Conformational Disorder and Its Dynamics Within the Crystalline

13C 2D exchange NMR under conditions of magic-angle-spinning has revealed that the ... call a macromolecular condis crystal. The presence of motion wi...
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Chapter 14

Conformational Disorder and Its Dynamics Within the Crystalline Phase of the Form II Polymorph of Isotactic Poly(1-butene) 1

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Haskell W. Beckham , Klaus Schmidt-Rohr , and H. W. Spiess 1

School of Textile and Fiber Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0295 Max-Planck-Institut für Polymerforschung, Postfach 3148, D-55021 Mainz, Germany

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C 2D exchange NMR under conditions of magic-angle-spinning has revealed that the metastable form II polymorph of isotactic poly(1butene) exhibits significant slow conformational exchange (in the milliseconds to seconds time regime) above the amorphous-phase glass transition. Comparison with spectra of the form I polymorph proves that this motion occurs within the crystalline regions. The observed dynamic conformational disorder within the crystalline regions of this semicrystalline polymer is characteristic of what some call a macromolecular condis crystal. The presence of motion within the crystalline regions is consistent with previous calculations of the conformational flexibility of this polymer.

Dynamic conformational disorder has recently been shown to accurately describe the chain motions within amorphous polymers above their glass transitions (T ) (1,2). The disordered nature of these materials provides a wide distribution of intermolecular environments, and therefore potentials, which manifests itself by a distribution of correlation times for the molecular motions activated above To. The motions themselves have been analyzed experimentally in terms of both conformational transitions (e.g., trans gauche), and rotational motions of individual segments resulting from various changes in the torsional angles. While amorphous-phase motions are relatively nondescript, the ordered nature of crystalline arrays typically restricts the motions to more discrete processes. Due to bonding and symmetry arrangements, the energetically allowed conformational movements of segments within such an environment are fewer than those allowed in a disordered amorphous region. Note, nevertheless, that large-angle reorientations of chains about their long axes are possible if the atomic positions are occupied by equivalent units before and after the reorientation. The presence of molecular motions within crystalline regions of semicrystalline polymers has been documented for some time (3). They have been attributed to the presence of dynamic mechanical α relaxations in semicrystalline polymers (4) and correlated with such bulk physical properties as solid-state g

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Current address: Department of Polymer Science and Engineering, University of Massachusetts, Amherst, MA 01003 0097-6156/95/0598-0243$12.00/0 © 1995 American Chemical Society In Multidimensional Spectroscopy of Polymers; Urban, M., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1995.

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extrudability and temperature-utility range (5). However, the detailed nature of some of these motions has only been revealed recently through the application of solidstate NMR techniques. A variety of molecular motions are being fully characterized and catalogued in detail in the scientific literature (6,7). Within the crystalline lamellae of semicrystalline polymers, one such motion proposed for some time is the helical jump (8,9) This involves the rotation of the chain about the helix axis by 360°w/m where m is the number of repeat units per η turns of the helix, accompanied by translation of the chain by one monomer unit. Thus, for a single monomer unit, the relative position to the surrounding polymer chains within the crystallite is the same before and after the jump. For the following semicrystalline polymers exhibiting α relaxations, helical jump motions have been shown to occur at temperatures between the glass transition and melting transitions: (6) polyoxymethylene (10), isotactic polypropylene (77), polyethylene (72), and polyoxyethylene (13). Molecular model calculations indicate the mechanism involves a "defect" diffusion of the helix rotation through the crystal lattice, as opposed to a rigid-rod rotation of the crystal stem (although this latter process becomes more important as crystal thickness decreases) (14,15). Other types of crystalline-phase motions include conformational changes (16), functional group jumps, phenyleneringflips, and librations (17). For each of the polymers shown to exhibit helical jump motions (POM, iPP, ΡΕ, PEO), the crystalline structure provides a relatively well-defined conformational energy landscape through which the chain stems jump between successive energy minima (72). None of these polymers have flexible side groups. The presence of side-group mobility might "smear out" a conformational energy map thereby making any main-chain motion less discrete. For longer side groups, a type of liquid-crystal­ like translation/rotation might be expected, similar to those shown for discotic liquid crystals with flexible side chains (18,19). Another alternative is that the side chains would interdigitate in such a fashion that any main-chain motion at all would be prevented. These possibilities are being explored by the investigation of the chain dynamics of isotactic poly(l-butene) (PB), which has an ethyl side group, and isotactic poly(4-methyl-l-pentene), which consists of isobutyl side groups. The results for PB are presented here. Polymorphism is quite common among the semicrystalline polyolefins. When processed from the melt, isotactic poly(l-butene) forms a metastable crystalline structure (form Π, II3 helix) (20) that transforms over the course of days to a more stable structure (form I, 3\ helix) (27). This conversion is greatly accelerated by the application of external stresses (22,23). Solid-state CP/MAS NMR studies on PB have been conducted (24) and revealed the isotropic chemical shifts to be dependent on the chain conformation of the respective helical microstructure: forms I and Π, along with a form ΠΙ (4i helix). While form ΙΠ is prepared by crystallization from solution and therefore is not as commercially significant (25), forms I and Π are well-known by melt processers of PB. Wideangle X-ray diffractograms are shown in Figure 1 and confirm the existence of the different respective crystalline structures and high crystalline content for both forms: form I is hexagonal, form Π is tetragonal. Dynamic mechanical spectra show no indication of motional processes above the glass transition (T = -20 °C) for either form (26). However, the crystalline transformation can only occur through some type of chain movement. g

Experimental Isotactic poly(l-butene) of high molecular weight was obtained from Aldrich. Differential scanning calorimetry (DSC) with a Mettler DSC 30 (10 °C/min) indicated T = 130 °C for PB (form I). After heating this sample to 200 °C and m

In Multidimensional Spectroscopy of Polymers; Urban, M., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1995.

BECKHAM ET AL.

Form II Polymorph of Isotactic Poly (1-butène)

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TWO - THETA

Figure 1. Wide-angle X-ray diffraction patterns of isotactic PB. Bottom diffractogram was taken one hour after cooling from the melt; top diffractogram is the same sample after annealing at room temperature for two weeks.

In Multidimensional Spectroscopy of Polymers; Urban, M., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1995.

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holding for five minutes before cooling, the subsequent DSC scan revealed a melting peak at 115 °C indicating production of the form Π (27). For both forms the glass transition was detected at -23 °C. Wide-angle X-ray diffractograms of PB melt-cast films were obtained with a Siemens D-500 diffractometer operated in reflection mode. The initial production of form Π from the melt was confirmed. At ambient temperature with no applied stress, the transformation to form I was nearly complete after about 10 days. The crystallinity was similar for both forms: 40% in form Π and 50% in form I. The as-received polymer pellets were prepared for NMR studies by melting at 150 °C in a cylinder-shaped mold (5.5 mm diameter) followed by slow cooling to room temperature. For the PB, form Π was generated by simply melting the solid polymer plug inside the rotor. The transformation from form II to form I is definitely accelerated by the applied stress of magic-angle spinning (MAS), the consequences of which are discussed below. NMR measurements were conducted on a Bruker MSL 300 spectrometer (7 Tesla). Proton and carbon 90° pulses of 3.8 - 4.2 were used. The C 2D exchange NMR experiment has been described previously (6,28,29,30). With magic-angle spinning (31), changes in isotropic chemical shifts, reflecting conformational changes of the polymer, can be detected as off-diagonal exchange intensity. Without magic-angle spinning, exchange due to isotropic chemical shift changes is superposed with exchange intensity due to reorientation of anisotropic chemical shift tensors. All experimental parameters were optimized and kept constant for the same polymer at different temperatures. 1 3

Results and Discussion 1 3

In Figure 2 are displayed the solid-state C CP/MAS spectra of PB forms I and Π. The well-defined peaks of form I can be identified with the chemical structure; the splitting of the methylene peaks indicates some nonequivalent solid-state packing due to the arrangement of the chains within the crystallites. The crystalline structure has hexagonal symmetry, with neighboring left- and right-handed helices which may exist either as isoclined or anticlined pairs in equal probability (32). The resulting two local environments affect only the methylene groups to produce two peaks of equal intensity. As opposed to the α modification of isotactic polypropylene (33,34), this coexistence is not disorder, but rather the ability of either chain modification to fit into the crystal lattice. Most significant for the present study is the poorly resolved methylene and methine region of the form Π spectrum as compared to the form I spectrum. The broadening may be related to dynamics, structure, or both. It cannot be structure-related alone because the broad peaks would signify a distribution of isotropic chemical shifts so large that an amorphous material might be expected. The WAXD diffractogram of Figure 1 confirms the crystalline nature of PB form Π. That the broadening is related to dynamics is proven in Figure 3, which is the CP/MAS spectrum of the same sample of PB form II taken at 273 K. Some resolution is revealed upon cooling of the sample. Thus, the broadening of the roomtemperature spectrum is due to some type of chain motions present in the PB form Π. However, the breadths of the peaks compared to the form I spectrum indicates that the room-temperature broadening is related to both structure and dynamics. Instead of well-defined chemical shifts, the form Π crystalline structure at 273 Κ appears to be characterized by some distribution of isotropic chemical shifts for each chemical site. The chemical shifts for both forms are listed in Table I, along with the chemical shifts reported for form ΙΠ (24). For form Π, the chemical shifts are reported as ranges. Because these ranges encompass the chemical-shift values of both the form I and form HI, the molecular conformations of form Π must also include those of form I and form ΙΠ.

In Multidimensional Spectroscopy of Polymers; Urban, M., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1995.

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14.

Form II Polymorph of Isotactic Poly (1-butène)

BECKHAM ET AL.

1

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I

50

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I

ί

40

I

ι

30 ΡΡΜ

I

ι

20

I



10

ι

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Figure 2. C CP/MAS spectra of isotactic PB forms I and II at room temperature. The spinning speed is 4 kHz. Peaks are labeled for the form I ("sc" means side-chain). WAXD-determined helical structures are shown as projections along the helix axis.

I

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I 40

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I 20

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PPM 1 3

Figure 3. C CP/MAS spectrum of isotactic PB form Π at 273 K. Spinning speed is 4 kHz.

In Multidimensional Spectroscopy of Polymers; Urban, M., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1995.

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Table I. Isotropic Chemical Shifts of Isotactic Poly(l-butene) polymorph

CH2

CH

sc-CH2

form 1

38.9, 38.2

32.1

27.3, 26.5

13

form II

44 - 35.4

38.5 - 30.7

30.7 - 24.8

14.8-8.8

28.4

14.5, 13.7

a

form lll 41.2 36.6 values adaptedfromthose reported in ref. 24. "sc" means side-chain.

CH

b

3

a

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b

Since the form Π obviously contains a variety of isotropic chemical shifts, as well as some degree of chain mobility, exchange among these chemical shifts is foreshadowed. This is proven in the * C 2D exchange NMR spectra of Figure 4 measured under conditions of magic-angle spinning. The methylene and methine regions of 2D exchange spectra for form Π just above and below T are shown. Above Tg, the off-diagonal exchange intensity is evidence for conformational exchange with timescales in the milliseconds to seconds regime (the methyl region also shows the off-diagonal exchange signal). Upon lowering the temperature below Tg, these motions cease as indicated by all signal intensity confined to the diagonal. Tnis diagonal spectrum contains not only the conformationally broadened peaks of form Π, but also narrower peaks characteristic of form I. It is known that stress accelerates the transition from form Π to form I in PB (35); this effect due to MAS has also been observed before. The ratio of the form I narrow peaks to form Π broad peaks continuously increases under constant MAS and after about three days, the form I peaks dominate the spectrum. The origin of the conformational exchange can be the crystalline phase, amorphous phase, or both. For the form Π of PB, it is straightforward to establish the origin of the exchange by comparing the spectra with those of form I. The C 2D exchange spectra of static samples of both forms are shown in Figure 5. By not doing the exchange experiment under MAS, any type of exchange, due to changes in isotropic chemical shifts or torsional reorientations, can be detected. The spectra of Figure 5 were measured at 258 K, the same temperature at which the conformational exchange was observed for the form Π (Figure 4). Besides a small low-intensity signal under the maximum, the form I spectrum consists of a diagonal. Especially compared to the form Π spectrum, no significant exchange intensity is observed. Thus, no significant molecular motions in the millisecond to second time regime are present, neither from the crystalline nor from the amorphous regions. Since the amorphous regions are practically identical in both forms with respect to content (see the X-ray diffractograms of Figure 1) and dynamics (same T ), then the observed conformational exchange in form Π above T is attributed to motions within the crystalline regions. Although such dynamic conformational disorder is well-known in amorphous polymers (or regions) above Tg, it has never before been observed within crystalline regions by 2D exchange NMR, and may in fact be the first such evidence of a macromolecular condis crystal (36). For a mobile and conformationally disordered structure to exhibit a sharp Xray pattern is not contradictory. There are many examples of such materials. The presence of dynamic conformational disorder does not preclude the existence of long-range positional order. For plastic crystals (57), long-range positional order is present despite orientational dynamic disorder. These materials certainly have relatively sharp X-ray reflections. Even with dynamic conformational disorder, 3

g

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g

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In Multidimensional Spectroscopy of Polymers; Urban, M., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1995.

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Form II Polymorph oflsotactic Poly (I-butène)

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1 3

Figure 4. C 2D MAS exchange spectra for isotactic PB form Π (T = 250 K): top, T + 8 K; bottom, Tg - 7 K. Only the methylene and methine regions of the spectra are shown. Partial conversion of form Π to form I is observed in the spectra. g

g

In Multidimensional Spectroscopy of Polymers; Urban, M., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1995.

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MULTIDIMENSIONAL SPECTROSCOPY OF POLYMERS

Form I

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Form II

1 3

Figure 5. C 2D exchange spectra of isotactic PB at Tg + 8 K: left, form Π; right, form I. Contour plots are shown below their respective stacked plots.

In Multidimensional Spectroscopy of Polymers; Urban, M., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1995.

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Form II Polymorph of Isotactic Poly(l-butene)

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long-range orientational as well as positional order may be preserved. The spatial autocorrelation function can retain a periodic part even in the presence of local disorder, and therefore its Fourier transform, the scattering pattern, can exhibit sharp peaks. The effects of molecular dynamics in X-ray diffraction studies are handled by a thermal-motion analysis (38), which provides structures with nuclei characterized by ellipsoids whose size represents the uncertainty in atomic positioning. A usual consequence of mobility-induced disorder is that the intensities of higher-order reflections are reduced. Comparison of the diffractograms of Figure 1 reveals that this is the case for form Π in relation to form I. Conformational energy maps have been computed for both forms of PB (39). For the form Π, it has been shown that the potential energy minima describing the preferred conformations of the backbone are very flat and broad (40,41). Thus, the conformational flexibility exists. The frozen-in conformations of form Π may be deduced from Figure 3 to cover isotropic chemical shift ranges of 8 - 9 ppm for the backbone carbons, and 5 - 6 ppm for the side-group carbons. These can be understood in terms of the semiempirical γ gauche effect (42), which has recently been quantitatively reproduced by ab initio calculations (43). Carbons whose γ substituents are in gauche conformations will experience an additional nuclear shielding of 4 - 5 ppm per γ gauche substituent. For a polymethylene chain, an 8 - 9 ppm spread would indicate that the two γ gauche substituents exist across the range from both trans to both gauche. Due to the presence of the ethyl side groups in PB, however, each backbone carbon has four γ substituents. The combination of shieldings from the four γ substituents easily provides the observed range in isotropic chemical shifts. The backbone γ substituents of a selected backbone carbon need not be both trans or both gauche. At the same time, the two side-chain carbons have only two γ gauche substituents each, which explains the smaller 4 - 5 ppm range of observed isotropic chemical shifts. The foregoing discussion also excludes sidegroup motion alone as the origin of the exchange, and side-group conformational disorder as the origin of the chemical-shift dispersion. The reason is that the chemical shifts of the backbone methine carbon would not be affected since there is no γ substituent for this carbon in the side group. The data of Figures 3 and 4 clearly indicate that the methine chemical shift is affected by the motion. The transformation from the metastable form Π to the stable form I can be followed spectroscopically as the form I peaks grow at the expense of the form Π signal. It can also be followed with X-ray diffraction in which peaks attributed to both forms can be observed at times intermediate between the initial melting and the complete conversion. From the data presented here, some generalizations may be made regarding this transformation. The form Π helix is in a constant state of motion in which the nuclei oscillate via rotations about torsion angles described by very flat potentials. As conformational space is explored via these motions, the torsional angles corresponding to the stable form I can be discovered. The energy barrier separating the form I from the form Π is very small. It is perhaps instructive to point out that for screws of opposite handedness (representing helices with side chains), the closest packing density is achieved for tetragonal symmetry (44). Local preferred chain interactions and packing of side chains are not important for screws. When the PB solidifies from the melt, the production of form Π (tetragonal) is obviously kinetically favored. Another semicrystalline polymer shown to exhibit similar motional behavior is trans- 1,4-polybutadiene (45). Using solid-state C and H NMR, the dynamics of the high-temperature polymorph of this polymer was characterized as conformational interconversions superposed with diffusive rotations. The presence of such motions in PB could result in a helix reversal, which would convert an isoclined helix into an anticlined helix. For the form I helix, such an arrangement is isoenergetic. For this form I helix, only the position of the methylene groups would be changed after the 1 3

2

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motion. As discussed above, the statistical placement of such helices within crystallites results in the observed splitting of the methylene peaks into two peaks of equal height. For the form Π helix, however, a helix reversal would not leave all atoms in the same position thus providing a source of exchange signal as observed in Figure 5. The motion would proceed along the helix direction as a defect diffusion, analogous to the helical jump motions observed for other semicrystalline polymers without side groups, except that the motion in PB would be superposed on diffusive rotations. In fact, the presence of helical jump motions cannot be discounted; the disordered nature of the form II helix coupled with the presence of diffusive rotations, could very well lead to an exchange pattern as that shown in Figure 5 for helical jumps (6). Simulations and isotopic labeling studies will further resolve the motional mechanism. Conclusions Dynamic conformational disorder within the crystalline regions of the form Π polymorph of isotactic poly(l-butene) has been proven to occur at temperatures above the glass transition (T = 250 °C). The crystalline-phase chain motions were directly revealed as off-diagonal exchange intensity in a 2D solid-state NMR exchange experiment under conditions of MAS. Comparison of form Π spectra with those of form I containing equivalent amorphous regions (same T and WAXDdetermined content) confirm the crystalline origin of the off-diagonal exchange signal. The existence of such crystalline chain mobility is undoubtedly related to the transformation of the metastable form II to stable form I of this semicrystalline polyolefin. The exact nature of the motion was postulated and is under further investigation. g

g

Acknowledgment Support for HWB was provided by an NSF-NATO Postdoctoral Fellowship. Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

Zemke, K.; Chmelka, B. F.; Schmidt-Rohr, K.; Spiess, H. W. Macromolecules 1991, 24, 6874. Zemke, K.; Schmidt-Rohr, K.; Spiess, H. W. Acta Polymer 1994, 45, 148. McCrum, N. G.; Read, Β. E.; Williams, G. Anelastic and Dielectric Effects in Polymeric Solids; Dover: New York, 1991. Boyd, R. H. Polymer 1985, 26, 323. Aharoni, S. M.; Sibilia, J. P. J. Appl. Polym. Sci. 1979, 23, 133. Schmidt-Rohr, K.; Spiess, H. W. Multidimensional Solid-State NMR and Polymers; Academic Press: London, 1994. Schmidt-Rohr, K.; Kulik, A. S.; Beckham, H. W.; Ohlemacher, Α.; Pawelzik, U.; Boeffel, C.; Spiess, H. W. Macromolecules 1994, accepted. Fröhlich, H. Proc. Phys. Soc. Lond. 1942, 54, 422. Boyd, R. H. Polymer 1985, 26, 1123. Kentgens, A. P. M.; de Boer, E.; Veeman, W. S. J. Chem. Phys. 1987, 87(12), 6859. Schaefer, D.; Spiess, H. W.; Suter, U. W.; Fleming, W. W. Macromolecules 1990, 23, 3431. Schmidt-Rohr, K.; Spiess, H. W. Macromolecules, 1991, 24, 5288. Spiess, H. W.; Schmidt-Rohr, K. Polym. Prepr. (Am. Chem.Soc.,Div. Polym. Chem.) 1992, 33(1), 68. Syi, J.-L.; Mansfield, M. L. Polymer 1988, 29, 987. Rutledge, G. C.; Suter, U. W. Macromolecules 1992, 25, 1546.

In Multidimensional Spectroscopy of Polymers; Urban, M., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1995.

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16. Hirschinger, J.; Schaefer, D.; Spiess, H. W.; Lovinger, A. J. Macromolecules 1991, 24, 2428. 17. Hirschinger, J.; Miura, H.; Gardner, Κ. H.; English, A. D. Macromolecules 1990, 23, 2153. 18. Werth, M.; Vallerien, S. U.; Spiess, H. W. Liq. Cryst. 1991, 10, 759. 19. Leisen, J.; Werth, M.; Boeffel, C.; Spiess, H. W. J. Chem. Phys. 1992, 97, 3749. 20. Jones, A. T. Polym. Lett. 1963, 1, 455. 21. Jones, A. T. Polymer 1966, 7, 23. 22. Weynant, E.; Haudin, J. M.; G'Sell, C. J. Mat. Sci. 1982, 17, 1017. 23. Hong, K.-B.; Spruiell, J. E. J. Appl. Polym. Sci. 1985, 30, 3163. 24. Belfiore, L. Α.; Schilling, F. C.; Tonelli, A. E.; Lovinger, A. J.; Bovey, F. A. Macromolecules 1984, 17, 2561. 25. Holland, V. F.; Miller, R. L. J. Appl. Phys. 1964, 35, 3241. 26. Goldbach, G. Die Angew. Makromol. Chem. 1973, 29/30, 213. 27. Kishore, K.; Vasanthakumari, R. J. Macromol. Sci. - Chem. 1987, A24(l), 33. 28. Szeverenyi, N.; Sullivan, M. J.; Maciel, G. E. J. Magn. Reson. 1982, 47, 462. 29. Hagemeyer, Α.; Schmidt-Rohr, K.; Spiess, H. W. Adv. Magn. Reson. 1989, 13, 85. 30. Beckham, H. W.; Spiess, H. W. In NMR - Basic Principles and Progress 32; Blumich, B.; Kosfield, R., Eds.; Springer: Berlin, 1994. 31. Szeverenyi, Ν. M.; Bax, Α.; Maciel, G. E. J. Am. Chem. Soc. 1983, 105, 2579. 32. Natta, G.; Corradini, P.; Bassi, I. W. Del Nuova Cimento 1960, 15, 52. 33. Corradini, P.; Giunchi, G.; Petraconne, V.; Pirozzi, B.; Vidal, H. M. Gazz. Chim. Ital. 1980, 110, 413. 34. Corradini, P.; Guerra, G. Advances in Polymer Science 100; Springer: Berlin, 1992; p 183. 35. Gohil, R.; Miles, M.; Petermann, J. J. Macromol. Sci.-Phys. 1982, B21(2), 189. 36. Wunderlich, B.; Möller, M.; Grebowicz, J.; Baur, H. Advances in Polymer Science 87; Springer: Berlin, 1988. 37. Sherwood, N., Ed. The Plastically Crystalline State; J. Wiley & Sons: Chichester, 1979. 38. Dunitz, J. D. X-ray Analysis and the Structure of Organic Molecules; Cornell University Press: Ithaca, 1979; p 244. 39. Corradini, P.; Napolitano, R.; Petraconne, V.; Pirozzi, B. Eur. Polym. J. 1984, 20, 931. 40. Petraccone, V.; Pirozzi, B.; Frasci, Α.; Corradini, P. Eur. Polym. J. 1976, 12, 323. 41. Ajo, D.; Granozzi, G.; Zannetti, R. Makromol.Chem. 1977, 178, 2471. 42. Tonelli, A. E. NMR Spectroscopy and Polymer Microstructure; VCH: New York, 1989. 43. Born, R.; Spiess, H. W.; Kutzelnigg, W.; Fleischer, U.; Schindler, M. Macromolecules 1994, 27, 1500. 44. Wunderlich, B. Macromolecular Physics, Vol. 1; Academic: New York, 1973; p 86. 45. Möller, M. Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 1987, 28(2), 395. RECEIVED February 2, 1995

In Multidimensional Spectroscopy of Polymers; Urban, M., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1995.