Asymptotic Behavior of the Light-Scattering Function of Coiled Molecules

Abstract

This paper discusses the asymptotic solution of the scattering function P(θ) for large x, where x is proportional to the scattering angle, radius of gyration, and the wavenumber. The theoretical model employed for the calculation of the P(θ)-vs-x curves was presented in the preceding paper. The results are discussed with respect to the experimental data, after the results for P(θ) are corrected for various values of polydispersity. A general analysis of the theoretical P(θ)-vs-x curves is presented, and the effect of the shape of the chain-end distribution function on the asymptotic behavior of the light-scattering function is discussed.

The behavior of the structure function at large wavevectors for polymers in different regimes

“…In the long chain limit the interiorinterior distances dominate the calculation of the structure factor. Indeed, the des Cloizeaux value of 1.40 for h = 0.273 is essentially the same as the Mazur et al [9] value of 1.41.…”

“…In order to compute S(k) we have repeated the analytical procedure outlined in the paper by Mazur et al [9] but have employed, for the first time to our knowledge, the more accurate des Cloizeaux form [15] for the distance distribution function in place of their empirical form. The des Cloizeaux form [15] is…”

“…(9) when m = 0.5. Mazur et al [9] also assumed the same functional form of R 2 ij as Peterlin but they used an empirical end-to-end distance distribution function to examine the asymptotic behavior of S(k). They found for large X that…”

Intramolecular distances and form factor of cyclic chains with excluded volume interactions

“…[7] by Mazur et al, but employing Eq. (3) instead of their empirical expression for the end-to-end distance distribution.…”

“…Time ago, Mazur et al [7] calculated S(x) for linear chains with excluded volume at high x by using an empirical form for both the mean quadratic intramolecular distances between units and the end-to-end distance distribution function. The results were not completely satisfactory since the distribution of intramolecular distances does not have exactly the same functional form as the end-to-end distance distribution function.…”