Analysis of the nonlinear frequency response of a chromatographic column for two adsorbed compounds

The nonlinear frequency response of a chromatographic column in a case of two adsorbed compounds is analyzed using the concept of higher order frequency response functions (FRFs) and generalized Fourier transform. This concept is based on a replacement of a nonlinear model with an indefinite series of linear FRFs of the first, second, etc. order. The same approach is applied as previously for the analysis in case of single component adsorption ([1],[2]). Using the nonlinear frequency response method local derivatives of adsorption isotherms are estimated at various steady-state concentrations from the phases and the first derivatives of the FRFs up to the third order. Absolute values of the isotherm derivatives are obtained from the low frequency asymptotic values of the FRFs first derivatives and their signs from the low frequency asymptotes of the FRFs phases. The nonlinear frequency response method appears to be in particular convenient for estimation of adsorption isotherms with complex shape ([1]). An experimental realization of the method shows some of its advantages ([2]). Therefore an extension of this method is made in order to determine competitive isotherms assuming the same principle for estimation of local partial derivatives of competitive isotherms as for single solute isotherm. The adsorption of ethyl benzoate and 4-tert-butylphenol is studied numerically by analyzing inlet and outlet concentrations obtained from simulations of the frequency response of a chromatographic column. The inlet concentration is perturbed in a sine waveform around certain steady-state concentrations. The adsorption of these two compounds on Octadecyl Silica as adsorbent using methanol and water as solvent can be described by the binary Langmuir-BET competitive isotherms ([3]). Analysis of the frequency response of this system for different inlet concentration changes (concentration change of only one compound or of both), several steady-state concentrations and different ratios between compounds shows the potential of the developed method for estimation of competitive isotherms. [1] Ilić M., Petkovska M. and Seidel-Morgenstern A., Nonlinear frequency response method for estimation of single solute adsorption isotherms. Part 1. Theoretical basis and simulations, submitted [2] Ilić M., Petkovska M. and Seidel-Morgenstern A., Nonlinear frequency response method for estimation of single solute adsorption isotherms. Part 2. Experimental study, submitted [3] Gritti F. and Guiochon G., Band splitting in overloaded isocratic elution chromatography II. New competitive adsorption isotherms, Journal of Chromatography A, 2003, 1008, 23-4