Thermodynamic Equilibria in Systems with Nanoparticles
Thermodynamic description of systems with nanoparticles in the frame of the Gibbs theory of interfaces is presented. Although much attention has been paid to thermodynamic modelling of nanosystems, the calculation of phase diagrams of nanoalloys as well as the assessment of effects of surface-related phenomena on the solubility of nanoparticles and gas–solid reactions, some discrepancy still remains dealing with the expression of the surface contribution to molar Gibbs energy and chemical potential of components. It is shown that due to the non-extensive nature of the surface area, these contributions are different for molar and partial molar quantities. The consistent expressions for molar Gibbs energy and chemical potentials of components of spherical nanoparticles are put forward along with the correct forms of equilibrium conditions. Moreover, the applicability of the shape factor α = A non-spherical/A spherical (V non-spherical = V spherical) which is used in the expressions involving surface-to-volume ratio of non-spherical particles is addressed. A new parameter, the differential shape factor α′ = dA non-spherical/dA spherical (V non-spherical = V spherical, dV non-spherical = dV spherical), is proposed which should be used in equilibrium conditions based on the equality of chemical potentials. The enhanced solubility of paracetamol nanoparticles in water and thermal decomposition of GaN nanowires are demonstrated as examples of size effect in nanosystems.
KeywordsGibbs Energy Homogeneous Function Surface Term Molar Gibbs Energy Regular Polyhedron
This work was supported by Czech Science Foundation, grant number No. 13-20507S.
- 8.Guisbiers G, Mejia-Rosales S, Khanal S, Ruiz-Zepeda F, Whetten RL, José-Yacaman M (2014) Gold-copper nano-alloy, “Tumbaga”, in the era of nano: phase diagram and segregation. Nano Lett 14:6718–6726Google Scholar
- 21.Cui Z, Duan H, Li W, Xue Y (2015) Theoretical and experimental study: the size dependence of decomposition thermodynamics of nanomaterials. J Nanopart Res 17:321 (11 pp)Google Scholar
- 25.Letellier P, Mayaffre A, Turmine M (2007) Solubility of nanoparticles: nonextensive thermodynamics approach. J Phys: Condens Matter 19:436229 (9 pp)Google Scholar
- 26.Letellier P, Mayaffre A, Turmine M (2007) Melting point depression of nanosolids: nonextensive thermodynamics approach. Phys Rev B 76:045428 (8 pp)Google Scholar
- 30.Tanaka T, Hack K, Iida T, Hara S (1996) Application of thermodynamic databases to the evaluation of surface tensions of molten alloys, salt mixtures and oxide mixtures. Z Metallknd 87:380–389Google Scholar
- 37.Jesser WA, Shneck RZ, Gile WW (2004) Solid-liquid equilibria in nanoparticles of Pb-Bi alloys. Phys Rev B 69:144121 (13 pp)Google Scholar
- 40.Cammarata RC (2009) Generalized thermodynamics of surfaces with applications to small solid systems. In: Egrenreich H, Spaepen F (eds) Solid state physics, vol 61. Elsevier, Amsterdam, p 1Google Scholar
- 52.Wang Z, Zu X, Gao F, Weber WJ (2007) Size dependence of melting of GaN nanowires with triangular cross sections. J Appl Phys 101:043511 (4 pp)Google Scholar
- 54.Antoniammal P, Arivuoli D (2012) Size and shape dependence of melting temperature of gallium nitride nanoparticles. J Nanomater 2012:415797 (11 pp)Google Scholar
- 56.Assael MJ, Armyra IJ, Brillo J, Stankus SV, Wu J, Wakeham WA (2012) Reference data for the density and viscosity of liquid cadmium, cobalt, gallium, indium, mercury, silicon, thallium, and zinc. J Phys Chem Ref Data 41:033101 (16 pp)Google Scholar