ADVANTAGES OF THE EQUATION ORIENTED MIXED MICELLIZATION MODELING

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

Córdoba

Congreso; 6to Encuntro Argentino de Materia Blanda, 6EAMAB; 2016

FAMAF, Universidad Nacional de Córdoba

The determination of the composition of mixed micellar systems is a major problem since only thecomposition of the total micellar solution is accessible to the experimenter because the molar fractionof each surfactant in the aggregate is fixed by the partition equilibria of the species between theaggregate 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 ofsurfactant mixtures. However, this model assumes symmetric thermodynamic behavior of the systemand that the excess entropy of mixing is zero. Moreover, as it is solved for each mixture compositionindependently, achieving the optimum values of the Margules parameters is not guaranteed andusually different values are obtained for each mixture composition. Thus, the Gibbs-Duhem equation isnot 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: AmericanChemical Society; 1992. p. 31?44, Chapter 2]. However as symmetry is assumed, it does not take intoaccount ternary interactions. When asymmetric Margules-type formulations are employed, which is amore general case than the symmetric ones, the systems are much better represented considering highorder 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 equationoriented 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 theminimum total free energy. Thus, the optimum Margules parameters are obtained when the problem issolved to global optimality and the Gibbs-Duhem relation is fulfilled. This method is not restricted to thenumber 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 mathematicalrepresentations of the excess free energy is required. Moreover, other excess free energyrepresentations 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 stronglynon-ideal and asymmetric due to the very different structures of the surfactants: the aqueous solutionsof the catanionic system sodium dehydrocholate (NaDHC) and hexadecyltrimethylammonium bromide(HTAB), and a very non-ideal tricomponent system that presents a coacervate domain and withpotential medical applications: dodecyltrimethylammonium bromide (DTAB; with bactericideproperties), sodium 10-undecenoate (SUD; used as fungicide) and sodium dodecanoate (SDD). Weused a well-known, state of the art, tool/language to solve the algebraic model, GAMS (GeneralAlgebraic 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 andCONOPT [GAMS Development Corporation: The solvers manuals, 2014].