drops with decreasing carbon number k of the oil, or, for a given k, with decreasing hydrophilicity 0') of the head group of the amphiphile (at fixed i). Accordingly, one may make T drop gradually by adding either an oil with a lower k, or an amphiphile with a lower j. Instead of adding an oil or an amphiphile, one may also add an alcohol, denoted by C,&, Alcohols distribute between the water-rich and the oil-rich phases, their distribution coefficients depending only weakly on temperature, but sensitively on their carbon numbers i as well as on the carbon number k of the oil. Short-chain alcohols (i 5 3) are completely miscible with water and thus make the 'pseudocomponent" (C,E, C,&) effectively more hydrophilic. As a consequence, adding a short-chain alcohol to a ternary A-Bk-C,E, mixture, makes 7' rise.2 Medium- and long-chain alcohols (i 1 4), on the other hand, dissolve mainly in the oil-rich phase and thus make the pseudocomponent (oil C,&) effectively less hydrophobic, which makes T drop. Because they are partially miscible with H20, they, simultaneously, make the (C,E C , h ) mixture effectively less hydrophilic, which also makes +drop. As a consequence, adding a medium- or long-chain alcohol to the mixture makes T drop. Equivalent considerations hold for ternary mixtures H20oil-ionic amphiphiles. The phase behavior of such mixtures is the reverse of that with nonionic amphiphiles:' for a given ionic amphiphile, T rises with decreasing hydrophobicity of the oil or, for a given oil, with decreasing hydrophilicity of the amphiphile. Because many experiments in the literature are performed with rather hydrophilic single-tailed ionic amphiphiles, as e.g. SDS, one has to apply oils with very low effective carbon numbers in order to enforce a separation into three phases between the melting and boiling temperatures of the mixture. This is done by choosing aromatic oils, as e.g. toluene, which, however, is apparently still too hydrophobic. One therefore has to add a medium-chain alcohol, as e.g. C4%, which decreases the hydrophobicity of the pseudocomponent (toluene C4&) further, and thus makes T rise. Because this still does not suffice, one has to proceed to a quinary mixture by adding e.g., NaCl, which decreases the mutual solubility between water and SDS, thereby makes the ionic amphiphile effectively less hydrophilic, and thus, finally, enforces a separation into three liquid phases within the experimental window. If SDS is replaced by the more hydrophobic double-tailed AOT, one may achieve a separation into three phases even with n-alkanes without having to add an alcohol, though one still has to add a lyotropic salt. The above considerations suggest alcohols be considered as "molvents" that act mainly on the chemical potentials of the components of the mixture and, because of the Gibbs-Duhem relation between the variations of the interfacial exquantities
+
+
+
+
o = s " b ~+ ba + Crhr,
(1.2)
thereby also on the interfacial tensions between the various bulk phases. Alternatively, the effect of medium-chain alcohols on the phase behavior of H,O-oiI-amphiphile mixtures has been explained by considering medium-chain alcohols as "cosurfactants" that act mainly on the properties of the interfacial layer, the reason being that adding an alcohol at constant temperature may lower the interfacial tension 0.b between the water-rich (a) and the oil-rich (b) phases. Hitherto, two models have been proposed: the first model is based on the 'wedge model", that is, the assumption that the monolayer possesses a 'natural curvature" which "is deter( 2 ) &, e.&, Yoshida, M.; Kunieda, H. J. Colloid Inrerjiice Scf. 1990,138, 213.
C,Ea
(D1
Figure 1. Unfolded phase tetrahedron of a water (A)-oil (B)-nonionic amphiphile (C)-alcohol(D)mixture with schematicphase diagrams of the four ternary mixtures at 7'" < T < T p
mined by the difference in size between the two ends of the (amphiphile) molecules, just as the size of an arch is dependent upon the relative sizes of the two ends of stones of which the arch is con~tructed".~Accordingly, Mitchell and Ninham' assumed that alcohol molecules enter the monolayer and thereby change its natural curvature. In the second model, it is assumed that the alcohol molecules adsorb preferentially at the regions of strong curvature of the interfacial layer, and thereby decrease its "rigidityns5 11. The Phase Tetrahedron At constant external pressure, a quaternary mixture has four independent variables. For representing its phase behavior in three-dimensional space, one either has to dispense with temperature by keeping it constant or to disperse with one of the composition variables by combining two of the components at a fixed ratio into a "pseudocomponent". If T i s kept constant, the phase behavior can be represented exactly in a phase tetrahedron, whereas, if two of the components are combined into a pseudocomponent, the phase behavior may be represented in a pseudoternary phase prism with T as the ordinate. Which of the two representations is chosen is a matter of convenience. Because in the literature most experiments with quaternary (or quinary) mixtures were performed at constant T,we shall represent the phase behavior in a phase tetrahedron with the A-B-C triangle as the base, and the alcohol (D) placed on top. Again, the phase behavior of the quaternary mixture is essentially determined by the phase diagrams of the four corresponding ternary mixtures that are shown schematically on the unfolded tetrahedron in Figure 1. The central triangle represents the phase diagram of the A-B-C mixture. For a given oil and amphiphile, its features depend sensitively on temperature, as shown schematically on the left of Figure 3. When discussing the effect of an alcohol on this phase diagram, one therefore has to distinguish between three cases: (i) the mixture is studied at a temperature T < TIat which the amphiphile is mainly dissolved in the water-rich phase (2); (ii) it is studied at a temperature TI < T < Tuat which the mixture separates into three liquid phases (3); or (iii) it is studied at Tu < T at which the amphiphile is mainly dissolved in the oil-rich phase (2) as shown in Figure 1. The triangle on the upper right is blank because the oils, nonionic amphiphiles, and alcohols applied in this study are completely miscible. The phase diagram on the bottom is rather simple and, furthermore, practically temperature independent. When a medium-chain alcohol ( i 2 4) is chosen, both the oil and the alcohol are only partially miscible with water, which results in a connected miscibility gap extending from the A-B to the A-D side, with the mutual solubility between water and the nonpolar phase gradually increasing. The phase diagram on the upper left depends again sensitively on temper( 3 ) Langmuir, I. Mer. Chem. Eng. 1916, 15. 468. (4) Mitchell, D. J.; Ninham,B. W.J . Chem. Sm., Faraday Tronr.2 1981, 77, 601. ( 5 ) de Gennes, P.G.; Taupin, C . J . Phys. Chem. 1982,86. 2294.
Kahlweit et al.
5346 The Journal of Physical Chemistry, Vol. 95, No. 13, 1991 H,O/oil = l / l
1
i
H20 - C,H,,
-c ~ E ~ J
jH20 - C,H12 -CLEO]
tLO
a
I mN m”1 :30
t
li0 20
0.1
1
-
10 CLEolwt%1
100
H20/oil =1/1
1
I ’0 10 100 CaEL [wt%I Figure 2. Interfacial tensions u vs concentration of the third 01
1
-
component
(in wt %), measured at 25 OC: Top, H2()-C6H12-c8E4 (c);Center, H20C6Hi2.-C4E,(D);Bottom, H2(FC4E&E4 (C). The C4E, concentrations i n the center refer to the straight path from 50 wt % C6Hi2 on the A-B side to 43.8 wt % C4E, on the A-D side.
ature. In this case, one has to distinguish between two possibilities: (i) the mixture is studied at a temperature below the (lower) critical temperature T, of the A-C loop, T < T,; or (ii) it is studied at T > T,. In the first case, one finds a miscibility gap extending from the A-D side into the triangle, with the plait point lying on the water-rich side as shown in Figure 1; in the second case, a connected gap extending from the A-D to the A-C side is found. Consider now the interfacial tensions between the equilibrium phases in the three triangles. The interfacial tension g a b between pure water and oil is about 50 mN m-l. As one adds CiE that is, as one proceeds through the central triangle from the A-k side to the plait point of the A-B-C miscibility gap, gab drops steeply, as shown on Figure 2, top for the H20-cyclohexaneX8E4mixture, until one reaches the lower of the two cmc tie lines. For T > Tu, it is the cmcb tie line (see Figure 3, upper right). From then on remains practically constant on a very low plateau ( T,, it drops to the very low value between the two equilibrium phases of the H20-C,E, loop on the A-C side of the triangle. From this we deduce that there is a characteristic difference between the adsorption of alcohols at water/air and at water/oil interfaces. Experiment shows that in aqueous solutions, the interfacial tension of the water/air interface drops almost as steeply upon addition of an alcohol (CiE,,) as upon addition of a nonionic amphiphile (CiE,) with the same i. This implies that at water/air interfaces, alcohols adsorb almost as strongly as nonionic amphiphiles, the driving force being essentially determined by the carbon number i. In water/oil mixtures, however, the interfacial tension of the water/oil interface decreases much slower upon addition of an alcohol than upon addition of an amphiphile, which implies that at water/oil interfaces, alcohols adsorb much more weakly than amphiphiles. This difference in adsorption can be qualitatively interpreted as being the consequence of the inverse role of the interactions between the hydrophobic tails and the hydrophilic heads, respectively, and the two solvents. In the water-rich phase, the driving force for adsorption (as well as for micellization) is essentially determined by the repulsive hydrophobic interaction between the hydrocarbon tails and water! whereas the attractive hydrophilic interaction between the heads and water determines the solubility of the micelles, that is, the lower critical temperature T, of the (upper) miscibility gaps.’ In the oil-rich phase, on the other hand, the interactions change their roles. Here, the repulsive interaction between the head groups and the nonpolar solvent determines the driving force for adsorption. Although one expects the OH groups of the alcohols to be weakly hydrated, the attractive interaction between their tails and the oil seem to suffice for keeping (medium-chain)alcohols in solution. With amphiphiles, on the other hand, the strong hydration of their head groups leads to a stronger repulsive interaction with oil, which reflects itself in a strong adsorption at water/oil interfaces, and the formation of (inverse) micelles. From these considerations it follows that at water/oil interfaces in the absence of amphiphiles, alcohols can only be considered as rather weakly surface active substances. In the presence of an amphiphilic monolayer, however, one expects alcohols to dissolve in that layer due to their tendency to seek an environmental with an intermediate polarity between that of oil and water which, in turn, will also affect the interaction energies between the amphiphile molecules in the monolayer and the adjacent bulk phases, and thereby the interfacial tension 0.b between the two. This again suggests medium-chain alcohols be considered as m i v e n t s that distribute between the two bulk phases and the interfacial layer, the distribution depending, evidently, on the carbon number of the alcohol, that of the oil, and the properties of the amphiphile. 111. A-B-C Mixture
Consider now the A-B-C mixture with a nonpolar oil and a nonionic amphiphile. As we have shown in ref 1, such a mixture possesses two cmc surfaces that ascend almost vertically in the phase prism of the mixture. The cmcl surface starts at the (almost vertical) cmc curve in the phase diagram of the binary A-C mixture (see, e.g., Figure 14, left in ref 1) and proceeds through the narrow homogeneous solution toward the water-rich side of the binodal surface of the miscibility gap where it shapes an (almost vertical) c m p curve. From there it continues along the corresponding tie lines through the gap to terminate at a curve on the oil-rich side of the binodal surface, as shown schematically on the right of Figure 3. The cmcb surface, on the other hand, may be somewhat diffuse in dry oil, but becomes well defined on the oil-rich side of the binodal surface where it shapes an (almost vertical) cmcb curve (see, e.&, Figure 14, right in ref 1). From there it continues along the corresponding tie lines through the miscibility gap to terminate at a curve on the water-rich side of (6) Sec, e.g., Tanford, Ch. The Hydrophobic E’fwr, 2nd ed.;Wiley: New
York, 1980.
(7) See, e.g., Figure 8 in ref 1 .
Effect of Alcohols on Phase Behavior of Microemulsions
The Journal of Physical Chemistry, Vol. 95. No. 13, 1991 5347
nonionic amphiphile
H20/oil = 1/1
0
I
0
5
10
15
20
25
[Wt%]
Figure 3. Left: phase prism of a H2D-oil-nonionic amphiphile mixture (schematic). Right: temperature dependence of the cmc tie lines (schematic; for discussion see text).
that surface. Because the energy of formation of (normal) micelles in the water-rich mixture differs from that of (inverse) micelles in the oil-rich mixture, the cmc? and the cmcb tie lines will, in general, not coincide. While cmc? and cmcbdepend only weakly on temperature, the distribution of the amphiphile between the water-rich and the oil-rich phases, that is, the inclination of the tie lines, changes strongly with rising temperature. Conceptually, the cmc? curve on the water-rich side, and the cmcb curve on the oil-rich side of the binodal surface can be looked at as a sequence of pivot points around which the corresponding cmc tie lines turn. Because nonionic amphiphiles are more soluble in water than in oil at ambient temperatures, but more soluble in oil than in water at elevated temperatures, both tie lines turn counterclockwise with rising temperature (if looked at from above), the cmcb tie lines, however, somewhat faster than the cmc?tie lines. At temperatures below T, the cmc? tie lines lie at a lower amphiphile concentration than the cmcb tie lines, as shown on the lower right of Figure 3. At mean concentrations between the cmc? and the cmcb surface, one therefore finds for T < T (normal) micelles with solubilized oil in their interiors in the water-rich phase (a), in equilibrium with a molecularly disperse oil-rich phase (b). As one raises the temperature, the two cmc surfaces approach each other until they intersect at T (Figure 3, center right). At this temperature, the cmc* and cmcb tie lines coincide with the a-b tie line of the three-phase triangle, so that the amphiphile-rich phase (c) is now in equilibrium with the two molecularly disperse phases a and b. At temperatures above T,the cmcb tie lines lie at a lower amphiphile concentrations than the cmca tie lines, as shown schematically on the upper right of Figure 3. At mean concentrations between the cmcb and the cmca surfaces, one therefore finds for T > T (inverse) micelles with solubilized water in their interiors in the oil-rich phase, in equilibrium with a molecularly disperse water-rich phase. The existence of a cmc surface exhibits itself in a sudden increase of the apparent solubility of the minority component, that is, of oil in the water-rich and of water in the oil-rich phases. This is demonstrated on Figure 4, bottom, which shows an isothermal section through the phase prism of the H20-C6H,2%8E4mixture at 25 OC. In the shaded region, L, and L3 intrude into the miscibility gap. We note in parenthesis that the oil-free mixture shows no lyotropic mesophases, which implies that these appear only upon addition of the oil. The three-phase body of this mixture extends from TI= 19.0 to Tu = 23.5 OC (Figure 4,top). At 25 OC (>Tu), the mixture thus separates into two phases, with the plait point lying on the water-rich side (z), and the cmcb surface lying at a lower amphiphile concentration than the c m e surface (Figure 3, upper right). Consequently, as one increases the amphiphile concentration gradually, one first crosses the cmcb tie line, which leads to the formation of (inverse) micelles in the oil-rich phase. This leads to a sudden increase of the apparent solubility of water in that phase, which exhibits itself in a sharp change of the slope of the binodal on the oil-rich side. As one
Figure 4. Top: vertical section through phase prism of the H20C6HI2-C8E4mixture at water/oil = 1/1. Bottom: isothermal section through the phase prism at 25 O C with cmcbtie line. In the shaded area La and L3 intrude into the miscibility gap. The filled circle represents the plait point. nonionic amphiphile (C)
Figure 5. Phase prism of a H20-oil-nonionic amphiphile mixture with cmca and cmcb surfaces (schematic).
increases the amphiphile concentration further, the solubility of water increases, at first, practically linearly, which indicates that the number density of water-in-oil droplets increases linearly with increasing amphiphile concentration, with their radii remaining constant. For T < TIfor which the cmca tie lines are the lower ones, one finds a corresponding change of slope of the binodal on the water-rich side (Figure 18 in ref 1). Experiment, furthermore, shows that the change of slope at the cmc’s increases as one approaches TI from below, or Tu from above. From this, one deduces that the radii of the droplets of the oil-in-water or water-in-oil dispersions, respectively, increase as one approaches the three-phase body until, at T = TIor = Tu,respectively, the droplets start aggregating to connected, chain-like structures. IV. Cmc Surfaces and Curvature On the basis of the considerations presented in section 111, we suggested in ref 1 that the sign of the curvature c of the droplets is determined by that cmc surface, which is the lower one at the corresponding temperature. As for the sign of c, we define c < 0, if the interface is convex toward the water-rich (o/w) phase c > 0, if it is convex toward the oil-rich (w/o) phase. Figure 5 shows schematically the two cmc surfaces as they pass through
5348 The Journal of Physical Chemistry, Vol. 95, No. 13, 1991
HO , 70
- n-octane - CeEL
Kahlweit et al. to the experimental points, with T = 39.65 OC,uo u,b(T=T) = 3.60 loV2mN m-l, and 8 = 1.27 mN m-I K-2. Inserted into (IV.1) this yields r / r o = (T/T)’/2[1 ( 8 / u o ) ( T- T)2]-1/2 (IV.4)
1
+
Because is practically symmetric with respect to T,this result predicts that the radii of the o/w droplets along the straight portion of the binodals on the water-rich side at T = T- A should be equal to those of the w/o droplets along the straight portion of the binodals on the oil-rich side at T = T A. The slopes of the binodals, being a measure for the amount of solute solubilized by the droplets, differ, of course, because of the difference between the molar volumes of water and oil. As temperature approaches T either from above or below, the radii of the droplets, and thus the amount of solubilized solute increases until the droplets start aggregating. The transition from isolated droplets to chain-like structures, as well as that to sponge-like structures of water and oil domains in the amphiphile-rich phase (c) near T will be considered in a forthcoming paper. As for discussing the effect of alcohols on the phase behavior of microemulsions, we shall leave it with the above semiquantitative considerations.
+
0‘ 0
02
OL
06
08
I 10
a [mN m-’I
Figure 6. Temperature dependence of interfacial tension 0.b between the
water-rich and the oil-rich phases, measured at the cmc tie lines, for H2D-octantC8E4.
the body of heterogeneous phases in an A-B-C phase prism. The lighter shaded surface represents the cmcl surface; the darker, the cmcbsurface. For T C T,the cmcP surface is the lower one. Consequently, it enforces the formation of micelles in the water-rich phase (a). Because the sign of the curvature of (normal) micelles is by definition negative, this also holds for the curvature of the droplets in o/w dispersions. For T > T, the cmcb surface is the lower one, and thus enforces the formation of (inverse) micelles with a positive curvature in the oil-rich phase (b). From this it follows that the change from an o/w to a w/o dispersion with rising temperature is a consequence of the temperature dependence of the energy of micellization in the two phases as well as of that of the distribution of the amphiphile between the two phases, which determines the change of inclination of the tie lines. On the basis of considerations by various authors on the stability of colloidal dispersions, in particular by Reiss,8we furthermore assumed the radii r of (isolated) droplets in either o/w or w/o dispersions in equilibrium with the corresponding (molecularly disperse) phase at the other end of the tie line to be related to the interfacial tension Cab of the planar interface between the two phases by $uab/(kBT) ir 1 (IV.1) Thus, while the competition between the two cmc surfaces determines which of the two solvents is dispersed (and thereby the sign of the curvature of the droplets), the interfacial tension between the two phases determines their radii. The number density N, of droplets, finally, is given by the amphiphile concentration that determines the interfacial area A, per unit volume A, = 4 d N , (IV.2) The interfacial tension u,b between water and oil in the amphiphile-free mixture is about 50 mN m-I. As one adds an amphiphile, b,b drops steeply until one crosses the lower of the cmc tie lines, as shown on Figure 3, top. From then on it remains practically constant up to rather high amphiphile concentrations. For T < T,the u,b value is thus practically equal to that at the cmcl surface; for T > T,it is practically equal to that at the cmcb surface. Experiment, furthermore, shows that the temperature dependence of gab can be represented in sufficient approximation by a parabola with its minimum at T,as shown in Figure 6 for the H20-nsctantC8E, mixture. The full line represents the tit of b& = go( T=T) + e( T - 73’ (IV.3) (8) Reiss,
H.J. Colloid Interface Sei. 1975, 53, 61.
V. Effect of Third Component on Mutual Solubility between Two Partially Miscible Liquids The mutual solubility between nonpolar solvents and water is very low, which makes determining the effect of an added amphiphile on the initial slopes of the binodals virtually impossible. Alcohols and water, however, show a higher mutual solubility so that these mixtures permit comparing the predictions of theory as to the effect of an amphiphile on the mutual solubility between the two. The effect of a third component on the mutual solubility between two partially miscible liquids has been studied experimentally by a number of authors. A quantitative thermodynamic interpretation was first given by Wagner? and thereafter by Prigoginelo and Rice.” While the two latter authors put the emphasis on the effect on the critical temperature T,, Wagner also considered the effect of the mutual solubility at temperatures below T,. Consider the effect of a third component (3) on the mutual solubility between two partially miscible liquids (1) and (2) at 6T = 6p = 0. The phase rich in (1) will be denoted by (‘), the one rich in (2) by (”). Let the compositions be defined by x2=x x3=y x,=l-x-y so that the chemical potentials are functions of x and y only. Wagner’s result, a slightly modified derivation of which can be found in the Appendix, then predicts for the initial slope of the binodal on the side rich in (1) lim (bx/by)’ = (1 - K)[(G‘,/RT)(x”- x?]-’ (V.1) Y‘O
and for that on the side rich in (2) lim (6x/6y)” = (K-’- l)[(G‘‘,/RT)(x”-
x’)]-’ (V.2)
Y=o
is the distribution coefficient of component (3) between phases (”) and (’), and ,G‘ (#AG,/a~~),,y~.o > 0 (V.4a)
G‘:,
= ( # A G , , , / ~ X ~ ) , , ~ ,>~ ,o~
(V.4b)
AG, denoting the Gibbs free energy of mixing. Because 6y as well as the second brackets on the right sides of (V.l) and (V.2) are always positive, the sign of 6x is determined by the value of K. If component (3) is more soluble in (1) than (9) Wagner, C. Z . Phys. Chem. 1928,132,273. (10) Prigogine, I. Bull. Soc. Chim. Belg. 1943, 52, I 1 5. See also: Prigogine, I.; Defay, R. Chemical Thermodynamics; Everett, D. H., Trans].; Longmans: London. 1954; p 256 ff. (11) Rice, 0. K.; MacQueen. J. T. J. Phys. Chem. 1962.66, 625.
Effect of Alcohols on Phase Behavior of Microemulsions
in (2), that is, if K < 1, then 6x > 0; the miscibility gap moves towards the phase rich in (2). If component (3) is more soluble in (2) than in (l), that is, if K > 1, then 6x < 0; it moves towards the phase rich in (1). Finally, if component (3) is equally well soluble in (1) and (2), that is, if K = 1, then 6x = 0: the mutual solubility between ( 1 ) and (2) increases. In phase (’), the ratio of (2)/( 1) molecules increases, the ( 1 ) molecules being replaced by (3) molecules, and in phase (”) the ratio of (1)/(2) molecules increases, the (2) molecules being replaced by (1) molecules. For wide miscibility gaps, ( x ” - x ’ ) = 1 , one may consider phases (‘) and (”) to be ideally diluted. Then G‘,/RT
-
The Journal of Physical Chemistry, Vol. 95, No. 13, 1991 5349
- CLEO - CbEj
H2O
25 o c
-
2
0
L
l / x ’ and G‘’,/RT = 1/(1 - x ” )
6
8
10
C‘E, [wt%l
so that (V.l) and (V.2) simplify to
lim (6 In x/6y)’ = ( 1
- K)
YE0
(V.5)
and lim (6 In (1 - x)/6y)” = (1 - IC’) Y-0
(V.6) 24
VI. H20-C,&-C,Ej Mixtures In this section we shall compare the above predictions with the effect of nonionic amphiphiles C,Ej on the mutual solubility between H 2 0 and n-alcohols C& ( i 2 4). As long as one chooses a temperature below the lower critical temperature T, of the H20-C,E loop, both the H20C,E, and the C,E&,Ej mixtures are completely miscible, whereas the H20-C,&mixture shows a miscibility gap (upper left triangle in Figure 1). The question then arises as to the effect of added C,Ej.on the mutual solubility between H 2 0 and C,E, that is, on the initial slopes of the binodal of the H20-C,& gap. As long as the ternary mixture is molecularly disperse, that is, at low C,Ej concentrations, one expects the sign of the right sides of eqs V.l and V.2, respectively, to be determined by the distribution of the amphiphile between the alcohol-rich (”) and the water-rich (9 phases. Because C,&-C,Ej mixtures are completely miscible between melting and boiling temperatures, whereas H,O-C,E, mixtures show an upper laop at elevated temperatures, one expects C,Ej to be more soluble in the alcohol-rich than in the water-rich phase, that is, K > 1. Accordingly, one expects the binodals on both sides of the miscibility gap to move toward the H,O-rich side of the triangle upon addition of small amounts of C,E However, as one increases the d;E, concentration, the binodal on the water-rich side will eventually intersect with the cmc curve, which starts at the cmc of the alcohol-free mixture, and proceeds into the triangle. Because the C,E, micelles solubilize alcohol molecules, this increases the apparent solubility of C,E, in phase (‘), so that the binodal on the water-rich side should bend around to proceed toward the alcohol-rich side until both branches of the binodal merge at the plait point. The plait point lies on the critical line, which starts at the lower critical point of the H20-C,Ej loop and descends into the phase prism. Accordingly, one expects the plait point of the central miscibility gap to lie on the water-rich side, in spite of the solubilization of alcohol by micelles in the water-rich phase. These predictions are confirmed by experiment. Figure 7 shows the initial portions of the binodals on the water-rich (top) and on the alcohol-rich (bottom) sides for the H20-C4Eo-C8Ej (j = 4 3 ) mixtures at 25 OC. The empty points represent the binodals, determined by titrating the alcohol-free mixture with C4E0, and the water-free mixture with H20, respectively. The full points represent the trajectory of the cmc in the mixture with C8E4, determined by interfacial tension measurements, when we prepare H2OC4& mixtures with 2, 3 and 4 wt % C4&, respectively, as solvent, and then add C8E4. The result is shown in Figure 8. As one can see, both the cmc, ycrand the interfacial tension a, at the cmc decrease smoothly upon addition of C4%, with the slope aula log y no longer being constant for y d yc,as is the case for pure water as solvent. At 25 ‘C, the solubility of C4E,, in H20is 7.45 wt %. As one adds C8E4,both branches of the binodal first move toward the
70
0
-
80 90 100 CLEO[wt%l Figure 7. Initial portions of binodals on the water-rich (top) and the oil-rich (bottom) sides for H20C,E.&E, (j = 43) at 25 OC. The filled circles at the top represent the cmc’s. 60
0 wt% CLEO
7
0
0.1
0.01
-
1 C8EL Iwt%I
10
Figure 8. Interfacial tension u of the water/air interface of ( H 2 0 + C4E,,)-C8E4 mixtures at 25 OC.
water-rich side until the one on the water-rich side starts to bend toward the oil-rich side. More interesting, however, is the fact that, within experimental error, the cmc curve and the lower part of the binodal appear to lie on a straight line that connects the cmc in the alcohol-free mixture with the solubility limit of C4E, in the amphiphile-free mixture. With y denoting the wt % of the amphiphile in the mixture, and 8 that of the alcohol, the relation between 8 and y along that line can thus be described by (VI.1) = 1 - (Y/Yc)
s/a’,
where is the solubility of the alcohol in pure water, and yc is the cmc of the amphiphile in pure water. From this one obtains for the initial slope of the binodal on the water-rich side, expressed in wt 9% (VI.2) K’= lim (68/67)’= - ( & / y c ) C 0 Y-0
The solubility of the alcohol in pure water is related to the free energy of mixing G of the amphiphile-freemixture appearing on
Kahlweit et al.
5350 The Journal of Physical Chemistry, Vol. 95, No. 13, 1991
HZO - CkEo - &E,,
0 0
2
L
6 8 CLEO[wt%l
10
Figure 9. Temperature dependence of initial portions of binodals on the water-rich side for H20+&-c&
the right side of eq V.l by the tangent rule, whereas the relation between the nature of the amphiphile, exhibiting itself in its cmc yc in pure water, and its distribution K between phase (‘) and phase (”) is more difficult to derive, though it should exist. The binodals on the alcohol-rich side, on the other hand, show no indication for a sudden increase of the apparent solubility of water with increasing amphiphile concentration. We further remark that if the nonionic CsE4 is replaced by the ionic SDS, the initial slope of the binodals on the water-rich side is of opposite sign, because SDS is more soluble in water than in alcohol (K < 1). 1. Water-Rich Side. When discussing the effect of a nonionic amphiphile on the mutual solubility between H 2 0 and Ci&, one thus has to distinguish between the water-rich and the alcohol-rich sides of the miscibility gap. On the water-rich side it appears as if the lowest portion of the binodal lies on a straight line that connects the cmc of the amphiphile in the alcohol-free mixture and the solubility of the alcohol in the amphiphile-free mixture. This could be interpreted by assuming the alcohol molecules form association complexes in pure water that separate, however, as a second phase because the hydrophilic interaction between the OH group and water does not suffice to keep the complexes in solution. In order to keep them in solution, one has to add a certain amount of a more hydrophilic amphiphile, which makes the mixed complexes soluble. At which amphiphile concentration the binodal starts deviating from the cmc trajectory is experimentally difficult to clarify because in this concentration range the interfacial tensions of H 2 W 4 & mixture are already rather low to start with so that detecting a change of slope at the lower part of the binodals is virtually impossible. We presume, however, that the mixed micelles gradually disappear as one proceeds towards the amphiphilefree mixture. This presumption is supported by measuring the interfacial tension between the water-rich and the alcohol-rich sides vs amphiphile concentration, as shown on Figure 2, bottom for the mixture H20-CiEo-CsE4 ( i = 4,6) at 25 “C. For the interfacial tension of the amphiphile-free mixture we found for C4& u(y=O) = 1.60 mN m-I, in good agreement with the value (1.59) published in the literature.12 As one adds C8E4, the interfacial tension drops smoothly, showing no indication for a cmc tie line, as is observed in mixtures with a truly nonpolar oil instead of alcohol. Figure 9 shows the temperature dependence of the binodals on the water-rich side for the H20+& 1. One would then expect K“ to decrease with decreasing xA,because, in particular, G‘iXshould increase with decreasing solubility of water in the pure alcohol. If, on the other hand, both the alcohol and the amphiphile molecules were hydrated, one, too, would expect the water con-
Effect of Alcohols on Phase Behavior of Microemulsions
The Journal of Physical Chemistry, Vol. 95, No. 13, 1991 5351 H20 - octane
D
A/B=l
- CE, ,
- CLEO
C
-
Figure 11. Temperature dependence of vertical sections through the phase tetrahedron of H20(A)-oil (B)-nonionic amphiphile (C)alcohol (D), erected at A/B 1/1 (for discussion see text).
centration in the alcohol-rich phase to increase (at first) linearly with increasing amphiphile concentration because the number of water molecules bound by the OH group of the alcohol molecules should be lower than that bound by the (OCH2CH2),0H group of the CiE molecules. The slope K" would then represent the difference &tween the number of water molecules bound by CiE. and CiE, molecules. In this case one would expect K f fto depend only weakly on the carbon number of the alcohol, but to increase with increasing j (at fixed i). Although the latter is qualitatively supported by experiment (see Figure 7,bottom), further systematic experiments with "dry" substances are required before well-substantiated conclusions can be drawn.
VII. Conclusion As mentioned in the Introduction, the reason for considering alcohols as cosurfactants is based on the fact that adding an alcohol at constant temperature may lower the interfacial tension c a b between the water-rich and the oil-rich phases. In this final section, we shall show that this effect is by no means general but depends on the position of the temperature of experiment, Tap with respect to the mean temperature T of the three-phase body of the temary A-B-C mixture. For this purpose one may consider the A-BC-D tetrahedron as an elevator that is moved up or down in the A-B-C phase prism (see Figure 25 in ref 13). Figure 11 shows schematical vertical sections through the tetrahedron erected at the water/oil ratio = 1/ 1. The section on top is made at Tcxp> Tu. Because the three-phase body of the temary A-B-C mixture lies below T,, , the A-B-C base of the tetrahedron shows state (2). As one aids alcohol, the miscibility gap merely widens, with the amphiphile in the oil-rich phase being gradually replaced by the alcohol and the interfacial tension c a b value-measured at a fixed weight fraction of water + oil-increasing smoothly to that in the amphiphile-free mixture. As one lowers Terp,that is, lowers the position of the base of the tetrahedron in the prism, one gradually approaches the three-phase body of the ternary mixture until it appears at Tcxp = Tuon the base with its upper critical tie line (see Figure 3, left). The section in the center is made at TeFP= T,that is, with the base showing the isosceles three-phase tnangle. Accordingly, the diagram shows on its bottom the upper half of the three-phase "fish" (see Figure 4, top). As one adds alcohol, one first passes through the three-phase body, after which both the amphiphile and the alcohol dissolve mainly in the oil-rich phase (2). Again (13) Kahlweit, M.;Strey, R.Angm. Chcm., Inr. Ed. Engl. 1985,24,654.
0
-
10
HWo"
= 111
20
30
LO
&E, [wt %I
Figure 12. Left: vertical section through a phase prism with the threephase body of H20-xtane-C8E4. Right: sections through some tetrahedra with C,E, as alcohol, made at 60 (top), 44 (center), and 25 OC (bottom), to be compared with the schematic sections shown in Figure
11. the c a b value increases from its very low minimum at the base to that in the amphiphilefree mixture. As one lowers ToIpfurther, the three-phase body moves gradually into the tetrahedron until it disconnects at Tcxp= Ti from the base with its lower critical tie line (see Figure 3, left). The section on the bottom is made at Tcxp< TI,that is, with the base in state (2). As one adds alcohol, one first passes through then through the three-phase body (3) into (2). Only in this case, c a b first decreases, passes through a minimum at that alcohol concentration at which the mean composition lies on the (tilted) isosceles three-phase piangle, and increases again. As one lowers T,, further, point X of the three-phase body moves toward higher aicohol concentrations,as does the minimum of the interfacial tension. As an experimental example, Figure 12 shows on its left a section through a phase prism with the three-phase body of the ternary H20-n-octane-C8E4 mixture, and on its right sections through some tetrahedra with C,E, as alcohol. For reasons of convenience, the sections through the tetrahedra are not plotted in their correct shapes as shown on Figure 11, but on triangular coordinate graphs, which facilitates reading the compositions. The section on top is made at Toxp= 60 OC > Tu,corresponding to the one at the top of Figure 11. The section in the center is made at 44 OC = T,corresponding to the middle section of Figure 11. The section at the bottom is made at 25 OC < TI,corresponding to the one at the bottom of Figure 11. The effect of adding a medium-chain alcohol on the phase behavior of a ternary mixture H20-oil-nonionic amphiphile is in many respects similar to that of adding a lyotropic salt (E). Lyotropic salts dissolve mainly in the aqueous phase, and "salt out" nonionic amphiphiles,14 thereby driving the alcohol out of the aqueous phase into the oil-rich phase. As a consequence, the (lower) critical temperature TBof the (upper) (A + E)-C loop drops, whereas the oil becomes effectively less hydrophobic. Both effects make T drop (Figure 7 in ref 1). If they are represented in phase tetrahedra as in Figure 11 with salt (E) instead of alcohol (D), one finds the same phase sequence. As one adds salt to a
(z),
(14) Firman.
1985, 1, 718.
P.;Haase, D.;Jen, J.; Kahlweit, M.;Strey. R. Longmulr
Kahlweit et al.
5352 The Journal of Physical Chemistry, Vol. 95, No. 13, 1991
--
temary H2D-oi14,E, mixture at TW < TI (bottom of Figure 1l), one again finds the sequence 2 3 2, with a minimum Of at that salt concentration (in the literature frequently referred to as “optimum salinity”) at which the mean composition lies on the isosceles triangle. The same considerations hold for the effect of salt on temary H,D-oil-C,F!,, mixtures with short-chain alcohols as “amphiphiles”, as studied, e.g., by Davis, Scriven, and cow o r k e r ~ . ~Bemuse ~ of the absence of true amphiphiles, one expects in these mixtures only a weak adsorption of the alcohols at the water/oil interface and, therefore, only weakly structured solutions. We finally note that if ionic amphiphiles are applied instead of nonionic, the temperature dependence is reversed: for making u , decrease ~ (at first) upon addition of a medium-chain alcohol (or a lyotropic salt) to mixtures with nonionic amphiphiles, one has to choose Tup < T,whereas with ionic amphiphiles, one has to choose Tcxp> T.I6 Acknowledgment. We are indebted to J. Da Corte, B. Faulhaber, and T. Lieu for their assistance with the experiments, and to D. Luckmann for drawing the figures. Appendix: Effect of Third Component on Mutual Solubility between Two Partially Miscible Liquids Consider the effect of a third component (3) on the mutual solubility between two partially miscible liquids (1) and (2) at bT = bp = 0. The phase rich in (1) will be denoted by ( r ) , the one rich in (2) by (”). Let the compositions be defined by x,=x x3=y x,=l-x-y
so that the chemical potentials are functions of x and y. Chemical equilibrium requires pj
= p l that is
6p;
+ p;,sy’
= &$x)’
&bXr
+ p;,6y‘
= &6x”
+ &,by“ + p;yby“
0 = [(l
+
G:,
(dZAG,/d~2),,dy,=o
(~cc,/~Y),=iy,=O
and, correspondingly, for (”). Multiplying (la) by (1 - xr?, (lb) by x”, and observing that for the binary mixture 0,= 0) 0 = (1 - x’?& x“&
+
we find that addition yields [(l - x’?&;lx+ X”i2,]6Xt = by'' - p;,by’)( 1 - x”)
+ (iiY6yrr- /&,by’)~” (A.2)
(‘4.3)
AG,,, being the Gibbs free energy of mixing. Setting for the distribution coefficient of component (3) between (’) and (”) y”/y’= K thus 6y” = K6y‘
gives for the right side of (A.2) (p’;,6y”- p;,6yf)(l - x’? + (iiy6y”- izy6yf)x”= (KpYy - p i y ) ( 1- xr’)6yr (Kpiy - piY)xr’6yr(A.4)
+
For evaluating the derivatives ply, one starts with the GibbsDuhem relation for the ternary mixture
0 = ( 1 - x - Y)ky + xr2y + YP3y
(A.5)
Considering low y only, Wagner neglected they in parentheses. With pi = pm R T In ai, with the a, denoting the activities, (A.5) then becomes 0 = (1 - x)(d In al/dy) x(d In a2/dy) y(d In a3/dy)
+
+
+
This relation was satisfied by Wagner by setting a2 = a20,=O) exp(-y)
Ay
(A.6)
where A does not depend on y. Then PI^ = ~
=
z y -~13y
= -RT
so that the right side of (A.4) becomes
(KpYy - piy)(l - xr’)6y’ Piy
x’)
where
(A.la) (A.lb)
+ x’cc;,]Sx’
yields for the left side of (A.2) (1 - x”)prlX ~ ‘ ’ $ 2 ~= ( ~ ’ 2 , - prI,)(xrr- x’) = G:,(x”-
a3 =
where
r;, = (dr,/~x)x-,,=o
- x’)&
al = al(y=O) exp(-y)
=6~;
Applied to components (1) and (2), the latter equations read explicitly p;,bX‘
Subtracting from the left side of (A.2)
+ (Kpiy - piY)xr’6y’= (1 - K)RTby’ (A.7)
Combination with (A.3) then yields for the initial slope of the binodal on the side rich in (1) lim (6x/6y)’ = (1 - K)[(G‘,/RT)(x”-
x7l-I
(A.8)
Y’O
For evaluating (bx/6y)”, one multiplies (A.la) by (1 - x?, and (A.lb) by x’. The corresponding calculation then yields for the initial slope of the binodal on the side rich in (2) lim (6x/6y)” = (K-I - l)[(G‘’JRT)(x”
- x’)]-’ (A.9)
Y 10
(IS) !he, e.&, Knickubockcr, B. M.;Paheck, C.V.; Davis, H. T.; Scriven, L. E. J . Phys. Chem. 1982,86, 393. (16) See, e.& Shincda, K.; Kunicda, H. J . Colloid Interface Sei. 1987, 118, 586.
R a S q NO. C6H12, 110-82-7; CgE4, 19327-39-0; C4&, 71-36-3; CgEs, 19327-40-3; c6&,1 1 1-27-3; c&, 1 1 1-87-5; cl&, 112-30-1; C12F&,112-53-8; octane, 1 1 1-65-9.
