Pair and many-body interactions between ligated Au nanoparticles

We report the results of molecular dynamics simulations of the properties of a pseudo-atom (united atom) model of dodecane thiol ligated 5-nm diameter gold nanoparticles (AuNPs) in a vacuum as a function of ligand coverage and particle separation in three states of aggregation, namely, the isolated AuNPs, the isolated pair of AuNPs, and a square lattice of four AuNPs. Our calculations show that the ligand density along a radius emanating from the core of an isolated AuNP has the same gross features for all values of the coverage; it oscillates around a constant value up to a distance along the chain corresponding to the position of the fourth pseudo-atom and then smoothly decays to zero, reflecting both the restricted conformations of the chain near the core surface and the larger numbers of conformations available further from the core. Interaction between two AuNPs generates changes in the ligand distributions of each. We examine the structure and general shape of the ligand envelope as a function of the coverage and demonstrate that the equilibrium structure of the envelope and the deformation of that envelope generated by interaction between the NPs are coverage-dependent so that the shape, depth, and position of the minimum of the potential of mean force display a systematic dependence on the ligand coverage. We propose an accurate analytical description of the calculated potential of mean force as a function of a set of parameters that scale linearly with the ligand coverage. Noting that the conformational freedom of the ligands implies that multiparticle induced deviations from additivity of the pair potential of mean force are likely important; we define and calculate a "bond stretching" effective pair potential of mean force for a square lattice of particles that contains, implicitly, both the three- and four-NP contributions. We find that the bond stretching effective pair potential of mean force in this cluster has a different minimum and a different well depth from the isolated pair potential of mean force. Previous work has found that the three-particle contribution to deviation from pair additivity is monotonically repulsive, whereas we find that the combined three- and four-particle contributions have an attractive well, implying that the three- and four-particle contributions are of comparable magnitude but opposite sign, thereby suggesting that even higher order correction terms likely play a significant role in the behavior of dense assemblies of many nanoparticles.