Van Deemter equation

The van Deemter equation in chromatography, named for Jan van Deemter, relates the variance per unit length of a separation column to the linear mobile phase velocity by considering physical, kinetic, and thermodynamic properties of a separation. These properties include pathways within the column, diffusion (axial and longitudinal), and mass transfer kinetics between stationary and mobile phases. In liquid chromatography, the mobile phase velocity is taken as the exit velocity, that is, the ratio of the flow rate in ml/second to the cross-sectional area of the ‘column-exit flow path.’ For a packed column, the cross-sectional area of the column exit flow path is usually taken as 0.6 times the cross-sectional area of the column. Alternatively, the linear velocity can be taken as the ratio of the column length to the dead time. If the mobile phase is a gas, then the pressure correction must be applied. The variance per unit length of the column is taken as the ratio of the column length to the column efficiency in theoretical plates. The van Deemter equation is a hyperbolic function that predicts that there is an optimum velocity at which there will be the minimum variance per unit column length and, thence, a maximum efficiency. The van Deemter equation was the result of the first application of rate theory to the chromatography elution process. The van Deemter equation relates height equivalent to a theoretical plate (HETP) of a chromatographic column to the various flow and kinetic parameters which cause peak broadening, as follows: Where HETP = a measure of the resolving power of the column [m] A = Eddy-diffusion parameter, related to channeling through a non-ideal packing [m] B = diffusion coefficient of the eluting particles in the longitudinal direction, resulting in dispersion [m2 s−1] C = Resistance to mass transfer coefficient of the analyte between mobile and stationary phase [s] u = speed [m s−1] In open tubular capillaries, the A term will be zero as the lack of packing means channeling does not occur.