J. Phys. Chem. 1984,88, 1937-1944
1937
FEATURE ARTICLE Phase Behavior of Quaternary Systems of the Type H,O-Oil-Nonionic Surf actant- Inorganic Electrolyte. 2 M. Kahlweit,* E. Lessner, and R. Strey Max- Planck-Institut fuer biophysikalische Chemie, 0 - 3 4 0 0 Goettingen, West Germany (Received: September 23, 1983: In Final Form: December 30, 1983)
In the first paper of this series we discussed the phase behavior of ternary systems of the type H20-oil-surfactant in a phase prism with temperature as ordinate. In this second part we extend these studies to quaternary systems with an inorganic electrolyte as a fourth component. After demonstrating the difference between electrolyteswhich decrease the mutual solubility between H 2 0 and surfactant (lyotropic salts) and those which increase it (hydrotropic salts), we restrict the studies to the influence of lyotropic salts, in particular NaCl. The phase behavior is discussed in a phase tetrahedron at constant temperature. It is shown that the phase behavior of the quaternary system is analogous to that of the ternary system, the miscibility gap on the H20-surfactant4ectrolyte plane of the tetrahedron playing the role of the upper loop on the H20surfactant-temperature plane of the prism. It is shown that the more hydrophilic the surfactant-with given oil-the more salt has to be added to achieve a three-phase triangle (3PT) at a certain temperature. The region of existence of the 3PTs in a temperature-salt concentration diagram has the shape of a cusp which terminates in a tricritical point. The position of the cusp as function of the nature of the oil and the surfactant is determined for open paraffins from octane to hexadecane as oils andd C,E, and C,E, as surfactants. The diagrams permit one to choose the appropriate surfactant in order to achieve a 3PT, if temperature, oil, and brine concentration are given. Furthermore they permit one to predict the position of the tricritical points in such systems. In the third paper of this series we shall discuss the influence of hydrotropic salts and the phase behavior of pentanary systems.
1. Introduction In the first paper of this series’ dealing with ternary systems of the type H 2 0 (A)-oil (B)-nonionic surfactant (C) we have shown how the phase diagrams of such systems change with temperature and how the formation of a three-phase triangle (3PT) arises from this change. These studies have led us to two sufficient conditions for the appearance of a 3PT: (i) the binary system A-C must show an upper miscibility gap with a lower consolute boundary terminating in a lower critical point cpa; (ii) at that temperature at which the endpoint of the critical line cpa touches the central gap A-B on the water-rich side, the plait point of the latter must lie on the oil-rich side. In this paper we shall extend these studies to quaternary systems of the type H 2 0 (A)-oil (B)-nonionic surfactant (C)-inorganic electrolyte (E). It is well-known2that such quaternary systems may show a 3PT within a certain salt concentration range which varies with temperature (see Figure 19 in ref 1). It has also been recognized3v4 that their phase behavior is quite analogous to that of pentanary systems with an ionic surfactant as the fifth component. We shall show that this phase behavior can be readily explained on the basis of the theory presented in ref 1 for ternary systems. As surfactants we have again used short alkyl polyglycol ethers C,E, ( i = 2, ..., 4; j = 1, ..., 3) including short chain alcohols (j = 0), in order to avoid anisotropic phases. Available information on the phase behavior of typical “detergents” indicates, however, that the short and the longer chain homologues share similar (1) Kahlweit, M.; Lessner, E.;Strey, R. J . Phys. Chem. 1983, 87, 5032. (2) Lang, J. C.; Widom, B. Physicu A 1975, 81, 190. (3) Herrmann, C.-U.; Klar, G.; Kahlweit, M. J . Colloid Interface Sci.
qualitative features that are governed by the same forcesa5 For experimental details see ref 1. 11. The Phase Tetrahedron We shall represent the phase diagrams of a quaternary system in a tetrahedron at a fixed temperature. Again, the appropriate procedure to discuss the phase behavior of the system within this tetrahedron is to first consider the phase diagrams of the corresponding four ternary systems. Figure 1 shows schematically the unfolded tetrahedron. Let us first consider the central diagram of the ternary system A-B-C. We recall that its phase behavior was discussed in ref 1 in a prism with the Gibbs triangle A-B-C as basis and temperature as ordinate. In Figure 2 we have reproduced the c-T diagram of such a system (see Figure 2 in ref l ) , which shows on the left-hand side the phase diagram vs. temperature on a plane perpendicular to the A-B-C basis. The position of the plane is defined by the ascending critical line cp, of gap B-C on the right, and by the descending critical line cpa of the (upper) gap A-C on the left, assuming for simplicity both these critical lines including their endpoints to lie in the same plane (which is in general not the case). The 3PT appears as a lower critical tie line at T, and disappears as an upper critical tie line at Tu.The A-B-C triangles on the right-hand side of Figure 2 show the phase diagrams of the ternary system at the corresponding temperature. If one now proceeds to the quaternary system, one may move its tetrahedron A-B-C-E within this prism up- or downward like an elevator. The position of the A-B-C basis of the tetrahedron on the T ordinate then defines the temperature at which the phase behavior of the quaternary system is discussed. Accordingly, the basis of the tetrahedron may be located below, within, or above
1981, 82, 6.
(4) Knickerbocker, B. M.; Pesheck, C. V.; Scriven, L. E.; Davis, H. T. J . Phys. Chem. 1979,83, 1984.
0022-3654/84/2088-1937$01.50/0
( 5 ) See, e.g.: Lang, J. C. In “Surfactants in Solution” (Lund), Mittal, K. L., Ed.; Plenum: New York, 1983; Vol. 1 .
0 1984 American Chemical Society
Kahlweit et al.
1938 The Journal of Physical Chemistry, Vol. 88, No. 10, 1984
NaCIO, HO ,
NaCl
A
A
/
C,E,
C$
H,O
cPp
CL Ei
Figure 3. Phase diagrams of the ternary systems H20-C4EI-NaCI (left) and H20-C4E,-NaC104 (right) at 25, 48, and 75 “C.
The effect of an added electrolyte on the mutual solubility
I
the three-phase (temperature) interval of the ternary system. Consequently, the central triangle in Figure 1 may look like either one of the diagrams on the right-hand side of Figure 2: if one chooses a temperature below TI,one finds a gap with only one plait point (cp,) lying on the oil-rich side. If one chooses a temperature between T, and Tu,one finds a gap with a 3PT and two plait points, one (cp,) lying on the oil-rich side, the other one (cpa) lying on the water-rich side. If, finally, one chooses a temperature above Tu,one finds a gap without a 3PT and only one plait point (cpa), now lying on the water-rich side. From this it follows that the phase behavior of a quaternary system depends crucially on the temperature at which it is studied. Let us consider, for example, two rather similar systems, namely, H20-n-octane-C4El and H20-n-dodecane-C4El, If, however, one studies the influence of NaCl on their phase behavior at 25 “C, one finds an apparently different behavior. With octane the ternary system is above its Tu ( 2 2 4 “C, see Figure 15), whereas with dodecane it is below its TI (-32 “C). Accordingly, with n-octane the A-B-C basis of the tetrahedron will look like the upper one in Figure 2, whereas with dodecane it will look like the lower one. As a consequence, with octane the addition of NaCl leads to the formation of a connected gap A-B - A-C, whereas with dodecane it leads to the formation of a 3PT (see Figure 17). Let us now consider the lower triangle A-B-E in Figure 1: The miscibilitv gaD A-B extends, of course, into the A-B-E diagram. On the k--gand B-E sides one finds homogeneous soluti&s up to the solubility of E in the corresponding solutions. Since the solubility of E in A is much higher than in B, the tie lines in the two-phase region between these homogeneous phases decline
I
C104- salts show in some respects a similar effect on the phase behavior of quaternary systems. One thus has to distinguish between two classes of inorganic electrolytes: (i) “lyotropic” salts which decrease the mutual solubility between H 2 0 and surfactant, for example, C1-; (ii) “hydrotropic” salts which increase the mutual solubility between H 2 0 and surfactant, for example, C104-. In order to illustrate the above distinction, Figure 3 shows the phase diagrams of the ternary systems H20-C4E,-E with NaCl and NaC104, respectively, as electrolyte at 25, 48, and 75 “C. At 25 “C, the addition of both salts leads to a phase separation. With NaCl (Figure 3, left), however, a rather small amount of salt suffices, whereas with NaC104 (Figure 3, right) the phases separate only at very high salt concentrations. The binary system HZO-C4E1shows a closed loop with a LCT Ta = 48 “C. Accordingly, as one raises the temperature, the two-phase region with NaCl grows toward the A-C side until its plait point cp, merges with the (lower) critical point cpa of the binary system A-C at 48 “C. With NaC104, on the other hand, the two-phase region remains at high salt concentrations, while the binary system starts to separate at cpa at 48 “C. At 75 “C, the two-phase region with NaCl extends from the A-C side up to the 3PT, thus showing a phase diagram similar to that of the A-B-E system (lower triangle in Figure 1 ) . The ( 6 ) Hofmeister, F. Arch. Exp. Pathol. Pharmakol. 1888, 24, 247. (7) Luck, W. A. P. Top. Curr. Chem. 1976, 64, 113, 130. (8) McBain, J. W. “Colloid Science”; Heath Boston, 1950; p 131 ff. (9) Neuberg, C. Biochem. Z . 1916, 76, 107.
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The Journal of Physical Chemistry, Vol. 88, No. 10, 1984 1939
Feature Article
100
I
I
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20 -
0‘ 0
1
1
1
2
I
3
I
1
L
5
w % Salt
Figure 4. Apparent lowering of the lower critical temperature T, of the
binary system H20-C4EI by NaCl and NaC104. Figure 6. Change of the phase diagram of the ternary system oil-surfactant-electrolyte with temperature (schematic).
n- C,Eo
t-C,Eo
/
‘
:
200 0
Figure 5 shows the results of our measurements on the two systems H20-n-C3Eo-NaC1 H20-t-C,Eo-NaC1
2
L
-
6
a
10
12
g NaCI/100g H,O
Figure 5. Phase separation in the binary systems HzO-n-C3Eo and Hz0-t-C4Eoby NaCl vs. temperature.
system with NaC104, on the other hand, now shows two two-phase regions: one a t high salt concentrations and one along the A-C side with another plait point, extending only slightly into the triangle. Thus, with NaCl the two-phase region along the A-C side widens with increasing salt concentration, whereas with NaC104 it narrows, which reflects the different influence of a lyotropic and a hydrotropic salt on the mutual solubility between A and C. Furthermore, one can deduce from the phase diagrams with NaC104 that this salt changes its nature gradually with respect to its influence on the mutual solubility between A and C as one increases its concentration: at low concentrations it acts as a hydrotropic salt to gradually change into a lyotropic salt which then, at high concentrations, enforces a phase separation. As we shall show in the third paper of this series, this change in nature has important consequences for the phase behavior of quaternary systems with C104- salts. With respect to the upper miscibility gap between H 2 0 and surfactants, the addition of a lyotropic salt will, accordingly, widen this gap which reflects itself in an apparent lowering of its LCT TB,whereas the addition of a hydrotropic salt will narrow the gap and thus apparently raise T p This effect is demonstrated in Figure 4, which shows the apparent change of TBof the binary system H20C4EI with the addition of NaCl and NaC104. As expected, C1- lowers Ta, whereas C104- raises Ta. In H,O-surfactant systems which do not show an (upper) miscibility gap at atmospheric pressure, the application of an appropriate lyotropic salt may lead to the appearance of such gap, the position of which depends on the nature of both the surfactant and the salt. This effect has been studied first by Timmermanslo and more recently by Schneider and co-workers.” The latter authors, in particular, showed that with KCl the gap between H 2 0 and n-C3Eo appears a t about 50 ‘C and widens rather symmetrically with increasing salt concentration. They further found that an increase in pressure has the opposite effect, namely, an increase of the mutual solubility. (10) Timmermans, J. “Les solutions concentrEe”; Masson: Paris, 1936. (1 1 ) Schneider, G.; Russo, C. Eer. Eunsenges. Phys. Chem. 1966,70,1008.
at 70 wt. % H 2 0 (+ NaCl), to be compared with Figure 2 in ref 11. With n-CsEo, the gap appears at about 45 OC and about 9.2 g of NaC1/100 g of H 2 0 , the demixing curve having the shape of a parabola. With the less hydrophilic t-C4b,on the other hand, the vertex of the parabola appears to lie well above 100 O C . In that respect the NaCl curve in Figure 4 can be looked at as the lower branch of a parabola, the vertex of which lies at a “negative” salt concentration (or high pressure). The effect of inorganic electrolytes on the mutual solubility between oil and surfactant is less well studied. It appears to depend mainly on the solubility of the electrolyte in water: Figure 6 shows schematically the change of the phase diagram in the B-C-E triangle with temperature. At temperatures below the UCT T, of the (lower) binary gap B-C, the triangle A-B-C shows a connected gap A-B-B-C (see Figure 1 in ref 1). This gap extends, of course, into the B-C-E triangle (a) which, consequently, in this temperature range shows a phase diagram similar to the A-B-E diagram in Figure 1. At T = T, both two-phase regions disconnect from the B-C side of‘ the tetrahedron (b). At a temperature somewhat above T,, triangle A-B-C shows a single gap with plait point cp, still lying on the oil-rich side, whereas the B-C-E triangle shows a two-phase region with plait point cp,‘ pointing, of course, also toward the B-C side (c). Between this two-phase region and the E corner one finds a 3PT with solid E as third phase, flanked by two two-phase regions with solid E as second phase. The liquid two-phase region in the B-C-E triangle shrinks rather rapidly with further rising temperature until it disappears, as does cp,‘ and the 3PT (d). From then on the phase diagram B-C-E shows a solubility curve declining from C to B. If the temperature T, at which the two-phase region disappears lies above Tu of the three-phase (temperature) interval of the ternary system A-B-C (see ref l), one finds a phase diagram as shown in the upper part of Figure 7 , Le., with plait point cp, of the central gap already lying on the water-rich side. If, however, the temperature lies below Ti, one finds a diagram as shown schematically in Figure 1, i.e., with plait point cp, of the central gap still lying on the oil-rich side. Intuitively, one expects T , to be the higher the more soluble the electrolyte in the surfactant. The solubility of E, on the other hand, decreases from water to surfactant to oil. Accordingly, one expects, for a given surfactant, T, to be higher the more soluble the electrolyte in water, and, for a given salt, the higher T,, Le., the more hydrophilic the surfactant. For the rather well-soluble CaC12, for example, being of considerable relevance in tertiary oil recovery, T, lies below 25 ‘C in the system n-octane-C4E,-E, but above 25 OC with the more hydrophilic C4E2. In Figure 7 , finally, we have summarized the relevant differences between NaC1, LiC1, and NaC10,. It shows the phase
1940 The Journal of Physical Chemistry, Vol. 88, No. 10, 1984 C,E.
NaCl
Kahlweit et al.
NaCl
011 Figure 8. Three-phase triangle within the phase tetrahedron (schematic). The critical line cp, descends from plait point cp, on the H20-CiEpalt plane, whereas the critical line cp, ascends from plait point cp, on the H,O
n-Octane
Figure 7. Phase diagrams of the systems HzO-n-octane-C4El-E with NaCl (top), LiCl (center), and NaC1O4.H20(bottom) at 25 OC (omitting the A-B-E diagrams).
diagrams A-B-C, A-C-E, and B-C-E for the systems H20-noctane-C4El-E at 25 OC, omitting the triangle A-B-E which should look similar for all three salts. The upper diagram shows the situation for NaCl, that in the center that for LiC1, and the lower one that for NaC104. NaCl and LiCl are both lyotropic salts. They both decrease the mutual solubility between H 2 0 and C4E1and, therefore, enforce a phase separation which gives rise to the appearance of a plait point cp,. NaC104, on the other hand, is a hydrotropic salt. It increases the mutual solubility between H,O and C4El. At very high salt concentrations, however, it too enforces a phase separation. Thus, with respect to the ternary system A-C-E, lyotropic and hydrotropic salts differ mainly in the position of plait point cp,: for lyotropic salts it is located close to the A-C side, whereas with hydrotropic salts it is located close to the E corner. With respect to the ternary diagram B-C-E, one finds a similarity between LiCl and NaC104. While NaCl dose not lead to a phase separation between oil and surfactant, the other two more soluble salts do, giving rise to the appearance of another plait point CP,'. The two sufficient (!) conditions for the appearance of a 3PT in the ternary system A-B-C, suggested in ref 1 and repeated in the Introduction, may now be extended to the quaternary system A-B-C-E as follows: (i) at least one of the ternary systems A-C-E or B-C-E must show a lower plait point cp, (or cp,'), (ii) at that salt concentration at which the critical line cpc (or cp,') touches the central gap A-B-C, the plait point of the latter must lie on the opposite side of that gap.
IV. The Influence of Lyotropic Salts In this paper we shall discuss the influence of lyotropic salts on the phase diagram of the quaternary system, in particular, NaCl as the most relevant electrolyte in practice. In the third paper of this series we shall consider the influence of hydrotropic salts as well as that of ionic surfactants. In Figure 1 we have assumed a temperature between T , and TI. Accordingly, plait point cp, of the central gap A-B is still lying on the oil-rich side of the tetrahedron, whereas plait point cp,' has disappeared. We claim that in such a quaternary system the 3PT appears at that salt concentration cIat which the critical line cpt, descending from the A-C-E plane into the tetrahedron, touches the central gap A-B. The corresponding lower critical tie line PQ of the latter, however, is now tilted with respect to the A-B-C basis due to the uneven distribution of the salt between the two phases. This situation is shown schematically in Figure
H,O-oil-C,E, basis: PQ, lower critical tie line; RS, upper critical tie line; PS, locus of the aqueous phase; PR, locus of the surfactant phase; QR, locus of the oil phase with increasing salt concentration.
H,O
C,H,
Figure 9. Change of shape of the projections of the three-phase triangles with increasing salt concentration for the system H20-C6H6-C2E,,(NH4)zS0,at 21 'C (after ref 2).
8, to be compared with Figure 5 in ref 1.12 With further increasing salt concentration the aqueous phase again moves counterclockwise toward S, whereas the surfactant phase moves clockwise toward R, as does the oil phase, but counterclockwise. The 3PT disappears at that salt concentration c,,, at which the surfactant and the oil phase merge at the endpoint R of the critical line cpa, which ascends into the tetrahedron. Since the distribution coefficient of the salt will be mainly determined by the water content of the corresponding phases, the line SPRQ descends monotonically from S to Q, in contrast to the corresponding curve in a ternary system (Figure 5 in ref l), which shows a minimum at P and a maximum at R. Accordingly, in the quaternary system both the tie lines and the three-phase triangles are tilted with respect to the A-B-C basis. Insofar the phase behavior of the quaternary system is quite analogous to that in the ternary system, the 3PT appears at the endpoint of a critical line (cp, instead of cps) and disappears at the endpoint of cp,. If the solubility of the salt is reached before the 3PT disappears, the system will show four condensed phases with solid E as fourth phase. In order to determine the shape and position of the 3PTs as function of the salt concentration, one has to measure the concentration of at least three of the components in each phase. Since this is rather time consuming, we have not attempted such an experiment. Instead, we refer to the beautiful paper by Lang and (12) When comparing Figure 8 with figures in ref 2, note the inverted symmetry of the tetrahedra.
7'he Journal of Physical Chemistry, Vol. 88, No. 10, 1984 1941
Feature Article
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~J
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l
l
1
c, E,
I
A '
~
H2O Oil Figure 11. Projections of the lower (PQ) and the upper (RS) critical tie lines from the E corner onto the A - B C basis of the tetrahedron. Choice of mean concentrations of the A-B-C system for determining the lower, c,(V), and upper, c,(W), salt concentration (see text). HO , 100
- Octane - CE,, -
NaCl
1
T
0
2
-
4
6
8
10
NaCI I w % l
Figure 12. Width of the three-phase salt intervals cl-cI for the system
H20-n-octane-C,E2-NaC1 vs. temperature. when comparing different systems. For that purpose one chooses a surfactant concentration in the upper half of the center line of the A-B-C triangle and increases the salt concentration until the 3PT appears. Then one adds either further surfactant or equal masses of H 2 0 and oil, keeping the phase volume ratio between phases (a) and (c) equal to unity, until phases (a) and (c) merge, which yields the lower salt concentration cI at V. The corresponding procedure is then repeated with a somewhat lower surfactant concentration in order to determine the upper salt concentration c, a t W, now keeping the phase volume ratio between (c) and (b) equal to unity and adding salt until phases (c) and (b) merge. In the first experiment both phases (a) and (c) will show an increasing light scattering as one approaches the end point of cp,, whereas in the second experiment phases (c) and (b) will do so, as one approaches the endpoint of cp,. This can be easily followed by observing a laser beam passing through the corresponding phases. Figure 12 shows the result of such an experiment on the system HzO-n-octane-C4E2-NaC1. The ternary system shows a 3PI between 68 and 95 OC. As was to be expected, the lower the temperature, the more salt has to be added to obtain a 3PT. Furthermore, the three-phase (salt) interval widens with decreasing temperature. At 25 OC,finally, the 3PI extends up to the saturation concentration of NaCl, so that above 10.4 wt % NaCl one observes four condensed phases with solid salt as fourth phase. If compared with the corresponding experiment on the system H2~6H6-C,E,-(NH,)zS04 as performed by Lang and Widom2 (see Figure 19 in ref l), one notices a qualitative discrepancy: in Figure 12 the cI and the c, curves flatten with increasing salt concentration, Le., decreasing temperature, whereas in Figure 19 in ref 1, the curves appear to steepen. The reason for this difference is not clear but is possibly due to the difference between the two salts, of which (",),SO4 is much more lyotropic. We shall now turn to the comparison between different quaternary systems with respect to the influence of the nature of the surfactant and the oil on cI and c.,
Kahlweit et al.
1942 The Journal of Physical Chemistry, Vol. 88, No. 10, 1984
100
f Figure 13. Phase diagrams of the ternary systems H,O-CiE,-NaC1 with C,Eo, n-C3Eo,and r-C,Eo at 25 OC.
t-C, E,
:: 40 20
0
n-C,Eo
Hexa- Tetradecane decane
Dodecane Decane Octane
Cyclohexane
Toluene
Figure 15. Three-phase temperature intervals of the ternary systems
HzO-oil-C4E, with the toluene, cyclohexane, and the paraffins from n-octane to n-hexadecane (see also Figure 15 in ref 1). I
I t
t (A! - - - - - - - - c12
.
I
7, [h 1
cl,
A
:I I ,r , ,f= - c,,
lCO 2o
I&
-..__. ,
0
0
-
IO 20 30 g NaCI/ 1009 H20
Figure 14. Width of three-phasesalt intervals (full bars) for C4Eo and &Eo with the paraffins from n-octane ( C , ) to hexadecane (C,& vs temperature. Data from ref 4 at 25 OC (broken bars).
With respect to the surfactants it appears appropriate to distinguish between systems which do not show 3PTs without salt and those which do. Let us first consider the first type of systems. Figure 13 shows the phase diagrams of the ternary system H20-C,E,-NaC1 with C2E0,n-C3Eo,and t-C4Eo at 25 "C. The hydrophilicity of these surfactants decreases in the same order, and none of them shows a 3PT without salt between 5 and 90 OC except t-C4Eo with dodecane. As one can see, Cl- is too weak to salt out C2&, for which reason Lang and WidomZhad to apply the stronger SOP. With the other two less hydrophilic surfactants, however, C1- suffices. As was to be expected, the more hydrophobic the surfactant, the lower the salt concentration at the plait point cp,. Accordingly, these three surfactants (including i-C3&) should be the simplest possible surfactants to obtain 3PTs with oils and C1-, provided the plait point cp, of the ternary system A-B-C faces the B-C side at the corresponding temperature. Figure 14 shows the three-phase (salt) intervals as function of temperature for n-C3Eo and t-C4Eo with open paraffins from n-octane to n-hexadecane. As one can see, the results suggest representing the figures by a two-dimensional cusp which terminates in a tricritical point. In accord with our predictions, the position of the cusp is higher the more hydrophobic the oil and the more hydrophilic the surfactant. And the more hydrophilic the surfactant-with a given oil-the more NaCl has to be added to achieve a 3PT at a certain temperature. Furthermore, the shape of the cusps reflects the "parabola" of the A-C-E system shown in Figure 5: with n-C3Eo it shows a vertex at about 45 OC-at least with the more hydrophobic oils-whereas with t-C4E0the cusp appears to have a vertex well above 100 OC. One thus finds again that the properties of the phase diagrams of the four ternary systems can be traced deep into the tetrahedron. We note that for i-C3Eothe corresponding
figures look similar to those for n-C3Eo,only shifted to a slightly lower temperature and a slightly higher salt concentration. Similar experiments have been performed by the group of Davis and S ~ r i v e n . ~These , ' ~ authors prepared mixtures of equal volumes of HzO, paraffins, and short-chain alcohols and then determined c, and c, at 25 OC with different lyotropic salts, among them NaCl and LiCl. Due to the different densities of the liquids the mean compositions of their mixtures were on the water-rich side of the center line of the triangle (see Figure 11). Furthermore, since the surfactant concentration was kept constant, the mean composition did, most probably, not correspond to either the lower or upper critical tie line. In spite of this, their results (broken bars) are in good agreement with ours. Figure 14 also shows how the position of the tricritical point changes with the nature of the oil and the surfactant, and how both should be chosen in order to shift the tricritical point to an experimentally easily accessible position. The only easily accessible tricritical point in Figure 14 is that in the system H20-n-decane-t-C4Eo-NaC1. In approaching it we have verified critical opalescence in all three phases at a temperature of 31.8 OC and a composition of 10.66 wt % n-decane, 52.48 wt % t-C4E0,and 0.1 14 wt % NaC1. Due to the similarity of the refractive indices at this point of the phase diagram, this system shows only moderate opalescence which makes it particularly interesting for light scattering studies close to a tricritical point. In this context it should be emphasized that with rising temperature, i.e., with narrowing salt interval, the area covered by the 3PTs within the body of heterogeneous phases shrinks and moves toward the surfactant-rich part of the body.I3 This is nicely demonstrated in Figure 9-1 1 in ref 2. (See also Figure 19 in ref 1). Accordingly, the intersection U (see Figure 11) moves with rising temperature toward the surfactant-rich part of the miscibility gap on the A-B-C basis and may even cross the center line. Thus, if one chooses a mean concentration with a too low surfactant fraction (see Figure 9), one may miss the_
