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Abstract:
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Chromatography is a widely used technology for separating mixed compounds by partitioning them into mobile and stationary phases. A mathematical model is essential for predicting the retention time and the peak shape of the chromatogram, and also for understanding the separation mechanism of chromatography and detecting whether conditions were correct (e.g., if there was an overload of the sample). Various statistical distributions such as exponential, Gaussian, exponential modified Gaussian, Weibull, and log-normal have been used to approximate chromatography peaks, and further applied to the deconvolution of stacked peaks. We developed a statistical model for the separation process of all types of chromatography using a discrete distribution. We propose the first generalized theorem to model peaks for all types of chromatography using chromatography tables. We rigorously prove our theorem using induction. We also establish the relationship between on-chromatography peak distributions and out-flow peak distributions by the principle of mass conservation. Based on this relationship, we propose the binomial-negative binomial theorem, which is rigorously proven by induction.
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