Nanoscopic Thermodynamics.

Conventional thermodynamics for bulk substances encounters challenges when one considers materials on the nanometer scale. Quantities such as entropy, enthalpy, free energy, melting temperature, ordering temperature, Debye temperature, and specific heat no longer remain constant but change with the crystal dimension, size, and morphology. Often, one phenomenon is associated with a variety of theories from different perspectives. Still, a model that can reconcile the size and shape dependence of the thermal properties of the nanoscaled substances remains one of the goals of nanoscience and nanotechnology. This Account highlights the nanoscopic thermodynamics for nanoparticles, nanowires, and nanofilms, with particular emphasis on the bond energy model. The central idea is that the atomic cohesive energy determines the thermodynamic performance of a substance and the cohesive energy varies with the atomic coordination environment. It is the cohesive energy difference between the core and the shell that dictates the nanoscopic thermodynamics. This bond energy model rationalizes the following: (i) how the surface dangling bonds depress the melting temperature, entropy, and enthalpy; (ii) how the order-disorder transition of the nanoparticles depends on particle size and how their stability may vary when they are embedded in an appropriate matrix; (iii) predictions of the existence of face-centered cubic structures of Ti, Zr, and Hf at small size; (iv) how two elements that are immiscible in the bulk can form an alloy on the nanoscale, where the critical size can be predicted. The model has enabled us to reproduce the size and shape dependence of a number of physical properties, such as melting temperature, melting entropy, melting enthalpy, ordering temperature, Gibbs free energy, and formation heat, among others, for materials such as Pd, Au, Ag, Cu, Ni, Sn, Pb, In, Bi, Al, Ti, Zr, Hf, In-Al, Ag-Ni, Co-Pt, Cu-Ag, Cu-Ni, Au-Ni, Ag-Pt, and Au-Pt on the nanometer scale. Furthermore, this model predicts the phenomena of the thermal stability of metal particles on graphene, the superheating of embedded nanoparticles, the order-disorder transition of nanoalloys, the size-temperature phase diagram for low-dimensional solids and the alloying ability on the nanoscale. Extensions of this model may lead to the design of new functional nanomaterials.