Small-angle X-ray scattering from polystyrene polymacromonomers in cyclohexane

Abstract

Small-angle X-ray scattering measurements have been made on seven polymacromonomer samples consisting of polystyrene with a fixed side chain length of 15 styrene residues in cyclohexane at 34.5°C to obtain the z-average mean-square radius of gyration 〈S2〉z and the particle scattering function P(θ). The dependence of 〈S 2〉z on the weight-average molecular weight M w, which ranges from 5.1 × 103 to 1.8 × 105, is described by the wormlike chain with the model parameters explaining previous light scattering 〈S2〉z data for high molecular weights (6 × 105-7 × 106), when the effect of the chain diameter d and that of side chains near the main-chain ends on the polymacromonomer contour length L are incorporated into analysis. Scattering profiles in the form of the Kratky plot are also explained by the recent theory for the wormlike chain with a circular cross section unless the axial ratio L/d is less than 2, i.e., unless Mw is lower than 2.6 × 104. The conventional cross-section plot, i.e., the plot of ln[kP(θ)] vs. k2 with slope -d2/16, is found to be applicable to samples with L/d > 2, where k denotes the magnitude of the scattering vector. It is concluded from further analysis of the 〈S 2〉z data combined with previous transport coefficient data that the wormlike cylinder model, a smeared model for regular comb polymers, consistently explains the molecular weight dependence of 〈S 2〉z, intrinsic viscosity, and translational diffusion coefficient for the polystyrene polymacromonomer in cyclohexane over a broad range of molecular weight. The applicability of a semiflexible comb model consisting of wormlike main and side chains to 〈S2〉 z and P(θ) is also examined.