A Y-γ segmented linear framework for non-equilibrium UV-Vis titration: stage-resolved exploratory analysis of a...

Non-equilibrium UV-Vis titration data are difficult to interpret when multiple processes overlap and strict equilibrium assumptions no longer hold. We propose a non-equilibrium titration framework that transforms UV-Vis matrices into reaction-progress space using a dimensionless γ and a volume-corrected absorbance Y. Under mass and proton-balance constraints, locally single-process intervals obey Y_λ = a_λ + b_λγ; segmented linear regression then yields wavelength-dependent slope fingerprints (b_λ) that delineate coordination stages. In the EGCG-iron system, the Y-γ analysis resolves a progression from low-coordination mononuclear species to higher-coordination complexes, multinuclear/bridged units, and iron-rich aggregates across metal-to-ligand ratios and pH. Single-wavelength initial-rate measurements and solid-state characterization support rapid deprotonation-coordination coupling and the formation of cross-linked multinuclear networks at high γ. To benchmark soft-modeling, we performed MCR-ALS decompositions under weak constraints (post-normalized closure) and strong constraints (iterative simplex projection plus monotonic decay-to-zero of the initial dominant component). Both fits achieve similar residual levels, yet the recovered spectra/concentration profiles differ, evidencing rotational ambiguity and emphasizing the dependence of chemometric solutions on constraint choice. In contrast, the Y-γ segmented linear model relies on explicit stoichiometric/proton-balance transformations, providing robust stage boundaries and compact spectral descriptors while remaining computationally simple. This combined hard/soft analysis offers a practical route to mechanistic interpretation of complex titration spectra and motivates future integration of Y-γ descriptors with advanced chemometrics and hybrid hard-soft modeling.