Estimation of single solute adsorption isotherms applying the nonlinear frequency response method using non-optimal frequencies
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2008
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In order to estimate single solute adsorption isotherms, the nonlinear frequency response (FR) of a chromatographic column is analyzed experimentally and evaluated using the concept of higher order frequency response functions (FRFs) based on the Volterra series and generalized Fourier transform. In this case study, it has been investigated the adsorption ofethyl benzoate on octaclecyl silica from a mixture of methanol and water (60:40) as a solvent. Experiments are performed using a standard gradient HPLC unit. For estimation of adsorption isotherms by the nonlinear FR method the column inlet concentration is changed in a nearly sine waveform around several steady-state concentrations. Using this method the first three local derivatives of a single solute adsorption isotherm are estimated from the low frequency asymptotes of the corresponding functions, i.e. the phase and first order derivative of the FRFs. For an accurate estimation of isotherm coefficients periodical experiments sho...uld be preformed for frequencies below a certain critical frequency. This is the frequency needed for approaching the low frequency asymptotic behaviour of the corresponding functions close enough, so that errors due to the non-feasibility of experiments with zero frequency can be neglected. Unfortunately, depending on the properties ofthe system, it can happen (as for the system investigated here) that experiments for the critical frequency would be too long and cannot be realized. In order to study the loss ofaccuracy ofthe nonlinear FR method, when it is applied for non-optimal frequencies, experiments are performed for frequencies approximately one order of magnitude higher than the critical frequency required to evaluate the FRF phases. The obtained isotherm model coefficients are compared with the ones estimated using conventional frontal analysis as a reference method. The isotherms determined by two methods are similar, however a closer look reveals that peaks predicted under overloading conditions differ.
Ključne reči:
adsorption isotherms / liquid chromatography / nonlinear frequency response / higher order frequency response functions / parameter estimationIzvor:
Journal of Chromatography A, 2008, 1200, 2, 183-192Izdavač:
- Elsevier, Amsterdam
DOI: 10.1016/j.chroma.2008.05.063
ISSN: 0021-9673
PubMed: 18555261
WoS: 000257959000011
Scopus: 2-s2.0-46149121708
Institucija/grupa
Tehnološko-metalurški fakultetTY - JOUR AU - Ilić, Milica AU - Petkovska, Menka AU - Seidel-Morgenstern, Andreas PY - 2008 UR - http://TechnoRep.tmf.bg.ac.rs/handle/123456789/1252 AB - In order to estimate single solute adsorption isotherms, the nonlinear frequency response (FR) of a chromatographic column is analyzed experimentally and evaluated using the concept of higher order frequency response functions (FRFs) based on the Volterra series and generalized Fourier transform. In this case study, it has been investigated the adsorption ofethyl benzoate on octaclecyl silica from a mixture of methanol and water (60:40) as a solvent. Experiments are performed using a standard gradient HPLC unit. For estimation of adsorption isotherms by the nonlinear FR method the column inlet concentration is changed in a nearly sine waveform around several steady-state concentrations. Using this method the first three local derivatives of a single solute adsorption isotherm are estimated from the low frequency asymptotes of the corresponding functions, i.e. the phase and first order derivative of the FRFs. For an accurate estimation of isotherm coefficients periodical experiments should be preformed for frequencies below a certain critical frequency. This is the frequency needed for approaching the low frequency asymptotic behaviour of the corresponding functions close enough, so that errors due to the non-feasibility of experiments with zero frequency can be neglected. Unfortunately, depending on the properties ofthe system, it can happen (as for the system investigated here) that experiments for the critical frequency would be too long and cannot be realized. In order to study the loss ofaccuracy ofthe nonlinear FR method, when it is applied for non-optimal frequencies, experiments are performed for frequencies approximately one order of magnitude higher than the critical frequency required to evaluate the FRF phases. The obtained isotherm model coefficients are compared with the ones estimated using conventional frontal analysis as a reference method. The isotherms determined by two methods are similar, however a closer look reveals that peaks predicted under overloading conditions differ. PB - Elsevier, Amsterdam T2 - Journal of Chromatography A T1 - Estimation of single solute adsorption isotherms applying the nonlinear frequency response method using non-optimal frequencies EP - 192 IS - 2 SP - 183 VL - 1200 DO - 10.1016/j.chroma.2008.05.063 ER -
@article{ author = "Ilić, Milica and Petkovska, Menka and Seidel-Morgenstern, Andreas", year = "2008", abstract = "In order to estimate single solute adsorption isotherms, the nonlinear frequency response (FR) of a chromatographic column is analyzed experimentally and evaluated using the concept of higher order frequency response functions (FRFs) based on the Volterra series and generalized Fourier transform. In this case study, it has been investigated the adsorption ofethyl benzoate on octaclecyl silica from a mixture of methanol and water (60:40) as a solvent. Experiments are performed using a standard gradient HPLC unit. For estimation of adsorption isotherms by the nonlinear FR method the column inlet concentration is changed in a nearly sine waveform around several steady-state concentrations. Using this method the first three local derivatives of a single solute adsorption isotherm are estimated from the low frequency asymptotes of the corresponding functions, i.e. the phase and first order derivative of the FRFs. For an accurate estimation of isotherm coefficients periodical experiments should be preformed for frequencies below a certain critical frequency. This is the frequency needed for approaching the low frequency asymptotic behaviour of the corresponding functions close enough, so that errors due to the non-feasibility of experiments with zero frequency can be neglected. Unfortunately, depending on the properties ofthe system, it can happen (as for the system investigated here) that experiments for the critical frequency would be too long and cannot be realized. In order to study the loss ofaccuracy ofthe nonlinear FR method, when it is applied for non-optimal frequencies, experiments are performed for frequencies approximately one order of magnitude higher than the critical frequency required to evaluate the FRF phases. The obtained isotherm model coefficients are compared with the ones estimated using conventional frontal analysis as a reference method. The isotherms determined by two methods are similar, however a closer look reveals that peaks predicted under overloading conditions differ.", publisher = "Elsevier, Amsterdam", journal = "Journal of Chromatography A", title = "Estimation of single solute adsorption isotherms applying the nonlinear frequency response method using non-optimal frequencies", pages = "192-183", number = "2", volume = "1200", doi = "10.1016/j.chroma.2008.05.063" }
Ilić, M., Petkovska, M.,& Seidel-Morgenstern, A.. (2008). Estimation of single solute adsorption isotherms applying the nonlinear frequency response method using non-optimal frequencies. in Journal of Chromatography A Elsevier, Amsterdam., 1200(2), 183-192. https://doi.org/10.1016/j.chroma.2008.05.063
Ilić M, Petkovska M, Seidel-Morgenstern A. Estimation of single solute adsorption isotherms applying the nonlinear frequency response method using non-optimal frequencies. in Journal of Chromatography A. 2008;1200(2):183-192. doi:10.1016/j.chroma.2008.05.063 .
Ilić, Milica, Petkovska, Menka, Seidel-Morgenstern, Andreas, "Estimation of single solute adsorption isotherms applying the nonlinear frequency response method using non-optimal frequencies" in Journal of Chromatography A, 1200, no. 2 (2008):183-192, https://doi.org/10.1016/j.chroma.2008.05.063 . .