Monte Carlo study of melting of a model bulk ice

摘要

The methods of NVT (constant number, volume and temperature) and NPT (constant number, pressure and temperature) Monte Carlo computer simulations are used to examine the melting of a periodic hexagonal ice (ice Ih) sample with a unit cell of 192 (rigid) water molecules interacting via the revised central force potentials of Stillinger and Rahman (RSL2).;In NVT Monte Carlo simulation of P-T plot for a constant density (0.904g/cm$sp3$) is used to locate onset of the liquid-solid coexistence region (where the slope of the pressure changes sign) and estimate the (constant density) melting point. The slope reversal is a natural consequence of the constant density condition for substances which expand upon freezing and it is pointed out that this analysis is extremely useful for substances such as water. In this study, a sign reversal of the pressure slope is observed near 280 K, indicating that the RSL2 potentials reproduce the freezing expansion expected for water and support a bulk ice Ih system which melts $<$280 K. The internal energy, specific heat, and two dimensional structure factors for the constant density H$sb2$O system are also examined at a range of temperatures between 100 and 370 K and support the P-T analysis for location of the melting point. This P-T analysis might likewise be useful for determining a (constant density) freezing point, or, with multiple simulations at appropriate densities, the triple point.;For NPT Monte Carlo simulations preliminary results are presented. In this study the density, enthalpy, specific heat, and structure factor dependences on temperature are monitored during a sequential heating of the system from 100 to 370 K at a constant pressure (1 atm.). A jump in density upon melting is observed and indicates that the RSL2 potentials reproduce the melting contraction of ice. From the dependences of monitored physical properties on temperature an upper bound on the melting temperature is estimated.;In this study we made the first analysis and calculation of the P-T curve for ice Ih melting at constant volume and the first NPT study of ice and of ice melting. In the NVT simulation we found for $rho$ = 0.904g/cm$sp3$ T$sb{rm m}$ $simeq$ 280 K which is much closer to physical T$sb{rm m}$ than any other published NVT simulation of ice. Finally it is shown that RSL2 potentials do a credible job of describing the thermodynamic properties of ice Ih near its melting point.