(189b) Modeling the Solid-Liquid Equilibrium of Organic Compounds with the SAFT-g Mie Group Contribution Approach

The accurate modeling of the solubility of organic solids in solvents and solvent mixtures is essential for the reliable design of a range of processes (e.g. crystallization, solubilization, etc.) in the pharmaceutical and agrochemical industries. The successful modeling of solid solubilities can be achieved by accurately describing the activity coefficient of the solute of interest in the solvent or the solvent mixture in combination with the Shroeder-van Laar equation [1]. Versatile thermodynamic tools have been developed that can accurately describe the required activity coefficients, such as the general family of SAFT-type equations of state (EoSs) [2,3]. However, the successful application of theories of this kind requires an extensive amount of experimental information for the accurate characterisation of the substance(s) of interest. Typically pharmaceutical compounds are complex molecules for which experimental data are scarce and rather costly to produce. Moreover, when it comes to the study of solutions of pharmaceuticals in solvents, additional experimental information is required in order to determine the binary interaction parameters. A way to overcome these limitations is a modeling approach using predictive thermodynamic tools, typical examples of which are group contribution methods. UNIFAC and COSMO-RS are two popular group contribution approaches for the prediction of activity coefficients in the liquid phase [4,5]. Despite significant progress, the accuracy of the predictions that can be obtained for solid-liquid equilibrium remains variable for pharmaceutical compounds. There is therefore a need for further research in this area.

In this work, we use the SAFT-γ Mie group contribution equation of state as a predictive thermodynamic tool. The SAFT-γ Mie EoS is a formulation of the SAFT-VR Mie EoS [6] within a group contribution formalism, where molecules are modeled as consisting of distinct functional groups that interact via the Mie potential of variable attractive and repulsive range. The advantage of the approach presented here over standard SAFT EoSs is that the compounds of interest are characterised in a group contribution fashion; complex molecules are studied based on group parameters for functional groups that have been characterised previously, for which experimental data are generally available (e.g. alkanes, alkanols and aromatic hydrocarbons and, in some cases, mixtures of these). In addition, it is possible to take advantage of the fact that binary group interaction parameters can be derived from pure component data, an unusual feature of the SAFT-γ Mie framework which reduces the amount of experimental data needed to build the group parameter matrix. In this work, group parameters required for the prediction of the solubility of a set of organic compounds (such as benzene derivatives, paracetamol, and ibuprofen) in organic solvent and solvent mixtures are presented. The quality of the predictions of the temperature and composition (in the case of solvent blends) effects on the solubility of these complex molecules will be discussed.

[1] J.M. Prausnitz, R.N. Lichtentaler and E.C. de Azevedo, Molecular Thermodynamics of Fluid-Phase Equilibria, Prentice-Hall PTR, New Jersey (1999)

[2] W.G. Chapman, K.E. Gubbins, G. Jackson and M. Radosz, Fluid Phase Equilib. 52 (1989), pp. 31-38

[3] E. A. Müller and K. E. Gubbins, Ind Eng Chem Res, 40 (2001), pp. 2193-2211

[4] S. Gracin, T. Brinck and Å.C. Rasmuson, Ind Eng Chem Res, 41 (2002), pp. 5114-5124

[5] A. Klamt, F. Eckert, M.Hornig, M.E. Beck and T. Bürger, J Comput Chem, 23 (2002), pp. 275-281

[6] T. Laffite, A. Apostolakou, C. Avendaño, A. Galindo, C.S. Adjiman, E.A. Müller and G. Jackson (2011), in preparation