11.7 : Column Efficiency: Rate Theory

The rate theory of chromatography provides quantitative insight into the shapes and widths of elution bands. These bands are based on the random-walk mechanism governing molecular migration within a column. The Gaussian profile of chromatographic bands arises from the cumulative effect of random molecular motions as they progress through the column.

During elution, a solute molecule experiences numerous transitions between stationary and mobile phases, exhibiting irregular residence times in each phase. As a solute zone travels down the column, its width increases due to the increased dispersion time. This zone width is directly proportional to the column residence time and inversely proportional to the mobile-phase flow velocity.

The van Deemter equation elucidates the influence of the mobile phase's flow rate on the height of a theoretical plate. This equation comprises three factors: A, B, and C. Factor A represents the multiple paths available to a solute traversing a packed column (eddy diffusion). Factor B accounts for the longitudinal (axial) or molecular diffusion arising from solute dispersion between high-concentration central regions and low-concentration peripheral regions, and factor C pertains to the mass transfer of solutes within stationary and mobile phases.

Overall, a high mobile phase velocity increases the plate height, resulting in band broadening.