Mathematics of Optimization and Scaling for the Practicing Chromatographer

Interactions between minimum run time, modifier concentration, and efficiency parameters in a high performance liquid chromatography separation

We modeled and studied the separation of uracil, nicotinamide, resorcinol, theobromine, theophylline, and caffeine on four C-18 columns of different lengths packed with the same stationary phase using water/methanol mobile phase at one temperature. Predictions of retention times and peak widths were compared with experimental results and were found to be sufficiently accurate for performing optimization calculations. With limits set on the required resolution and on maximum values for pressure and flow rate, calculations were performed for numerous virtual column lengths seeking the smallest possible analysis time for each length while allowing methanol concentration and flow rate to vary as required to minimize run time. Predictions were experimentally verified for the column lengths actually available. These calculations revealed the dependence of best-possible analysis time on column length, modifier concentration, flow rate, and pressure for the real system that was modeled, and provided insight into parameter interactions with respect to analysis times meeting the needs and limits specified. We show that when these parameters are considered in concert, rather than individually, conventional guidelines regarding setting their values may not always lead to the optimum.