Minimum Free-Energy Shapes of Ag Nanocrystals: Vacuum vs Solution

Abstract

We use two variants of replica-exchange molecular dynamics (MD) simulations, parallel tempering MD and partial replica exchange MD, to probe the minimum free-energy shapes of Ag nanocrystals containing 100−200 atoms in a vacuum, ethylene glycol (EG) solvent, and EG solvent with a PVP polymer containing 100 repeat units. Our simulations reveal a shape intermediate between a Dh and an Ih, a Dh-Ih, that has distinct structural signatures and magic sizes. We find several prominent features associated with entropy: pure FCC nanocrystals are less common than FCC crystals containing stacking faults, and crystals with the minimum potential energy are not always preferred over the range of relevant temperatures. The shapes of the nanocrystals in solution are influenced by the chemical identities of the solution-phase molecules. Comparing Ag nanocrystal shapes in EG to those in an EG+PVP solution, we find more icosahedra in EG and more decahedra in EG+PVP across all of the nanocrystal sizes probed in this study. At certain critical sizes, nanocrystal shapes can change dramatically with the addition and removal of a single atom or with a change in temperature at a fixed size. The information in our study could be useful in efforts to devise processing routes to achieve selective nanocrystal shapes.

Size and temperature dependent shapes of copper nanocrystals using parallel tempering molecular dynamics

“…116 is not a magic size for the Ih and the surface atoms of this nanocrystal are distorted from those in a perfect Ih – thus, we designate it as a “twisted Ih”. We note that 116 is a magic size for the Dh–Ih 39 and the “twisted Ih” bears similarity to the Dh–Ih in its surface atoms. Previously unclassified atoms with CNA are shown in yellow in Fig.…”

“…Interestingly for Ag, we observed that SCSF structures had a lower free energy (more frequent occurrence) than FCC structures – at sizes where such shapes occurred. 39 We attributed the preference for SCSF to the low stacking-fault energy for Ag, 53 which complements the high configurational entropy associated with stacking faults to produce a majority of SCSF shapes. Cu has a higher stacking-fault energy than Ag 53 and though the most probable structures for the FCC and SCSF are close in energy (see Fig.…”

“…This was not observed in earlier studies of Au 37 and Cu 38 – though a limited number of sizes were probed in these studies – and it was observed to a lesser extent for Ag. 39 Since the Helmholtz free energy (the relevant free energy for our PTMD simulations) is given by A = U − TS , where U is the potential energy and S is the entropy, we expect structures with the lowest potential energies to occur at low temperatures, and those with a significant entropic component to emerge at sufficiently high temperatures.…”

“…In our recent study of Ag nanocrystals, 39 we added a category for particles with intermediate structures between Dh and Ih: Dh–Ih. We note this shape category bears similarity to the mix category defined by Settem et al in their recent study.…”

“…In this work, we use Parallel Tempering Molecular Dynamics (PTMD) to probe the temperature-dependent, minimum free-energy shapes of Cu nanocrystals in the 100–200 atom size range. A few recent studies have used PTMD 36–39 or variants 39 to obtain temperature-dependent shape distributions of Au, 36–38 Cu, 38 and Ag 38,39 nanocrystals. In PTMD simulations, parallel, canonical MD simulations are used to simulate a series of nanocrystal replicas whose temperatures span the lowest temperatures of interest to temperatures above melting.…”