Fast estimation of adsorption isotherm parameters in gradient elution preparative liquid chromatography II: the competitive case.

Experimental competitive adsorption isotherms were successfully determined directly from overloaded elution profiles in gradient elution mode using an extended inverse method. This approach differs from the existing methods in one important aspect - no isocratic experiments are necessary which makes it possible to study adsorption of substances whose retention factors vary strongly with the mobile-phase composition. The approach was verified with simulated binary data and with experimental data from gradient separations of a cyclohexanone/cycloheptanone mixture. For the synthetic data, the original adsorption isotherm parameters were found using a two-step estimation procedure. In the first step analytical peaks were used to estimate the "analytical" part of the Langmuir equation and in the second step the association equilibrium parameters were estimated from two simulated overloaded elution profiles. For the experimental data, a three-step approach was used. The two first steps were used to reduce the calculation time so that parameter estimation could be performed on an ordinary computer. In the first step, analytical peaks were used to estimate the "analytical" part of the bi-Langmuir equation. In the second step, initial guesses for all other parameters were determined separately for each solute using the faster Rouchon algorithm. In the final and third step, the more accurate orthogonal collocation on finite elements algorithm, was used to fine-tune the isotherm parameters. The model could accurately predict the shape of overloaded elution profiles. The shape of the adsorption isotherms agreed well with those determined with the standard isocratic method, although the numerical values were not the same. The extended inverse method is well suited for process optimization where few experiments and accurate predictions are important.