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, σgσg, and the size of the nanoparticles b  , we determine the equilibrium particle penetration depth δδ and the average concentration of nanoinclusions ϕ¯nano in the penetration layer δδ at constant pressure. In agreement with a recent theoretical prediction, we demonstrate that for nanoinclusions of size b⩾b∗b⩾b∗ the thickness of this layer δ∝h(b∗/b)3δ∝h(b∗/b)3 where h   is brush height and b∗∝σg-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 bmaxbmax do not mix with the brush. The mean density of nanoinclusions is found to scale as ϕ¯nano∝(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⊥nano and D||nano changes with growing volume fraction of the nanoparticles in agreement with theoretical predictions.

Graphical abstractInterpenetrating concentration density profiles of a polymer brush, ϕp(z)ϕp(z), and of nanoinclusions of different size (given as parameter), ϕnano(z)ϕnano(z). The system is kept at constant pressure by a barostat.Figure optionsDownload full-size imageDownload as PowerPoint slide