Currently, there are three fundamental models of column overload which lead to closed-form equations for the peak profile. All use some simplifying assumption(s) to make the mathematics tractable, while at the same time retaining important features of the non-linear chromatographic behavior. In this work, the kinetic model based on the work of Thomas and the equilibrium models of Houghton, and Haarhoff-Van der Linde are used to study overload processes in reversed-phase chromatography. By adjustment of the parameters, all three models can be made to closely match the experimental peak shapes under conditions of moderate overload (up to 2.5% of the column capacity), but for higher overloads the Haarhoff-Van der Linde model fails to reproduce the experimental peak shape. All of the models involve a set of three physico-chemical parameters. These parameters are related to retention (capacity factor, k′) and peak width under dilute conditions, and to the degree of isotherm overload. Experimental results show that only the parameter related to k′ is essentially independent of the solute concentration and flow-rate. In principle, for all three models the peak width parameter should be independent of solute concentration, but in all cases this parameter was found to vary such that the intrinsic peak width increased with concentration. Given that all three models display this same trend, even at moderately low overloads where we feel the mathematical approximations are reasonable, we believe that the change in the peak width parameters shows an as yet unknown additional band broadening phenomenon which is related to the degree of overload and independent of flow-rate. The solute loading capcity, in terms of the adsorption site density, can be calculated from the isotherm overload parameter. The capacity is independent of flow-rate for all three models, but only that from the kinetic model is also independent of the amount of sample loaded onto the column. The adsorption site density derived from the kinetic model for a number of different mobile phases and solutes is consistent with results from more traditional isotherm studies. For chemically simple solutes such as the benzyl alkanols, a site density about 3-4 μmol/m2 was obtained.
Bibliographical noteFunding Information:
This work was supportedi n part by grantsf rom the Institutef or Advanced Studies in Biological Process Technology, University of Minnesota, and the 3M Company.C harlesL ucy wass upportedb y Tif ellowshipf rom theN atural Sciencea nd EngineeringR esearchC ouncil of Canada. We also would like to thank Professor Abraham Lenhoff for his commentsd uring the courseo f this work.