The phase coexistence method to obtain surface free energies and nucleation barriers: a brief review

A recently developed method where one analyses the finite size effects associated with liquid–solid phase equilibria including vapour–crystal coexistence is briefly reviewed. It is shown that the estimation of the chemical potential of the vapour surrounding the crystal as function of the crystal volume yields information on the bulk coexistence conditions, when an extrapolation to the thermodynamic limit is performed. Estimating the pressure of the fluid surrounding the crystal nucleus in the finite simulation box and the volume of this nucleus that coexists with the fluid in thermal equilibrium, an estimate for the total surface excess free energy can be obtained, which to a very good approximation is independent of the size of the simulation box. The free energy barrier against homogeneous nucleation of crystals thus can be estimated as a function of the nucleus volume. Monte Carlo simulations for the soft effective Asakura–Oosawa model of colloid-polymer mixtures which form face-centered cubic colloidal crystals are used to exemplify this method, computing the surface excess free energy of these crystals over a wide range of crystal volumes, without the need to characterise the non-spherical crystal shape. A possible extension of these concepts to heterogeneous nucleation is also briefly discussed.