Colloids in Brushes: The Insertion Free Energy via Monte Carlo Simulation with Umbrella Sampling

Abstract

The insertion of spherical, nonadsorbing colloidal particles into a swollen planar polymer brush is characterized using Monte Carlo simulations with umbrella sampling focusing on small particles whose radius Rp is smaller than the unperturbed brush thickness, h0. This process plays a key role in the modeling antifouling poly(ethylene glycol) brushes that repress protein adsorption. Two properties are studied as a function of Rp and the altitude within the brush z: (i) The particle induced perturbation of the monomer concentration profile and (ii) The insertion free energy penalty, Fins. The perturbation of the concentration profile is short ranged involving pure depletion at high z and depletion followed by a maximum at low z. When the particle does not experience the surface depletion layer Fins grows with the monomer volume fraction ϕ and Rp. Fins ∼ Rp3 for the larger Rp reflects an osmotic insertion penalty at the high ϕ range of the brush. At the lower ϕ range a surface tension correction plays a role. In the range explored there is no evidence for Fins ∼ Rp4/3 as was suggested for small particles.