Correlation Between Interfacial Tension and Microemulsion Structure in Winsor Equilibria. Role of the Surfactant Film Curvature Properties

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Col l oi ds and Surf aces, 19 (1986) 159-170Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands 159

CORRELATION BETWEEN INTERFACIAL TENSION ANDMICROEMULSION STRUCTURE IN WINSOR EQUILIBRIA.ROLE OF THE SURFACTANT FILM CURVATURE PROPERTIES

D. LANGEVIN, D. GUEST and J. MEUNIERLabor at oi re de Spectr oscopi c Hert zi enne de l%.N.S., 24, rue Lhomond, 75231Par i s Cedex 05 (France)(Received 15 October 1985; accepted 16 January 1986)

ABSTRACTWe present here a correlation between measured interfacial tensions, dispersion sizes

and surfactant film curvature properties in two model multiphase microemulsion systems.This correlation was performed with the help of recent microemulsion theories. Thecharacteristic dispersion size L is found to be close to the spontaneous radius of curvatureof the film when Ro is small, and to the persistence length of the film when Ro is larger(bicontinuous microemulsions). Interfacial tensions correlate only approximately withkT/L' . It is proposed that this occurs because film curvature contributions are dominantin two-phase systems. The situation is less clear in three-phase systems.

INTRODUCTION

Microemulsions are dispersions of oil and water prepared with surfactants[l] Unlike emulsions, they are thermodynamically stable, because thecharacteristic size of the dispersion is very small, -100 A. It has been-showntheoretically by Ruckenstein and Chi [2] that thermodynamic stabilityarises from the fact that the surface energy, which is equal to the product ofthe interfacial tension, yaw and the total area between oil and water, can becompensated by the dispersion entropy, when yaw is sufficiently small:typically yaw 5 10m2 dyn cm- . Such ultralow interfacial tensions arecommonly obtained by using a cosurfactant which is usually an alcohol.Note that typical interfacial tensions between oil and water without sur-factant are about rtw - 50 dyn cm- .Depending on the spontaneous curvature of the surfactant film whichcovers oil-water interfaces, the structure of the dispersion may be, as foremulsions, of the oil-in-water type (O/W: oil droplets in a water-continuousphase) or of the water-in-oil type (W/O: water droplets in an oil phase). Anevolution from the first type to the second can be obtained, for instance, byvarying the temperature with non-ionic surfactants or the salinity with ionicsurfactants. If a cosurfactant is used inversion may also be obtained bychanging the amount of cosurfactant in the layer.0166-6622/86/ 03.50 o 1986 Elsevier Science Publishers B.V.


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In this paper, we will restrict the discussion to ionic surfactants andpresent studies of two model systems where the curvature properties of thesurfactant layers are different. We will present data at variable salinity (fixedamount of cosurfactant in the layers).

At low water salinity (S) one obtains an O/W microemulsion which cancoexist with excess oil. In such a case the radius of the droplets has almostreached the spontaneous radius of curvature: the droplets cannot accom-modate more oil without a large increase in curvature energy and the excessoil is rejected in an excess phase [3]. The interfacial tension between themicroemulsion (M) and the excess phase is very small, 70M N


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taken a study of model systems with different surfactants: one which formsmicelles in pure water and one which forms lamellar phases. According tothe theory of de Gennes and Taupin, the elastic curvature modulus must behigher for the surfactant film-forming lamellar phases in water [8]. Con-sequently, the characteristic dispersion size L in the second system should behigher and the tensions lower.

In the following, we will briefly recall the existing theories of inter-facialtensions. We will then present the data obtained on the model systems andcompare them with the theories.THEORETICAL BACKGROUND

Structural models

The Talmon-Prager-de Gennes-Widom model can be used to describedroplet dispersions and bicontinuous structures as well. In the simplest versiongiven by de Gennes, the microemulsion volume is divided into consecutivecubes of linear size l randomly filled with either oil or water. The interface be-tween cubes of different types is covered by a surfactant film, the volume ofwhich is neglected.If $o and & are the oil and water volume fractions, the average total areabetween oil and water per cube is 6 @o Gw t2 and the corresponding surfaceenergy is 6 @O 4~ t YOW . The entropy of dispersion per cube is k (ti e In Go+ Gw In rjw ). The statistic of the interface is thus reduced to a lattice-gasmodel. When

a single-phase microemulsion is thermodynamically stable. With t - 100 A,it follows that: yaw 2 10m2 dyn cm- .The area per surfactant molecule, z1, is generally reasonably constantwhatever the spontaneous curvature may be. It follows then that t is deter-mined when the total number of surfactant molecules ns is given. The totalarea is given by ns C, and with Cs = ns /V, where V is the total volume, wehave:

A similar expression holds for the average size of the polygons in the Talmon-Prager model: & = 5.82 $. +w /Cs C. In the limit of isolated oil or waterdroplets of radius R. or Rw one would have:

340R. = -CSC (24


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If the spontaneous radius of curvature is large and K small, the thermalfluctuations of the interface might become the dominant effect in deter-mining the characteristic size of the dispersion. This has been predicted byde Gennes and Taupin [8]. This size will be determined by the persistencelength of the interface gk: at scales smaller than ,$k the interface is essen-tially flat, whereas at scales larger than $k it is strongly wrinkled. gK isrelated to the elastic modulus of curvature by:tK = a exp (27rK/kT) (5)where a is the molecular length.Inter-facial tension between a microemulsion and an excess phase

Most existing calculations apply to microemulsions containingdroplets of radius R. spherical

Israelachvili [18] provides a simple description of the nature of the con-tributing terms. Let us call pN the chemical potential of the surfactantmolecule in an aggregate of N molecules:PN

& + E lnXhN Nwhere &, is a standard chemical potential containing the interaction termsbetween the surfactant molecules in the droplet; XN is the surfactant con-centration fraction present in the droplet.The interface between the microemulsion and the excess phase is coveredby a surfactant layer which can be considered as an infinite aggregate. Thisaggregate is subjected to a tension. The surfactant chemical potential istherefore:Ps = Pm --yc = &-rcThe interfacial tension is finally obtained by putting pN equal to ps :

(f-3)The first term, Ye, is an entropic contribution arising from mixing. It is

analogous to the expression derived by Ruckenstein on a different thermo-dynamical basis [ 191.The second term yC, is a curvature contribution, which has been calcu-lated explicitly by other authors [ 20-221. With:


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and

these calculations are equivalent to:Yc = R 0 (7)

The orders of magnitude of the two terms are the same: NC = 47rR*,R - R. and K - kT, thus yc - 7e - kT/R* . It can be seen that the tensiondepends ultimately on the droplet radius, although it does not change whenthe microemulsion is replaced by its continuous phase, i.e. as the dropletsare removed [4]. In fact both y and R are determined by the properties ofthe surfactant layer and it is not surprising to find a relation between them.Equation (6) does not contain any contribution from interaction betweendifferent droplets. This contribution is expected to be negligible as soon asone is sufficiently far from a critical point. This is certainly the case when yis equal to yaw , which does not contain any interaction term.When the microemulsion is bicontinuous, it is not so easy to calculate itsinterfacial tension with an excess phase. The curvature energy is small (smallK, large R,) and comparable to the dispersion entropy. A calculation hasbeen performed recently by Borzi et al. [23] : the separation between cur-vature and entropy contributions is less straightforward than in Eqn. (6).However, it may be expected that the curvature contributions will be small[they sould tend to zero according to Eqn. (7)] and that the entropy con-tributions will be dominant, although the curvature term in the free energyis needed to obtain the three-phase equilibria [9].EXPERIMENTAL PROCEDURE

Sample composition

We will now discuss the results obtained with two model systems. Thefirst is a mixture of brine (37 wt%), toluene (37 wt%), butanol (4 wt%) andsodium dodecyl sulfate (SDS, 2wt%). The brine is an aqueous solution ofSwt% sodium chloride. The salinity was varied between 3.5 and 10. Thesalinities of phase separation have been found to be S1 = 5.4 and S2 = 7.4 at20C.The second model system is a mixture of brine (56.83 wt%), dodecane(38.19wt%), butanol (3.32wt%) and sodium hexadecylbenzenesulfonate(SHBS or Texas No. 1, 1.66wt%). This composition corresponds to equiv-alent volumes of oil and brine. The brine is an aqueous solution of S wt%sodium chloride. The salinity was varied between 0.4 and 0.9. The salinitiesof phase separation have been found to be S, = 0.52 and S2 = 0.61 at 20C.


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Experimental techniquesInter-facial tensions have been measured using surface light scattering

experiments. The frequency broadening of the scattered light was measuredwith a wave analyzer after photon beating detection. The width of thespectrum is directly proportional to y [24].The characteristic sizes in microemulsion phases were measured with elas-tic and quasi-elastic bulk light scattering techniques in the two-phase regionswhere the microemulsion structure is that of droplets dispersed in a con-tinuous phase [ 14, 251.In the three-phase region, dilution is not possible. The characteristiclength in the dispersion has been deduced from X-ray and neutron experi-ments [ 11-131.Ellipsometry experiments have been performed to investigate the elas-ticity properties of the surfactant layer: in the three-phase domain, theinterfaces between excess phases have been studied; and in the two-phasedomain the interfaces between the excess phase and the microemulsion con-tinuous phase have been studied. All these interfaces show the same features:they exhibit ultralow tensions yaw [4, 141, and the phases in equilibriacontain no microstructures. The ellipsometry signal is then dominatedby the roughness of the interface due to thermal motion. The measuredellipticity is in this case [26] :

e. and +, are the dielectric constants of the two phases, and X is the wave-length of the light.EXPERIMENTAL DATA AND DISCUSSION

Sizes in microemulsion phasesThe normalized sizes LC,C/6, with L = 2R for droplets and L = t inmiddle phases, are plotted in Fig. 1, together with the theoretical pre-dictions for spheres (Eqn. (2), lines) and bicontinuous structures (Eqn.(l), parabola).It is seen that in the two-phase region, sizes L vary as r ~~or w, as pre-dicted by Eqn. (2). In the three-phase region there is a remarkable continuity

between droplets radii and characteristic size [. [ varies as tie @I~, as pre-dicted by Eqn. (1). It was observed that the [ values were unexpectedly con-stant over the three-phase domain. The surfactant concentration C, and thearea per surfactant C are also constant, which occurs because the productGo&, is approximately constant. This result is strongly in favor of the


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Fig. 1. Characteristic length in the microemulsion phases LC,c/G versus oil volumefraction ,. SDS system: (0) light scattering data [9] ; (a) X-ray data [20] ; x) neutrondata [ 221. SHBS system: (0) light scattering data [19] ; (A) X-ray data [21]. Lines cor-responds to Eqn. (3) with L = 2R, the parabola to Eqn. (2) with L = gK.

existence of bicontinuous structures, and demonstrates that droplet struc-tures are unlikely.A large difference between the L values for the two systems is oberved. In

the three-phase region, assuming [ N {x (Eqn. (5)], the difference between gvalues should be associated with larger elastic moduli in SHBS films than inSDS ones. This happens although the SHBS films contain more alcohol thanthe SDS ones: respectively three and one alcohol molecules per molecule ofsurfactant. This confirms that pure SHBS films are much more rigid thanpure SDS ones, thus favoring the formation of lamellar phases in water asobserved [ 271.In the two-phase region, the droplet radius is close to the spontaneousradius of curvature R, . For the SDS system the difference between R andR is of the order of 10% in the O/W microemulsions and 20-30% in theW/O microemulsions as obtained with Eqn. (4) and K values deduced fromellipsometry data (Table 1). For the SHBS system, K has not yet been


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10 4L0.2 0.3 0.4 05 0.6 Cl,-Fig. 2. Interfacial tensions versus salinity for SHBS system, and SDS system (insert).

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The agreement between the calculated values of yC and y is better for theW/O microemulsions. The difference between R and R, becomes significanthere (20-30%) and has been taken into account.CONCLUSION

We have performed a detailed study of multiphase microemulsion modelsystem where successively an O/W microemulsion coexists with excess oil, amiddle phase microemulsion coexists with excess oil and water and a W Omicroemulsion coexists with excess water. The surfactants were SDS and apure alkylbenzenesulfonate, SHBS.The interfacial tensions between the microemulsion and the excess phases,as measured with surface light scattering methods, are ultralow, with theSHBS system being even lower.The sizes of the droplets were obtained in the O/W and in the W/O micro-emulsions using bulk light scattering methods. They are very close to the


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Correlation Between Interfacial Tension and Microemulsion Structure in Winsor Equilibria. Role of the Surfactant Film Curvature Properties