Peak dispersion in gradient elution: An insight based on the plate model

Gradient elution in liquid chromatography reduces the analysis time, improves the efficiency and increases the peak capacity. The study of this chromatographic mode has been based mainly on kinetic dispersion models. The plate model has been applied to a lesser extent, despite being the basis for the concepts of plate height and chromatographic efficiency. In this work, a general equation describing peak dispersion in HPLC gradient elution is derived from the plate model. This equation is studied and validated for three types of gradients: (i) a reference gradient without ramp in which the retention factor varies with time identically throughout the column, (ii) a gradient of stationary phase in which the nature of the stationary phase varies continuously inside the column, resulting in a ramp of constant retention factor over time, and finally, (iii) a mobile phase gradient, which produces a retention factor ramp that varies over time. In the latter case, the results are similar to those derived from the mass-transport equation in linear solvent gradients when the linear solvent strength model is applied. The final equations are expressed based on the initial and final instantaneous retention factors, thus they can be applied independently of the deviation of the elution model, being fully compatible with isocratic elution. Results predicted with the proposed equations are identical to those obtained by numerical resolution of the elution differential equation system. The additional compression due to the presence of a ramp of modifier is also verified. However, useful compressions will appear only when the retention factor changes with time. Finally, the study indicates that the extra-column variance undergoes a compression process when the retention factor varies over time, whether or not there is a ramp inside the column.