Separation Speed and Power in Isocratic Liquid Chromatography: Loss in Performance of Poppe vs Knox-Saleem Optimization

The best separation possible at a given analysis time and maximum system pressure is achieved by simultaneously optimizing column length, eluent velocity, and particle size. However, this three-parameter optimization is rarely practicable because only a few commercially available particle sizes exist. Practical optimization for systems described by the van Deemter equation therefore proceeds by first selecting an available particle size and then optimizing eluent velocity and column length. This two parameter ("Poppe") optimization must result in poorer performance with respect to both speed and efficiency because one fewer degree of freedom is used. A deeper analysis identifies a distinct point on each pair of "Poppe" curves beyond which the more efficient (and faster) separation is maintained by changing from smaller to larger particles. Here, we present simple equations identifying these "crossover points" in terms of analysis time and plate count thereby allowing a practitioner to rapidly identify the correct particle size for use in tackling a particular separation problem. Additionally, we can now quantitatively compare two-parameter and three-parameter optimization. Surprisingly, we find that for systems well-described by the van Deemter equation there is little separating power lost (only about 11% in the worst case) as a result of the limited availability of different particle sizes in using two-parameter optimization when compared to the ideal three-parameter optimization so long as one changes particle size at the prescribed crossover points. If these crossover times are not used, a great deal of separating power will be needlessly lost. (Graph Presented).