Research into the rationality and the application scopes of different melting models of nanoparticles

A rational melting model is indispensable to address the fundamental issue regarding the melting of nanoparticles. To ascertain the rationality and the application scopes of the three classical thermodynamic models, namely Pawlow, Rie, and Reiss melting models, corresponding accurate equations for size-dependent melting temperature of nanoparticles were derived. Comparison of the melting temperatures of Au, Al, and Sn nanoparticles calculated by the accurate equations with available experimental results demonstrates that both Reiss and Rie melting models are rational and capable of accurately describing the melting behaviors of nanoparticles at different melting stages. The former (surface pre-melting) is applicable to the stage from initial melting to critical thickness of liquid shell, while the latter (solid particles surrounded by a great deal of liquid) from the critical thickness to complete melting. The melting temperatures calculated by the accurate equation based on Reiss melting model are in good agreement with experimental results within the whole size range of calculation compared with those by other theoretical models. In addition, the critical thickness of liquid shell is found to decrease with particle size decreasing and presents a linear variation with particle size. The accurate thermodynamic equations based on Reiss and Rie melting models enable us to quantitatively and conveniently predict and explain the melting behaviors of nanoparticles at all size range in the whole melting process.

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Graphical abstract Both Reiss and Rie melting models are rational and capable of accurately describing the melting behaviors of nanoparticles at different melting stages. The former is applicable to the stage from initial melting to critical thickness of liquid shell, while the latter from the critical thickness to complete melting. The critical thickness of liquid shell decreases with decreasing particle size and a linear relationship between them is observed. This paper provides us an effective and convenient method to address the fundamental issue regarding the melting temperature of nanoparticles.