Shear Modulus of Molten Polymer Brush

1. PS brush SiOH NH2 NH2 NH2 NH2 7 Å Si Si Si Si O O O O O PS-COOH O O O O Si/SiOX Si/SiOx Shear Modulus of Molten Polymer Brush Ophelia K. C. Tsui, Department of Physics, Boston University Fifteen years ago, Fredrickson et al. [Macromolecules 1992, 25, 2882-2889] predicted that a molten polymer brush possesses a shear modulus that would cause the surface spectrum of the brush film, Aq2, to deviate from that of a liquid: where m0 = (3kBT/v)(h/Na)2 is the shear modulus of the brush, h is the brush film thickness, kB is Boltzmann constant, q is wavevector, T is temperature, a is segmental length, v is monomer volume. Insofar, this prediction has been largely unchecked. Here, we prepare carboxy-terminated polystyrene brush films (PS-COOH) end-grafted on surfaces silanized with a monolayer of 3-aminopropyltrimethoxysilane that interacts weakly with the brush chains. We measure the surface spectrum of the films by using atomic force microscopy and deduce the shear modulus from the measurements. The result, plotted below, demonstrates an excellent agreement with the theory.