Thermodynamic properties of Pt nanoclusters: an ab initio study

Abstract

Nanoparticles (NPs) and subnanometer clusters exhibit novel physical andchemical properties that differ significantly from their counterpart bulkmaterials. This is mainly originatedfrom the large fraction of subordinated atoms at the surface for NP of small sizes.Concerning thermodynamic properties, in spite of the fact that a large amountof research has been performed, there are still fundamental questions not yetresolved since in general the conventional thermodynamic knowledge of macroscopic metals does notapply for these nanoscopic systems. As thesize of the NPs is reduced, anomalous behaviors have been reported in theirthermodynamic properties, such as deviations from the Debye law of the specificheat and negative thermal expansion [[1],[2]].The Debyetemperature is a fundamental property, since it is closely related to changesin the vibrational properties and specific heat. For Pt NPs capped with PVP-k30the Debye temperature (QD) wasmeasured by the extended X-ray absorption finestructure (EXAFS) technique leading to values higher than for the bulk [[3]].On the other side for small subnanometer Pt NPs (of approximately 0.9 ± 0.2 nm and Navg ~16 atoms) supported on Al2O3 experimental studies based on scanning transmissionelectron microscopic (STEM) and X-ray absorptionspectroscopy exhibit marked contractions of thePt-Pt bond distances with respect to bulk values, and a negative thermalexpansion of these interatomic distances [[4]].In principle, in both works, the surface atom contraction and the interactionof the Pt atoms with capping molecules or support, both enhanced because of thenanosized dimensions of the NP, were indicated as possible reasons to explainthese anomalous thermodynamic properties. Motivatedby these experimental findings, and, as a first step to investigate theseproblems, in this work we calculate the thermodynamic properties of isolated PtNPs for sizes between 13-55 atoms. By considering isolated NPs, we expect toshed some light on the problem by considering only the intrinsic effects of thesmall dimension of NPs. We first determine their equilibrium geometries, tofurther evaluate their vibrational density of states (VDOS), the specific heatand the Debye temperature. The explicit thermal evolution of the averageinteratomic distances is determined at various temperatures by developing abinitio molecular dynamics. We find that the relaxed interatomic distances arereduced with respect to the bulk ones, in agreement with the experiments. The VDOSare very different from the bulk ones, with the presence of discrete states,which give rise to deviations from the typical Debye model of the specific heatat constant volume and low temperatures. Estimations of the Debye temperatureindicate values lower that those calculated for the solid.