過冷却水の凍結機構の研究

Abstract

The author studied theoretically the process of freezing of supercooled water, on the basis of the following assumptions:(1) Free energy of an interface between ice and water is, for every molecule of water in contact with the interface, expressed by α-kTlog 2, where α=1/2{(inner energy of water per molecule) - (inner energy of ice per molecule)}=1/2 {(evaporation heat of ice per molecule) - (evaporation heat of water per molecule) } k=Boltzmann constant, and T=temperature.(2) Freezing begins with the formation of an ice bud of hexagonal prism in shape whose main axis is perpendicular to the nuclear surface, and the bud is to be formed on a plane surface of a solid “ freezing nucleus ” in supercooled water.(3) The ice bud sprouts at such portions of the nuclear surface as the molecules in the base of the ice prism can adhere to. An ice molecule can adhere to an atom of the nuclear surface only in the case where the displacement along the nuclear surface between to molecule and the atom is less than 12 per cent of lattice constant of ice. The radius of the ice prism should grow to that of this adhesion domain which can be calculated from both lattice structures and lattice constants for each of the nuclear surface and the base of the ice prism.Starting from these assumptions, the author calculated the following quantities:(i) the increase in the free energy, _??_F, caused by the formation of the ice bud;(ii) the temperature at which the ice bud of a given size will be formed, to satisfy either of the equations, where l means the radius of the ice bud in a number of molecular layers, and x the length of the ice bud in a number of molecular layers;(iii) the nucleation rate of the ice bud in a water droplet;(iv) the maximum radius of the ice bud determined by the lattice structure of the nuclear surface, -the critical freezing temperature which is characteristic of each nuclear substance.Calculated values of temperature agree well with the critical temperatures of ice crystal formation observed in the expansion chamber (-41°C, -32°C etc.), and also with the temperatures of freezing beginning in supercooled water droplets with various sorts of nuclei (AgI, PbI2, CdI2, NaNO3, CuI, NH4I, KI, NaCl, MgO, NaF, CdO, I2, CsI), obtained by many investigators. “-41°C” is thought to be the temperature at which an ice bud, consisting of 6 molecules or 24 molecules, forms in a droplet of supercooled water. “-32°C” is thought to be the eutectic point of a thin layer of NaCl solution, which is enveloped by newly condensed water and which envelops the freezing nucleus of NaCl crystal.