Behavior of the intramolecular scattering function in its representation by Nagairsquo;s series

摘要

The intramolecular scattering function for a polymer molecule is known to be related by Nagairsquo;s series to the even moments of the distance separating two scattering centers. Numerical values of the coefficients in this series have been computed for a rigid molecule. Application of these coefficients to the computation of the scattering function for several rigid molecules and a flexible molecule establishes that the series converges rapidly only at small values of the scattering angle. Oscillation is obtained at higher scattering angles. The origin of this behavior is readily apparent from an examination of the coefficients. The oscillation will be obtained with any molecule, whether flexible or not, at sufficiently high scattering angle. A more practical approach to the computation of the scattering function for a flexible polymer molecule may be to evaluate lang; (sinmgr;rij)/mgr;rijrang; directly from a suitable Monte Carlo sample.