Modeling of the mass-transfer kinetics in chromatographic columns packed with shell and pellicular particles

The equations of the general rate model of chromatography and those of simple models (the POR, equilibrium-dispersive, and transport-dispersive models) are derived for beds packed with shell particles. Shell particles are made of a solid, nonporous core surrounded by a shell of a porous material that has properties similar to those of the fully porous materials conventionally used in HPLC. These equations have no algebraic solutions, but the moments of the peaks eluted under linear conditions can be calculated, affording the HETP equation for these columns. The discussion of the contribution to the HETP of the mass-transfer resistances shows that shell particles exhibit much lower plate heights for large molecular size compounds (e.g., peptides and proteins) than do fully porous particles, this advantage increasing with decreasing thickness of the shell. In contrast, the efficiencies of columns packed with shell particles and with fully porous particles having the same diameters are nearly the same for low molecular weight compounds. In practice, the gain in efficiency due to the use of shell particles to separate high molecular weight compounds does not depend on the thickness of the shell provided that this thickness does not exceed 30-40% of the particle diameter. For larger thicknesses, it decreases with increasing thickness. Shell particles can also be used in preparative chromatography. For compounds that have a high internal mass-transfer resistance, the gain in efficiency compensates the reduction in sample capacity due to the lower volume of porous adsorbent. For proteins like BSA, the production rate could be doubled. The gain decreases with decreasing mass-transfer resistance, e.g., with decreasing molecular weight.