Coupled Thermal Activation and Autocatalytic Cure Kinetics: A Theoretical and Computational Study of Delayed Reactive Transformation
- 1Independent Researcher
Abstract
The delayed transformation of a reactive material into a solid phase is limited, in most thermal-management approaches, by a basic trade-off between transport stability and transformation speed. We formulate and computationally analyze a coupled zero-dimensional model in which (i) a lumped thermal energy balance governs the fluid element's temperature, including exothermic self-heating from the reaction itself; (ii) the release of a reaction-triggering species follows a physically motivated first-order relaxation toward a temperature dependent, Arrhenius-rate-controlled saturation level (a lumped analog to shell-diffusion-limited release), rather than a prescribed availability function; and (iii) the triggered reaction follows Kamal–Sourour autocatalytic kinetics. Four dimensionless groups — Λ=0.911 (release-to-reaction timescale ratio), Θ=0.454 (thermal-to-reaction timescale ratio), ψ=10.08 (reduced exothermicity), and Ar=18.9 (activation-sensitivity number) — are used to organize the parameter space. An objectively matched (not arbitrarily scaled) comparison against a first-order control, whose rate constant is root-solved for equal t50 rather than assigned an assumed scaling factor, shows that the coupled autocatalytic system is Pareto-optimal: across 60 sampled first-order rate constants spanning a wide range, none simultaneously matches or beats the coupled system on both premature conversion (α at t=25 min) and completion time (t90). A two-parameter regime map over (Θ, Λ) identifies thermally limited, release-limited, and reaction-limited regions, with the thermally limited region driving peak exothermic overshoots up to 204°C above the setpoint. Because complete suppression of conversion below the nominal activation threshold is a structural consequence of the idealized (zero-width) gate rather than an independent prediction, we reframe the falsifiable claim around a finite-width thermal gate: increasing the gate width from 0.5°C to 15°C is predicted to reduce premature conversion (α at t=25 min falling from 0.073 to 0.039) at the cost of slower completion (t90 rising from 34.1 to 40.4 min) — a quantified, directly testable trade-off. Vectorized Monte Carlo propagation of joint uncertainty across nine kinetic, release, and thermal parameters (N=20,000) indicates that 69.9% of the draws satisfy both a minimum induction time and a 75-minute completion target, with reaction-kinetics parameters (most notably Ea2, Spearman r=0.69) dominating the predicted variance over thermal or release-timescale parameters. Three falsifiable predictions, each paired with a standard dynamic-DSC or rheo-DSC validation protocol, are stated for future experimental testing.
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BibTeX
@misc{sandler2026coupled,
title = {{Coupled Thermal Activation and Autocatalytic Cure Kinetics: A Theoretical and Computational Study of Delayed Reactive Transformation}},
author = {Leon Sandler},
howpublished = {ChemRxiv},
year = {2026},
month = sep,
doi = {10.26434/chemrxiv.15008366/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15008366/v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - Coupled Thermal Activation and Autocatalytic Cure Kinetics: A Theoretical and Computational Study of Delayed Reactive Transformation
AU - Leon Sandler
PY - 2026
DA - 2026/09/06
PB - ChemRxiv
DO - 10.26434/chemrxiv.15008366/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15008366/v1
AB - The delayed transformation of a reactive material into a solid phase is limited, in most thermal-management approaches, by a basic trade-off between transport stability and transformation speed. We formulate and computationally analyze a coupled zero-dimensional model in which (i) a lumped thermal energy balance governs the fluid element's temperature, including exothermic self-heating from the reaction itself; (ii) the release of a reaction-triggering species follows a physically motivated first-order relaxation toward a temperature dependent, Arrhenius-rate-controlled saturation level (a lumped analog to shell-diffusion-limited release), rather than a prescribed availability function; and (iii) the triggered reaction follows Kamal–Sourour autocatalytic kinetics. Four dimensionless groups — Λ=0.911 (release-to-reaction timescale ratio), Θ=0.454 (thermal-to-reaction timescale ratio), ψ=10.08 (reduced exothermicity), and Ar=18.9 (activation-sensitivity number) — are used to organize the parameter space. An objectively matched (not arbitrarily scaled) comparison against a first-order control, whose rate constant is root-solved for equal t50 rather than assigned an assumed scaling factor, shows that the coupled autocatalytic system is Pareto-optimal: across 60 sampled first-order rate constants spanning a wide range, none simultaneously matches or beats the coupled system on both premature conversion (α at t=25 min) and completion time (t90). A two-parameter regime map over (Θ, Λ) identifies thermally limited, release-limited, and reaction-limited regions, with the thermally limited region driving peak exothermic overshoots up to 204°C above the setpoint. Because complete suppression of conversion below the nominal activation threshold is a structural consequence of the idealized (zero-width) gate rather than an independent prediction, we reframe the falsifiable claim around a finite-width thermal gate: increasing the gate width from 0.5°C to 15°C is predicted to reduce premature conversion (α at t=25 min falling from 0.073 to 0.039) at the cost of slower completion (t90 rising from 34.1 to 40.4 min) — a quantified, directly testable trade-off. Vectorized Monte Carlo propagation of joint uncertainty across nine kinetic, release, and thermal parameters (N=20,000) indicates that 69.9% of the draws satisfy both a minimum induction time and a 75-minute completion target, with reaction-kinetics parameters (most notably Ea2, Spearman r=0.69) dominating the predicted variance over thermal or release-timescale parameters. Three falsifiable predictions, each paired with a standard dynamic-DSC or rheo-DSC validation protocol, are stated for future experimental testing.
ER -