Differential Coats-Redfern Framework for Conversion-Resolved Temperature-Programmed Kinetics

Temperature-programmed measurements such as thermogravimetry (TG) are routinely interpreted with Coasts-Redfern (CR) or isoconversional methods. Classical CR provides model-dependent activation energies (Ea) and pre-exponential factors (A) from a single heating ramp but relies on a global straight-line fit of ln[g(α)/T2] versus 1/T, which does not provide a rigorous differential definition of Ea and averages over curvature, obscuring local kinetic information since 1964. In this study, we reformulate CR in a differential framework (d-CR) by recognizing that the rigorous activation energy is given by the local derivative of ln[g(α)/T2] versus 1/T. In the infinitesimal-window limit, the CR relation yields conversion-resolved kinetic triplets {Ea(α), A(α), dα/dt} along a single heating rate for any chosen solid-state model. This converts CR from a single {Ea, A} pair into a dense kinetic field that enables two internal consistency checks unavailable in the classical workflow: (i) point-by-point rate-parity tests between reconstructed and experimental rates and (ii) conversion-variant compensation analysis in the {Ea(α), ln A(α)} plane. We benchmark d-CR against classical CR on non-catalyzed and zeolite-catalyzed thermolysis of pristine low-density polyethylene (LDPE), quantifying the bias introduced by global CR linearization even at high R2 and embedding d-CR into the isoconversional model selection workflow. To test applicability beyond polymers and thermogravimetry under isoconversional-free conditions, we apply d-CR to dehydration of Na2HPO4 and temperature-programmed in-situ FT-IR at a single heating rate. The d-CR framework thus improves a long-standing integral linearization into a conversion-resolved, model-aware kinetic analysis that is directly applicable to existing temperature-programmed datasets beyond thermogravimetry.