Computer simulation of heterogeneous nucleation of colloidal crystals at planar walls

A mini-review of the classical theory of heterogeneous nucleation at planar walls is given, and tests by Monte Carlo simulations for simple models of colloidal suspensions exhibiting a fluid-solid transition are described. This theory (due to Turnbull) assumes sphere-cap-shaped "sessile" droplets at the substrate, and the nucleation barrier that appears in the classical theory of homogeneous nucleation then is reduced by a factor depending on the Young contact angle. Various approximations inherent in this theory are examined: curvature corrections to the interfacial free energy of small droplets; neglect of anisotropy of the surface tension between crystal and fluid; neglect of corrections due to the line tension of the three-phase contact line; continuum rather than atomistic description. Also the problem of precise identification of the particles belonging (or not) to the "droplet" is discussed, and an alternative concept of extracting droplet properties from an analysis of finite size effects on phase coexistence in finite simulation boxes is explored. While the focus of our treatment is on the Asakura-Oosawa model of colloid polymer mixtures, also simple Ising/lattice gas models are considered to test some of these questions.