The intrinsic viscosity [ ] was determined for 25 samples of isotactic oligo-and poly(methyl methacrylate)s (i-PMMA), each with the fraction of racemic diads ft -0.01, in the range of weight-average molecular weight Afw from 3.58 x 102 (trimer) to 1.71 x 10® in acetonitrile at 28.0 °C ( ). The translational diffusion coefficient D was also determined from dynamic light scattering measurements for 12 of them in the range of Afw from 6.58 x 102 (hexamer) to 9.46 x 10® under the same solvent condition. It is found that [77] is proportional to Af"1/2 for Afw £ 5 x 104 and its deviation from this asymptotic behavior is small even for smaller Afw, while D is inversely proportional to AfwV2 except for Aíw á 2 x 103. Such apparent Gaussian behavior of [77] and D over a wide range of Afw is the result expected from that previously obtained for the mean-square radius of gyration (S2). From an analysis of these transport coefficients on the basis of the helical wormlike (HW) chain model, it is shown that the above Mv dependences of [77] and D may be well explained by the HW theories with the values of the model parameters consistent with those previously determined from (S2). A comparison is also made of the present results for [ \ and D for i-PMMA with the previous ones for atactic (a-) PMMA with fT = 0.79. This leads to the confirmation of the previous conclusion derived from (S2) concerning the fT dependence of the chain stiffness and local chain conformation of PMMA. That is, the i-PMMA chain is of weaker helical nature than the a-PMMA chain that retains rather large and clearly distinguishable helical portions in dilute solution.

The mean-square radius of gyration

The translational diffusion coefficient D was determined from dynamic light scattering measurements for atactic (a-) and isotactic (i-) oligo-and poly(methyl methacrylate)s (PMMA) in acetone at 25.0 °C in the range of weight-average molecular weight Mw from 1.83 × 10 3 to 9.52 × 10 5 for the former and from 3.04 × 10 3 to 9.78 × 10 5 for the latter. For each PMMA, the values of the (perturbed) hydrodynamic radius RH (defined from D) in acetone were found to agree with those of the radius RH,Θ previously (and presently) obtained in the unperturbed (Θ) state (i.e., in acetonitrile at 44.0 °C for a-PMMA and at 28.0 °C for i-PMMA) in the oligomer region. The hydrodynamic-radius expansion factor RH was then determined correctly from the values of RH and RH,Θ. The results for RH as a function of the scaled excluded-volume parameter z ˜defined in the Yamakawa-Stockmayer-Shimada theory for the helical wormlike chain with excluded volume are consistent with the previous results for atactic polystyrene, poly(dimethylsiloxane), and polyisobutylene. This leads to the conclusion that the quasi-two-parameter scheme may be valid for RH as well as for the gyration-radius and viscosity-radius expansion factors RS and Rη irrespective of the large differences in chain stiffness, local conformation, and solvent condition. It is again found that the Barrett equation overestimates RH. This disagreement between theory and experiment may be explained only semiquantitatively by the Yamakawa-Yoshizaki theory, which takes account of the possible effect of fluctuating hydrodynamic interaction on RH. This indicates that it requires further theoretical investigations. It is also again found that RH coincides with Rη within experimental error over the whole range of Mw studied.

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 Mw ) 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 Mw. It is found that even in such a range of large Mw, the "universal" behavior cannot be realized; i.e., the plot of η0Ω(k)/kBTk 3 against 〈S 2 〉 1/2 k depends on the kind of polymer in the k 3 -region, where η0 is the solvent viscosity, kB 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.

The (excess) power spectrum J Γ of the depolarized component of scattered light intensity was measured for eight samples of isotactic oligo- and poly(methyl methacrylate)s (i-PMMA), each with the fraction of racemic diads f r ≃ 0.01, in the range of weight-average degree of polymerization x w from 4 to 70.1 in acetonitrile at 28.0 °C (ϑ). The spin−lattice relaxation time T 1 was also determined for the three samples with x w = 4, 5, and 70.1, and the nuclear Overhauser enhancement NOE, for the two samples with x w = 4 and 70.1, all in acetonitrile at 35 °C. As in the cases of atactic (a-) polystyrene (a-PS) and a-PMMA previously studied, it is found that J Γ may be well represented in terms of a single Lorentzian independently of x w and that the relaxation time τΓ defined from J Γ at infinite dilution increases with increasing x w and levels off to its asymptotic value in the limit of x w → ∞, being consistent with the recent theoretical prediction on the basis of the helical wormlike (HW) chain model. A comparison is made of the present data for τΓ, T 1, and NOE with the HW theory, and it is shown that the theory may explain satisfactorily the data in the range of x w ≳ 10, although semiquantitatively for τΓ. For x w ≲ 10, the rigid sphere model having the radius equal to the apparent root-mean-square radius of gyration of the HW chain may give a good explanation of τΓ but not of T 1, indicating that the dynamic depolarized light scattering and nuclear magnetic relaxation cannot be described in terms of a common single relaxation time. However, there is shown to be an effective (mean) magnetic relaxation time τM approximately equal to 0.6τΓ. From a comparison of the present results for τΓ for i-PMMA with the previous ones for a-PS and a-PMMA, it is shown that there is good correlation between the static and dynamic chain stiffness, the latter being defined as the ratio of the value of τΓ in the limit of x w → ∞ to that of the corresponding isolated repeat unit (monomer), as predicted by the HW theory.