Langmuir 1990,6, 611-620 as the effective potential affecting surface protonation seems to be largely valid.
Acknowledgment. This work was funded in part by a contract from the Ecological Research Division, Office of Health and Environmental Research, U.S. Depart-
611
ment of Energy (DE-FG02-87ER60508) and in part from a NSF grant (CESA504276). We gratefully acknowledge all support received. Registry No. FeO(OH), 20344-49-4; phosphate, 14265-442;goethite, 1310-14-1.
Structure and Phase Behavior in Five-Component Microemulsions John F. Billman? and Eric W. Kaler*?' Department of Chemical Engineering BF-10, University of Washington, Seattle, Washington 98195, and Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716 Received June 16, 1989. I n Final Form: October 2, 1989 Droplet-to-bicontinuous structure transitions in a family of five-component microemulsions formed with sodium 441'-heptylnonyl)benzenesulfonate, isobutyl alcohol, D,O, sodium chloride, and alkanes with even carbon numbers from octane to hexadecane are probed by using small-angle neutron scattering, electrical conductivity, and NMR self-diffusion measurements. The phase behavior and structure of these microemulsions are intimately linked and depend on salinity and the chain length of the alkane. Both the range of salt concentration in which the three-phase region is observed and the range of microemulsion water volume fraction within the three-phase region decrease with decreasing alkane chain length. Further, the appearance of the three-phase region is preceded by droplet-to-bicontinuous transitions. Microemulsions not exhibiting three-phase regions become bicontinuous only when they contain equal amounts of oil and water. The coincidence of the so-called percolation thresholds as determined by using electrical conductivity and self-diffusion measurements shows that electrical conduction in a dispersion of water droplets occurs with the exchange of material between the droplets. The scattering of dilute microemulsions is interpreted by using a variety of models in which the microemulsion is treated as a dispersion of hard or attractive spheres or as a dispersion of charged ellipsoids. The effect of alkane chain length on the droplet-to-bicontinuous transitions is interpreted in terms of the droplet interaction potentials.
Introduction Microemulsions are isotropic, thermodynamically stable dispersions of oil, water, surfactant, and often salt and cosurfactant. The oleic and aqueous components of microemulsions reside in distinct domains with length scales on the order of 100 A. These domains are separated by an interfacial sheet rich in surfactant and cosurfactant. The diversity of structure found in microemulsions and the ability of microemulsions to solubilize both polar and nonpolar substrates have generated great interest in microemulsion-forming systems.' Nevertheless, the relationship between the phase behavior of these systems and the structure of the microemulsions is unclear. The purpose of this paper is to delineate that relation for a model five-component microemulsion of a type often used commercially. The phase behavior of microemulsion-forming systems has been rationalized by Kahlweit and co-workers2-8 in terms of a simple phenomenological model. Studies
* Author to whom correspondence
should be addressed. University of Washington. University of Delaware. (1)Langevin, D. Acc. Chem. Res. 1988,21, 255.
*
0743-7463/90/2406-0611$02.50/0
of homologous series of oils and surfactants2-*have shown the phase behavior of three-component nonionic mixtures to be a consequence of their proximity to a tricritical point. By considering the effect of added electrolyte and ionic surfactant, Kahlweit et aLk8 argue that the phase behavior of microemulsions containing both ionic and nonionic surfactants and salt evolves continuously from a line of tricritical points. Further, these systems may be driven toward their tricritical point with systematic variation of the nature of their components. This model provides a basis for understanding the phase behavior in microemulsion-forming mixtures, but no account of structure in the microemulsion phase($ is made. The composition of many microemulsions can be varied continuously from oil-rich to water-rich within a sin(2) Herrmann, C. U.; Klar, G.; Kahlweit, M. J. Colloid Interface Sci. 1981,82,6. (3) Kahlweit, M. J. Colloid Interface Sci. 1982, 90, 197. (4) Kahlweit, M.; Lessner, E.; Strey, R. J . Phys. Chem. 1983,88,1937. (5) Kahlweit, M.; Strey, R.; Hasse, D. J . Phys. Chem. 1985,89, 163. (6) Kahlweit, M.; Strey, R.; Firman, P.; Hasse, D. Langmuir 1985, I , 281. (7) Kahlweit, M.; Strey, R. J. Phys. Chem. 1986, 90, 5239. (8) Kahlweit, M.; Strey, R.; Firman, P.; Hasse, D.; Jen, J.; Schomiicker, R. Langmuir 1988, 4,499.
0 1990 American Chemical Society
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gle phase by changing a thermodynamic variable such as temperature or, as is the case here, salinity of the aqueous The structure of the oil and water domains in such microemulsions necessarily reflects such composition changes. With notable exceptions,",l2 it has been shown that microemulsions dilute in either water or oil exist as droplets of the dilute component coated with surfactant and dispersed in the major ~ o r n p o n e n t . ' ~ The -~~ structure of these dilute microemulsions is conveniently probed in small-angle scattering experiments. The resulting intensity spectra can be compared with spectra calculated by using statistical mechanical models of the droplet dispersions; such models can include a variety of droplet interaction potentials.'6-18 With the approach of a critical point, the droplet interactions become attractive and critical scaling behavior is observed.lg2' On the other hand, concentrated microemulsions containing nearly equal amounts of oil and water have been shown to possess bicontinuous s t r u ~ t u r e s , again ~ ~ - ~with ~ exception^.^^ In these bicontinuous microemulsions, the interfacial surfactant sheet has been shown to have zero mean curva t ~ r eand , ~ the ~ sample-spanning oil and water domains have been successfully modeled as distorted lamellae.26 Recently the static scattering intensity of microemulsions has been interpreted in terms of a Landau free energy This three-parameter model predicts intensities consistent with experiments previously interpreted in terms of bicontinuous structures or disordered cubic arrangements of spheres. The dispersed and bicontinuous structures of microemulsions are two extremes of microemulsion structure. The transition between the two dispersed states, waterin-oil (w/o) and oil-in-water (o/w), and the bicontinuous state can be documented by using a variety of techniques. The transition from a w/o dispersion to a bicontinuous structure results in a nonconducting to conducting transition in electrical conductivity as sample-spanning water channels are formed.2s This phenomena has been modeled as dynamic percolation in dispersions of nonin(9) Lindman, B.; Shinoda, K.; Jonstromer, M.; Shinohara, A. J . Phys. Chem. 1988,92,4702. (10) Borkovec, G.; Eicke, P. J . Phys. Chem. 1986, 92,206. (11) Chen, S. J.; Evans, D. F.; Ninham, B. W.: Mitchell. D. J.: Blum. F. D.: Pickuu. S. J . Phvs. Chem. 1986.90.842. (12) Zem6,'T. N.; Hide, S. T.; Derian,'J. P.; Barnes, I. S.; Ninham, B. W. J . Phys. Chem. 1987,91, 3814. (13) Cebula, D. J.; Harding, L.; Ottewill, R. H.; Pusey, P. N. Colloid Polvm. Sci. 1980, 258, 973. (14) Dvolaitzky, M.; Guyot, M.; Lagues, M.; LePesant, J. P.; Ober, R.; Sauterey, C.; Taupin, C. J . Phys. Chem. 1978, 69, 3279. (15) Kaler, E. W.; Bennett, K. E.; Davis, H. T.; Scriven, L. E. J . Chem. Phys. 1983, 79,5673. (16) Magid, L. J. Colloids Surf. 1986, 19, 129. (17) Chang, N. J.; Billman, J. F.; Licklider, R. L.; Kaler, E. W. Statistical Thermodynamics of Micellar and Microemulsion Systems;Chen, S . H., Ed.; Springer Verlag: New York, 1990. (18) Huang, J. S.; Safran, S. A.; Kim, M. W.; Grest, G. S.; Kotlarchyk, M.; Quirke, N. Phys. Reu. Lett. 1984,53, 592. (19)Kotlarchyk, M.; Chen, S. H.; Huang, J. S.; Kim, M. W. Phys. Reu. A 1984,29, 2054. (20) Fourche, G.; Bellocq, A. M.; Brunetti, S. J. Colloid Interface Sci. 1982,89, 427. (21) De Geyer, A.; Tabony, J. Chem. Phys. Lett. 1985, 133, 83. (22) De Geyer, A.; Tabony, J. Chem. Phys. Lett. 1986, 124, 357. (23) Kaler, E. W.; Davis, H. T.; Scriven, L. E. J . Chem. Phys. 1983, 79, 3685. (24) Kotlarchyk, M.; Chen, S.-H.; Huang, J. S.; Kim, M. W. Phys. Reu. Lett. 1985, 55, 1888. (25) Auvray, L.; Cotton, J. P.; Ober, R.; Taupin, C. J . Phys. Chem. 1984,88,4586. (26) Vonk, C. G.; Billman, J. F.; Kaler, E. W. J . Chem. Phys. 1988, 88, 3970. (27) Teubner, M.; Strey, R. J . Chem. Phys. 1987,87,3195. (28) Lagues, M.; Sauterey, C. J . Phys. Chem. 1980,84, 3503. (29) Gawlinski, E. T.; Redner, S. J . Phys. A 1983, 16, 1063.
Billman and Kaler teracting and interacting The droplet-tobicontinuous transition in both o/w and w/o microemulsions can be observed with NMR self-diffusion meas u r e m e n t ~ . ~Comparison ~'~~ of self-diffusion rates in microemulsions to those in neat solution yields insight into the structure of microemulsion and the location of components within the m i c r o s t r ~ c t u r e . ~ ~ The mechanism of both droplet-to-bicontinuous transitions is not understood. The formation of droplet clusters in advance of the percolative phenomena observed in both w/o and o/w microemulsions has been documented by using a variety of experimental technique^.^^ A t issue is the structure of the droplets comprising the clusters; do the droplets retain their closed structure or do they coalesce into an extended "open" structure? Electrical conductivity and self-diffusion measurements have been cited in support of both ~ l o s e dand ~ ~open , ~ ~droplet3s,39clusters. Fletcher et a1.40have considered the mechanism and kinetics of solubilite exchange between droplets. Using a two-step model for the coalescence of droplets, they demonstrate that the exchange of material between droplets can be correlated to the thermodynamic stability of microemulsions. This simple model provides a basis for rationalizing the percolative phenomena in microemulsions. The formation, structural transitions, and phase behavior observed in microemulsions have been qualitatively reproduced by a variety of models. Phenomenological m ~ d e l s , ~describe l - ~ ~ microemulsion in terms of their macroscopic properties. Ruckenstein41 and others42 calculate that microemulsions will spontaneously form when the negative contribution to the free energy from the entropy of dispersion overcomes the positive contributions from the low interfacial tension and curvature of the extensive interface. Other models based on the tessellation of space by V ~ r o n o or i ~cubic ~ ~ e l l sdescribe ~ ~ , ~ ~ the structural and phase transitions of microemulsions. When water or oil volume fractions, 4w and 40, respectively, are low, these models are equivalent to droplet dispersions. The isolated water or oil domains interconnect to form bicontinuous structures for $uIor 4o between 0.2 and 0.8. The conductivity transition in w/o microemulsions has been shown to be consistent with the predictions of the Voronoi Recently, Milner et a1.* have calculated correlation functions that can be compared to experiment. Microscopic models, on the other hand, determine the phase behavior and structures of (30) Safran, S. A; Webman, I.; Grest, G. S. Phys. Rev. A 1985, 32, 506. (31) Seaton, N. A.; Glandt, E. D. J . Chem. Phys. 1987,86,4668. (32) Lindman, B.; Stilbs, P. Surfactants in Solution; Mittal, K., Lindman, B., Eds.; Plenum: New York, 1984. (33) Guering, P.; Lindman, B. Langmuir 1985, I, 464. (34) Ceglie, A,; Das, K. P.; Lindman, B. J . Colloid Interface Sci. 1987, 115, 115. (35) Bellocq, A. M.; Bais, J.; Clin, B.; Lalanne, P.; Lemanceau, B. J . Colloid Interface Sci. 1979, 70, 317. (36) Eicke, H. F.; Hilfiker, R.; Holz, M. Helu. Chim. Acta 1984, 67, 361. (37) Mathew, C.; Patanjali, P. K.; Nabi, A.; Maitra, A. Colloids Surf. 1988, 20, 253. (38) Cazabat, A. M.; Chatenay, D.; Langevin, D.; Meunier, J. Faraday Discuss. Chem. SOC.1982, 76, 291. (39) Jada, A.; Lang, J.; Zana, R. J. Phys. Chem. 1989, 93, 10. (40) Fletcher, P. D. I.; Howe, A. M.; Robinson, B. H. J . Chem. SOC., Faraday Trans. I 1987,83, 985. (41) Ruckenstein, E.; Chi, J. C. J . Chem. SOC.,Faraday Trans. 2 1975, 71, 1690. (42) Miller, C. A.; Neogi, P. AIChE J. 1980,26,212. (43) Talmon, Y.; Prager, S. J . Chem. Phys. 1978, 69, 2984. (44) de Gennes, P.-G.; Taupin, C. J. Phys. Chem. 1982,86, 2294. (45) Widom, B. J . Chem. Phys. 1984,81, 1030. (46) Milner, S. T.; Safran, S. A.; Adelman, D.; Cates, M. E.; Roux, D. J . Phys. (Les Ulis, Fr.) 1986, 49, 1065.
Structure and Phase Behavior of Microemulsions microemulsion by considering the interaction of the individual molecules of the microemulsion upon regular lattices. These lattice models also re roduce the phase behavior4'@ and structural transitions' observed in microemulsions. Moreover, correlation functions4' and the wetting phenomena" of microemulsions can be reproduced qualitatively by these lattice models. Here we probe the relationship between the phase behavior and structure in a family of five-component microemulsions. Changes in both the phase behavior and structure of these microemulsions are observed as the alkane chain length is varied. These changes are monitored by electrical conductivity, NMR self-diffusion, and SANS measurements. This investigation demonstrates a clear relationship between structure and phase behavior of these microemulsions as the appearance of the three-phase region follows a droplet-to-bicontinuous transition in both of the dilute microemulsions. The structures of the two dilute microemulsions are inferred from their SANS spectra in terms of models of microemulsions as dispersions of interacting droplets. Both the shapes and interactions of the droplets in these microemulsions reflect changes in the chain length of the alkane. The properties of the midrange microemulsions in this family have been reported previously.26
Small-Angle Scattering Theory The analysis of neutrons scattered by a sample yields information about the distribution of scattering centers (atoms) within the sample. Small-angle neutron scattering probes the static time-averaged structure of the sample a t length scales proportional to the inverse of the magnitude of the scattering vector q: q = 4 i sin ~ (8/h), where X is the wavelength of the incident radiation and 8 is one-half of the scattering angle.51,52 In the absence of multiple scattering, the observable ( q # 0), coherent differential scattering cross section per unit irradiated volume of a sample containing N, particles or droplets is
Langmuir, Vol. 6, No. 3, 1990 613 disperse population of spherical droplets, eq 1 assumes the familiar form
where the term in parentheses is called the structure factor, S(q). Structure factors have been calculated for three interparticle potentials within the mean spherical approximation: (1) the hard-sphere potential (HS)53 UHs(r) = m for r < u and 0 for r > u, where u is the droplet diameter; (2) the Yukawa (Y) potential54 Uy(r)= for r u and (&$eoeu2/r) exp[-a(r - a)] for r > u, where \Eo2 is the surface potential, K is the inverse of the Debye screening length, eo is the permittivity of free space, and t is the solvent dielectric constant; (3) the square-well (SW) potential,55 usw(r) = m for r < u,-t/kbT for u < r < Xu, and 0 for P > Xa, where u(X - 1) is the width of the well of depth e, k b is the Boltzmann constant, and T is the temperature. The monodisperse sphere structure factors determined for the HS and the Y potentials are exact, while the SW potential is obtained by using a perturbation method. The important effect of a polydispersed population of droplets on the measured intensity can also be treated. A rigorous calculation of the differential scattering cross section (eq 1)for the HS potential acting between droplets of various sizes is available.56 For other potentials and particle shapes, a variety of "decoupling" approximations must be made in which the polydispersity and interaction problems are treated inde~endently.~'The approximate scattered intensity resulting from decoupling assumptions is expressed in terms of averages over the particle form factors (eq 2) and the monodisperse spherical droplet structure factors S(q) appropriate for the assumed interdroplet potential, i.e.
where S'(q) = 1 + @(q).[S(q)- 11 and @(q)is given by
where the sums range over the number of particles in the irradiated volume, N , each located by vectors R, and R,; F,(q) and F,(qfare the form factors of particle N and M , r e ~ p e c t i v e l y . The ~ ~ angular brackets signify an ensemble average over all particle positions and orientations, and V is the irradiated sample volume. The scattering from a dispersion of droplets is made up of the sum of two terms: the first depending on the intradroplet scattering and the second on the interparticle interactions. The first term is simply the average of the square of the form factor and can be calculated for particles of any geometry. The interparticle term, however, can be evaluated in closed form only if assumptions about the interactions between the particles and about correlations between the spacing of the particles and their orientations and sizes are made. For a mono(47) Widom, B. J.Phys. Chem. 1984,88,6508. (48) Schick, M.; Shih, W.-H. Phys. Rev. Lett. 1987, 59, 1205. (49) Gompper, G.; Schick, M. Phys. Rev. Lett. 1989, 62, 1647. (50) Dawson, K. A. Phys. Reu. A 1987,35, 1766. (51) Hayter, J. B. Physics 0fAmphiphile.s:Micelles, Vesicles, Microemulsions; Degiorgio, V., Corti, M., Eds.; North Holland; 1985. (52) Kaler, E. W. J. Appl. Crystallogr. 1988,21, 729.
The meaning of the angular brackets in eq 3 and 4 depends upon the nature of the decoupling assumptions. For a polydisperse population of spherical droplets, the decoupling is that of droplet separations and droplet sizes, and the averages are over particle size. For a dispersion of identical nonspherical droplets the separation and orientation of the droplets are decoupled, and the averages are then over particle orientations. These decoupling approximations are expected5' to be better for the repulsive Yukawa model than for the HS model, as the repulsion between droplets prevents the close approach of the droplets and therefore reduces the correlation of droplet separations and either the droplet sizes (polydisperse spherical droplets) or the droplet orientations (identical nonspherical droplets). (53) Wertheim, M. S. Phys. Reu. Lett. 1963, 10, 321. (54) Hayter, J. B.; Hansen, J. P. The Structure Factor of Charged Colloidal Dispersions at Any Density; Institute Law-Langevin Report, 1982. -_
(55) Sharma, P. V.; Sharma, K. C. Physica (Utrecht) 1977,89A, 213. (56) Vrij, A. J. Chem. Phys. 1979, 71, 3267. (57) Kotlarchyk, M.; Chen, S. H. J. Chem. Phys. 1983, 79, 2461. (58) Hayter, J. B.; Penfold, J. Colloid Polym. Sci. 1983,261, 1022.
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614 Langrnuir, Vol. 6, No. 3, 1990
In the vacinity of a critical point, the scattering from a polydispersed population of spheres has been successfully modeled by replacing the structure factor in eq 3 with a structure factor based upon the modified OmsteinZernike (OZ) form:" (5)
where Y is equal t o N k J x , xT is the isothermal compressibility, and € is t i e correlation length - of the critical fluctuations. Finallv. the intensitv of radiation scattered bv a sample proAdes some information regarding the skucture of the sample independent of assumption. First, the intensity scattered in the q-range corresponding to length scales intermediate between the characteristic size of the structure L and the interface length scale 1 (i.e., for q such that 1
