Nanobattery Charging: The R² Diffusion Law

Nanostructuring is one of the biggest levers battery engineers have for fast-charge performance, and the reason is pure diffusion geometry: the time it takes lithium ions to fill an electrode particle scales with the square of that particle's radius. This simulator renders a 3D field of electrode particles spanning nano to micron scale, all beginning a charge step at the same instant, and colours each one live from blue (empty) to amber (full) using the exact spherical-diffusion solution for its own radius. Tune the mean particle size and the solid-state Li⁺ diffusion coefficient and watch the smallest particles saturate almost instantly while the largest ones are still barely tinted, with live readouts for elapsed time, average state of charge, and the analytically computed 80%-charge time for the smallest and largest particles on screen.