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

Numerical simulations are performed for isolated cyclic, or ring, 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.