SURFACE-MODES AND DEFORMATION ENERGY OF A MOLTEN POLYMER BRUSH

We report on an analysis of the free energy of distortion of a molten polymer brush, such as a layer of block copolymer at an air interface. Within the Alexander-de Gennes approximation of a delta function distribution of chain ends, but rigorously enforcing incompressibility, we calculate the change in the free energy of a brush associated with a small-amplitude sinusoidal displacement of the free surface about the equilibrium height. Unlike the surface of a liquid, long-wavelength modes in a brush are suppressed due to the lateral chain stretching required to maintain constant density. We demonstrate the existence of a preferred wavelength for the surface modes of a molten brush and estimate the fluctuation amplitude. The energy cost to deform a brush with a blunt object, e.g., the tip of an atomic force microscope, is also discussed.