Chemical Engineering Science 56 (2001) 6511–6524 www.elsevier.com/locate/ces Modeling the chromatographic response of inverse size-exclusion chromatography N. Venkata Saritha, Giridhar Madras * Department of Chemical Engineering, Indian Institute of Science, Bangalore 560012, India Received 2 January 2001; received in revised form 4 May 2001; accepted 19 June 2001 Abstract The pore-size distribution of a liquid-saturated porous medium can be determined by inverse size-exclusion chromatography under suitable conditions. A pair of coupled partial dierential equations describes the mathematical model quantifying the limitations of longitudinal dispersion, intraparticle diusion and adsorption. A temporal moment solution technique is usually used to obtain the moments of the elution curve with simplifying assumptions on the boundary conditions. The moments are then used to determine the chromatographic response and the pore-size distribution. A computational procedure based on the nite-dierence method has been developed to solve the model. The validity of the moment technique to solve these equations has been investigated by comparing the solution obtained by the numerical method with that obtained by the moment technique. The eect of the simplication of the boundary condition is examined and the elution curves for the cases of linear and non-linear adsorption of the solute are determined. ? 2001 Elsevier Science Ltd. All rights reserved. Keywords: Inverse size-exclusion chromatography; Modeling elution curves; Adsorption; Non-linear adsorption; Moment method; Numerical techniques 1. Introduction Inverse size-exclusion chromatography (ISEC) is used to determine the pore-size distribution (PSD) of column packing by monitoring the residence times of solutes of varying molecular diameters. A monodisperse solute is injected into a column packed with a porous particulate material and is used to probe the pores that are larger than the solute size. Each monodisperse standard provides the average pore-size within the range of pore sizes up to the next larger monodisperse standard. Solutes larger than the intraparticle pores probe only the external col- umn voids. While solutes with a larger molecular size have fewer chances to penetrate the macropores of the adsorbent and thus have a smaller retention time, smaller solutes penetrate more pores and are retained longer in the column. The solute retention time is proportional to the volume capacity of the chromatographic medium for ∗ Corresponding author. Tel.: +91-080-309-2321; fax: +91-080- 360-0683. E-mail address: giridhar@chemeng.iisc.ernet.in (G. Madras). the solute. The PSD is determined by calibration with monodisperse solute standards. In principle, an in- nite number of monodisperse standards would yield the complete continuous PSD. Interference from unwanted solute adsorption, intraparticle diusion resistance, lon- gitudinal (hydrodynamic) dispersion, and other mass transfer processes should be minimized to facilitate this ISEC procedure. Size exclusion packing should have minimum adsorption ability, since adsorption is often considered an undesirable side eect in SEC. It disrupts the retention sequence determined by molecular size dis- tribution of the solute components (Gu, Tsai, & Tsao, 1991). Since adsorption and mass transfer cannot be elim- inated, they need to be estimated quantitatively. Uneven saturation capacities caused by size exclusion or other reasons bring serious complications in mathematical modeling (Ruthven, 1984; Huang & Guichon, 1989). Knox and Scott (1984) have reported that size- exclusion chromatography (SEC) calibration curves can be predicted with remarkable accuracy from mercury porosimetry data, on the assumption that the matrix con- sists of an assembly of cylindrical channels having the 0009-2509/01/$ - see front matter ? 2001 Elsevier Science Ltd. All rights reserved. PII:S0009-2509(01)00302-5