Polymer Reptation 2D: Brownian Bead-Spring Chain in a Fixed Obstacle Lattice

This simulator runs a real two-dimensional Brownian-dynamics integration of a bead-spring polymer chain — an overdamped Langevin equation with harmonic spring forces and genuine Gaussian thermal noise, stepped forward every animation frame. Rather than pre-rendering a tube and sliding a window along it, the chain here is confined the way Evans & Edwards' 1981 fixed-obstacle model does it: a lattice of pinned point obstacles that each bead feels as a short-range repulsion, forcing the chain to snake around them. The simulator measures its own trajectory live — tracking the center of mass, accumulating a mean-squared-displacement curve, and fitting a diffusion coefficient from its slope — and compares that measured number directly against de Gennes' reptation prediction that entangled diffusion should be suppressed by roughly 1/(3Z) relative to unconfined Rouse motion, where Z is the number of entanglements per chain. Adjust chain length, obstacle-lattice density and temperature to watch the measured suppression grow as the chain becomes more entangled.