Modeling chromatographic dispersion: a comparison of popular equations

An analyte that is introduced onto a column as a finite band broadens as it moves along the column. This band-broadening is generally attributed to three independent processes, including flow path inequalities, molecular diffusion, and resistance to mass transfer. Many equations have been derived in attempts to mathematically model the process. Some of the more popular of these include the equations of van Deemter, Giddings, Horvath and Lin, and Knox. Although the basis of each equation is theoretically different, the differences among them are minor, and most of the equations can be used to adequately fit plate height data. Chromatographers often collect efficiency data to monitor the performance of their columns, and then use one of the above equations to fit the data. The choice of which equation to use can be daunting, since the theories are conflicting. Using an extensive collection of data, we have compared these equations on the basis of the resulting fit. This study was performed using analytes covering a wide range of retention values and mobile phases of differing strengths. The Foley-Dorsey equation was used to calculate the number of theoretical plates for the efficiency study and special precautions were taken to ensure that the observed broadening was due to only processes occurring in the column and that the peaks were adequately sampled. The variance from extra-column sources was measured and subtracted from the system variance. Although more complex equations gave very slightly better fits, 50 years after its introduction the van Deemter equation remains an incredibly accurate representation of band-broadening processes.