Cahn–Hilliard-type density functional calculations for homogeneous ice nucleation in undercooled water

Abstract

The free energy of ice nuclei and the nucleation rate in undercooled water are calculated in the framework of a single-order parameter Cahn–Hilliard theory. The coefficients of the quartic free energy-order parameter relationship and of the square-gradient term are chosen in order to reproduce the measured Gibbs free energy difference, the ice–water interfacial free energy, and the interface thickness predicted by molecular dynamics simulations. Without adjustable parameters, the model reproduces fairly the experimental nucleation rates down to −40°C. A simple one-parameter model is adopted to describe the specific heat anomaly of liquid water at lower temperatures. The range of nucleation rates allowed by thermodynamically consistent choices of this parameter encloses extreme experimental values (∼1030m−3s−1) Bartell and Huang obtained at deep undercoolings (∼− 73°C). The temperature and size-dependencies of the interfacial properties (free energy, Tolman-length, etc.) are discussed.