MEMBRANES ON ROUGH SELF-AFFINE SURFACES

We study the effective potential U-e between a rough self-affine surfa ce, and a membrane bounded by this surface. We find that the effect of the substrate roughness exponent H on U-e is significant for zeta<xi. zeta is a healing length, and xi the in-plane roughness correlation le ngth. However, the effect of H is negligible for membrane-surface sepa rations larger than a characteristic membrane-surface separation tau. Moreover. the roughness contribution to U-e scales as similar to zeta( 2H) for zeta<xi, and as similar to zeta(-4) for zeta much greater than xi.