Graphical Method for Choosing Optimized Conditions Given a Pump Pressure and a Particle Diameter in Liquid Chromatography.

The general limitations on liquid chromatographic performance in isocratic and gradient elution are now well understood. Many workers have contributed to this understanding and to developing graphical methods, or plots, to illustrate the capabilities of chromatographic systems over a wide range of values of operational parameters. These have been invaluable in getting a picture, in broad strokes, about the value of changing an operational parameter or the value of one separation approach over another. Here we present a plotting approach more appropriate for determining how to use chromatography most efficiently in one's own laboratory. The axes are linear: column length vertical and mobile phase velocity horizontal. In this coordinate system, straight lines with intercept zero correspond to different values of t0. Hyperbolas correspond to values of pressure as the product of length and velocity is proportional to pressure. For a given relationship between theoretical plate height and velocity (e.g., van Deemter), the number of theoretical plates as a function of column length and mobile phase velocity is a surface (z direction) to the x and y of velocity and length. By representing the surface as contours, a two-dimensional plot results. Any point along a constant pressure hyperbola represents the best one can do given the particle diameter, solute diffusion coefficient, and temperature. The user can quickly see how to use the pressure for speed or for more theoretical plates. Sets of such plots allow for comparisons among particle diameters or temperatures. Analogous plots of peak capacity for gradient elution are equally revealing. The plots lead instantly to understanding liquid chromatographic optimization at a practical level. They neatly illustrate the value (or not) of changing pump pressure, particle diameter, or temperature for fast or slow separations in either isocratic or gradient elution. They are illustrated with a focus on maximizing plate count with a given analysis time (isocratic), the effect of volume overload (isocratic), and separations of a limited number of peptides with a peak capacity coming from statistical peak overlap theory (gradient).