Understanding interactions between capped nanocrystals: Three-body and chain packing effects

Abstract

Self-assembly of capped nanocrystals ͑NC͒ attracted a lot of attention over the past decade. Despite progress in manufacturing of NC superstructures, the current understanding of their mechanical and thermodynamic stability is still limited. For further applications, it is crucial to find the origin and the magnitude of the interactions that keep self-assembled NCs together, and it is desirable to find a way to rationally manipulate these interactions. We report on molecular simulations of interacting gold NCs protected by capping molecules. We computed the potential of mean force for pairs and triplets of NCs of different size ͑1.8-3.7 nm͒ with varying ligand length ͑ethanethiol-dodecanethiol͒ in vacuum. Pair interactions are strongly attractive due to attractive van der Waals interactions between ligand molecules. Three-body interaction results in an energy penalty when the capping layers overlap pairwise. This effect contributes up to 20% to the total energy for short ligands. For longer ligands, the three-body effects are so large that formation of NC chains becomes energetically more favorable than close packing of capped NCs at low concentrations, in line with experimental observations. To explain the equilibrium distance for two or more NCs, the overlap cone model is introduced. This model is based on relatively simple ligand packing arguments. In particular, it can correctly explain why the equilibrium distance for a pair of capped NCs is always Ϸ1.25 times the core diameter independently on the ligand length, as found in our previous work ͓Schapotschnikow, R. Pool, and T. J. H. Vlugt, Nano Lett. 8, 2930 ͑2008͔͒. We make predictions for which ligands capped NCs self-assemble into highly stable three-dimensional structures, and for which they form high-quality monolayers.

Can nonadditive dispersion forces explain chain formation of nanoparticles?

“…Still, in the CDM, the triangular configuration is overall more favorable, and the linear configuration is not stable enough to predict stable linear chains in a Brownian environment. From this, we can conclude, as already suggested by Schapotschnikow et al,28 that an important role in explaining chain formation could be played by effective three-body interactions between the particles' capping layers that make triangular configurations unfavorable. Many-atom VdW interactions, while not strong enough by themselves to make linear chains favorable, do provide a local minimum at this configuration, making it the most favorable configuration if triangular ones are excluded by steric interactions.…”

“…In the work by Schapotschnikow et al, 28 where simulation methods are used to arrive at an effective three-body interaction energy between triplets of nanoparticles stabilized by capping layers, it is suggested that linear chains are the overall most favorable orientation. In our work, we find that the CDM, which includes many-body VdW interactions between atoms but ignores steric interactions between the capping layers, shows that many-body linear chains are metastable, whereas the two-body HdB method exhibits no local minimum at the linear configuration.…”

“…The linear conformation of the chains is explained by migration of ligands when two particles attach, making the site diametrically opposite the first contact point the most attractive for attachment of a third particle. 27 A detailed simulation study of the influence of the type of capping layer on two-and three-body interactions between nanoparticles 28 indeed suggests, among other things, that, due to the influence of the capping layer, a linear configuration of particles is energetically preferred over a triangular structure. These studies thus provide a possible explanation for spontaneous chain formation that does not depend on the presence of a permanent dipole.…”

A computer simulation study of the interaction between passivated and bare gold nanoclusters

“…Overall, the nanoparticles are roughly spherical in appearance at all temperatures studied. These effects are consistent with the solvation of the nanoparticle by ethane (Lal et al 2004;Patel & Egorov 2007;Pool et al 2007;Schapotschnikow & Vlugt 2009). Within the nanoparticles, the gold nanocores are misshapen without the regular FCC structure or the truncated octahedral morphology of the original structure.…”

“…Egorov (2005) devised a model for the nanoparticle interaction based on the classical density functional theory and Patel & Egorov (2007) performed molecular dynamics simulations similar in character to those presented there. Schapotschnikow et al (2007aSchapotschnikow et al ( ,b, 2008, Schapotschnikow & Vlugt (2009) and Pool et al (2007) have completed a comprehensive series of simulation studies, including a study of nanoparticle interactions (Schapotschnikow & Vlugt 2009), that is also highly relevant. Much of what we report here for passivated nanoparticles partly confirms what these authors have found; however, our model is sufficiently different in detail to show effects not previously reported and shed additional light on the subject.…”