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

TL;DR

This paper investigates the structure of cyclic polymer chains with excluded volume effects using numerical simulations, analyzing form factors, intramolecular distances, and comparing results with theoretical models and linear chains.

Contribution

It provides new simulation data and analytical formulas for the form factor and intramolecular distances of cyclic chains with excluded volume interactions, extending understanding beyond linear chains.

Findings

Form factor S(x) data fitted with new simple formulas

Distribution functions compared with des Cloizeaux form

Differences between cyclic and linear chains analyzed

Abstract

Numerical simulations are performed for isolated cyclic chains with excluded volume. Data are reported for the form factor, S(x), where x is the reduced scattering variable, and also for averages and distributions of the distance between intramolecular units. The averages of distances are compared with two alternative expressions describing their dependence with the number of segments separating the units. The distribution function results are compared with the des Cloizeaux form. Finally the S(x) data are compared with theoretical functions also derived from the des Cloizeaux expression for the distribution function. Moreover, the low x and asymptotic expansions of these functions are obtained. Based on these expansions, simple formulas are proposed to give a good description of the simulation data in the whole range of values of x. A comparison with similar results for linear chains is also included.