Nanoparticles — Brownian motion + van der Waals clustering
Scale: — nm wide
Mean Squared Displacement vs Time
Every nanoparticle suspended in a fluid is pushed around by two competing physical effects. Thermal energy from countless molecular collisions drives a genuine random walk (Brownian motion), whose diffusion coefficient follows the Stokes-Einstein relation D = kBT / (6πηr) — smaller particles and hotter, less viscous fluids diffuse faster. At the same time, once two particles get close enough their induced-dipole van der Waals attraction takes over, following a Lennard-Jones-like force law with a ~1/r⁶ attractive tail and a steep repulsive core that prevents overlap. Raise the attraction slider or lower the temperature and clusters form as van der Waals wins; raise temperature or shrink particles and thermal jitter keeps breaking clusters apart. The right-hand plot tracks mean squared displacement against the theoretical 4Dt line — pure Brownian motion tracks it exactly, and visible flattening is the fingerprint of aggregation slowing diffusion down.