On the statistical independence of various column contributions to band broadening. Part 3: Independent treatment of longitudinal diffusion in the plate model

Abstract

AbstractIt is shown theorectically that the classical formula for calculating the theoretical plate number from squared first central moment, t, and second central moment, σ2, according to ntheor = t/σ2 is valid only when the capacity ratio, k approaches infinity. The general relation between the classical experimental HETP value, H = L/nmtheor, and the underlying true theoretical plate height, ΔL, is found to be when (σ′)2 is the total column contribution to band broadening, L is the column length, Dm is the average diffusion coefficient of the sample component in the mobile phase, Ds is its value in the stationary phase, and u is the average linear velocity of the mobile phase. The mobile phase displacement, as well as the mass exchange process, is assumed to be continuous, but the application of the plate concept conditions leads to a mass balance equation that can be interpreted as belonging to a modified discontinuous plate model. The contributions 2Dm/u and k 2 Ds/u from longitudinal sample diffusion in the mobile and stationary phases, respectively, are consistent with the assumption that the processes are statistically independent, although the common solution technique of the differential equations does not take full account of this independence.