J. Phys. Chem. 1985, 89, 163-171 studied in aggregates with a range of experimentally determined dimensions. In most cases, the model provides close quantitative agreement both in magnitude and trend with experimentally determined order parameters. 2. In common with other models, our model provides good agreement with both the NMR relaxation experiments of Cabane” and with the neutron diffraction experiments of Bendedouch et alelaon (roughly) spherical micelles. However, both experiments provide evidence supporting the assumptions inherent in the models, rather than distinguishing between different models based on those assumptions. 3. Defining t / l c as the ratio of the average half-thickness of the chain region to the fully extended chain length, the model suggests for Cll chains that at a free energy cost of less than 0.5kT per chain these aggregates may be formed: bilayers with ? / I c < 0.75, cylinders with ?/I, < 1.00, and spheres with t / I , < 1.25. The chains in any of these aggregates have, on average, more than 80% of the number of gauche bonds that they would have in the random-coil state characteristic of bulk n-alkane. For most of the experimentally observed aggregate dimensions which were examined, the above numbers (0.5kT free energy cost and 20% reduction in number of gauche bonds) represent upper bounds. Those internal bond sequences which contribute substantially to the properties of the chain in a bulk n-alkane environment suffer only modest changes in their probabilities when the chain is incorporated into an aggregate. In an aggregate, the chains exist as “slightly perturbed random coils”. 4. The fully extended chain length, I,, is almost universally used as the radius of the largest possible “spherical micelle”. Our model suggests that this is misleading, because micelles containing 50% more monomers should be only marginally more aspherical than micelles with an average radius equal to I,. Both exist in an equilibrium distribution of shapes, and the model suggests that for both the spherical shape makes a nonnegligible contribution to this equilibrium distribution.
163
5. A unifying idea is introduced: the mean area available per chain in any aggregate. When results for the three aggregate shapes are compared, a close similarity is observed both between the order parameter profiles at the same mean area per chain and between the variations in free energy with mean area per chain. For any proposed aggregate (including irregularly shaped and inverted structures), calculation of the mean area per chain should provide a good measure of the extent of chain straightening required and the free energy penalty incurred when chains are packed into that structure. Note Added in Proof: In an elegant paper, Ben-Shad et al.29 have established an important result for single-chain calculations. They show that minimization of the chain free energy subject to the constraint of constant density in any number of distinct regions in the hydrophobic core leads directly to the condition imposed in eq 3 of paper 1. Ben-Shad et here, i.e. to the term (njajk) al. solve a Dill-Flory type model using this superior statistical mechanical approximation and derive results in semiquantitative agreement with those presented here. Acknowledgment. I am indebted to Professor J. Charvolin for much informative correspondence about his past experiments and for doing the experiment which forms the basis of Figure 3. I am grateful to Olle Soderman and Bernard Cabane for sending me preprints of their papers and to Jacob Israelachvili for his artistic rendition of Figure 16. I have also benefited from discussions and comments from Bernard Cabane, Bertil Halle, Jacob Israelachvili, Roland Kjellander, Stjepan Marcelja, Professor Theo Overbeek, Thomas Zemb, and a most diligent reviewer. During the course of this work, I have been in receipt of a Queen Elizabeth I1 Fellowship. This research was not supported by any military agency. (29) Ben-Shaul, A.; Schleifer, I.; Gelbart, W. M. In “Physics of Amphiphiles: Micelles,Vesicles and Microemulsions”;Degiorgio, V., Corti, M., IUS.; North-Holland: Amsterdam, 1984.
Phase Behavior of Multicomponent Systems Water-Oil-Amphiphile-Electrolyte.
3
M. Kahlweit,* R. Strey, and D. Haase Max-Planck-Institut fuer biophysikalische Chemie, 0 - 3 4 0 0 Goettingen, West Germany (Received: April 12, 1984; In Final Form: July 24, 1984)
In the two preceding papers of this series we studied the phase behavior of ternary systems of the type H20-oil-nonionic surfactant and of quaternary systems of the type H20-oil-nonionic surfactant-inorganic electrolyte. We showed that in applying inorganic electrolytes one has to distinguish between lyotropic salts, Le., salts which decrease the mutual solubility between H 2 0 and surfactant, and hydrotropic salts, which increase the mutual solubility. This difference leads to a qualitatively different phase behavior of the two types of the above quaternary systems. In part 2 we presented the influence of lyotropic salts, in particular of NaCl, on the phase behavior. In this third paper we compare the influence of hydrotropic salts, in particular of NaC104 and (C6HS).,PC1, which are not surface active, with that of NaDS as an ionic detergent. We find the influence of both types of salts on the phase behavior of the ternary system H20-oil-nonionic surfactant to be quite similar, which is of importance for the further discussion of the microstructure of so-called microemulsions. Finally, we suggest discussing the phase behavior of multicomponent systems of the type. H20-nonpolar liquids-nonionic surfactants-hydrotropic salts-lyotropic salts in terms of a pseudoquaternary phase tetrahedron. This leads to a transparent interpretation of the phase behavior of such systems on the basis of that of “simple” systems as treated in parts 1 and 2.
I. Introduction In section I1 of this paper we discuss the influence of the hydrotropic NaC104 on the phase behavior of ternary systems of the type H 2 0 (A)-oil (B)-nonionic surfactant (C). In section I11 we discuss the phase behavior of quaternary systems in a pseudoternary phase prism. In section V we compare the effect of ionic detergents with that of hydrotropic salts which are not surface active. In section VI we show that the effect of adding an electrolyte is equivalent to that of adding a second nonionic surfactant C’. In section VII, finally, we discuss the phase behavior 0022-3654/85/2089-0163$01.50/0
of multicomponent systems in a pseudoquaternary phase tetrahedron by placing pure H20 (A) in one comer of the basic triangle A-B-C, all nonpolar liquids as an oil (B) of effective hydrophobicity in the second corner, all nonionic surfactants and hydrotropic salts as an amphiphile (C) of effective hydrophilicity in the third corner, and all lyotropic salts (E) on top of the tetrahedron. 11. NaCIO4 as Hydrotropic Electrolyte
In the second paper of this series2 we showed that with respect 0 1985 American Chemical Society
Kahlweit et al.
164 The Journal of Physical Chemistry, Vol. 89, No. I , 1985 C, Ej
100 I
t 0
I
-
20
LO
Salt /H,O 1/99
60 wt %
80
H2O
1 100 CLE,
-
n-Octane-C,E, -Salt
H,O-
I LO c 3 ["Cl
A
Oil
Hydrotropic Salt
H20 - Cyclohexane
2 NaCIO,
- C,E2 - NaCIO,
(42OC)
500
I
400 t [PSI -0
0
1
2
3
L
w t % Salt
1
300
Figure 1. Above: Influence of a lyotropic (NaCl) and a hydrotropic (NaC104) salt on the mutual solubility between H 2 0 and C4E1 in a pseudobinary representation. Below: Influence of NaCl and NaC104 on the three-phase interval (shaded) of the system H20-octane-C4El (1 /
200
1/1).
100
to the influence of electrolytes on the phase behavior of quaternary systems H 2 0 (A)-oil (B)-nonionic surfactant (C)-electrolyte (E) one has to distinguish between lyotropic and hydrotropic salts (see section I11 in ref 2): lyotropic salts like NaCl decrease the mutual solubility between H 2 0 and nonionic surfactants, whereas hydrotropic salts like NaC104 increase it. This difference is demonstrated in Figure 1, the upper part of which shows the influence of NaCl (empty points) and of NaC104 (triangles) on the upper miscibility gap between H20-n-C4El (full points). This result can be expressed as follows: the addition of a lyotropic salt is equivalent to a decrease of the effective hydrophilicity of the nonionic surfactant, whereas the addition of a hydrotropic salt is equivalent to an increase. Accordingly, the addition of lyotropic salts lowers the threephase interval (3PI) of a ternary system A-B-C temperaturewise, whereas the addition of hydrotropic salts raises it, as demonstrated in the lower part of Figure 1, which shows the onsets of the threephase cusps of the system H20-n-octane-C4El-E with NaCl and NaC104 as E. As further difference one observes that with NaCl the width of the 3PI widens with increasing salt concentration, whereas with NaC104 it narrows. It was further shown in ref 2 that, with increasing concentration of a lyotropic salt (at constant temperature), the 3PI appears at c1 at the lower critical tie line PQ (Figure 8 in ref 2) by separation of the lower phase into an aqueous and a surfactant phase. With further increasing salt concentration, the surfactant phase moves clockwise around the central miscibility gap to merge with the oil phase at c,, at the upper critical tie line RS. With a hydrotropic salt, however, one observes the reverse: the 3PT appears at c1 by separation of the upper phase into an oil and a surfactant phase (see schematic representation in Figure 2). With further increasing salt concentration, the surfactant phase moves counterclockwise to merge with the aqueous phase at c,,. Accordingly, with hydrotropic salts, RS is the lower and PQ the upper critical (1) Kahlweit, M.; Lessner, E.; Strey, R. J. Phys. Chem. 1983, 87, 5032. (2) Kahlweit, M.; Lessner, E.; Strey, R. J. Phys. Chem. 1984, 88, 1937.
0 0
0.1
-
0.2
0.3
wt OO/ NaCIO, Figure 2. Above: Evolution of the three-phase triangle with increasing concentration of a hydrotropic salt at constant temperature above Tu (schematic). Below: M curve for the system H20-cyclohexaneC4E2-NaC104 with increasing salt concentration at 42 OC.
tie line. The change of shape of the 3PT (see triangle at top of Figure 2) is thus the reverse of that with a lyotropic salt (see Figure 9 in ref 2). This difference can be readily understood on the basis of Figure 7 in ref 2, which shows the phase diagrams of the ternary systems A-B-C, A-C-E, and B-C-E for H 2 0 (A), octane (B), C4E1 (C), and NaC104 (E) at 25 OC, i.e., just above Tu. Above Tu, plait point cpg of the central miscibility gap in the A-B-C triangle lies on the water-rich side. Accordingly, the tie lines decline toward the H 2 0 corner. The A-C-E triangle shows plait point cp, at a rather high salt concentration, whereas the B-C-E triangle shows an additional plait point cp,' at a rather low salt concentration. Consequently, as one increases the salt concentration (at constant temperature), the three-phase triangle emerges from the collision of the descending critical line cp,' with the central gap at R on the oil-rich side. This can again be demonstrated by means of dynamic light scattering measurements. For experimental details see section IV in ref 1. Again we chose the system H20-cyclohexane-C4E2, which shows a narrow 3PI between 39.1 and 40.4 OC. In ref 1 we presented the change of the correlation time constant T in the ternary system with rising temperature. The 3PT appeared at T1 by separation of the lower phase and disappeared at Tu by merging of the two upper phases. In ref 2 we presented the change of 7 in the quaternary system with increasing concentration of the lyotropic NaCl at 25 "C, Le., below T1. Again the 3PT appeared (at cl) by separation of the lower phase and disappeared (at c,) by merging of the two upper phases.
The Journal of Physical Chemistry, Vol. 89, No. I , 1985 165
Phase Behavior of Multicomponent Systems
H20
-
Oil
-
CLE3
I
P
50
a
T
t
1 b
3 [“I
t
L
0 H2O
Phase Volume
TP
40
OI
20
if
10
0
111. Pseudoternary Representation of Quaternary Systems For the further discussion of quaternary systems it appears convenient to recall the phase prism of a ternary system A-B-C which shows a 3PI at zero salt concentration, and of such a system which does not. Figure 3 shows the prism for the second type of system at constant (atmospheric) pressure with temperature as ordinate. It shows a connected critical line which starts at the upper critical point of the (lower) miscibility gap of the binary system oil-surfactant and ascends into the prism on the oil-rich side of the central miscibility gap. With rising temperature, the influence of the lower B-C gap becomes weaker, whereas that of the upper loop of the H,O-surfactant gap becomes increasingly stronger, irrespective of whether the loop does actually show up on the A-C-T plane of the prism or just “lurks” behind it (as, e.g., with C,E, or C4E2). Accordingly, the critical line winds itself around the central gap to ascend further on the water-rich side. If the loop shows up on the A-C-T plane of the prism, the critical line terminates in the lower critical point of that loop. If the loop is only lurking behind the plane (as assumed in Figure 3), the critical line ascends further to terminate in the upper critical point of the H20-oil system. Accordingly, the declination of the tie lines of the central gap changes with rising temperature: at low temperatures they decline toward the oil corner, whereas at high temperatures they decline toward the H 2 0 corner. The change of the critical line from the oil-rich to the water-rich side can be demonstrated by measuring the phase volume ratio of the two phases. For that purpose one chooses a H20/oil ratio of 1/1 and then adds an appropriate amount of nonionic surfactant. At low temperatures the surfactant dissolves mainly in the aqueous phase; i.e., the phase volume of the lower phase (a) exceeds that
‘0 0
\I
m
7p
Figure 3. Left: Phase prism of a ternary system A-B-C without a three-phase interval with critical line cp. Right: Phase volume ratio vs. temperature (schematic).
Figure 2 shows the results for the corresponding experiment with the hydrotropic NaC104 at 42 OC, Le., above Tu. Again one finds a M-shaped curve, but now it is the upper phase which separates into two phases at cl, at the same time showing strong critical opalescence. With increasing salt concentrations, the surfactant phase (c) moves toward P, where it merges with the lower aqueous phase (a) at c,, both again showing strong critical opalescence. Conceptually, it is like standing in a staircase watching the elevator, i.e., the 3P1, moving down- or upward: if one stands at T < T I ,i.e., below the 3P1, and pulls it downward by adding a lyotropic salt, one first observes the bottom of the elevator, Le., the lower critical tie line PQ, whereas, if one stands at T > Tu, i.e., above the 3P1, and pulls it upward by adding a hydrotropic salt, one first observes the top of the elevator, i.e., the upper critical tie line RS. With rising temperature (at constant salt concentration), on the other hand, both quaternary systems show the same change of shape of the 3PT as the ternary system A-B-C (Figure 6 in ref 1).
P
30
1
[%I
O\
a0
I \
Benzene
\
1 cb
A.
\
0
0
20
40
60
80
100
Phase Volume %
Figure 4. Phase volume ratio vs. temperature for the system H20-oilC4E3with aromatic oils (1.2/1.2/ 1.4).
TL
T
t 0
100
Phase Volume
[%I
0
Interfacial Tension
Figure 5. Left: Phase prism of a ternary system A-B-C with a threephase interval: cp,, ascending critical line; cpB,descending critical line; a-c, loci of the aqueous, surfactant, and oil phases, respectively. Center: Phase volume ratio vs. temperature. Right: Interfacial tension a/c and c/b vs. temperature (schematic).
of the upper phase (b). At high temperature, on the other hand, the surfactant dissolves mainly in the oil phase; i.e., the phase volume of the upper phase exceeds that of the lower one. The phase volume ratio thus shows a sigmoidal curve, if plotted vs. temperature, the inflection point of which indicates that temperature at which the influence of the upper A-C loop overcomes that of the lower B-C gap. As an example, Figure 4 shows the phase volume ratios for H20, C4E3(which does not show an upper loop at 1 bar), and some aromatic oils. As one can see, the inflection point rises with increasing hydrophobicity of the oil as a consequence of the rising upper critical temperature of the oil-surfactant gap. The critical line around the central gap can be looked at as an elastic spring: as one increases its bending tension by increasing the hydrophobicity of either the oil or the surfactant, the spring eventually breaks at a “tricritical point”. With further increasing hydrophobicity of either oil or surfactant the end points of each part of the critical line mcve gradually toward their corresponding side of the central gap, that of the ascending cp, toward the oil-rich side, that of the descending cp8 toward the water-rich side. This break of the connected critical line gives rise to the appearance of threephase triangles within the central miscibility gap as shown
166 The Journal of Physical Chemistry, Vol. 89, No. 1, 1985
Kahlweit et al. extend increasingly deeper into the central gap. Consequently, the compition of the intersection U of the projections of the lower and upper critical tie lines of the 3PI (see Figure 11 in ref 2) moves from the surface of the central gap gradually into its interior. As a consequence, the exact determination of the boundaries of such a cusp is rather time-consuming. We, therefore, restricted ourselves to an approximate determination as described in section VI in ref 2.
T
I
0
-
Salt
Figure 6. Three-phase cusp (shaded) for a quaternary system with a 3PI at zero salt concentration (schematical).
schematically in Figure 5. While with a connected critical line the surfactant is transferred continuously from the aqueous phase to the oil-rich phase as one raises the temperature, in a system with a broken critical line this is done by means of the three-phase triangle, the surfactant phase of which moves like a “ferry” from the end point of cp8 to that of cp, with rising temperature. Accordingly, if one measures the phase volumes in such a system, one finds the well-known diagrams first published by Shinoda and co-~orkers,~ as also shown schematically in Figure 5, as well as the dependnce of the interfacial tension between the corresponding phases on temperature. On the basis of Figures 3 and 5 one may now discuss the dependence of the position and width of the 3PI as function of an added electrolyte (see Figure 1) in a pseudoternary representation: The addition of a lyotropic salt is equivalent to decreasing the hydrophilicity of the surfactant. Due to the uneven distribution of the salt between the phases this lowers the end point of cps (CJ more than that of cp, (c,,). Accordingly, the 3PI is lowered and widened both temperature- and saltwise. The addition of a hydrotropic salt, on the other hand, is equivalent to increasing the hydrophilicity of the surfactant. This raises the end point of cp8 (c,,) more than that of cp, (q).Accordingly, the 3PI is raised and narrowed. By adding a sufficient amount of an appropriate hydrotropic salt, one should thus be able to make the 3PI disappear at the tricritical point at which the end points of the two critical lines collide. If the 3PI of the ternary system is sufficiently narrow at zero salt concentration, this can be achieved even with inorganic hydrotropic salts as NaC104 as it will be shown el~ewhere.~With systems with a wide 3PI at zero salt ooncentration, one has to apply more efficient hydrotropic electrolytes like, e.g., ionic detergents (see section V). IV. cusps In section VI1 of ref 2 we suggested representing the region of the existence of three-phase triangles in quaternary systems with lyotropic salts by a cusp. In view of the effect of hydrotropic salts we now have to complete Figure 18 in ref 2 by adding the cusp for hydrotropic electrolytes. Figure 6 shows the cusp schematically for a system with a 3PI a zero salt concentration. The lower cusp is that for lyotropic salts, and the upper one is that for hydrotropic salts. Figure 1 is thus simply a section of Figure 6 at low salt concentrations. For reasons of clarity, let us recall the physical meaning of such a cusp: The shaded area between its boundaries defines that temperature and salt concentration range in which one can find a 3PT somewhere (!) within the central miscibility gap of the quaternary system. At the tricritical point, Le., at the tip of the cusp, the 3PTs degenerate to a point on the surface of that central gap. As one proceeds from the tip into the interior of the cusp by changing both temperature and salt concentration, the 3PTs (3) Saito, H.; Shinoda, K. J. Colloid Interface Sci. 1970, 32, 647. (4) Kahlweit, M.;Strey, R. manuscript in preparation.
V. Ionic Detergents as Hydrotropic Electrolytes We shall now show that ionic detergents can be looked at as very efficient hydrotropic electrolyte^.^ We are aware that such detergents form micelles in aqueous solutions above their cmc and that these micelles can solubilize a Iimited number of oil molecules. We are furthermore aware that ionic detergents form mixed micelles with nonionic surfactants and that they give rise to highly viscous mesophases at high concentrations which may extend deep into the tetrahedra. We thus cannot exclude the possibility that the microstructure of quaternary solutions with an ionic detergent as fourth component differs from that of a solution with an inorganic hydrotropic electrolyte. With respect to the phase behavior, however, the influence of such a detergent is equivalent to that of a very efficient hydrotropic salt. First, we recall that ionic detergents increase the mutual solubility between H 2 0 and nonionic surfactants, as inorganic hydrotropic electrolytes do. Many examples can be found, e.g., in a review article by Ekwall.6 Since, however, most of the ternary phase diagrams were determined at one temperature only, we thought it informative to demonstrate how the entire upper loop of the binary system H20-nonionic surfactant shrinks as one adds an ionic detergent. As an example we chose the system H20n-C4&-NaDS, a combination which has been applied frequently in studies of pentanary systems. The binary system H20-C4Eo shows a rather wide loop with an UCT at about 126 OC7 (full line in Figure 7). We have then measured the change of the loop boundaries with increasing NaDS concentration. Figure 7 shows the results in a pseudobinary representation in which NaDS and C4Eoare combined into one amphiphilic compound. The loops shown in the upper part of Figure 7 thus correspond to different NaDS/C4Eo ratios. Consequently, the planes of the loops are not parallel to the H20-C4E$ plane of the prism (except for the loop with zero NaDS concentration) but tilted toward the H 2 0 edge. The lower part of Figure 7 shows the ternary phase diagram at 25 “C. The upper part of the triangle shows the multiphase region including anisotropic planes which was not investigated in detail (see for comparison Figure 5 in ref 6). As one can see, the loop shrinks with increasing NaDS concentration to completely disappear at about 3 wt % NaDS at a bicritical point near 30 “C. Adding a hydrotropic salt thus has a similar effect as increasing the pressure. For comparison see, e.g., Figure 5 in ref 8, which shows the effect of pressure on the loop of the binary system H20-C4E1. Accordingly, the addition of an ionic detergent raises the 3PI of a ternary system temperaturewise. In order to compare the efficiency of NaDS with that of NaC104, we again chose the system H20-n-octane-C4El. Figure 1 shows the effect of NaC104, and Figure 8 that of NaDS. While NaC104 is too weak a hydrotropic salt to reach the tricritical point in this particular system, the more efficient NaDS does it readily. The lower part of Figure 8 shows the intersections U of the projections of the lower and upper critical tie lines at the corresponding temperatures. At Tu = 23.5 OC, the upper critical tie line RS of the ternary system is identical with the lower critical tie line of the quaternary system. As one adds NaDS, the upper phase splits, and surfactant phase moves counterclockwise to merge with the aqueous phase at P of the upper critical tie line PQ (see Figure 2). The intersection U ( 5 ) Lawrence, A. S. C. In “Proceedings of the 2nd International Liquid Crystal Conference, 1968”; Brown, G. H., Ed.; Gordan and Breach: London, 1969; Vol. I, p 1. (6) Ekwall, P. Ado. Liq. Cryst. 1975, 1 , 1. (7) “Landolt-BomsteinTables”; Springer-Verlag: West Berlin, 1962; Vol. II/2b, pp 3-406.
The Journal of Physical Chemistry, Vol. 89, No. 1, 1985 167
Phase Behavior of Multicomponent Systems 140
1
HzO- n-Octane - C,E,
- NaDS
I
9 ["CI Lo
0' 0
I
I
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01
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I
0.4
0.5
wt % NaDS
0 H20
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40
60
-wt%
80
100 NaDS/ n-C,Eo
NaDS n-Octane
HP
Figure 8. Above: Three-phase cusp for the system H20-octaneC4El-NaDS. Below: Projections of the intersections of the lower and upper critical tie lines at the corresponding temperatures. The projection of the tricritical point is practically identical with the intersection at 30.8 "C. Full line: miscibility gap of the ternary system at 25 OC. 100
80 -3 I"C1
I" Figure 7. Above: Influence of NaDS on the mutual solubility between H 2 0and n-C413, in a pseudobinary representation. The parameters refer to the concentration of NaDS in the NaDS/C413, solution. Below: Ternary phase diagram at 25 "C; ( 0 )boundary of the two-phase region; (0)boundary of the multiphase region.
LO
of the projections of these two tie lines lies close to the center line of the basis. As one raises the temperature and, accordingly, increases the NaDS concentration, U moves toward the surface of the central gap to reach it at the tricritical point (3 1.O O C ; H20: 24.4; C4E1: 38.3; NaDS: 0.43 wt 76) at about "one o'clock". The full line in the triangle shows the boundary of the central gap of the system without NaDS at 25 OC. This demonstrates how much the central gap shrinks after adding 0.4 wt % NaDS only.
0
VI. Mixtures of Two Nonionic Surfactants The effective hydrophilicity of a nonionic surfactant can be changed, of course,not only by adding a lyotropic or a hydrotropic electrolyte, but also by adding a more or less hydrophilic second nonionic surfactant. Figure 9 shows again the upper miscibility gap between H 2 0 and C4E1 (full points), as it is changed by addition of the less hydrophilic n-C4Eo(triangles) and the more hydrophilic n-C4E2(squares). In this pseudobinary representation we again combined the two surfactants into one amphiphilic compound of an effective hydrophilicity. Accordingly, the planes of the upper and lower loop are again tilted toward the H 2 0 edge as in Figure 8. One may now discuss the influence of the second nonionic surfactant (C') on the phase behavior of the ternary system A-B-C
2o1, m 0
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t
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30 20 10 0' 0
I
1
I
2
I
3
L
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Figure 9. Above: Influence of the less hydrophilic (n-C4Eo) and of the more hydrophilic (C4&) on the mutual solubility between H 2 0 and C4E, in a pseudobinary representation. Below: Influence of n-C4Eo and of C4E2 on the three-phase interval (shaded) of the system H20-octaneC4E1 ( l / l / l ) *
in a phase tetrahedron at constant temperature by placing C' on the top of the tetrahedron (which of the two surfactants is chosen
Kahlweit et al.
168 The Journal of Physical Chemistry, Vol. 89, No. 1, 1985
as C and which as C’ is a matter of convenience) or in a pseudoternary representation in a phase prism with temperature as ordinate as described in section I11 with the two surfactants combined into one of an effective hydrophilicity. Both representations are equivalent. However, in view of the fact that we are proceeding toward the discussion of pentanary (or rather “quinquienary”) systems of the type H 2 0 (A)-oil (B)-nonionic surfactant (C)-ionic detergent (D)-inorganic lyotropic electrolyte (E), we suggest applying the pseudoternary representation of quaternary systems. The lower part of Figure 9 shows the onsets of the cusps for the system H20-octane-C
