Modeling of preparative chromatography processes with slow intraparticle mass transport kinetics

Mathematical modeling of the preparative chromatography process accompanied with complex intraparticle mass transport mechanism involving surface diffusion is discussed. As an experimental base for the analysis two steroid compounds, methyl esters of hydroxycholanic acids (bile acids), deoxycholic and cholic acids were selected. For these compounds surface diffusion kinetics were found to have a marked influence on the band broadening. The isocratic chromatography process was performed in a normal-phase preparative system with ternary mixture of solvents containing hexane, ethyl acetate and methanol as a modifier under different operating conditions, e.g., at various mobile phase compositions and inlet concentrations. The efficiency of the system was found to be dependent on the mass of sample injected as well as on the contents of the modifier. Such a phenomenon was suggested to originate from the contribution of the surface diffusion kinetics to the overall mass transport mechanism. For identifying the general trends and concentration dependencies of the surface diffusion coefficient the simplified approach was proposed. The set of chromatographic band profiles registered at different inlet concentration and mobile phase composition were used for determining the influence of the local solid-phase concentration on the mass transport mechanism. For the simulations the transport-dispersive model was used, in which all sources of mass transport resistances were lumped in the properly adjusted mass transport coefficient. The accuracy of this model was verified by comparing its predictions to the solutions of the general rate model.