Closed-Form Storage Stability, Induction Delay, and Thermal- Feedback Criticality of Melt-Gated Autocatalytic Cure

Abstract We derive closed-form results for a lumped model of a cure triggered by the melting of an encapsulated catalyst, and test each against the full equations. At constant temperature the gated cure equals the ungated cure evaluated on the cumulative amount of catalyst released, so the gate delay grows with conversion and approaches the release time constant only late in the cure. The storage conversion of a Gaussian population of capsules follows from the fraction of capsules that are open, which bounds the spread of melting temperatures to within 3% of the full equations. For a fully released catalyst, the thermal balance at fixed conversion has a critical value of the product of the reduced exothermicity and the ratio of thermal to reaction time, given in closed form (1.96 for reaction order 3/2); integrated thresholds approach it for fast heat loss, and Arrhenius kinetics raise it by about exp(1/ Ar ), with Ar the reduced activation energy (within 5% on the tested grid). In a continuous-flow reactor with ungated kinetics, two folds of the steady-state curve do not imply two stable states: the upper branch can lose stability at a Hopf-type point before its fold. The window of two stable states is computed on an Arrhenius temperature path (24 K here), while sweep loops through that point depend on noise. All parameters are illustrative; no experimental data are used.