Effects of Polydispersity in the End-Grafted Polymer Brush

We consider the effects of polydispersity in molecular weight on the equilibrium statistics of the grafted polymer brush. We use a self-consistent field method, exploiting the fact that the chains in the brush are strongly stretched, to map the problem onto one involving the trajectories of classical particles. A general solution for the density or pressure profile and the force required to compress a brush is given in terms of the distribution of molecular weights. The profile is a unique function of the molecular weight distribution and vice versa. Results are also given for a “brush” whose density profile is constrained to be uniform, as is appropriate to the description of lamellar mesophases of block copolymer melts. Consequences for force-balance experiments and for colloid stabilization are discussed.