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

Abstract

ABSTRACT:The spin-lattice relaxation time T 1 and nuclear Overhauser enhancement NOE were determined for three samples of atactic oligo-and poly(-methylstyrene)s (a-PMS) with weight-average degree of polymerization x w ¼ 2, 3, and 67.1 in cyclohexane at 30 C. A comparison is made of the present data for T 1 and NOE with the helical wormlike (HW) chain theory, and it is shown that the theory may explain well the data for large x w (& 10). For smaller x w , the rigid sphere model having the radius equal to the apparent root-mean-square radius of gyration of the HW chain fails to give a quantitative explanation of T 1 in contrast to the case of the relaxation time À determined from dynamic depolarized light scattering measurements, indicating that the nuclear magnetic relaxation and dynamic depolarized light scattering cannot be described in terms of a common single relaxation time. However, it is shown that there is an effective (mean) magnetic relaxation time M approximately equal to 0:6 À . From a comparison of the present results for T 1 for a-PMS with previous ones for typical flexible polymers, it is also shown that the behavior of T 1 for them, including a-PMS, may be consistently explained by the use of M (proportional to À ).[DOI 10.1295/polymj.37.14] KEY WORDS Poly(-methylstyrene) / Nuclear Magnetic Relaxation / Spin-Lattice Relaxation Time / Nuclear Overhauser Enhancement / Helical Wormlike Chain / In the preceding paper, 1 we have examined the behavior of the relaxation time À defined by the reciprocal of the half-width at half-maximum of the spectrum J À of the excess depolarized component of the light scattered by atactic oligo-and poly(-methylstyrene)s (a-PMS) in cyclohexane at 30.5 C (Â). The quantity À represents a mean of relaxation (correlation) times of time-correlation functions of the spherical tensor components of the polarizability tensor affixed to the repeat unit of a polymer chain. In the framework of the dynamic theory for the (unperturbed) helical wormlike (HW) chain, 2,3 those timecorrelation functions are associated with the subspace LðnÞ ¼ 2ð1Þ (of full Hilbert space) spanned by the basis set with the ''total angular momentum quantum number'' L ¼ 2 and the number of ''excited'' subbodies n ¼ 1. The spin-lattice relaxation time T 1 and nuclear Overhauser enhancement NOE determined from nuclear magnetic relaxation measurements may also be written in terms of the time-correlation functions of the same class 2(1), 2,4,5 and therefore have a close relation to À . In the present paper as a continuation of the preceding one, 1 we report results of a nuclear magnetic relaxation study of a-PMS.We have already investigated T 1

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

“…1,8 Here, by the term ''helical nature,'' we mean that the chain tends to retain large and clearly distinguishable helical portions in dilute solution. 1 In the present and following 9 papers, we proceed to make a study of dynamical properties of a-PMS and its oligomers at Â. We have already investigated as those properties the spectrum J À of the (excess) depolarized scattered component, spin-lattice relaxation time T 1 , and nuclear Overhauser enhancement NOE for atactic polystyrene (a-PS), 10 a-PMMA, 11 and isotactic (i-) PMMA.…”

“…Results of nuclear magnetic relaxation measurements and their analysis are reported in the following paper. 9 …”

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 .…”

“…The dimensionless parameters r 1 t =3 0 a and r 2 r =a 2 t with 0 the solvent viscosity are used in place of t and r themselves. The values of r 1 is set equal to 1, as usually done, [3][4][5][6]12,21 and r 2 as an adjustable parameter is determined from a best fit of the theoretical values to the data for T 1 , as previously done. In Figure 1, the heavy solid, dashed, and dotted curves represent the generalized KP theoretical values of T 1 , T 2 , and NOE, respectively, so calculated from eqs 1-7 with r 2 ¼ 320 along with the above mentioned values of the parameters, where N has been converted to M w by M w ¼ NM 0 , ðQ 0 pk Þ 2 in eq 5 has been replaced by N À1 , and the value 0.299 cP has been used for 0 for n-hexane at 25 C. The crude subspace approximation is invalid for small M (for N .…”

“…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. Unfortunately, however, such literature data for typical semiflexible polymers are not available except those obtained by Budd et al 7 for T 1 and T 2 for poly(-benzyl L-glutamate) (PBLG).…”