Nanoinclusions in Dry Polymer Brushes

Abstract

A theory of dry polymer brushes containing nanoinclusions is presented. Polymer brush−nanoparticle mixtures arise in various applications and in experimental systems where block copolymer materials, providing brushlike environments, organize nanoparticles to generate materials with novel properties. The ease with which a nanoinclusion enters a brush is measured by the free energy cost to introduce the inclusion, ΔFinc. This depends strongly on particle shape and size b, as does the degree to which brush chain configurations are perturbed. For inclusions smaller than the typical chain fluctuation scale or blob size ξblob, by extending the self-consistent mean field (SCF) theory for pure brushes, we show ΔFinc = P(z)Vp for an inclusion of volume Vp a distance z from the grafting surface. Here P(z) is the quadratic SCF “pressure” field. Equilibrium particle distributions within a brush of chains of length N grafted at density σ depend strongly on particle size: (i) particles smaller than a scale b* ∼ σ-2/3 ...