Theory of linear focusing in chromatographic columns with exponential retention. Part 1: Basic solutions

Abstract

This report is the first of 2-part study of the effect of gradients in column parameters on the column performance. If t, x and p are, respectively, time since sample introduction, distance from column inlet and some parameter of solute migration along the column then ∂p/∂t and ∂p/∂x are, respectively, the rate of changing p and the gradient of p. Unified approach to study of gradients and rates in different chromatographic techniques (LC, GC, etc.) has been developed. To facilitate a unified approach, the umbrella term mobilization (y) representing column temperature (T) in GC, solvent composition (ϕ) in LC, etc. is introduced. Differential equations for migration of a solute band (collection of solute molecules) under the following conditions are formulated and solved:•exponential dependence of the solute retention factors (k) on y•linear changes in y as function of x and t (constant gradients and rates of changing y)•column itself is linearly not uniform so that, in the absence of gradient in y(∂y/∂x=0), k is a linear function of x (k has a fixed gradient, ∂k/∂x)The key solutions describe the time of migration of a solute band and the band width – both as functions of the distance traveled by the band. The solutions are used in Part 2 for the study of the effects of the negative gradients in y on column performance in several practically important cases. A reduction of the key general solutions to much simpler equations for gradient LC has been demonstrated herein as an example.