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 numer ical estimates of the coefficients of an isotherm model from the individual elution profiles of the two components of a binary mixture. The sample siz e must be large enough for the two bands to interfere strongly and for thei r maximum concentrations to exceed the range within which the isotherm equa tion is needed. In two cases, excellent agreement was observed between the equilibrium isotherm equations obtained by this new method and those determ ined by the classical combination of elution by characteristic points and b inary frontal analysis. In the first case, the adsorption of the ketoprofen enantiomers on a cellulose-based chiral phase is accounted for by a compet itive Bilangmuir isotherm. In the second case, the adsorption of benzyl alc ohol and 2-phenylethanol on C18 silica is accounted for by a competitive La ngmuir model. The importance of using the proper boundary conditions (i.e., a realistic injection profile) is stressed. The new method seems especiall y well suited for the rapid determination of the isotherms of enantiomers n eeded for the computer-assisted optimization of the separation of mixtures of these compounds, e.g., in simulated moving-bed applications. (C) 1999 El sevier Science Ltd. All rights reserved.