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Excess of Solubilization and Curvature in Nonionic Microemulsions
Journal of Colloid and Interface Science 219, 11–19 (1999) Article ID jcis.1999.6466, available online at http://www.idealibrary.com on
Excess of Solubilization and Curvature in Nonionic Microemulsions F. Testard 1 and Th. Zemb CEA/Saclay, Service de Chimie Mole´culaire DRECAM, Bat 125, F91191 Gif-sur-Yvette Cedex, France Received December 14, 1998; accepted July 30, 1999
vature dependence at saturation, i.e., when excess solute is present as a solid (2). As in the previous paper, we have chosen lindane, the g-isomer of hexachlorocyclohexane (4), as a model solute, since it was one of the most widely used organochlorine pesticides for agricultural purposes. Lindane is slowly degraded in the environment and therefore can accumulate in organic tissues (5). This hydrophobic molecule binds extensively to organic soils, clay systems (6), humic substances (7), and biological membranes (8, 9). In the last few years, considerable information has been acquired relating to human exposure and soil pollution with pesticide residues: more than 1000 papers describe analysis results of lindane accumulation in different soils, but without relating this adsorption to phase diagrams of surfactant systems (10, 11). However, numerous papers (12–14) describe the effect of lindane on synthetic and native membranes to establish the undesirable toxic effect of such a pesticide. Our model system is a quaternary system: water– oil–nonionic surfactant solutions with added lindane. The use of C i E j nonionic surfactants of the polyoxyethylene glycol family is particularly attractive as microemulsions could be obtained with only three constituents without any cosurfactant, adjusting the temperature range. Moreover, by varying the relative volumes of the polar and apolar parts of those surfactant molecules, it is easy to modify the hydrophilic/hydrophobic balance. The hydration of the headgroups of those surfactants is temperature dependent and so the phase diagram is governed by the temperature: due to dehydration of the nonionic headgroups, the spontaneous curvature turns from oil to water by increasing temperature. Shinoda and co-workers’ (15–17) pioneering study, as well as the work of Kahlweit’s group (18, 19), made the ternary phase prism of nonionic ternary systems available. Microemulsions exhibit a microstructure: oil microdomains are separated from water microdomains by a surfactant film (20). The type of microstructure (w/o, o/w or bicontinuous) is determined by the distribution of the amphiphile between water and oil and by the water-to-oil ratio. At each temperature, the surfactant film has a different spontaneous curvature H 0 , and the water-to-oil ratio imposes the sign of the average curvature ^H& produced in the sample. For example, curvature can be directed only toward the minority component. The magnitude
We measure separately the amount of solute dissolved in a surfactant monolayer and the average curvature of the relevant sample to establish a link between these two quantities. The model system chosen involves the common hydrophobic pesticide lindane (g-C 6H 6Cl 6) in a nonionic surfactant solution of the ethylene oxide type. Excess solubilization, defined as the solubilization in the surfactant film by comparison with bulk oil, is quantified by the interfacial composition l (molar ratio solute/surfactant) within the interfacial film. A linear relationship between the amount of solute adsorbed on the film and the induced variation in curvature of the surfactant film is deduced from the phase diagram, dosage, and small-angle scattering experiments in the case of micellar, Winsor I, and several Winsor III domains at equilibrium in the same ternary system. We discuss the linear relationship obtained with constraints set by molecular packing. © 1999 Academic Press Key Words: curvature; microemulsions; micelles; solubilization.
INTRODUCTION
To develop predictive models about solubilization in heterogeneous media, the mechanism of solubilization of a solute in surfactant solution and the possible consequences on the properties of surfactant film such as curvature have to be understood (1). In a previous work (2), we established that maximum solubilization of a model apolar (3) constituent in a microemulsion (a) exceeds the solubilization in pure oil and (b) induces a shift in the temperature of the zero spontaneous curvature, and (c) that the maximum solubilization, when in equilibrium with excess solid, is curvature dependent. To investigate this curvature effect in different physical situations, we generalize this approach and compare in this paper the effect of adsorption in differently curved structures as micelles or o/w microemulsions, as well as adsorption in microemulsions with a zero curvature. The aim of the work presented here is to quantify the curvature variation with the amount of solute adsorbed in the interfacial film at variable solute/oil concentrations. This extends the previous observations, which have evidenced a cur1
To whom correspondence should be addressed. E-mail: testard@ nanga.saclay.cea.fr. 11
0021-9797/99 $30.00 Copyright © 1999 by Academic Press All rights of reproduction in any form reserved.
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of the average curvature depends on the topology of the interface (1). For a given sample, the spontaneous curvature H 0 differs from the average curvature ^H&; the difference is traduced by the bending energy which depends on the magnitude of the bending constants (21). In the limit k c @ kT, a predictive model is available for the composition where the local microstructure is composed of spheres, cylinders, and bilayers (22). Single-chain nonionic surfactants have bending constants typically on the order of 1 kT (23, 24). C i E j family surfactants show the same variation of local microstructure (25) and are stable within a large range of curvature ^H&, since the emulsification failure requires a large difference between ^H& and H 0 (26). Localization of our solute molecule model could occur in the two molecular environments: either oil microdomains or the surfactant film. The existence of such an excess of solubilization was first demonstrated by Fletcher (27) and Leodidis and Hatton (28). Solubilization within the surfactant film is the origin of the observed excess of solubilization, by comparison with bulk oil. They have quantified the excess solubilization by the interfacial composition parameter l, which is the molar ratio of solute to surfactant located at the interface. We also use this interfacial molar ratio to quantify the excess lindane at the interface. The extreme case of the micelle, the binary system without any oil, where all the solubilized lindane is located at the interface has been studied in (2). In this approach, the solubilization is considered as an adsorption study of the solute at the interface. Solubilization of lindane in bicontinuous and oil-in-water microemulsions is limited by thermodynamic saturation, which is evidenced by the slow growth of excess lindane crystals. In this paper, our study in microemulsions is performed before saturation, when the interfacial film is not saturated with lindane.
the samples by mixing a volume V of a surfactant aqueous solution at 15% in surfactant volume fraction, with a volume V9 of an organic solution (cyclohexane 1 lindane) at a given composition in lindane. After mixing and cycling the temperature above 30°C, we let the solutions phase separate. The solutions separate into two phases: an oil-in-water microemulsion with an excess of oil. By dosage, we determine the compositions of the two phases and use the usual assumption that the microdomains oil in the microemulsion and oil in excess are at the same composition (28). From the difference between the compositions of the oil in excess and the oil in the microemulsion, we calculate the value of the interfacial composition parameter l. We used a gas chromatograph equipped with an OV-17 column (T 5 140–2258C) to dose the lindane and surfactant in the solution. Water was titrated by the Karl-Fisher method with a KF 684 coulometer, and cyclohexane was obtained by difference. Small-Angle X-ray Scattering Scattering experiments on the microemulsions were performed in 0.2-mm-thick borosilicate capillaries for good temperature control. We employed a home-built Huxley–Holmestype, high-flux camera using a pinhole geometry. The X-ray source was a copper rotating anode operating at 12 kW. The K a 1 radiation was selected by the combination of a nickelcovered mirror and a bent, asymmetrically cut germanium ^111& monochromator. Data correction, radial averaging, and absolute scaling were performed using routine procedures. The precise description of this camera is given in Refs. (30, 31). The spectra were recorded with a two-dimensional gas detector which had an effective q range from 0.02 to 0.4 Å 21 [q 5 (4 p / l )sin u]. Small-Angle Neutron Scattering
MATERIALS AND METHODS
Materials Hexaoxyethylene glycol mono-n-octyl ether (C 8E 6) was purchased from NIKKO Chemicals, Tokyo, and shown to be .99% pure by gas chromatography. Cyclohexane was obtained from SDS (Peypin) with a nominal purity .99%. We used Millipore-filtered water. Lindane was supplied by Aldrich with a nominal purity .97%, and was recrystallized in a mixture of CHCl 3/EtOH. The molecular densities (in g/cm 3) used to calculate the volume fractions are 1 for H 2O, 1.01 for C 8E 6, 0.779 for cyclohexane, and 1.73 for lindane at 25°C. The melting point of lindane is 112.5°C. Composition Analysis in the Winsor Microemulsions Details of the method used for the phase diagram determination and for titration in the Winsor III region are given in Ref. (29). For the study of the Winsor I samples, we prepared
Small-angle neutron scattering was carried out on the spectrometers D11 at the ILL, Grenoble, France. SANS spectra were measured at two sample-to-detector distances to investigate a wide range of scattering vectors: 0.011 , q , 0.1 Å 21 and 0.056 , q , 0.42 Å 21. The neutron wavelength resolution used was Dl/l 5 10%. The scattered intensity was recorded on a two-dimensional detector and the data were radially averaged. Absolute calibration was made using the incoherent scattering of water. The overlap is acceptable for the two data sets with a precision of 10% on the intensity scale. SANS and SAXS Data Treatment in the Winsor I Case To obtain a good estimation of curvature from the scattering experiment, the aggregates are treated to the first order as monodisperse spheres (32), covered by a surfactant layer. The oil core has the radius R i while the surfactant shell extends to the radius R o. The center of the film is located at R at the polar/apolar interface. In this case, the intensity I(q) may be
EXCESS SOLUBILIZATION/CURVATURE IN NONIONIC MICROEMULSIONS
13
written as the product of the form factor P(q), the structure factor S(q), the volume fraction of the droplets F, the volume of one droplet V, and the contrast variation Dr 2. I~q! 5 F 3 V 3 D r 2 3 P~q! 3 S~q!. We use for the structure factor S(q) the analytical expression for monodisperse particles interacting through a Baxter potential, given by Menon et al. (33). For SANS experiments, we consider for the form factor one interface and two media: hydrogenated medium and deuterated medium. This is a consistent hypothesis, as at high q values, Porod limit-type asymptotic decay occurs with q 24 behavior. The form factor for monodisperse spheres is the square of the first-order spherical Bessel function (34). Therefore, the classic fit for monodisperse interacting droplets in a SANS experiment depends on two parameters: the inner radius of the droplet R i and the stickiness parameter t. The hard-sphere diameter is deduced from the volume of the droplet considering the total volume of the surfactant at the interface. The fits were obtained by comparison of the intensity divided by the invariant value Q* for experimental and theoretical data. The invariant is calculated by integration of the intensity as it is described in the following equation for experimental and theoretical data (34):
Q* 5
E
q max
i~q! 3 q 2 3 dq.
q min
The q min and q max of the experiments are 0.011 and 0.44 Å 21, respectively. This corresponds to a resolution of 14 to 571 Å in the sample. The droplet size is of the order of 35 Å; therefore, we could calculate the invariant in the experimentally accessible q range. For SAXS experiments, we use the form factor of monodisperse concentric spheres, considering three contrasts for the core made of oil and surfactant chain, the shell made of surfactant headgroup and hydration water, and the outer medium made of water. The fit depends on three parameters: the core radius R, the hydration per glycol unity h of the polar head of the surfactant, and the stickiness parameter t. The hardsphere radius of the droplets is not a parameter; it is deduced from the inner radius and the droplet density. RESULTS AND DISCUSSION
Winsor III Microemulsion The Winsor III regime is obtained when a microemulsion is in equilibrium with excesses of both oil and water. These microemulsions solubilize lindane molecules located in the bulk oil or in the form of an “excess” solubilized at the interface. We focus on the case of lindane in water–surfactant–
FIG. 1. Pseudo-binary phase diagram (T, temperature, g, weight fraction of surfactant) at equal water-to-oil volume fractions for water– cyclohexane– C 8E 6. T˜ is the temperature of the zero spontaneous curvature. g˜ is the efficiency of the surfactant: the minimal amount of surfactant needed to solubilize an equal volume of water and oil. (h) Experimental points. (F) Two schematic representations of the microstructure of the microemulsion sample at two temperatures.
oil bicontinuous ternary microemulsion solution at the temperature T˜ of zero spontaneous curvature to determine the curvature variation of the surfactant film induced by the solubilization. Previously, we demonstrated that an excess of solubilization at the interface exists in such microemulsions and we quantified this excess for C 6E 5 (29), C 8E 6 (2), and C 10E 8 surfactants (35). In this section, we demonstrate the link between the excess of solubilization and the induced curvature variation. To measure the variation of the surfactant film curvature, we have to use the water-oil-surfactant ternary phase diagram: existing domains of Winsor III microemulsions are localized in the ternary phase diagram by a cut at equal water-to-oil volume ratio (18, 19). The temperature of the zero spontaneous curvature is obtained at the “fish tail” in the pseudo-binary phase diagram: temperature versus surfactant mass fraction at 50% in volume of water and oil (19). For nonionic surfactants (C i E j ), the spontaneous curvature H 0 is strongly temperature dependent (23) and quantitative evaluations are available for such surfactants. For one temperature T˜ , H 0 is zero by definition, while a variation of temperature depending on the surfactant induces a curvature variation. If we consider a part of the pseudo-binary phase diagram (T, g ) of the water– cyclohexane–C 8E 6 system (2) reproduced in Fig. 1, we see that at low surfactant weight fraction, we observe the classic sequence by increasing temperature: 1. At temperature T˜ the film would be at the zero spontaneous curvature, where bicontinuous microemulsions, lamellar phases, or locally lamellar phases such as sponge structure can
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be encountered. A Winsor III domain is observed in the case shown here. 2. At temperature higher than T˜ the film prefers the curvature toward water (H 0 , 0) and water-in-oil droplet microemulsions with water in excess are observed at the emulsification failure; a Winsor II phase separation is observed. 3. At temperature T 1 lower than T˜ , the film prefers the curvature toward oil (H 0 . 0) and oil-in-water droplet microemulsions with an excess of oil are observed at the emulsification failure; this dispersion is the so-called Winsor I phase separation. As symbolized by the arrow in Fig. 1, for the sample corresponding to surfactant composition g˜ , the curvature of the film increases from an average curvature equal to zero ^H& 0 at temperature T˜ to a nonzero curvature ^H& at lower temperature T 1 5 T˜ 2 DT. With the convention of an average curvature positive toward oil, the average curvature of the film increases when the temperature decreases. This variation with temperature is consistent with a monotonic increase in the curvature ^H& with decreasing temperature. At first order a linear relationship for the curvature dependence with the temperature could be assumed (23). This proportionality is expressed by
FIG. 2. Pseudo-binary phase diagram (T, g ) at equal water-to-oil volume ratios for water–(cyclohexane 1 lindane)–C 8E 6 system at two initial lindane compositions given by b, the weight percentage of lindane in the oil: (h) b 5 0%, (‚) b 5 9.8%. Two schematic representations of the microstructure of the microemulsions are drawn to illustrate the variation induced by the solubilization of lindane.
^H& being the average curvature, ^H& 0 the average curvature at the zero spontaneous curvature, and c the proportionality constant. To determine the constant c, using SAXS and SANS, it is necessary to determine the curvature radius R of water– cyclohexane–C 8E 6 o/w microemulsions at temperature T 1 . At this temperature, the Winsor I microemulsion is assimilated to a dispersion of spherical droplets with average radius R. The curvature is given by ^H& 5 1/R. Using these two experimental results (refer to the next paragraph for the Winsor I study), ^H& 5 1/36 at 30°C and ^H& 0 5 0 at 53°C, we obtain an explicit relation equation for the curvature–temperature relationship for the C 8E 6 surfactant used in this study:
croemulsion to a bicontinuous microemulsion is observed while the oil composition varies from pure cyclohexane to a mixture of (cyclohexane 1 lindane) at b 5 9.8% in lindane. Therefore, by comparison of Figs. 1 and 2, we conclude that adding lindane to oil at constant temperature modifies the surfactant curvature of the film in the same way as increasing temperature with a pure oil. At a given temperature, the microstructure varies from a film curved toward oil (^H& . 0) to a flat film when lindane is added to the oil. The average curvature is decreasing as the amount of lindane solubilized in the microemulsion is increasing. The average curvature of the film without lindane at T˜ (b 5 9.8%) can be obtained from Eq. [2]. Therefore, we deduce a new expression that scales the curvature induced by b% of lindane in the oil to the variation of the balanced temperature T˜ :
^H& 2 ^H& 0 5 21.2 3 10 23 ~T˜ 2 T!.
^H~0!& 2 ^H~ b !& 5 1.2 3 10 23 ~T˜ ~0! 2 T˜ ~ b !!.
^H& 2 ^H& 0 5 c 3 ~T˜ 2 T!,
[1]
[2]
Curvatures are expressed in Å 21 and temperatures in Kelvin. In the preceding paper (2), we reported the phase diagrams of water–(cyclohexane 1 lindane)–C 8E 6 for different weight percentages b of lindane in oil. The mixture cyclohexane 1 lindane is considered a pseudo-component. We showed that the solubilization of lindane in bicontinuous microemulsions induces a decrease in the temperature at which zero spontaneous curvature occurs. In Fig. 2, we report a part of two pseudobinary phase diagrams of the water–(cyclohexane 1 lindane)– C 8E 6 system with the two initial weight compositions in lindane b 5 0% and b 5 9.8%. At point B 1, at temperature T˜ (b 5 9.8%) 5 39.5°C, a transition from an oil-in-water mi-
[3]
Figure 3 summarizes the variation in temperature T˜ versus weight percentage b of lindane in the initial oil. This figure was obtained from the fish determination of pseudo-ternary system water–(cyclohexane 1 lindane)–C 8E 6 (2). A linear relationship between T˜ and b (Fig. 4) is obtained: T˜ ~ b ! 5 T˜ ~0! 2 1.33 3 b .
[4]
This relation is limited by the saturation value l max 5 0.281, b 5 11.5%. Using the temperature dependence of the average curvature of the system water–(cyclohexane 1 lindane)–C 8E 6 on the
EXCESS SOLUBILIZATION/CURVATURE IN NONIONIC MICROEMULSIONS
15
This relationship gives the ratio between induced curvature variation and solute content in the surfactant film. The curvature induced by the presence of a solute molecule in the interfacial film is linear with the molar fraction of solute adsorbed at the interface. Is this due to some molecular constraint? To scale curvature, we introduce the natural molecular length l and take from Eq. [6] the product of the average curvature and the length of a C 8 hydrocarbon chain (l > 11 Å). We obtain a direct relationship between the reduced curvature and the molar fraction of solute adsorbed at the interface: D^H& 3 P > 20.7 l .
[7]
DH is the curvature difference between the final state (with FIG. 3. (■) Variation of the temperature of the zero spontaneous curvature of water–(cyclohexane 1 lindane)–C 8E 6 versus the initial weight percentage b of lindane in the oil. (‚) Linear variation of the average curvature versus the initial composition b of the oil.
initial composition b of lindane in oil (i.e., [4]), we translate [3] by directly relating curvature induced by the quantity b of lindane to the composition b [5]: ^H~0!& 2 ^H~ b !& 5 2D^H& 5 1.6 3 10 23 b .
[5]
This expression expresses the variation of the curvature induced by the initial composition of the oil which is also shown in Fig. 3. Our aim is to obtain a curvature dependence on the amount of lindane adsorbed at the interface. In a former study, we demonstrated that excess solubilization exists in bicontinuous microemulsions at zero spontaneous curvature for different surfactants C 6E 5 (29), C 8E 6 (35), and C 10E 8 (35). We quantified this excess with the interfacial molar composition l, which is the solute/surfactant molar ratio at the interface. We obtained for C 6E 5 a curve analoguous to an isotherm adsorption curve of a gas on a solid surface (29). This “isocurvature” adsorption curve described the evolution of the interfacial molar ratio l at constant zero curvature versus the initial bulk composition. A linear relationship between the excess parameter composition of the film l and the initial composition b of the oil with lindane is measured. A similar relationship was obtained for the C 8E 6 microemulsion (35): l 5 0.024b between interfacial composition and initial bulk composition of the oil. The curvature variation with the bulk composition described by Eq. [5] can be transposed in a direct relationship between the curvature variation and the amount of lindane adsorbed at the interface given by the relation D^H& 5 ^H~ b !& 2 ^H~0!& 5 20.065l.
[6]
FIG. 4. Experimental and best fits in absolute intensities. (a) For SAXS experiments performed with samples A (}, experimental curve) and B (F, experimental curve). The dashed lines correspond to the best fit to determine the curvature. (b) For SANS experiments performed with samples A ({, experimental curve) and B (E, experimental curve). The dashed lines correspond to the fit. The representation is in I/Q* (intensity in cm 21 divided by invariant value) versus the wavevector q.
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TESTARD AND ZEMB
TABLE 1 Oil Represents the Mixture Cyclohexane 1 Lindane a
f oil f s/f oil l
Sample A
Sample B
0.055 3 0
0.06 2.5 0.1
a f oil is the oil volume fraction, f s is the surfactant volume fraction, and l is the interfacial composition parameter.
lindane in the film, l) and the initial state (without lindane in the film, l9 , l). Therefore “adsorption” of lindane in the film induces a curvature toward water and this variation is quantified by Eq. [7]. Winsor I Microemulsion We now turn to the determination of the excess solubilization l when the microstructure is a single-phase oil-in-water microemulsion with a curved interface. The low temperature limit from single-phase microemulsions is shown in Fig. 2. Increasing the fraction of lindane in the oil modifies the singlephase domain boundaries. At temperature T 2 (,T˜ ) the emulsification failure represents the maximum swelling of a microemulsion at a water-to-oil volume ratio equal to one. At this solubilization phase boundary, when the microstructure is made of droplets as for an o/w microemulsion, the droplet size corresponds to the spontaneous monolayer curvature. The droplets are assumed to be spherical and behave as hard spheres. At one temperature, this phase limit shifts toward smaller weight fraction of surfactant when part of the cyclohexane is replaced by lindane (2). The solubilization limit is located at a smaller surfactant/oil volume fraction when the oil is a pseudo-component mixture made of “cyclohexane 1 lindane” than for pure cyclohexane. The oil-in-water microemulsion at the emulsification failure is composed of droplets with a larger average radius when the oil contains lindane. As for bicontinuous microemulsions, our aim is to determine if some fraction of the available lindane is located within the interfacial film. To quantify this excess solubilization, we study the equilibrium of Winsor I where an oil-in-water microemulsion is in equilibrium with an excess of oil. Assuming that the oil in excess is of the same composition as the oil in the microemulsion (28), we obtain by dosage the value of the interfacial composition l for one o/w microemulsion as described under Materials and Methods. A strictly positive value for this interfacial molar ratio l is evidence for an excess of solubilization of lindane in the Winsor I system. The composition of the microemulsion and the obtained l value are reported in Table 1. We observe here also an excess of solubilization (l . 0) for such Winsor I microemulsions. To determine the influence on the structure of the aggregates of the amount of lindane adsorbed at the interface, we have to
measure at 30°C the average curvature as a function of the excess of solubilization l. By SANS experiments, using isotopic substitution, we determine the microstructure of the aggregates. This contrast is set by deuterated cyclohexane and protonated water and surfactant. Those experiments were completed by SAXS experiments to determine with precision the average radius at the polar/apolar interface. The SAXS and SANS scattering data for sample A without lindane and sample B with 5% lindane in the initial oil are shown in Figs. 4a and 4b. In each case, the scattering profile exhibits a single intensity maximum at q Þ 0. This scattering peak is at the same position for SANS and SAXS experiments. Therefore we are sure that this peak is dominated by the interparticle correlation peak, not by form factors. The results of the best fits toward monodisperse droplets are shown in Fig. 4a for SAXS experiments and in Fig. 4b for SANS experiments. The fitting parameters are listed in the Table 2. The radius value obtained by SAXS experiments represents the radius of the droplets at the polar/apolar interface and is increasing with excess adsorption of lindane in the film. Assuming the average curvature for droplets as the inverse of the radius, we obtain the variation of the induced curvature variation D^H& 5 20.066 for l 5 0.1, the amount of lindane adsorbed at the interface, and hence D^H& 3 P 5 20.66 at this point. Geometric Interpretation of the Observed Curvature Variations The general constraint on the film is imposed microscopically by the packing parameter P 5 V/ s l introduced by Ninham and co-workers (1, 36), where V is the volume of the apolar part of the surfactant, l is the thickness of the film or the length of the surfactant chain, and s the interfacial area per molecule. Surfactant parameter P and curvatures are linked by the fundamental coverage relationship (1) V/ s l 5 1 2 ^H&l 1 ^K&l 2 /3,
[8]
where ^H& is the average curvature and ^K& the Gaussian curvature with the convention of P relating to the apolar volume and ^H& positive toward the oil. This coverage rela-
TABLE 2 Fit Parameters of the Experimental Scattering Spectra a
SAXS: R, h, t SANS: R i, t
Sample A
Sample B
36, 1, 100 28, 100
47, 1, 10 33, 10
a R is the radius of the droplets at the apolar/polar interface, h is the hydration number per OCH 2CH 2 of the surfactant head, and t is the stickiness parameter.
EXCESS SOLUBILIZATION/CURVATURE IN NONIONIC MICROEMULSIONS
tionship provides a constraint between the packing parameter and the possibility of coverage of the oil/water interface with a film without tearing the latter (1). If a constraint induces a modification of the packing parameter P, the response of the system is a variation of the microstructure to still satisfy the coverage relationship. An energetic cost is needed if the geometry of the film is modified. In particular, if the constraint induces a curvature variation, there is some bending energy associated with this variation. This bending energy is related to the deviation of the effective surfactant parameter from its preferred value (1), E 5 12 k*~P eff 2 P 0 ! 2 , where k* is an elastic constant, and P eff and P 0 denote the effective and preferred values of the surfactant parameter. The relationships between k* and the usual choice of two separate bending constants are established and discussed in Ref. (21). By considering the molecular volumes of the two components of the interfacial film, we explain at first order all the experimental results of the variation of curvature induced by the adsorption of lindane at the interface in the different physical situations encountered. a. Low reduced curvature. The solubilization of lindane induces a variation of the curvature, and so it induces a variation of the packing parameter P. Consider first the water–(cyclohexane 1 lindane)–C 8E 6 system with initial composition b (b Þ 0) of lindane in oil. At the temperature of the zero spontaneous curvature T˜ ( b ), the curvature of the surfactant film is ^H( b )& 5 0 and the coverage relationship gives the relation [9] ~V 1 l V L!/ s l 5 1 2 ^H~ b !&l > 1,
[9]
where V L is the volume of the solute and V the volume of the apolar chains. We neglect the nonlinear term compared with the other terms because we are in the case of reduced curvature much lower than 1. If we consider at the same temperature the water– cyclohexane–C 8E 6 system, with pure oil (b 5 0) the microstructure is now an o/w microemulsion and the curvature ^H(0)& of the film is not equal to zero; the coverage relationship gives the following equation, because for large spherical droplets the second term is still negligible compared with the other terms: V/ s l 5 1 2 ^H~0!&l Þ 1.
[10]
We have determined by SANS (29, 35) that the surfactant headgroup area does not depend on the amount of lindane in the sample. We also know that the temperature dependence of area per headgroup is negligible in the neutral plane. Therefore we can take the area per surfactant s independent of lindane content. We find the value of 68 Å 2 for those C 8E 6 microemul-
17
sions (35). This value is similar to that found by Strey in water–n-alkane–C 8E 6 microemulsions (37). Thus, the variation in curvature as a function of the interfacial composition parameter l is obtained by difference, based on the simple argument that the solute acts as a wedge of volume V in the interfacial film: D^H&l 5 2~V L/ s l ! l .
[11]
Numerically, taking V L 5 277 Å 3, s 5 68 Å 2, and l 5 11 Å, we obtain a relationship due only to steric insertion of the molecule in the interfacial film between the induced curvature and the amount of lindane at the interface: D^H&l 5 20.4l.
[12]
We underline at this point that the effective volume V, which has to be taken into account, includes the penetrating oil volume, as already pointed out for the mixture C 6/C 14 in Ref. (38). In our case the volume of the chain of the surfactant is V 5 242 Å 3, while at temperature T˜ we know that V/ s l 5 1 and with the known values l 5 11 Å and s 5 68 Å 2, we have V eff 5 748 Å 3 including the solvent penetration. Therefore, on average 506 Å 3 5 2.8 molecules of cyclohexane per surfactant wet the interfacial film. This relationship obtained only from the packing of the solute molecule as a wedge in the film is similar to that obtained experimentally [7]. This suggests that lindane acts like a wedge penetrating the hydrophobic chains. We do not consider the adsorption/desorption of the oil at the interface; this probably explains the difference between relationship [12] and the relationship [7] obtained experimentally. We illustrate the variation in reduced curvature versus interfacial molar composition l of the solute for different experimental cases and the geometric model in Fig. 5. This comparison illustrates the generality of the curvature variation induced by a hydrophobic solute: We see that the experimental value obtained in the Winsor I sample is close to the experimental points obtained in bicontinuous microemulsions, following Eq. [7]. b. Small droplets. For “small” droplets where radius of object and film thickness coincide as in micelles, we cannot neglect the nonlinear term in the coverage relationship. In the case of spherical droplets, Gaussian curvature is equal to the square of the average curvature, and ^H& is the inverse of the radius. This second term in Eq. [8] is negligible in our case for Winsor I microemulsions, where the radius of the droplet is larger than three lengths of the surfactant chain. But in the case of micelles where the average curvature is ^H& 5 1/l, we cannot neglect the second term in Eq. [8]. Therefore, the relationship obtained is described in the micellar case by DHl 5 23~V L/ s l ! l .
[13]
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TESTARD AND ZEMB
imation even if we would have to take into account the penetration of the solvent to obtain the experimental value. Finally, we show here a strikingly general linear relationship between induced curvature variation and solute content of the interfacial film for a hydrophobic solute. This study was performed in bicontinuous microemulsions and o/w microemulsions until the limit case of the micellar system without any oil. Leodidis and Hatton (40) described a complete study of the solubilization of amino acid in “reverse micelles” of A.O.T., an anionic ternary microemulsion. They demonstrated that the reverse micelle curvature radius at equilibrium varies also linearly with solute content: in their case, the induced curvature variation originates from electrostatic equilibrium while in the case of nonionic microemulsions, the molecular volume term is dominant. FIG. 5. Variation of the reduced average curvature D^H&l versus the interfacial composition l. The dotted line corresponds to the relationship found with the wedge model. Experimental points (■) were obtained from phase diagrams and dosage from the variation of the Winsor III domain with the amount of lindane solubilized in the oil. (E) Corresponds to the Winsor I sample. (Œ) Obtained in the micellar domain (2).
We see that the induced variation is now three times larger than that obtained in the case of low curvature. This would imply an increase in the radius of the micelles of 45%. This is unacceptably large since the radius of the micelles is limited by the chain length. In a former study (2) we did not observe any curvature variation in average resulting from the solubilization of lindane in C 8E 6 micelles. We also noted that the solubilization of lindane in micellar solution is quite small (l max 5 0.025) (2) compared to the value obtained in bicontinuous microemulsions (0 , l , l max 5 0.28). At saturation l max 5 0.025 for H 5 1/l, l being the chain length of the C 8E 6 surfactant. This point is evidence of the small capacity of micellar solution to solubilize lindane compared with microemulsion solutions. CONCLUSION
Our aim was to establish a quantitative relationship between the variation in film curvature induced by the amount of lindane solubilized at the interface and molecular volume. In a former study, Hatton et al. gave a curvature dependence for solubilization of amino acid in w/o A.O.T. microemulsions (39, 40), amino acid being water soluble. Therefore our question was: Is it possible to find such a dependence for an oil-soluble solute with nonionic surfactant solutions? We have shown this relationship is valid within a factor of 2 by using geometrical packing and considering only the solute molecule as a wedge. The topological coverage relationship gives the right value for the variation in curvature induced by solubilization. If we suppose that the solute acts as a “wedge” of known molecular volume, this model gives a good approx-
REFERENCES 1. Hyde, S., Anderson, S., Larsson, K., Blum, Z., Landh, T., Lidin, S., and Ninham, B. W., “The Language of Shape, The Role of Curvature in Condensed Matter: Physics, Chemistry and Biology.” Elsevier, Amsterdam, 1997. 2. Testard, F., and Zemb, Th., Langmuir 14, 3175 (1998). 3. Tanford, C., “The Hydrophobic Effect: Formation of Micelles and Biological Membranes.” Wiley, New York, 1973. 4. Van Vloten, G. W., Kruissink, Ch. A., Strijk, B., and Bijvoet, J. M., Acta Crystallogr. 3, 139 (1950). 5. Turk, J., and Turk, A., “Environmental Science.” Saunders, Philadelphia. 6. Lee, J. F., Mortland, M. M., Boyd, S. A., and Chiou, C. T., J. Chem. Soc. Faraday Trans. 1 85, 2953 (1989). 7. Hesketh, N., Jones, M. N., and Tipping, E., Anal. Chim. Acta 327, 191 (1996). 8. Lee, A. G., and Malcolm East, J., Pestic. Sci. 32, 317 (1991). 9. Antunes-Madeira, M. C., and Madeira, M. C. V., Biochim. Biophys. Acta 820, 165 (1985). 10. Chevalier, Y., and Zemb, Th., Rep. Prog. Phys. 53, 279 (1990). 11. Sjo¨blom, J., Lindberg, R., and Fridberg, S. E., Adv. Colloid Interface Sci. 95, 125 (1996). 12. Antunes-Madeira, M. C., and Madeira, V. M. C., Biochim. Biophys. Acta 820, 165 (1985); 982, 161 (1989). 13. Antunes-Madeira, M. C., Almeida, L. M., and Madeira, V. M. C., Biochim. Biophys. Acta 1022, 110 (1990). 14. Sabra, M. C., Jorgensen, K., and Mouritsen, O. G., Biochim. Biophys. Acta 1233, 89 (1995). 15. Shinoda, K., and Kunieda, H., in “Microemulsion, Theory and Practice” (L. Prince, Ed.). Academic Press, New York, 1977. 16. Kunieda, H., and Friberg, S., Bull Chem. Soc. Jpn. 54, 1010 (1981). 17. Kunieda, H., and Shinoda, K., J. Dispersion Sci. Technol. 3, 233 (1982). 18. Kahlweit, M., and Strey, R., Angew. Chem. Int. Ed. Engl. 24, 654 (1985). 19. Kahlweit, M., Strey, R., and Busse, G., J. Phys. Chem. 94, 3881 (1990). 20. Winsor, P. A., “Solvent Properties of Amphiphilic Compounds.” Butterworth, London, 1954. 21. Fogden, A., Hyde, S. T., and Lundberg, G., J. Chem. Soc. Faraday Trans. 87, 949 (1991). 22. Zemb, Th., Colloids Surf. A 129/130, 435 (1997). 23. Strey, R., Colloid Polym. Sci. 272, 1005 (1994). 24. Gradzielski, M., Langevin, D., Sottmann, T., and Strey, R., J. Chem. Phys. 106, 19, 8232 (1997). 25. Strey, R., Glatter, O., Schubert, K.-V., and Kaler, E. W., J. Chem. Phys. 105, 1175 (1996).
EXCESS SOLUBILIZATION/CURVATURE IN NONIONIC MICROEMULSIONS 26. Tlusty, T., Safran, S. A., Menes, R., and Strey, R., Phys. Rev. Lett. 78, 2617 (1997). 27. Fletcher, P. D. I., J. Chem. Soc. Faraday Trans. 1 82, 2651 (1986). 28. Leodidis, E. B., and Hatton, T. A., J. Phys. Chem. 94, 6400 (1990); J. Phys. Chem. 94, 6411 (1990). 29. Testard, F., Zemb, Th., and Strey, R., Progr. Colloid Polym. Sci. 105, 332 (1997). 30. Leflanchec, V., Gazeau, D., Taboury, J., and Zemb, Th., J. Appl. Crystallogr. 29, 110 (1996). 31. Ne´, F., Gazeau, D., Lambard, J., Koksis, M., and Zemb, Th., J. Appl. Crystallogr. 26, 763 (1993). 32. Zemb, T. N., Barnes, I. S., Derain, P. J., and Niham, B. W., Progr. Colloid Polym. Sci. 81, 20 (1990).
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33. Menon, S. V. G., Khekar, V. K., and Manohar, C., Phys. Rev. A 43, 43 (1991). 34. Guinier, A., and Fournet, G., “Small Scattering of X-rays.” Wiley, New York, 1995. 35. Testard, F., Thesis, Univ. of Paris VI, 1997. 36. Israelachvili, J. N., Mitchell, D. J., and Ninham, B. W., J. Chem. Soc. Faraday Trans. II 72, 1525 (1976). 37. Sottman, T., Strey, R., and Chen, S. H., J. Chem. Phys. 105, 6483 (1997). 38. Chen, S. J., Evans, D. F., Ninham, B. W., Mitchell, D. J., Blum, F. D., and Pickup, S., J. Phys. Chem. 90, 842 (1986). 39. Leodidis, E. B., Bommarius, A. S., and Hatton, T. A., J. Phys. Chem. 95, 5943 (1991). 40. Leodidis, E. B., and Hatton, T. A., J. Phys. Chem. 95, 5957 (1991).
Excess of Solubilization and Curvature in Nonionic Microemulsions F. Testard 1 and Th. Zemb CEA/Saclay, Service de Chimie Mole´culaire DRECAM, Bat 125, F91191 Gif-sur-Yvette Cedex, France Received December 14, 1998; accepted July 30, 1999
vature dependence at saturation, i.e., when excess solute is present as a solid (2). As in the previous paper, we have chosen lindane, the g-isomer of hexachlorocyclohexane (4), as a model solute, since it was one of the most widely used organochlorine pesticides for agricultural purposes. Lindane is slowly degraded in the environment and therefore can accumulate in organic tissues (5). This hydrophobic molecule binds extensively to organic soils, clay systems (6), humic substances (7), and biological membranes (8, 9). In the last few years, considerable information has been acquired relating to human exposure and soil pollution with pesticide residues: more than 1000 papers describe analysis results of lindane accumulation in different soils, but without relating this adsorption to phase diagrams of surfactant systems (10, 11). However, numerous papers (12–14) describe the effect of lindane on synthetic and native membranes to establish the undesirable toxic effect of such a pesticide. Our model system is a quaternary system: water– oil–nonionic surfactant solutions with added lindane. The use of C i E j nonionic surfactants of the polyoxyethylene glycol family is particularly attractive as microemulsions could be obtained with only three constituents without any cosurfactant, adjusting the temperature range. Moreover, by varying the relative volumes of the polar and apolar parts of those surfactant molecules, it is easy to modify the hydrophilic/hydrophobic balance. The hydration of the headgroups of those surfactants is temperature dependent and so the phase diagram is governed by the temperature: due to dehydration of the nonionic headgroups, the spontaneous curvature turns from oil to water by increasing temperature. Shinoda and co-workers’ (15–17) pioneering study, as well as the work of Kahlweit’s group (18, 19), made the ternary phase prism of nonionic ternary systems available. Microemulsions exhibit a microstructure: oil microdomains are separated from water microdomains by a surfactant film (20). The type of microstructure (w/o, o/w or bicontinuous) is determined by the distribution of the amphiphile between water and oil and by the water-to-oil ratio. At each temperature, the surfactant film has a different spontaneous curvature H 0 , and the water-to-oil ratio imposes the sign of the average curvature ^H& produced in the sample. For example, curvature can be directed only toward the minority component. The magnitude
We measure separately the amount of solute dissolved in a surfactant monolayer and the average curvature of the relevant sample to establish a link between these two quantities. The model system chosen involves the common hydrophobic pesticide lindane (g-C 6H 6Cl 6) in a nonionic surfactant solution of the ethylene oxide type. Excess solubilization, defined as the solubilization in the surfactant film by comparison with bulk oil, is quantified by the interfacial composition l (molar ratio solute/surfactant) within the interfacial film. A linear relationship between the amount of solute adsorbed on the film and the induced variation in curvature of the surfactant film is deduced from the phase diagram, dosage, and small-angle scattering experiments in the case of micellar, Winsor I, and several Winsor III domains at equilibrium in the same ternary system. We discuss the linear relationship obtained with constraints set by molecular packing. © 1999 Academic Press Key Words: curvature; microemulsions; micelles; solubilization.
INTRODUCTION
To develop predictive models about solubilization in heterogeneous media, the mechanism of solubilization of a solute in surfactant solution and the possible consequences on the properties of surfactant film such as curvature have to be understood (1). In a previous work (2), we established that maximum solubilization of a model apolar (3) constituent in a microemulsion (a) exceeds the solubilization in pure oil and (b) induces a shift in the temperature of the zero spontaneous curvature, and (c) that the maximum solubilization, when in equilibrium with excess solid, is curvature dependent. To investigate this curvature effect in different physical situations, we generalize this approach and compare in this paper the effect of adsorption in differently curved structures as micelles or o/w microemulsions, as well as adsorption in microemulsions with a zero curvature. The aim of the work presented here is to quantify the curvature variation with the amount of solute adsorbed in the interfacial film at variable solute/oil concentrations. This extends the previous observations, which have evidenced a cur1
To whom correspondence should be addressed. E-mail: testard@ nanga.saclay.cea.fr. 11
0021-9797/99 $30.00 Copyright © 1999 by Academic Press All rights of reproduction in any form reserved.
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TESTARD AND ZEMB
of the average curvature depends on the topology of the interface (1). For a given sample, the spontaneous curvature H 0 differs from the average curvature ^H&; the difference is traduced by the bending energy which depends on the magnitude of the bending constants (21). In the limit k c @ kT, a predictive model is available for the composition where the local microstructure is composed of spheres, cylinders, and bilayers (22). Single-chain nonionic surfactants have bending constants typically on the order of 1 kT (23, 24). C i E j family surfactants show the same variation of local microstructure (25) and are stable within a large range of curvature ^H&, since the emulsification failure requires a large difference between ^H& and H 0 (26). Localization of our solute molecule model could occur in the two molecular environments: either oil microdomains or the surfactant film. The existence of such an excess of solubilization was first demonstrated by Fletcher (27) and Leodidis and Hatton (28). Solubilization within the surfactant film is the origin of the observed excess of solubilization, by comparison with bulk oil. They have quantified the excess solubilization by the interfacial composition parameter l, which is the molar ratio of solute to surfactant located at the interface. We also use this interfacial molar ratio to quantify the excess lindane at the interface. The extreme case of the micelle, the binary system without any oil, where all the solubilized lindane is located at the interface has been studied in (2). In this approach, the solubilization is considered as an adsorption study of the solute at the interface. Solubilization of lindane in bicontinuous and oil-in-water microemulsions is limited by thermodynamic saturation, which is evidenced by the slow growth of excess lindane crystals. In this paper, our study in microemulsions is performed before saturation, when the interfacial film is not saturated with lindane.
the samples by mixing a volume V of a surfactant aqueous solution at 15% in surfactant volume fraction, with a volume V9 of an organic solution (cyclohexane 1 lindane) at a given composition in lindane. After mixing and cycling the temperature above 30°C, we let the solutions phase separate. The solutions separate into two phases: an oil-in-water microemulsion with an excess of oil. By dosage, we determine the compositions of the two phases and use the usual assumption that the microdomains oil in the microemulsion and oil in excess are at the same composition (28). From the difference between the compositions of the oil in excess and the oil in the microemulsion, we calculate the value of the interfacial composition parameter l. We used a gas chromatograph equipped with an OV-17 column (T 5 140–2258C) to dose the lindane and surfactant in the solution. Water was titrated by the Karl-Fisher method with a KF 684 coulometer, and cyclohexane was obtained by difference. Small-Angle X-ray Scattering Scattering experiments on the microemulsions were performed in 0.2-mm-thick borosilicate capillaries for good temperature control. We employed a home-built Huxley–Holmestype, high-flux camera using a pinhole geometry. The X-ray source was a copper rotating anode operating at 12 kW. The K a 1 radiation was selected by the combination of a nickelcovered mirror and a bent, asymmetrically cut germanium ^111& monochromator. Data correction, radial averaging, and absolute scaling were performed using routine procedures. The precise description of this camera is given in Refs. (30, 31). The spectra were recorded with a two-dimensional gas detector which had an effective q range from 0.02 to 0.4 Å 21 [q 5 (4 p / l )sin u]. Small-Angle Neutron Scattering
MATERIALS AND METHODS
Materials Hexaoxyethylene glycol mono-n-octyl ether (C 8E 6) was purchased from NIKKO Chemicals, Tokyo, and shown to be .99% pure by gas chromatography. Cyclohexane was obtained from SDS (Peypin) with a nominal purity .99%. We used Millipore-filtered water. Lindane was supplied by Aldrich with a nominal purity .97%, and was recrystallized in a mixture of CHCl 3/EtOH. The molecular densities (in g/cm 3) used to calculate the volume fractions are 1 for H 2O, 1.01 for C 8E 6, 0.779 for cyclohexane, and 1.73 for lindane at 25°C. The melting point of lindane is 112.5°C. Composition Analysis in the Winsor Microemulsions Details of the method used for the phase diagram determination and for titration in the Winsor III region are given in Ref. (29). For the study of the Winsor I samples, we prepared
Small-angle neutron scattering was carried out on the spectrometers D11 at the ILL, Grenoble, France. SANS spectra were measured at two sample-to-detector distances to investigate a wide range of scattering vectors: 0.011 , q , 0.1 Å 21 and 0.056 , q , 0.42 Å 21. The neutron wavelength resolution used was Dl/l 5 10%. The scattered intensity was recorded on a two-dimensional detector and the data were radially averaged. Absolute calibration was made using the incoherent scattering of water. The overlap is acceptable for the two data sets with a precision of 10% on the intensity scale. SANS and SAXS Data Treatment in the Winsor I Case To obtain a good estimation of curvature from the scattering experiment, the aggregates are treated to the first order as monodisperse spheres (32), covered by a surfactant layer. The oil core has the radius R i while the surfactant shell extends to the radius R o. The center of the film is located at R at the polar/apolar interface. In this case, the intensity I(q) may be
EXCESS SOLUBILIZATION/CURVATURE IN NONIONIC MICROEMULSIONS
13
written as the product of the form factor P(q), the structure factor S(q), the volume fraction of the droplets F, the volume of one droplet V, and the contrast variation Dr 2. I~q! 5 F 3 V 3 D r 2 3 P~q! 3 S~q!. We use for the structure factor S(q) the analytical expression for monodisperse particles interacting through a Baxter potential, given by Menon et al. (33). For SANS experiments, we consider for the form factor one interface and two media: hydrogenated medium and deuterated medium. This is a consistent hypothesis, as at high q values, Porod limit-type asymptotic decay occurs with q 24 behavior. The form factor for monodisperse spheres is the square of the first-order spherical Bessel function (34). Therefore, the classic fit for monodisperse interacting droplets in a SANS experiment depends on two parameters: the inner radius of the droplet R i and the stickiness parameter t. The hard-sphere diameter is deduced from the volume of the droplet considering the total volume of the surfactant at the interface. The fits were obtained by comparison of the intensity divided by the invariant value Q* for experimental and theoretical data. The invariant is calculated by integration of the intensity as it is described in the following equation for experimental and theoretical data (34):
Q* 5
E
q max
i~q! 3 q 2 3 dq.
q min
The q min and q max of the experiments are 0.011 and 0.44 Å 21, respectively. This corresponds to a resolution of 14 to 571 Å in the sample. The droplet size is of the order of 35 Å; therefore, we could calculate the invariant in the experimentally accessible q range. For SAXS experiments, we use the form factor of monodisperse concentric spheres, considering three contrasts for the core made of oil and surfactant chain, the shell made of surfactant headgroup and hydration water, and the outer medium made of water. The fit depends on three parameters: the core radius R, the hydration per glycol unity h of the polar head of the surfactant, and the stickiness parameter t. The hardsphere radius of the droplets is not a parameter; it is deduced from the inner radius and the droplet density. RESULTS AND DISCUSSION
Winsor III Microemulsion The Winsor III regime is obtained when a microemulsion is in equilibrium with excesses of both oil and water. These microemulsions solubilize lindane molecules located in the bulk oil or in the form of an “excess” solubilized at the interface. We focus on the case of lindane in water–surfactant–
FIG. 1. Pseudo-binary phase diagram (T, temperature, g, weight fraction of surfactant) at equal water-to-oil volume fractions for water– cyclohexane– C 8E 6. T˜ is the temperature of the zero spontaneous curvature. g˜ is the efficiency of the surfactant: the minimal amount of surfactant needed to solubilize an equal volume of water and oil. (h) Experimental points. (F) Two schematic representations of the microstructure of the microemulsion sample at two temperatures.
oil bicontinuous ternary microemulsion solution at the temperature T˜ of zero spontaneous curvature to determine the curvature variation of the surfactant film induced by the solubilization. Previously, we demonstrated that an excess of solubilization at the interface exists in such microemulsions and we quantified this excess for C 6E 5 (29), C 8E 6 (2), and C 10E 8 surfactants (35). In this section, we demonstrate the link between the excess of solubilization and the induced curvature variation. To measure the variation of the surfactant film curvature, we have to use the water-oil-surfactant ternary phase diagram: existing domains of Winsor III microemulsions are localized in the ternary phase diagram by a cut at equal water-to-oil volume ratio (18, 19). The temperature of the zero spontaneous curvature is obtained at the “fish tail” in the pseudo-binary phase diagram: temperature versus surfactant mass fraction at 50% in volume of water and oil (19). For nonionic surfactants (C i E j ), the spontaneous curvature H 0 is strongly temperature dependent (23) and quantitative evaluations are available for such surfactants. For one temperature T˜ , H 0 is zero by definition, while a variation of temperature depending on the surfactant induces a curvature variation. If we consider a part of the pseudo-binary phase diagram (T, g ) of the water– cyclohexane–C 8E 6 system (2) reproduced in Fig. 1, we see that at low surfactant weight fraction, we observe the classic sequence by increasing temperature: 1. At temperature T˜ the film would be at the zero spontaneous curvature, where bicontinuous microemulsions, lamellar phases, or locally lamellar phases such as sponge structure can
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TESTARD AND ZEMB
be encountered. A Winsor III domain is observed in the case shown here. 2. At temperature higher than T˜ the film prefers the curvature toward water (H 0 , 0) and water-in-oil droplet microemulsions with water in excess are observed at the emulsification failure; a Winsor II phase separation is observed. 3. At temperature T 1 lower than T˜ , the film prefers the curvature toward oil (H 0 . 0) and oil-in-water droplet microemulsions with an excess of oil are observed at the emulsification failure; this dispersion is the so-called Winsor I phase separation. As symbolized by the arrow in Fig. 1, for the sample corresponding to surfactant composition g˜ , the curvature of the film increases from an average curvature equal to zero ^H& 0 at temperature T˜ to a nonzero curvature ^H& at lower temperature T 1 5 T˜ 2 DT. With the convention of an average curvature positive toward oil, the average curvature of the film increases when the temperature decreases. This variation with temperature is consistent with a monotonic increase in the curvature ^H& with decreasing temperature. At first order a linear relationship for the curvature dependence with the temperature could be assumed (23). This proportionality is expressed by
FIG. 2. Pseudo-binary phase diagram (T, g ) at equal water-to-oil volume ratios for water–(cyclohexane 1 lindane)–C 8E 6 system at two initial lindane compositions given by b, the weight percentage of lindane in the oil: (h) b 5 0%, (‚) b 5 9.8%. Two schematic representations of the microstructure of the microemulsions are drawn to illustrate the variation induced by the solubilization of lindane.
^H& being the average curvature, ^H& 0 the average curvature at the zero spontaneous curvature, and c the proportionality constant. To determine the constant c, using SAXS and SANS, it is necessary to determine the curvature radius R of water– cyclohexane–C 8E 6 o/w microemulsions at temperature T 1 . At this temperature, the Winsor I microemulsion is assimilated to a dispersion of spherical droplets with average radius R. The curvature is given by ^H& 5 1/R. Using these two experimental results (refer to the next paragraph for the Winsor I study), ^H& 5 1/36 at 30°C and ^H& 0 5 0 at 53°C, we obtain an explicit relation equation for the curvature–temperature relationship for the C 8E 6 surfactant used in this study:
croemulsion to a bicontinuous microemulsion is observed while the oil composition varies from pure cyclohexane to a mixture of (cyclohexane 1 lindane) at b 5 9.8% in lindane. Therefore, by comparison of Figs. 1 and 2, we conclude that adding lindane to oil at constant temperature modifies the surfactant curvature of the film in the same way as increasing temperature with a pure oil. At a given temperature, the microstructure varies from a film curved toward oil (^H& . 0) to a flat film when lindane is added to the oil. The average curvature is decreasing as the amount of lindane solubilized in the microemulsion is increasing. The average curvature of the film without lindane at T˜ (b 5 9.8%) can be obtained from Eq. [2]. Therefore, we deduce a new expression that scales the curvature induced by b% of lindane in the oil to the variation of the balanced temperature T˜ :
^H& 2 ^H& 0 5 21.2 3 10 23 ~T˜ 2 T!.
^H~0!& 2 ^H~ b !& 5 1.2 3 10 23 ~T˜ ~0! 2 T˜ ~ b !!.
^H& 2 ^H& 0 5 c 3 ~T˜ 2 T!,
[1]
[2]
Curvatures are expressed in Å 21 and temperatures in Kelvin. In the preceding paper (2), we reported the phase diagrams of water–(cyclohexane 1 lindane)–C 8E 6 for different weight percentages b of lindane in oil. The mixture cyclohexane 1 lindane is considered a pseudo-component. We showed that the solubilization of lindane in bicontinuous microemulsions induces a decrease in the temperature at which zero spontaneous curvature occurs. In Fig. 2, we report a part of two pseudobinary phase diagrams of the water–(cyclohexane 1 lindane)– C 8E 6 system with the two initial weight compositions in lindane b 5 0% and b 5 9.8%. At point B 1, at temperature T˜ (b 5 9.8%) 5 39.5°C, a transition from an oil-in-water mi-
[3]
Figure 3 summarizes the variation in temperature T˜ versus weight percentage b of lindane in the initial oil. This figure was obtained from the fish determination of pseudo-ternary system water–(cyclohexane 1 lindane)–C 8E 6 (2). A linear relationship between T˜ and b (Fig. 4) is obtained: T˜ ~ b ! 5 T˜ ~0! 2 1.33 3 b .
[4]
This relation is limited by the saturation value l max 5 0.281, b 5 11.5%. Using the temperature dependence of the average curvature of the system water–(cyclohexane 1 lindane)–C 8E 6 on the
EXCESS SOLUBILIZATION/CURVATURE IN NONIONIC MICROEMULSIONS
15
This relationship gives the ratio between induced curvature variation and solute content in the surfactant film. The curvature induced by the presence of a solute molecule in the interfacial film is linear with the molar fraction of solute adsorbed at the interface. Is this due to some molecular constraint? To scale curvature, we introduce the natural molecular length l and take from Eq. [6] the product of the average curvature and the length of a C 8 hydrocarbon chain (l > 11 Å). We obtain a direct relationship between the reduced curvature and the molar fraction of solute adsorbed at the interface: D^H& 3 P > 20.7 l .
[7]
DH is the curvature difference between the final state (with FIG. 3. (■) Variation of the temperature of the zero spontaneous curvature of water–(cyclohexane 1 lindane)–C 8E 6 versus the initial weight percentage b of lindane in the oil. (‚) Linear variation of the average curvature versus the initial composition b of the oil.
initial composition b of lindane in oil (i.e., [4]), we translate [3] by directly relating curvature induced by the quantity b of lindane to the composition b [5]: ^H~0!& 2 ^H~ b !& 5 2D^H& 5 1.6 3 10 23 b .
[5]
This expression expresses the variation of the curvature induced by the initial composition of the oil which is also shown in Fig. 3. Our aim is to obtain a curvature dependence on the amount of lindane adsorbed at the interface. In a former study, we demonstrated that excess solubilization exists in bicontinuous microemulsions at zero spontaneous curvature for different surfactants C 6E 5 (29), C 8E 6 (35), and C 10E 8 (35). We quantified this excess with the interfacial molar composition l, which is the solute/surfactant molar ratio at the interface. We obtained for C 6E 5 a curve analoguous to an isotherm adsorption curve of a gas on a solid surface (29). This “isocurvature” adsorption curve described the evolution of the interfacial molar ratio l at constant zero curvature versus the initial bulk composition. A linear relationship between the excess parameter composition of the film l and the initial composition b of the oil with lindane is measured. A similar relationship was obtained for the C 8E 6 microemulsion (35): l 5 0.024b between interfacial composition and initial bulk composition of the oil. The curvature variation with the bulk composition described by Eq. [5] can be transposed in a direct relationship between the curvature variation and the amount of lindane adsorbed at the interface given by the relation D^H& 5 ^H~ b !& 2 ^H~0!& 5 20.065l.
[6]
FIG. 4. Experimental and best fits in absolute intensities. (a) For SAXS experiments performed with samples A (}, experimental curve) and B (F, experimental curve). The dashed lines correspond to the best fit to determine the curvature. (b) For SANS experiments performed with samples A ({, experimental curve) and B (E, experimental curve). The dashed lines correspond to the fit. The representation is in I/Q* (intensity in cm 21 divided by invariant value) versus the wavevector q.
16
TESTARD AND ZEMB
TABLE 1 Oil Represents the Mixture Cyclohexane 1 Lindane a
f oil f s/f oil l
Sample A
Sample B
0.055 3 0
0.06 2.5 0.1
a f oil is the oil volume fraction, f s is the surfactant volume fraction, and l is the interfacial composition parameter.
lindane in the film, l) and the initial state (without lindane in the film, l9 , l). Therefore “adsorption” of lindane in the film induces a curvature toward water and this variation is quantified by Eq. [7]. Winsor I Microemulsion We now turn to the determination of the excess solubilization l when the microstructure is a single-phase oil-in-water microemulsion with a curved interface. The low temperature limit from single-phase microemulsions is shown in Fig. 2. Increasing the fraction of lindane in the oil modifies the singlephase domain boundaries. At temperature T 2 (,T˜ ) the emulsification failure represents the maximum swelling of a microemulsion at a water-to-oil volume ratio equal to one. At this solubilization phase boundary, when the microstructure is made of droplets as for an o/w microemulsion, the droplet size corresponds to the spontaneous monolayer curvature. The droplets are assumed to be spherical and behave as hard spheres. At one temperature, this phase limit shifts toward smaller weight fraction of surfactant when part of the cyclohexane is replaced by lindane (2). The solubilization limit is located at a smaller surfactant/oil volume fraction when the oil is a pseudo-component mixture made of “cyclohexane 1 lindane” than for pure cyclohexane. The oil-in-water microemulsion at the emulsification failure is composed of droplets with a larger average radius when the oil contains lindane. As for bicontinuous microemulsions, our aim is to determine if some fraction of the available lindane is located within the interfacial film. To quantify this excess solubilization, we study the equilibrium of Winsor I where an oil-in-water microemulsion is in equilibrium with an excess of oil. Assuming that the oil in excess is of the same composition as the oil in the microemulsion (28), we obtain by dosage the value of the interfacial composition l for one o/w microemulsion as described under Materials and Methods. A strictly positive value for this interfacial molar ratio l is evidence for an excess of solubilization of lindane in the Winsor I system. The composition of the microemulsion and the obtained l value are reported in Table 1. We observe here also an excess of solubilization (l . 0) for such Winsor I microemulsions. To determine the influence on the structure of the aggregates of the amount of lindane adsorbed at the interface, we have to
measure at 30°C the average curvature as a function of the excess of solubilization l. By SANS experiments, using isotopic substitution, we determine the microstructure of the aggregates. This contrast is set by deuterated cyclohexane and protonated water and surfactant. Those experiments were completed by SAXS experiments to determine with precision the average radius at the polar/apolar interface. The SAXS and SANS scattering data for sample A without lindane and sample B with 5% lindane in the initial oil are shown in Figs. 4a and 4b. In each case, the scattering profile exhibits a single intensity maximum at q Þ 0. This scattering peak is at the same position for SANS and SAXS experiments. Therefore we are sure that this peak is dominated by the interparticle correlation peak, not by form factors. The results of the best fits toward monodisperse droplets are shown in Fig. 4a for SAXS experiments and in Fig. 4b for SANS experiments. The fitting parameters are listed in the Table 2. The radius value obtained by SAXS experiments represents the radius of the droplets at the polar/apolar interface and is increasing with excess adsorption of lindane in the film. Assuming the average curvature for droplets as the inverse of the radius, we obtain the variation of the induced curvature variation D^H& 5 20.066 for l 5 0.1, the amount of lindane adsorbed at the interface, and hence D^H& 3 P 5 20.66 at this point. Geometric Interpretation of the Observed Curvature Variations The general constraint on the film is imposed microscopically by the packing parameter P 5 V/ s l introduced by Ninham and co-workers (1, 36), where V is the volume of the apolar part of the surfactant, l is the thickness of the film or the length of the surfactant chain, and s the interfacial area per molecule. Surfactant parameter P and curvatures are linked by the fundamental coverage relationship (1) V/ s l 5 1 2 ^H&l 1 ^K&l 2 /3,
[8]
where ^H& is the average curvature and ^K& the Gaussian curvature with the convention of P relating to the apolar volume and ^H& positive toward the oil. This coverage rela-
TABLE 2 Fit Parameters of the Experimental Scattering Spectra a
SAXS: R, h, t SANS: R i, t
Sample A
Sample B
36, 1, 100 28, 100
47, 1, 10 33, 10
a R is the radius of the droplets at the apolar/polar interface, h is the hydration number per OCH 2CH 2 of the surfactant head, and t is the stickiness parameter.
EXCESS SOLUBILIZATION/CURVATURE IN NONIONIC MICROEMULSIONS
tionship provides a constraint between the packing parameter and the possibility of coverage of the oil/water interface with a film without tearing the latter (1). If a constraint induces a modification of the packing parameter P, the response of the system is a variation of the microstructure to still satisfy the coverage relationship. An energetic cost is needed if the geometry of the film is modified. In particular, if the constraint induces a curvature variation, there is some bending energy associated with this variation. This bending energy is related to the deviation of the effective surfactant parameter from its preferred value (1), E 5 12 k*~P eff 2 P 0 ! 2 , where k* is an elastic constant, and P eff and P 0 denote the effective and preferred values of the surfactant parameter. The relationships between k* and the usual choice of two separate bending constants are established and discussed in Ref. (21). By considering the molecular volumes of the two components of the interfacial film, we explain at first order all the experimental results of the variation of curvature induced by the adsorption of lindane at the interface in the different physical situations encountered. a. Low reduced curvature. The solubilization of lindane induces a variation of the curvature, and so it induces a variation of the packing parameter P. Consider first the water–(cyclohexane 1 lindane)–C 8E 6 system with initial composition b (b Þ 0) of lindane in oil. At the temperature of the zero spontaneous curvature T˜ ( b ), the curvature of the surfactant film is ^H( b )& 5 0 and the coverage relationship gives the relation [9] ~V 1 l V L!/ s l 5 1 2 ^H~ b !&l > 1,
[9]
where V L is the volume of the solute and V the volume of the apolar chains. We neglect the nonlinear term compared with the other terms because we are in the case of reduced curvature much lower than 1. If we consider at the same temperature the water– cyclohexane–C 8E 6 system, with pure oil (b 5 0) the microstructure is now an o/w microemulsion and the curvature ^H(0)& of the film is not equal to zero; the coverage relationship gives the following equation, because for large spherical droplets the second term is still negligible compared with the other terms: V/ s l 5 1 2 ^H~0!&l Þ 1.
[10]
We have determined by SANS (29, 35) that the surfactant headgroup area does not depend on the amount of lindane in the sample. We also know that the temperature dependence of area per headgroup is negligible in the neutral plane. Therefore we can take the area per surfactant s independent of lindane content. We find the value of 68 Å 2 for those C 8E 6 microemul-
17
sions (35). This value is similar to that found by Strey in water–n-alkane–C 8E 6 microemulsions (37). Thus, the variation in curvature as a function of the interfacial composition parameter l is obtained by difference, based on the simple argument that the solute acts as a wedge of volume V in the interfacial film: D^H&l 5 2~V L/ s l ! l .
[11]
Numerically, taking V L 5 277 Å 3, s 5 68 Å 2, and l 5 11 Å, we obtain a relationship due only to steric insertion of the molecule in the interfacial film between the induced curvature and the amount of lindane at the interface: D^H&l 5 20.4l.
[12]
We underline at this point that the effective volume V, which has to be taken into account, includes the penetrating oil volume, as already pointed out for the mixture C 6/C 14 in Ref. (38). In our case the volume of the chain of the surfactant is V 5 242 Å 3, while at temperature T˜ we know that V/ s l 5 1 and with the known values l 5 11 Å and s 5 68 Å 2, we have V eff 5 748 Å 3 including the solvent penetration. Therefore, on average 506 Å 3 5 2.8 molecules of cyclohexane per surfactant wet the interfacial film. This relationship obtained only from the packing of the solute molecule as a wedge in the film is similar to that obtained experimentally [7]. This suggests that lindane acts like a wedge penetrating the hydrophobic chains. We do not consider the adsorption/desorption of the oil at the interface; this probably explains the difference between relationship [12] and the relationship [7] obtained experimentally. We illustrate the variation in reduced curvature versus interfacial molar composition l of the solute for different experimental cases and the geometric model in Fig. 5. This comparison illustrates the generality of the curvature variation induced by a hydrophobic solute: We see that the experimental value obtained in the Winsor I sample is close to the experimental points obtained in bicontinuous microemulsions, following Eq. [7]. b. Small droplets. For “small” droplets where radius of object and film thickness coincide as in micelles, we cannot neglect the nonlinear term in the coverage relationship. In the case of spherical droplets, Gaussian curvature is equal to the square of the average curvature, and ^H& is the inverse of the radius. This second term in Eq. [8] is negligible in our case for Winsor I microemulsions, where the radius of the droplet is larger than three lengths of the surfactant chain. But in the case of micelles where the average curvature is ^H& 5 1/l, we cannot neglect the second term in Eq. [8]. Therefore, the relationship obtained is described in the micellar case by DHl 5 23~V L/ s l ! l .
[13]
18
TESTARD AND ZEMB
imation even if we would have to take into account the penetration of the solvent to obtain the experimental value. Finally, we show here a strikingly general linear relationship between induced curvature variation and solute content of the interfacial film for a hydrophobic solute. This study was performed in bicontinuous microemulsions and o/w microemulsions until the limit case of the micellar system without any oil. Leodidis and Hatton (40) described a complete study of the solubilization of amino acid in “reverse micelles” of A.O.T., an anionic ternary microemulsion. They demonstrated that the reverse micelle curvature radius at equilibrium varies also linearly with solute content: in their case, the induced curvature variation originates from electrostatic equilibrium while in the case of nonionic microemulsions, the molecular volume term is dominant. FIG. 5. Variation of the reduced average curvature D^H&l versus the interfacial composition l. The dotted line corresponds to the relationship found with the wedge model. Experimental points (■) were obtained from phase diagrams and dosage from the variation of the Winsor III domain with the amount of lindane solubilized in the oil. (E) Corresponds to the Winsor I sample. (Œ) Obtained in the micellar domain (2).
We see that the induced variation is now three times larger than that obtained in the case of low curvature. This would imply an increase in the radius of the micelles of 45%. This is unacceptably large since the radius of the micelles is limited by the chain length. In a former study (2) we did not observe any curvature variation in average resulting from the solubilization of lindane in C 8E 6 micelles. We also noted that the solubilization of lindane in micellar solution is quite small (l max 5 0.025) (2) compared to the value obtained in bicontinuous microemulsions (0 , l , l max 5 0.28). At saturation l max 5 0.025 for H 5 1/l, l being the chain length of the C 8E 6 surfactant. This point is evidence of the small capacity of micellar solution to solubilize lindane compared with microemulsion solutions. CONCLUSION
Our aim was to establish a quantitative relationship between the variation in film curvature induced by the amount of lindane solubilized at the interface and molecular volume. In a former study, Hatton et al. gave a curvature dependence for solubilization of amino acid in w/o A.O.T. microemulsions (39, 40), amino acid being water soluble. Therefore our question was: Is it possible to find such a dependence for an oil-soluble solute with nonionic surfactant solutions? We have shown this relationship is valid within a factor of 2 by using geometrical packing and considering only the solute molecule as a wedge. The topological coverage relationship gives the right value for the variation in curvature induced by solubilization. If we suppose that the solute acts as a “wedge” of known molecular volume, this model gives a good approx-
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