Stability and Free Energy of Nanocrystal Chains and Superlattices

Abstract

We discuss the stability and free energy of 1D (chains), 2D (planar superlattices), and 3D (bcc or fcc superlattices) nanocrystals (having hydrocarbons as capping ligands) structures. We start by introducing the method to compute the pressure and free energy. We then analyze the magnitude of many body (or nonadditive) effects, those not described by two body interactions. For 3D superlattices, we examine the relative stability of fcc vs bcc as well as the prevalence of rotator vs crystal phases. We identify a bundling phenomena that occurs during bcc assembly, when next to nearest neighbors begin to make contact. We precisely calculate the density and lattice constant as well as the presence of ligand vortices and find that overall, the simulations fully support the recently introduced Orbifold Topological Model (OTM). By comparing our results with the considerable experimental data available in the literature, we identify a number of subtle effects.

Energy vs. Entropy in Superlattices of Ligand-Covered Nanoparticles

“…Calorimetric measurements by Quan and coworkers showed that a bcc superlattice of nanoparticles with λ ≈ 0.9 was indeed energetically favored over fcc. 17 Simulations by Zha and Travesset have recently confirmed a stable bcc superlattice due to ligand interactions between next-nearest neighbors, 18 but indicate an entropic advantage of bcc over fcc, in contrast to the energetic one suggested by Whetten and coworkers and the OPM model.…”

Assembly by solvent evaporation: equilibrium structures and relaxation times

“…where λ = L/R core and ξ = σ/σ max , with L the maximum extension of the ligands and σ max the maximum grafting density. From previous studies, 36 σ max = 0.666 chains per Å 2 . Note that if R d (to be precisely defined further below) is the radius of the liquid droplet, the hard sphere packing fraction is defined by:…”

Superlattice assembly by interpolymer complexation

“…The free energy of a fcc SL is obtained by following the same methods as previous work, 16 where it is computed as the reversible work of compressing the lattice at a given nearest-neighbor separation a NN (or lattice constant a), see Fig. 10a.…”

“…In our previous work, 16 we calculated many body effects in the lattice by subtracting from the free energy the collection of calculated pair PMFs. Unfortunately, this cannot be done here as different values of x in periodic lattices and pair systems correspond to number densities that are not easily related.…”