Polymer Spherulite Growth & Avrami Crystallization

Nucleation Mode

Parameters

Nucleation rate Ṅ 6.0

Growth rate G 0.35

Time scale 1.0×

Live Readouts

Elapsed time t

0.0 s

Active nuclei

Crystallized X(t)

0.0%

Avrami exponent n

Crystallized fraction X(t)t≤0

Measured (Monte Carlo) Analytic JMAK fit

How it works

This models semicrystalline polymer crystallization from the melt using Johnson–Mehl–Avrami–Kolmogorov (JMAK) theory. Crystal nuclei appear inside the amorphous melt and each grows radially outward at a constant linear growth rate G, forming a spherulite — the classic radiating spherical crystalline domain seen in polyethylene, polypropylene and nylon under a polarizing microscope.

Extended volume (unimpeded growth):
  sporadic nucleation:      X_ext(t) = (π/3) Ṅ G³ t⁴   → n = 4
  instantaneous nucleation: X_ext(t) = (4π/3) N₀ G³ t³  → n = 3

Avrami equation:  X(t) = 1 − exp(−K tⁿ)

Avrami's trick is to first compute the "extended volume" as if every spherulite grew through its neighbors unobstructed, then correct for real impingement (crystals stop growing where they touch) with the exponential — exactly the X(t) formula above. That's why the spheres you see here are drawn without clipping at their boundaries: they represent the idealized unimpeded growth used in the derivation, while the measured curve reports the true crystallized volume fraction.

Sporadic mode (n=4) — new nuclei keep appearing at a constant rate Ṅ throughout the transformation, typical of polymers crystallizing well below their melting point.
Instantaneous mode (n=3) — all N₀ nuclei exist from t=0 (e.g. pre-seeded by nucleating agents/impurities), so only growth — not birth — drives the kinetics.
Measured curve — computed live by Monte-Carlo sampling: thousands of fixed points inside the cell are tested each frame against every growing sphere; the fraction enclosed is the true crystallized volume fraction, converging to the analytic Avrami curve as sampling accumulates.
Real-world relevance — the exponent n and rate constant K measured this way (via DSC or dilatometry) tell a polymer processor whether nucleation or growth dominates, directly setting cooling-rate and mold-temperature choices for injection molding.

Spherulite (growing crystal) Melt cell boundary

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