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Abstract:
Knowledge of the underlying thermodynamic equilibrium functions is the key information for the design and optimization of chromatographic separation processes. However, adsorption isotherms cannot be predicted accurately and have to be determined experimentally. There are a lot of methods developed for this purpose, which have certain advantages and disadvantages [1]. In order to overcome some problems of the classical methods for measuring adsorption isotherms a new method is suggested. This method is based on the analysis of the nonlinear frequency response (FR) of a chromatographic column. The response of a column subjected to periodical changes of the inlet concentration is analyzed using the concept of higher order frequency response functions (FRFs), which is based on Volterra series developments and generalized Fourier transforms. This concept is based on the replacement of a nonlinear model of a system by an infinite series of the linear FRFs of the first, second, etc. order [2]. The nonlinear FR method analyzes concentration changes over time. Contrary to classical dynamic methods, which analyze these changes in the time domain, the nonlinear FR method does this in the frequency domain. For convenience, a dimensionless form of an adsorption isotherm is defined, which characterizes the local equilibrium around certain steady-state concentration. The dimensionless isotherm is expressed as a Taylor series developed at the steady-state concentration. Its coefficients are proportional to the isotherm derivatives of different order. The dimensionless isotherm coefficients can be estimated from the low frequency asymptotes of the corresponding FRFs and their derivatives [3]. In order to verify the nonlinear FR method, 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)was studied experimentally. Experiments were 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. A comparison of the isotherms estimated with this method and frontal analysis, as an independent reference method, was successful. To obtain accurate isotherms FR experiments must be performed at only a few steady-state concentrations, for at least one excitation amplitude and two periods of the time waveform.
