Monte Carlo Computer Simulation of Chain Formation from Nanoparticles

Abstract

Spontaneous assembly of long chains of nanoparticles (NPs) has been experimentally observed for many different materials including nanocolloids of semiconductors, metal oxides, and metals. While the origin of dipole moment in various colloids can be different, a universal explanation of chain assembly can be provided by the hypothesis of dipole-dipole attraction of nanocolloids. In this paper, we describe the application of the Monte Carlo method for modeling of self-organization of large ensembles of NPs. As the first approximation, the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory provides an adequate description of self-organization of several hundreds of NPs. Unlike microscale colloids that served as a classical model for DLVO, we used a distance-dependent media dielectric constant. The simulated chains are morphologically and geometrically similar to those observed experimentally. This establishes the fundamentally important ability of NPs to self-assemble due to their intrinsic anisotropy. Thermodynamic analysis of Monte Carlo results reveals the role of partial removal of the stabilizer shell in CdTe nanocolloids necessary for reduction of interparticle repulsion. Analysis of the field distribution around short chains demonstrates that the growth of linear agglomerates is kinetically controlled by a high activation barrier for NPs approaching from all of the directions except one end of the chain. The presented algorithm can be applied to other interparticle interactions, such as induced dipoles, which can stimulate chain formation in the absence of permanent dipole moment. It can also serve as a theoretical foundation for the understanding of the large complex superstructures forming from anisotropic and anisometric NPs. Monte Carlo simulation of nanoscale dipoles can also be extended to the interactions of NP with proteins, and related biological systems important for a variety of applications in medicine.

Dipole−Dipole Interactions in Nanoparticle Superlattices

“…21 Recently, Sinyagin et al used more accurate form of the interparticle potential to describe electrostatic interaction between nanoparticles. 22 The analytical form of electrostatic potential between two spherical particles was originally developed for dilute polyelectolyte solutions and took into account the nonlocal charge distribution effects, however, it showed significant errors at small interparticle separations, especially in the presence of dielecric discontinueties at the particle boundaries. 23 This is not appropriate for a superlattice of semiconductor nanoparticles, where the length of the dipoles exceeds the interparticle distances.…”

Catalyst-free synthesis and shape control of CdTe nanowires

“…The latter has been extensively studied by the Kotov group in the case of aqueous CdTe nanoparticle solutions, which were found to form not only wires [18], but also two-dimensional assemblies [23]. Low surface coverage by ligands and the presence of a dipole moment in the nanoparticles turned out to be key factors controlling nanowire formation in this case [24]. The wires formed out of cubic nanoparticles were shown to undergo a phase change, which gives rise to nanowires having a hexagonal crystallographic structure [18].…”

“…The formation of nanowires turned out to be possible only if the building blocks possess a dipole moment; otherwise spherical aggregates will be generated [24]. Existence of a dipole moment in particles having a cubic crystallographic structure could be explained by having a closer look at the exact shape of the particles.…”

Modeling of cellular pearl chain formation using a double photoconductive layer biochip

“…To date, this method is utilized to simulate motion of micro or nanoparticles such as magnetic fluid particles [13], colloidal nanoparticles [14], and silver nanoparticles [15]. Detailed forces related to the applied electric field have been described below.…”