Past exam of the soft condensed matter course of the University of Cambridge / 2021 / Section B / 5 / d / Solution

Colloidal particles experience attractive Van der Waals forces, arising from correlated molecular charge fluctuations and other dipolar interactions. Integrating many weak molecular attractions over two particles can give a deep near-contact well. For identical spheres of radius $a$ and surface gap $h\ll a$, a positive Hamaker constant gives approximatelyBrownian motion brings particles into encounters. Without a repulsive barrier, they can reach the attractive primary minimum; if the binding energy is much larger than $k_{B}T$, thermal motion rarely separates them again. Repeated sticking produces aggregates. This is a kinetic stability statement: thermal agitation causes encounters but does not itself supply a stabilizing interparticle repulsion. The molecular cutoff and hard sphere exclusion prevent the unphysical $h\to 0$ divergence of the continuum attraction.