The origin and mathematical properties of the split peak phenomenon are described for both linear and non-linear elution conditions. Through a series of computer calculations, the theoretical behavior of split peaks is predicted for a wide variety of conditions where chemical adsorption, as opposed to solute mass transfer, is the rate-limiting adsorption step. Our results, which derive from the fundamental solution of the non-linear chromatographic equations with an impulse input [δ(t)], are found to be in excellent agreement with the recent numerical simulations of Hage and Walters. The fraction of solute eluting at the dead volume (f) is found to be a complex function of both the flow-rate and the amount injected (C0). Although it is theoretically possible to use the split peak mass to derive values for the adsorption rate constant and the density of binding sites, this methodology is difficult and time-consuming to apply. Split peak theory may be useful, however, in engineering design computations where it is desired to maximize solute throughput, yet keep the non-retained fraction below a certain percentage of the total mass of solute applied to the column. Universal working curves for this purpose are presented and discussed. and the optimum throughput is found for each of several specified split peak fractions.
Bibliographical noteFunding Information:
This work was supported by a grant form the Bio-Process Technology Center of the University of Minnesota. The authors also thank David Hage for advance copies of his publications, and his helpful comments.
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