Dynamics and Thermodynamics of Nanoclusters

Abstract

Abstract:The dynamic and thermodynamic properties of nanoclusters are studied in two different environments: the canonical and microcanonical ensembles. A comparison is made to thermodynamic properties of the bulk. It is shown that consistent and reproducible results on nanoclusters can only be obtained in the canonical ensemble. Nanoclusters in the microcanonical ensemble are trapped systems, and inconsistencies will be found if thermodynamic formalism is applied. An analytical model is given for the energy dependence of the phase space volume of nanoclusters, which allows the prediction of both dynamical and thermodynamical properties.

Development of Copper Nanoclusters for In Vitro and In Vivo Theranostic Applications

“…Compared to the bulk metal whose thermodynamics is determined predominately by atoms of the volume, effects of the fluctuations and contributions from the surface on the overall properties of the system become significant in clusters. Alternations by only one atom in an NC can remarkably change the physical, optical, and electronic properties of the system . Furthermore, in a bulk metal, different possible symmetries (e.g., the body centered cubic structure, the face centered cubic structure, and the hexagonal close packed structure) are separated by a very large energy barrier in the state space .…”

“…This barrier can be overcome only at the time of melting. Different symmetries inherent to NCs, however, are often separated from each other by an energy barrier that is lower than the melting energy . Solid‐to‐solid transitions can, therefore, occur even before melting.…”

“…[11] Furthermore, in a bulk metal, different possible symmetries (e.g., the body centered cubic structure, the face centered cubic structure, and the hexagonal close packed structure) are separated by a very large energy barrier in the state space. [11] This barrier can be overcome only at the time of melting. Different symmetries inherent to NCs, however, are often separated from each other by an energy barrier that is lower than the melting energy.…”

“…Different symmetries inherent to NCs, however, are often separated from each other by an energy barrier that is lower than the melting energy. [11] Solid-to-solid transitions can, therefore, occur even before melting. This is one of the challenges to be tackled when NCs are generated for theranostics, which is stringent on the uniformity and properties of the clusters to be adopted.…”

Invalid Microstate Densities for Model Systems Lead to Apparent Violation of Thermodynamic Law

“…Functions of sums of two power laws (for example Ω(E) ∝ (E/E * ) D + (E/E * ) G ), with the powers greater than zero but different, can also fail to satisfy (9) near the energy E * . This latter case is directly related to the erroneous determination of negative heat capacity for nanoclusters [16], which are often trapped in the microcanonical ensemble (see below and [17]).…”