SURFACE THERMODYNAMICS AND THE CONUNDROM OF THE HEAT CAPACITY OF NANOCLUSTERS AND NANUSTRUCTURED MATERIALS

The heat capacity is one of the most important properties of materialsю It should be taken into account in view of their applications. And the same time, the behavior of the heat capacity of metal nanoclusters and nanostructured materials demonstrates an important unsolved problem: for such materials experiments demonstrate the values of the heat capacity which are greater than the heat capacity of corresponding bulk homogeneous phases in 2 – 5 times! According to [1], the heat capacity of cost-grained Cu clusters (50nm in size) exceeds the he capacity of usual bulk copper in 1.2 – 2.0 times in the temperature range from 200 to 450K. Analogous results were obtained for Ni nanoclusters (22nm in diameter): their heat capacity was in 2 times higher than the heat capacity of the bulk Ni at temperatures 300 – 800K [2]. In these papers the high temperature range was treated for which quantum effects can not explain the effect in question. In [3] the problem of the cluster heat capacity was investigated using the molecular dynamics simulation. It was found that for Ni clusters of 2mn in diameter the heat capacity is greater in 14% and the effect diminishes up to 10% for clusters of 6nm in diameter. Theoretical treatment of the problem under discussion can be based on the Gibbs thermodynamics of surfaces. The isobaric heat capacity of a nanocluster can be found by the differentiation of the particle enthalpy H by the temperature T: . A distinctive feature of the cluster heat capacity reduces to taking into account the surface enthalpy : where is the enthalpy of the bulk phase. The resulting equation for the reduced surface heat capacity can be written as

where is the specific total surface energy, is the molar mass, is the density, is the Avogadro constant, is the molar heat capacity of the bulk phase and is the number of atoms the cluster consists of. For Ni clusters , . So, for () we have that satisfactorily agrees with our molecular dynamics result (14%). So, a conclusion can be made that enormous experimental values of for nanoclusters and nanostructured materials should be incorrect.

Acknowledgements

The author is grateful to Prof. U.M. Gufan and Prof. K.S. Gavrychev for discussion. Financial support of Ministry for Education and Science of Russian Federation is acknowledged (grant program ‘Scientific and pedagogical stuff of the innovation Russia, 2009-2013’).

References:

1. Y.Y. Chen et al., Nanostruct. Matter. 1995, 6, 597-600.
2. Y.D. Yao et al., Nanostruct. Matter. 1995, 6, 933-936.
3. S.L. Gafner et al., Journal Nanoparticle Research. Published online: 11 May 2011.