Deformation of Chromatographic Peaks Under the Influence of Mass Transfer Phenomena

Abstract

Mass transfer processes and kinetic retention mechanisms influencing chromatographic peak shapes are investigated using the methods of chemical engineering and system dynamics. The assumptions are those of linear chromatography, allowing the column to be considered as a linearly distributed parameter system. A synthetic and progressive modeling of the column transfer function (i.e. the retention time distribution Laplace Transform) is proposed at three successive levels: stationary phase particle, elementary column volume and column as a whole. A useful theorem allowing any kind of flow in the mobile phase to be dealt with is demonstrated. Peaks are simulated by numerical inversion of the Laplace transform using the Fast Fourier Transform method. In order to characterize the relative ease of access to retention sites, a new concept is introduced, namely the transfer time distribution f(τ) (TTD), τ being the global mass transfer time constant pertaining to each site population. The influence of the TTD on peak shape and tailing is investigated in various situations. Special attention is paid to the case of bidispersed TTD occurring when two kinds of retention sites with different τ and τ₂ coexist. A noticeable variation in the peak maximum and even two maximum peaks may be observed, whereas the center of gravity (the total number of sites) remains constant. An experimental illustration of such a behavior can be found in the adsorption of hydrogen on a Ni-Al₂O₃ supported caltalyst, allowing an activated adsorption rate constant to be determined. Chromatography thus proves to be a possible tool for the study of mass transfer kinetics provided a correct interpretation of peak deformations is used.