Thermodynamic analysis and modification of Gibbs–Thomson equation for melting point depression of metal nanoparticles

doi:10.1016/j.cjche.2020.11.035

中国化学工程学报 ›› 2021, Vol. 29 ›› Issue (3): 198-205.DOI: 10.1016/j.cjche.2020.11.035

• Special Issue on Frontiers of Chemical Engineering Thermodynamics • 上一篇下一篇

Thermodynamic analysis and modification of Gibbs–Thomson equation for melting point depression of metal nanoparticles

Nanhua Wu^1,2,3, Xiaohua Lu², Rong An⁴, Xiaoyan Ji¹

1 Division of Energy Science/Energy Engineering, Luleå University of Technology, 97187 Luleå, Sweden;
2 State Key Laboratory of Materials-Oriented and Chemical Engineering, Nanjing Tech University, Nanjing 211816, China;
3 Key Laboratory of Advanced Catalytic Materials and Technology, School of Petrochemical Engineering, Changzhou University, Changzhou 213164, China;
4 Herbert Gleiter Institute of Nanoscience, Nanjing University of Science & Technology, Nanjing 210094, China

收稿日期:2020-06-28 修回日期:2020-10-26 出版日期:2021-03-28 发布日期:2021-05-13
通讯作者: Xiaohua Lu, Xiaoyan Ji
基金资助:
Financial supports from Key Project (21838004), Joint Research Fund for Overseas Chinese, Hong Kong, Macao Young Scientists of National Natural Science Foundation (21729601) of China are acknowledged.

Thermodynamic analysis and modification of Gibbs–Thomson equation for melting point depression of metal nanoparticles

Nanhua Wu^1,2,3, Xiaohua Lu², Rong An⁴, Xiaoyan Ji¹

1 Division of Energy Science/Energy Engineering, Luleå University of Technology, 97187 Luleå, Sweden;
2 State Key Laboratory of Materials-Oriented and Chemical Engineering, Nanjing Tech University, Nanjing 211816, China;
3 Key Laboratory of Advanced Catalytic Materials and Technology, School of Petrochemical Engineering, Changzhou University, Changzhou 213164, China;
4 Herbert Gleiter Institute of Nanoscience, Nanjing University of Science & Technology, Nanjing 210094, China

Received:2020-06-28 Revised:2020-10-26 Online:2021-03-28 Published:2021-05-13
Contact: Xiaohua Lu, Xiaoyan Ji
Supported by:
Financial supports from Key Project (21838004), Joint Research Fund for Overseas Chinese, Hong Kong, Macao Young Scientists of National Natural Science Foundation (21729601) of China are acknowledged.

摘要/Abstract

摘要： Abnormal melting point depression of metal nanoparticles often occurs in heterogeneous catalytic reactions, which leads to a reduction in the stability of reactive nanoclusters. To study this abnormal phenomenon, the original and surface-energy modified Gibbs–Thomson equations were analyzed in this work and further modified by considering the effect of the substrate. The results revealed that the original Gibbs–Thomson equation was not suitable for the particles with radii smaller than 10 nm. Moreover, the performance of the surface-energy modified Gibbs–Thomson equation was improved, and the deviation was reduced to (-350-100) K, although further modification of the equation by considering the interfacial effect was necessary for the small particles (r < 5 nm). The new model with the interfacial effect improved the model performance with a deviation of approximately -50 to 20 K, where the interfacial effect can be predicted quantitatively from the thermodynamic properties of the metal and substrate. Additionally, the micro-wetting parameter α_w can be used to qualitatively study the overall impact of the substrate on the melting point depression.

关键词: Melting point depression, Metal nanoparticle, Gibbs–Thomson equation, Substrate, Interfacial effect

Abstract: Abnormal melting point depression of metal nanoparticles often occurs in heterogeneous catalytic reactions, which leads to a reduction in the stability of reactive nanoclusters. To study this abnormal phenomenon, the original and surface-energy modified Gibbs–Thomson equations were analyzed in this work and further modified by considering the effect of the substrate. The results revealed that the original Gibbs–Thomson equation was not suitable for the particles with radii smaller than 10 nm. Moreover, the performance of the surface-energy modified Gibbs–Thomson equation was improved, and the deviation was reduced to (-350-100) K, although further modification of the equation by considering the interfacial effect was necessary for the small particles (r < 5 nm). The new model with the interfacial effect improved the model performance with a deviation of approximately -50 to 20 K, where the interfacial effect can be predicted quantitatively from the thermodynamic properties of the metal and substrate. Additionally, the micro-wetting parameter α_w can be used to qualitatively study the overall impact of the substrate on the melting point depression.

Key words: Melting point depression, Metal nanoparticle, Gibbs–Thomson equation, Substrate, Interfacial effect

Nanhua Wu, Xiaohua Lu, Rong An, Xiaoyan Ji. Thermodynamic analysis and modification of Gibbs–Thomson equation for melting point depression of metal nanoparticles[J]. 中国化学工程学报, 2021, 29(3): 198-205.

Nanhua Wu, Xiaohua Lu, Rong An, Xiaoyan Ji. Thermodynamic analysis and modification of Gibbs–Thomson equation for melting point depression of metal nanoparticles[J]. Chinese Journal of Chemical Engineering, 2021, 29(3): 198-205.

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Thermodynamic analysis and modification of Gibbs–Thomson equation for melting point depression of metal nanoparticles

Thermodynamic analysis and modification of Gibbs–Thomson equation for melting point depression of metal nanoparticles

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