Apparent efficiency of serially coupled columns in isocratic and gradient elution modes

The goal of this work was to understand the variation of apparent efficiency when serially coupling columns with identical stationary phase chemistries, but with differences in their kinetic performance. For this purpose, a mathematical treatment was developed both for isocratic and gradient modes to assess the change in plate numbers and peak widths when coupling arbitrary several columns. To validate the theory, experiments were also carried out using various mixtures of compounds, on columns packed with different particle sizes, to mimic highly efficient (new, not used) and poorly efficient columns (used one with many injections). Excellent agreement was found between measured and calculated peak widths. The average error in prediction was about 5% (which may be explained by the additional volume of the coupling tubes). In isocratic mode, the plate numbers are not additive when the coupled columns possess different efficiencies, and a limiting plate count value can be calculated depending on the efficiency and length of the individual columns. Theoretical efficiency limit can also be determined assuming one column in the row with infinite efficiency. In gradient elution mode, the columns' order has a role (non-symmetrical system). When the last column has high enough efficiency, the gradient band compression effect may outperform the competing band broadening caused by dispersive and diffusive processes (peak sharpening). Therefore, in gradient mode, the columns should generally be sequentially placed according to their increasing efficiency.