A Hierarchical Model for Longitudinal and Intraparticle Diffusion Coefficients in Liquid Chromatography

The model for the effective longitudinal diffusion coefficient <i>D</i>_eff, recently derived from the two-zone moment analysis approach, is adapted to predict the intraparticle diffusion coefficient <i>D</i>_part of the general rate model for chromatography. The model for <i>D</i>_part, coupled with the model for <i>D</i>_eff, allows us to predict with great accuracy numerical data for <i>D</i>_eff obtained by solving the detailed diffusion-adsorption transport model, via the Brenner-Adler method of moments, in different 2D and 3D hierarchical retentive porous structures. The proposed models make explicit the dependence of <i>D</i>_eff and <i>D</i>_part on the obstruction factors of the macroporous and mesoporous zone, internal and external porosity, equilibrium constant, specific surface area, and surface diffusion coefficient. Detailed numerical simulations also allowed us to verify the inaccuracy of the parallel-connection model for <i>D</i>_part when surface diffusion in the stationary phase layer contributes significantly to the transport of the analyte in the mesoporous zone.