Simulation of Elution Curves for Chromatography Columns with a Low Number of Theoretical Plates

W. Brüchle, GSI, Darmstadt, Germany Chromatographic techniques are among the most effective chemical methods to separate and characterize closely related chemical substances or ions. More than half a century ago the main theoretical fundaments for these methods were developed; even a Nobel Price was awarded to Martin and Synge [1] for their theoretical and practical methodic developments. There is a lot of pioneering theoretical descriptions of peak position and peak width, often based on the molecular dynamic theory of chromatography, originally developed by Giddings and Eyring [2]. The model represents the progress of a single molecule through the column as a chain of elementary adsorptiondesorption stochastic processes. The majority of these papers have started with partial differential equations leading to Bessel functions. The asymptotic expansion of the Bessel functions weighed by the probability of the initial state of the molecule should yield the distribution curve for the elution. Rather complicated calculations using the characteristic function method are described in [3]. An easier way to describe the chromatographic process is the "theoretical plate" concept. It is the imaginary section of a column in which a complete equilibrium step takes place. The model was successfully used in [1] for liquid-solid chromatography. In most cases textbooks dealing with chromatography will present the following formula without derivation: Kd = (Tr-T0)*F/m = (V-V0)/m (1)