Statistical mechanics of helical wormlike chains. III. Scattering functions

Abstract

The scattering function for the helical wormlike chain is evaluated by the use of the Hermite polynomial expansion of the distribution function, and its general behavior is studied. The convergence of this series is first discussed; upper and lower Tchebychev bounds for the exact scattering function are also examined. Recalling that the model may be regarded as a hybrid of the three extreme forms of rod, random coil, and regular helix, the results are then compared with the scattering functions for these forms. Thus, it is understood that the scattering function for the helical wormlike chain exhibits first coil-like and then helical damped-oscillatory or rodlike behavior as the scattering angle is increased. A comparison of theory with experiment is made for the small-angle scattering of x-rays and neutrons by tactic and atactic poly(methylmethacrylate) chains. Copyright © 1977 American Institute of Physics.