Mean-Square Radius of Gyration of Oligo- and Poly(α-methylstyrene)s in Dilute Solution

Abstract

The mean-square radius of gyration 〈S2〉 was determined from small-angle X-ray and light scattering measurements for 20 samples of atactic oligo- and poly(α-methylstyrene)s (a-PαMS), each with the fraction of racemic diads fr = 0.72, in the range of weight-average molecular weight from 6.48 × 102 (pentamer) to 3.22 × 106 in cyclohexane at 30.5 °C (ϑ). The ratio 〈S2〉/xw as a function of the weight-average degree of polymerization xw first increases steeply for xw ≲ 20, then passes through a flat hump at xw ≃ 40, and finally approaches its asymptotic value for xw ≳ 1 ×103. On the basis of the helical wormlike (HW) chain model the HW model parameters are λ-1κ0 = 3.0, λ-1τ0 = 0.9, λ-1 = 46.8 Å, and ML = 39.8 Å-1, where κ0 and τ0 are the differential-geometrical curvature and tortion, respectively, of the characteristic helix of the HW chain taken at the minimum zero of its elastic energy, λ-1 is the stiffness parameter, and ML is the shift factor defined as the molecular weight per unit contour length of the chain. The local chain conformations of a-PαMS are discussed in detail on the basis of the above values of the model parameters and compared with those of atactic polystyrene (fr = 0.59), atactic poly(methyl methacrylate) (a-PMMA) (fr = 0.79), and isotactic PMMA (fr ≃ 0.01) previously studied. It is then concluded that the a-PαMS chain tends to retain large and clearly distinguishable helical portions in dilute solution like the a-PMMA chain, as was expected from their chemical structures, although the helical nature of the former is somewhat weaker. To illustrate the situation, pictures are given of representative instantaneous contours of HW Monte Carlo chains for the above four polymers.