Brownian Dynamics of a Suspension of Particles with Constrained Voronoi Cell Volumes

Abstract

Solvent-free polymer-grafted nanoparticle fluids consist of inorganic core particles fluidized by polymers tethered to their surfaces. The attachment of the suspending fluid to the particle surface creates a strong penalty for local variations in the fluid volume surrounding the particles. As a model of such a suspension we perform Brownian dynamics of an equilibrium system consisting of hard spheres which experience a many-particle potential proportional to the variance of the Voronoi volumes surrounding each particle (E = α(Vi-V0)(2)). The coefficient of proportionality α can be varied such that pure hard sphere dynamics is recovered as α → 0, while an incompressible array of hairy particles is obtained as α → ∞. As α is increased the distribution of Voronoi volumes becomes narrower, the mean coordination number of the particle increases and the variance in the number of nearest neighbors decreases. The nearest neighbor peaks in the pair distribution function are suppressed and shifted to larger radial separations as the constraint acts to maintain relatively uniform interstitial regions. The structure factor of the model suspension satisfies S(k=0) → 0 as α → ∞ in accordance with expectation for a single component (particle plus tethered fluid) incompressible system. The tracer diffusivity of the particles is reduced by the volume constraint and goes to zero at ϕ ∼ 0.52, indicating an earlier glass transition than has been observed in hard sphere suspensions. The total pressure of the suspension grows in proportion to (αkBT)(1/2) as the strength of the volume-constraint potential grows. This stress arises primarily from the interparticle potential forces, while the hard-sphere collisional contribution to the stress is suppressed by the volume constraint.

Simulating electropulse fracture of granitic rock

“…A Voronoi tesselation is used to generate the rock microstructure, with the Voronoi cells representing individual mineral grains (Figure 3). To obtain the desired volumetric percentage and grain size of each of the mineral types, initially randomly distributed cell volumes were iteratively relaxed until the desired material composition was achieved [59,60,61]. The rock composition properties are shown in Table 3, and the generated material microstructure is shown in Figure 3.…”

Scaling Laws for Polymer Chains Grafted onto Nanoparticles

“…Chain conformations are thought to depend strongly on both grafting density and surface curvature, but such dependence is not well‐established due to a lack of direct experimental verification. Although, there has recently been marked rise in investigations probing the dynamics of PGNPs in polymer matrices, the effort on single‐component PGNPs is more limited both for experiments and simulations . Surprisingly, the study of neat PGNP structure is even more limited than is the study of neat PGNP dynamics.…”

Simulation of Electrical and Thermal Properties of Granite under the Application of Electrical Pulses Using Equivalent Circuit Models

“…The mineral distribution was chosen randomly meeting the conditions of Table 1 and Table 3 . Some works [ 19 , 20 ] reported mineral distributions arranged with Voronoi networks in order to describe any random distribution of particles, minerals, etc. Though our simulation works used a 5 times larger void, comparing to their works, the proportion of void and minerals was maintained as described in Table 3 .…”