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Abstract: A set of accurate expressions of elution-curve moments are derived from the moments of residence time and displacement in a step based on probability theory. Then the problems about residence time and displacement in a step of a solute molecule in the porous layer of capillary columns and in the moving mobile phase are described by a set of mass-balance equations respectively. The set of equations are solved in Fourier–Laplace domain, and the characteristic functions of residence time of a step, as well as the moments, are obtained by means of computing software Mathematica. At last, using numerical inverse Laplace transform, the elution curves for various conditions are calculated. In the case of large desorption constant the results entirely coincide with those of mass-balance-equation theory and in the case of small desorption constant they are equivalent to those of stochastic theory. [Copyright &y& Elsevier]

Abstract: Based on the mass-balance principle, a particular diffusion equation to describe the movement of solute molecules in the stagnant layer of multiple-site solid surfaces is constructed. From the equation, the moments of residence time in a step on multiple-site surfaces are derived. Similarly, the moments in a step in the mobile phase are also derived from a diffusion-drift equation. According to the probability theory, there exists a general relationship between the moments of an elution curve and the moments in a step. Through this relationship, the expressions of the elution-curve moments are derived from the step moments. In this paper, the details related to multiple-site linear wall-adsorption capillary chromatography are described and added in the equations to determine the step moments. The resultant expressions of the elution-curve moments involve various factors, such as adsorption–desorption rate constants, equilibrium constants, axial and radial dispersions in the mobile phase. Afterwards, the moment expressions are used to analyze the peak tailing. The results show that a small quantity of sites with a slow desorption rate will lead to a large peak asymmetry. [Copyright &y& Elsevier]