New Monte Carlo method to compute the free energy of arbitrary solids. Application to the fcc and hcp phases of hard spheres

Abstract

We present a new method to compute the absolute free energy of arbitrary solid phases by Monte Carlo simulation. The method is based on the construction of a reversible path from the solid phase under consideration to an Einstein crystal with the same crystallographic structure. As an application of the method we have recomputed the free energy of the fcc hard-sphere solid at melting. Our results agree well with the single occupancy cell results of Hoover and Ree. The major source of error is the nature of the extrapolation procedure to the thermodynamic limit. We have also computed the free energy difference between hcp and fcc hard-sphere solids at densities close to melting. We find that this free energy difference is not significantly different from zero: −0.001<ΔF<0.002.

Calculation of Free Energies and Chemical Potentials for Gas Hydrates Using Monte Carlo Simulations

“…Free Energy of the Zero-Occupancy Hydrate. The zerooccupancy hydrate may be viewed as a metastable ice phase, and we use the Frenkel-Ladd (FL) method 66 to calculate its Helmoltz free energy. Our use of the FL method follows closely the original work, with modifications to treat the orientational degrees of freedom 83 and the effect of a fixed center of mass.…”

“…The third term in eq 9 is determined using a coupling parameter integration over λ T and λ R . 66,68,83 The final term in eq 9 is given by A -A CM ) ln(V/N). 67 We assume that the hydrate is proton-disordered but that the contribution to the free energy from the disorder is independent of the molecular interactions and approximated by the residual entropy of ice as determined by Nagle.…”

Twinning of Polymer Crystals Suppressed by Entropy

“…Its numerical evaluation using standard procedures such as the Einstein crystal method [31,32] is also a major computational challenge, chiefly due to the difficulty of finding a kinetically accessible path between the untwinned and twinned states along which to carry out thermodynamic integration. However, the geometrically simple structure of the ideal pentagonal twin shown in Figure 3 suggests an alternative, approximate method based on a decomposition of the entropy change ΔS in contributions stemming from:…”

Competing ordered structures formed by particles with a regular tetrahedral patch decoration

“…In Figure 5 we have depicted U ⋆ and η (both obtained via simulations) along the isotherm T ⋆ = 0.10 over a relatively large pressure interval, namely P ⋆ ∈ [2,10]. Values for the two quantities are depicted for structures labeled "b", "d", "e", "f", "g", and "h" over the respective ranges of stability; we note that mechanical stability (i.e., a positive compressibility) is guaranteed as long as η increases monotonically with increasing pressure.…”

“…In another contribution [8] we have demonstrated that a suitable combination of two complementary numerical approaches is able to provide a highly satisfactory answer to this yet open issue. To be more specific, we have combined the following two methods: (i) on one hand, an optimization technique, which employs ideas of evolutionary algorithms [9] that is able to predict efficiently and with high reliability ordered equilibrium structures at vanishing temperature; (ii) on the other hand, suitably developed Monte Carlo simulations [10,11] which allow to evaluate accurately, via thermodynamic integration, the thermodynamic properties of a particular ordered structure formed by patchy particles at finite temperature. The most favourable structures with respect to the enthalpy identified in the first step are considered in the second step as candidate configurations at finite temperature.…”