2D Polymer Spherulite Growth & Avrami Crystallization

When a thin semicrystalline polymer film cools below its melting point, crystals nucleate at scattered points in the plane and grow outward as circular "spherulites" until they run into their neighbors — the same physical mechanism as bulk 3D crystallization, but confined to two dimensions, as in a spin-coated coating or blown film observed under a polarizing microscope. This simulator reproduces that process directly in the plane: nuclei appear either continuously (sporadic nucleation, n=3) or all at once (instantaneous nucleation, n=2), each seeding a disk that expands at a constant radial growth rate G. A Monte-Carlo sampler measures the true crystallized area fraction every frame and plots it live against the analytic Johnson–Mehl–Avrami–Kolmogorov curve X(t) = 1 − exp(−K tⁿ), letting you see directly how confining the same growth process to a plane instead of a volume shifts the Avrami exponent down by exactly one — a dimensionality signature real thin-film DSC and microscopy measurements can detect.