The phase diagram of Mercedes Benz model of water using nested sampling algorithm and molecular dynamics simulations

Abstract

The Mercedes Benz (MB) model of water is quite popular for explaining the properties of water, but the complete phase diagram has not yet been published. In the MB model, water molecules are modelled as two-dimensional Lennard-Jones discs, with three orientation-dependent hydrogen-bonding arms arranged as in the MB logo. Nested Sampling (NS) is a powerful sampling algorithm for the parameter space that directly calculates the partition function. NS can be used for sampling the equilibrium thermodynamics of atomistic systems and allows access to all thermodynamic quantities in absolute terms, including absolute free energies and absolute entropies. Here, NS is used to calculate the phase diagram of the simple two-dimensional Mercedes-Benz (MB) model of water. 32 water particles were used in NS. While this number of particles provides sufficient agreement with the simulations, the results from fewer particles slowly begin to diverge from the result from NS with 32 particles as some of the equilibrium lines begin to shift. By combining the results from NS and molecular dynamics (MD) simulations, different phases were located and identified. In total, 5 different solid phases, 3 liquid phases and one gaseous phase were observed.