Polymer Glass Transition 2D: Lattice Free-Volume Model

Every amorphous polymer — from a rubber band to an acrylic sheet — switches between a hard, brittle glass and a soft, flowable rubber over a narrow temperature window centered on its glass transition temperature, T_g. This 2D simulator represents polymer chains as bead-snakes living on a lattice, mostly surrounded by empty cells that stand in for free volume, and drives their reptation — a discrete end-to-end slithering move used in lattice models of polymer dynamics — directly from real free-volume theory: as temperature crosses T_g, the Williams–Landel–Ferry equation predicts how often a segment can now hop into a neighboring empty site. Sweep temperature, pick a real polymer's T_g, adjust the free-volume constants, or run a live cooling ramp and watch both the specific-volume curve and the measured lattice hop rate collapse exactly where the chains freeze from a wiggling melt into a rigid glass.