Properties of surfactant monolayers in relation to microemulsion phase behaviour

Advances in Colloid and Interface Science, 49 (1994) 85-112 Elsevier Science B.V.

85

00191 A

PROPERTIES OF SURFACTANT MONOLAYERS IN RELATION TO MICROEMULSION PHASE BEHAVIOUR

H. KELLAYa, B.P. BINKSb, Y. HENDRIIM”, L.T. LEEd, J. MEUNIER”

aLaboratoire de Physique Statistique de I’ENS, URA 1306 du CNRS, Associe’ aux

Universites Paris VI et VII, 24 rue Lhomond, 75231 Paris Cedex 05, France

bSurfactant Science Group, School of Chemistry, University of Hull, Hull HU6

7RX, U.K.

‘Laboratoire de Physique des Solides, URA 2 du CNRS, Universite’ Paris Sud,

91405 Orsay, France

‘Laboratoire Leon Brillouin, C.E. de Saclay, Laboratoire mixte CEA-CNRS,

91191 Gifl Yvette Cedex, France

CONTENTS

Abstract ......................................... I. Introduction .................................... II. Winsor Behaviour in AOT, Brine, Alkane Mixtures and Determination of

the Structure of Third Phases ........................... a. Heptane to nonane .............................. b. Decane ..................................... C. Undecane to tetradecane ...........................

III. Low Tensions and Bending Elasticities (K) of Monolayers ........... IV. Estimation of K in Winsor II Systems ...................... V. Wetting by Oils of AOT Monolayers at Air-Water Surfaces ........... VI. Conclusions ..................................... VII.References .....................................

85 86

90 92 92 93 96

100 104 109 110

ABSTRACT

The relationship between the properties of surfactant monolayers at oil-water interfaces and the phase behaviour in bulk of mixtures of oil + water + surfactant is discussed. Such monolayer properties include the spontaneous curvature, co, the inter-facial tension, ‘I, the elasticity K (or rigidity) associated with the mean curvature, and the elasticity K associated with the Gaussian curvature. The model system chosen for investigation is the anionic surfactant AOT + aqueous NaCl + n-alkane at 20°C. In such systems, inversion of microemulsion type from oil-in-water (o/w) to water-in-oil (w/o) is possible with increasing electrolyte concentration. The tension, ‘I, passes through an ultralow minimum value at conditions corresponding to the formation of three phases. Using small angle neutron scattering, we have determined the structure of surfactant-rich third phases (co - 0) formed with the different alkanes. Lamellar phases consisting of surfactant monolayers separated alternately by oil and water appear with short alkanes, whereas Ls and

OOOl-8686/94/$26.00 0 1994 - Elsevier Science B.V. All rights reserved. SSDZ OOOl-8686(93)00191-Z

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bicontinuous phases form in systems containing longer alkanes. The bending elasticity K has been measured for planar monolayers at the oil-water interface by ellipsometry. K is independent of salt concentration but depends markedly on alkane chain length N, falling from - 1 kBT for N c 11 to -0.1 kBT for N = 14. This is discussed in terms of the differing extents of oil penetration into the surfactant chains. Higher rigidities favouring lamellar phases and lower rigidities favouring bicontinuous microemulsions are in line with the theoretical predictions of de Gennes and Taupin. Estimates of the constant K have been obtained in droplet microemulsions (w/o) from a knowledge of their size, K and y. The sign of the constant is in agreement with the geometry of the phases formed in three phase systems. Finally, the ideas and concepts developed in the oil-water systems described above are used to explain the wetting behaviour by alkanes of AOT monolayers at the air-water surface.

INTRODUCTION

Microemulsions are thermodynamically stable dispersions of oil and water stabilised by surfactant molecules. For a given set of conditions (e.g. component composition, temperature) microemulsions form well-defined structures. The most common structure is that of droplets, either of oil or water, surrounded by a surfactant monolayer, and dispersed in either water or oil. The phase type depends upon the water/oil ratio. At low ratios one has a water-in-oil droplet microemulsion and at large ratios an oil-in-water droplet microemulsion. A bicontinuous microemulsion is obtained for ratios - 1. The typical size in the microemulsion (i.e. the droplet diameter in droplet microemulsions or the mean distance between two oil or water domains in bicontinuous microemulsions) is [ 11:

(1)

where $, and $, are the volume fractions of oil and water respectively and A is the area of the surfactant film in the unit volume. In many cases one can prescribe the water/oil ratio, but in other cases, when the surfactant concentration is low, the microemulsion appears in equilibrium with an excess of oil (Winsor I equilibrium), or water (Winsor II equilibrium) or water and oil (Winsor III equilibrium). In these cases the oil/water ratio and consequently the nature of the microemulsion phase depend upon the elastic properties of the surfactant film. In particular, they depend upon the spontaneous curvature c, of the monolayer. c, is controlled by steric interactions and electrostatic repulsions for ionic surfactants [2]. Roughly, one can say that if c, >> 0 (i.e. by convention the layer curves towards water) an oil-in-water (o/w) microemulsion forms. If c, CC 0, the monolayer curves towards oil and a water-in-oil (w/o) microemulsion is obtained.

87

When the mean spontaneous curvature c, vanishes a different type of structure is obtained which depends upon the bending elasticity of the surfactant monolayer [3]: lamellar phases, bicontinuous microemulsions and the so-called L, or L,’ phases. Lamellar phases are water and oil layers separated by surfactant monolayers [41. Bicontinuous microemulsions are isotropic phases containing roughly equal amounts of oil and water. The structure is random and sponge-like, continuous in oil and water [5,6], which are separated by surfactant monolayers, a structure observed in pictures obtained by freeze fracture electron microscopy [7]. L, phases are mainly composed of surfactant and water (or oil) and made up of multiconnected surfactant bilayers, eventually swollen by thin films of oil (or water), separating two equivalent domains of water (or oil) [8,9]. This structure is confirmed by freeze fracture electron microscopy [lo]. All three types of surfactant-rich phase are represented schematically in Fig. 1.

One can attribute a bending energy to the inter-facial film of the system. This energy per unit area is written as [ll]

F = + K(cr + c2 - 2cJ2 + K cl c2 (2)

where cl and c2 are the local principal curvatures of thesurfactant layer, K is the mean bending elastic constant (or rigidity) and Kis the Gaussian bending elastic constant. K is a positive constant and K can be positive or negative. The contribution of F to the total free energy of the system is crucial in determining the type and characteristic size of the structure. The rigidity K represents the energy to bend unit area of surface by a unit amount of curvature. The summation of cl c2 on a surface gives a number depending only on the genus of the surface, i.e. the second term in Eqn. (2) affects the topology of the surfactant film and consequently the nature of the phase [9,12].

De Gennes and Taupin [3J have developed a model for bicontinuous microemulsions in the case K=O. For c, = 0, the layer is supposed to be flat in the absence of thermal fluctuations. They introduced the persistence length C& of the layer related to K by:

5K= a exp( 2xK/kBT) (3)

where kB is the Boltzmann constant, a is a molecular length and cK is the correlation length for the normals to the layer i.e. the distance over which this layer remains flat in the presence of thermal fluctuations.

Experiments reveal that K is typically between 100knT (condensed insoluble monolayers [13]) and about 10knT (lipid bilayers [l&16]) but

Fig. 1. Schematic representation of the types of surfactant-rich phases in oil + water systems. (a) lamellar phases, (b) bicontinuous microemulsion or L3 phase.

can decrease below k,T in microemulsion systems [17-301. When K > k,T, Eqn. 2 shows that L& is macroscopic meaning that the layers are flat over large distances; a lamellar phase is then obtained as soon as the distance between two surfactant layers is smaller than gR Since this

89

phase possesses long-range orientational order, it differs from microemulsion phases which are disordered phases. If K can be reduced until comparable to k,T, & is microscopic, the order is lost and either bicontinuous microemulsions or L, (L,‘) phases appear. It turns out that in this case cK is very similar to the average distance 5 between two oil or water domains,

The role of K is also important. There are few measurements of this modulus in the literature [24,25,32,331 and its importance in determining the structure of surfactant/oil/water mixtures is far from clear_ In the absence of thermal fluctuations (T = 0 K) and for co = 0 and K<O, the minimum of F is obtained when the surfactant film is flat, i.e. for lamellar phases. The case K > 0 is very different because the minimum of the first term of Eqn. (2) is obtained for cl = -c2 whilst the minimum of the second term is obtained for c1c2 c 0 and 1 cl 1 = 1 c2 1 + 00, i.e. for a saddle-shaped surfactant film. In practice I cl I and I c2 I keep a finite value due to the finite thickness of the surfactant film which is not taken into account in Eqn. (2) and a periodic bicontinuous phase such as a cubic phase is obtained, i.e. a bicontinuous ordered phase having no mean curvature and a negative Gaussian curvature (Fig. 2). In this case, the average

Fig. 2. A bicontinuous cubic phase with a null mean curvature and a negative Gaussian curvature.

90

distance 5, between two oil or water domains is determined by terms not included in Eqn. (2). The thermal fluctuations affect this picture as soon as SK I 5. Consequently one expects lamellar phases for K > k,T and K < 0 and bicontinuous microemulsions or Ls phases for K 2 k,T and K z 0 Ml.

Microemulsions, lamellar phases or L, phases frequently occur in equilibrium with other phases; excess oil or water, other microemulsion phases. The planar interfacial tension between these different phases is ultralow (5 0.1 mN m-l) and is closely related to the surfactant film and the structure of the aggregates in the bulk. In the following we will disc_uss in detail the relationship between the interfacial properties (co, K, K and $ and the aggregate structure in bulk, in an attempt to test some of the above theoretical predictions. The work to be described concerns the system containing the anionic surfactant sodium bis-2- ethylhexylsulphosuccinate (AOT) + aqueous NaCl + n-alkane, in which c, has been varied by increasing electrolyte concentration. The role of the salinity of the water and the length of the alkane chain has been studied in detail.

II. WINSOR BEHAVIOUR IN AOT, BRINE, ALKANE MIXTURES AND

DETERMINATION OF STRUCTURE OF THIRD PHASES

In systems containing equal volumes of oil and water and a suitable surfactant at concentrations above the system cmc (critical micellar concentration), microemulsions may be inverted from o/w to w/o by a number of variables. Such variables change the hydrophile-lipophile balance of the system. For an ionic surfactant, increase in the concentration of inorganic electrolyte is often employed. At low salt concentrations, two phases form consisting of an o/w microemulsion in equilibrium with an excess oil phase (Winsor I system 1341). At high salt concentration, the two coexisting phases are a w/o microemulsion and an excess water phase (Winsor II system). At intermediate salinities, three phases can form consisting of a surfactant-rich third phase and excess oil and water phases (Winsor III system). Most surfactants require the use of a second surfactant or cosurfactant (e.g. an alcohol) to effect this transformation. The reason for this has been rationalised in terms of the effective area per molecule changes occurring in the mixed film at the interface [35]. Using AOT has the advantage of observing such microemulsion inversion without the addition of cosurfactant, thus simplifying the interpretation of the findings.

91

A detailed study of the phase diagram of AOT + aqueous NaCl + alkane mixtures has been carried out by Gosh and Miller [36], along with a similar study reported by Shinoda and Kunieda [37] with decane as oil. Our own study [38] is very detailed but limited to the region of the phase diagram where the alkane and aqueous phases are of equal volume initially and where the concentration of AOT is low. To obtain the equilibrium phase sequence, equal volumes of aqueous NaCl (of varying concentration) and AOT solution in alkane were shaken at 20°C. Imme- diately after shaking, the mixture is a white, opaque emulsion, which breaks down to give rise to the different phases in equilibrium. The time required for this to occur depends on both salt concentration and alkane chain length, N. In general, emulsion stability is least for higher salt concentrations and longer N. For AOT, the succession of phases is similar, but not exactly the same, to that described by Winsor in the case of microemulsions. At low salt concentrations an aqueous phase containing all the surfactant is in equilibrium with excess oil. We call this a Winsor I system but we have not determined the structure in the aqueous phase, partly because the study of this region of the phase diagram is difficult due to the slowly breaking emulsions, especially for the short chain alkanes. At high salt concentrations a w/o microemulsion coexists with excess aqueous phase containing surfactant close to its cmc (Winsor II). At intermediate concentrations, the behaviour is markedly dependent on N. In most cases, three phases appear. This region of salt concentrations we denote as Winsor III systems although the phase rich in AOT is not necessarily a microemulsion. The Winsor III region is obtained, as for microemulsions, close to the optimal salt concentration, i.e. when c, is close to zero.

Neutron scattering has been employed to study the AOT-rich phases obtained in the Winsor III regions for octane, decane and dodecane [38]. Information about the structures of the different phases and about the surfactant film has been deduced. Enhanced film contrast was obtained using deuterated water and, in some cases, deuterated oil. This allows the observation of the AOT film alone (deuterated oil and water) or the AOT film plus the oil domains (protonated oil and deuterated water).

The scattered neutron intensity I(q) has been measured for different samples in the Winsor III region over a large q range. Spectra of I(q) may be treated in a number of ways depending on the q range investigated.

At the largest q, oscillations reflecting the form factor are observed in a plot of q*I(q) versus q [39]. They result from the scattering by locally flat objects, the surfactant film. The film thickness d was deduced from these oscillations. The oscillations are damped because there are fluctua-

92

tions in the thickness d of the layer. The damping gives the mean square amplitude Ad of the fluctuations of the thickness.

At lower q, for planar structures we anticipate [40,41] log [q21(q)] - d,q2/12, where d, is the apparent dry thickness of the film and is obtained from a plot of log q21(q) versus log q. This gives another estimation of the film thickness.

Information on the phase structure is deduced from a plot of log I(q) versus log q. A gradient equal to two indicates that the scattering objects are flat i.e. a surfactant film which is flat at the scale of observation. This film may be a monolayer or a bilayer of AOT incorporating oil, the thickness of which is measured by two different methods. A gradient equal to three indicates the scattering by three dimensional objects.

The phase behaviour and neutron scattering findings are best sum- marised for the different oils as:

(a) Heptane to nonane - The Winsor III region for N = 7-9 consists of a surfactant-rich third phase plus excess oil and water phases. The third phase, which forms the middle phase, is birefringent and incorporates similar quantities of alkane and aqueous phase. It is a lamellar phase constituted of a succession of thick films of oil and water separated by monolayers of AOT. The salt concentration range AC over which lamellar phases are formed is very narrow. Only the case of octane was studied in detail. It was found that AC is less than 0.01 M. The measured film thickness is d = 10 A and d, = 10.85 A and the mean square amplitude of the fluctuations of the thickness Ad =l A. The thickness of the oil and the water films was estimated to be -200 A.

(b) Decane - In the Winsor III region, the surfactant-rich phase which forms contains less oil than in the shorter alkane systems. Close to the Winsor II boundary (-0.075-0.08 M NaCl) the third, middle phase which is birefringent and lamellar is in equilibrium with excess oil and water. However, close to the Winsor I boundary (-0.066-0.071 M NaCl) this lamellar phase incorporates all the aqueous phase such that there is none of the latter in excess. It contains approximately 3.3 molecules of decane per AOT molecule. At [NaCl] < 0.066 M, a Winsor I system appears in which the AOT-containing aqueous phase is isotropic. The lamellar phase is constituted of a succession of thick films of water separated by bilayers of AOT swollen by decane. The bilayer thickness is d =31 A with large fluctuations Ad - 12 L$ while the monolayer thickness is about 10 A (d = 10 A, d, =11.4 A> and exhibits only small fluctuations of the thickness (Ad -1 A). The bilayer is constituted of two surfactant monolayers and an oil film. The oil layer thickness fluctuates between approximately 0 and 20 A.

93

g 0.6- ‘3 8 b 0.5 -

il - 2 0.4

p 0.3 -

0.2 -

[AOT]=lSmM I I I

do&cane I

0.1 -

0 0.05 0.1 0.15 0.2 0.25

[NaCllFI

Fig. 3. Volume fraction versus the salinity for the different phases obtained when equal volumes of brine and a solution of AOT in dodecane at 15 mM are mixed.

(c) Undecane to tetradecane - For these oils, the phase rich in AOT in the Winsor III region is not birefringent and the phase progression is more complex. It is noticeable that the Winsor III systems form over a larger salt concentration range (-0.1 M for dodecane) than with the previous oils. This can be seen in Fig. 3 for systems containing (initially) 15 mM AOT in dodecane. There are several parts to the Winsor III region. At the Winsor I-III transition there is no discontinuity in the volume fraction of the AOT-rich phase. With increasing salt concentration, the third phase decreases in volume at the expense of the excess aqueous phase, the volume of oil phase in excess remaining constant. This is followed by two successive marked reductions in the volume of the third phase close to the Winsor III-II transition. These discontinuities in the volume versus [NaCll indicate that the AOT-rich phase is probably a succession of phases of different structure that we call B,, B, and B, respectively. B, is reasonably fluid but B, and B,, being more concen- trated in AOT, are viscous. B1 and B, contain mainly surfactant and water and appear at the bottom phase (with < 1 molecule of oil per AOT molecule).

B, is probably an L, phase. Neutron scattering experiments indicate that phase B, consists of locally flat bilayers of AOT incorporating very small amounts of dodecane 1381. Values deduced for the bilayer thickness are d - 22 A and the thickness fluctuations Ad - 6 A.

94

Phase B, incorporates more oil than B, and B, but has the smallest volume; the volume of oil and water in it are similar and it appears as the middle phase being less dense than water.

Phase B, is probably a bicontinuous disordered phase like a bicontinuous microemulsion in which the oil and water domains are separated by an AOT monolayer. Neutron scattering experiments indicate that the surfactant monolayer is locally flat while the oil domains are three dimensional objects (not a flat oil film). However two important differ- ences between a classical bicontinuous microemulsion and phase B, must be noticed. Firstly, the surfactantioil or surfactant/water ratio is very large. Secondly, it was observed that a more ordered structure develops with time as seen by the appearance of a narrow peak in the spectra log(I) versus log(q) in neutron scattering experiments after several months compared with the spectra obtained soon after preparation of the sample [38]. The characteristic size 5 in the microemulsion deduced from the position of this peak (7dq,,) is small (-60 A> in this case.

No neutron scattering experiments have been performed on sample B, since, being of low volume and more difficult to locate in the phase diagram made with deuterated water (in this case both B, and B, are middle phases), it was difficult to sample.

It must be remarked that at low AOT concentrations (say 15 mM), the aqueous phase of the Winsor I region is optically isotropic but at higher AOT concentrations a birefringent phase coexists with the isotropic phase. The quantity of oil incorporated into the birefiingent phase is low, being about 0.3 molecules of dodecane per AOT molecule. The behaviour within the Winsor III region remains the same.

It can be seen that the behaviour of mixtures of AOT + aqueous NaCl + alkane depends on both the salt concentration and the chain length of the alkane. The oil chain length plays an essential role in determining the nature and structure of the phases obtained in the Winsor III systems. Long chain alkanes give third phases which are isotropic and which contain very little oil. Shorter chain alkanes on the contrary give lamellar third phases containing more oil. The lamellar phase with octane is constituted of films of water and oil separated by a monolayer of surfactant of thickness -10 A. The lamellar phase with decane is constituted of bilayers of surfactant in water swollen slightly by oil. The thickness of the monolayer is the same as that in octane. The isotropic phases with dodecane can be, depending on salinity, an La phase constituted of bilayers of surfactant in water, containing virtually no oil, or a bicontinuous phase constituted of monolayers of surfactant se arating water and oil domains. The monolayer thickness is again -10 R . A summary of the phase types is given in Fig. 4.

95

\ water

h)

Oil

Fig. 4. Summary of the third phase structures in the system AOT + aqueous NaCl + alkane at 20°C. (a> the carbon number N of the alkane is ~10, (b) N = 10, (cl N = 12.

96

III. LOW TENSIONS AND BENDING ELASTICITIES (K) OF MONOLAYERS

Since the nature of the phases obtained from mixtures of AOT + aqueous NaCl + alkane depends on the alkane chain length, it is of interest to see if the elastic properties ofAOT monolayers at the oil-water interface also depend on this parameter. We first examine the case of the bending elastic constant. There have been several measurements of K in AOT systems recently 123-311. Table 1 summarises the values reported for made-up (i.e. one phase) droplet water-in-oil microemulsions. The size of the droplets is dependent on the mole ratio of water to surfactant, or w value. Huang et al. 1231 have used the neutron spin-echo technique to study the dynamics of the shape fluctuations of the droplets. Thermal fluctuations of the surfactant film distort the droplet from its average spherical form, the fluctuations being driven mainly by the bending modes on the surface. They measure a value for K = 5ksT in decane. In a subsequent paper, Farago et al. [241 analyse the polydispersity (i.e. size fluctuations) of the droplets (measured by small angle neutron scattering) and calculate K = 0.5ksT for the same system, in contradiction to the previous result. In these papers, the authors only take into account the bending elastic constant as a restoring force. But by including the Gaussian curvature contribution in their analysis, a value of K ranging between 2.0 and 3.8k,T (dependent on the purity of the AOT) is finally deduced from these two experiments [25].

Kerr effect studies have also been used to measure the monolayer rigidity. Such an experiment measures directly the deviation of the droplets from spherical shape, namely the mean square amplitude of ellipsoidal shape deformation due to the applied electric field. The values reported by Borkovec and Eicke for large droplets 1261, and by van der Linden et al. for small droplets [27,281, centre around K - 0.5knT. But these measurements are very sensitive to the polydispersity of the droplets, and a large correction due to the polydispersity gives K - lk,T [26 erratum]. A quite different analysis of the polydispersity in droplets (measured via time resolved fluorescence quenching) yields a value for (2K + K)/2 = l.lk,T for both octane and dodecane as oils 1291. In this paper the authors suppose that K = 0 (an assumption which is probably not valid, see below) and deduced K = l.lk,T for both oils. Finally, a very recent study by Alexandridis et al. [301 describes the decrease in K with dispersed phase salt concentration, falling from 0.4ksT in pure water to 0.2knT in 0.05 M NaCl. The iodine laser temperature jump technique was used to increase the microemulsion temperature rapidly (c 1 ms) and

97

TABLE 1

Experimental determinations or calculations of K in w/o droplet microemulsions stabilised by AOT

Dispersed phase

Oil w value K&T Method Ref.

water water

water water

water water water

water

0.01 M NaCl 0.05 M NaCl water

decane decane

decane 24.4 hexane 100

iso-octane iso-octane hexane octane dodecane

75 to 100 5tu35 10 to 35 5 to 13

iso-octane

8tQ40

16to41

5to50

5to45

5.0 0.5

5.0

2.0

3.8 0.50 1.0 0.46 0.46 0.38 1.1 1.1

0.4

0.4 0.2 0.4

neutron spin-echo (NSE) 23 small angle neutron 24 scattering neutron spin-echo small angle neutron scattering (SANS)+ K contribution included NSE and SANS 25 Kerr effect measurements 26

erratum 26

Kerr effect measurements 27 Kerr effect measurements 28 Analysis of 29 polydis~~ities from time resolved fluorescence quenching experiments Iodine laser temperature 30

j-p

SANS ~ly~spersity analysis

3 1

thus disturb the system equilib~um. The observed relaxation was attributed to the relaxation of the surfactant interface.

It is apparent from the values given in Table 1 that the rigidity measured for AOT monolayers coating droplets varies depending on the technique employed. We have chosen to deduce K from a study of the thermal ~uctuations of a flat monolayer by ellipsomet~ [19,42]. A flat monolayer at the oil-water interface is constantly distorted by thermal fluctuations. There are three restoring forces; gravity, interfacial tension and bending elasticity. The energy required to overcome these forces is the sum of three terms:

98

E(q) = (A/2) Up g + m2 + Kq4> 4; (4)

where Ap is the density difference between the two bulk phases, g is the acceleration due to gravity and & is the amplitude of a sinusoidal deformation of the wavevector q at the interface of area A. Ellipsometry allows the measurement of the cut-off q,, = m which is the upper q-limit for capillary waves and the lower q-limit for the bending elastic waves. So, K is deduced from inter-facial tension measurements and ellipsometric measurements on flat monolayers at oil-water interfaces. K is weakly scale dependent. This technique gives K at the scale l/q,,. Renormalisation of the rigidity to different length scales has been discussed theoretically [42] but will not be taken into account in this paper. Several studies have shown that K for such monolayers depends on a number of parameters. In AOT systems containing heptane, K-l.lk,T and is independent of salt concentration [20]. K is lowered to values c k,T by the addition of a short-chain cosurfactant to films of ionic surfactant [19,21]. With nonionic surfactants, the results of Lee et al. [22] suggest that K increases with the length of the surfactant molecule, resulting from the thickening of the monolayer, predicted theoretically

[NaCUFI

091 092 093 094

Fig. 5. Variation of the post-cmc oil-water interfacial tension with salt concentration for AOT at 20°C using different alkanes. The widths of the Winsor III regions are indicated by the bars. (0) octane, (0) decane, (0) dodecane, (0) tetradecane, (+) hexadecane.

99

[43]. However, it is not clear that this is the sole effect, since in these experiments the oil chain length was changed simultaneously, and as we will see below, this can be an important variable in dictating the value of K. The rigidity is also independent of temperature in these systems. The parameter of interest here is the chain length N of the oil phase and hence the role of the surfactant chain region in determining the bending elasticity of the film.

The oil-water interfacial tension yaw is independent of AOT concentration above the cmc, but passes through a low minimum value with respect to salt concentration within the Winsor III range where three phases form. It has been shown previously that the low tension is due to the presence of an adsorbed monolayer of surfactant at the oil-water interface [44-46]. Figure 5, depicting such low tension minima in AOT systems [47], shows that both the value of the minimum tension and the salt concentration range over which three phases form, increase with an increase in N.

The values of the elasticity constant K, measured as described above, for the different alkanes are plotted in Fig. 6 [471. This rigidity was found independent of the salinity, but depends strongly on the oil chain length; it is of the order of -1 k,T for short alkanes (N c 11) decreasing to -0.1 k,T for longer chain homologues (N > 11). This dependence may be related to the differing degrees of oil penetration into the surfactant chain

c-( 192

g l,o

098

096

094

092

090

P

I I y\g-

8 10 12 14

alkane chain length, N

Fig. 6. Variation of the bending elastic constant of the AOT monolayer at the alkane- water interface with the alkane chain length.

100

region [48]. As a result of the more favourable entropies of mixing, it is known that, for a given surfactant chain, short alkanes penetrate more strongly than long chain alkanes [49] rendering the film more rigid as a result.

The values of the rigidity K are in accord with the type of third phase formed in Winsor III systems. Large values of K imply the formation of ordered lamellar phases as evidenced for short chain oils (N < ll), while lower rigidities promote disordered phases like the Ls phase (or a bicontinuous ~~roemulsion) for N > 11.

IV. ESTIMATION OF ii IN WINSOR II SYSTEMS

Within the Helfrich framework, the Gaussian curvature modulus K couples to the product of the two principal radii of curvature. Positive K means that the system energy is lowest when these two radii have opposite signs (then the energy is negative). This corresponds to a sadd& structure as in bicontinuous microemulsions and L, phases. Negative K means that the system energy is lowest when the two radii of curvature have the same@n. This corresponds to spheres or planes (as in lamellar phases), Thus K plays a role in determining the topology of the interfaces, There exist very few measuremgnts of this modulus in the literature. Farago et al. [251 have measured Kin the w/o droplet system AOT + water + decane. Both the size and the shape fluctuations of the droplets were investigated by neutron sc&tering and neutron spin-echo spectroscopy. Their resu&.s show that K/K is close to -2. Boltenhagen et al. [33] measured K in lamellar phases of the cetylpyridinium chloride + hexanol + aqueous NaCl system by studying the defects of the lamellar phase close &I its transition to the La phase. Their results gave values for the ratio m between 6 and 10 depending on the surfactant to cosurfactant ratio. K was also estimated for an AOT monolayer in the AOT, brine, heptane system for two salinities; one in the Winsor I, close to the Winsor III and the second in the Winsor II, close to the_Winsor III, using the method described below [321. The results were K/K = -1.75 and -1.2 respectively.

K for the AOT monolayer was estimated as a function of the salinity and for octane, decane and dodecane [50], using a method which applies to systems made of a dilute droplet microemulsion in equilibrium with an excess of oil or water (Winsor I or II systems) [21,32]. In principle the method relies on the following ar~ment. The interfacial tension of the monolayer at the planar microemulsion-excess phase (or oil-water)

101

interface may be defined as the energy required to increase this interfacial area by a unit amount. When the area is increased, the new area created must be covered by a monolayer of surfactant, which is taken from bulk. This energy may be calculated in the case of Winsor I or II systems since the surfactant monolayer is taken from around the curved microemulsion droplets. To do this it is necessary to unbend the surfactant film, which introduces a contribution from the mean bending elasticity K. The resulting change in the number of microemulsion droplets introduces an entropiAcontribution and a contribution due to the change in topology involving K. The sum of these three terms gives the inter-facial tension between the microemulsion and its excess phase [50]:

(5)

where R is the radius of the neutral surface of the droplets (this is the surface that does not change area as the droplet is unbent), R + h = R, is the external radius of the droplets and @ the volume fraction of droplets in the microemulsion.

Equation (5) thus indicates that in order to calculate K, we need values of the interfacial tension Y,,~, the rigidity K and the radius of the droplets R,, and an estimation of the radius R. We have already obtained values for yOw and K [47]. It has been argued [50] that the neutral surface (where the area per molecule is not changed when the monolayer is unfolded) is close to the AOT headgroup, so R = R, - h, where h is the surfactant film thickness. The measurement of R, has been done in the following way. In Winsor II systems, the concentrations of water and surfactant in w/o microemulsion phases were determined using Karl Fischer and Hyamine titrations respectively as a function of excess aqueous phase salt concentration. The mole ratio of water to surfactant, [H,Ol/[AOTl = w, is related to the volume of the droplets through a simple geometrical model [51] in which

R, = 3 (v/a) [H,O]/[AOTl

where R, is the water core radius, v is the molecular volume ofwater (0.03 nm3) and a is the area per surfactant at the headgroup surface. In addition we have determined the hydrodynamic radius R, of the large droplets by dynamic light scattering in the limit of low droplet concentration. Since R, is close to but higher than R, (RH - R, + 12 A), the area

102

2K+ii

kJ3T 3

2.5

2

1.5

1

0.5 \

4 6 8 10 12 14

Fig. 7. Variation of (2K + k) with the Debye length lk for AOT droplets film at 20°C. Filled circles: octane; open circles: decane; diamonds: dodecane.

a may be deduced from Rn, w and Eqn. (6). The value of a found is 53.5 A2 and is assumed independent of salt concentration. This allows the calculation of R, from Eqn. (6) at any salt concentration.

The quantity (2K + K) has thus been calculated from Eqn (5). The results are shown in Fig. 7 as a function of the Debye length in Winsor II systems and for different alkanes (the Debye length is proportional to S-o.5, where S is the salinity). For a given oil, (2K + K) decreases linearly with the DebyeJength at low salinity. The linear dependence of the quantity (2K + K) on the Debye length at low salinity is accounted for theoretically by models that calculate the elejrostatic contribution of the electrical double layer to the moduli K and K for a highly charged film. The electrical free energy per unit area of the double layer is equated with the curvature elastic free energy given by Eqn. (2). Such calculations have been performed by Winterhalter and Helfiich [521 using the linear- ised Poisson-Boltzmann (PB) equation valid for low surface charge or high salt concentration, and later by Lekkerkerker [53] and Mitchell and Ninham [54] using the non-linear PB equation which includes systems of high surface charge (or low salt concentration). But the experimental gradients of the variation of 2K + K with the Debye length are 10 to 40 times larger than the calculated ones showing that probably the main origin of this variation has not been taken into account.

103

1.4

1.2

1

0.8

0.6

0.4

0.2

0 0.06 0.1 0.14 0.18 0.22

Fig. 8. The spontaneous curvature c, of an AOT monolayer as a function of the inverse Debye length for AOT f!ilm at 20°C. Point types as in Fig 7.

Since K - lkBT for octane and decane, and K = 0. 12kBT for dodecane, it can be seen from Fig. 7 that value of K close to the WII-WI11 transition changes sign with alkane chain length. It is positive for dodecane (-1 k,T), close to zero b&negative for decane and negative for octane (- -1.2 k,T). Consequently, K/K close to the transition is -1.2,O and 8 for octane, decane and dodecane respectively.

The predictions of the same models are that the spontaneous curvature c, varies as the inverse Debye length (K), for surfactant films with high charge densities. The spontaneous curvature c, (= l/2 R,) of the film has also been calculated from equation [501:

R 2K+K k,T -- - RO 2K +&K ln’- ,(,“:h, 1 (7)

As seen from Fig. 8, the variation of c, with salt concentration agrees with that predicted by the electrostatic model (c,, a K), at least for low salt concentrations. The curvature decreases with decreasing salt concentration, going to zero as the Winsor II/III boundary is approached as expected. The slopes for the different alkanes are seen to differ, depending on whether the oil has a long or a short chain. However the slopes of c,WknT with the inverse Debye length are the same for the different oils.

The nature of the third phase-formed in Winsor III systems can be related to the values of K and K in the vicinity of the Winsor II/III

104

transition. The negative values of K along with high values of K (SK - 500a - 5000 A> for short alkanes are consistent with the lamellar phases formed when the AOT film has a spontaneous curvature close to zero in the Winsor III range. Conversely, the positive value of K for a long chain alkane is in accord with the appearance of the bicontinuous phase (B,) favouring a saddle-splay structure. It is probable that the order that appears with time in the B, phase is due to this positive value of K that favours a periodic structure with a null mean curvature. However the low K value and consequently the low value of the persistence length in this case (& - 2a - 20 A> introduces disorder in this structure. Similarly, the L, phase (B,) observed with dodecane results from the low bending elastic constant of the_bilayer (K, - 2K - 0.24k,T). For this phase the saddle splay modulus Kb can be estimated. It is that of a bilayer [9]:

&,=2K-2dccK (8)

In this phase co is negative but close to 0 as can be deduced from Fig. 8, supposing that co varies linearly with the &verse Debye length as observed at higher salinity. One deduces that I$, is probably positive.

This study represents the first systematic test of such theoretical predictions.

V. WETTING BY OILS OF AOT MONOLAYERS AT AIR-WATER

SURFACES

The penetration of short oils into surfactant monolayers is an indica- tion that an attractive interaction exists between the oil and surfactant chains. Since this interaction depends on the chain length of the oil, it is reasonable to suppose that it will manifest itself in the wetting properties of the oils on AOT monolayers at air-water surfaces. Several processes may occur on addition of a drop of alkane to the surface of an aqueous surfactant solution. The drop may remain as a lens in the surface, with or without molecular spreading at the surface. In the molecular spreading process, alkane molecules are solubilised by surfactant chains in the monolayer [55,56]. The drop may however spread as a macroscopic (duplex) film, or, as in the case of short alkanes on AOT, as a thinner but multimolecular layer 1571. For such experiments, the concentration of AOT is above the cmc and so these surfaces are covered by a saturated monolayer of surfactant. When a drop of a short alkane (N < 11) is deposited on the surface, it spreads rapidly leaving a film of oil at the

105

surface coexisting with a residual drop (with a finite contact angle) which resists spreading. Drops of the longer chain alkanes (N > 11) do not spread but remain as lenses on the surface. The behaviour of non-spreading alkanes on su~actant monolayers has been discussed by Aveyard et al. [55] for various surfactants. The surface concentration of alkane can be obtained from the lowering of the surface tension caused by alkane solubilisation. Alkane uptake is found to decrease with increasing alkane chain length, but to increase with increasing surfactant chain length. It is demonstrated that solubilisation does not si~i~cantly affect the surface concentration of surfactant, but rather it increases the film thickness.

The observations on AOT monolayers led us to a more detailed study of the wetting behaviour of these alkanes. The study has been done by ellipsomet~, a method very sensitive to the structure of the surface. In these experiments, we begin by measuring the ellipticity of reflected light from the AOT monolayer at the air-water surface, FAoT. Then a drop of oil is added to the surface far from the laser beam. After the deposition of a drop of long chain oil (N > ll), the ellipticity is unchanged. However, after deposition of a drop of short chain oil (N < 11) the ellipticity changes. This ellipticity attains a value stable with time, 6, corresponding to an oil film a few nm thick on the surface. Its thickness 1 does not depend on the quantity of oil added as drops or on the concentration of AOT in the aqueous phase (varied between 3 and 30 mM). The oil film coexists with a residual drop which usually adheres to the walls of the teflon cells used for the experiments. If a large quantity of oil is added to the surface however, the residual drop increases in volume and occupies the whole surface; ellipticity measurements are made before this occurs.

The stable value of the oil film thickness 1, depends on the salt concentration in the aqueous phase and on the alkane chain length. The results of these measurements are shown in Fig. 9 for octane and decane. Tbe oil thickness increases with salt concentration, reaches a maximum and then decreases. The behaviour is similar for the two oils as far as the dependence on salt concentration is concerned. The salinity at which 1 is maximum is exactly the salinity at which the interfacial tension yoW of the AOT layer at the oil-water interface is minimum indicating that this interfacial tension plays a role in the spreading. This was utilised to understand the forces contributing to the stability of this film.

In order to understand the stability of the oil film between the oil-air surface and the oil-water interface (created after wetting has occurred>, it is necessary to determine the different interaction potentials between these two interfaces. The equilibrium of a drop coexisting with a thin film

106

70

60

50

40

30

20

I

_l(A> /g I I I

P 0 , I :A \ 0

/ I \\

-0.

,/f

0. \ O-0 0 -@ 0

v 9

10 I I I I

0 0.05 0.1 0.15 0.2 0.25

Fig. 9. Variation of the oil film thickness 1 with salt concentration for the wetting oil films at the surface of post-cmc aqueous AOT at 20°C. Filled circles: octane; open circles: decane.

[NaCllFI.

has been observed in the wetting of solids by liquids. It is referred to as pseudopartial wetting and has been studied independently by Hirasaki [58] and Brochard-Wyart et al. [59]. Such a situation may result from a competition between an attractive van der Waals potential (disfavouring wetting) and a short-range repulsive potential (favouring wetting). The total interaction potential between the interfaces shows a minimum at a small but non-zero separation, favouring the case of a surface coated by a thin film coexisting with a residual drop. In this case, the spreading coefficient S is positive and the Hamaker constant A is negative.

In our case of alkanes added to a water surface, a van der Waals potential V,,w does not favour wetting. Normal alkanes with N < 7 probably wet, and adsorb at, the air&pure) water surface 1601, although this has been disputed [61]. The higher alkanes do not spread on water but form microlenses instead. The Hamaker constant (appearing below) for the interaction between air and water across oil for N 2 7 is thus probably negative (not favouring wetting), a result confirmed by calculation [62], In addition, the initial spreading coefficient for oil on aqueous AOT solutions (with or without salt), S = ya, - yOw - yoYoa (where a, w, and o refer to air, water and oil respectively), is positive for alkanes up to and including decane, but negative for dodecane and higher alkanes [631. The positive value of S for short alkanes favours wetting. The repulsive short-ranged potential V,, introduced to take this into account is un- known at this stage but its shape can be deduced from the experiments.

107

However introducing Vvdw and V,, is not sufficient to describe the variation of the thickness 1 of the oil film with salt concentration (Fig. 9). In order to explain the coincidence of the maximum in 1 with the minimum

in YNXV of the oil-water interface, it is necessary to introduce a repulsive potential between the two interfaces which depends on the tension ‘y,,. Obviously this potential is due to the fluctuations of the oil-water interface of very low tension constrained by the plane oil-air surface of high tension. This is the only contribution capable of explaining the variation of 1 with salt concentration (or with the change in interfacial tension). The amplitude of the fluctuations at the oil-water interface is a function of yO,; it increases as yaw diminishes. The oil-water interface fluctuates against the flat oil-air surface and induces a distance of separation which increases as the mean-square amplitude of the fluctuations increases. The mutual collisions of the two interfaces produce a repulsive steric interaction which is an entropic force (Fig. 10).

\AOT monolayer

Fig. 10. Schematic representation of the wetting oil film at the surface of post-cmc aqueous AOT.

Helfrich has already derived the repulsive contribution due to the fluctuations for the case of a membrane of zero tension between parallel rigid plates [64]. We have used the same idea but have retained the interfacial tension in the treatment [571. The wall constraining the fluctuating monolayer is the oil-air surface in this case. The fluctuations of the oil-water interface keep the oil-air surface at a distance 1 from the mean plane of the oil-water interface. The pressure exerted by the oil-water interface on the oil-air surface can then be accurately calculated. The oil film thickness results from the equilibrium between these three forces; the van der Waals force, the attractive short-range force, and the repulsive entropic force. Two interesting cases have been consid- ered:

108

(a) Large thickness and low interfacial tension

The effect of the fluctuations is most pronounced at low ‘y,,. The short-range force becomes negligible. Making the assumption that the van der Waals force is balanced only by the entropic force, one deduces the value of the Hamaker constant A - -0.6knT for octane and - -0.47 k,T for decane, in good agreement with Hamaker constants measured in different but similar systems 165,661.

(b) Smaller thickness and higher interfacial tension

To obtain the repulsive short-range pressure stabilising the film at lower thicknesses, we evaluate the sum of the pressure of the van der Waals contribution (with A calculated as above) and that of the entropic force, which is balanced by this additional pressure. The short-range pressure is plotted in Fig. 11 as a function of oil film thickness 1. The larger the thermal fluctuations, the larger is the distance 1 at which the pressure is probed. This can be varied by varying the oil-water tension

Y ow, effected by changing the salt concentration. For large l(2 25 A), each value of 1 is obtained for two different salt concentrations (Y,,~ being the same) giving the same pressure within experimental accuracy. Thus the short-range force does not depend to any great extent on salt concentra-

14

12

10

8

6

4

2

0 0 10 20 30 40 50 60 70

Fig. 11. The short-range repulsive pressure between the brine-oil and the oil-air interfaces versus the thickness 1 for octane (filled circles) and decane (open circles).

109

tion. At low 1 the same argument cannot be used since, due to the unsymmetrical shape of the tension curves (Fig. 5), higher tensions are obtained at low salt concentrations only. This potential is visibly short- ranged (-10 A for octane and 15 A for decane) and becomes the dominant stabilising potential for the film at low thicknesses. Its origin is most likely due to a direct attractive interaction between the alkane chains and the chains of the surfactant molecules, which gives rise to a repulsive interaction between the two interfaces since the presence of these adsorbed oil molecules prevents their approach. This overcomes the attractive van der Waals potential at short distances.

VI. CONCLUSIONS

It is clear from the foregoing that close relationships exist between the properties of surfactant monolayers and the corresponding phase behaviour in bulk. Experimental findings are broadly in line with theoretical predictions. One of the exciting future developments is to measure directly the detailed structure of the monolayers. Neutron reflection offers such a possibility. The first studies of mixed alkane/surfactant monolayers at air-water surfaces 1671 and single surfactant monolayers at oil-water interfaces 1681 reveal the kind of detail these measurements provide. This includes determination of the area per surfactant molecule, the surface concentration of alkane and, by selective deuteration, the relative positions within the monolayer of surfactant and alkane. Our understanding of the molecular origins of oil + water + surfactant behaviour will be greatly improved with a knowledge of such monolayer organisation. An NMR study of the lamellar phases in the Winsor III of the mixtures with short alkane chains and the lamellar phase in the Winsor I with dodecane gives interesting results on the oil behaviour in the AOT monolayer depending on whether the alkane chain is short or long 1691.

The following conclusions may be drawn from our studies on systems containing AOT, aqueous NaCl and alkane:

1. From a study of the phase equilibria of mixtures of AOT + aqueous NaCl + alkane, it is found that the surfactant-rich phase formed in Winsor III systems is birefringent and contains significant amounts of oil and water for short chain alkanes (< undecane), but is isotropic containing very little oil for longer chain homologues (2 dodecane).

2. The surfactant-rich phases are lamellar phases for short alkanes, L, phases and bicontinuous microemulsions for long alkanes. The lamel-

110

lar phase in octane consists of AOT monolayers separating oil and water layers; that in decane consists of AOT bilayers, swollen by oil, in water. The L, phase in dodecane is made up of AOT bilayers, slightly swollen by oil, separating two domains of water.

3. The bending elasticity constant K has been measured for monolayers at planar oil-water interfaces by ellipsometry. K is of the order of -k,T for short chain alkanes, but only -O.lk,T for long chain alkanes (2dodecane). This softening of the rigidity with oil chain length has been attributed to the differing extents of oil penetration into the surfactant chain regions, and confirms the predictions of the de Gennes and Taupin model [3] with respect to the type of phee formed in bulk.

4. The Gaussian curvature elasticity K and the spontaneous curvature c, of the monolayer in Winsor II droplet systems have been estimated from measurements of the rigidity, interfacial tension and droplet size. K is negative for octane and decane as oils, but is positive for dodecane. This is in a=ement with the topology of the phases formed in Winsor III systems. K is proportional to the Debye length and c, is proportional to the inverse Debye length as predicted. But the slope of this variation for K is much larger than the predicted one.

5. The wetting properties of alkanes on AOT monolayers at air-water surfaces are dependent on the chain length of the oil. Short alkanes spread leaving a thin oil film in equilibrium with a residual drop. Long chain alkanes do not spread, remaining as drops on the surface. In the case of short alkanes the thickness of the oil film, measured by ellipsometry, is determined by a combination of van der Waals forces, entropic forces and short-range repulsive forces.

ACKNOWLEDGEMENTS

The authors thank the British Council and la Direction des Etudes Doctorales for Alliance Programme funding, and the Government of Morocco for the provision of a studentship to HK.

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Properties of surfactant monolayers in relation to microemulsion phase behaviour

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