Conformational properties of multiply twisted ring systems and daisy-like structures

Two multiple ring systems are considered and relationships are derived for the angular dependence of the scattered light (P(q)), the radius of gyration (R(g)) and the hydrodynamic radius (R(h)) The two models of consideration are (i) the multiply twisted ring system and (ii) the daisy-like ring structure. The derivations are made on the basis of the Wang-Uhlenbeck theorem on Gaussian distributions for the static properties and the Kirkwood-Riseman preaverage approximation for the hydrodynamics. The derived particle scattering factors show significant differences for the two different ring systems. To distinguish the multiply twisted ring system from a linear open chain, it is necessary to measure the scattering intensity over a large q range. The daisy-like structures resemble star-branched macromolecules but with numbers of subrings 4 to 5 times smaller than the arm numbers in a star. Differences between the shrinking factors and the rho parameter of the various systems are noticeable and can be used to discern these systems.