Polymer Electrolyte: Li⁺ Hopping (2D Lattice Model)

This is a 2D kinetic-Monte-Carlo counterpart to the 3D chain-bundle visualization of the same material: a lattice of amorphous and crystalline coordination sites, over which Li⁺ ions perform a genuine hard-core-exclusion random walk gated by the Vogel–Tammann–Fulcher segmental-hopping physics. Rather than only reading a formula off the sliders, this model actually simulates every ion's trajectory, measures its real mean-squared displacement, and derives a live diffusion coefficient and Nernst–Einstein conductivity from that measurement — then checks the result against the closed-form theory live on screen. Watch conduction collapse inside the crystalline band, speed up with temperature, and peak at an intermediate salt loading, while the measured and predicted conductivities track each other but never quite agree, exactly as real simulation-versus-theory comparisons in the polymer-electrolyte literature do.