SSP2 32

A0005 Magnetic Resonance: Polymer Applications of NMR

K Saalwachter and Detlef Reichert, Martin-Luther-Universitat Halle-Wittenberg, Institut fur Physik, Halle,Germany

& 2010 Elsevier Ltd. All rights reserved.

S0005 Introduction: Synthetic Polymers

P0005 Synthetic polymers, with repeat unit numbers of a fewtens up to millions, are chemically simpler than theirbiological counterparts (proteins, DNA, polysaccharides).Homopolymers ideally consist of only one and the samerepeat unit (monomer), and copolymers have a few, up tomaybe three or four, chemically different monomers.Nevertheless, synthetic polymers are characterized by awide complexity in their structure and dynamics, andthis article highlights the possible investigation of avariety of important aspects in this field by nuclearmagnetic resonance (NMR). Complexity in synthetic

polymers arises for different reasons, which shall besummarized in this section.

P0010Generally, one can distinguish different linear andbranched chain architectures, as shown in Figure 1. Thedifferent branch points in such structures are readilydistinguishable by NMR, provided their concentration ishigh enough. However, the most important structuralaspects arise more locally within the chains. First, and incontrast to most biological macromolecules, weaklyhindered rotation around different bonds is usuallypossible, giving rise to different conformational states,and these exhibit distinct chemical shifts in many cases.For the trans and gauche conformations of a saturatedalkane chain (¼ polyethylene) sketched in Figure 1, a13C chemical shift difference of � 5.2 ppm arises due tothe so-called g-gauche effect, which describes changes inshielding when main- or side-chain atoms, that are sep-arated by three bonds, come closer to each other for aspecific conformation. For other substituents or com-positions, the effect can be even bigger (� 7.2 ppm forC0yOg). Depending on the physical state (solutions ofvarying viscosity, bulk melt, or glassy state), the differentconformations either interconvert rapidly, leading to theobservation of a Boltzmann-weighted average chemicalshift, or are fixed on the timescale defined by the inversefrequency separation, leading to the observation of dis-tinct shifts for distinct conformations. In molten poly-ethylene, the 13C shift differs by B2 ppm from the all-trans conformation; the latter being independentlymeasurable on the crystalline phase. If the three con-formations were equally populated, an average shift of2� 5.2/3¼ 3.5 ppm would be expected. The lower ob-served shift indicates that the trans conformation isfavored. The intermediate situation corresponds to thewell-known scenario of chemical shift exchange and co-alescence, and is characterized by broad lines. Such a linebroadening may either be a valuable source of infor-mation on conformational dynamics, or can be avoidedby heating or cooling, or using a more or less viscoussolvent.

P0015Second, despite their chemical regularity, local con-figurations may well be different, and in this regard,geometrical and positional isomerism, as well as stereo-chemistry, plays an important role. Geometrical and

CC0

CγCC C

Graft (co)polymer

C0

Cγ

H

H

H

HC0

Cγ

H

H

H

H

� = 0° (trans) � = ±120° (gauche)

�

Linear random coil Star

F0005 Figure 1 Overview of different polymer architectures and

relationship of large-scale chain flexibility and local

conformational freedom. The g-gauche effect on the 13C chemicalshift of C0 arises from the closer approach of C0 and Cg in the

gauche conformation (3 A as opposed to 4 A, see arrow).

SSP2 00032

1

positional isomers arise when polymerizable monomerscan be attached to each other in different ways, for ex-ample head-to-head versus heat-to-tail connections. Thisleads to distinctly different structural motifs and con-sequently, to meaningful differences in the NMR spectra,readily interpreted by standard rules and procedures.Depending on the specific mode of polymerization, suchforms of isomerism are usually easy to control by thespecific chemistry, leaving stereoisomerism as a moreimportant structural parameter.

P0020 Stereochemical sequence analysis is thus the mostfrequently studied aspect in solution-state NMR ofpolymers, as the stereoregularity is in most cases thedominant factor that determines to which extent thepolymer is semicrystalline or amorphous, with largeimpact on the physical properties of the material. In vinylpolymers, a stereoregular polymer is either isotactic orsyndiotactic. These two tacticity patterns differ in thestereochemical diad composition (meso, m vs. racemic, r) ofthe main chain, as is shown in Figure 2. Importantly,polymers with extended isotactic (ymmmy) or syn-diotactic (yrrry) trains usually crystallize, as the re-gularity allows long-range ordering of the chain

molecules, resulting in material with very specific prop-erties. The tactic sequences usually form regular helices,with polyethylene as the simplest case forming a 21 helix(2 monomers per 3601 turn), corresponding to an all-trans structure. Owing to the g-gauche effect, valuableinformation on the helical structure may be attained byhigh-resolution 13C solid-state NMR. Atactic polymersusually do not crystallize (with poly(vinyl alcohol) as aprominent exception).

P0025Four major factors determine the bulk properties of apolymer: the glass transition temperature (Tg), the tac-ticity, the degree of branching, and the monomer com-position and distribution in the case of copolymers.Schematic structures are given in Figure 3. Tg is largelydetermined by the chemical structure, where as a rule ofthumb, more rigid (e.g., aromatic or conjugated) back-bone structures lead to a higher Tg. Stereoirregular linearhomopolymers, highly branched structures, and randomcopolymers do not tend to crystallize well, and may ei-ther exist as a disordered melt above Tg or as a glassbelow Tg (such as plexiglas), the difference being thesegmental mobility and thus the overall dynamics. Al-though a polymer melt may still be able to flow (de-pending on the molecular weight and the degree ofbranching), cross-linking of the chains (Figure 3(b))leads to a shape-persistent material that is either elastic(above Tg) or rigid (below Tg), the latter being referredto as a thermoset. Most important polymer materials arethermoplastics or thermoplastic elastomers, which flow

A A A A A A

B B B B B B

Isotactic

A B A B A B

A A B A B A

B B A B A B

B A B A B A

Syndiotactic

Atactic

C CC CC

CC

H2 H2 H2 H2

CC

H2

A B A B A B A B

C

A

meso (m) diad

racemic (r) diadmr triad

F0010 Figure 2 Different forms of tacticity of vinyl polymers made

from a H2C¼CAB monomer. Sequences of two or morestereocenters (diads, triads, tetrads, etc.) are referred to by their

stereochemical diad succession, for example, mrrrr for the

specific hexad example at the bottom.

(a) (b)

(c) (d)

F0015Figure 3 Schematic structures of bulk polymers. (a) Melt or

glass, (b) network, that is, elastomer or thermoset, (c)

semicrystalline structure, (d) phase-separated (here lamellar) di-

or tri-block copolymer. Polymer melts and glasses, and

elastomers and thermosets, respectively, differ in their dynamics.

Although rapid segmental as well as larger-scale motion is

possible in the former, dynamics in the latter is restricted to local

vibrations and side-chain motions (b, g,y subglass processes).

SSP2 00032

2 Magnetic Resonance: Polymer Applications of NMR

and can be injection-molded at high temperatures, andare either rather rigid or elastomeric and shape persistentat ambient temperature.

P0030 Generally, even perfectly stereoregular, and thuscrystallizable polymers never crystallize completely dueto arrested kinetics associated with the necessary large-scale topological reorganization, leaving a material withrigid crystalline lamellae interleaved with a mobileamorphous phase (see Figure 3(c)). Consequently, thesepolymers are thermoplastics below the crystalline melt-ing point, Tm. Thermoplastic behavior can also beachieved with block copolymers, in which chemicallydifferent subchains are connected by a bond. Chemicallydifferent polymers usually do not mix, and in the case ofblock copolymers, which exist as di-, tri-, or multiblockstructures, the phase separation length scale is limited bythe size of the chemically homogeneous blocks (usually afew tens of nanometers). This leads to a rich variety ofpossible nano- and microstructures (see Figure 3(d)),lamellae of a symmetric di-block being one example. Ifone of the blocks is below Tg at ambient temperature, thematerial is again a thermoplastic, as the rigid subphaseacts as a cross-linker. From these examples, it is clear thatthe understanding of polymer materials requires struc-tural and dynamic information over length scales fromthe molecular to the micrometer range, and dynamicsfrom picoseconds (local vibrations) to seconds (flow, yieldprocesses). NMR is essentially capable of covering theselength and timescales, and it is thus a valuable toolproviding atomic-level information that can complementmany macroscopic property measurements.

P0035 In the following sections, the investigation of many ofthe above aspects by either solution- or solid-state NMRis addressed. The amount of literature on these subjects isvast, and while the authors have tried to cover what theyconsider the most important aspects, the choice of thepresented topics is of course a matter of their personalpreference. They have deliberately omitted pulsed gra-dient methods, as applied in diffusion or imaging studiesof polymeric systems. Covering these fields is beyond thescope of this short contribution, and the authors refer thereader to specialized texts such as those of Kimmich andBlumich mentioned in the Further Reading section. Theauthors have also chosen not to cover multinuclear NMRusing for instance 29Si, 15N, 31P, and many other quad-rupolar nuclei, which play an important role in the studyof inorganic and functional polymers. It should be clearthat the principles to be discussed here in relation to 13Cand 2H are similarly valid for other heteronuclei. 19FNMR is omitted as well, but it is certainly important forthe characterization of many fluorinated polymers, and isalso a wide field of its own. The acquisition of high-resolution solid-state 19F spectra is a particular challengebecause of its 100% abundance and high Larmor fre-quency, leading to large dipolar line broadening similar

to that of 1H spectra, and the problem of heteronucleardecoupling from 1H due to the closeness of the Larmorfrequencies.

S0010Solution-State Studies

P0040The standard procedures of solution-state 1H and 13CNMR of small molecules may directly be applied topolymers, provided that a suitable solvent exists. Often, itis in fact not easy to prepare a polymer solution of suf-ficiently low viscosity, which is necessary to ensure rapidtumbling of the polymer coils as well as fast averagingover the different conformational states. Otherwise,broad lines or, for the case of fixed conformations,complex multiplet signals can challenge the interpret-ation of the spectra. In particular, solutions of high-mo-lecular-weight polymers may be very viscous even underhigh dilution, requiring significant reductions of theconcentration. Often, when the solvent is thermo-dynamically poor, the polymer tends to aggregate, againcausing a broadening of the lines. Not uncommonly yetcounterintuitively, the thermodynamic quality of a solv-ent can in fact decrease upon heating, such that in-creasing the temperature is generally not feasible. Moreserious solubility problems arise for block copolymers,where a common solvent for the different blocks must befound. Otherwise, the less soluble blocks aggregate,which leads to a highly viscous gel. Finally, cross-linkedstructures (elastomers) do not dissolve at all, but can onlybe swollen. In the latter cases, line-narrowing techniquesadapted from solid-state NMR can, however, be used toobtain highly resolved solution-like spectra.

S0015Chemical Identification and Molecular WeightDetermination

P0045Once a high-resolution spectrum can be recorded, thechemical identification is often straightforward. When thespectra are more complex than expected, the reason maybe defects in a structure that was only assumed to beregular. For example, in vinyl polymers made frommonomers of the type H2CQCHR, the common head-to-tail arrangement (y–CH2–CHR–CH2–CHR–y)may be disrupted by head-to-head units (y–CH2–CHR–CHR–CH2–y), which are easily distinguishable by thechemical shifts of the involved atoms, and their concen-tration is easily determined by integration. Similar argu-ments hold for the analysis of copolymer composition,where different modes of arrangement (different blocki-ness, e.g., yABABABy vs. yABAABABBBy) lead tocorrespondingly different and potentially complex spectra.In general, such NMR studies of the chemical micro-structure are commonly used to elucidate details of themechanism of the polymerization reaction. Other areas ofapplications are the study of polymerization kinetics by

SSP2 00032

Magnetic Resonance: Polymer Applications of NMR 3

real-time NMR, and of the chemical modification ofpolymers, for example, the substitution of side groups forproperty tuning.

P0050 An important aspect is represented by the chemicallydifferent and thus usually distinguishable end groupsignals. Provided that the polymer is linear or the degreeof branching is known, integration of these signals andcomparison with the main signals readily yields the de-gree of polymerization, and thus the molecular weight ofthe polymer (see Figure 6 for a similar application).However, as the end groups comprise only a small frac-tion of the overall signal, the method is limited to low tointermediate molecular weights, with the upper cutoffbeing determined by the dynamic range of the receiverand the resolution of the analog-to-digital converter ofthe spectrometer. Note that nowadays, hyphenatedtechniques, such as the combination of size-exclusionchromatography and NMR, have become commerciallyavailable. They even allow for detailed chemical analysesof the different subspecies in polymer mixtures or, inparticular, of samples with broad distributions of mo-lecular weight.

S0020Sequence Analysis

P0055As explained in the first section, the proton or carbonchemical shifts of a polymer are sensitive to the stereo-chemical composition in much the same way as prochiralprotons are distinguishable in small molecules. In poly-mers, such effects can be rather long-ranged (see Fig-ure 2). Consider, for example, a vinyl polymer of the type[CH2–CHR–CH2–CHR–CH2–CHR–]n. It is relativelyobvious that the methylene (CH2) signal will mainlydistinguish the relative stereochemistry of the CHR unitsleft and right of it; it is thus sensitive to a single (m or r)diad structure, with potential fine structure caused bytetrads (e.g., mrm). In contrast, signals from the CHRgroup are mainly split by the triad structure (mm, mr, orrr), as both the central stereocenter as well as the adjacentmonomer units contribute. The fine structure then dif-ferentiates pentads, or even heptads in favorable cases.The fine structure due to pentad sequences is highlightedin Figure 4(b) on the example of the methyl resonancesof atactic polypropylene. Note that these microstructuraleffects on chemical shifts ultimately arise from differentBoltzmann weights for different conformational states,which in turn depend on the bulkiness and position ofdifferent substituents. The experimental shift thus arisesas a fast-limit average, and sufficiently fast conforma-tional dynamics, that is, the use of lowly viscous solventor high temperatures is vital.

P0060Once the signals are assigned to different sequences,the integrated signal can again be used to gain importantknowledge on the polymerization mechanism. For ex-ample, if only the probabilities of formation of m or rdiads upon attachment of a new monomer to the growingpolymer chain are different, the probability to find spe-cific triads, tetrads, and so on, which is directly pro-portional to the corresponding relative signal intensities,can be readily calculated from Bernoullian statistics. Ifthe probability to form an m triad is given by pm, thenpr¼ 1-pm, and the triad probabilities are pmm¼ pm

2 ,pmr¼ 2pm(1-pm), and prr¼ (1-pm)

2. Therefore, in such acase, the intensities of the triad signals must be ex-plainable by a single parameter, pm. If for chemical rea-sons, the attachment process is influenced by thestereostructure of a longer part of the chain end, a first-or higher-order Markov process determines the micro-structure, and different independent conditional prob-abilities such as pm�r are necessary to explain theintensity distribution. Obviously, the longer-ranged theinfluence of the chain end structure on the attachmentprocess is, the more independent probabilities are in-volved, and the higher is the required n-ad resolution todetermine all these probabilities.

203040

ppm versus TMS

mmmmmmmr

rmmr

mmrrrmrr+mmrm

rrrrmrrr

mrrm

CH3CHCH2

mmrr

mr

(a)

(b)

(c)

F0020 Figure 4 Twenty-five megahertz 13C NMR spectra of (a)

isotactic, (b) atactic, and (c) syndiotactic polypropylene (PP:

� [CH2�CHCH3]n� ). For the methyl groups in (b), the distinctregions of the different triad resonances are indicated, and the

enlarged inset shows the resolution and assignment of pentad

sequences. Reproduced from Tonelli AE and Schilling FC (1981)13

AU1

C NMR chemical shifts and the microstructure of polymers.

Accounts of Chemical Research 14: 233–238, with permission

from the American Chemical Society.

SSP2 00032

4 Magnetic Resonance: Polymer Applications of NMR

S0025 Relaxation Studies

P0065 It is well known from classical Redfield and Bloomber-gen-Purcell-Pound (BPP) relaxation theories that T1 andT2 relaxation times (as well as nuclear Overhauser en-hancements) depend on the spectral density of molecularmotion in the range of the Larmor frequency. In the caseof polymers, solution-state relaxation studies thereforeprovide access to fast local segmental motions in themegahertz to gigahertz range, and to a limited degreealso to the slower overall tumbling of the dissolvedmacromolecule as a whole. For the latter case, the re-laxation data (relaxation times, preferably measured atdifferent temperatures, Larmor frequencies, or both)AU2 can,

for instance, be analyzed within the framework of the‘model-free’ approach of Lipari and Szabo, originallyestablished for proteins, which describes the dynamics interms of two associated correlation times and an orderparameter characterizing the spatial restrictions of thelocal segmental processes. More elaborate analyses re-quire the consideration of additional motional modes, oreven more accurately, a full spectrum of relaxation times,as predicted by established theoretical models of polymerdynamics.

P0070Since fast local motions dominate the T1 relaxationtimes and are usually characterized by large-amplitudeconformational jumps, it is possible to use relatively

G1

G2G3

G4

1.0

0.8

0.6

0.4

0.2

0.00 2 4 6 8 10 0 2 4 6 8 10

Terminal site

Terminal site

Internal sites

10−7

10−8

10−9

10−10

10−11

Internal sites

Molecular size (Generation)Molecular size (Generation)

23 °C75.4 MHzDMSO-d6

23 °C75.4 MHzDMSO-d6

τ (s

)

τ 1 (

s)

(a)

(b)

PAMAM−{−CH2CH2N− [−CH2CH2CNHCH2CH2OH]2}m

(c)

F0025 Figure 5 Investigation of dendrimer dynamics in solution by T1 relaxation. (a) Schematic structure of a fourth-generation dendrimer

and chemical structure of a PAMAM dendrimer, (b) 13C T1 relaxation times (at 75MHz) of terminal and internal sites as a function of

PAMAM dendrimer generation, and (c) derived motional correlation times. Parts (b) and (c) reproduced from Meltzer AD, Tirrell DA,

Jones AA, et al. (1992) 13C chain dynamics in poly(amido amine) dendrimers. A study of 13C relaxation parameters.Macromolecules 25:

4541–4548, with permission from the American Chemical Society.

SSP2 00032

Magnetic Resonance: Polymer Applications of NMR 5

simple one-component BPP expressions to obtain at leastapproximate correlation times of these motions, andcompare them among different polymers for qualitativeinsights into their local dynamics in solution. A prom-inent example is shown in Figure 5 for the case of aspecific class of macromolecules, namely dendrimers (or‘starburst’ molecules), which are characterized by aregularly branched structure, with the number of bran-ches growing regularly as a function of chemical gener-ation. Note that the end groups, either unreacted ormodified in the last step, are chemically distinguishablefrom the interior of the molecule.

P0075 A long-standing debate in polymer science was thequestion whether the end groups of such tree-likestructures cluster together in a dense outer shell, leavingcavities in the inside of the molecule (as implied byFigure 5(a)), or whether the arms eventually fold back,leading to a homogeneous distribution of more freelymobile ends throughout the structure. The correlationtimes for local segmental motions in Figure 5(c), derivedfrom the T1 relaxation times in Figure 5(b), both plottedas a function of generation, immediately proved that thelatter is in fact correct: The terminal sites move muchfaster, which would not be possible if they clustered in adense shell.

S0030High-Resolution MAS Investigations

P0080Finally, as mentioned above, the solution-state studieshighlighted in this section are not limited to actual iso-tropic, molecularly disperse solutions. In fact, the onlyimportant requirement is fast local mobility of thepolymer, needed to achieve full conformational aver-aging. In many cases, the polymer in question may not becompletely soluble, as is the case for block copolymers,aggregated systems in poor solvent, or most importantly,polymer networks. In all these cases, the polymer canonly be swollen locally, that is, at least parts of thestructure are surrounded by solvent and the segmentsmove rapidly. On a larger scale, the tumbling of the re-spective substructure (aggregate, chain tagged to a sur-face of a network) is slow or even completely hindered.This leads to broadened spectra, where the line broad-ening arises from typical solid-state effects, that is,orientation-dependent interactions that are not averagedout completely, leaving on the solid-state scale a small,but potentially devastating residual broadening. Con-sequently, line-narrowing techniques from solid-stateNMR, first and foremost magic-angle spinning (MAS),can be applied to very successfully remove this residualbroadening and obtain spectra that are by and largecomparable to solution-state spectra. This holds in

6 4 2 0

6.0 5.9 5.8 5.7 1.0 0.5 0.0 −0.5 −1.0

6.0 5.9 5.8 5.7

(a)

(b)

(c)

1.0 0.5 0.0 −0.5 −1.0

×100

Irel = 2.1%

Irel = 0.36%

Si(CH3)2O—Si(CH3)2O—Si(CH3)—

+(H(CH3)2Si)2O

(Pt cat.)

H(CH3)2SiO—Si(CH3)2—CH2

—

H2C

—Si(CH3)2O—Si(CH3)—

—

ppm

6 4 2 0 ppm

[ ] ][

[ [

n m

n

F0030 Figure 6 NMR analysis of poly(dimethyl siloxane) (PDMS) elastomer formation via cross-linking of PDMS with methyl-vinyl-siloxane

co-units and a difunctional silane cross-linker: (a) reaction scheme, (b) 1H solution-state spectrum of the linear precursor polymer in

CDCl3, and (c)1H MAS spectrum (4 kHz rotation frequency) of the bulk elastomer. The insets are vertically magnified by a factor of

B100. For comparison, a static spectrum of octane-swollen PDMS is shown as a dotted line in (c).

SSP2 00032

6 Magnetic Resonance: Polymer Applications of NMR

particular for 1H spectra, which are hard to obtain at highresolution in a truly rigid solid. Note that MAS cannotremove line broadening arising from true relaxation ef-fects such as slow conformational exchange. In such cases,temperature variation is the only remedy.

P0085 For the investigation of soft solid systems, MASprobes with very good magnetic field homogeneity (shim)and thus good spectral resolution, and a deuterium locksystem for field stabilization, have recently becomeavailable for solution-state narrow-bore magnets underthe label HRMAS, for high-resolution MAS. Spinningfrequencies of a few kilohertz are usually sufficient toobtain spectra of solution quality, and HRMAS hasgained popularity for the investigation of membrane- orcarrier-bound but locally dissolved, thus mobilized, bio-logical macromolecules.

P0090 Even without elaborate shimming and a lock, simpleslow-MAS 1H spectroscopy, potentially using a cost-ef-ficient narrow-bore MAS probe, allows for many fruitfulapplications in polymer science, and appears somewhatunderestimated to date. An example is given in Figure 6,which shows solution-state and bulk-state MAS spectraof a vinyl-functionalized poly(dimethylsiloxane) pre-cursor polymer, and the derived silicone elastomer aftercross-linking with a bifunctional silane via a hydro-silylation reaction, respectively. Here, swelling of theelastomer to enhance chain motion is not even necessary,as the chains are very mobile (far above Tg) at roomtemperature. Figure 6(c) demonstrates that even theaddition of solvent does not yield a spectrum with goodresolution without MAS (dotted line), while the MASspectrum is sufficiently resolved to identify all of thedifferent functional groups. From this spectrum, the re-sidual content of unreacted vinyl groups, as well as thecontent of –CH2–CH2– cross-linking groups, isstraightforwardly obtained by integration. Therefore, theaverage cross-link density, inversely related to the molarmass of the different network chains, can directly beobtained from such spectra. There is, in fact, no otherdirect method that serves this purpose, since networksand elastomers are per se nonsoluble; alternatives arethermodynamic (swelling), mechanical, or NMR relax-ation measurements, all of which are indirect and requirecalibration or models.

S0035 Solid-State NMR

P0095 The major challenges posed by bulk polymers are thatthey are either at least two-phase systems (semicrystal-line or block copolymers) or they undergo dramaticchanges in their properties with temperature at aroundthe glass transition. Amorphous phases below Tg andcrystalline phases behave as rigid solids that require thefull spectrum of methods from solid-state NMR, whereas

soft melt-like phases (well above Tg) can in the NMRsense be treated as liquids, however with some residualsolid-like properties. It is thus not uncommon thatpolymer scientists apply both solid- and solution-stateexperiments to their sample, to elucidate the potentialmultiphase character or to infer the ‘softness’ of thematerial on a molecular scale.

0.00

(a)

(b)

0.0

0.6

0.7

0.8

0.9

1.0

FID

inte

nsity

Acquisition time (ms)

200 kHz

Crystalline

Amorphous

700

600

500

400

300

200

100

00 10 20 30 40 50 60

Number of bonds/crosslink

T2f

P (

μs)

0.02 0.04 0.06 0.08

F0035Figure 7 Low-resolution 1H NMR of semicrystalline polymers

and networks. (a) FID of syndiotactic polypropylene at 382K –

the two-component decomposition (dashed line: melt signal

extrapolation) indicates a crystallinity of B20%. The inset showsthe corresponding Fourier transform, with the shaded area as the

(Gaussian) crystalline component. Data replotted from Maus S,

Hertlein C, and Saalwachter K (2006) A robust proton NMR

method to investigate hard/soft ratios, crystallinity, and

component mobility in polymers. Macromolecular Chemistry and

Physics 207: 1150–1158. (b) Linear correlation of the high-

temperature plateau value of T2 of thermoset epoxy networks

with the number of bonds (Bmonomers) per network chain. Thelines are fits to different models. Reproduced from Fry CG and

Lind AC (1988) Determination of cross-link density in thermoset

polymers by use of solid-state 1H NMR techniques.

Macromolecules 21: 1292–1297, with permission from the

American Chemical Society.

SSP2 00032

Magnetic Resonance: Polymer Applications of NMR 7

S0040 Low-Resolution 1H NMR

P0100 The simplest way to explore the multiphase character ofa polymer system is to study its overall 1H relaxationbehavior, often simply reflected in the time-domain free-induction decay (FID), or by lineshape analysis afterFourier transformation. Proton spectra, by virtue of thestrong orientation-dependent homonuclear dipolarcouplings among the many abundant spins, with couplingconstants on the order of 30 kHz for two nearby CH2

protons, are very sensitive to molecular motion. Large-amplitude reorientations exceeding 105 kHz mark thetransition into the soft, liquid-like domain, with sub-stantially reduced couplings and thus narrower lines. In asemicrystalline polymer below Tm, with an amorphousphase well above Tg, a broad crystalline line (up to50 kHz, due to multiple couplings) coexists with a nar-rower amorphous line (B102 to 104Hz), which in thetime domain corresponds to a rapidly decaying crystal-line contribution (B20 ms) and an amorphous partdecaying in the milliseconds range. Simple de-composition into two components yields the approximatecrystallinity in many cases. An example is displayed inFigure 7(a) for a measurement of syndiotactic poly-propylene. Note that the detection of signal immediatelyafter the excitation pulse is subject to a dead timeproblem (needed for pulse ring-down before detectioncan start), which must be overcome by suitable spin echomethods.

P0105 Such experiments are not restricted to semicrystallinepolymers, but may also be of use for phase determinationin phase-separated block copolymers or polymer blends,where the different components exhibit sufficient dy-namic contrast. An important caveat is, however, thenontrivial, in most cases nonexponential, T2 behavior inpolymeric systems, leading to ambiguities in multi-component fits. The transverse relaxation behavior of arigid system is almost Gaussian, because the decay is nota true motion-induced T2 process, but rather a dipolardephasing (dipolar couplings cannot be refocused by asimple Hahn echo). A more mobile, amorphous phasecan exhibit any decay shape between a Gaussian and anexponential or even a stretched, multicomponent ex-ponential, depending on whether the decay is dominatedby residual dipolar couplings that arise from partiallyanisotropic chain motion or by the timescale of seg-mental fluctuations, respectively. Sample heterogeneity,such as mobility gradients, also plays a role here. Thismeans that the apparent ‘T2’ mostly has only heuristicvalue – the decay curves are hard to interpretquantitatively.

P0110 The relaxation behavior of networks or elastomers isusually completely dominated by residual dipolar coup-lings, as network chains are fixed at both ends and cannever move isotropically. This is why T2 in networks

approaches a high-temperature plateau when heatedsufficiently far above Tg, where the segmental motion istoo fast to exert an appreciable influence. In this regime,the apparent T2 is inversely proportional to the averageresidual dipolar coupling constant, which in turn is in-versely related with the number of monomers in a net-work chain. An example is shown in Figure 7(b).Therefore, T2 results are directly related to the mech-anical properties of elastomers, in that they providemolecular-level information on the cross-link density.Yet, as stated above, a direct conversion requires manymodel assumptions. Nowadays, much more elaboratemultiple-quantum experiments provide a more directand quantitative means to not only measure residualdipolar couplings, but also assess aspects of its distri-bution. In this way, details on the microstructure ofnetworks have become accessible.

P0115The fact that a mesoscale motional anisotropy, leadingto residual couplings, plays a role in such experimentsmeans that they provide information on the chain dy-namics on a semilocal scale. T2 and related phenomenaare thus not only useful for the study of elastomers, butalso provide valuable tools to study, for instance, thedynamics of the amorphous/mobile chains in semi-crystalline polymers or block copolymers, and of en-tangled polymer melts. Complementarily, the timescaleand details of fast segmental motions are well in the ‘li-quid’ range, and may be studied by T1 relaxation, and incombination, polymer dynamics can be studied overseveral orders of magnitude in time. It should be notedthat such experiments do not necessarily require super-conducting high-field spectrometers – cost-efficient, low-field equipment is often fully sufficient, as the effects inquestion are based on dipolar couplings and are thus fieldindependent. This of course only holds if chemicalresolution is not necessary.

P0120The low-resolution assessment of phase compositionin any heterogeneous polymer system is of course crit-ically based on sufficient mobility contrast. If, for in-stance, the amorphous phase of a semicrystalline polymeris not mobile enough, and temperature variation wouldalter the structure or the morphology, high-resolution13C spectroscopy is inevitable.

S0045High-Resolution 13C NMR

P0125High-resolution 13C NMR spectroscopy in solids iscommonly achieved by MAS in combination with high-power dipolar decoupling (DD) and cross polarization(CP). MAS and DD provide spectral resolution, that is,they split up the wide and, in polymers, often featurelesspowder line shapes into relatively narrow lines. AlthoughMAS-DD spectra often do not reach the line resolutionof solution-state spectra (the line width in solids is on theorder of few parts per million, whereas in liquids it is

SSP2 00032

8 Magnetic Resonance: Polymer Applications of NMR

typically down to 0.1 ppm), they still provide usefulspectral information. First, the larger line width is oftendue to distributions in conformations, thus it carries in-formation on disorder. In fact, the 13C lines of crystallinephases in semicrystalline polymers are often almost asnarrow as solution-state lines. Second, the line widthmust be considered in relation to the overall chemicalshift range of approximately 200 ppm and compared withthe very limited resolution of 1H solid-state spectra,which – even under very fast MAS or multipulse linenarrowing – exhibit line widths on the order of 1 ppm ona chemical shift scale of only approximately 10 ppm.

P0130 CP, on the other hand, permits a substantial short-ening of the experimental time, as it produces a strongersignal (theoretically up to a factor of 4 for 13C, practicallybetween 2 and 3, as compared to direct 13C excitation)and permits a shorter repetition time between sub-sequence signal averages due to its dependence on theshorter 1H T1, which is approximately one order ofmagnitude shorter than the 13C T1, which in turn governsthe repetition time of directly excited 13C spectra. MAS

and DD had already been combined with CP in the1980s, and still represent the major methodology for al-most all solid-state 13C experiments. A comparison of CPspectra with DD (removing dipolar couplings), with andwithout MAS (removing the 13C chemical shift an-isotropy), is presented in Figure 8. The dramatic increasein resolution (accompanied by a large time saving) isreadily apparent.

P0135Although, owing to the limited resolution, infor-mation on the monomer sequence is hard to obtain fromsolid-state spectra, supramolecular structural featuressuch as amorphous or crystalline phases are more easilyrecognizable. Usually, chemical segments in the crystal-line phase are more rigid or they feel a chemically similarenvironment, leading to relatively narrow lines, whereassegments in the amorphous phase are in a disorderedenvironment, leading to a distribution of isotropicchemical shifts and broad lines, which might additionallybe subject to dynamic broadening. Thus, depending ontemperature, the molecules exhibit a molecular mobilityin the kilohertz range, which interferes with the linenarrowing by MAS and DD and leads to temperature-dependent line broadening. As an example, Figure 9shows the structure of the crystalline phase of a specificsemicrystalline polyolefin, the crystallite chains of whichform 72 helices. The broad bases of the lines in the 13CCPMAS spectrum (dotted ellipses) arise from contri-butions of the amorphous phase, which can be suppressedby a relaxation filter.

P0140The authors would like to draw the attention to acomparison between the inset of Figure 7, where theamorphous and crystalline components were assigned tothe narrow and wide proton subspectra, respectively, andthe just explained reversed assignment in the carbonspectrum. The apparent contradiction can be understoodon the basis of the dynamic properties of the differentphases and the different origins of line broadening in 1Hand 13C spectra: the molecules in the crystalline phaseare rigid and experience a large 1H-1H dipolar coupling,resulting in a wide 1H spectrum that is almost entirelygoverned by this interaction, whereas the higher mobilityof the molecules in the amorphous part partially averagethis coupling, resulting in a narrower line. This assign-ment is generally valid, and challenged only in caseswhere Tg of the amorphous phase is not low enough torender it sufficiently mobile.

P0145In 13C spectra, however, the dominant interaction isthe isotropic chemical shift of the carbons, since theanisotropic chemical shift as well as the dipolar couplingsare (usually) efficiently suppressed by MAS and DD.Thus, the line widths are determined by the degree oforder of the local environment of the probe nucleus,explaining the reversed assignment.

P0150This component assignment in 13C spectra is, un-fortunately, not unique. In unfavorable cases, amorphous

COO

(a)

(b)

C1−5, CH3

C4 C5

C2

C1

C5

C4

C3

C2C1

C3

COO

OO

C

CH3

CH3

250

* ** *

* **

150 50 ppm

CH3

×10

F0040 Figure 8 13C CPMAS spectrum of poly(n-butyl methacrylate):

(a) nonspinning and (b) under MAS condition with a spinning rate

of 4 kHz. Note that in (a), the resonances of the aliphatic carbons

overlap, whereas they are well resolved in (b). Also, the powder

pattern of the carboxyl resonance is well recognizable in the static

spectrum, due to its large high frequency (deshielded) shift and

the large chemical shift anisotropy. The information about the

chemical shift anisotropies still appears in the MAS spectrum in

the form of spinning sidebands (*).

SSP2 00032

Magnetic Resonance: Polymer Applications of NMR 9

and crystalline line widths and positions can in fact behardly distinguishable. A particularly unusual case ispoly(ethylene oxide), where the assignment of the roomtemperature 13C spectrum is again reversed, as thecrystalline resonance is extremely broad due to inter-mediate (kilohertz) mobility of the chains in the crys-tallites (helical jumps) that interfere with the decouplingand MAS (details on such motional broadening effectsare addressed in the next section). In addition, the crys-talline helix in this polymer is disordered, such that theline remains B3 ppm broad even at low temperaturewhen the chain motion is slowed down. From this ex-ample, it could be noted that complex motional effectsand other origins of line broadening may always con-tribute to the line widths of carbon MAS spectra ofpolymers, and must be carefully considered and ex-plored, for example, by temperature variation.

P0155 Given the lack of or an ambiguity in spectral dis-tinction between different phases or components, theirseparation can be aided by relaxation-time filters that arebased on different mobilities. The easiest of these is asimple change in the repetition delay between sub-sequent scans for signal averaging (corresponding to a 1HT1 filter when CP is used, or a 13C T1 filter in case ofdirect excitation). A good general way to explore coex-isting mobile amorphous and rigid crystalline or glassyregions (in semicrystalline polymers or block co-polymers, respectively) is to simply compare 13C directexcitation spectra with repetition delays on the 1 stimescale (emphasizing mobile amorphous regions), andCPMAS spectra with short CP (emphasizing rigid re-gions). Other possibilities are, for instance, using thedifferent T1r of either 1H or 13C by changing the CPspin-lock time, or exploiting T2 differences by adding

Hahn echo delays on either channel (either before orafter the CP). An example of a T1r filter procedure forcomponent separation in a semicrystalline polyolefin ispresented in Figure 9(c).

S0050Multidimensional 13C NMR

P0160It is obvious from the above that in solid-state 13Cspectra, the structural information (provided by the iso-tropic chemical shift value) is often concealed by dy-namic information, which arises from different degrees ofaveraging of anisotropic interactions by molecular mo-tions. Such interactions are the anisotropic chemical shiftand the homo- and heteronuclear dipolar coupling, aswell as the quadrupolar coupling when nuclei withI4 1/2 are measured (this will be addressed in the nextsection). Basically, all these interactions (except thequadrupolar coupling) contribute to the appearance ofthe 13C spectrum and in principle, the spectra can besimulated to determine the different contributions and toextract the desired information. Note that even indirectcouplings, such as 1H-1H homonuclear dipolar couplings,affect 13C spectra in a way that they interfere with theefficiency of DD and increase the line width.

P0165However, in particular under conditions of finite sig-nal-to-noise and due to the large number of potentiallyinvolved spins and the complex dynamics, full spectralsimulation is in practice almost impossible. Instead, it isdesirable to separate the different effects in different(spectral or time) dimensions of multidimensional ex-periments. The probably simplest example is the acqui-sition of 13C CP spectra as a function of the above-mentioned relaxation filter durations, incremented inregular intervals. One can then achieve a component

ppmppm

C3 C1 C2

C4, C5

(a)

(b)

(c)

C6

299 K

488 K

Difference

Difference

60 50 40 30 20 10 60 50 40 30 20 10

C5

C4C6C2

C3

C1

F0045 Figure 9 13C CPMAS spectra of poly(1-methyl-1-pentene). (a) The 72 helical structure of the crystallites (view down the c axis). (b)

CPMAS spectrum and resonance assignment. (c) Separation of amorphous and crystalline signals by a T1r filter at two temperatures.

The spin-lock times tCP are 0.01ms for the full spectra, containing both components, whereas longer tCP times (10ms at 299K and 4msat 448K) allow the signals from the amorphous molecules to relax away, leaving only the signals from the crystallites (dotes lines). The

difference spectra contain the amorphous signals only. Reproduced from Miyoshi T, Pascui O, and Reichert D (2004) Slow chain

dynamics in isotactic-poly(4-methyl-1-pentene) crystallites near the glass transition temperature characterized by solid-state 13C MAS

exchange NMR. Macromolecules 37: 6460–6471, with permission from American Chemical Society.

SSP2 00032

10 Magnetic Resonance: Polymer Applications of NMR

decomposition of the spectrum and at the same timeestimate the respective relaxation times.

P0170 Turning to ‘true’ 2D spectroscopy, such experimentscan, for instance, correlate the isotropic chemical shift inone dimension with the anisotropic chemical shift or

heteronuclear dipolar coupling in a second dimension.The latter are termed ‘separated local field’ (SLF) ex-periments, and are among the most popular approaches,because they are robust, easy to implement and requirestandard hardware only. Last but not least, the hetero-nuclear dipolar interaction is well defined (as it reflectsthe arrangement of heterospins in the immediate sur-roundings of the nucleus) and thus easy to interpret. Aparticularly simple and correspondingly popular se-quence is the so-called WISE (wideline separation) ex-periment, which is not strictly an SLF experiment, butsimilar to it, in that it correlates the carbon CPMASspectrum with the 1H wideline spectrum of the protonsclosest to the carbon. The pulse sequence is identical tothe CPMAS sequence with a short CP time (for localtransfer), with the only difference that an incrementeddelay is inserted between the first 1H pulse and the CPspin lock, during which the 1H FID is probed. The pulsesequence, as well as typical proton and carbon spectraalong with their separation in a 2D WISE spectrum, isdepicted in Figure 10.

P0175As mentioned already in the preceding section, a verysimple alternative and the most recommendable firstapproach to asses dynamic heterogeneity is to compareCP spectra acquired with rather short contact time (po-larizing only rigid, strongly dipolar-coupled 13C) withone-pulse direct-polarization spectra taken with a shortrecycle decay on the order of a few seconds (emphasizingsignals from highly mobile liquid-like 13C with cor-respondingly short T1). With such experiments, or bycomparing the wide or narrow lines in the proton di-mension of 2D WISE spectra, it is very easy to dis-tinguish carbons from rigid and mobile domains.However, even from the resolved proton line shapes, it isdifficult to draw truly quantitative conclusions, since thehomonuclear 1H-1H coupling involves many nuclei andis hard to simulate correctly.

P0180More elaborate, true SLF experiments utilize 1Hhomonuclear decoupling, which leaves the 13C-1H di-polar interaction as the only remaining coupling for thesecond dimension and thus, provide a much clearerpicture. Examples are the DIPSHIFT (correlation ofdipolar and chemical shift information) and LG-CP(Lee-Goldburg cross polarization) experiments. Thelatter is in fact just a more quantitative version of thetraditional CP experiment, in which the 13C-1H dipolarcoupling is extracted from the intensity buildup as afunction of the variable CP time. Such experiments arealso particularly suited for the quantitative measurementof residual heteronuclear dipolar couplings, as addressedbelow.

DDCP

CP

(a)

(b)

(c)

Mobile

Rigid

1H

1H

PS PS

PVME

13C t2

13C

13C

1H

t1

150 100 50 0 ppm

50−50 0 50 kHz 0100150ppm

100

kHz

F0050 Figure 10 (a) Pulse sequence

AU3

of the WISE experiment.

Typical magnetization decays are shown for mobile (full line) and

rigid components (dotted line). (b) 1H (left) and 13C spectrum

(right) of a 1:1 blend of poly(styrene) and poly(vinyl methyl ether).

The 1H spectrum is the superposition of wide and narrow

components that originate from the different polymers, due to

their different mobilities. They cannot be distinguished here,

whereas in the 13C spectrum the resonances of the two polymers

are well separated. These two different sets of information can be

nicely separated in the 2D WISE spectrum (c). Reproduced from

Schmidt-Rohr K, Clauss J, and Spiess HW (1992) Correlation of

structure, mobility, and morphological information in

heterogeneous polymer materials by two-dimensional wideline-

separation NMR spectroscopy. Macromolecules 25: 3273–3277,

with permission from John Wiley & Sons Ltd.

SSP2 00032

Magnetic Resonance: Polymer Applications of NMR 11

S0055 Dynamic and Exchange NMR

P0185 As already alluded to, indirect structural information canalso be inferred from dynamic data, for example, from thedifferent mobility of molecules residing in amorphous orcrystalline phases. Thus, and in particular due to the factthat many mechanical properties depend crucially on themolecular mobility of the polymer chains, it is desirableto determine the kinetic parameters quantitatively, thatis, both amplitudes and time constants. Molecular dy-namics in polymers spans a wide range of correlationtimes, from very fast processes on the order of pico- andnanoseconds, up to slow motions on the order of milli-seconds or even seconds. To cover this entire range,different techniques have to be applied.

P0190 For fast processes, relaxation techniques as explainedin the Solution-State Studies section can be employed.Additionally, the measurement of partially averaged an-isotropic couplings is particularly informative in thisregime, as in solids or soft semisolids (such as glassy orrubbery polymers), and in contrast to the liquid state,anisotropic motions do not average the interactionscompletely, even though they may be very fast. Thedegree of averaging depends on the amplitude of themotional process and is commonly parameterized by aso-called dynamic order parameter, which is just the ratioof the measured, partially averaged coupling to the valuefor a completely rigid segment, that is, the full coupling.For specific models, the order parameter can be recastinto amplitudes of motion, however, in most cases, theorder parameter itself, and its temperature dependenceor the comparison between different samples, providesuseful information.

P0195 So-called intermediate motions with correlation timesin the microsecond range can be easily recognized fromthe temperature dependence of the carbon spectra, as themolecular process occurs on the timescale of the lifetimeof the NMR signal (as reflected in the T2 relaxation time,or the decay time of the FID). In combination with high-resolution line-narrowing techniques such as MAS orDD, it has to be kept in mind that these remove contri-butions from the anisotropic chemical shifts or dipolarcouplings by modulating the spin interactions (either inreal space or in spin space, respectively) with a typicalfrequency (the MAS rotation frequency or the nutationfrequency of the 1H irradiation, respectively). Now, if theinverse of the correlation time of the molecular motionapproaches these modulation frequencies, the efficiencyof the line-narrowing mechanism deteriorates and a so-called dynamic line broadening appears, permitting asimple qualitative assignment of a correlation time to theinverse modulation frequency at the temperature atwhich the maximum broadening appears.

P0200 More quantitative information can be obtained fromthe comparison of calculated/simulated spectra with

experimental ones, and the application of SLF experi-ments in this dynamic range. However, the by far mostaccurate approach for intermediate motions is the ac-quisition of 2H spectra and the comparison with calcu-lated line shapes. These experiments have an inherentlylow resolution, as the lines are very broad (but wellstructured), and the price to pay is the effort in thepreparation of selectively 2H labeled substances, in orderto study the motional processes with molecular reso-lution. On the positive side, the 2H quadrupolar inter-action as the dominant spin interaction is an extremelylocal and well-defined dynamic probe, as it is merelysensitive to orientations of the (asymmetric) local elec-tronic environment of the nucleus, and the spectra cantherefore be simulated rather accurately. This is dem-onstrated in Figure 11 for local motions in glassypoly(carbonate), where the different chemical groups

Observed

100 kHz

Calculated

T = 380 k

T = 293 k

Phenyl − 2H

50 kHz

T = 380 k

T = 293 k

Methyl − 2H

CH3 CH3CH3CH3

C

O OX

O

CC

F0055Figure 11 Observed and calculated 2H spectra of selectively

deuterated polycarbonate. The methyl deuterons exhibit for both

temperatures the typical spectrum of a rotating methyl group with

a quadrupolar coupling constant that is reduced by a factor of 3.

At room temperature, the spectrum of the phenyl ring

corresponds to a deuteron attached to a fast flipping ring,

whereas at higher temperature, an additional small-angle motion

of the polymer chain contributes to reducing the line width and

changing the shape. Reproduced from Spiess HW (1983)

Molecular dynamics of solid polymers as revealed by deuteron

NMR. Colloid and Polymer Science 261: 193–209, with

permission from Springer-Verlag GmbH.

SSP2 00032

12 Magnetic Resonance: Polymer Applications of NMR

have been labeled and studied separately. The thus- quantified phenyl flip motion is in fact an importantcontributor to the efficient dissipation of mechanicalenergy in this high impact strength polymer.

P0205On the slow end of the dynamic range of NMR ex-periments are the so-called exchange experiments, whichare capable of detecting molecular reorientations thatoccur on timescales much longer than T2. Such motionsdo not lead to notable spectral changes. Exchange NMRrelies on the fact that molecular orientations are encodedin NMR frequencies via anisotropic interactions, and thatany change in molecular orientation results in a changein the resonance frequency of the probe nucleus, inprinciple on any timescale. A technique that can detectthese frequency changes can thus be used to detect suchdynamic processes. The general principle is always thatafter measuring the interaction frequency (¼ orientation)during an evolution delay, the magnetization is storedalong the magnetic field axis (along z) by a 901 pulse. It isthen read out again after a mixing time that is limitedonly by the (often very long) T1 relaxation time, and asecond frequency measurement (most often just a spec-trum acquisition) follows right after.

P0210These experiments are therefore most often two-di-mensional: NMR data (FIDs) are sampled in two timedimensions that are separated by a freely chosen mixingtime, during which the molecular dynamic process canoccur. A two-dimensional Fourier transform correlatesthe data from the two time domains in a 2D spectrum,and whenever a process has changed the molecularorientation, peaks off the main diagonal of the spectrumimmediately reveal the dynamic process. The widespreadapplication of such methods started out in the 1980s, withapplications of 2H- and 13C-CSA AU4-based methods,prominently by the Spiess group, and MAS variants for13C samples in natural abundance. An example for theformer is shown in Figure 12, where the more compli-cated phenyl ring motion in poly(styrene) is elucidatedby 2D 2H exchange methods on the slow (low-tem-perature) end, and is complemented by information fromother dynamic NMR experiments in order to charac-terize the process over almost 10 orders of magnitude intime. It should be noted that the off-diagonal intensitydistribution in the 2D spectra sensitively encodes thereorientation angle, which is in this case distributed overa wide range, as the underlying process corresponds torotational diffusion.

P0215On the down side, the 2D acquisition scheme rendersthe 2D approach rather time consuming, and as one ofthe most recent improvements, the so-called CODEXsequence, illustrated in Figure 13, was established as aneasy-to-implement and robust one-dimensional MASmethod that permits the reliable determination of boththe correlation time of motion as well as its amplitude innatural isotopic abundance. In this high-resolution 1Dmethod, the sampling of the time-domain signal in the

2.3 2.4

τ c [S

]

2.5

1000/T (k−1)

2.6 2.7

440

3 decades

1.104

1.102

1.100

1.10−2

1.10−4

1.10−6

1.10−8

425 410T (K)

395 380 365

2D NMR

Spin-LatticeRelaxation

β

α

0 20 40 60 80

<�c> = 6 ms

Tg

−126

−126

126

126

0

(a)

(b)

(c)

0

T = 391 Ktm = 6 ms ω1 (kHz)

CH2 CH x

�

P(�)

2π

ω1 (kHz)2π

F0060 Figure 12 (a) Experimental and (b) calculated 2D exchange2H spectra of chain-deuterated poly(styrene) (PS) at 391K and a

mixing time of 6ms. The calculated spectrum is generated on the

basis of an isotropic rotational diffusion model with a log-

Gaussian distribution of correlation times (width B3 decades,centered around 6ms), and the corresponding jump-angle

distribution is shown in the inset. (c) Arrhenius plot of the mean

correlation times for PS resulting from different experiments, with

a common Williams-Landel-Ferry fit to the data describing the

temperature dependence of the a process associated with theglass transition. Reproduced from Kaufmann S, Wefing S,

Schaefer D, and Spiess HW (1990) Two-dimensional exchange

NMR of powdered samples. III. Transition to motional averaging

and application to the glass transition. Journal of Chemical

Physics 93: 197–214, with permission from American Institute of

Physics.

SSP2 00032

Magnetic Resonance: Polymer Applications of NMR 13

indirect dimension is replaced by a fixed evolution timeduring which the magnetization can acquire a certainphase, arising from the anisotropic chemical shift (CSA)frequency, thus encoding the molecular orientation. Thesame is done after the mixing time, and the signal in-tensity in the highly resolved 13C spectrum finally de-pends on whether the nucleus in question along with itsanisotropic shielding environment has rotated or not.The 1801 pulses during these periods manipulate theacquired phase, in a sense that they actually reverse theaveraging by MAS (which would in principle precludethe CSA measurement, see Figure 8). This is called‘recoupling’ and represents a very general techniqueoften applied in solid-state MAS NMR. The length ofthe evolution/recoupling time necessary to observe theexchange process is in fact a quantitative measure of themotional amplitude, and actually provides an even bettersensitivity for small-amplitude motions as compared totraditional static 2D exchange spectroscopy.

S0060 Spin Diffusion NMR

P0220 Truly structural methods are the so-called spin diffusionexperiments, which can be used to determine domainsizes in materials that are not suited for scattering studies(e.g., by missing long-range order). Spin diffusion is an

effect driven by homonuclear dipolar interactions be-tween abundant spins, mostly protons, by which mag-netization is transported between spatially fixed spinsover distances as large as some 100 nm by a quantum-mechanical flip-flop process. It can in fact be measuredwith the same one- or two-dimensional versions of ex-change spectroscopy mentioned above, just because spindiffusion occurs on similar, rather long timescales be-tween the z components of differently polarized spins.Spin diffusion is often a competing process to dynamicexchange, and temperature variation can be used todistinguish between the two: spin diffusion is only weaklytemperature dependent, and if at all, the process becomesslower with increasing temperature, due to dynamicaveraging of the dipolar interaction that is responsible forit.

P0225A typical experimental scheme is shown in Figure 14.Two phases A and B that can be discriminated by theirNMR parameters (e.g., crystalline and amorphous), inthis case by the resonance frequencies, contribute to theNMR spectrum. By a selection process that can berealized either by selective excitation or the applicationof relaxation filters or dipolar filters, a single component(in this case A) is selected. Then the magnetization ispermitted to spread by spin diffusion throughout thesample during a mixing time, and eventually, the

MAS rotor

(a)

(b) (c)

2N−1 2N−1

1.0Experiment1.0

0.8

0.6

0.4

S/S

0

S/S

0

0.2

0.00.1 1 10 100

�m (ms)

1000

0.8

10°20°30°50°70°103°

0.6

0.4

0.00.0 1.5 3.0 4.5

NTR (ms)

t

π/2 π/2 π/2 ππ

13C �m= nTR

F0065 Figure 13 Pulse sequence and data of the 1D MAS exchange experiment CODEX, as applied to slow motions in the crystalline phase

of a polyolefin. (a) Pulse sequence (13C channel only). The essential parts are the mixing period tm, which is sandwiched between tworecoupling cycles, applying trains of rotor-synchronized p-pulses. (b) To extract the correlation time of motion, the number of recouplingcycles is kept constant while the length of the mixing period tm is incremented logarithmically. The longer the tm, the more moleculesperform a reorientation, leading to signal decay. The straight line is a fit to a stretched exponential function yielding the average tc. (c)For information on amplitude of motion, tm is kept constant at a value larger than tc and the number of recoupling cycles is incremented.For more details, see Miyoshi T, Pascui O, and Reichert D (2002) Helical jump motion in isotactic-poly(4-methyl-1-pentene) crystallites

revealed by 1D-MAS exchange NMR spectroscopy. Macromolecules 35: 7178–7181.

SSP2 00032

14 Magnetic Resonance: Polymer Applications of NMR

polarized B spin signal reappears in the spectrum. Givena dynamically heterogeneous multiphase structure, suchexperiments can in fact be performed under low-reso-lution conditions (see Figure 7), using the mobilitycontrast both for the phase-specific selection of mag-netization, as well as for the component-specificdetection.

P0230 The experiment is repeated for different mixingtimes, and the increase of the B component or the decayof the A component yields information on the domainsizes, provided the NMR parameters (i.e., the spin

diffusion coefficients) and the overall structure of thephases (1D diffusion in a lamellar system vs. 2D diffusionamong cylinders, etc.) are known. Another distinguishingfactor is that spin diffusion is described by a square rootof time law in its initial stages (cf. the Einstein-Smo-luchowski equation), whereas a dynamic exchange pro-cess follows an exponential rate law, which is linear in theearly stage. Thus, a linear behavior in a plot of the in-tensity versus the square root of time reveals a spindiffusion process, and the initial slope encodes the size ofthe domain, as is apparent from Figure 14(b).

Selection Spin diffusion

A B A

x

A A A

A

BB

AB

B

x x x x

100

80

60

Sig

nal i

nten

sity

PS

40

20

00 2 4 6 8 10 12 14

1 2 5 10 20 50 100 200

> 500 nm M

80 nm B4

67 nmB3

24 nmB2

10 nmB1

1.5 nmS

tm (ms)

tm½ (ms½)

tmNMR spectra

1H magnetization(a)

(b)

mz

lz lz lz lz lz

mz mz mz mz

�cs �cs �cs �cs �cs

F0070 Figure 14 (a) Schematic representation of 1H spin diffusion in a two-phase system with spatially constant proton density. After the

selection period, protons are polarized only in one phase A, and the NMR spectrum only shows the corresponding signals. The

redistribution of magnetization by 1H spin diffusion is monitored in the spectrum: with increasing mixing time, the intensity of signals

corresponding to the selected region A decreases, whereas the signal intensity of the initially depleted region B increases. (b) Spin

diffusion diagrams as obtained for different PS-PMMA block copolymer samples. The values at the simulation curves indicate the long

periods daþdb. Reproduced from Clauss J, Schmidt-Rohr K, and Spiess HW (1993) Determination of domain sizes in heterogeneous

polymers by solid-state NMR. Acta Polymerica 44: 1–17, with permission from Wiley Interscience.

SSP2 00032

Magnetic Resonance: Polymer Applications of NMR 15

S0065 Oriented Polymers

P0235 Last but not least, it is possible to make use of theorientation dependence of the NMR resonance fre-quency to obtain information on molecular orientationsin anisotropic polymeric systems such as stretchedpolymers or fibers. Since the resonance frequency of anucleus is – for anisotropic interactions – determined byits orientation versus the external magnetic field, it isobvious that the distribution of orientations immediatelyshows up in the solid-state NMR spectrum. Such studiesare limited to samples where dynamic effects on thespectra are absent, that is, the samples are either com-pletely rigid (e.g., cooled below Tg), or motions that arepresent must be anisotropic and in the fast limit (e.g.,methyl rotation or phenyl flips).

P0240 The principle of the approach is illustrated by perfectpowder spectra (‘Pake’ patterns) such as the CSA patternof the carbonyl carbon in Figure 8(a) or the quasi-static(pre-averaged) 2H spectrum of the methyl group inFigure 11, which only arise if the distribution of differentorientations in the sample is completely isotropic. Anysuch prototypical solid-state spectra become distortedonce a macroscopically oriented or otherwise orderedsample is measured: if not all orientations are presentwith the same probability, the deviations of the spectralshape from the Pake pattern arise and allow for aquantitative extraction of the orientation distribution.Even better quantification is possible if spectra withdifferent orientations of the magnetic field with respectto the sample axes (e.g., the stretching direction) areacquired and analyzed simultaneously. A limiting case isrepresented by liquid-crystalline systems, which oftenorient perfectly in the magnetic field, or simply by sin-gle-crystal samples, where the Pake spectrum is reducedto a single line (or a single splitting), corresponding to asingle orientation. Observing and analyzing spectra atdifferent sample orientations is often referred to as‘NMR crystallography’.

P0245 As is also obvious from the two figures addressed,again, 2H is the most useful nucleus for such

investigations, since the quadrupolar interaction isstrictly local, large, and dominant (whereas the CSAspectrum can be broadened by imperfect decoupling,conformational disorder, etc.). Further, the orientation ofthe quadrupolar symmetry frame is in good approxi-mation parallel to the chemical bond that connects thedeuteron to the rest of the molecule, rendering a quan-titative interpretation of the orientation distribution ra-ther straightforward. Again, the price to pay is thesynthetic effort to label the polymers with 2H. However,multidimensional (recoupling) MAS methods, whichwork for 13C in natural abundance, have also been ap-plied for this purpose. In this case, numerical proceduresto extract structural information from the intensities ofspecific spinning sidebands are needed, and are often lessquantitative than fits to perfect static EQ1

2H spectra.

Further Reading

Blumich B (2000) NMR Imaging of Materials. Oxford: Oxford UniversityPress.

deAzevedo ER, Bonagamba TJ, and Reichert D (2005) MolecularDynamics in Solid Polymers. Progress in Nuclear MagneticResonance Spectroscopy 47: 137--164.

Hatada K and Kitayama T (2004) NMR Spectroscopy of Polymers.Berlin, Germany: Springer-Verlag.

Ibbett RN (ed.) (1993) NMR Spectroscopy of Polymers. London:Chapman & Hall.

Kimmich R (1998) NMR: Tomography, Diffusometry, Relaxometry.Berlin, Germany: Springer-Verlag.

Komoroski RA (ed.) (1986) High-Resolution NMR Spectroscopy ofSynthetic Polymers in Bulk. Weinheim, Germany: VCH.

Mathias LJ (ed.) (1988) Solid State NMR of Polymers. New York:Plenum Press.

McBrierty VJ and Packer KJ (1993) Nuclear Magnetic Resonance inSolid Polymers. Cambridge, UK: Cambridge University Press.

Reichert D and Saalwachter K (2008) Dipolar coupling: Molecular-levelmobility AU5. In: Grant DM and Harris RK (eds.) Encyclopedia of NuclearMagnetic Resonance, vol. 10, Chichester, UK: Wiley.

Schmidt-Rohr K and Spiess HW (1994) Multidimensional Solid-StateNMR and Polymers. London: Academic Press.

Tonelli AE (1989) NMR Spectroscopy and Polymer Microstructure: TheConformational Connection. New York: VCH.

SSP2 00032

16 Magnetic Resonance: Polymer Applications of NMR