Net-Average Curvature Model for Solubilization and Supersolubilization in Surfactant Microemulsions Edgar Acosta, ² Erika Szekeres, ² David A. Sabatini,* ,‡ and Jeffrey H. Harwell ²,§ Chemical Engineering and Materials Science Department, Sarkeys Energy Center, University of Oklahoma, 100 East Boyd, Room T-334, Norman, Oklahoma 73019; Civil Engineering and Environmental Science Department, Carson Engineering Center, University of Oklahoma, 202 West Boyd, Room 334, Norman, Oklahoma 73019; and College of Engineering, Carson Engineering Center, University of Oklahoma, 202 West Boyd, Room 107, Norman, Oklahoma 73019 Received July 1, 2002. In Final Form: October 21, 2002 In this work, we propose a mathematical model to reproduce the solubilization, equivalent droplet radius, interfacial tension, and phase transitions of anionic surfactant microemulsions by scaling the curvature of the surfactant membranes to the electrolyte concentration required to obtain an optimum microemulsion formulation. At optimum formulation, equal amounts of oil and water are cosolubilized in a bicontinuous media that has a zero net curvature. Our first modeling approach is to use a single curvature term (inverse of an equivalent spherical droplet ratio) which proves to be inadequate as the system transitions to a bicontinuous microemulsion (supersolubilization), where the micelles become swollen and are no longer spherical. Later we introduce two curvature terms (net and average curvature) to interpret bicontinuous microemulsion behavior. The scaling constant (L), which has a length scale, was obtained for sodium dihexyl sulfosuccinate microemulsions with styrene, trichloroethylene, and limonene. This scaling constant (L) is shown to be independent of the oil type, temperature, surfactant, or additive concentration. We use this net-average curvature model to reproduce selected published data. We also compare the scaling constants (L values) for the different microemulsion systems studied, finding that this parameter is proportional to the length of the extended tail of the surfactant and reflects the surfactant solubilization potential. Additionally, the model was modified to account for palisade micellar solubilization. Finally, we introduce the interfacial rigidity concept to reproduce the interfacial tension of these systems. Introduction Surfactant micelles can increase the overall aqueous “solubility” of oils by 1 or 2 orders of magnitude compared to their molecular solubility. During solubilization in micelles, polar solutes can accumulate close to the micelle surface, amphiphiles in the palisade layer, and nonpolar oils in the hydrophobic core of the micelle. 1-4 The maximum micellar solubilization may be quantified by the micellar solubilization ratio (MSR). The MSR is small for oils with a large molar volume. For any particular oil, the maximum MSR is found when the hydrophilic/ lipophilic balance (HLB) of the surfactant fits that of the oil. 5,6 Microemulsion supersolubilization is an extension of the micellar solubilization concept, where reductions in the micelle curvature allow increased oil solubilization in the core of these “swollen” micelles. The solubilization capacity of these swollen micelles can be, on average, up to 1 order of magnitude higher than that of regular micelle solubilization. 7-10 The increased solubilization capacity in supersolubilization makes this approach attractive for many applications, including hard surface cleaners, aque- ous-based solvents, detergency, surfactant remediation of oil contaminated sites, emulsion polymerization, and so forth. Despite its economical benefits and numerous applica- tions, microemulsion supersolubilization has received only limited attention. In this paper, we introduce a thermo- dynamic model for microemulsion supersolubilization based on curvature and scaling law arguments. While most of the supersolubilization occurs in the core of the micelle, palisade layer solubilization is introduced to the model to link supersolubilization with the more traditional micellar solubilization and to reproduce interfacial tension data. Model Basis Excess Free Energy of an Oil Droplet. Consider an oil droplet of radius R with water/oil interfacial tension (γ 0 ) and molar volume (ν 0 ) suspended in water, as shown * Corresponding author. Phone: (405) 325-4273. Fax: (405) 325- 4217. E-mail: sabatini@ou.edu. ² Chemical Engineering and Materials Science Department, Sarkeys Energy Center. ‡ Civil Engineering and Environmental Science Department, Carson Engineering Center. § College of Engineering, Carson Engineering Center. (1) Smith, G. A.; Christian, S. D.; Tucker, E. E.; Scamehorn, J. F. J. Solution Chem. 1986, 15 (6), 519-529. (2) Smith, G. A.; Christian, S. D.; Tucker, E. E.; Scamehorn, J. F. Langmuir 1987, 3 (4), 598-9. (3) Tucker, E. E.; Christian, S. D. J. Colloid Interface Sci. 1985, 104 (2), 562-8. (4) Rouse, J. D.; Sabatini, D. A.; Deeds, N. E.; Brown, R. E.; Harwell, J. H. Environ. Sci. Technol. 1995, 29 (10), 2484. (5) Shinoda, K.; Kunieda, H. J. Colloid Interface Sci. 1973, 42 (2), 381-7. (6) Diallo, M. S.; Abriola, L. M.; Weber, W. J., Jr. Environ. Sci. Technol. 1994, 28 (11), 1829-37. (7) Wu, B.; Harwell, J. H.; Sabatini, D. A.; Bailey, J. D. J. Surfactants Deterg. 2000, 3 (4), 465-474. (8) Pope, G. A.; Wade W. H. In Surfactant-Enhanced Subsurface Remediation; Harwell, J. H.. Sabatini, D. A.. Eds.; ACS Symposium Series 594; Washington, DC, 1995; pp 142-160. (9) Dwarakanath, V.; Kostarelos, K.; Pope, G. A.; Shotts, D.; Wade, W. H. J. Contam. Hydrol. 1999, 38 (4), 465-488. (10) Nagarajan, R.; Ruckenstein, E. Langmuir 2000, 16 (16), 6400. 186 Langmuir 2003, 19, 186-195 10.1021/la026168a CCC: $25.00 © 2003 American Chemical Society Published on Web 12/02/2002