An Approximate Expression for the Minimum Plate Height Produced by Knox's Equation

The van Deemter (h = A + B/v + Cv) and the Knox equations (h = av^1/3 + b/c + cv) are the most widely accepted equations for describing the dependence of the plate height on mobile phase linear velocity. The simple form of the analytical solution for the minimum plate height obtained from van Deemter's equation allows one to locate the optimum velocity and minimum plate height and to obtain insight into the contribution of A, B, and C terms to the minimum plate height. Although Knox's equation provides better fit s to liquid chromatography data than van Deemter's equation, the exact solution of the minimum plate height based on Knox equation is too complicated to be informative. In this work, we describe a simple approach to estimating the minimum plate height based on Knox's equation. For typical HPLC conditions, the relative error of the estimates is generally less than 3%. The approximate analytical solution for the minimum plate height based on Knox's equation indicates the important contribution of the column packing term to the minimum plate height.