On the inherent data fitting problems encountered in modeling retention behavior of analytes with dual retention mechanism

Some valuable insights have been obtained in the inherent fitting problems when trying to predict the retention time of complex, multi-modal retention modes such as encountered in HILIC and SFC. In this study, we used mathematical models with known input parameters to generate different sets of numerical test curves representative for systems exhibiting a complex, non-LSS dual retention behavior. Subsequently, we tried to fit these data sets using some popular (non-linear) literature models. Even in cases where a physical fitting model exists (e.g., the mixed model in case of pure additive adsorptive and partitioning retention), the fitting quality can only be expected to be relatively good (prediction errors expressed in terms of a normalized resolution error ɛRs) when carefully selecting the scouting runs and the appropriate starting values for the fitting algorithm. The latter can best be done using a comprehensive grid search scanning a wide range of different starting values. This becomes even more important when no good physical model is available and one has to use a non-physical fitting model, such as the empirical Neue-model. The use of higher-order models is found to be quasi indispensable to keep the prediction errors on the order of some ΔRs = 0.05. Also, the choice of the scouting runs becomes even more important using these higher-order models. For highly retained compounds we recommend using scouting runs with long tG/t0-values or to include a run with a higher fraction of eluting solvent at the start of the gradient. When trying to predict gradient retention, errors with which the isocratic retention behavior is fitted are much less important for high retention factors k than errors made in the range of k near the one at the point of elution. The results obtained with a so-called segmented Neue-model (containing 7 parameters) were less good and thus practically not interesting (because of the high number of initial runs).