ADVANTAGES OF THE EQUATION ORIENTED MIXED MICELLIZATION MODELING

ERICA P. SCHULZ; PABLO C. SCHULZ; GUILLERMO A. DURAND; ROMINA BELÉN PEREYRA; HERNÁN RITACCO

Córdoba

Congreso; VI Encuentro Argentino de Materia Blanda; 2016

FAMAF-UNC

The determination of the composition of mixed micellar systems is a major problem since only the composition of the total micellar solution is accessible to the experimenter because the molar fraction of each surfactant in the aggregate is fixed by the partition equilibria of the species between the aggregate and the surrounding medium. The Regular Solution Theory (RST) [Holland P.M.; Rubingh D.N. J. Phys. Chem. 1983, 87, 1984-1990] is the most frequently applied model for interpreting the behavior of surfactant mixtures. However, this model assumes symmetric thermodynamic behavior of the system and that the excess entropy of mixing is zero. Moreover, as it is solved for each mixture composition independently, achieving the optimum values of the Margules parameters is not guaranteed and usually different values are obtained for each mixture composition. Thus, the Gibbs-Duhem equation is not fulfilled. There is an extension of the RST which deals with multi-component nonideal mixed micellar (MRST) systems [Holland P.M.; Rubingh DN. Mixed surfactant systems. Washington, DC: American Chemical Society; 1992. p. 31?44, Chapter 2]. However as symmetry is assumed, it does not take into account ternary interactions. When asymmetric Margules-type formulations are employed, which is a more general case than the symmetric ones, the systems are much better represented considering high order interactions [Mukhopadhyay, B.; Basu,S.; Holdaway, M.J..Geochim. Cosmochim. Acta, 1993, 57, 277-283].We have recently proposed a new approach for the mixed micellization modeling based on equation oriented optimization [E.P. Schulz; G.A. Durand. Computers and Chemical Engineering, 2016, 87, 145?153]: the system of equations is solved simultaneously for all the mixtures considered in order to find the minimum total free energy. Thus, the optimum Margules parameters are obtained when the problem is solved to global optimality and the Gibbs-Duhem relation is fulfilled. This method is not restricted to the number of components and does neither assume symmetric thermodynamic behavior of the system, nor null excess entropy. High order Margules formulations can be used when a complex mathematical representations of the excess free energy is required. Moreover, other excess free energy representations different from the Margules formalism can be employed within the same framework.The advantages of this procedure are shown addressing a system which seems prima facie strongly non-ideal and asymmetric due to the very different structures of the surfactants: the aqueous solutions of the catanionic system sodium dehydrocholate (NaDHC) and hexadecyltrimethylammonium bromide (HTAB), and a very non-ideal tricomponent system that presents a coacervate domain and with potential medical applications: dodecyltrimethylammonium bromide (DTAB; with bactericide properties), sodium 10-undecenoate (SUD; used as fungicide) and sodium dodecanoate (SDD). We used a well-known, state of the art, tool/language to solve the algebraic model, GAMS (General Algebraic Modelling System) [McCarl, B. A.; Meeraus, A.; Van Der Eijk, P.; Bussieck, M.; Dirkse, M.; Steacy, P.: McCarl GAMS User Guide, 2013], which provides the interface for the solving packages BARON and CONOPT [GAMS Development Corporation: The solvers manuals, 2014].