Davidchack RL, Elmajdoub AA, Laird BB. Analysis of probability of inserting a hard spherical particle with small diameter in hard-sphere fluid.
J Chem Phys 2023;
159:184503. [PMID:
37955327 DOI:
10.1063/5.0170928]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2023] [Accepted: 10/23/2023] [Indexed: 11/14/2023] Open
Abstract
The probability of inserting, without overlap, a hard spherical particle of diameter σ in a hard-sphere fluid of diameter σ0 and packing fraction η determines its excess chemical potential at infinite dilution, μex(σ, η). In our previous work [R. L. Davidchack and B. B. Laird, J. Chem. Phys. 157, 074701 (2022)], we used Widom's particle insertion method within molecular dynamics simulations to obtain high precision results for μex(σ, η) with σ/σ0 ≤ 4 and η ≤ 0.5. In the current work, we investigate the behavior of this quantity at small σ. In particular, using the inclusion-exclusion principle, we relate the insertion probability to the hard-sphere fluid distribution functions and thus derive the higher-order terms in the Taylor expansion of μex(σ, η) at σ = 0. We also use direct evaluation of the excluded volume for pairs and triplets of hard spheres to obtain simulation results for μex(σ, η) at σ/σ0 ≤ 0.2247 that are of much higher precision than those obtained earlier with Widom's method. These results allow us to improve the quality of the small-σ correction in the empirical expression for μex(σ, η) presented in our previous work.
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