Dynamics and Structure of Amorphous Polymers Studied by

Chapter 12

Dynamics and Structure of Amorphous Polymers Studied by Multidimensional SolidState NMR Spectroscopy 1

Downloaded by UNIV OF PITTSBURGH on May 3, 2015 | http://pubs.acs.org Publication Date: May 5, 1995 | doi: 10.1021/bk-1995-0598.ch012

Klaus Schmidt-Rohr

Chemistry Department, University of California, Berkeley, CA 94720 and Max-Planck-Institut für Polymerforschung, Postfach 3148, D-55021 Mainz, Germany Multidimensional exchange NMR techniques have been used to study dynamics, and conformational structure of amorphous polymers. The molecular motions underlying the β relaxations in poly(methyl methacrylate) (PMMA) and poly(ethyl methacrylate) (ΡΕΜΑ) were elucidated by two-dimensional (2D) and three-dimensional (3D) C exchange NMR of the carboxyl moiety. 3D NMR proves a relatively well-defined motion between two potential-energy minima for the ca. 50% of the sidegroups that are mobile. 2D spectra show that the sidegroup OCO planes undergo 180°(±20°) flips which are accompanied by a main-chain rotation about the local chain axis, with a 20° rms amplitude. In ΡΕΜΑ, the merging of the β and the α process has been investigated. At 20 Κ above the glass transition temperature T , most sidegroups undergo 180° flips. While the flip-angle imprecision remains similar to that of the pure β process, the amplitude of the rotations around the main-chain axis increases strongly with temperature according to the α-process WLF curve. Nevertheless, the reorientations of the chain axes themselves remain restricted up to more than 60 Κ above Tg. This anisotropic glass-transition dynamics is in contrast to the predominantly isotropic behavior of most other amorphous polymers investigated so far. Conformational structure and dynamics have been investigated in amorphous aliphatic polymers by magic-angle spinning NMR, exploiting the γ-gauche effect on the isotropic chemical shifts of C H units. In amorphous poly(propylene), trans and gauche are the preferred but not the only accessible conformations. Major conformational dynamics are found to set in only above T , with correla tiontimescomparable to those of segmental reorientations. Nevertheless, the absence of orientational memory in 3D NMR shows that dynamics on a slightly distorted diamond lattice is not a suitable model for polymer dynamics above Tg. 13

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Current address: Department of Polymer Science and Engineering, University of Massachusetts, Amherst, MA 01003 0097-6156/95/0598-0191$13.00/0 © 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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MULTIDIMENSIONAL SPECTROSCOPY OF POLYMERS

Solid-state NMR has proven to provide powerful techniques for investigating the dynamics, structure and order of polymers. Multidimensional NMR spectroscopy in particular (1) has yielded ample molecular-scale information on reorientational and translational dynamics in semicrystalline and amorphous polymers (2-7), on their chemical and phase structure (8-10), and on orientational order (11-14). In this paper, results obtained recently on amorphous polymers will be in focus: the elucidation of the molecular nature of the β relaxation in methyl methacrylates (15), and its merging with the α relaxation above the glass-transition temperature T„ (16), isotropic and anisotropic chain dynamics above T (16), as well as the investigation of conformational structure and dynamics in amorphous aliphatic polymers (17). Major parts of this article have been adaptedfromreferences (1517). Downloaded by UNIV OF PITTSBURGH on May 3, 2015 | http://pubs.acs.org Publication Date: May 5, 1995 | doi: 10.1021/bk-1995-0598.ch012

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Experimental 1 3

The C spectra of PMMA and ΡΕΜΑ were acquired with cross polarization (contact time of 2 ms) and proton decoupling (18) in a variable-temperature *H- C probehead on a Bruker MSL-300 spectrometer operating at a C resonance frequency of 75.47 MHz, with 90° pulse lengths of 5 μ$ and recycle delays of 2 sec. ID and 2D MAS spectra were acquired in a Bruker variable-temperature MAS probehead, with 90° pulse lengths of 3.5 μβ. All 2D spectra were measured off-resonance, so that only a single-phase (cosine) dataset had to be acquired (1,2). Measuring times for a 2D spectrum ranged between 8 and 24 hours. 13

1 3

NMR Background 1 3

This section gives a short introduction to the aspects of solid-state C NMR spectra that are relevant in this study. More detailed descriptions can be found in references (1) and (2). Angle-Dependent N M R Frequencies. Solid-state NMR methods can yield information on molecular reorientations due to the angle dependence of anisotropic NMR interactions. The NMRfrequencyreflects the orientation of a given molecular unit relative to the externally applied magnetic field BQ according to (1,19) 2

2

2

ω(θ,φ) = a>(cos4> sine) + ω^ίδίηφ sin9) + a>$ (co&Q) . n

(1)

3

Here, ω , ω , and ω are the principal values of the chemical-shift interaction tensor and (θ,φ) are the polar angles of B in the principal-axes system of the C chemical-shift, whose orientation with respect to the molecular unit is an inherent property of every type of functional group and reflects its local symmetry [cf. Fig. 1(a)]. In carboxyl groups, for symmetry reasons one principal axis of the C shift tensor must be perpendicular to the OCO plane; it corresponds to ω , the most upfield tensor principal value. (19) The axis in esters is usually close to the C=0 bond. (19) The simulated 2D exchange patterns shown below were obtained with an angle of 3° between the C=0 bond and the axis. In an isotropic sample (a "powder '), segments with all possible values of θ and φ are present, givingriseto an inhomogeneously broadened powder spectrum with a η

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0

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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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Dynamics and Structure of Amorphous Polymers 193

SCHMIDT-ROHR

characteristic lineshape (20,1). It extends from ω to 0033, with steep edges at ω and from which the intensity increases monotonically towards the maximum at 0*22- If reorientational motions set in with rates on the scale of the width ω - ω 3 of the powder spectrum, thefrequencieschange during the acquisition of the NMR signal. This results in lineshape changes which contain some information on the rate and geometry of the motion. η

η


η

Conformation-Dependent NMR Frequencies. The angle dependence of the NMR frequency, though useful for many studies, results in an inhomogeneous broadening of the spectrum, which is undesirable in complex spectra. Magic-angle spinning (MAS) of the sample is a well-established technique for removing this broadening, leaving only lines at the isotropic-chemical-shift position. While very narrow lines may be observed in crystalline materials, amorphous materials show inhomogeneous linebroadenings of up to 20 ppm. This is due to the variation of the chemical shift with conformation-induced changes in the local electronic structure (21). Recently, the spectra of a few aliphatic polymers have been simulated by abinitio computer calculations of corresponding oligomers (22). More traditionally, the conformational effect on the chemical shift has been analyzed semiempirically, most extensively for CH units, in terms of the "γ-gauche effect" (21). It is observed that for a given carbon site, the conformations that determine the positions of the carbons in the γ positions have the largest influence on the chemcial shift. This γ-gauche effect amounts to a 4-7 ppm upfield shift for each γ-gauche conformation. That means that the difference between t*.*t and g*.*g is twice that value. In solution, fast interconversion between the conformations removes the conformational linebroadening, and slightly different shifts (~ 1 ppm) remain only for different configurations, since they average the conformations with different weights. 2

Figure 1. (a): Geometry of the PMMA repeat unit and the orientations of the carboxyl C chemical-shift tensor, with ω , ,a>) and (.


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Figure 3. (a): 2D exchange C NMR spectrum of PMMA with 20% of COO-labeled sidegroups. Τ = 333 Κ, ^ = 50 ms. (b): Attempted simulation of the 2D spectrum in (a) assuming a Gaussian distribution of side-group flip angles of ± 25° rms amplitude (i.e., 60° full width at half maximum) centered on 180°. The pronounced elliptical ridge is not observed experimentally, (c): Best simulation of the spectrum in (a), with a 180° ± 10° flip angle and a concomitant rotation around the 0 & 3 3 direction (local chain axis) with a rms amplitude of ± 20°. (d): Unsatisfactory simulation which results for a rocking motion without 180° flips, i.e., when only rotations around the ω direction (local chain axis) with a rms amplitude of ± 25° are assumed. (Reproduced with permissionfromref. IS. Copyright 1994 ACS.) 13

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Figure 4. Selective-excitation 3D exchange C NMR spectrum of the labelled PMMA carbonyl groups of PMMA at Τ = 333 Κ and mixing times W = t ^ = 50 ms. Only two straight ridges, along (O3 = ω and (O3 = ω are observed in the relevant region of Ofy unequal ω } , proving that the reorientation of each segment involves only two relevant potential-energy minima, in spite of the diffusive appearance of the corresponding 2D spectrum in Fig. 3(a). (Reproduced with permissionfromref. 15. Copyright 1994 ACS.) 2

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SCHMIDT-ROHR

minima. This arises from the fact that different sidegroups have different environments in the glassy state, requiring varying degrees of rearrangement of the main chain in the energy-minimization after the jump. In order to analyze the geometries of the two-site jumps in more detail, we compare the experimental 2D NMR spectrum of Figure 3(a) to simulated spectra for various motional models [Fig. 3(b)-(d)]. The simulated 2D exchange NMR spectrum resulting from 180° sidegroup flips without main-chain motion is plotted in Fig. 3(b). The simulation shows a pronounced elliptical, nearly circular ridge, which is, however, absent in the experimental 2D spectrum. There, except for straight ridges tapering at the (033 end of the spectrum, the exchange intensity is rather featureless. In the simulation, the circularridgecannot be broadened appreciably by assuming a distribution of the rotation angle around 180°. In fact, such a distribution with a rootmean-square (rms) amplitude of σ = 25° (corresponding to a full width at half maximum of nearly 60°) was assumed in simulating the spectrum shown in Fig. 3(b).

Coupling of the Sidegroup Flips to Rotations around the Local Chain Axis. Because the ω and CD22 values are quite similar for the carboxyl chemical33

shift anisotropy in PMMA, and since the ω axis is not involved in die exchange process, the exchange intensity mainly reflects the reorientation-angle distribution of the ω axis of the C chemical-shift tensor. The featureless experimentally observed 2D intensity distribution in Fig. 3(a) indicates a wide reorientation-angle distribution for the ω axes. As indicated above, simulated 2D spectra such as that of Fig. 3(b) show that some limited deviations of the flip angle from a central value of 180° do not cause such a broadening in the spectral region between 0^ and ay On the other hand, for these deviations an upper limit of σ = 40° is established by detailed lineshape analysis, in particular by considering the approximate invariance of the (D33 frequency in the 2D spectrum. Distributions in this angle therefore cannot be invoked as the major source of the smearing-out of the exchange pattern. However, a distribution of rotation angles around the ω axis, which is perpendicular to the OCO plane, is very effective in broadening the exchange features in the region between ω and a>22> while producing no exchange at ω . Structural studies (32-34) and simulations (35) have shown that the normal of the OCO plane is parallel to the local chain axis within about 20°, as indicated in Figure 1. The spectral analysis of Fig. 3 shows that the amplitude of these restricted rotations around the local chain axis that accompany the 180° sidegroup flips is σ = 20° ± 7 ° . The corresponding simulated spectrum is shown in Figure 3(c). If only such main-chain motions are assumed, without sidegroup flips, the spectral intensity is confined closer to the diagonal, Figure 3(d), than is found in the experimental spectrum, Figure 3(a). As schematically indicated in Figure 5(a) - (c), due to the asymmetry of the sidegroup it is indeed expected that a rotation of limited amplitude around the normal of the OCO plane accompanies a sidegroup 180° flip. As shown in Figure 5(b), a simple 180° flip without main-chain readjustment will in general lead to steric clashes of the OCH3 group with surrounding units. Figure 5(c) indicates how these can be avoided by a -20° rotation around the normal of the OCO plane, which is approximately parallel to the local chain axis. Then, only slight changes in the environment are necessary to accomodate the asymmetric sidegroup after the 180° flip. Significant lineshape changes on the diagonal are observed in the C NMR 2D spectra. Figure 6 compares the stacked plots of C 2D spectra at 233 Κ and 333 K. 33

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η

3 3

η

33

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1 3



200


Figure 5. Schematic sketches of the dynamics of the asymmetric sidegroup in its correspondingly asymmetric environment [cf. also Fig. 1(b)]. (a): Initial sidegroup orientation, (b): Steric clash with the environment if an exact 180° flip without main-chain motion is assumed, (c): To fit the asymmetric sidegroup into the volume that it had occupied before the flip, a twist around the local chain axis is required. This in turn slightly deforms the environment (d): A second jump takes the group back close to its original orientation in (a), but not exactly, due to the previous change in the environment in (c), which is enhanced by rotation of other sidegroups that make up that environment. Rearrangements of the main chain by neighboring flipping sidegroups will also induce such an effect of an effective small-angle rotation around the local chain axis, (e) Reorientation-angle distribution R(p) for the ω axis of the carbonyl chemical-shift tensor that was used for the simulation of the C 2D NMR spectrum of Figure 3(c). The component labelled " 1 " represents the 25% of the sidegroups that have flipped once (or 2N+1 times) and has a rms amplitude of 20°. Another 25% of the sidegroups have flipped back to the original orientation with an imprecision of 12° (two or 2N flips, labelled "2"), and the remaining 50% are trapped but rock with an amplitude of ca. 7° (no flips, labelled "0"). (Adaptedfromref. 15.) η

13



Figure 6. Stacked plots of exchange NMR spectra taken with ^ = 50 ms (a): Diagonal powder pattern for Τ = 233 Κ (b): At Τ = 333 Κ, significant changes of the intensity distribution on the diagonal are observed. The (033 end of the spectrum is enhanced in part because the 180° inversion of the sidegroup leaves this frequency invariant, but mainly due to small-angle motions around the normal of the OCO plane. They occur naturally when the sidegroups have flipped twice [see Fig. 5(d)]. (Adapted from ref. 15.)


202


While a perfect diagonal powder pattern is observed at the lower temperature, at 333 Κ the intensity at the edges of the spectrum, in particular at the ω$ end, is enhanced relative to other parts of the spectrum. As explained in the theoretical section above, this is characteristic of the frequency-dependent broadening caused by anisotropic small-angle reorientations. The experimental spectrum is best matched by including rotations around the local chain axis by an rms amplitude of 7° for the sidegroups that do not flip, and by 12° rms amplitude for those that do. These reorientations arise due to the twisting of the chains when neighboring sidegroups reorient. The larger amplitude of the latter process results naturally when after two 180° flips, a given sidegroup does not return exactly to its original orientation due to a change in its environment. This is schematically displayed in Figure 5(d). The change in the environment could be due to the rearrangement of the surrounding moieties caused by the slight misfit of the given asymmetric sidegroup after the flip, or it might be caused by flips of other sidegroups within this environment, which also change the structure slightiy. Figure 5(e) displays the overall reorientation-angle distributions of the carboxyl chemical-shift ω direction. Component "0" represents the 50% of the sidegroups that only rock, with an average amplitude of 7°. Component "1" results from the 25% of the sidegroups that have undergone one 180° flip, or an odd number of flips, and concomitant reorientations around the normal of the OCO plane with a rms amplitude of 20°, which resultfromdie asymmetry of the sidegroup [see Fig. 5(c)]. Component "2" in the distributions, made up by another 25% of the groups, corresponds to two, or an even number, of flips with an effective rotation by typically 12° around the local chain axis.


3

π

Motional Rates in PMMA. The motional rates of the large-angle reorientation process have been determinedfromthe mixing-time dependence of the exchange intensity found at different temperatures. At higher temperatures they can be estimated from the onset of ID lineshape changes, where the rate l/x is comparable to the powder linewidth Ι ω - ω Ι. Figure 7(a) displays these data in an Arrhenius plot together with literature values obtained from dielectric {30,36) and dynamicmechanical (37) relaxation. The straight line in the plot corresponds to an activation energy of 65 kJ/mol. The good agreement of the corrrelation times around and above 300 Κ shows that the motion detected by NMR is indeed directly related to the β relaxation. Integration of the experimental exchange intensity of the C 2D NMR spectrum at Τ = 333 Κ, shows that the asymptotic value of the integrated exchange intensity for long mixing times makes up 25 ± 10 % of the total. In a symmetric two-site jump process as indicated by the 3D experiment, at least half of the intensity is found on the diagonal for any mixing time. This means that 2·(25 ± 10)% of the sidegroups participate in the exchange process on the time-scale of the correlation time of the β process. The remaining 50 ± 20% which are slow on that time scale must be trapped in environments with higher activation barriers. Such a heterogeneous distribution of correlation times has been confirmed by the MESSAGE experiment (15). η

33

1 3

Relation to Mechanical Relaxation. Due to the asymmetry of the sidegroup, its motion occurs between energetically inequivalent sites; therefore, it is mechanically active. Our spectra show that the sidegroup dynamics are accompanied by main-chain motion and we can quantify the corresponding motional amplitudes to be as large as (±)20°. The 0033-features of the C 2D NMR spectra show that rearrangements of the 13


12· SCHMIDT-ROHR


a


373 Κ

233 Κ

1

1000/T [Κ" ]

Figure 7. (a) Arrhenius plot of correlation times of the β-relaxation dynamics in PMMA, estimated from ID and 2D NMR spectra, compared to both dielectric data obtained from the β-relaxation loss maxima (30,36) and relaxation timesfromdynamic-mechanical studies (37). (b) Arrhenius plot of the α and β-relaxation dynamics in ΡΕΜΑ, including the region where the two relaxations merge. Light-scattering (58), dielectric (59), and 1D/2D NMR (16) data are shown. (Continued on next page.)


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12. SCHMIDT-ROHR

205

Dynamics and Structure of Amorphous Polymers

main chain, which result in an effective rotation around the local chain axis, are at least as important in the energy minimization as are deviations from the 180° angle of the sidegroup motion. This indicates the dominance of steric interactions between different segments, compared to intramolecular bond-rotation potentials.


Merging of α and β Processes Dielectric and dynamic-mechanical relaxation show similar activation energies of ca. 75 kJ/mol for the β processes in various poly(methacrylates) with different alkyl residues of the sidegroups. The α relaxation process, or glass-transition dynamics, has much larger (apparent) activation energies close to Tg. Therefore, the α and β processes merge within a relatively narrow temperature interval, as shown by the Arrhenius plot for ΡΕΜΑ in Figure 7(b), combining photon-correlation-spectroscopy (38), dielectric (39), and 1D/2D NMR (16) data. So far, only speculations have existed on the mechanism of the merging. ΡΕΜΑ is particularly suitable for investigating this α-β coalescence, since it occurs closer to Tg, and thus over a narrower range, than in PMMA, and within the range of correlation times accessible by 2D exchange NMR. Figure 8(a) displays contour and stacked plots of a 2D exchange spectrum of COO-labeled ΡΕΜΑ at Τ = 298 Κ and ^ = 500 ms. The exchange pattern closely resembles that of PMMA in Figures 3(a) and 6(b), which shows that the β relaxation processes in PMMA and ΡΕΜΑ have the same molecular origin. The spectrum of Figure 8(b) was aquired at 17 Κ above the glass-transition temperature T with a mixing time of 500 ms, in the time-temperature region where the β process merges with the α process. The spectrum exhibits stronger exchange intensity but the pattern resembles that of the spectrum below T . The peak at ω$ is again the overall spectral maximum, which proves directly that the motion is pronouncedly anisotropic. The quantitative analysis shows that nearly all sidegroups are exchanging, undergoing 180° flips with similar imprecision as below T , but increased amplitude of rotation around the local chain axis.. This indicates that above T«, the volume accessible to the sidegroups between chains is increased and trapped sidegroups are freed by slow fluctuations of their environment. ID and 2D spectra at higher temperatures show the amplitude of the rotations around the main-chain axis increases strongly, while the reorientations of the chain axes themselves are restricted up to meure than 60 Κ above T and the 180° flips remain relatively precise (16,40). In other words, the relaxation process at and above the region of α-β merging exhibits the features of both processes: The 180° sidegroup flip characteristic of the β process remains a distinctive mode of motion, while the rotation around the local chain axis, restricted for the original β process, becomes activated with very high apparent activation energy as typical for an α process. The spectra indicate that not only the correlation time, but also the amplitude of this rotation is activated with temperature. The anisotropic glass-transition dynamics of ΡΕΜΑ is in contrast to the predominantly isotropic behavior of most other amorphous polymers investigated so far. The 2D spectrum of the COO group of PVAc (3 ) which has a spectral asymmetry parameter (η=0.27) comparable to that of ΡΕΜΑ (η=0.41), provides a good example, see Figure 9. In the PVAc spectrum of Figure 9(b) at T +20 Κ and ^ 13

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In Multidimensional Spectroscopy of Polymers; Urban, M., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1995. 13

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Figure 8. 2D exchange C NMR spectra, (a) ΡΕΜΑ with 20% of COOlabeled sidegroups with ^ = 500 ms, below T , at Τ = 298 Κ. Note the similarity to the spectrum of PMMA in Fig. 3(a) and 6(b). (b) Similar to (a), at 17 Κ above Tg, Τ = 365 Κ. Note the increase of the exchange intensity compared to (a) and the similarity of the exchange patterns. Reorientationangle distributions for the ω axis of the carbonyl chemical-shift tensor are shown as inserts. (Adapted fromref.16.)


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SCHMIDT-ROHR

Dynamics and Structure ofAmorphous Polymers

Figure 9. Dynamics above T~ probed by carbonyl chemical-shift tensors, (a) ΡΕΜΑ at Τ = T-+17 Κ, ^ = 500 ms. (b) Unlabeled PVAc at Τ = T +20 Κ, ^ = 100 ms. The 2D lineshapes show that the motion in ΡΕΜΑ is anisotropic compared to the reorientations in PVAc. In ΡΕΜΑ, the ω axis of the carbonyl tensor remains nearly invariant, which means that the local chain axis does not reorient significantly, and also proves that the sidegroup flip angles do not deviate farfrom180°. (Adaptedfromref. 16.) g

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MULTIDIMENSIONAL

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O F POLYMERS

= 100 ms, the diagonalridgehas nearly vanished, and the peak at 0)22 is the overall spectral maximum, as is expected for any isotropic process.

Conformational Information from Structured CH MAS Lines 2

The top of Figure 10 shows MAS spectra of three amorphous aliphatic polymers near Tg (17)- The resonances of several peaks, in particular of the CH bands, exhibit significant broadening and some fine structure. It is due to conformational effects on the chemical shifts, the γ-gauche effect, as discussed in the Theory section. The assignment of the chemical shifts to the conformations is particularly clear in armophous poly(propylene) from comparisons with isotactic and syndiotactic poly(propylene), where the conformations in the crystalline regions are known to be trans*.*gauche and t*.*t/g*.*g, respectively (41). Below the ID spectra in Figure 10 are shown corresponding 2D "exchange" spectra. They are exploited here not to obtain dynamical information, but instead to determine the homogeneous linewidth, perpendicular to the spectral diagonal, of the various resonances. The elongated patterns along the diagonal prove that the broadening of the ID spectra is predominantly inhomogeneous. Thus, the 2D spectra show that the intensity between the maxima of the ID CH patterns is not due to homogeneous linebroadening. It strongly suggests that there are conformations intermediate between trans and gauche. This is in accordance with the diffusive reorientational dynamics discussed below.


2

2

Conformational Dynamics. The relatively small off-diagonal and large inhomogeneous broadening of the CH resonances obvious from the 2D spectra of Figure 10 and Figure 11(a) show that no major conformational motions occur below T . Above T , strong conformational exchange is observed, see Figure 11(b). It is interesting to compare this isomerization dynamics with the reorientational dynamics. Quantitative analysis of the mixing-time dependence of the exchange intensities has shown that the exchange between gauche-like and trans-like conformations exhibits similar non-exponentiality as the reorientational motions. In the Arrhenius plot of Figure 12, the correlation times for conformational exchange (full symbols) and rotational dynamics (open symbols) are compared and found to be equal within the error margins. The data, inculding results from a C relaxation study (42), follow a WLF (WUliam-Landel-Ferry) relation shown as a solid line in Figure 12. By means of slow magic-angle spinning 2D exchange NMR (2), reorientational and conformational dynamics can actually be detected separately in one and the same spectrum. For a sample subject to slow MAS, the NMR powder spectrum splits up into a spinning sidebands spaced by the rotation frequency. In a suitable designed MAS 2D exchange experiment, off-diagonal sidebands indicate molecular reorientations. At the same time, conformational (i.e., isotropic-shift) changes can be detected in terms of exchange within each MAS band. Both features are observed in the experimental aPP spectrum of Figure 11(c). In the interpretation of this equality of correlation times, it will be noted that the correlation times for the conformational exchange cannot be shorter that those of the reorientations, since the former must always be accompanied by the latter. On the other hand, it would have been well conceivable that the conformational exchange is slower than the rotational motion: The ill-defined, diffusive reorientational motions could have been produced by many small, possibly random, changes in successive torsion angles, with only a small percentage of large conformational changes. Only on a longer time-scale would all segment have undergone a conformational change. 2

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Figure 10. C CP MAS spectra of aliphatic polymers near T . Top: ID spectra, bottom: 2D exchange spectra with short mixing time (no significant motion), providing a measure for the homogeneous linebroadening (width perpendicular to the spectral diagonal). These 2D spectra prove that the broadening of the ID spectra is predominantly inhomogeneous. (a) Atactic poly(propylene). (b) Poly(isobutylene) with short (50 |is) cross polarization time to suppress the signal of the quaternary carbon, (c) Polyvinyl acetate). (Adapted from ref. 17.)

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Figure 11. MAS exchange spectra of atactic poly(propylene). (a) and (b) fast spinning (no sidebands), (c) slow spinning, (a) t = 5 ms, Τ = Τ·- 5 K, diagonal spectrum, (b) ^ = 500 ms, Τ = T + 12 K. The off-diagonal intensity is due to conformational exchange, (c) Slow spinning, zoom on the CH region of the 2D spectrum. Arrows mark exchange spinning sidebands produced by molecular reorientation. Within each band, full conformational exchange is observed while the exchange sidebands are small. This indicates that conformational exchange is not slower than reorientational exchange. (Adaptedfromref. 17.) g



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SCHMIDT-ROHR

Dynamics and Structure of Amorphous Polymers

0,4

0,5

0,6

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Figure 12. Reduced-temperature Arrhenius plot of correlation times Xq for various amorphous poly(propylene) samples. Filled symbols: conformational dynamics. Open symbols: reorientational dynamics. Solid line: WLF fit. (Adapted from ref. 17.)


211

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Figure 13. Selective-excitation 3D spectrum of aPP at Τ = 252 Κ = Tg + 1 IK, with = tmt, = 50 ms. The arrow maries the line (03 =

Dynamics and Structure of Amorphous Polymers Studied by

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