Mean-field theoretical analysis of brush-coated nanoparticle dispersion in polymer matrices

The equilibrium dispersion of nanoparticles with grafted polymer chains into polymer matrices, of the same chemical structure as the brush, is studied through the device of mean-field theory. Our results show that the disperion of brush-coated nanoparticles into a matrix polymer is improved with (i) decreasing particle radius and (ii) increasing brush chain length. Both of these aspects can be understood based on the fact that, unlike the case of planar surfaces, homopolymer chains end-grafted to spherical nanoparticle surfaces tangentially spread away from the surface thus alleviating the packing frustration that is created by the relatively high grafting densities. This permits significant brush/matrix overlap, even at high grafting densities, a regime that has only recently become experimentally available due to advances in polymer synthesis (i.e., the "grafting-to" methods). (c) 2008 Wiley Periodicals, Inc.