A statistical mechanical model of polymer brushes: Equilibrium and growth

We construct a statistical mechanical model for a polymer brush in theta-solvent. The model is exactly solvable for realistic polymer models (e.g. the freely rotating chain and the rotational isomeric state models) and it readily accounts for inhomogeneities of the brush with respect to the plane parallel to the grafting surface. The interactions between neighboring chains is mimicked by the presence of a confinement potential centered on the grafting point of each chain. We explore the model to calculate the equilibrium and kinetic properties of the polymer brush. We find that the variations of the brush free energy and height with the coverage depend strongly on the stiffness of the polymer chain (bond angle) and on the severity of the chain confinement. The results for the growth kinetics of the brush are compared with recent measurements on the formation of a PEG2000 brush from solution.