Some insights on the description of gradient elution in reversed-phase liquid chromatography

The so-called "fundamental equation for gradient elution" has been used for modeling the retention in gradient elution. In this approach, the instantaneous retention factor (k) is expressed as a function of the change in the modifier content (φ(ts )), ts being the time the solute has spent in the stationary phase. This approach can only be applied at constant flow rate and with gradients where the elution strength depends on the column length following a f(t-l/u) function, u being the linear mobile phase flow rate, and l the distance from the column inlet to the location where the solute is at time t measured from the beginning of the gradient. These limitations can be solved by using the here called "general equation for gradient elution", where k is expressed as a function of φ(t,l). However, this approach is more complex. In this work, a method that facilitates the integration of the "general equation" is described, which allows an approximate analytical solution with the quadratic retention model, improving the predictions offered by the "linear solvent strength model." It also offers direct information about the changes in the instantaneous modifier content and retention factor, and gives a meaning to the gradient retention factor.