Journal of Chromatography A, 1202 (2008) 34–39 Contents lists available at ScienceDirect Journal of Chromatography A journal homepage: www.elsevier.com/locate/chroma Numerical determination of competitive adsorption isotherm of mandelic acid enantiomers on cellulose-based chiral stationary phase Yan Zhang, Sohrab Rohani, Ajay K. Ray ∗ Department of Chemical and Biochemical Engineering, The University of Western Ontario, London, Ontario N6A 5B9, Canada article info Article history: Received 10 December 2007 Received in revised form 6 June 2008 Accepted 16 June 2008 Available online 24 June 2008 Keywords: Inverse method Competitive adsorption isotherm Least-square fitting Genetic algorithm Orthogonal collocation on finite element abstract The use of inverse method for the determination of competitive adsorption isotherm of mandelic acid enantiomers on cellulose tris(3,5-diethylphenyl carbamate) stationary phase is proposed in this work. Non-dominated sorting genetic algorithm with jumping genes (NSGA-II-JG) was applied to acquire the isotherm parameters by minimizing the sum of square deviations of the model predictions from the measured elution profiles. Three different competitive isotherm models, i.e., Langmuir, biLangmuir and T´ oth, combined with transport-dispersive chromatographic model were used in predicting the elution profiles. Orthogonal collocation on finite element (OCFE) method was applied to obtain the calculated elution profiles. Results indicate that biLangmuir isotherm and T ´ oth isotherm give remarkably similar equilibrium isotherms within the investigated liquid concentration range. Band profiles calculated from both isotherm models are in good agreement with the experimental data. The validity of the determined parameters was verified by comparing the model predictions with experimental elution profiles at various experimental conditions. © 2008 Elsevier B.V. All rights reserved. 1. Introduction Preparative high performance liquid chromatography is cur- rently the most widely used method for separation and purification of optical enantiomers [1,2]. Preparative chromatographic enan- tioseparations are performed essentially under nonlinear condi- tions and separations are governed by the equilibrium isotherm of the solutes in the feedstock [3]. The study of phase equilibriums and more specifically the determination of adsorption isotherm of the optical enantiomers are extremely important, either from a scientific or an industrial point of view. Frontal analysis [4,5] and perturbation peak [6–8] method are frequently used for determination of binary or multi-component isotherm. In frontal analysis, successive or abrupt step changes in the feed are introduced and the breakthrough curves are mon- itored from the beginning until final compositions are reached. For a system with N components, (N - 1) intermediate plateau concentrations and N retention times of shock fronts from each breakthrough curve have to be analyzed so that the equilibrium data can be calculated by the integral mass balance equations. Adsorption parameters are then determined by fitting these equi- ∗ Corresponding author. Tel.: +1 519 661 2111x81279; fax: +1 519 661 3498. E-mail address: aray@eng.uwo.ca (A.K. Ray). librium data to the isotherm models using linear or nonlinear regression. Perturbation peak method determines the isotherm by measuring the retention times of small-size perturbations injected into the column equilibrated with sample solutions at different concentrations. A least-square fitting of the retention times of cal- culated perturbation peaks to those of measured ones is used to obtain the isotherm parameters. Although both methods can help to acquire very accurate isotherm parameters, they share a draw- back of consuming a large amount of expensive pure enantiomers [5,9]. Inverse method [10,11] is another choice for isotherm determi- nation of binary systems. This method allows the rapid estimation of the best values of the isotherm parameters by minimizing the differences between experimental overloaded profiles of binary mixtures and the profiles calculated by solving the mass bal- ance equation for the system under examination. Due to the low consumption of enantiopure chemicals, inverse method has been applied in many preparative enantioseparations, particularly simu- lated moving bed separations, to determine nonlinear competitive equilibrium isotherms [12–15]. Numerical determination of the competitive isotherm parame- ters of recemic mandelic acid on cellulose tris(3,5-diethylphenyl carbamate) stationary phase (ChiralCel OD) is presented in this work. Cellulose tris(3,5-diethylphenyl carbamate) is the most pow- erful cellulose derivative chiral stationary phases (CSPs). It has been 0021-9673/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.chroma.2008.06.026