Synchrotron Small-Angle X-ray Scattering from Polystyrene Polymacromonomers in Toluene

Abstract

Synchrotron small-angle X-ray scattering (SAXS) measurements have been made on toluene solutions of six polystyrene polymacromonomer samples having a fixed side chain length of 15 styrene residues and ranging in the polymerization degree of the main chain N_w from 6.5 to 106 (in weight average) at 25 °C. The z-average mean-square radii of gyration <S²>_z from the present SAXS and previous light scattering as a function of N_w and the particle scattering functions P(θ) in the form of k²P(θ) against k (the magnitude of the scattering vector) are compared with theoretical values for three models: (a) the wormlike cylinder with a uniform cross section, (b) the wormlike chain with Gaussian density distribution within the cross-sectional plain, and (c) the touched-bead comb with wormlike main and side chains. Theoretical curves for the models (a) and (b) equally fit the data points for <S²>_z and k²P(θ) (for k<1nm⁻¹) with a set of model parameters consistent with that describing the previously determined N_w-dependence of intrinsic viscosity in toluene, but the latter model explains the P(θ) behavior up to a slightly larger k. The model (c) allows similarly good fits to <S²>_z and better fits to k²P(θ) over a wider k range if the Kuhn segment length of each side chain and the bead diameter are adjusted to values much larger than those expected for an isolated polystyrene molecule. The decoupling approximation to P(θ) invoked in the literature is also examined for the models (a) and (b).