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Solute Effect on Connectivity of Water-in-Oil Microemulsions F. Testard* and Th. Zemb C.E.A./D.R.E.C.A.M./C.E.N. Saclay, Service de Chimie Mole´ culaire, Laboratoire de Diffusion de Rayonnement X aux petits Angles, Bat 125, 91191 Gif sur Yvette Cedex, France Received April 26, 1999. In Final Form: August 16, 1999 The effect on microstructure of solubilizing a solute in a ternary microemulsion has been examined. We used the water-didodecyldimethylammonium bromide (DDAB)-dodecane ternary solution as a model for microemulsions with a rigid interfacial film. The apolar model solutes chosen are lindane, which is an organochloride pesticide (γ-isomer of hexachlorocyclohexane), and phenol as a semipolar molecule. The curvature variation of the surfactant film induced by the solute has been determined using conductivity and small-angle X-ray scattering experiments. This curvature effect is rationalized by means of the DOC cylinders model, combining fixed area per molecule, volume fraction, a strongly preferred spontaneous curvature constraint, and a low flexibility of the interfacial film (kc . kBT). Scattering and conductivity properties examined together demonstrate that the shift in the surfactant packing parameter induced by solubilization corresponds to an increase of surfactant layer volume combined with a slight decrease of the area per headgroup.
Introduction The influence of solute on phase boundaries of microemulsions has been extensively studied in the past decade, particularly in water-in-oil (w/o) microemulsions.1 However, few studies have investigated the correlation between curvature and solubilization.2-7 The influence of solute on the percolation behavior in w/o microemulsion has been also studied.8,9 Our aim is to combine the two approaches to relate the modification of the microstructure of microemulsions with the curvature variation induced by the presence of a solute. As model solutes, we use the common hydrophobic pesticide lindane (γ-C6H6Cl6)10,11 and phenol, which is more surface active. Phenol is therefore expected to be more located at the oil/water interface. In preceding papers,6,7 we have already investigated the effect of a solute on ternary microemulsions with high flexibility of the interface, illustrated by the case of nonionic single-chain surfactants. We studied particularly the influence of solubilizing lindane in ternary nonionic microemulsions. We have shown that part of the lindane molecule is located at the interface and that the presence of lindane induces a curvature of the interface toward water. By measuring separately the amount of solute dissolved within the surfactant monolayer and the average curvature of the relevant sample, we established a link between these two quantities for ternary microemulsions. (1) Kremer, F.; Lagaly, G. Horizons 2000saspects of colloid and interface science at the turn of the millenium. Prog. Colloid Polym. Sci. 1998, 109. (2) Leodidis, E. B.; Bommarius, A. S.; Hatton, T. A. J. Phys. Chem. 1991, 95, 5943. (3) Leodidis, E. B.; Hatton, T. A. J. Phys. Chem. 1991, 95, 5957. (4) Jo¨nsson, B.; Wennerstro¨m, H. J. Phys. Chem. 1987, 91, 338. (5) Aamodt, M.; Landgren, M.; Jo¨nsson, B. J. Phys. Chem. 1992, 96, 945. (6) Testard, F.; Zemb, Th. Langmuir 1998, 14, 3175. (7) Testard, F.; Zemb, Th. Submitted for publication. (8) Amaral, C. L. C.; Brino, O.; Chaimovich, H.; Politi, M. Langmuir 1992, 8, 2417. (9) Schu¨bel, D.; Ilgenfritz, G. Langmuir 1997, 13, 4246. (10) Van Vloten, G. W.; Kruissink, C. A.; Strijk, B.; Bijovet, J. M. Acta Crystallogr. 1950, 3, 139. (11) Ware, G. W. The Pesticide Book; Freeman, W. H.: San Fransisco, CA, 1978; part II, pp 27-52.
The aim of this work is to demonstrate a similar link in the case of stiff ionic layers. In the present paper, we focus on the influence of a solute on w/o ternary microemulsions with rigid interfaces (cationic double-chain synthetic lipid: didodecyldimethylammonium bromide (DDAB)). Since bending constants are larger than kBT, the microstructure of the microemulsionsreflected physical propertiessis set by interfacial curvature. This one is defined by the interfacial packing parameter12 or effective surfactant parameter Pd V/al, where V is the effective volume of the apolar part of the surfactant film (including the penetration of the oil), a is the area of film per surfactant, and l is the film thickness. P is a scalar value related to the geometry of the surfactant in solution. For a precise definition of surfactant parameter through differential geometry and global packing, see reference 13. A variation of the effective surfactant parameter is associated with the nature of the oil or with the addition of a cosurfactant. Ninham et al.14 introduced the notion of “penetrating power” of the oil in the surfactant chains and measured the variation of the surfactant parameter for a mixture of oils.15 They demonstrated too,16 that for a given surfactant changes in curvature can be effected by at least six general “routes”: temperature variation (changing l and chain stiffness), salt concentration (changing a), use of a cosurfactant (changing V), mixing surfactants, variation in solvent, and counterion exchange. We extend here this approach to the case of a solute added to a w/o microemulsion. Why does the addition of a solute induce microstructure variation in a w/o microemulsion? Is it possible to quantify these variations with the surfactant parameter? The physical situation is examined here using model microemulsions offering a rigid interface, when the (12) Israelachvili, J. N.; Mitchell, D. J.; Ninham, B. W. J. Chem. Soc., Faraday Trans. 2, 1976, 72, 1525. (13) Hyde, S. T. J. Phys. Chem. 1989, 93, 1458. (14) Evans, D. F.; Mitchell, D. J.; Ninham, B. W. J. Phys. Chem. 1986, 90, 2817. (15) Chen, S. J.; Evans, D. F.; Ninham, B. W.; Mitchell, D. J.; Blum, F. D.; Pickup, S. J. Phys. Chem. 1986, 90, 842. (16) Ninham, B. W.; Chen, S. J.; Evans, D. F.; J. Phys. Chem. 1984, 88, 5855.
10.1021/la990502u CCC: $19.00 © 2000 American Chemical Society Published on Web 11/16/1999
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flexibility constant kc is larger than kBT. In this case, known as “stiff microemulsions”, local fluctuations of the curvature are strongly damped at room temperature. Therefore sterical constraints introduced by the presence of solute molecules induce strong constraints on the microstructure, with easily measurable effects as consequences. The most easily detected effect is the displacement of the composition of the antipercolation threshold. Antipercolation has been discovered by the group of Kaler17 and has been shown to be general in microemulsions with rigid interfaces.18 The antipercolation characterized by an increase of the conductivity with decreasing water content is incompatible with purely thermodynamical models of microemulsions, such as those developed by Cates et al.19 We focus here on the case of water-DDAB-dodecane water-in-oil (w/o) microemulsions. For a constant surfactant to oil weight ratio, the microstructure changes from interconnected cylinders to water-in-oil separated droplets as the amount of water increases. Conductivity measurements evidence an antipercolation threshold as the microemulsions are conducting at low water content and nonconducting at high water content.20 The addition of a solute in the w/o microemulsion induces a variation of the conductivity and of the microstructure. These perturbations could be related to a variation of the film curvature and hence to a variation of the effective surfactant parameter. We study the variation of the antipercolation threshold and of the structure of the microemulsion as a function of the amount of solute added in the microemulsion by conductivity measurements and SAXS experiments. The DOC model15 is still the unique microemulsion model able to predict both conductivity and peak position obtained by small-angle X-ray scattering.21 We use the DOC model to predict the macroscopic behavior of the w/o microemulsion when a solute is added to the microemulsion. For any imposed volume fraction (φ), specific area (Σ in Å2 per Å3 of sample), and curvature imposed by the value of the surfactant parameter P, the DOC model gives analytically the position of the scattering peak position D*, as well as the connectivity Z (0 < Z 97%, was recrystallized from chloroform/ethanol before use; n-dodecane (Merck) was used without any purification. The water was Millipore-filtered of conductivity (18 MΩ/cm-1). Pure phenol was used without any purification. Small-Angle X-ray Scattering (SAXS). Small-angle X-ray scattering experiments were performed in cells with Kapton windows on two laboratory spectrometers to measure a wide range of the scattering vectors. The X-ray source is a copper rotating anode operating at 15 kW. The first camera is a Bonse-Hart type22 which was built in our laboratory:23 two channel cut Ge (111) crystals allow beam collimation and reach a very high q resolution: 3 × 10-4 Å-1. All the scattering curves have been desmeared from the instrumental effect due to the slit geometry used in USAXS. We used the method proposed by Strobl,24 but absolute intensities were obtained independently of deconvolution method used.25 The second camera is a home-built Huxley-Holmes type, high flux camera using a pinhole geometry.26,27 The KR1 radiation is selected and separated from high-energy radiations by the combination of a nickel-covered mirror and a bent, asymmetrical cut germanium 〈111〉 monochromator. The spectra are recorded with a two-dimensional, 33 cm diameter gas detector which had an effective q-range from 0.02 to 0.4 Å-1 (q ) 4π/λ sin θ). The spatial resolution of this detector is 0.2 mm. Data correction, radial averaging, and absolute scaling were performed using routine procedures.28 The overlap is acceptable for the two data sets with a precision of 10% on the absolute intensity scale. We use the unified units of scattering cross section per unit of sample volume (cm-1), common to neutron and X-ray scattering as introduced by Stuhrmann.29 Structural Models of W/O Microemulsions. The Cubic Random Cell Model (CRC).30 This model assumes that the microstructure can be approximated by a set of cubes of size ζ filled at random with water or oil. The persistence length is directly fixed by the surfactant volume fraction. This model has only one distance D* ()2π/qmax), and the expression used for CRC model is D*Σ ) 5.8φ(1 - φ).31 A decorated version of random cells widely used in the literature and successful in the case of flexible interfaces has been introduced by Cates.19 The predicted peak position corresponds to the reciprocal length between neighboring polyhedra, since the underlying lattice of the centers of cells has a preferred distance, or even a single one, in the packing of model cubes. Hard Sphere Model.32 We consider the scattering by a dispersion of slightly repulsive monodisperse hard spheres with a contact potential of few kBT. Assuming that microstructure is just a dispersion of slightly repulsive hard spheres leaves no free parameter, since the water droplet radius has to be R ) 3φ/Σ. We note the position of the structural factor for each composition. Once the number of droplets per cubic centimeter and the reverse micelle radius are known, the full scattering curve can be obtained on an absolute scale by the hypothesis of interacting independent spheres of known volume fraction. The scattering peak position can be obtained numerically (Hayter-Penfold32) and compared to experiment. DOC Cylinders Model.33 The disordererd open connected cylinders model was introduced by Ninham33 in 1986. The (22) Bonse, U.; Hart, M. Appl. Phys. Lett. 1965, 7, 238. (23) Lambard, J.; Lessieur, P.; Zemb, Th. J. Phys. I Fr. 2 1992, 1191. (24) Strobl, G. R. Acta Crystallogr. 1970, A26, 367. (25) Lesieur, P.; Zemb, Th. In Chen et al., S. H., Eds.: Kluwer Academic Publishers: Norwell, MA, 1992; pp 713-729. (26) Ne´, F.; Gazeau, D.; Lambard, J.; Lessieur, P.; Zemb, Th. J. Appl. Crystallogr. 1993, 26, 763. (27) Leflanchec, V.; Gazeau, D.; Taboury, J.; Zemb, Th. Appl. Crystallogr. 1996, 29, 110. (28) Ne, F.; Gabriel, A.; Koksis, M.; Zemb, Th. J. Appl. Crystallogr. 1997, 30, 306. (29) Stuhrmann, H. B.; Miller, A. J. Appl. Crystallogr. 1978, 11, 325. (30) Jouffroy, J.; Levinson, P. de Gennes P. G. J. Phys. 1982, 43, 1241. (31) Talmon, Y.; Prager, S. J. Phys. Chem. 1978, 69, 2984. (32) Hayter, J. B.; Penfold, J. Mol. Phys. 1981, 42, 109. (33) Ninham, B. W.; Barnes, I. S.; Hyde, S. T.; Derian, P.-J.; Zemb, Th. Europhys. Lett. 1987, 4, 561.
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microstructure of the microemulsion is assimilated to a purely geometric question neglecting entropy and curvature fluctuation effects. The microstructure is defined by the three constraints: the volume fraction φ, the specific surface Σ (in Å2/Å3 of sample), and the effective surfactant packing parameter P ) V/al. If the curvature radius is smaller than Σ-1, the structure can be approximated by a random network of cylinders with spheres at the points of intersection. The conservation rules taken into account in the description of the microemulsion to use the DOC cylinders model are as follows: (a) The system is assumed to be two media separated by one interface. The macroscopic polar volume fraction is constrained by the available water and the headgroup volume of the surfactant. (b) The polar volume can be covered continuously by the surfactant film. This requires satisfaction of the coverage relation relating the effective surfactant parameter P to the average 〈H〉 and Gaussian 〈K〉 curvature.
P)
1 V ) 1 + 〈H〉l + 〈K〉l2 al 3
The difference between the effective value P of the surfactant parameter and the spontaneous value P0 induces a high bending energy term in the case of stiff microemulsions:34
E ) (1/2)k*(P - P0)2 where k* is the elastic constant related to the deviation of the average value of P in a given microstructure. For a fixed connectivity, the “granularity” of the microstructure is determined, knowing the internal volume fraction and the specific surface. The explicit analytic equations are given in refs 18, 35, and 36. To apply the DOC model, we have to know the internal volume fraction φ and the specific surface Σ for a given sample, deduced from the composition of the sample. Then, knowing the specific packing parameter P, the model predicts the position of the scattering maximum and the conductivity of the solution (connectivity Z), or knowing the conductivity (Z), the model permits calculation of the scattering maximum and the packing parameter P.
Results Surfactant Parameter Determination for a Given Oil. The conductivity γ and the boundaries of the singlephase w/o microemulsion domain in the phase diagram are perturbed by the solubilization of a solute. This is attributed to a change in curvature of the surfactant film. To quantify this variation, we determine experimentally the variation of the effective surfactant parameter P with the amount of solute solubilized in a DDAB w/o microemulsion. We deduce the surfactant packing parameter from the high-water region of the microemulsion phase at the emulsification failure boundary in the ternary phase diagram. Experimental determination of different ternary phase diagrams of DDAB-water-oil systems had shown that the maximum water concentration of the single-phase regions form straight lines of constant water to surfactant ratios.37 At this boundary, it has been proven35 that the microstructure is consistent with a random distribution of monodisperse water spheres of known radius in oil. Therefore for a constant surfactant to oil mass ratio, by determining experimentally the maximum amount of (34) Fogden, A.; Hyde, S. T.; Lundberg, G. J. Chem. Soc., Faraday Trans. 1991, 87, 949. (35) Barnes, I. S.; Hyde, S. T.; Ninham, B. W.; Derian, P. J.; Drifford, M.; Zemb, T. N. J. Phys. Chem. 1988, 92, (8), 2286. (36) Barns, I. S. Microstructure of bicontinuous phases in surfactant system. Thesis, Australian National University, 1990. (37) Hyde, S. T.; Ninham, B. W.; Zemb, T. J. Phys. Chem. 1989, 93, (4), 1464.
Figure 1. Variation of packing parameter P determined from the position of the observed emulsification failure versus the weight percentage of solute in the oil: (4) phenol; (9) lindane. The straight lines are guides for eyes.
water which can be solubilized in the microemulsion, we obtain the maximal radius R ) 3φ/Σ of the largest droplets which are stable for the given oil and solute. φ denotes the hydrophilic volume fraction (water plus headgroups of the surfactant) and Σ the total surface area per unit volume (specific surface area). Knowing the radius of the droplets and assuming a surfactant tail length of l ) 13 Å,35,37 corresponding to about 80% of the maximum length expected from the formula of Tanford,38 the coverage relation gives the effective surfactant parameter for the oil considered:
P)1+
l Rmax
+
1 l2 3R
2 max
We assume that the packing parameter does not change significantly throughout the water dilution, and this value P is taken to be characteristic of the oil used as solvent. This is an approximation for the water-DDAB-dodecane ternary system since the phase boundary shows a deviation of the straight line at constant surfactant to water volume ratio.41 We take the asymptotic value for our experiments and assume that the surfactant parameter is constant along a dilution line for one surfactant to oil ratio. Using this procedure, we have determined P in the w/o microemulsion domain for the water-dodecane-DDAB ternary system and the water-dodecane + solute-DDAB quaternary system, assuming that the mixture dodecane + solute behaves as a pseudocomponent. The results are shown in Figure 1. We see that the surfactant parameter is increasing as the amount of solute solubilized in the oil is increasing even if the solute is successively lindane or phenol. An increase of the surfactant parameter results from an increase of the apolar volume (more penetrating oil) or a diminution of the surfactant area at constant film thickness, or a more complex mechanism including both variation of the apolar volume and of surfactant area or film thickness. We remark that the variation is more important for the phenol than for the lindane solute. The small numerical variation of the surfactant parameter deduced from the phase diagram hides a large variation of the average curvature related to molecular length. Ignoring Gaussian curvature, one could write (38) Tanford, C. J. Phys. Chem. 1972, 76, 3020.
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Table 1. Weight Composition of the Samples Analyzed by SAXSa solute lindane lindane lindane phenol phenol
sample A B C D E
water, %
DDAB, %
dodecane, %
solute, %
β, wt %
W
φpolar ) φint
Σ ) C sa
28.7 23 19.4 43 23.5
10.6 11.25 11.75 14.1 18.9
60.7 65 67.2 42.9 56.8
0 0.75 1.65 0 0.8
0 1 2 0 1.2
0.37 0.5 0.62 0.336 0.82
0.2478 0.1993 0.1698 0.3885 0.2145
0.00778 0.00820 0.00854 0.01093 0.01403
a The weight percentage of the solute in the mixture solute + dodecane is given by β; W is the volume ratio of surfactant over water. The polar volume fraction φint includes water and surfactant headgroup. The specific area Σ is calculated with a value of the surfactant headgroup area given by a ) 68 Å2.
(P - 1) ≈ 〈H〉 l The difference P - 1 corresponds to the inverse of radius in unit of surfactant length. In one of our cases spontaneous radius of curvature varies from 8 times the surfactant length to 6 times, as the surfactant parameter varies from 1.12 to 1.17. Therefore, the variation of the packing parameter with the amount of the solute solubilizing in the oil is a direct consequence of the curvature variation induced by the solute in the microemulsion. Conductivity Experiments. The conductivity γ of water-DDAB-dodecane microemulsion is known to decrease as the amount of water is increasing. This effect is the known reverse percolation behavior for DDAB microemulsions.14 This reverse conductivity percolation threshold signals a major change of the microstructure: bicontinuous structure changes toward water in oil droplets as the amount of water in the microemulsion is increasing. To understand the influence of solubilization of a solute on the curvature, we determine the variation of the conductivity reverse percolation threshold with the amount of solute added in the microemulsion. Conductivities of water-DDAB-dodecane + solute microemulsions along water dilution lines are shown in Figure 2a for the lindane solute and in Figure 2b for the phenol solute. For each solute, the curves are made with a constant surfactant/oil weight ratio. We see that as the amount of solute solubilized in the microemulsion is increasing, the conductivity of the microemulsion is decreasing. The water-DDAB-dodecane microemulsion at 20 wt % in water has a high electrical conductivity. The microemulsion is conducting and therefore the microstructure is interconnected. When 1 wt % lindane is solubilized in the oil, the microemulsion is less conducting. The microstructure changes toward less connected water droplets in the oil. This is a direct consequence of the structural change induced by the solubilization of lindane. Lindane induces a curvature of the surfactant film toward water. This is coherent with the observation made in nonionic surfactant when lindane is solubilized in o/w bicontinuous micremulsions.6,7 In the preceding paragraph, we have determined that the surfactant parameter P is increasing with the amount of added lindane. The value of this parameter is related to the preferred curvature of the surfactant film. A large parameter (P > 1) implies that the preferred curvature is toward water. Therefore, an increase of P implies that the curvature turns toward water under the influence of the solute. When phenol is used as model solute, the effect is more important: the reverse conductivity percolation threshold is translated toward smaller weight fraction of water as a small percentage of phenol is solubilized in the microemulsion. Indeed, phenol presents more surface affinity than lindane. To identify the origin of the effect of these two solutes on the conductivity of the microemulsion, we characterize
Figure 2. Variation of conductivity γ(Ω-1‚cm-1) versus water content in water-DDAB-(dodecane + solute) w/o microemulsions along water dilution line for different compositions of the pseudocomponent (solute + dodecane). The composition of the pseudocomponent is detemined by the weight percentage β (solute/(solute + dodecane)) of solute in the oil. (a) The solute is lindane: surfactant/dodecane ) 0.174 with β ) (b) 0, (2) 1, and (9) 2 wt %. (b) The solute is phenol: surfactant/dodecane ) 0.334 with β ) (b) 0 and (]) 1.2 wt %.
by SAXS experiments the microstructure of the microemulsion at the antipercolation point. Small-Angle X-ray Scattering (SAXS). We compare the peak position at the antipercolation threshold of the microemulsion with and without an added solute. The experiment is more sensitive close to the antipercolation threshold to separate the curvature fluctuation or longrange attraction effects from the structural effect in the microemulsion. The compositions of the sample studied are given in Table 1. SAXS spectra obtained with the microemulsions at the reverse percolation thresholds are shown in Figure 3a in the case of lindane solute and in Figure 3b in the
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Figure 4. Logarithmic representation of absolute intensity versus wave vector (q) for samples with lindane as solute. (solid line) sample A; (broken line) sample B; (thick solid line) sample C. The straight line represents the asymptotic Porod law. Table 2. Experimental Results Obtained for Water-DDAB-Dodecane + Solute Microemulsionsa solute lindane lindane lindane phenol phenol
Figure 3. Small-angle X-ray scattering spectra of waterDDAB-dodecane + solute w/o microemulsion at the composition listed in Table 1. The curves represent Iq2 (cm-1‚Å-2) versus q (Å-1). (a) The solute is lindane: (O) sample A; (s) sample B; (×) sample C. (b) The solute is phenol: (+) sample D; (0) sample E.
case of phenol solute. The spectra are drawn in Iq2 versus q to exhibit clearly the scattering peak position. The full scattering curve can be calculated numerically35 or considered as the convolution of one cell content by the lattice of centers of Voronoı¨ cells. The validity of this approximation has been tested for random bilayers (sponge) and connected cylinder microstructure.39,40 In our case, the content of one “Voronoı¨ cell” is a sphere with Z half-cylinders connecting it to neighbors. In the q-range where the scattering peak occurs close to the diameter of one cell, the form factor of one cell content varies as q-2. Therefore, the most precise determination of peak position in the structure factor is the maximum of Iq2. This distance is compared to the different models of microemulsions. We show in Figure 4, in a logarithmic representation, the absolute intensity versus the wave vector obtained for the microemulsions with lindane. We remark that at large q (q > 0.1 Å-1), the intensity follows a Porod law for the three samples studied, a reminder of the presence of a sharp water/oil interface. The value of the Porod limit gives the specific surface and therefore the area per surfactant. We find 68 ( 8 Å2 for the area per surfactant for all the samples. The uncertainty is estimated to be 15% on the absolute value of surface due to the limited q-range and uncertainty in the contrast ∆F. (39) Welberry, T. R.; Zemb, T. N. J. Colloid Interface Sci. 1988, 123 (2), 413. (40) Zemb, T. N.; Welberry, T. R. Colloid Polym. Sci. 1993, 271, 124.
sample A B C D E
(surfactant/oil)w
(V/al)exp
qmax
D*exp
0.174 0.174 0.174 0.334 0.334
1.120 1.14 1.17 1.12 1.2
0.0245 0.0295 0.0345 0.0255 40.046
256 213 182 246 136
a The effective packing parameter (V/al) exp has been determined from the position of the observe emulsification failure at high water content with a fixed surfactant to oil ratio. qmax is the position of the maximum of the experimental scattering peak obtained from the I × q2 curve. The characteristic size or granularity D* is given by the position of the maximum scattering D* ) 2π/qmax.
Table 2 summarizes the experimental results obtained by SAXS for all the samples studied in the present work. Discussion Antipercolation Threshold. At first, we chose to study samples near the antipercolation threshold to avoid the effects of the presence of critical demixing points which hide scattering peaks due to large attraction between droplets in the microemulsion. Olsson et al.41 demonstrated that at high water content in the water-DDAB-dodecane ternary phase diagram, near the demixing line, the phase diagram is not exactly a straight line at constant surfactant to water volume ratio. The authors attribute this effect to a van der Waals attraction which conducts to a demixing. Far from this limit the effect of this attraction is negligible. We compare in Figure 5 the predictions for the scattering peak position versus volume fraction given by the DOC model,33 the cubic random cell model30 (CRC), and the charged hard sphere model.32 The scattering peak position is given in reduced units D*Σ where D* is the peak position. The abscissa is the polar volume fraction. The plot represents the peak shift expected according to the different microemulsion models along a dilution line. To use the DOC model, we consider the internal volume fraction φint and the specific surface Σ calculated with the composition of the sample. On a dilution line, we take the experimental surfactant parameter found for one surfactant to oil ratio, and we note for each composition in water the size D* predicted by the model. Then, we deduced the reduced quantity D*Σ. (41) Skurtveit, R.; Olsson, U. J. Phys. Chem. 1992, 96, 8640.
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Figure 5. Predictions of the reduced peak position (D*Σ) given by different models of microemulsions. D* is given by 2π/qmax, if qmax is the position of the scattering peak. Σ represents the specific area of the sample. The crosses are calculated assuming scattering by a dispersion of slightly repulsive monodisperse hard spheres; the triangles are calculated with the CRC model. The circles are calculated with the DOC model assuming a weight ratio surfactant/dodecane ) 0.174 and a constant packing parameter P ) 1.12. The lines are only guides for eyes. The experimental point is shown. (9) for sample A.
The formation of a coalesced microstructure requires only a low area per unit volume to cover the water regions: therefore CRC models produce scattering peaks corresponding to small granularity for a given surface. Independent spheres of an “ad hoc” volume represent an intermediary case, since the sphere is the object with the lowest surface to volume ratio. More complicated topologies require more interface to solubilize the same amount of water. Therefore, the general “dilution plot” shown on Figure 5 allows an immediate classification of the coalesced versus complex topologies. Values of D*Σ as low as 1.5 are obtained for flexible microemulsions when entropy is dominant. More and more stiffness of interfacial film and influence of curvature induce an increase of D*Σ. The maximum value yet reported was close to 3 in the case studied by Barnes et al.42 Figure 5 illustrates the predictions for the sample corresponding to a water-DDAB-dodecane ternary microemulsion with a surfactant to oil weight ratio equal to 0.174. We found similar predictions for the sample waterDDAB-dodecane microemulsions with a surfactant to oil weight ratio equal to 0.33. Therefore, we follow our interpretation of the effect of solute within the frame of the DOC model. In Figure 6a, we report the same predictions of the reduced peak position given by the DOC model for the samples (A, B, C) containing β% lindane in the oil solvent. Each line corresponds to a water dilution line for a known value of the packing parameter in the presence of a solute. The values calculated using the DOC model are shown as open symbols for nonconducting samples (Z < 1.2) and full symbols for conducting samples (Z > 1.2). The graph also shows the experimental points. We see that experimental and predicted values are in good agreement. The experimental points are close to the scattering peak position and conducting properties predicted by the DOC model without any adjustable parameter. Therefore, based on the variation in the packing parameter, the DOC model is able to predict the observed shift in D*Σ and simultaneously the conductivity, even if (42) Barnes, I. S.; Derian, P.-J.; Hyde, S. T.; Ninham, B. W.; Zemb, Th. J. Phys. Fr. 1990, 51, 2605.
Figure 6. Predictions of the reduced peak position (D*Σ) given by the DOC model along water dilution lines. The predictions are made for water-DDAB-dodecane + solute microemulsions with different compositions of the pseudocomponent. We use the experimental packing parameter P for each composition β of the oil to determine the geometric quantity D*Σ with the DOC model. (a) The solute is lindane: (b, O) P ) 1.12, β ) 0%, (2, 4) P ) 1.14, β ) 1%, (9, 0), P ) 1.17, β ) 2%. (b) The solute is phenol: (b, O) P ) 1.12, β ) 0%, ([, ]) P ) 1.245, β ) 1.2%. The open symbols correspond to a nonconducting microemulsion (Z < 1.2) and the filled symbols to a conducting microemulsion (Z > 1.2). The large dark squares (9) correspond to the experimental points: samples A, B, and C for (a) and D, E for (b).
the amount of the solute added to the microemulsion is quite small, of the order of 1%. We conclude that the observed variation of D*Σ is consistent with an increase of the packing parameter, and therefore with an increase of the curvature toward water when lindane is solubilized in reverse microemulsions. We report in Figure 6b, the same comparison between experiments and DOC model for the phenol. We have the same agreement between the experimental and theoretical values. Thus, knowing the composition of the sample and the packing parameter, the variation of the microstructure induced by the solubilization of a solute is directly predicted by the DOC model. This approach is similar to the one described in references 21 and 4343 for fluorocarbon microemulsions, where microstructures and microstructural transitions are described in terms of shape, dimension, and connectivity. (43) Monduzzi, M. Curr. Opion. Colloid Interface Sci. 1998, 3, 467.
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Figure 7. Variation of conductivity versus water content in water-DDAB-dodecane + lindane w/o microemulsions along water dilution line for different compositions of the pseudocomponent. The composition of the pseudocomponent is determined by the weight percentage β (lindane/(lindane + dodecane)) of solute in the oil. The weight ratio surfactant/oil is equal to 0.334. (b) β ) 0 wt %; (2) β ) 2 wt %.
Discussion in Terms of Solute Localization. The established variation of the surfactant parameter P under the influence of a solute may result from a variation of the apolar volume (V), of the surfactant headgroup area (a), or of the film thickness (l), or of all these parameters at the same time. Now we will illustrate in a concrete example that it is possible to deduce the location of a solute in a microemulsion from the scattering peak and conductivity shifts. This is a direct illustration of the general principle described in ref 18 on the location of a solute deduced from variation of size of microemulsion. The best practical condition to determine solute effect on the surfactant parameter is to use regions of the phase diagrams where high variations in packing parameter avoid variations of volume fractions. A high variation in volume fraction φ hides the variations of the microstructure due to the localization effect. Basically, if a solute is mainly located in the core, the droplet radii will increase while curvature decreases if the solute is a cosurfactant. The simple case of ionic droplets has been described in the case of AOT.44 We consider microemulsions at a fixed composition in water, with two solute contents in the case of lindane. The internal volume fraction is constant and dodecane is replaced by a mixture of dodecane + lindane at 2% weight fraction in lindane. We see in Figure 7 that for a fixed water composition (36 wt %), the conductivity is decreasing when dodecane is replaced by the pseudocomponent (dodecane + lindane) at 2 wt % in lindane. In the presence of dodecane, the microemulsion is conducting and with the pseudocomponent the microemulsion is less conducting. Surprisingly, the observed SAXS experimental shift for the two samples is negligible (Figure 8). We summarize in Table 3 the predictions of the DOC model for different combinations of variation of the specific surface Σ and of the thickness l of the film, assuming a constant internal volume fraction φint. The packing parameter has been experimentally determined and increases from 1.12 to 1.17 (∆P/P ∼ +5%) when dodecane is replaced by the pseudocomponent. Table 3 compares possible effects on localization and macroscopic consequences in terms of scattering peak shift and conductivity variation. Only one combination is compatible with the (44) Pileni, M. P.; Zemb, Th. N.; Petit, Ch. Phys. Lett. 1985, 118, (4), 414.
Testard and Zemb
Figure 8. Small-angle X-ray scattering spectra of waterDDAB-dodecane + solute w/o microemulsion at two compositions of the oil. The water composition is equal to 36 wt % for the two samples. The curves represent I (cm-1) versus q (Å-1) where (O) sample F, water-DDAB-dodecane; (b) sample G, water-DDAB-dodecane + lindane; β ) 2 wt %. Table 3. Predictions of the DOC Model for Water-DDAB-Dodecane + Solute Microemulsions with Variation of the Specific Surface ∆Σ/Σ and of the Film Thickness ∆l/l, Assuming a Constant Internal Volume Fraction Oint and an Increase of the Effective Surfactant Parameter P of 5%a ∆Σ/Σ (Σ), %
∆l/l (l), %
?
?
0 (0.0121) -5 (0.0115) +5 (0.0127) cst (0.0121) -5 (0.0115) +5 (0.0127)
0 (13) 0 (13) 0 (13) +7 (14) +7 (14) +7 (14)
∆V/V, %
∆D*
∆Z
+5
0
-3
+5 0 +10 +12 +7 +17
-13 -3 no geometrical solution -23 -3 -13 -3 0 -3 -30 -3
a The variation of the apolar volume ∆V/V is deduced from ∆Σ/Σ, ∆l/l, and ∆P/P. The first line of the table corresponds to the experimental results (samples F and G in Figures 7 and 8) where at a fixed water composition the dodecane is replaced by a pseudocomponent (dodecane + lindane) with β ) 2 wt %. This induces an increase of the effective surfactant parameter P from 1.12 to 1.17 (∆P/P∼ +5%). The internal volume fraction is constant and equal to 0.326. The initial specific surface for the sample with dodecane (F) is equal to 0.0121 Å2/Å3 assuming a specific surfactant area equal to 68 Å2. The experimental peak position is D* ) 212 ( 4 Å. The peak position predicted by the DOC model for the sample with dodecane is D* ) 198 ( 2 Å. Z represents the conductivity of the solution.
Table 4. Predictions of the Variations in Scattering Peak Position with Slight Repulsive Hard Sphere Potential for the Same Samples F and Ga Σ
∆D*, Å
0.0121 0.01125 0.0129
0 +6 -9
a The internal volume fraction is equal to 0.326. The initial specific surface for the sample with dodecane is equal to 0.0121 Å2/Å3. With a repulsive hard sphere potential we find a scattering peak at 137 Å instead of 212 Å for the sample F. This model does not take into account the conductivity variation.
experimental results: specific surface is decreasing, the thickness of the surfactant film is increasing, and we have no peak variation by SAXS together with a transition from conducting to less conducting sample. Table 4 summarizes for the same samples F and G the predictions of the variations in scattering peak position with a slightly repulsive hard sphere potential. This model
Connectivity of W/O Microemulsions
gives a peak position at 137 Å instead of 212 Å for the experimental one, and this model does not take into account the conductivity variation. Therefore the DOC model is the only one to permit the location of the solute in the microemulsion with both conductivity and scattering peak position. We conclude that solubilizing lindane in a ternary water-DDAB-dodecane reverse microemulsion induced an increase of the curvature toward water, a diminution of the specific surfactant area, and an increase of the film thickness. This is quite coherent with the fact that with lindane the oil is more penetrating.45 The net increase of the surfactant parameter of 5% is the result of three concomitant effects: decrease of area per surfactant a, increase of the film thickness l, and increase of the effective apolar volume V of the film. This variation of interfacial area, simultaneous to slight shifts in electronic density, is too small to be experimentally detectable. We could note here that the variation of apolar volume of the surfactant film due to lindane solubilization corresponds within 20% to the volume of the lindane molecules. Therefore, direct sterical effect due to solute packing in hydrophobic chains seems to be the mechanism underlying the variation of packing parameter. This is similar to the former study in nonionic microemulsion. We have established a quantitative relation between the variation of the film curvature induced by the amount of solute solubilized at the interface and the molecular (45) Testard, F.; Zemb, Th.; Strey, R. Prog. Colloid Polym. Sci. 1997, 105, 332.
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volume. This relation was explained by only considering the solute model as a wedge. We consider here the bulk properties of the microemulsions to determine the curvature variation induced by the solubilization. Even if we do not know the molar fraction of solute located within the interfacial film, we are able to quantify the curvature variation. Conclusion This study demonstrates that we rationalize the microstructural modification induced by the addition of a solute in a w/o microemulsion within the frame of the DOC model. This prediction is based on the geometrical parameter P ) V/al, which has been determined experimentally for each composition in solute. The DOC model predicts the variation of the conductivity and of the geometrical quantity D*Σ for different dilution lines and for two solutes. The bulk properties of the microemulsions are directly related to the curvature change induced by the solubilization. We demonstrate too that it is possible to determine the localization of a solute by knowing the variation of the packing parameter, the scattering peak position, and the conductivity behavior. Acknowledgment. We thank Sandrine Lyonnard for very careful help in the deconvolution of the spectra resulting from experiments performed on the Bonse-Hart camera. LA990502U
