Abstract
The plate model proposed by Martin and Synge has been used for the characterization of columns up-to-date. In this approach, the column is divided into a large number (N) of identical theoretical plates. Mobile phase transference between plates takes place in infinitesimal steps with mixing of the solutions in the adjacent plates during the flow. The plate height is related to the band broadening that occurs in the mixing process due to the microscopic heterogeneities in the mobile phase flow. According to the original Martin and Synge model, solutes reach the equilibrium instantaneously in each theoretical plate, where dispersion is produced by: (i) convection or mixing of the mobile phase reaching a theoretical plate with that existing in that plate; and (ii) the equilibrium of the solute that is partitioned between mobile phase and stationary phase. In this work, a general method is proposed to solve the problem of chromatographic elution by means of an extended plate model assuming slow mass transfer, longitudinal diffusion in both mobile phase and stationary phase, and the extra column dispersion. The final equation was validated by comparing the results with those obtained through the numerical simulation of the solute migration using the finite differential approach. Experimental data were also used to check the validity of the derived equations.
Highlights
In 1941, Martin and Synge developed the principles of partition chromatography [1,2], and proposed the theoretical plate model to describe the elution in linear chromatography
A, B and C are constants that account for the contributions to band broadening from the eddy diffusion, longitudinal diffusion, and mass transfer resistance, respectively. This equation is known as “van Deemter equation” [24], and provides a basis to study the properties of chromatographic columns that affect the peak shape, usually characterized by relating H to the linear mobile phase velocity (u), showing the different contributions to band broadening [25]
Equilibrium between the mobile phase and stationary phase according to a Craig process: σ2eq “
Summary
In 1941, Martin and Synge developed the principles of partition chromatography [1,2], and proposed the theoretical plate model to describe the elution in linear chromatography. This equation is known as “van Deemter equation” [24], and provides a basis to study the properties of chromatographic columns (column performance) that affect the peak shape, usually characterized by relating H to the linear mobile phase velocity (u), showing the different contributions to band broadening [25] In another approach, proposed by Giddings and Eyring [26], the random migration of a single molecule is considered from a probabilistic point of view to describe the distribution function of the solute in the elution process [27], the elution profile being the probability density function of the retention time of the individual molecules. Experimental data were used to check the validity of the derived equations
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