Self-affine surfaces of polymer brushes

The diffuse X-ray scattering from the surface morphology of polystyrene (PS) and poly(n-butyl acrylate) (PnBA) brushes synthesized by conventional free radical polymerization is found to be well described by a model of a surface with self-affine roughness. To date, such models have only been used with solid surfaces. The signature behavior of capillary waves is not observed. Data collected from transverse scans at multiple values of the out-of-plane momentum transfer q(z) can be fit simultaneously using a single set of the roughness parameters: the root-mean-square roughness, sigma, the lateral correlation length, xi, and the roughness exponent, h. The surfaces of the PnBA brushes are the same at temperatures 75 and 130 degrees C above the glass transition temperature, T-g, of PnBA in the bulk. In contrast, the correlation lengths of the surface structures of PS brushes annealed at 140 degrees C are lower than those of the as-deposited brushes, and the roughnesses increase with annealing. The lateral correlation length, xi, of the annealed PS brushes varies with brush thickness, d, as xi similar to d(0.75), which matches the power law dependence expected for the variation of the predominant wavelength of surface fluctuations with brush thickness for a melt brush in the limit of high surface tension. The roughness of the annealed PS brushes increases as a power law of d, with an exponent similar to those characterizing kinetic roughening in plasma deposited polymer films.