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<p>This paper undertakes a theoretical exploration of the effects of particle size and shape on various thermodynamic characteristics of rhodium (Rh) nanoparticles, including the melting point, Debye temperature, specific heat at constant pressure, and atomic mean-square displacement (MSD). The bond energy model and Debye model were employed to derive expressions for these properties as functions of particle size, shape, and temperature (for MSD). Numerical calculations reveal that both the Debye temperature and melting point increase significantly as the surface-to-volume ratio decreases, while the specific heat and MSD decrease sharply, particularly when the particle diameter is below approximately 3&#xa0;nm. Beyond this size, all studied thermodynamic properties gradually converge toward their bulk values. The theoretical melting points align well with molecular dynamics simulations and calculations based on Guisbiers et al’ model. Furthermore, the MSD of Rh nanoparticles exhibits a stronger temperature dependence compared to the bulk material.</p>

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Thermodynamic properties of rhodium nanoparticles: size, shape, and temperature dependence

  • 期刊论文

  • 发表日期：

    2025年6月5日

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  • Nguyen Trong Tam,
  • Ho Khac Hieu

摘要

This paper undertakes a theoretical exploration of the effects of particle size and shape on various thermodynamic characteristics of rhodium (Rh) nanoparticles, including the melting point, Debye temperature, specific heat at constant pressure, and atomic mean-square displacement (MSD). The bond energy model and Debye model were employed to derive expressions for these properties as functions of particle size, shape, and temperature (for MSD). Numerical calculations reveal that both the Debye temperature and melting point increase significantly as the surface-to-volume ratio decreases, while the specific heat and MSD decrease sharply, particularly when the particle diameter is below approximately 3 nm. Beyond this size, all studied thermodynamic properties gradually converge toward their bulk values. The theoretical melting points align well with molecular dynamics simulations and calculations based on Guisbiers et al’ model. Furthermore, the MSD of Rh nanoparticles exhibits a stronger temperature dependence compared to the bulk material.