Nonequilibrium Effects in Chromatography the van Deemter Equation

Separation of solutes in a chromatographic column requires that the analytes, initially injected in a common voliune of solvent, wiU move apart from one another in the column as a result of their differences in retention characteristics, i.e., differences in the partition coefficients K (Equation [3.1]), while their dispersion (broadening) is restricted sufficiently that the analyte bands elute as resolved peaks. Until now only the retention 

The rate theory of chromatography was introduced some 50 years ago by physicists and chemical engineers (van Deemter 1956). Despite all the work, both theoretical and experimental, that has been done since then on dispersion in chromatographic columns, the van 

Deemter equation still provides the most commonly used description of these dispersion processes, van Deemter theory is especially useful near the optimum value of the linear velocity of the mobile phase, where optimum in this context implies maximum column efficiency . 

When discnssing column efficiency in the context of the Plate Theory, the concept of the height of the equivalent theoretical plate (HETP) was introduced as H = (Z/N), where I is the length of the bed of stationary phase in the column and N is the number of theoretical plates (Section 3.3.5). H can conveniently be expressed as  

The van Deemter approach deals with the effects of rates of nonequilibrium processes (e.g. diffusion) on the widths (ct ) of the analyte bands as they move throngh the column, and thus on the effective value of H and thns of N. Obviously, the faster the mobile phase moves through the column, the greater the importance of these dispersive rate processes relative to the idealized stepwise equilibria treated by the Plate Theory, since equilibration needs time. Thus van Deemter s approach discusses variation of H with u, the linear velocity of the mobile phase (not the volume flow rate (U), although the two are simply related via the effective cross-sectional area A of the column, which in turn is not simply the value for the empty tube but must be calculated as the cross-sectional area of the empty column corrected for the fraction that is occupied by the stationary phase particles). This approach identifies the various nonequilibrium processes that contribute to the width of the peak in the Gaussian approximation and shows that these different processes make contributions to Ox (and thus H) that are essentially independent of one another and thus can be combined via simple propagation of error (Section 8.2.2)  

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