Combined effect of solvent content, temperature and pH on the chromatographic behaviour of ionisable compounds. III:...

We previously reported a model able to predict the retention time of ionisable compounds as a function of the solvent content, temperature and pH [J. Chromatogr. A 1163 (2007) 49]. The model was applied further, developing an optimisation of the resolution based on the peak purity concept [J. Chromatogr. A 1193 (2008) 117]. However, we left aside an important issue: we did not consider incidental overlaps caused by shifts in the predicted peak positions, owing either to uncertainties in the source data, modelling errors, or the practical implementation in the chromatograph of the optimal mobile phase (or any other). These shifts can ruin the predicted separation, since they can easily amount several peak-width units at pH values close to the logarithm of the solutes' acid-base constants. A probabilistic optimisation is proposed here, which is able to evaluate the uncertainties associated with the model and the consequences when the optimal mobile phase is implemented in the chromatograph. This approach assumes peak fluctuations in replicated assays obtained through Monte Carlo simulations, which gives rise to a distribution of elementary peak purities. The results yielded by the conventional (i.e. non-robust), derivative-penalised, and probabilistic optimisations were compared, checking the predicted and experimental chromatograms at several critical experimental conditions. Among the three approaches, only the probabilistic one was able to appraise properly the practical difficulties of the separation problem.