A simple combinatorial method to describe particle retention time in random media with applications in chromatography

We propose a foundational model to explain properties of the retention time distribution of particle transport in a random medium. These particles are captured and released by distributed theoretical plates in a random medium as in standard chromatography. Our approach differs from current models, since it is not based on simple random walks, but on a directed and coordinated movement of the particles whose retention time dispersion in the column is due to the imprisonment time of the particle spent in the theoretical plates. Given a pair of fundamental parameters (λc,λe) the capture and release probabilities, we use simple combinatorial methods to predict the Probability Distribution of the retention times. We have analyzed several distributions typically used in chromatographic peak fits. We show that a log–normal distribution with only two parameters describes with high accuracy chromatographic distributions typically used in experiments. This distribution show a better fit than distributions with a larger number of parameters, possibly allowing for better control of experimental data.