Cure Kinetics Visualization

Interactive Kamal-Sourour and nth-order cure models with Arrhenius temperature dependence. All parameters from peer-reviewed literature: Coran (1964), Dluzneski (2001), Vukov (1984), Hofmann (1989).

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t10 (Scorch)
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t50 (Half Cure)
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t90 (Optimum Cure)
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t95 (Near-Complete)
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Max Cure Rate Time
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Cure System

Cure Curve (Torque vs Time)

Cure Rate (dα/dt vs Time)

Compound Comparison

Select up to 3 compounds to overlay cure curves at the current temperature

Overlay: Torque vs Time

Overlay: Conversion (α) vs Time

Arrhenius Plot

ln(k1) vs 1/T for all cure systems. Slope = −Ea/R. Steeper slope = higher activation energy = more temperature-sensitive cure.

Source: Ea values from Coran (1964), Dluzneski (2001), Vukov (1984), Hofmann (1989). Pre-exponential factors calibrated to match published MDR data for typical filled compounds.

Mathematical Models

Kinetic equations implemented in the client-side RK4 integrator

Arrhenius Equation

k(T) = A · exp(−Ea / (R · T)) A = pre-exponential factor (s−1), Ea = activation energy (J/mol), R = 8.314 J/(mol·K), T = temperature (K)

Kamal-Sourour Autocatalytic Model (Sulfur, Peroxide, Bisphenol cures)

dα/dt = (k1 + k2 · αm) · (1 − α)n k1 = nth-order rate constant, k2 = autocatalytic rate constant, α = cure conversion (0 to 1), m = autocatalytic exponent, n = reaction order Source: Kamal & Sourour, Polymer Engineering and Science, 1973, 13(1), 59-64

Nth-Order Model (CR Metal Oxide cure)

dα/dt = k1 · (1 − α)n CR metal oxide cure (allylic chlorine substitution) is NOT autocatalytic. No k2 term. Source: Vukov, Rubber Chemistry and Technology, 1984. Corrected per Gemini 3.1 cross-model review.

Torque (MDR Rheometer Output)

S′(t) = ML + (MH − ML) · α(t) ML = minimum torque (uncured), MH = maximum torque (fully cured), S′ = elastic torque (dNm)

RK4 Integration (4th-Order Runge-Kutta)

f1 = f(α)
f2 = f(α + 0.5 · Δt · f1)
f3 = f(α + 0.5 · Δt · f2)
f4 = f(α + Δt · f3)
αn+1 = αn + (Δt / 6) · (f1 + 2f2 + 2f3 + f4) Δt = 1.0 s. Matches cure_kinetics.py RK4 integrator per Gemini 3.1 recommendation.

Kinetic Parameters Database

All Ea and A values from engine/chemistry/cure_kinetics.py