Determination of the free volume and the entropy by a Monte Carlo method

Abstract

The configurational integral can in principle, though not in practice, be determined from the ratio of accepted to rejected moves ( ) in the Monte Carlo method of Metropolis et al., if the moves consist of simultaneous random displacements of N particles uniformly distributed over the sample volume v. In the usual Monte Carlo process only one particle at a time is displaced within a small volume. If this volume is suitably chosen (VD), the acceptance ratio ( ) determines the mean free volume per particle (Vf = vD ). Evidence is presented supporting the appioximate validity of the relationship = '' which permits the evaluation of the configurational integral. The entropies calculated in this way for a system of 108 Lennard— Jones particles with parameters corresponding to argon, are in good agreement with the experimental values for solid and liquid argon. The results indicate that the full amount of the communal entropy appears on fusion. In the well-known Monte Carlo (MC) method of Metropolis et a!.' certain many-dimensional integrals containing the Boltzmann factor as weighting function are evaluated by means of the following procedure: configurations of a system of N particles are generated by small random displacements of single particles; if r is the configuration after moves and the next trial move leads to r, then this move is rejected (by setting r' = r') if and only if the difference between the potential energies — 1i(r) LP > 0 and exp (— A/kT) (1)

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