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#### Influence of the relative composition of a binary mixture on the nonlinear frequency response of a chromatographic column

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Ilic, M., Petkovska, M., & Seidel-Morgenstern, A. (2007). *Influence
of the relative composition of a binary mixture on the nonlinear frequency response of a chromatographic column*.
Talk presented at 19th Polish Conference of Chemical and Process Engineering. Rzeszow, Poland. 2007-09-03 - 2007-09-07.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-9761-5

##### Abstract

The analysis of the nonlinear frequency response (FR) of a chromatographic column for single component adsorption using the concept of higher order frequency response functions (FRFs) gives valuable information about adsorption systems and their nonlinearity. This analysis is based on the Volterra series and generalized Fourier transform ([1]). Single solute adsorption isotherms can be accurately estimated from the low frequency asymptotic behavior of the FRFs up to the third order using the nonlinear FR method based on determination of the local isotherm derivatives at different steady-state concentrations ([2]). The same approach can be applied for investigating binary adsorption in a chromatographic column. Doing this, it has been found that the local partial derivatives of competitive isotherms can be also estimated from the low frequency asymptotes of the FRFs and their first derivatives. However, in order to get all required coefficients different inlet concentration changes have to be used, i.e. the concentration of one of the components at the input should be changed periodically keeping the concentration of the other component constant or the concentrations of both components at the input should be changed periodically ([3]).
The nonlinear FR of a chromatographic column for the adsorption of mixtures of ethyl benzoate and 4-tert-butylphenol to sinusoidal concentration changes of one and two components at the input is simulated for different relative compositions of the mixture. In this case the components compete for adsorption sites and therefore a relative increase of the liquid phase concentration of one of the components causes differences between the corresponding equilibrium loadings. Comparison of results from the harmonic analysis of the input and output data shows specific (small) differences for the cases studied. These differences influence more the estimation of the second and third order FRFs, than the estimation of the first order FRF. This is due to the fact that the first harmonic in the output for the single harmonic input function is at least one order of magnitude larger than the other higher harmonics. The different values of the low frequency asymptotes of the corresponding FRFs correctly indicate different shapes of the competitive isotherms for different relative compositions of the mixture. The method described appears to be applicable to determine isotherms for multicomponent mixtures. This still needs to be verified experimentally.
[1] WEINER, D.D., SPINA, J.F., (1980): Sinusoidal Analysis and Modelling of Weakly of Nonlinear Circuits, Van Nostrand Reinhold, New York
[2] ILIĆ, M., PETKOVSKA, M., SEIDEL-MORGENSTERN, A. (2006): Nonlinear frequency response method for estimation of single solute adsorption isotherms, submitted to Journal of Chromatography A
[3] ILIĆ, M., PETKOVSKA, M., SEIDEL-MORGENSTERN, A. (2007): Investigation of binary adsorption in a chromatographic column using the nonlinear frequency response technique. Part I: Derivation of the frequency response functions and their correlation with derivatives of competitive isotherms, in preparation