Novel computational modeling of trimodal chromatographic retention using Box-Cox and multivariate analysis

This study systematically investigated the retention behavior of 45 antidiabetic-related compounds using a trimodal stationary phase that combines reversed-phase (RP), cation-exchange (CEX), and anion-exchange (AEX) mechanisms. Multiple three-parameter retention models were developed using Box-Cox transformations to fit complex U-shaped and multimodal retention curves. Special attention was given to turning points, symmetry, and curve shape, introducing new mathematical descriptors such as higher-order derivatives to assess steepness and asymmetry. In addition to traditional volume fraction modeling (φ), alternative independent variables were tested, including molar fraction and Hansen solubility theory. These were compared using principal component analysis (PCA) and parallel factor analysis (PARAFAC) to determine their effectiveness in modeling retention behaviour. The results revealed that the molar fraction of acetonitrile offered the best predictive performance across most compounds, followed by Hansen parameters and volume fraction. A generalized Box-Cox equation was shown to effectively unify and simplify the modeling process. The study introduced symmetry-based tools and average retention descriptors (log k_A, log k_R, log k_H) to offer deeper fundamental interpretation of chromatographic behaviour. PARAFAC analysis further grouped compounds and equations based on their retention characteristics, confirming the flexibility and robustness of the generalized modeling framework. Overall, this work presents a comprehensive, mathematically grounded strategy for analyzing trimodal retention systems in chromatographic studies.