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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14 November 2023
Research Article|
November 13 2023
Analysis of probability of inserting a hard spherical particle with small diameter in hard-sphere fluid
Ruslan L. Davidchack
;
Ruslan L. Davidchack
a)
(Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Supervision, Visualization, Writing – original draft, Writing – review & editing)
1
School of Computing and Mathematical Sciences, University of Leicester
, Leicester LE1 7RH, United Kingdom
a)Author to whom correspondence should be addressed: [email protected]
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Aisha Ahmed Elmajdoub
;
Aisha Ahmed Elmajdoub
(Data curation, Formal analysis, Investigation, Methodology, Software, Writing – original draft, Writing – review & editing)
1
School of Computing and Mathematical Sciences, University of Leicester
, Leicester LE1 7RH, United Kingdom
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Brian B. Laird
Brian B. Laird
(Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Visualization, Writing – original draft, Writing – review & editing)
2
Department of Chemistry, University of Kansas
, Lawrence, Kansas 66045, USA
3
Freiburg Institute for Advanced Studies, University of Freiburg
, Albertstraße 19, 79104 Freiburg, Germany
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Ruslan L. Davidchack
1,a)
Aisha Ahmed Elmajdoub
1
Brian B. Laird
2,3
1
School of Computing and Mathematical Sciences, University of Leicester
, Leicester LE1 7RH, United Kingdom
2
Department of Chemistry, University of Kansas
, Lawrence, Kansas 66045, USA
3
Freiburg Institute for Advanced Studies, University of Freiburg
, Albertstraße 19, 79104 Freiburg, Germany
a)Author to whom correspondence should be addressed: [email protected]
J. Chem. Phys. 159, 184503 (2023)
Article history
Received:
August 05 2023
Accepted:
October 23 2023
Citation
Ruslan L. Davidchack, Aisha Ahmed Elmajdoub, Brian B. Laird; Analysis of probability of inserting a hard spherical particle with small diameter in hard-sphere fluid. J. Chem. Phys. 14 November 2023; 159 (18): 184503. https://doi.org/10.1063/5.0170928
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