Macro- and Microemulsions - ACS Publications - American Chemical

8 Phase Diagrams and InteractionsinOil-Rich Microemulsions D. ROUX and A. M. BELLOCQ

Downloaded by UNIV OF PITTSBURGH on May 3, 2015 | http://pubs.acs.org Publication Date: March 27, 1985 | doi: 10.1021/bk-1985-0272.ch008

Centre de Recherche Paul Pascal, Domaine Universitaire, 33405 Talence Cedex, France

Pseudoternary phase diagrams of the water-dodecane-SDS-pentanol and water-dodecane-SDS-hexanol systems have been investigated in detail. A great variety of new domains has been evidenced in the o i l rich part of these diagrams including, one-, two-, three- and four-phase liquid regions. An interpretation of these diagrams i s proposed : it is shown that interactions between water domains play an important role in microemulsion stability.

In several t h e o r e t i c a l models of microemulsion s t a b i l i t y (1-4), the free energy includes an entropie term mainly due to dispersion of water and o i l domains and two types of enthalpic contributions : a term of i n t e r f a c i a l tension and terms of interaction between domains of same nature (water-water or o i l - o i l ) . These interactions r e s u l t from coulombic and Van der Waals forces. Recently i t has been shown that a balance between entropy and i n t e r f a c i a l tension could also interpret phase t r a n s i t i o n (5-6). However these models only generate two-phase e q u i l i b r i a i n d i s t i n c t i o n to the experiments which show the existence of multiphase e q u i l i b r i a . In order to find three-phase e q u i l i b r i a where a microemulsion coexist with a nearly pure water phase and a nearly pure o i l phase, Talmon and Prager have taken into account curvature e f f e c t s . They found a three-phase region but they had to assuraea very special form for the curvature energy. In a recent publication De Gennes et a l . (6) suggest that the curvature term i s not s u f f i c i e n t to reproduce three-phase e q u i l i b r i a and conclude that more complex effects involving strong a t t r a c t i v e interactions are r e quested to explain the three-phase e q u i l i b r i a . But up to now, i n teraction terms are neglected i n the models proposed by Talmon and Prager and De Gennes et a l . Several structural studies have shown that i n the o i l r i c h part of the phase diagram, microemulsions consist of a dispersion of monodisperse water droplets i n interaction (7-8). In recent papers (9-10), we have investigated by l i g h t scattering the effect of the micellar

0097-6156/85/0272-0105$06.00/0 © 1985 American Chemical Society

In Macro- and Microemulsions; Shah, D.; ACS Symposium Series; American Chemical Society: Washington, DC, 1985.


106

MACRO- AND MICROEMULSIONS

size and of the molecular structure of the components on the i n t e r micellar interactions. Our results evidence that interactions are depending on the size of the droplets and on the length of alcohol, the molecular volume of oil and the polar head area of the surfactant. However, it is shown that one of the most important molecular parame ter is the alcohol chain length. The intermicellar interactions are a l l the more a t t r a c t i v e as the alcohol is shorter. When interactions become strongly a t t r a c t i v e a c r i t i c a l behavior is evidenced (11). Then f o r example in the series of systems : water-dodecane-SDS-pentanol or hexanol or heptanol a c r i t i c a l behavior is only observed with pentanol. I t appears therefore of p a r t i c u l a r interest to investigate the phase diagrams of the water-dodecane-SDS-pentanol (A) and waterdodecane-SDS-hexanol (B) systems. One of the main objectives of this paper is to examine the im portance of the interactions between water in oil micelles on the s t a b i l i t y of oil r i c h microemulsions. For t h i s purpose, we have in vestigated the phase diagrams of the systems A and Β made with pen tanol and hexanol. We examine not only the micellar one-phase region but also the polyphasic regions around it. This study allows us to locate c r i t i c a l points in system A and also to evidence in both sys tems a great v a r i e t y of new domains including one-, two-, three- and four-phase regions. In the f i r s t part of this paper, we describe in d e t a i l several pseudoternary diagrams. In the second part, we show that a model of droplets in interaction allows us to interpret the existence of a l i n e of c r i t i c a l points in the oil r i c h region of sys tem A (12) . Experimental s t u d y ; phase diagrams of the water-dodecane-pentanol (or hexanol)-sodium dodecyl sulfate (SDS) systems The phase diagrams of quaternary mixtures have to be represented in a three dimensional space. I t is useful to present pseudoternary sec tions of this diagram. The W/S representation (which keeps constant the water over surfactant r a t i o ) gives a good description of the oil r i c h side of the phase diagram. In figure 1 are shown the experimen t a l pseudoternary phase diagrams obtained with hexanol and pentanol. In a f i r s t step, the W/S volumic r a t i o has been fixed at 1.8. This value corresponds to the microemulsions previously studied by l i g h t scattering (9-10). Both diagrams present a great variety of one-, two- or three-phase domains. The sequence of phases observed along the paths AA and BB is described. The variable along AA is the alcohol concentration. The path BB follows the demixing l i n e . Two points can be noticed : i ) Both systems exhibit similar phase diagrams; s p e c i a l l y two one-phase regions are observed below the demixing l i n e which bounds the microemulsion region : in region I I the microemulsions are biréfringent and in region I I I , which is poor in alcohol, microemulsions are i s o t r o p i c . i i ) The main difference between the two diagrams is the existence, in the case of pentanol, of a c r i t i c a l point (P ) and of two l i q u i d - l i q u i d i s o t r o p i c regions V and XII around P . These l a t t e r are separated by the three-phase region XI where the three microemulsion phases in equilibrium are i s o t r o p i c . Near P , the two phases in equilibrium have very close compositions. The LL region V is separated 1

f

1

1

c

c

c


8.

107

Oil-Rich Microemulsions

ROUX A N D BELLOCQ


HEXANOL

DODECANE

Β ΒΘ 0ΒI Βϋ *

4

m

n

m

m

m

WATER/SOS : 1,8

η

VJ

ι

DODECANE

'ΘΟΒΙΟΒΒΙΒΟ*" m 6

m

w

β

θ

VI

Χ

a

m

τ

ν

Θg

g

7

HI

H

E

m

Τ

Β-

Figure 1 . W/S = 1.8 pseudoternary diagrams at Τ = 21.5°C (expressed in volume) of the : a) water-dodecane-SDS-hexanol system b) water-dodecane-SDS-pentanol system. The dark regions correspond to l i q u i d biréfringent phases.



108

M A C R O - A N D MICROEMULSIONS

from the two-phase l i q u i d - l i q u i d biréfringent region VI by a narrow three-phase zone X. In these e q u i l i b r i a the middle phase is biréfringent and the two others are i s o t r o p i c . The four regions Χ, V, XI and XIII do not exist in the phase diagram with hexanol. An enlarged drawing of the oil r i c h part of the pentanol diagram is given in f i gure 3c. For each system several pseudoternary diagrams corresponding to different values of the W/S r a t i o have been investigated. In the hexanol system, small changes of the phase diagram are observed as the W/S r a t i o is varied between 1.8 to 5. (figure 2). The effect of an increase of t h i s W/S r a t i o is the s h i f t of the isotropic one-phase region (I) towards the high alcohol concentrations. But q u a l i t a t i v e l y the phase diagram remains unchanged. In the three pseudoternary phase diagrams studied one can notice that there is no c r i t i c a l point. In a l l the cases, the inverted micellar domain is bounded by a two-phase region where t h i s isotropic phase is in equilibrium with either the lamellar phase (II) or the other isotropic phase ( I I I ) . In this sys tem one does not observe a region where two inverted micellar phases are in equilibrium. We emphasize that in this system which does not present a c r i t i c a l point in the oil r i c h region, the micellar phase located along BB separateswith an organized biréfringent phase. On the contrary, in the pentanol system which presents a c r i t i c a l point, the system separates in the L-L region XII around P into two i s o t r o pic microemulsions in equilibrium. This remark seems to be general. Indeed, a c r i t i c a l behavior has been observed in the water-SDS-butanol-toluene system by l i g h t scattering (13). We have observed that the mixtures which are far in composition from the c r i t i c a l point separate with an organized phase whereas those which are close of t h i s point separate into two isotropic phases. In the pentanol system as the W/S r a t i o is changed, a new c r i t i cal point is evidenced; the set of these points constitutes within the three-dimensional phase diagram a l i n e of c r i t i c a l points. One can ask the question to know where are the ends of this l i n e . Several p o s s i b i l i t i e s can be considered : i ) the l i n e crosses the whole d i a gram and goes from one face of the diagram to another one, i i ) the l i n e abuts on a three-phase region either on a c r i t i c a l end point or on a t r i c r i t i c a l point. We have examined in d e t a i l the pseudoternary diagrams defined by the following W/S r a t i o s : 1, 1.2, 1.4, 1.8 and 2.2. The oil r i c h part of some of these diagrams is shown in figures 3a-3d. Analysis of these pseudoternary diagrams allows one to e l i m i nate the f i r s t proposal. Indeed, the pseudoternary diagram defined by W/S = 1 is similar to those observed with hexanol. The zone XII and i t s c r i t i c a l point as well as the zones Χ, V and XI are no longer observed in t h i s plane. Moreover, this study shows that the extent of these regions decreases with the W/S r a t i o . They disappear f o r a W/S r a t i o included between 1 and 1.1. This study allows us to evidence a new one-phase region noticed L* on figures 3. The microemulsions located in t h i s region scatter l i g h t and exhibit a flow birefringence when their oil content is l a r ger than 85 %. In the planes W/S = 1.2 and 1.4 we have also observed a four-phase l i q u i d region : LL*L L where one of the phases is biréfringent (Lg) and the three other ones are isotropic however one of them is flow biréfringent ( L * ) . Three of the four three-phase regions which surround the four-phase region have been observed in the plane 1

c

fi


8. R O U X A N D B E L L O C Q

109


Γ/ο hexanol


W/S =3

90

100

Vo dodecane

Figure 2 . W/S pseudoternary diagrams at Τ = 21,5°C ( i n volume) of the water-dodecane-SDS-hexanol system. L, Lg designate respectively an isotropic phase and a b i réfringent phase.


110


St penUnoi

w

/

$

:

1

13

11 9


7 5

75

80

85

% penUnol

-I

75

90

% dodecane

w

1

80

I

85

/

s

.

w

I

90

% dodecane

F i g u r e 3. W/S p s e u d o t e r n a r y diagrams a t Τ = 21.5 °C ( in volume) o f the water-dodecane-SDS-pentanol system. Top: W/S = 1; bottom: W/S = 1.4. L, L g , and L" d e s i g n a t e r e s p e c t i v e l y an i s o t r o p i c phase, a biréfringent phase and a flow biréfringent l i q u i d phase.


8. ROUX AND BELLOCQ


% pentanol

111


W/S:

1,8

% dodecane



112

it it defined by W/S = 1.2; these e q u i l i b r i a are the following LL L,L LgL and LL Lg. Systematic progression from three phases to four phases to three phases with changing either oil or alcohol concentration is r e ported for the f i r s t time. As the W/S r a t i o increases, the two f o l l o wing e f f e c t s are observed : the disappearance of the four-phase r e gion, and the s h i f t s of the biréfringent (L ) and flow biréfringent (L ) regions towards the water and surfactant r i c h region. Thus the study of several W/S pseudoternary diagrams of system A leads us to observe a great variety of one-phase regions and of phase e q u i l i b r i a . In addition this study allows us to evidence a l i n e of c r i t i c a l points which l i m i t s are within the tetrahedron of represent a t i o n of the states of the system. On the contrary in the system B, any c r i t i c a l point is evidenced as the W/S r a t i o is changed up to 5. The phase behavior observed in the quaternary systems A and Β is also evidenced in ternary systems. Figure 4 shows the phase diagrams for systems made of AOT-water and two d i f f e r e n t o i l s . The phase d i a gram with decane was established by Assih (14) and that with isooctane has been established in our laboratory. At 25°C the isooctane sys tem does not present a c r i t i c a l point and the inverse micellar phase is bounded by a two-phase domain where the inverse micellar phase is in equilibrium with a l i q u i d c r y s t a l l i n e phase, as for system Β or system A when the W/S r a t i o is below 1.1. In the case of decane, a c r i t i c a l point has been evidenced by l i g h t scattering (15). Assih and a l . have observed around the c r i t i c a l point a two-phase region where two microemulsions are in equilibrium. A three-phase equilibrium con nects the l i q u i d c r y s t a l l i n e phase and this l a s t region. In conclusion, the same phase behavior is evidenced when we change the alcohol or the W/S r a t i o in a quaternary system, and the oil in a ternary system. This behavior can be characterized by two types of phase diagrams. In the f i r s t type no c r i t i c a l point occurs. In t h i s case, the inverse micellar phase is bounded by a two-phase region where it is in equilibrium with a l i q u i d c r y s t a l l i n e phase. The second type is characterized by the occurence of a c r i t i c a l point. In t h i s case, the inverse micellar phase is bounded by a region where two m i c e l l a r phases are in equilibrium.


fi

Discussion Some features of these diagrams can be explained with the help of l i g h t scattering r e s u l t s . Indeed existence of a c r i t i c a l point is a l ways related with strong a t t r a c t i v e interactions. Light scattering experiments in inverted m i c e l l a r phase have shown that interactions increase as the alcohol chain length decreases or as the W/S r a t i o increases ( i . e . as the m i c e l l a r size increases). Therefore one can assume that the l i n e of c r i t i c a l points observed in the pentanol sys tem above a l i m i t value of the W/S r a t i o is due to a strengthening of the i n t e r a c t i o n s . At W/S equal to 1.1 interactions between droplets are s u f f i c i e n t to induce a liquid-gas type phase separation. On the same manner, interactions can explain the differences observed in the phase diagrams of the ternary systems containing AOT and water as isooctane is replaced by decane. Indeed it has been shown that in teractions increase with the molecular volume of oil (10). In the following we present a quantitative interpretation of the phase diagram based on a model of i n t e r a c t i n g p a r t i c l e s . We show that



8.

ROUX A N D BELLOCQ


113

Figure 4 . Phase diagrams of the ternary systems. Water, AOT, i s o octane or decane. The phase diagram with decane has been established by Assih et a l .


114



the LL zone XII observed in the diagram of the pentanol system where two microemulsions coexist can be interpreted as a liquid-gas t r a n s i t i o n due to interactions between inverse micelles. The l i q u i d phase has a high micellar concentration and the gas phase has a low concen t r a t i o n of micelles. Using the hard sphere adhesive state equation proposed by Baxter (16), it is possible to calculate the demixing l i n e due to i n t e r a c tions. This state equation corresponds to the exact solution of the Percus-Yevick equation in the case of an hard sphere potential with an i n f i n i t i v e l y thin a t t r a c t i v e square w e l l . In our c a l c u l a t i o n we assum that the range of the p o t e n t i a l is short in comparison to the size of the p a r t i c l e s ( i n fact less than 10 % ) . The Baxter's state equation includes only one parapeter τ which is related to the a t t r a c t i v e i n t e r a c t i o n s . Ρ pkT

with :

λ

=

6

- τ

1 +η + η (1-η)

2

18 (2 +η) - η 36 (1-η)3

Λ

3

71

Λ

2

+

Ι - [( -τ ΐ) -6 6

+

λ

2

2Π* [ΐ - \)]

η is the volumic f r a c t i o n of p a r t i c l e s and ρ the density number. Baxter has shown that below a certain value of τ (τ =T ) a phase separation of liquid-gas type occurs, τ is related to the second v i r i a l c o e f f i c i e n t Β of the osmotic pressure which value can be expe rimentally determined from l i g h t scattering experiments. c

τ-

1 2

8 - Β

In previous papers, the experimental values of Β for several ω/ο microemulsions have been measured. As already pointed out, these values are function of both the radius of the micelles and the a l cohol chain length (9-10). The a t t r a c t i v e interactions between micel les increase as the micellar radius increases and as the alcohol chain length is shorter. We have proposed an i n t e r a c t i o n potential between ω/ο micelles which allows to account for the scattering r e sults (10). This potential V(r) r e s u l t s from the p o s s i b i l i t y of pene t r a t i o n of the micelles. V(r) is proportional to the volume of i n t e r penetration of micelles. The penetration is limited by the molecules of alcohol located inside the i n t e r f a c i a l f i l m , r is the distance between two m i c e l l e s . V(r) kT

r > 2R

=-J V(r) kT

=

+

00

Δρ (2R - r )

2

[2R

+ f)

2R - £ < r < 2R

r < 2R

where R is the radius of micelles and £ is the difference between the lengths of surfactant and alcohol. Δρ is a parameter depending only


8.

ROUX AND BELLOCQ


115

on the oil and surfactant. Its value was determined from l i g h t scat tering experiments (10). In the case gtudied Δρ = O.00071 A" and & = 8.82 A for pentanol and il = 7.56 A for hexanol. For the c a l c u l a t i o n of B, numerical integration is requested 3

2R V(r) kT

24 (2R)3

Β = 8 +

dr 2R-£

Following Barboy (17) the coexistence curve is obtained by nume r i c a l resolution of the two following equations : ΡΟϋ,τ^) = Ρ ( τ , η ) Downloaded by UNIV OF PITTSBURGH on May 3, 2015 | http://pubs.acs.org Publication Date: March 27, 1985 | doi: 10.1021/bk-1985-0272.ch008

2

μίτ,τ^) = μ(τ,η ) 2

where η and η are the micellar volumic fractions of the low and high density micellar phases in equilibrium, μ is the chemical po t e n t i a l , it is related to Ρ by χ

2

8P 3η

3y 3ÏÏ

an a n a l y t i c a l expression f o r μ is where V is the micellar volume given by Barboy (17). The demixing curves in the W/S pseudoternary diagrams for the hexanol and pentanol systems have been calculated according to the above theoretical treatment. These lines have been determined in the following way. The c a l c u l a t i o n of the state equation is applied to a d i l u t i o n l i n e ; along such a l i n e the inverse micelles have a cons tant radius R. The micelles contain the whole water (volume V ) , the surfactant (volume V ) and a part of the alcohol V g . The rest of a l cohol V £ is in the oil continuous phase. We suppose that the alcoholoil r a t i o in the continuous phase is constant and is equal to k. Be sides, in the c a l c u l a t i o n of the micellar radius R one assumes that the surfactant and the alcohol molecules which are situated at the interface have a constant area per chain s. In mosÇ of the previous studies s has been found constant and equal to 25 A . This value is taken equal for the alcohol and surfactant chains. Consequently : q

w

2

3v

( k

k —

V

(V a

ws

+

1 )

(V

ws

- 1) +

+

V

V ™ χ + 1

k

" +

( k

+

1 }

s

ν ν

A

a 3

- v is the molecular volume of surfactant (412 A for SDS) - v is the molecular volume of the alcohol (180 A for pentanol and 209 A f o r hexanol) - k is the r a t i o of the alcohol (V°^) and oil volumes in the oil continuous phase (k = O.133) = V /V = V + V V?A + vA w s A w s A l l the parameters involved in the c a l c u l a t i o n of the phase se paration curve are deduced from experimental values. Application of g

3

a

3

m

V

=




116

this calculation to the W/S = 1.8 plane leads to a calculated demixing l i n e very close to the experimental one in the case of pentanol, p a r t i c u l a r l y in the region XII (figure 5). Besides a c r i t i c a l point P^ is found near the experimental one P^. On the contrary in the case of hexanol the theoretical demixing l i n e is found largely below the experimental one. These results corroborate our hypothesis of liquid-gas t r a n s i t i o n for the region XII of the phase diagram with pentanol where two microemulsions are in equilibrium. In the hexanol system, the phase separation is not due to micellar interactions but results from other factors such as i n t e r f a c i a l tension or curvature and leads to the formation of a lamellar phase. The coexistence curve corresponding to such effects is termed "lamellar" demixing l i n e . In the case of the pentanol system, it exists a competition between these l a s t effects and interactions. This competition gives r i s e to the three-phase e q u i l i b r i a observed in region X. In our model a c r i t i c a l radius R appears; i t s value is 52 A in the pentanol system. Then in each W/S plane a c r i t i c a l d i l u t i o n l i n e corresponding to such a radius is obtained. Its location depends on the W/S r a t i o . As t h i s r a t i o decreases, the c r i t i c a l l i n e l i e s at a lower alcohol content. In the case, where the c r i t i c a l d i l u t i o n l i n e is below the "lamellar" demixing l i n e , the phase diagram is expected to be similar to that observed with the hexanol system for which the interactions are not predominant. This is the case of the pseudoternary sections defined by a W/S r a t i o less than 1.1. Besides t h i s provides an explanation for the simultaneous disappearance of the r e gions X, V, XI, XII. A similar interpretation of phase diagrams has been recently proposed by Safran and Turkevich (18). These authors have considered the effects of interaction and curvature on the s t a b i l i t y of microemulsions. They suggest that u n s t a b i l i t i e s of spherical microemulsion droplets lead the system to separate with water in order to prevent micellar growth above a l i m i t radius R^. Taking into account interactions with a phénoménologie treatment, they show that phase separat i o n due to interaction is also possible and they found a c r i t i c a l radius R . I f R is greater than R^ a water phase is formed and i f R is lower than R^ phase separation gives r i s e to two micellar phases with a c r i t i c a l point. This theoretical treatment r e f l e c t s very well the behavior we observe but it is not in f u l l accordance with our experimental r e s u l t s . The main difference is that when interactions are not preponderant the phase separation does not occur with a water phase but with a lamellar phase. Our theoretical treatment is based on the same physical idea. But in our interpretation the comparison with the experimental behav i o r is quantitative and the c a l c u l a t i o n of the demixing l i n e is based on the experimental dependence of the interactions upon micell a r radius or alcohol chain length. We can notice that calculations made by Safran et a l . lead the authors to suppose interactions increasing with the radius what is experimentally well established. For the water, AOT and decane system, light scattering experiments are in progress in view to apply the proposed interaction pot e n t i a l to ternary systems. As expected the f i r s t results c l e a r l y indicate that interactions increase as the system approaches the c r i t i c a l point. Besides preliminary calculations confirm that a l i q u i d gas type t r a n s i t i o n must occur very close to the experimental demixing l i n e . o

c

c

c


Q


8.

ROUX AND BELLOCQ

117


W/S:1,8

Oil

Figure 5 . Comparison between experimental ( f u l l line) and c a l c u l a ted (dashed line) demixing curves in the oil r i c h region of the hexanol and pentanol systems. PJ=j is the experiment a l c r i t i c a l point. P£ is the theoretical c r i t i c a l point.



118 Conclusion

In conclusion the study of the phase diagram of the two following quaternary mixtures A : H 0 - C H - SDS - pentanol and Β : H 0 C H - SDS - hexanol leads us to observe several one-phase regions in the oil r i c h part of the phase diagram. These one-phase regions are connected the ones to the others by a great variety of multiple coexisting phases e q u i l i b r i a (two, three or four). In the case of the pentanol system, as the W/S r a t i o is greater than 1.1 a l i n e of c r i t i c a l point is evidenced. Light scattering measurements and theoretical treatment strongly support the idea that a t t r a c t i v e interactions between inverse micel les play an important role in the s t a b i l i t y of oil r i c h microemul sions. In the system containing pentanol, attractions between ω/ο micelles can be s u f f i c i e n t to give r i s e to a phase separation between two microemulsion phases. 2

1 2

2 6

2


12

Acknowledgments The authors are grateful to P. BOTHOREL, J . PROST, P. BAROIS, C. COULON, for many stimulating discussions. They wish to thank O. BABAGBETO and M. MAUGEY f o r t h e i r technical assistance.

Literature Cited 1. Ruckenstein, E., and J.C. Chi, J. Chem. Soc. Faraday Trans II, 71, 1960. 2. Miller, C.A., R. Hwan, W.J. Benton, and T. Fort, J. Coll. Int. Sci., 61, 554 (1977). 3. Huh,C.,J. Coll. Int. Sci., 71, 408 (1979). 4. Cantor, R., Macromolecules, 14, 1186 (1981). 5. Talmon, Y., and S. Prager, J. Chem. Phys. 69, 2984 (1978). 6. Jouffroy, J., P. Levinson, and P.G. De Gennes, J. Phys., 43, 1241 (1982). 7. Dvolaitzky, M., M. Guyot, M. Lagues, J.P. Le Pesant, R. Ober, C. Sauterey, and C. Taupin, J. Chem. Phys., 69, 3279 (1978). 8. Cazabat, A.M., D. Langevin, J. Chem. Phys., 74, 3148 (1981). 9. Brunetti, S., D. Roux, A.M. Bellocq, G. Fourche, and P. Bothorel, J. Phys. Chem., 87, 1028 (1983). 10. Roux, D., A.M. Bellocq, and P. Bothorel, Proceedings of the In ternational Symposium on Surfactants in Solution, Ed. by K.L. Mittal and B. Lindman (1984). 11. Fourche, G., A.M. Bellocq, and S. Brunetti, J. Coll. Int. Sci., 28, 302 (1982). 12. Roux, D., A.M. Bellocq, and M.S. Leblanc, Chem. Phys. Lett., 94, 156 (1983). 13. Cazabat, A.M., D. Langevin, and O. Sorba, J. Phys. Lett., L 505 (1982). 14. Assih, T., P. Delord, and F. Larché, Proceedings of the International Symposium on Surfactants in Solution, Ed. by K.L. Mittal and B. Lindman (1983). 15. Huang, J.S., and M.W. Kim, Phys. Rev. Lett., 47, 1462 (1981). 16. Baxter, R.J., J. Chem. Phys., 49, 2770 (1968). 17. Barboy, B., J. Chem. Phys., 61, 3194 (1974). 18. Safran,S.A., and L.A. Turkevich, Phys. Rev. Lett.,50,1930 (1983). RECEIVED June 8, 1984


Macro- and Microemulsions - ACS Publications - American Chemical

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