One way to improve a separation is to decrease the height of a column’s theoretical plate. The figures here consider four contributions to plate height: variations in paths length, longitudinal diffusion, mass transfer in the stationary phase, and mass transfer in the mobile phase.
The effect of multiple paths on a solute’s band broadening is illustrated here. The solute’s initial band profile is rectangular. As this band travels through the column, individual solute molecules take different paths, three of which are shown by the meandering colored arrows. The actual lengths of these paths are shown by the straight arrows at the bottom of the figure. Most solute molecules travel paths with lengths similar to that shown in blue, with a few traveling much shorter paths (green) or much longer paths (red). As a result, the solute’s band profile at the end of the column is broader and Gaussian in shape.
The second contribution to band broadening is the result of the solute’s longitudinal diffusion in the mobile phase. Solute molecules are constantly in motion, diffusing from regions of higher solute concentration to regions where the concentration of solute is smaller. The result is an increase in the solute’s band width, as illustrated here by the two horizontal cross-sections through the column and their corresponding concentration versus distance profiles with (a) being earlier in time. The red arrow shows the direction in which the mobile phase is moving.
As the solute passes through the column it moves between the mobile phase and the stationary phase. We call this movement between phases mass transfer. As illustrated here, band broadening occurs if the solute’s movement within the mobile phase or within the stationary phase is not fast enough to maintain an equilibrium partitioning of solute between the two phases: (a) ideal equilibrium Gaussian profiles for the solute in the mobile phase and in the stationary phase; (b, c) the movement of the solute’s band with the mobile phase disrupts this equilibrium and, as indicated by the red arrows, the solute most from the stationary phase to the mobile phase and from the mobile phase to the stationary phase to reestablish equilibrium; (d) once equilibrium is reestablished, the solute’s band is now broader.
The height of a theoretical plate, H, is a summation of the contributions from each of the four contributions to band broadening. As shown here, H is a complicated function of the mobile phase’s flow rate, u,
H = A + B/u + Cu
which also is known as the van Deemter equation.
In the van Deemter equation, A accounts for the contribution of multiple paths, B/u for the contribution of longitudinal diffusion , and Cu for the combined contribution of mass transfer in the stationary phase and mobile phase.
