SPLIT-PEAK PHENOMENON IN NONLINEAR CHROMATOGRAPHY .1. A THEORETICAL-MODEL FOR IRREVERSIBLE ADSORPTION

A simulation algorithm of the chromatographic process was developed that permits study of slow kinetic effects in mass-overload conditions. A numerical step procedure was used to solve the set of differential equations describing the solute migration along the column. The method, which accounts for the solute dispersion in the mobile phase, is based on strict mass balances, when the Fick law and the integrated kinetic law are solved. The initial conditions may include any shape for the injection signal. Simulations were used to study the influence of slow kinetics in nonlinear chromatography and to test the validity of the approximations introduced into simplified theoretical models. We examined the case where a solute is split into two fractions, of which one is eluted as a nonretained first peak. The solution of the system of different equations in the ideal case (absence of axial dispersion), based on Langmuir second-order kinetics, was used to derive the split-peak expression for reversible and irreversible adsorption. In this last case a relationship independent of time is found and relates the fraction of retained solute to the sample size. It can be used to determine the apparent rate constant of adsorption and the maximum loading capacity of the column by zonal elution from the analysis of the "split-peak" effect in mass-overload conditions. From the results of numerical simulations it was shown that the expression of the nonretained fraction in case of irreversible adsorption was still valid with a large injection signal or in the presence of dispersive effects.