Experimental validation of physico-chemical models of effective diffusion in chromatographic columns packed with superficially porous particles

Abstract

The effective diffusion coefficient of a non-retained compound (uracil) was measured with the peak parking (PP) method for two series (4.6 mm×100 mm and 2.1 mm×100 mm) of six replicate columns packed with the same batch of superficially porous 2.6 μ m Kinetex-C 18 particles. The abilities of four different models of effective diffusion in packed beds to account for the experimental data are compared. These models include the conventional Knox time-averaged model, the extension to molecular diffusion of the Landauer electrical conductance model, the Garnett diffusion model for the inclusion of core-shell spheres down to infinitesimal small sizes, and the stochastic Torquato model for a random dispersion of spheres in contact. The choice of a non-retained compound for this purpose is justified by the facts that the diffusivity of this compound through the porous shell can be estimated independently from its internal porosity derived from inverse size-exclusion chromatography (ISEC) data, that the internal obstruction factor can be assessed by nuclear magnetic resonance (NMR) using the spin-echo pulsed field-gradient method, and that the hindrance diffusion factor can be estimated with either the Renkin or the Brenner correlations. The experimental effective diffusion coefficient of uracil was found to be in excellent agreement with the value predicted by Knox semi-empirical model, in good agreement with those predicted by Torquato and Landauer models while the Garnett model failed definitely. In conclusion, the longitudinal diffusion terms of columns packed with core-shell particles cannot yet be accurately predicted by any of the sophisticated, physically relevant models of effective diffusion actually available in the scientific literature.