First Cumulant of the Dynamic Structure Factor for Polymers in Θ Solvents. Effects of Chain Stiffness and Local Chain Conformation

Abstract

The first cumulant Ω(k) of the dynamic structure factor as a function of the magnitude k of the scattering vector was determined from dynamic light scattering (DLS) measurements for two atactic poly(α-methylstyrene) (a-PαMS) samples with weight-average molecular weights Mw=3.22×106 and 5.46×106 in cyclohexane at 30.5 °C (Θ) and for one polyisobutylene (PIB) sample with Mw=6.63×106 in isoamyl isovalerate at 25.0 °C (Θ). The translational diffusion coefficient was also determined from DLS measurements for the a-PαMS sample with the larger Mw and for the PIB sample in the same solvent conditions. The mean-square radius of gyration was determined from static light scattering measurements for the PIB sample. From a comparison of the present data for a-PαMS and PIB along with the previous ones for atactic polystyrene and poly(n-hexyl isocyanate) with the helical wormlike chain theory, it may be concluded that the universality predicted by the Gaussian chain theory for the plot of η0Ω(k)/kBTk3 against 1/2k cannot be realized for flexible polymers even with very high Mw (\\simeq106–107), and that the height of the plateau in the k3-region depends on chain stiffness and local chain conformation, where η0 is the solvent viscosity, kB the Boltzmann constant, and T the absolute temperature.