Tethered-particle model: The calculation of free energies for hard-sphere systems

Craig Moir*, Leo Lue, Marcus Campbell Bannerman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
5 Downloads (Pure)


Two methods for computing the entropy of hard-sphere systems using a spherical tether model are explored which allow the efficient use of event-driven molecular-dynamics simulations. An intuitive derivation is given that relates the
rate of particle collisions, either between two particles or between a particle and its respective tether, to an associated hypersurface area which bounds the system’s accessible configurational phase-space. Integrating the particle-particle collision rates with respect to sphere diameter (or, equivalently, density) or the particle-tether collision rates with respect to tether length then directly determines the volume of accessible phase space and, therefore, the system entropy. The approach is general and can be used for any system composed of particles interacting with discrete potentials in fluid, solid, or glassy states. The entropies calculated for the liquid and crystalline hard-sphere states using these methods are found to agree closely with the current best estimates in the literature, demonstrating the accuracy of the approach
Original languageEnglish
Article number064504
Number of pages11
JournalThe Journal of Chemical Physics
Issue number6
Early online date11 Aug 2021
Publication statusPublished - 14 Aug 2021

Bibliographical note

Open Access via the AIP Agreement
The authors acknowledge the support of the Maxwell computing service at the University of Aberdeen, and the Aberdeen-Curtin Alliance26 between the University of Aberdeen (Scotland, U.K.) and Curtin University (Perth, Australia) which funded the Ph.D. of C.M.


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