Phase diagram of the hard-sphere potential model in three and four dimensions using a pseudo-hard-sphere potential
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| Format: | Preprint |
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2025
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| author | Bedolla-Montiel, Edwin A. Castañeda-Cerdán, Ramón A. Castañeda-Priego, Ramón |
| author_facet | Bedolla-Montiel, Edwin A. Castañeda-Cerdán, Ramón A. Castañeda-Priego, Ramón |
| contents | The hard-sphere potential has become a cornerstone in the study of both molecular and complex fluids. Despite its mathematical simplicity, its implementation in fixed time-step molecular simulations remains a formidable challenge due to the discontinuity at contact. To circumvent the issues associated with the ill-defined force at contact, a continuous potential--referred to here as the pseudo-hard-sphere (pHS) potential--has recently been proposed [J. Chem, Phys. 149, 164907 (2018)]. This potential is constructed to match the second virial coefficient of the hard-sphere potential and is expected to mimic its thermodynamic properties. However, this hypothesis has only been partially validated within the fluid region of the phase diagram for hard-sphere dispersions in two and three dimensions. In this contribution, we examine the ability of the continuous pHS potential to reproduce the equation of state of a hard-sphere fluid, not only in the fluid phase but also across the fluid-solid coexistence region. Our focus is primarily on hard-sphere systems in three and four dimensions. We compare the results obtained from Brownian dynamics simulations of the pHS potential with those derived from refined event-driven simulations of the corresponding hard-sphere potential. Furthermore, we provide a comparative analysis with theoretical equations of state based on both mean-field and integral equation approximations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_03959 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Phase diagram of the hard-sphere potential model in three and four dimensions using a pseudo-hard-sphere potential Bedolla-Montiel, Edwin A. Castañeda-Cerdán, Ramón A. Castañeda-Priego, Ramón Soft Condensed Matter The hard-sphere potential has become a cornerstone in the study of both molecular and complex fluids. Despite its mathematical simplicity, its implementation in fixed time-step molecular simulations remains a formidable challenge due to the discontinuity at contact. To circumvent the issues associated with the ill-defined force at contact, a continuous potential--referred to here as the pseudo-hard-sphere (pHS) potential--has recently been proposed [J. Chem, Phys. 149, 164907 (2018)]. This potential is constructed to match the second virial coefficient of the hard-sphere potential and is expected to mimic its thermodynamic properties. However, this hypothesis has only been partially validated within the fluid region of the phase diagram for hard-sphere dispersions in two and three dimensions. In this contribution, we examine the ability of the continuous pHS potential to reproduce the equation of state of a hard-sphere fluid, not only in the fluid phase but also across the fluid-solid coexistence region. Our focus is primarily on hard-sphere systems in three and four dimensions. We compare the results obtained from Brownian dynamics simulations of the pHS potential with those derived from refined event-driven simulations of the corresponding hard-sphere potential. Furthermore, we provide a comparative analysis with theoretical equations of state based on both mean-field and integral equation approximations. |
| title | Phase diagram of the hard-sphere potential model in three and four dimensions using a pseudo-hard-sphere potential |
| topic | Soft Condensed Matter |
| url | https://arxiv.org/abs/2502.03959 |