Correlations in Grafted Polymer Layers

We discuss compositional fluctuations in densely end-grafted polymers when two species of chains are present. When the two species are identical except for labeling, we relate the two-point spatial correlation function of local composition to density-density correlations within a single chain and calculate it under melt and solvent-swollen conditions. We deduce structure factors that could be observed in scattering from a layer composed of two chain species that differ only in their coupling to the scatterers. We generalize these results to describe compositional fluctuations when the two species have a nonzero free energy of mixing. These fluctuations diverge at a critical molecular weight. We analyze the divergence to corroborate the recently predicted phase transition to a “rippled” phase.