Langevin agglomeration of nanoparticles interacting via a central potential

Abstract: Nanoparticle agglomeration in a quiescent fluid is simulated by solving the Langevin equations of motion of a set of interacting monomers in the continuum regime. Monomers interact via a radial, rapidly decaying intermonomer potential. The morphology of generated clusters is analyzed through their fractal dimension $d_f$ and the cluster coordination number. The time evolution of the cluster fractal dimension is linked to the dynamics of two populations, small ($k \le 15$) and large ($k>15$) clusters. At early times monomer-cluster agglomeration is the dominant agglomeration mechanism ($d_f = 2.25$), whereas at late times cluster-cluster agglomeration dominates ($d_f = 1.56$). Clusters are found to be compact (mean coordination number $\sim 5$), tubular, and elongated. The local, compact structure of the aggregates is attributed to the isotropy of the interaction potential, which allows rearrangement of bonded monomers, whereas the large-scale tubular structure is attributed to its relatively short attractive range. The cluster translational diffusion coefficient is determined to be inversely proportional to the cluster mass and the (per-unit-mass) friction coefficient of an isolated monomer, a consequence of the neglect of monomer shielding in a cluster. Clusters generated by unshielded Langevin equations are referred to as \textit{ideal clusters} because the surface area accessible to the underlying fluid is found to be the sum of the accessible surface areas of the isolated monomers. Similarly, ideal clusters do not have, on average, a preferential orientation. The decrease of the numbers of clusters with time and a few collision kernel elements are evaluated and compared to analytical expressions.