ABSTRACT
Hammerstein integral equations . . . . . . . . . . . . . . . . . . . . . . . . . 94 5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
In this chapter, the numerical solutions of nonlinear Hammerstein integral equations (HIEs) arising in chemical phenomena are discussed. First, we have solved an integral equation which forms the basis for the conductor like screening model for real solvent (COSMO-RS) which appeared in chemical phenomena. The conductor like screening model for real solvent (COSMORS) [100] is a quantum chemistry based equilibrium thermodynamics method with the purpose of predicting chemical potential µ in liquids. It processes the screening charge density σ on the surface of molecules to calculate the chemical potential µ of each species in solution. As an initial step a quantum chemical COSMO calculation for all molecules is performed and the results (e.g. screening change density) are stored in a database. In a separate step COSMO-RS uses the stored COSMO results to calculate the chemical potential of the molecules in a liquid solvent or mixture. The resulting chemical potentials are the basis for other thermodynamic equilibrium properties such
developed to provide a general prediction method with no need for system specific adjustment. Due to use of σ from the COSMO calculation, COSMO-RS does not require functional group parameters. Quantum chemical effects like group-group interaction, mesmeric effects and inductive effects also are incorporated into COSMO-RS by this approach.
