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 A, and ML = 39.8 A-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 c...