First Cumulant of the Dynamic Structure Factor for Flexible Polymers. Excluded-Volume Effects

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 an atactic polystyrene (a-PS) sample with the weight-average molecular weight Mw=8.04×106 in toluene at 15.0 °C, an atactic poly(methyl methacrylate) (a-PMMA) sample with Mw=1.31×107 in acetone at 25.0 °C, an atactic poly(α-methylstyrene) (a-PαMS) sample with Mw=5.46×106 in toluene at 25.0 °C, and a polyisobutylene (PIB) sample with Mw=6.63×106 in n-heptane at 25.0 °C. It was also determined for the a-PS and a-PαMS samples in cyclohexane in the vicinity of the respective Θ temperatures (34.5 and 30.5 °C). The translational diffusion coefficient D was also determined from DLS measurements for the a-PS, a-PMMA, a-PαMS, and PIB samples in the same solvent conditions mentioned above. From a comparison of the present data with the previous ones for all the samples in the respective Θ temperatures, it is found that the observed dimensionless coefficient C of the k4-term in the expansion of Ω(k) does not almost depend on excluded volume, as predicted by the Tanaka–Stockmayer first-order perturbation theory of C, being in good agreement with the theoretical value for the Gaussian chain with nonpreaveraged hydrodynamic interaction. Further, it is found that the excluded-volume effect is very small on the quantity [Ω(k)/Dk2−1]/<S2>k2 over the whole range of k2 examined, where <S2> is the mean-square radius of gyration. Their first-order perturbation theory of the height of the plateau in the k3-region, however, cannot explain the behavior of the present experimental data. The disagreement between theory and experiment may be regarded as arising from the fact that the theory based on the Gaussian chain model cannot take proper account of effects of chain stiffness and local chain conformation.