Dependence of the phase diagram on the coupling parameters in water-lattice models

This paper reports specific results obtained with the two previously proposed lattice models of water as based on the cluster variation method. The hydrogen-bonded lattice gas with next nearest neighbor repulsion has a Hamiltonian with three coupling parameters. We map out the region in the coupling parameter space which gives a phase diagram that has the same topology as the phase diagram of water. We first discuss, using the simple model, how one diagram evolves into a seemingly different topology and explain how the first order terminal points disappear in the metastable region. We then use the extended model, which contains two extra degrees of freedom, to describe four phase diagrams that show some of the desired features we want in a water potential. The final choice is made, using a potential labelled 9, which shows all desired features in a qualitative way. This potential has a critical point at Tc = 0.807Ep, and a triple point at T3 = 0.971Ep, where Ep is the nearest neighbor attractive energy in the absence of the H-bonding. The density-temperature and the pressure-density projection of the potential are given. The relative number of hydrogen-bonded pairs at constant pressure is given. A discussion is given about the limitations of the model.