Titration of Fatty Acids Solubilized in Cationic, Nonionic, and Anionic Micelles. Theory and Experiment Fernando Luı ´s B. da Silva,* ,²,‡ Dan Bogren, § Olle So 1 derman, § Torbjo 1 rn A ° kesson, ‡ and Bo Jo 1 nsson ‡ Departamento de Fı ´sica e Quı ´mica, FCFRP, UniVersidade de Sa ˜ o Paulo, AV. do cafe ´ , s/no., 14040-903 Ribeira ˜ o Preto, Sa ˜ o Paulo, Brazil, Department of Theoretical Chemistry, Lund UniVersity, P.O. Box 124, S-221 00 Lund, Sweden, and Department of Physical Chemistry 1, Lund UniVersity, P.O. Box 124, S-221 00 Lund, Sweden ReceiVed: May 30, 2001; In Final Form: December 27, 2001 The titration properties of a fatty acid solubilized in different types of micelles, cationic, anionic and nonionic, have been investigated experimentally and theoretically. The solution containing micelles, counterions, and added salt was treated as a dielectric continuum in the Monte Carlo simulations. The dielectric permittivity of the interior of the micelle can have a profound effect on the calculated pK shifts depending on how the dielectric discontinuity is chosen in the model. The simulated results are compared to data from Poisson- Boltzmann calculations and from experiments. The experimentally observed apparent pK a value changes from 7.6 to 4.9 when solubilizing lauric acid in anionic (SDS) and cationic (DoTAC) micelles, respectively. For the nonionic micelle it is found to be approximately 6.6. A significant ion specificity in the pK a value is observed for the DoTAC and DoTAB systems and surprisingly enough both systems show an upward pK shift. I. Introduction Almost all industrial processes involve colloidal systems and often charged amphiphilic molecules. There is consequently a strong interest to understand and control the colloidal stability, which depends among other things on the surface potential of the colloidal particles. Thus, much interest has focused on the measurement of the electrical potential at the interface between the aqueous solution and the aggregate core. 1-7 After the classical works of Mukerjee and Banerjee 1 and Fernande ´z and Fromherz, 2 a typical experimental approach has been to employ interfacially located acid-base indicators and to obtain the mean electrostatic potential (φ) from the equation where pK a obs is the measured pK a ,pK a 0 is the intrinsic interfacial dissociation constant of the probe, F is the Faraday constant, R is the universal gas constant, and T is the absolute temperature. The apparent simplicity of this equation hides several funda- mental problems: (i) a correct measurement of pK a 0 , (ii) the location of the probe, and (iii) the importance of nonelectrostatic interactions. The meaning of the intrinsic interfacial dissociation constant is that it should be the acid constant of the probe in the presence of the interphase but in the absence of any electrostatic interactions. This is a somewhat obscure and artificial property and its accurate determination is a nontrivial experimental task. The problem has sometimes been circumvented by assuming that pK a 0 would be equivalent to the pK a value obtained in pure water, pK a w . 1 However, recent studies have indicated that this is not always the case. 2-6 Instead, experiments with nonionic micelles are usually performed and believed to give better estimates of pK a 0 . 2-7 Although questionable and still an un- solved problem, the latter seems to be the more common approach today. Ideally, the probe should have a size compatible with the surfactants and reside, on the average, in the plane of the charged surfactant headgroups, i.e., at the interface. Available data in the literature for different probes indicates that their location may not always be at the interface. 4-6 In addition, rather bulky dye molecules are often used, the perturbation of which on the micelles is probably quite substantial. In this work, we have chosen to use a fatty acid probe molecule of the same hydrocarbon chain length as the surfactant. The probe concen- tration is adjusted so that each micelle will contain, on average, one probe molecule. The pK a values of the solubilized probe have been determined from pH titrations and are compared with the corresponding data obtained from theoretical modeling. Theoretical attempts to study such systems are predominantly done using the dielectric continuum model, where only solute molecules enter explicitly in the model. The solvent is taken into account in an average way via a uniform permittivity, ǫ s . 8 Spherical micelles are usually modeled by charged hard-spheres, whose interiors have a dielectric constant of ǫ m . Often micelle- micelle interactions are not fully taken into account and just a single micelle is placed in the center of a spherical cell together with its counterions and added salt. This is referred to in the literature as the cell model. 9-11 To solve such an effectiVe Hamiltonian model, analytical or numerical calculations may be performed. A widely used * Author to whom correspondence should be addressed. Phone: +55 (16) 602 4219. Fax: +55 (16) 633 2960. E-mail: fernando@fcfrp.usp.br. ² Universidade de Sa ˜o Paulo. ‡ Department of Theoretical Chemistry, Lund University. § Department of Physical Chemistry 1, Lund University. pK a obs ) pK a 0 - Fφ RT ln 10 (1) 10.1021/jp012033m CCC: $22.00 © xxxx American Chemical Society PAGE EST: 7.1 Published on Web 00/00/0000