The van Deemter equation: assumptions, limits, and adjustment to modern high performance liquid chromatography

The fundamental assumptions of the van Deemter height equivalent to a theoretical plate (HETP) equation were formulated nearly 60 years ago in its rigorous final mathematical derivation in 1956. The limit of applicability of this classical theory of band broadening in chromatographic columns is discussed on the basis of accurate measurements of diffusion coefficients (in the bulk, in particles, and in column beds), of peak moments in both RPLC and HILIC, on the recent numerical solution of the Navier-Stokes equation and on the results of the simulation of the advection-diffusion transport in the bulk region of computer-generated random packed beds. A result of this discussion is that serious errors are made in the interpretations of the mass transfer mechanism in HILIC and RPLC that are based on the use of the original van Deemter expressions of the longitudinal diffusion coefficient through packed bed, of the mass transfer resistance in the mobile phase, and of the mass transfer resistance in the stationary phase. These errors are discussed and quantitatively assessed. Physically acceptable and relevant expressions are proposed to account for the true mass transfer mechanism in packed columns.