Membranes on rough self-affine surfaces

We study the effective potential U-e between a rough self-affine surface, 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 length. However, the effect of H is negligible for membrane-surface separations 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.