On the difference in scattering behavior of cyclic and linear polymers in bulk

It has been suggested that, due to topological constraints, rings in the melt may assume a more compact shape than Gaussian chains. In this paper, we exploit the availability of narrow fractions of perdeuterated linear and cyclic polydimethylsiloxane (PDMS) and, through the analysis of the small angle neutron scattering (SANS) profiles, demonstrate the difference in scattering properties of linear and cyclic PDMS molecules. As expected for Gaussian chains, for the H/D linear PDMS samples, log-log plots of the scattered intensity versus scattering vector Q display a Q((-2)) dependence. However, for H/D cyclic blends, the scaling exponent is higher than 2, as predicted by computer simulations reported in the literature. We show that cyclic molecules in bulk display the characteristic maximum in plots of scattered intensity versus Q((-2)) that is expected on the basis of Monte Carlo calculations and from the Casassa equation [E. F. Casassa, J. Polym. Sci. A 3, 605 (1965)]. It is also shown that, for rings, the Debye equation [P. Debye, J. Appl. Phys. 15, 338 (1944)] is no longer appropriate to describe the SANS profiles of H/D cyclic blends, at least up to M(w) approximately 10 000. For these samples, the Casassa form factor gives a better representation of the SANS data and we show that this function which was developed for monodisperse cyclics is still adequate to describe our slightly polydisperse samples. Deviations from all above observations are noted for M(w)>11 000 and are attributed to partial contamination of cyclic samples with linear chains. The failure of both the Debye and the Casassa form factors could be due to contamination of the cyclic fractions by linear polymers or to a real conformational change.