Dynamic depolarized light scattering and nuclear magnetic relaxation studies of oligo- and poly(methyl methacrylate)s in dilute solution

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ABSTRACT:The object of this review article is to introduce and digest Yamakawa's new book, "Helical Wormlike Chains in Polymer Solutions." A brief description is given of a new model for polymer chains, called the helical wormlike chain, and its applications to dilute solution behavior of polymers, that is, equilibrium, steady-state transport, and dynamical properties. The description follows most of the chapters of the book. It is shown that all theoretical and experimental investigations on the basis of this model provide a new framework of polymer solution science, which takes the place of the Flory-Kirkwood framework.KEY The object of this review article is to introduce and digest Yamakawa's new book 1 entitled" Helical Wormlike Chains in Polymer Solutions." As stated in its Preface, it is intended to give a comprehensive and systematic description of the statistical-mechanical, transport, and dynamic theories of dilute solution properties of both flexible and semiflexible polymers, including oligomers, developed on the basis of the "helical wormlike (HW) chain" model, along with an analysis of extensive experimental data. Much of the material in the book arises from his research reported since the year of publication of his earlier (1971) book. 2 The results of this research were already very often reviewed. 3 -7 Now the framework of polymer solution theory constructed by Flory 8 • 9 consists of three concepts: (I) the excluded-volume effect in long flexible (Gaussian) polymer chains, (2) the universality of the unperturbed ( EJ) state without that effect, and (3) the rotational isomeric state (RIS) model for (unperturbed) real chains of arbitrary length. The study of dilute solution behavior of flexible polymers based on the first two concepts was almost completed around 1970, leading to the so-called two-parameter (TP) theory. 2 It is at almost the same time that the statistical-mechanical method for treating the RIS model, which takes account of the details of the chemical structure and local conformations of the chain on the atomic level, was established by Flory and coworkers.9 However, for many equilibrium and steadystate transport problems on stiff or semiflexible polymers, such details are not amenable to mathematical treatments, and moreover are often unnecessary to consider. Some coarse-graining may then be introduced to replace this discrete model by continuous models. In 1976, for this purpose we proposed a general continuous model, called the HW chain. 10 This new model may describe equilibrium conformational and steady-state transport properties of all kinds of real chains, both flexible and stiff, on the bond length or somewhat longer scales, thus bridging a gap between the RIS model and the classical continuous model, that is, the KratkyPorod (KP) wormlike chain. 11 Specifically, the transport t Professor Emeritus.

Section: Dynamic Depolarized Light Scatteringmentioning

confidence: 99%

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

Yamakawa

1999

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“…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 .…”

Section: Hw Theorymentioning

confidence: 99%

“…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 .…”

Section: Hw Theorymentioning

confidence: 99%

“…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.…”

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confidence: 99%

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

Nakatsuji

Yoshizaki

Yamakawa

2005

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ABSTRACT:The spin-lattice relaxation time T 1 , spin-spin relaxation time T 2 , and nuclear Overhauser enhancement NOE were determined from nuclear magnetic relaxation measurements on five well-fractionated samples of poly-(n-hexyl isocyanate) in the range of weight-average molecular weight M w from 1:65 Â 10 4 to 5:71 Â 10 4 in n-hexane at 25 C. It is found that T 1 increases and T 2 decreases monotonically with increasing M w in the range of M w examined, As is well known, the spin-lattice relaxation time T 1 , spin-spin relaxation time T 2 , and nuclear Overhauser enhancement NOE for 13 C nuclei may be expressed in terms of time-correlation functions of components of the dyadic of the internuclear vector 13 C! 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. 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). In the present paper, therefore, we examine experimentally the dependence on M of T 1 , T 2 , and also NOE for poly(n-hexyl isocyanate) (PHIC) as another example of semiflexible polymers. We note that DuPré and Wang 8 have determined T 1 , T 2 , and NOE for a PHIC sample with the weight-average molecular weight M w ¼ 3:39 Â 10 4 , and therefore have not examined the dependence of these quantities on M w .PHIC is a typical semiflexible polymer whose molecular characterization has almost completely been done by an analysis of dilute solution properties on the basis of the Kratky-Porod (KP) wormlike chain model. 9,10 Specifically, the KP model parameters for PHIC, i.e., the static stiffness parameters À1 , the shift factor M L as defined as the molecular weight per unit contour length of the KP chain, and the hydrodynamic diameter d, have been determined rather unambiguously.11 Thus, from a comparison of present experimental data with the theory previously 12 developed for the generalized KP chain [a special case of the helical wormlike (HW) chain] 10 by the use of the established values of the KP model parameters, 11 we may verify its validity. This is the main purpose of the present paper.A remark should be made ...

“…We have already investigated T 1 and NOE for atactic polystyrene (a-PS), 6 atactic poly(methyl methacrylate) (a-PMMA), 7 and isotactic (i-) PMMA, 8 and compared the results with those for À , [6][7][8] and found that T 1 and NOE are closely correlated with À , as mentioned in the INTRODUCTION in the preceding paper. 1 Thus the purpose of the present paper is to examine whether such a close correlation holds also for a-PMS.…”

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confidence: 93%

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

Osa

Ueda

Yoshizaki

et al. 2005

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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