Chemical-potential paradox in molecular simulation. Explanation and Monte Carlo results for a Lennard-Jones fluid

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Abstract
Monte Carlo simulation results are presented for uniform fluids which show that the discrepancies in the values of the chemical potential found by the Widom and the Shing–Gubbins methods arise from the introduction of molecular cores to prevent too close approach of the molecules. For dense fluids of molecules interacting according to a modified Lennard-Jones potential, excellent agreement (to kT) is found at reduced temperature T=kT/ε= 1 between the directly computed discrepancies and the results of a treatment based on ‘overlapping’ of cores provided that the core diameter is 0.875σ where σ is the Lennard-Jones collision diameter. In the same upper range of core sizes the dependence of the discrepancy on density also agrees well with the overlapping theory at least down to a relative density (=ρσ3) of 0.4. For small core sizes the discrepancy is, to a very good approximation, independent of core diameter, and this is explained in terms of ‘poor statistics’. Results for T= 2.5 are generally similar to those for T= 1, but agreement with the overlapping theory is not as good.

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