Bundles: End-Grafted Polymer Layers in Poor Solvent

The structure factor for a system of end-grafted neutral polymers is computed self-consistently in a random phase approximation. Both single-end-grafted, brushes, and twice-grafted layer are considered. We find that the polymer brush collapses uniformly, density variations in the direction parallel to the grafting plane being smoothed out by the positive osmotic pressure in the layer. The twice-grafted layer cannot collapse like a brush, and an instability in the mean-field solution to a novel bundled state is found. The characteristic bundle size is set by the amplitude of transverse fluctuations of individual stretched chains in the layer.