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 df and the cluster coordination number. The time evolution of the cluster fractal dimension is linked to the dynamics of two populations: small (k≤ 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 of ∼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 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 in the numbers of clusters with time and a few collision kernel elements are evaluated and compared to analytical expressions.

Morphology and mobility of synthetic colloidal aggregates

“…The cluster coordination number not only provides information on the openness of an aggregate and its compactness, but it is a factor that influences monomer hydrodynamic shielding within an aggregate [28]. Reference [24] used the coordination number as an indicator of cluster compactness, albeit for clusters generated by a completely different, physicallybased agglomeration mechanism. For the synthetic fractals analyzed herein, i.e., generated by the cluster-cluster aggregation algorithm, Gastaldi and Vanni [29] argued that the the coordination number is…”

“…[24]. These aggregates were generated by solving the Langevin equations of motion of a set of monomers interacting via a central potential in a quiescent fluid.…”

On the friction coefficient of straight-chain aggregates

“…The shielding factor provides a measure of the shielding of a monomer by other monomers in an aggregate; as such, it depends on aggregate morphology. It has been used to calculate corrections of the Stokes drag on a porous medium consisting of identical non-interacting spheres [19], in modifications of heat transfer to an aggregate due to monomer shielding [20], and it has been related to the aggregate diffusion coefficient [13]. The friction coefficient, calculated according to Eq.…”

“…[13,25], and in particular the diffusive motion of aggregates. The Brownian motion of an aggregate may be described by modelling the Brownian motion of a set of interacting monomers held together by strong monomer-monomer interaction forces.…”

“…The monomer friction coefficient is usually assumed to be independent of aggregate morphology and equal to the average monomer friction coefficient β k . In particular, in the free draining approximation (i.e., for ideal clusters) the monomer friction coefficient is taken to be the friction coefficient of an isolated monomer [13]. In the continuum regime, these assumptions yield the aggregate diffusion coefficient D k as given in Eq.…”