Self-Assembly of Ligated Gold Nanoparticles: Phenomenological Modeling and Computer Simulations

Abstract

We study the assembly of ligated gold nanoparticles by both phenomenological modeling and computer simulations for various ligand chain lengths. First, we develop an effective nanoparticle-nanoparticle pair potential by treating the ligands as flexible polymer chains. Besides van der Waals interactions, we incorporate both the free energy of mixing and elastic contributions from compression of the ligands in our effective pair potentials. The separation of the nanoparticles at the potential minimum compares well with experimental results of gold nanoparticle superlattice constants for various ligand lengths. Next, we use the calculated pair potentials as input to Brownian dynamics simulations for studying the formation of nanoparticle assembly in three dimensions. For dodecanethiol ligated nanoparticles in toluene, our model gives a relatively shallower well depth and the clusters formed after a temperature quench are compact in morphology. Simulation results for the kinetics of cluster growth in this case are compared with phase separations in binary mixtures. For decanethiol ligated nanoparticles, the model well depth is found to be deeper, and simulations show hybrid, fractal-like morphology for the clusters. Cluster morphology in this case shows a compact structure at short length scales and a fractal structure at large length scales. Growth kinetics for this deeper potential depth is compared with the diffusion-limited cluster-cluster aggregation (DLCA) model.

Which Forces Control Supracrystal Nucleation in Organic Media?

“…For Au 5 nanoparticles, clusters nucleate starting from a density of 0.004 (volume fraction: 0.002) (Figure 9 B). This is in good agreement with the simulations by Kahn et al [ 36 ] where cluster formation for volume fractions larger than 0.0027 is observed. In diluted systems for Au 6 and Au 7 nanoparticles, the fi rst small clusters appear which may grow due to cluster-cluster aggregation ( Figure 9 C and 9D).…”

“…The parameter β 1 is fi xed at its usual value of 0.34. [ 36 ] We assume that only the alkane chains take part in the attraction. Therefore, the solubility parameter of dodecane is used for the solubility parameter of the ligand.…”

“…Kahn et al [ 36 ] have recently used a similar interaction model to study the self-assembly of Au nanoparticles with a diameter of 5 nm in toluene.…”

Statistical model for nanoparticles formation: Self-consistent field approximation

“…Microscopic approach in the theory of nanosystems is mainly based on quantum mechanics methods [10,21] and numerical simulations [22][23][24]. Statistical theory of nanosystems is now at its initial stage of development in view of the principal problem connected with the limited number of particles considered in such systems.…”

Does Shining Light on Gold Colloids Influence Aggregation?

“…Later, the physical properties, e.g., fractal dimension ( D f ) and radius of gyration ( R g ) of colloidal aggregates in the sol were probed by static and dynamic light scattering, small angle x-ray scattering, and neutron scattering techniques2345. Various models have been developed to explain the observed short-range and long range structures of the particle aggregates in a stable colloidal dispersion6789101112. It is well-established that the effective forces acting between the particles at the microscopic scale determine the morphology of aggregates during pre-nucleation, nucleation and super-cluster formation in the solvent.…”