Tethered hard spheres : a bridge between the fluid and solid phases

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MacKinnon, James and Bannerman, Marcus N. and Lue, Leo (2022) Tethered hard spheres : a bridge between the fluid and solid phases. Journal of Chemical Physics, 157 (11). 114501. ISSN 0021-9606 (https://doi.org/10.1063/5.0101238)

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Abstract

The thermodynamics of hard spheres tethered to a Face-Centered Cubic (FCC) lattice is investigated using event-driven molecular-dynamics. The particle-particle and the particle-tether collision rates are related to the phase space geometry and are used to study the FCC and fluid states. In tethered systems, the entropy can be determined by at least two routes: (i) through integration of the tether collision rates with the tether length rT or (ii) through integration of the particle-particle collision rates with the hard-sphere diameter σ (or, equivalently, the density). If the entropy were an entirely analytic function of rT and σ these two methods for calculating the entropy should lead to the same results; however, a non-analytic region exists as an extension of the solid-fluid phase transition of the untethered hard-sphere system, and integration paths that cross this region will lead to values for the entropy that depend on the particular path chosen. The difference between the calculated entropies appears to be related to the communal entropy, and the location of the non-analytic region appears to be related to conditions where the regions of phase space associated with the FCC configuration become separated from those associated with the disordered fluid. The non-analytic region is finite in extent, vanishing below rT /a ≈ 0.55, where a is the lattice spacing, and there are many continuous paths that connect the fluid and solid phases that can be used to determine the crystal free energy with respect to the fluid.

ORCID iDs

MacKinnon, James, Bannerman, Marcus N. and Lue, Leo ORCID logoORCID: https://orcid.org/0000-0002-4826-5337;
  • Item type:Article
    ID code:81950
    Dates:
    Date
    Event
    15 September 2022
    Published
    22 August 2022
    Published Online
    19 August 2022
    Accepted
    30 May 2022
    Submitted
    Notes:Accepted manuscript first published online 22 August 2022. Note from publisher's website, "(c) 2022 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license: https://creativecommons.org/licenses/by/4.0/)".
    Subjects:Technology > Chemical engineering
    Department:Faculty of Engineering > Chemical and Process Engineering
    Strategic Research Themes > Society and Policy
    Depositing user: Pure Administrator
    Date deposited:19 Aug 2022 14:35
    Last modified:11 Nov 2024 13:32
    URI:https://strathprints.strath.ac.uk/id/eprint/81950
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