Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2021 / Paper 2 / Section B / 22 / i / Solution

Brownian motion is the irregular thermal displacement produced by fluctuating molecular forces from the surrounding liquid. In the overdamped regime its long-time displacement is diffusive, with mean squared displacement proportional to time. It brings nanoscale building blocks into contact and lets them sample orientations and escape weak incorrect contacts. Interparticle forces bias this exploration toward lower-free-energy structures; thermal motion alone does not select a particular crystal. Strong irreversible attraction, high viscosity or glassy arrest can stop the defect correction needed for successful self-assembly.