Determination of binary competitive equilibrium isotherms from the individual chromatographic band profiles

A numerical solution of the inverse problem of nonlinear chromatography is described and validated. This method allows the determination of best numerical estimates of the coefficients of an isotherm model from the individual elution profiles of the two components of a binary mixture. The sample size must be large enough for the two bands to interfere strongly and for their maximum concentrations to exceed the range within which the isotherm equation is needed. In two cases, excellent agreement was observed between the equilibrium isotherm equations obtained by this new method and those determined by the classical combination of elution by characteristic points and binary frontal analysis. In the first case, the adsorption of the ketoprofen enantiomers on a cellulose-based chiral phase is accounted for by a competitive Bilangmuir isotherm. In the second case, the adsorption of benzyl alcohol and 2-phenylethanol on C18 silica is accounted for by a competitive Langmuir model. The importance of using the proper boundary conditions (i.e., a realistic injection profile) is stressed. The new method seems especially well suited for the rapid determination of the isotherms of enantiomers needed for the computer-assisted optimization of the separation of mixtures of these compounds, e.g., in simulated moving-bed applications. (C) 1999 Elsevier Science Ltd. All rights reserved.