Evaluation of specific surface energy of Ag nanoparticles based on molecular dynamics results
K.K. Nebyvalova, I.V. Talyzin, S.A. Vasilyev, V.M. Samsonov
Tver State University
DOI: 10.26456/pcascnn/2025.17.455
Original article
Abstract: After analyzing the problem of extending the Gibbs surface excess method to nanoscale objects, applying the Gibbs method to evaluation of the specific surface energy of metallic nanoparticles is considered. The proposed approach, which we have exemplified on spherical Ag nanoparticles and nanodroplets, is based on the use of molecular dynamics results for the temperature and size dependencies of the potential term into the specific (per atom) internal energy. The calculations were performed for the equimolecular dividing surface. In this case, the excess surface energy was determined relative to the bulk mother phase (comparison phase), which was chosen to be the solid fcc phase of the same metal at the same temperature as the small object under consideration. The obtained values of the specific surface energy depend on temperature and are consistent with the experimental values for the corresponding bulk comparison phases. At the same time, a noticeable change (decrease) in the specific surface energy occurred only when the solid-liquid phase transition took place.
Keywords: metal nanoclusters, Gibbs method of surface excesses, molecular dynamics, surface energy
- Kristina K. Nebyvalova – 3rd year postgraduate student at the Faculty of Physics and Technology, Tver State University
- Igor V. Talyzin – Ph. D., Researcher, Management of Scientific Research, Tver State University
- Sergey A. Vasilyev – Ph. D., Docent, Department of Applied Physics, Tver State University
- Vladimir M. Samsonov – Dr. Sc., Full Professor, General Physics Department, Tver State University
For citation:
Nebyvalova K.K., Talyzin I.V., Vasilyev S.A., Samsonov V.M. Otsenka udelnoj poverkhnostnoj energii nanochastits Ag po rezultatam ikh molekulyarno- dinamicheskogo modelirovaniya [Evaluation of specific surface energy of Ag nanoparticles based on molecular dynamics results], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostruktur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2025, issue 17, pp. 455-465. DOI: 10.26456/pcascnn/2025.17.455. ⎘
Full article (in Russian): download PDF file
References:
1. Gibbs J.W. The Collection works. Termodinamics. London, New York, Toronto, Longmans, Green andCompany, 1928, vol. 1, XXVIII + 434 p.
2. Tolman R.C. The effect of droplet size on surface tension, Journal of Chemical Physics, 1949, vol. 17, issue 3, pp. 333-337. DOI: 10.1063/1.1747247.
3. Samsonov V.M., Vasilev S.A., Talyzin I.V. et al. Nanothermodynamics on the example of metallic nanoparticles, Russian Journal of Physical Chemistry A, 2023, vol. 97, issue 8, pp. 1751-1760. DOI: 10.1134/S003602442308023X.
4. Samsonov V.M., Vasilyev S.A., Talyzin I.V. et al. The Gibbs method extended to nanothermodynamics and exemplified by evaluations of the surface, line, and point excess energies for icosahedral metal nanoclusters, Journal of Chemical Physics, 2025, vol. 162, issue 7, art. no. 074304, 13 p. DOI: 10.1063/5.0250339.
5. Rusanov A.I. Fazovyye ravnovesiya i poverkhnostnyye yavleniya [Thermodynamics of surface phenomena]. Leningrad, Leningrad University Press, 1960, 180 p. (In Russian).
6. Vitol’ E.N. Opredeleniye zavisimosti poverkhnostnogo natyazheniya metallov ot krivizny granitsy razdela faz [Determination of the dependence of the surface tension of metals on the curvature of the interface], Kolloidnyj zhurnal [Colloid journal], 1992, vol. 54, issue 3, pp. 21-22. (In Russian).
7. Sdobnyakov N.Yu., Samsonov V.M., Bazulev A.N., Novozhilova D.A. Otsenka koeffitsienta proportsionalnosti v formule Rusanova dlya poverkhnostnogo natyazheniya po kinetike ispareniya nanochastits i usadki vakansionnykh por [Evaluation of the proportionality coefficient in the Rusanov’s formula for the surface tension using kinetic data on rates of evaporation of nanoparticles and shringkage of vacancy pores], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostruktur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2016, issue 8, pp. 337-344. DOI: 10.26456/pcascnn/2016.8.337. (In Russian).
8. Sdobnyakov N.Yu. [Modelirovanie strukturnykh prevrashchenij v odnokomponentnykh i mnogokomponentnykh metallicheskikh nanosistemakh: uchebnik] Simulation of structural transformations in single-component and multi-component metallic nanosystems: a textbook. Tver, Tver State University Publ., 2025, 408 p. DOI:10.26456/sny.2025.408. (In Russian).
9. Shebzukhov Z.A., Shebzukhova M.A., Shebzukhov A.A. Interfacial tension and Rusanov parameter for highly curved surfaces with different types of curvature, Bulletin of the Russian Academy of Sciences: Physics, 2009, vol. 73, issue 7, pp. 928-931. DOI: 10.3103/S1062873809070211.
10. Samsonov V.M., Bazulev A.N., Sdobnyakov N.Yu. On applicability of Gibbs thermodynamics to nanoparticles, Central European Journal of Physics, 2003, vol. 1, issue 3, pp. 474-484. DOI: 10.2478/BF02475858.
11. Ono S., Kondo S. Molecular theory of surface tension in liquids, Structure of Liquids / Struktur der Flüssigkeiten. Encyclopedia of Physics / Handbuch der Physik. Berlin, Heidelberg: Springer, 1960, vol. 3/10, pp. 134-280. DOI: 10.1007/978-3-642-45947-4_2.
12. Shebzukhov Z.A., Shebzukhova M.A., Shebzukhov A.A. Poverkhnostnoye natyazheniye i poverkhnostnaya energiya metallicheskikh nanochastits [Surface tension and surface energy of metallic nanoparticles], Vestnik Kabardino-Balkarskogo gosudarstvennogo universiteta [Izvestiya of Kabardino-Balkarian State University], 2010, issue 1, pp. 17-58. (In Russian).
13. Rusanov, A.I. Fazovyye ravnovesiya i poverkhnostnyye yavleniya [Phase equilibria and surface phenomena]. Leningrad, Khimiya Publ., 1967. 388 p. (In Russian).
14. Shcherbakov L.M. Evaluation of the excess free energy of small objects, Research in Surface Forces, ed. by B.V. Deryagin. New York, Consultants Bureau, 1966, vol. 2: Three-dimensional aspects of surface forces, pp. 26-32.
15. Samsonov V.M. Conditions for the applicability of thermodynamic description of highly dispersed and microheterogeneous systems, Russian Journal of Physical Chemistry A, 2002, vol. 76, issue 11, pp. 1863-1867.
16. Samsonov V.M., Talyzin I.V., Puytov V.V. et al. When mechanisms of coalescence and sintering at the nanoscale fundamentally differ: Molecular dynamics study, Journal of Chemical Physics, 2022, vol. 156, issue 21, art.no. 214302, 15 p. DOI: 10.1063/5.0075748.
17. Ali S., Myasnichenko V. S., Neyts E. C. Size-dependent strain and surface energies of gold nanoclusters, Physical Chemistry Chemical Physics, 2016, vol. 18, issue 2, pp. 792-800. DOI: 10.1039/c5cp06153a.
18. Holec D., Dumitraschkewitz P., Vollath D., Fischer F.D. Surface energy of Au nanoparticles depending on their size and shape, Nanomaterials, 2020, vol. 10, issue 3, art.no. 484, 15 p. DOI: 10.3390/nano10030484.
19. Allen M.P., Tildesley D.J. Computer Simulation of Liquids. Oxford, Clarendon Press, 2017. 626 p.
20. Thompson A. P., Aktulga H. M., Berger R. et. al. LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales, Computer Physics Communications, 2022, vol. 271, art. no. 108171, 34 p. DOI: 10.1016/j.cpc.2021.108171.
21. Verlet L. Computer «Experiments» on сlassical fluids. I. Thermodynamical properties of Lennard−Jones molecules, Physical Review, 1967, vol. 159, issue 1, pp. 98-103. DOI: 10.1103/PhysRev.159.98.
22. Nosé S. A unified formulation of the constant temperature molecular dynamics methods, The Journal of Chemical Physics, 1984, vol. 81, issue 1, pp. 511-519. DOI: 10.1063/1.447334.
23. Adams J.B., Foiles S.M., Wolfer W.G. Self-diffusion and impurity diffusion of FCC metals using the 5-frequency model and the embedded atom method, Journal of Materials Research, 1989, vol. 4, issue 1, pp. 102-112. DOI: 10.1557/JMR.1989.0102.
24. Samsonov V.M., Romanov A.A., Kartoshkin A.Yu. et al. Embedding functions for Pt and Pd: recalculation and verification on properties of bulk phases, Pt, Pd, and Pt–Pd, Applied Physics A, 2022, vol. 128, issue 9,
art. no. 826, 14 p. DOI: 10.1007/s00339-022-05922-1.
25. Khokonov Kh.B., Taova T.M., Alchagirov B.B. Poverkhnostnaya energiya i poverkhnostnoye natyazheniye metallov i binarnykh splavov v tverdom sostoyanii [Surface energy and surface tension of metals and binary alloys in the solid state], Vestnik Kabardino-Balkarskogo universiteta [Izvestiya of Kabardino-Balkarian University], 2019, vol. 9, issue 2, pp. 5-19. (In Russian).
26. Roduner E. Nanoscopic materials: size-dependent phenomena and growth principles. Cambridge, RSC Publishing, 2014, 439 p. DOI: 10.1039/9781839168970.
27. Fenelonov V.B., Kodenyov G.G., Kostrovsky V.G. On the dependence of surface tension of liquids on the liquid vapor interface, Journal of Physical Chemistry B, 2001, vol. 105, issue 5, pp. 1050-1055. DOI: 10.1021/jp9929972.