Teaching Nano-Thermodynamics: Gibbs Energy of Single-Component Nanoparticles

Jindřich Leitner^1, and David Sedmidubský²

¹Department of Solid State Engineering, University of Chemistry and Technology, Prague, Czech Republic

²Department of Inorganic Chemistry, University of Chemistry and Technology, Prague, Czech Republic

Cite this paper

Jindřich Leitner and David Sedmidubský. Teaching Nano-Thermodynamics: Gibbs Energy of Single-Component Nanoparticles. World Journal of Chemical Education. 2017; 5(6):206-209. doi: 10.12691/WJCE-5-6-4

Abstract

Much attention has been paid to thermodynamic modeling of nanosystems. A common approach consists in addition of a surface/interface term to the Gibbs energy of bulk materials and application of general conditions of equilibrium. Some discrepancy still remains dealing with the expression for surface contribution to molar Gibbs energy and chemical potential of components. It is shown, that due to the nonextensive nature of the surface area, these contributions are different for molar and partial molar quantities. The consistent expressions for the molar Gibbs energy and chemical potential of a single-component spherical nanoparticle are put forward along with the simple derivation of the Kelvin and Gibbs-Thomson equations.

Keywords

nanoparticle, Gibbs energy, chemical potential, Kelvin equation, Gibbs-Thomson equation

Copyright

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References

[1]	Guisbiers, G.; Mejia-Rosales, S.; Khanal, S.; Ruiz-Zepeda, F.; Whetten, R. L.; José-Yacaman, M. Gold-Copper Nano-Alloy, “Tumbaga”, in the Era of Nano: Phase Diagram and Segregation. Nano Lett. 14. 6718-6726. 2014.
[2]	Sim, K.; Lee, J. Phase stability of Ag-Sn alloy nanoparticles. J. Alloys Compounds 590. 140-146. 2014.
[3]	Sopoušek, J.; Vřešťál, J.; Pinkas, J.; Brož, P.; Buršík, J.; Stýskalík, A.; Škoda, D.; Zobač, O.; Lee, J. Cu-Ni nanoalloy phase diagram - Prediction and experiment. CALPHAD 45. 33-39. 2014.
[4]	Kroupa, A.; Káňa, T.; Buršík, J.; Zemanová, A.; Šob, M. Modelling of phase diagrams of nanoalloys with complex metallic phases: application to Ni-Sn. Phys. Chem. Chem. Phys. 17. 28200-28210. 2015.
[5]	Ghasemi, M.; Zanolli, Z.; Stankovski, M.; Johansson, J. Size- and shape-dependent phase diagram of In-Sb nano-alloys. Nanoscale 7. 17387-17396. 2015.
[6]	Du, J.; Zhao, R.; Xue, Y. Effects of sizes of nano-copper oxide on the equlibrium constant and thermodynamic properties for the reaction in nanosystem. J. Chem. Thermodynamics 45. 48-52. 2012.
[7]	Du, J.; Zhao, R.; Xue, Y. Thermodynamic properties and equilibrium constant of chemical reaction in nanosystem: An theoretical and experimental study. J. Chem. Thermodynamics 55. 218-224. 2012.
[8]	Cui, Z.; Duan, H.; Li, W.; Xue, Y. Theoretical and experimental study: the size dependence of decomposition thermodynamics of nanomaterials. J. Nanopart. Res. 17. 321 (11 pp.). 2015.
[9]	Li, W.; Cui, Z.; Duan, H.; Xue, Y. Effect of Nanoparticle size on the thermal decomposition thermodynamics in theory and experiment. Appl. Phys. A 122. 99 (12 pp.). 2016.
[10]	Kaptay, G. The Gibbs Equation versus the Kelvin and the Gibbs-Thomson Equations to Describe Nucleation and Equilibrium of Nano-Materials. J. Nanosci. Nanotechnol. 12. 2625-2633. 2012.
[11]	Kaptay, G. Nano-Calphad: extension of the Calphad method to systems with nano-phases and complexions. J. Mater. Sci. 47. 8320-8335. 2012.
[12]	Makkonen, L. Comments on “The Gibbs Equation versus the Kelvin and the Gibbs-Thomson Equations to Describe Nucleation and Equilibrium of Nano-Materials”. Adv. Sci. Focus 1. 367-368. 2013.
[13]	Lee, J.; Sim, K.J., General equations of CALPHAD-type thermodynamic description for metallic nanoparticle systems. CALPHAD 44. 129-132. 2014.
[14]	Guenther, G.; Guillon, O. Models of size-dependent nanoparticle melting tested on gold. J. Mater. Sci. 49. 7915-7932. 2014.
[15]	Bajaj, S.; Haverty, M. G.; Arróyave, R.; Goddard III FRSC, W. A.; Shankare, S. Phase stability in nanoscale material systems: extension from bulk phase diagrams Nanoscale, 7. 9868-9877. 2015.
[16]	Blinder, S.M. Mathematical method in elementary thermodynamics. J. Chem. Education 43. 85-92. 1966.
[17]	Letellier, P.; Mayaffre, A.; Turmine, M. Nonextensive approach to thermodynamics: Analysis and suggestion, and application to chemical reactivity. J. Phys. Chem. B 108. 18980-18987. 2004.
[18]	Letellier, P.; Mayaffre, A.; Turmine, M. Solubility of nanoparticles: nonextensive thermodynamics approach J. Phys.: Condens. Matter 19. 436229 (9 pp). 2007.
[19]	Letellier, P.; Mayaffre, A.; Turmine, M. Melting point depression of nanosolids: Nonextensive thermodynamics approach. Phys. Rev. B 76. 045428 (8 pp). 2007.
[20]	Cammarata, R.C. Generalized thermodynamics of surfaces with applications to small solid systems. in Solid State Physics. 61. 1-75. 2009.
[21]	Leitner, J.; Sedmidubský, D. Thermodynamic equilibria in system with nanoparticles. in Thermal Physics and Thermal Analysis. Springer International Publishing, 2017. 385-402.