Density functionals for polymers near surfaces

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Abstract
We derive a gradient expansion for the external field necessary to weakly perturb the density profile of noninteracting polymer chains near a surface. This result can be used as part of a more general methodology for analyzing the long-wavelength adsorptive properties of polymer solutions and melts. The coefficients appearing in the expansion are determined from the solutions of a hierarchy of linear, Fredholm integral equations that contain information about the reference (unperturbed) state. We illustrate the calculation of the two lowest-order coefficients for reflecting and absorbing reference boundary conditions. A similar gradient expansion of the intrinsic free energy functional suggests the need to exercise care in obtaining variational forms for the grand free energy from the Legendre transform of the grand partition function. Extremely simple symmetry arguments show that a proper application of gradient expansion techniques leads to a vanishing of the linear gradient contributions to the free energy.