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Abstract:
The nonlinear frequency response (FR) of a chromatographic column subjected to the periodical change of the inlet concentration is analyzed using the concept of higher order frequency response functions (FRFs). This concept is based on the Volterra series and generalized Fourier transform and it assumes a replacement of a nonlinear model of a system with an indefinite series of the linear FRFs of the first, second, etc. order ([1]). Using the nonlinear FR method the first, second etc. local derivatives of a single solute adsorption isotherm at several steady-state concentrations are estimated from the low frequency asymptotic behaviour of the corresponding FRFs (absolute values from the first derivatives of the FRFs and signs from the FRFs phases, [2]). The adsorption of 4-tert-butylphenol and ethyl benzoate as single solutes on octadecyl silica from a methanol and water mixture (60:40, v/v) is studied experimentally using this method ([3]). Experiments are performed using a standard gradient HPLC system which enables realization of the inlet concentration changes in a nearly sine wave form around the chosen steady-states. The concentration changes over time are analyzed in the frequency domain, which gives additional information about the nonlinearity of the adsorption isotherm. For accurate isotherm estimation it is necessary to perform experiments at different steady-state concentrations and for one or two different amplitudes of the inlet concentration change. The nonlinear FR method is able to detect existence of an inflection point by the sign change of the second isotherm derivative and therefore can be used for accurate estimation of adsorption isotherms with complex shape.
[1] Weiner, D.D. and Spina, J.F., Sinusoidal Analysis and Modelling of Weakly Nonlinear Circuits, Van Nostrand Reinhold, New York, 1980
[2] Petkovska M. and Seidel-Morgenstern A., Chem. Eng. Comm. 192 (2005) 1300-1333
[3] Ilić M., Petkovska M. and Seidel-Morgenstern A., J. Chromatogr. A, submitted
