Estimation of Extra-Column Dead Volume Effects Using a Mixing Cell Model

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Abstract
An alternate method for generating skewed Gaussians and other exponentially modified functions is described. This method employs a computer algorithim which uses simple arithmetic and is based on a physical model of dilution (mixing) in dead volumes. The resulting functions are shown to be equivalent to those generated by previous methods based on convolute intergrals derived by Laplace transform techniques. In this manner, complete mixing in chromatographic dead volumes and other first-order peak skewing processes can be simulated and theoretically described in simpler terms. Two variations of the algorithm are also considered. The first is the reverse operation, or numerical “de-skewing” of asymmetrical peaks; the second involves repeated exponential modification of pulse (δ) function, using several volumes in a cascade fashion. The latter variation is of theoretical interest because of its mathematical similarity to existing models of the chromatographic partitioning process. In addition, the cascase algorithm may have practical value for estimating skewing effects of multiple dead volumes (having equal or unequal sizes) on Gaussian peaks.

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