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Monte Carlo simulations of closed random walks on a body-centered cubic lattice are used to investigate the influence of the average knot structure on the root mean square radius of gyration Rg and scattering function P(q) of flexible ring polymers obtained by cyclization under Θ-conditions. Calculations are carried out for walks of 10 to 160 steps. Considered as an equivalent chain model for ring polystyrene, this corresponds to molecular weights Mn ≤ 120000. Up to 37% of the ring molecules are shown to be knotted. The influence of the number and kind of knots on Rg is presented in some detail. Removing part or all of the unknotted rings produces a more pronounced maximum in the Kratky plot of the scattering function. Comparisons are made with experimental small-angle neutron scattering data for cyclic polystyrene in deuteriated cyclohexane

Topological constraints and their influence on the properties of synthetic macromolecular systems. 1. Cyclic macromolecules