A comparison of mathematical models in the plate and rate theory of chromatography

The mathematical models in the plate theory of chromatography are solved by using a statistical approach. An equation for the number of theoretical plates is proposed which can unify the equations that are deduced from the continuous flow (CF) and discontinuous flow (disCF) model respectively. The models are compared with those in the rate theory of chromatography such as the equilibrium dispersive (ED), transport (TR), Wade-Lucy-Carr (WLC), transport dispersive (TD) and general rate (GR) model. In the case of high column efficiency, expressions are given to account for the relationship between the parameters in the CF and ED model and those in the disCF and TR model. A ratio parameter is proposed to account for the contribution to peak variance of the finite rate of the equilibrium or the mass transfer kinetics between mobile and stationary phase. It is used to calculate the plate height and can be measured in experiments by changing mobile phase composition slightly. It is also demonstrated that the TR and WLC model will be equivalent when the adsorption isotherm is linear. When the adsorption isotherm is nonlinear, a nonlinear driving force equation is deduced from the Langmuir kinetics equation, which can explain the concentration dependence of the rate coefficient in the TR model which has been reported in literature.