We determine the asymptotic behavior of the orientationally averaged structure factor S(q) for a large, flat membrane characterized by a roughness exponent {ζ}. We show that S(q){~}1/q² for q{}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{}q{}1/a, then S(q){~}1/q^3-ζ or S(q){~}1/q^4/ζ-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.
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Goulian et al. (1992) studied this question.
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