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

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 t heory. The coefficients of the quartic free energy-order parameter relation ship and of the square gradient term are chosen in order to reproduce the m easured 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 degrees C. A simple one-parameter model is ad opted to describe the specific heat anomaly of liquid water at lower temper atures. The range of' nucleation rates allowed by thermodynamically consist ent choices of this parameter encloses extreme experimental values (similar to 10(30) m(-3) s(-1)) Bartell and Huang obtained at deep undercoolings (s imilar to-73 degrees C). The temperature and size-dependencies of the inter facial properties (free energy, Tolman-length, etc.) are discussed. (C) 199 9 Elsevier Science B.V. All rights reserved.