Statistical mechanics of crystal nuclei of hard spheres

Marjolein de Jager*, Carlos Vega, Pablo Montero de Hijes, Frank Smallenburg, Laura Filion

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

In the study of crystal nucleation via computer simulations, hard spheres are arguably the most extensively explored model system. Nonetheless, even in this simple model system, the complex thermodynamics of crystal nuclei can sometimes give rise to counterintuitive results, such as the recent observation that the pressure inside a critical nucleus is lower than that of the surrounding fluid, seemingly clashing with the strictly positive Young-Laplace pressure we would expect in liquid droplets. Here, we re-derive many of the founding equations associated with crystal nucleation and use the hard-sphere model to demonstrate how they give rise to this negative pressure difference. We exploit the fact that, in the canonical ensemble, a nucleus can be in a (meta)stable equilibrium with the fluid and measure the surface stress for both flat and curved interfaces. Additionally, we explain the effect of defects on the chemical potential inside the crystal nucleus. Finally, we present a simple, fitted thermodynamic model to capture the properties of the nucleus, including the work required to form critical nuclei.

Original languageEnglish
Article number184501
Number of pages15
JournalJournal of Chemical Physics
Volume161
Issue number18
DOIs
Publication statusPublished - 7 Nov 2024

Bibliographical note

Publisher Copyright:
© 2024 Author(s).

Funding

We would like to acknowledge Rinske Alkemade and Willem Gispen for useful discussions. L.F. and M.d.J. acknowledge funding from the Vidi research program with Project No. VI.VIDI.192.102, which is financed by the Dutch Research Council (NWO). C.V. acknowledges funding from Grant No. PID2022-136919NB-C31 of the Ministry of Science, Innovation and Universities (MICINN). F.S. acknowledges funding from the Agence Nationale de la Recherche (ANR), Grant No. ANR-21-CE30-0051.

FundersFunder number
Nederlandse Organisatie voor Wetenschappelijk Onderzoekhttps://doi.org/10.13039/501100003246VI.VIDI.192.102
Vidi research programPID2022-136919NB-C31
Dutch Research Council (NWO)
Ministry of Science, Innovation and Universities (MICINN)ANR-21-CE30-0051
Agence Nationale de la Recherche (ANR)

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