Dynamic Depolarized Light Scattering and Nuclear Magnetic Relaxation Studies of Oligo- and Polystyrenes in Dilute Solutions

Abstract

The (excess) power spectrum Jr of the depolarized component of scattered light was measured for 10 samples of oligo-and polystyrenes, each with the fraction of racemic diads f, -0.59, in the range of weight-average molecular weight Mw from 3.70 x 102 (trimer) to 1.01 X104 and also for cumene in cyclohexane at 34.5 °C (6) and in carbon tetrachloride at 25.0 °C. The spin-lattice relaxation time 7\ was also determined for the trimer through pentamer and the sample with the highest Mw, and the nuclear Overhauser enhancement NOE, for the trimer and the sample with the highest Afw, both in cyclohexane at 40 °C. It is found that Jr may be well represented in terms of a single Lorentzian independently of Mw and solvent and that the relaxation time rr as defined as the reciprocal of the half-width at half-maximum of Jr evaluated at infinite dilution increases with increasing M" and levels off to an asymptotic value in the limit of Mm in each solvent, being consistent with the recent theoretical results on the basis of the helical wormlike (HW) chain model. The reduced relaxation time k^Trrhc with k% the Boltzmann constant, T the absolute temperature, and t)o the solvent viscosity is found to be almost independent of solvent for each sample, its asymptotic value in the limit of Mw -*• ® being ca. 4 x 103 A3. A comparison is made of the present data for rr, T\, and NOE with the HW chain theory, and it is shown that the theory may explain satisfactorily the data in the range of Afw S 103 except for NOE. For Mv 5 10s, 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 all the data. An analysis of the interrelation between these three quantities leads to the simple picture that the nuclear magnetic relaxation is also governed, although approximately, by a single relaxation time identical with rr.

A New Framework of Polymer Solution Science. The Helical Wormlike Chain

“…(Such measures may be defined also for dielectric and magnetic correlation times.) Figure 17 shows double-logarithmic plots of rr/r7 against x for a-PS in cyclohexane at 34.SOC (8), 76 a-PMMA in acetonitrile at 44.0oC (8), 77 and i-PMMA in acetonitrile at 28.0°C (e). 78 The heavy solid, dashed, and dotted curves represent the respective HW theoretical values.…”

Fine characterization of oligomers and polymers in dilute solution

“…Fig. 17 shows double-logarithmic plots of t G =t 0 G against x w for a-PaMS in cyclohexane at 30.5 1C ðYÞ [33] and a-PS in cyclohexane at 34.5 1C ðYÞ [34], where t 0 G is the t G of cumene, which may be regarded as corresponding to the monomer of each of a-PaMS and a-PS. From this figure, it is seen that t G =t 0 G for each of the polymers first increases with increasing x w and seems to level off in the limit of x w !…”

“…We note that the value of static chain stiffness l À1 is larger for a-PaMS than for a-PS, as seen in Sections 3 and 4. The heavy solid and dashed curves represent the theoretical values calculated on the basis of the dynamic HW chain model [36] with the parameter values determined from hS 2 i and proper values of the dynamic model parameters for a-PaMS and a-PS, respectively.The light solid and dashed curves represent the values for the rigid sphere model [34] for a-PaMS and a-PS, respectively. The behavior of the data points for x w t10 may be explained well by the rigid sphere model while those for x w \10 deviate downward from the theoretical values for the rigid sphere model, indicating that the orientation of the polarizability tensor affixed to each repeat unit relaxes due to the rotation of the entire chain for the oligomer with x w t10 but the former becomes independent of the latter for x w \10.…”

Nuclear Magnetic Relaxation of Poly(n-hexyl isocyanate) in Dilute Solution. Effects of Chain Stiffness

“…7 Then the model parameters describing the generalized KP chain in the present case are À1 and 0 . The basic equations necessary for the present analysis are in principle the same as those for the HW chain ( ¼ 0) used in the previous analyses [3][4][5][6] of the data for the typical flexible polymers. In order to apply the HW (or generalized KP) chain to an analysis of dynamic properties, we use its dynamic version, the discrete HW (or generalized KP) chain, 10 which is composed of N identical rigid subbodies, each with the translational and rotatory friction coefficients t and r .…”

“…1 H from a 13 C nucleus to a bonded 1 H one if we simply assume that the nuclear magnetism of 13 C relaxes only due to the heteronuclear dipolar interaction. 1,2 We have made so far experimental studies of T 1 and NOE for backbone 13 C of typical flexible polymers such as atactic polystyrene, 3 atactic poly-(methyl methacrylate), 4 isotactic poly(methyl methacrylate), 5 and atactic poly(-methylstyrene). 6 In the case of flexible polymers, tumbling motions of repeat units are hardly coupled with the entire chain motion, so that values of T 1 , T 2 , and NOE are almost independent of the molecular weight M except for oligomers with very small M. In the case of semiflexible polymers, on the other hand, the former motions may be considered to be coupled with the latter even in the range of rather large M, and therefore the dependence of T 1 , T 2 , and NOE on M must be different from that for flexible polymers.…”