Stochastic Theory of Chromatography: The Characteristic Function Method and the Approximation of Chromatographic Peak Shape

Abstract

The Stochastic Theory of Chromatography is reviewed in its fundamental aspects and achievements. Basic elements of the probability theory for linear-finite-time chromatographic model description are presented and the mathematical method of “Characteristic Function” (CF) for solving probabilistic models is described. Solutions are found in terms of CF for general chromatographic models of increasing complexity. These models are the constant mobile phase velocity model with general mechanisms of stationary phase entry and desorption process and non-constant mobile phase processes with Poisson mechanism of the stationary phase entry process. Among the solved models those belonging to the class of stochastic processes with stationary and independent increments are identified for which general description of the peak profile by the Edgeworth-Cramer series holds true. The convergence towards the Gaussian Law through the Berry-Esseen Theorem is discussed and the basic conditions for peak parameter determination by non-linear least squares fitting are discussed.