Thermodynamics of the melting process in Au nano-clusters: Phenomenology, energy, entropy and quasi-chemical modeling

Abstract

The paper presents a thermodynamic study of the melting transition in Au nano-clusters with a number of atoms (N) in the range 103 < N <106 using a Molecular Dynamics (MD) technique. This range of sizes allows an analysis of the relations between the properties of the clusters and macroscopic Au. Four steps in the progress of the transition occurring upon heating are identified on thermodynamic and structural basis, and the corresponding temperature ranges are determined. In particular, the step where most of the transition takes place (the “melting step”) is identified and described in terms of the change in the relative amount of two kinds of atoms, viz., those forming solid phase-like (SPL) aggregates and those in the liquid phase-like (LPL) aggregates. The energy and entropy change involved in the “melting step” are established as a function of N. These properties are used to evaluate the temperature T0 at which the SPL and the LPL have equal values of the Helmholtz energy. Furthermore, the possibility of describing the thermodynamics of the “melting step” by means of a formalism involving an isomerization-type reaction between the atoms in the SPL and the LPL is explored. To this aim, an equilibrium constant (Keq) involving the concentration of such types of atoms is introduced. Finally, it is shown that a thermodynamic, van't Hoff analysis of the size-dependence of Keq yields values of the T0 temperature which are in very good agreement with those obtained from the energy and entropy values.