Optimisation of gradient elution with serially-coupled columns Part II: Multi-linear gradients

• Multi-linear gradients are optimised for serially-coupled conventional columns.
• Genetic algorithms are used to reduce the calculation volume.
• Pareto plots were used to account both resolution and analysis time.
• The effect of column order on the separation performance is studied.
• Accurate predictions achieved in terms of retention time, peak width and asymmetry.

An interpretive approach is reported for the simultaneous optimisation of resolution and analysis time in the separation of complex samples by reversed-phase liquid chromatography, using serially-coupled columns of different lengths and nature, and multi-linear gradient elution. The results complement those reported in JCA 1350 (2014) 51 for single linear gradients, using combinations of five columns: three C18 columns of different characteristics, a cyano column and a phenyl column. The relationships between the logarithm of the retention factor (ln k) and the organic solvent content (φ), and between the peak half-widths and the retention times, for each analyte, were determined using isocratic retention times. From the established correlations, the gradient retention time was predicted using the fundamental equation for gradient elution (modified to be used for serially-coupled columns), and with this information, the peak profile. Two chromatographic goals (maximal peak purity and minimal analysis time) were simultaneously evaluated using the Pareto optimality concept. The rigorous predictive system can be easily applied to columns from different manufacturers and succeeds at different levels: single and combined columns, using isocratic and gradient elution. The computation time for gradient elution optimisation was significantly reduced to practical values with the help of genetic algorithms (GAs).