STRUCTURE FACTOR FOR RANDOMLY ORIENTED SELF-AFFINE MEMBRANES

We determine the asymptotic behavior of the orientationally averaged structure factor S(q) for a large, flat memorane characterized by a roughness exponent zeta. We show that S(q) approximately 1/q2 for q much less than 1/l, where l is controlled by the amplitude for transverse or longitudinal fluctuations. If l is much larger than the intermonomer distance a and 1/l much less than q much less than 1/a, then S(q) approximately 1/q3-zeta or S(q) approximately 1/q4/zeta-2 for a small or large amplitude for longitudinal fluctuations, respectively. We also consider the case where the surface is self-affine only at large distances.