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

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 R-p is smaller than the unperturbed brush thickness, h(0). 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 R-p and the altitude within the brush z: (i) The particle induced perturbation of We monomer concentration profile and (ii) The insertion free energy penalty, F-ins. 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 F-ins grows with the monomer volume fraction phi and R-p. F-ins R-p(3) for the larger R-p reflects an osmotic insertion penalty at the high phi range of the brush. At the lower phi range a surface tension correction plays a role. In the range explored there is no evidence for F-ins similar to R-p(4/3) as was suggested for small particles.