Theoretical investigation of the spatial progression of temporal statistical moments in linear chromatography

Migration and dispersion in chromatography are modeled by analogy to an effective eddy diffusion process. On the basis of this model, the spatial rates of temporal statistical moment change are derived for general chromatography in linear media. In most practical cases, these equations can be simplified so that temporal statistical moments can be calculated by solving a system of ordinary differential equations that depend only on the local HETP, solute velocity, and initial values of the temporal statistical moments. The calculations of temporal centroid, temporal variance, temporal skew, and temporal excess are demonstrated for the case of linear solvent strength gradients. It is shown for the case of temporally invariant separation environments, such as isocratic liquid chromatographic systems and isothermal gas chromatographic systems, that temporal variance contributions are spatially additive and that the temporal third normalized central moment is unaffected by spatial variations in the medium. A refined explanation is given for how peak symmetry is improved in gradient forms of chromatography.