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

Abstract

The mean-square radius of gyration 〈S 2 〉 was determined from small-angle X-ray and light scattering measurements for 20 samples of atactic oligo-and poly(R-methylstyrene)s (a-PRMS), each with the fraction of racemic diads fr ) 0.72, in the range of weight-average molecular weight from 6.48 × 10 2 (pentamer) to 3.22 × 10 6 in cyclohexane at 30.5°C (Θ). The ratio 〈S 2 〉/xw as a function of the weightaverage degree of polymerization xw first increases steeply for xw j 20, then passes through a flat hump at xw = 40, and finally approaches its asymptotic value for xw J 1 ×10 3 . On the basis of the helical wormlike (HW) chain model the HW model parameters are λ -1 κ0 ) 3.0, λ -1 τ0 ) 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-PRMS 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-PRMS 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.

Dynamic Depolarized Light Scattering by Oligo- and Poly(α-methylstyrene)s in Dilute Solution

“…In a new framework of polymer solution science on the basis of the helical wormlike (HW) chain model, 1,2 we have recently made a series of experimental studies [3][4][5][6] of dilute solution behavior of atactic oligoand poly(-methylstyrene)s (a-PMS) in the unperturbed  state. Specifically, we have determined the mean-square radius of gyration hS 2 i, 3 mean-square optical anisotropy hÀ 2 i, 4 scattering function, 5 and steady-state transport coefficients 6 in cyclohexane at 30.5 C (Â), 3 using well-fractionated a-PMS samples with the fraction of racemic diads f r regulated to be 0:72 AE 0:01.…”

“…Specifically, we have determined the mean-square radius of gyration hS 2 i, 3 mean-square optical anisotropy hÀ 2 i, 4 scattering function, 5 and steady-state transport coefficients 6 in cyclohexane at 30.5 C (Â), 3 using well-fractionated a-PMS samples with the fraction of racemic diads f r regulated to be 0:72 AE 0:01. 7 The results obtained have been analyzed to show that the a-PMS chain has rather large chain stiffness and strong helical nature like the atactic poly(methyl methacrylate) (a-PMMA) chain with f r ¼ 0:79.…”

Nuclear Magnetic Relaxation of Oligo- and Poly(α-methylstyrene)s in Dilute Solution

“…14 In Figure 2, the values of n CH T 1 and NOE calculated from eqs 1 and 2, respectively, with eqs 7-9 and with the above values of ! I , !…”

Fine characterization of oligomers and polymers in dilute solution

“…Fig. 3 shows the ratio hS 2 i=x w (hS 2 i inÅ 2 ) plotted against the weight-average degree of polymerization x w for a-PaMS in cyclohexane at 30.5 1C ðYÞ [3] and for a-PS in cylohexane at 34.5 1C ðYÞ [7][8][9] in a semi-logarithmic manner. The experimental values of hS 2 i have been determined from small-angle X-ray scattering measurements for the samples with x w t10 3 and from static light scattering measurements for those with x w \10 3 .…”

“…In this paper, we review our recent results of the fine characterizations carried out for two kinds of typical flexible polymers, atactic poly(a-methylstyrene) (a-PaMS) [3,4] and atactic polystyrene (a-PS) [5]. In Fig.…”