The Size and Shape Effects on the Melting Point of Nanoparticles Based on the Lennard-Jones Potential Function

Abstract

A model is proposed to calculate the melting points of nanoparticles based on the Lennard-Jones (L-J) potential function. The effects of the size, the shape, and the atomic volume and surface packing of the nanoparticles are considered in the model. The model, based on the L-J potential function for spherical nanoparticles, agrees with the experimental values of gold (Au) and lead (Pb) nanoparticles. The model, based on the L-J potential function, is consistent with Qi and Wang’s model that predicts the Gibbs-Thompson relation. Moreover, the model based on the non-integer L-J potential function can be used to predict the melting points Tm of nanoparticles.

Hexagonal Carbon Nanoplates Decorated with Layer-Engineered MoS2: High-Performance Cathode Materials for Zinc-Ion Batteries

“…At first, the electrochemical responses of HCN, HCN@MoS 2 , and C-MoS 2 were studied by cyclic voltammetry (Figures g–x and S8). While HCN did not show specific redox behavior (Figure g), HCN@MoS 2 -1 showed reversible redox peaks at 1.09 and 1.22 V (vs Zn/Zn 2+ ) (Figure h). − While the redox peaks of HCN@MoS 2 -2 increased significantly (Figure i), those gradually decreased in an order of HCN@MoS 2 -3 > HCN@MoS 2 -4 > C-MoS 2 (Figure j–l), indicating that the reversible insertion/desertion of zinc ions to/from MoS 2 is very sensitive to its layer numbers and that the 2–3 layered MoS 2 is promising as a cathode material for ZIBs, due to the reduced lattice energy, , in addition to the possible Zn storage on surface and carbon–MoS 2 interfaces …”

“…For example, the partial oxidation of MoS 2 induced structural defects, resulting in facilitated Zn insertion/desertion and enhanced electrochemical performance for aqueous ZIBs with the discharge capacities of 228–261 mAh/g (@0.1 A/g). , Recently, the graphene or carbon nanotube composites of MoS 2 have been engineered to improve conductivities and applied as cathode materials for ZIBs, showing the discharge capacities up to 180–284 mAh/g (@0.1 A/g). ,, The MoS 2 -based cathode materials for ZIBs in the recent literature studies have the 5–15 layered MoS 2 (Tables S1 and S2). − We think that MoS 2 materials with the layer numbers of <5 are explorable to further facilitate Zn insertion/desertion, due to the reduced lattice energy, , and to enhance cathode performance for ZIBs.…”

“…13,15,22 The MoS 2 -based cathode materials for ZIBs in the recent literature studies have the 5− 15 layered MoS 2 (Tables S1 and S2). 7−27 We think that MoS 2 materials with the layer numbers of <5 are explorable to further facilitate Zn insertion/desertion, due to the reduced lattice energy, 30,31 and to enhance cathode performance for ZIBs.…”

Laser‐induced heating of porous Ge layers implanted with Ag+ and Cu+ ions

“…However, in nanostructured material, a high surface‐to‐volume ratio can lower the melting point. [ 31,32 ] It was previously shown that size effect in nc‐Ge particles caused a downshift of the melting point to around 1100 K for particles with an average size of 5 nm. [ 33 ] In addition, melting point of amorphous solids is known to be lower than crystalline solids.…”

Diammonium Glycyrrhizinate-Based Micelles for Improving the Hepatoprotective Effect of Baicalin: Characterization and Biopharmaceutical Study

“…Another possible reason was that the average size of BAI-DG Ms was larger than that of DG Ms, and according to Gibbs–Thompson relationship, the melting points of nanoparticles are linearly proportional to the reciprocal of the nanoparticle’s thickness or diameter [ 18 ]. In addition, the change in micelle shape may also affect the melting point [ 19 ].…”