Nanoinclusions in polymer brushes with explicit solvent--a molecular dynamics investigation

We use molecular dynamics simulations with a dissipative particle dynamics (DPD) thermostat to study the behavior of nanosized inclusions (colloids) in a polymer brush which is in contact with an explicit solvent in the NPT ensemble. The brush is described by a bead-spring model for flexible polymer chains, grafted on a solid substrate, while the polymer-soluble nanoparticles in the solution are taken as hard spheres. By varying the chain length N, the grafting density of the brush, sigma(g), and the size of the nanoparticles b, we determine the equilibrium particle penetration depth delta and the average concentration of nanoinclusions phi(nano) in the penetration layer delta at constant pressure. In agreement with a recent theoretical prediction, we demonstrate that for nanoinclusions of size bb(*) the thickness of this layer delta is proportional to h(b(*)/b)(3) where h is brush height and b(*) is proportional to sigma(g)(-2/3) is a typical size below which smaller particles are uniformly distributed in the brush. We also observe that particles, larger than some threshold value b(max) do not mix with the brush. The mean density of nanoinclusions is found to scale as phi(nano) is proportional to (b(*)/b)(3) within the whole range of parameter variation. The diffusivity of nanoparticles, embedded in the polymer brush, in direction perpendicular to the grafting plane is found to be up to 20% higher than parallel to the plane. The variation of the respective diffusion coefficients D(perpendicular)(nano) and D(parallel)(nano) changes with growing volume fraction of the nanoparticles in agreement with theoretical predictions.