Statistical mechanics of water: lattice model with directed bonding

Abstract

In the model each molecule has four tetrahedrally-directed bonding directions and can form asymmetrical bonds with suitable oriented molecules on nearest neighbour sites of a body centred cubic lattice. An open four-bonded structure, like ice I(c), with half the BCC lattice sites vacant and a close packed structure, like ice VII, with interpenetrating four-bonded networks are thus possible. In the present fluid phase theory all BCC lattice sites are equivalent and these structures are present only as short range order, together with disordered regions due to molecular disorientation and displacement. Energies of bonding and of interaction with nonbonded nearest neighbours and also a close packing energy are introduced. The state surface of the fluid is investigated using a generalized first order statistical approximation based on a group of four sites. The isothermal compressibility and the coordination number (i.e. mean number of nearest neighbours of a given molecule) are also calculated. For suitable energy values there are maxima on the curves of density against temperature at constant pressure both in the liquid and in the supercritical region. In agreement with experiment this anomalous behaviour of the density ceases at a certain supercritical pressure. The observed minimum in the isothermal compressibility, both in the liquid and supercritical regions, occurs in the model.