Analysis of gradient elution chromatography using the transport model

Abstract A transport model is considered to describe gradient elution in liquid chromatography in packed beds with the linear isotherm dependent on the mobile phase modulator. By applying a coordinate transformation, the model is solved analytically using the Laplace transform approach. The moment generating property of the Laplace domain solution is used to derive analytical expressions for the first three moments of the response to rectangular injections. These moments are instructive for analyzing the retention time, band broadening and asymmetry of elution profiles. Compared to isocratic elution, the derivation of analytical solutions and moments for gradient elution is more complicated, because the retention behavior of the solutes depends on the varying mobile phase modulator. Several case studies are evaluated theoretically. To gain confidence on the derived analytical results, a high-resolution finite volume scheme is also applied to solve the same model equations numerically. The analytical solutions and moments provided are utilized to predict the effects of starting and ending times of gradient, magnitude of modulator concentration variation, gradient slopes, and mass transfer coefficient on retention and peak shape. The analytical moment expressions derived can be used to determine retention and mass transfer parameters from experimental peaks and to predict elution behaviors if these parameters are known.