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

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.