Dynamic Structure Factor of Polystyrene and Poly(methyl methacrylate) in ϑ Solvents

Abstract

The dynamic structure factor and its first cumulant Ω( k ) as functions of the magnitude k of the scattering vector were determined from dynamic light scattering (DLS) measurements for two atactic polystyrene samples having the weight-average molecular weights M w = 6.40 × 10 6 and 8.04 × 10 6 in cyclohexane at 34.5 °C (ϑ) and for two atactic poly(methyl methacrylate) samples having M w = 4.82 × 10 6 and 1.31 × 10 7 in acetonitrile at 44.0 °C (ϑ). The translational diffusion coefficient and the mean-square radius of gyration 〈 S 2 〉 were also determined from DLS and static light scattering measurements, respectively, for all the samples except for the a-PS sample with the smaller M w . It is found that even in such a range of large M w, the “universal” behavior cannot be realized; i.e., the plot of η 0 Ω( k )/ k B Tk 3 against 〈 S 2 〉 1/2 k depends on the kind of polymer in the k 3 -region, where η 0 is the solvent viscosity, k B the Boltzmann constant, and T the absolute temperature. This result is consistent with the theoretical prediction on the basis of the helical wormlike (HW) chain model, although the HW theory cannot quantitatively explain the experimental data for the individual polymer.