A grand ensemble Monte Carlo investigation of the Bell lattice model for water

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Abstract
The lattice model for water, previously investigated by Bell using a Guggenheim-McGlashan first-order type of approximation (FOA), has been examined at three reduced temperatures T*=(kT/w)=0.2, 0.5 and 0.9 using grand ensemble Monte Carlo simulations. The parameters of the model are epsilon , w, u associated with first-neighbour energies, a hydrogen bond increment to this, and a 'penalty' incurred by molecules in triad sets on the two intertwined cubic ice lattices of the model. These parameters were given values suggested to be optimum by Bell ( epsilon /w=2.0, u/w=1.25). Results indicate that the cooperativity of the model is significantly underestimated by the FOA, although the general behaviour of the model is correctly represented. The authors have also made a preliminary examination of the possibility of introducing values of epsilon , w and u into the model which are directly related to H2O dimer potentials, rather than being estimated a posteriori from thermodynamic criteria. It is shown that this approach is feasible and that the advantage of extremely rapid calculation offered by the lattice model would not be lost.

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