Backbone Dynamics of the Nafion Ionomer Studied by 19F-13C Solid-State NMR

Full Paper

Backbone Dynamics of the Nafion IonomerStudied by 19F-13C Solid-State NMR

Dedicated to Prof. Dr. HansWolfgang Spiess on the occasion of his 65th birthday

Qiang Chen, Klaus Schmidt-Rohr*

The chain dynamics of a perfluorinated ionomer, Nafion1, have been studied by 19F and19F-13C solid-state NMR at 295 K. The backbone of Nafion is essentially poly(tetrafluoroethy-lene) (PTFE), which was investigated for reference. Fast uniaxial rotations of the helicalbackbonewere confirmed in PTFE and detected similarly in Nafion, thoughwith a distributionof amplitudes. The rotations produce motionally averaged 19F-13C dipolar couplings andchemical shift anisotropies (CSAs) that are line-arly correlated. Additional narrowing of the CSAsindicated that the backbone axis in hydratedNafion moves with an amplitude >158. Motionalamplitudes of various backbone and side-branchsites were inferred from motionally averaged19F CSA parameters measured with CSA recoup-ling. They increase with the distance from thebranch point, e.g., to>258 in the center of the sidebranch. Implications for the chain and supramo-lecular structure of Nafion are discussed.

Introduction

Nafion1, a perfluorinated ionomer, is widely used as a

polymer-electrolyte- or proton-exchange membrane (PEM)

in all-solid H2/O2 fuel cells.[1–4] In its hydrated form, it is an

excellent proton conductor and highly permeable towater,

but a good barrier to gases and anions. Structurally, Nafion

combines a hydrophobic poly(tetrafluoroethylene) (PTFE)-

like backbone with a hydrophilic side branch containing

perfluorinated ethers ending in an ionizable sulfonate

group. Scheme 1 shows the typical structure of Nafionwith

an equivalent weight of 1 100; it should be noted that

the number of CF2 units between branch points is variable,

around the average value of 14.

Q. Chen, K. Schmidt-RohrAmes Laboratory and Department of Chemistry, Iowa StateUniversity, Ames, Iowa 50011, USAFax: (þ1) 515 294 0105; E-mail: [email protected]

Macromol. Chem. Phys. 2007, 208, 2189–2203

� 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

The nanometer-scale structure of Nafion has been the

focus of many studies, based mostly on small-angle scat-

tering.[2,5–7] However, dynamics of chains and side groups

can also affect important properties of polymer materials.

For instance, fast mobility of the side branch can increase

the diffusivity of water through Nafion,[8,9] while back-

bone dynamics can influence toughness, creep, and solid-

state processability. Therefore, we have investigated the

dynamics of Nafion, in particular the backbone.

Spiess and coworkers have shown that very detailed

information about segmental and chain motions can be

obtained by taking advantage of the orientation depen-

dence of NMR frequencies, which become time dependent

when segments rotate.[10–17] Not only the correlation

time, but also the geometry of the motion can be deter-

mined for slow motions on the millisecond to second

time scale.[10,12–16] For fast motions, the motionally nar-

rowed spectrum is independent of the correlation time but

reflects the amplitude and symmetry of the motion;[11,16,17]

DOI: 10.1002/macp.200700200 2189

Q. Chen, K. Schmidt-Rohr

Scheme 1. Average chemical formula of Nafion 117 in the sulfonicacid form.

2190 �

structural parameters, such as the angle between the

rotation axis for uniaxial motions, can often be extracted.

In this paper, we provide simple relations between spectral

narrowing and motional amplitude. Measuring the 19F

chemical shift anisotropy (CSA) as a function of tempera-

ture, Vega and English showed that in PTFE the helical

chains undergo rotations around their axes.[18] In 99%

crystalline, as-polymerized PTFE, the motion of all chains

is fast at ambient temperature, while it shows a strong

temperature dependence between 19 and 31 8C in

semicrystalline PTFE.[18] Analysis of diffuse scattering

and changes in vibrational spectra has yielded evidence

that the rotations are produced by twin helix reversal

defects that travel together along the chain.[19]

In this paper, we take advantage of the orientation-

dependent 19F-13C dipolar couplings as well as 19F and13C CSAs to probe fast, large-amplitude dynamics of both

backbone and side-branch segments in Nafion, mostly at

ambient temperature. PTFE is characterized for compar-

ison. Unusual technical challenges are posed by the

large (�40 kHz) dispersion of 19F frequencies (compared

to �5 kHz for 1H in nonfluorinated polymers), due to

relatively large isotropic and anisotropic 19F chemical

shifts, which are due to the larger number of shielding

electrons around the 19F nucleus. This dispersion has

become proportionally more challenging with increasing

magnetic field B0, i.e., by a factor of 4 since the work of

Vega and English at 2.35 T.[18] In this paper, we describe19F-13C experiments that circumvent or even utilize the

large chemical shift dispersion of 19F.

We had previously shown by high-resolution magic-

angle spinning (MAS) 13C NMR that the conformational

order of the backbone of Nafion is similar to that of

PTFE.[20,21] The dynamics of PTFE and Nafion backbones are

now compared in terms of motionally narrowed powder

spectra. Two-dimensional (2D) isotropic–anisotropic

chemical shift correlation NMR under MAS is used to

document differences in the motional amplitudes of the

various sites in the side branches of Nafion. Further, CSA

dephasing of different sites in Nafion under 30-kHz MAS is

studied to provide quantifiable information on motional

amplitudes and is measured for two hydration levels.

Relations of the observed side-branch dynamics to the

b-relaxation in Nafion are discussed briefly. We point out

structural implications of the observed dynamics for

backbone conformation and stiffness, and discuss which


2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

structural models of Nafion[2,5,6,22] are consistent with the

chain stiffness of Nafion.

Experimental Part

Samples

The DuPont Nafion ionomer was purchased in the form of

commercial fuel cell-quality Nafion 117 film, with an equivalent

weight of 1 100, in the protonated form. The membrane was

tightly rolled into a cylinder or cut into circular wafers that fit

snugly into the rotor and kept in a desiccatorwhen out of the NMR

spectrometer. Nevertheless, 1H NMR shows that the sample had

absorbed somewater from the atmosphere. This desiccator-stored

sample will be referred to as ‘‘Nafion’’, whereas the ‘‘wet Nafion’’,

rinsed with deionized water before packing, was stored in dei-

onized water when outside the NMR spectrometer. Dry Nafion

with tetramethylammonium (TMA) counterions[23] was provided

by K. Page and R. B. Moore (University of Southern Mississippi).1H NMR shows that this sample is essentially free of water.

A sample of PTFEwas taken from ‘‘Teflon’’ sealing tape,which is

a highly crystalline material. Poly(chlorotrifluoroethylene) (PCTFE),

known as Kel-F, was purchased from McMaster-Carr. The sample

materials were the same as those used in our previous 13C NMR

studies of fluoropolymers.[21] Cylindrical samples were packed

into rotors without further treatment and kept in a desiccator

when out of the NMR spectrometer.

NMR Hardware

NMR experiments were performed at 100 MHz for 13C and

376 MHz for 19F on a wide-bore Bruker DSX-400 spectrometer at

9.4 T. Samples were packed in zirconia NMR rotors with end-caps

made of Kel-F (4-mm rotor) or Vespel (2.5-mm rotor). 19F spectra

were referenced to the PTFE peak at �122 ppm, while the secon-

dary reference for 13C spectra was the a-glycine carbonyl signal at

176.4 ppm from TMS. At a given amplifier setting, radio-frequency

power absorption due to ionic conductivity resulted in longer

pulse lengths for Nafion than for PTFE. As expected, this effect is

most pronounced in wet Nafion.

19F-13C Dipolar Couplings

A 19F-13C 2D separated local field (SLF)[24] experiment for

measuring the 19F-13C heteronuclear dipolar coupling strength

was performed in a Bruker 4-mm X-H/F double-resonance probe

head with the pulse sequence of Figure 1(a), without sample

rotation. The experiment is not of the traditional SLF type,[24] but

rather a fluorine version of the proton-detected local field (PDLF)

method.[25,26] Fluorines detected indirectly via 13C magnetization

after crosspolarization (CP) have evolved in a dipolar field domi-

nated by a single nearby 13C nuclear magnet, producing a single,

well-defined splitting for a given orientation. In contrast, in a

traditional SLF experiment, a 13C spin would evolve in the fields

of two directly bonded and many more distant 19F spins, which

produce a more complex pattern of splittings of splittings.[25,26]

DOI: 10.1002/macp.200700200

Backbone Dynamics of the Nafion Ionomer Studied by 19F-13C Solid-State NMR

Figure 1. Pulse sequences for measuring 19F-13C dipolar couplingsand CSAs, in a static sample. (a) SLF NMR for correlation of 19F-13Cdipolar couplings and the chemical shift. MREV-8 multiple-pulseirradiation is used for 19F homonuclear decoupling, COMARO2 forbroad-band heteronuclear decoupling, and CP stands for CP. (b)Pulse sequence for measurement of the 19F chemical shift powderpattern in the indirect dimension. This can also be used for re-cording 19F chemical shift spinning side bands at slow MAS (2.3kHz). MREV-8 is applied in the indirect dimension for homonu-clear decoupling. (c) Measurement of the 13C chemical shiftpowder pattern with COMARO2 applied for broad-band hetero-nuclear decoupling. (d) Pseudo-2D 19F-13C chemical shift corre-lation NMR for fluoropolymers. The frequencyV1 of narrow-bandcw decoupling is systematically incremented across the full fre-quency range of the 19F chemical shift powder pattern. The Hahnspin echo before detection, with 2t¼ 1.2 ms, suppresses poorlydecoupled components.

Before every scan, four 13C 908 pulses were applied to destroy

any 13C magnetization. The 19F magnetization was excited by a

3.8-ms 908 pulse and evolved under the 19F-13C heteronuclear

dipolar coupling while the homonuclear 19F–19F dipolar coupling

was decoupled by MREV-8[27–29] with an irradiation strength of

gB1/2p¼60 kHz. The 19F 1808 pulse refocused the chemical shift

evolution during t1, while the simultaneous 7-ms 13C 1808 pulseprevented the refocusing of the 19F-13C dipolar evolution. The CP

contact time was set to 80 ms for local magnetization transfer.

Broad-band COMARO2[30] 19F decoupling was applied near the

maximum of the 19F chemical shift powder spectrum and the

strength was set to gB1/2p¼ 50 kHz. The t1 increment was one

MREV-8 block of 50.4 ms duration, and the dwell time in the t2dimension was 5 ms.

19F CSA Powder Pattern

19F CSA powder patterns were recordedwith the pulse sequence of

Figure 1(b), using a Bruker 4-mm MAS 19F/1H single-resonance

NMR probe headwithout sample rotation. After the 908 excitation



pulse of 2.3 ms duration, the 19F magnetization evolved under

the 19F chemical shift in the t1 dimension. The homonuclear19F–19F dipolar interactionwas decoupledwithMREV-8[27–29] with

irradiation at a B1 field strength of gB1/2p¼96 kHz. The 458 pulsetilted the magnetization from the plane perpendicular to the

effective field of MREV-8 back to the x-y plane and the signal

was detected after the 908 pulse. The spectra presented are

sum projections onto the v1 axis. The t1 increment was one

MREV-8 cycle of 31.2 ms duration and the dwell time in the t2dimension was 4 ms.

13C CSA Powder Pattern

Static 13C NMR experiments were performed using a Bruker 4-mm

MAS X-H/F probe head. As shown in Figure 1(c), the 19F magneti-

zation excited by a 4.4-ms 908 pulse was transferred to 13C during a

CP contact time of 0.5 ms and then the 13C signal was detected

with 19F COMARO2 broad-band decoupling[30] at gB1/2p¼ 50 kHz.

The decoupling carrier frequency was varied across the full range

of 19F signals, with a 5-kHz step width. The 13C isotropic chemical

shift was determined under the same conditions except that the

sample was spun at the magic angle with a 2.3-kHz rotation

frequency.

Pseudo-2D Experiment for 19F-13C Chemical

Shift Anisotropy Correlation

Static pseudo-2D 19F-13C chemical shift correlation experiments

were performed in a Bruker 7-mm X-H probe head modified for19F channel decouplingwith the pulse sequence of Figure 1(d). The

carrier frequency V1 of narrow-band 19F continuous wave (cw)

decoupling was incremented systematically and combined with

a Hahn spin echo for suppressing poorly decoupled components.

The spectra are presented as contour plots of a series of stacked

one-dimensional (1D) spectra obtained with systematically incre-

mented V1, in steps of 5.3 or 10.3 ppm. The CP contact time was

0.4 ms, the dwell time, 5 ms.

19F MAS Side-Band Patterns

19F CSA side-band patterns were measured at 2.5 kHz MAS. The

spectra are 1D projections on the indirect dimension of 2D19F spectra acquired using the pulse sequence of Figure 1(a) with a

Bruker 4-mmMAS 19F/1H single-resonance probe head. The 19F 908pulse length was 2.3 ms and the homonuclear decoupling frequen-

cy during MREV-8[27–29] was set to gB1/2p¼96 kHz. The spectra

were obtained with 200 t1 increments of one MREV-8 cycle

(31.2 ms) and a dwell time of 1 ms in the t2 dimension. The 19F NMR

experiments at 12 kHz MAS were performed in a Bruker 4-mm

CRAMPS probe head using single-pulse excitation with a Hahn

spin echo[31] before acquisition for a good baseline.

19F Isotropic–Anisotropic Chemical Shift Correlation

Two-dimensional 19F isotropic–anisotropic chemical shift correla-

tion experiments were performed in a Bruker 4-mm CRAMPS

probe head with the TOSS–deTOSS pulse sequence of Geen and

www.mcp-journal.de 2191


Figure 2. Pulse sequences for site-specific 19F CSA measurementsunderMAS. (a) 2D isotropic–anisotropic separationNMR at 12 kHzMAS. (b) Five-pulse sequence for recoupling the CSA at 30 kHzMAS. The CSA dephasing is detected, after a variable z-periodproviding g-averaging, in terms of the reduced intensity of thepeaks in the MAS spectrum.

2192 �

Bodenhausen,[32] see Figure 2(a), at 12 kHz MAS. The dwell time in

the direct dimension was 4.0 ms and the t1 increment was tr/

4¼20.83 ms, where tr¼2p/vr is the rotation period.

Recoupled 19F CSA Dephasing

Recoupled 19F CSA dephasing experiments were performed with

the five-pulse CSA dephasing technique[33,34] as shown in

Figure 2(b). The CSA recoupling efficiency can be varied by the

timing of rotation synchronized 1808 pulses. The signal intensity

at various tCSA values traces out the decay profile of different19F sites in Nafion. Spinning side bands distortions are minimized

by a g-integral, which sums up the spectra at four different

z-periods incremented by 1/4 of one rotation period.[35,36] The

experiments were performed in a 2.5mmX-H/F double-resonance

probe head at 30 kHzMASwith a 1.95-ms 19F 908 pulse, and a dwell

time of 0.5 ms. Each individual spectrum was the sum of 32 scans

with a recycle delay of 2.5 s.

Theoretical Background

19F-13C Dipolar Splitting

Due to the orientation dependence of dipolar fields, dipolar coup-

lings are sensitive tomolecularmotion.[11,12,16] Under fast uniaxial

motions, the motionally averaged heteronuclear 19F-13C dipolar

coupling constant d is given as[16]

Macrom

2007

d ¼ d

2h3 cos2uCF � 1i (1)

Figure 3. Static 2D 19F-13C chemical shift correlation for a uniaxiallyrotating helical chain. (a) Uniaxial rotation of a helical PTFEchain (schematically represented by a cylinder) and correspond-ing motional averaging of 13C and 19F CSAs. (b) Linear 19F-13Cchemical shift correlation pattern expected for fast uniaxiallyrotating PTFE chains. Due to the large 19F CSA and relatively weak19F–19F couplings, the 2D pattern is obtained most convenientlyusing the pseudo-2D method of Figure 1(d).

where d is the 19F-13C dipolar coupling constant in the rigid limit

and uCF is the angle between the C–F internuclear vector and the

rotation axis.

The 19F-13C dipolar couplings were measured in static 2D SLF

experiments with 19F evolution in the field of the 13C spin. With

homonuclear decoupling applied during t1, the19F frequency is

modulated only by the 19F-13C dipolar coupling. Due to the low

ol. Chem. Phys. 2007, 208, 2189–2203

WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

(1.1%) natural abundance of 13C, every 19F ‘‘sees’’ only one 13C, so

the 19F-13C dipolar couplings are well approximated as spin-pair

interactions. The 19F magnetization modulated by the 19F-13C

dipolar coupling then crosspolarizes its nearby 13C nucleus, and

the 13C signal is detected during t2 under heteronuclear de-

coupling. The short CP contact time minimizes the CP from more

distant fluorine spins, which produce smaller dipolar splittings

thatmaynot be resolved and give rise to a central ridge atv1¼ 0 in

the 2D spectrum. The spectra obtained correlate the 19F-13C dipolar

coupling along v1 with the anisotropic 13C chemical shift along v2.

Due to the large 19F CSA, the 19F decoupling range in v2 is

limited, even with the broad-band COMARO2 decoupling-pulse

sequence.[30] The decoupling frequency was set at the maximum

of the 19F powder pattern so that the maximum of the 13C powder

spectrum was well decoupled and detected. While the full 2D

correlation pattern depends on the relative tensor orientation, the

dipolar cross-section at the maximum of a powder pattern for

h¼ 0 always contains a dominant splitting with the magnitude

equal to the dipolar coupling constant.

Static 19F-13C Correlation

Motional averaging by fast uniaxial rotation, for instance in

PTFE[18] and liquid crystals, generates an effective chemical shift

tensors whose unique principal axis points along the rotation

axis. In PTFE, the rotation axis is the chain axis, see Figure 3(a).

All anisotropic interactions are ‘‘projected’’ onto this axis and

therefore depend only on the angle u between the chain axis

and the static magnetic field, B0. In the fast-motion limit, the

motionally averaged 13C and 19F chemical shift frequencies[16] in

DOI: 10.1002/macp.200700200


PTFE depend on u according to

Macrom

� 2007

vCðuÞ ¼dC

2ð3 cos2u � 1Þ þ vC;iso (2)

vFðuÞ ¼dF

2ð3 cos2u � 1Þ þ vF;iso (3)

with the 13C and 19F isotropic chemical shifts vC;iso and vF;iso, and

the motionally averaged 13C and 19F CSA parameters dCand dF,

respectively. According to Equation (2) and (3), the 13C and19F frequencies are linearly related as

vCðuÞ ¼dC

dFvFðuÞ � vF;iso

� �þ vC;iso (4)

Therefore, the 2D 13C and 19F chemical shift correlation spec-

trum of a fast-rotating chain will exhibit just a narrow ridge of

intensity along a straight line, as shown in Figure 3(b).

19F-13C Pseudo-2D Experiment

Regular 2D 19F-13C correlation is not possible on our spectrometer

because we cannot decouple the full�40-kHz range of 19F frequen-

cies, even using broad-band decoupling sequences like COMARO2.

However, we can take advantage of the narrow-band selectivity of

cw 19F decoupling to determine the frequency of the 19F bonded to

the 13C detected in a simple 19F-13C double-resonance experiment

without sample rotation. This is facilitated by the fact that the19F–19F dipolar couplings are only about half as strong as the cor-

responding 1H–1H interactions, due to the 25% larger geminal F–F

compared to H–H distances (as a result of C–F bonds being longer

than C–H bonds) and the 6% smaller gyromagnetic ratio of 19F.

After eliminating the short-T2 signal of all poorly decoupled

carbons in a Hahn echo with 2t¼1 ms, we only retain signals of

the 13C nuclei bonded to those 19F nuclei that resonate near the19F decoupling frequency. Thus, by stacking 13C spectra recorded

for systematically incremented 19F decoupling frequencies, as indi-

cated in Figure 1(d), we can obtain a pseudo-2D 19F-13C correlation

spectrum that correlates the orientation-dependent chemical shift

frequencies of directly bonded 19F-13C pairs. Such a 2D spectrum

enables us to characterize the relative orientation of the 19F and13C chemical shift tensors, in particular when they are parallel due

to uniaxial motional averaging as explained above.

Motional Narrowing and Amplitude

In most cases, the information provided by motional narrowing

due to fast dynamics is insufficient to fully analyze the geometry

of motion. To describe a reorientation accurately, at least three

parameters are required, such as three Euler angles relating the

orientation before and after the motion, or two angles character-

izing the orientation of the rotation axis plus the rotation angle

around that axis.[16,37] Complex motions, for instance between

multiple sites, require even more parameters. Therefore, seg-

mental dynamics cannot be fully characterized by one or two

parameters. Nevertheless, d/d, the extent of motional narrowing,

does reflect the motional amplitude, and we would like to provide

a relation that captures that connection semiquantitatively.

ol. Chem. Phys. 2007, 208, 2189–2203


The NMR experiment can only detect reorientations of the

principal axes of the interaction probed. As a result, motion

around a unique principal axis is not seen. This means that NMR

can only provide a lower limit to the amplitude of motion DQrms

(rigorously defined as a root-mean-square angular displacement).

For h<0.5, the motional narrowing factor is affectedmost strongly

by the reorientation of the z principal axis, which is the unique

principal axis for h¼0. The angle specifying the orientation of this

axis will be denoted by b. Since any motion by Db will contribute

to the overall amplitude DQ, we have

DQrms � Dbrms ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiDb2� �q

¼ h b� bh ið Þ2i1=2 (5)

For h¼ 0 and a general uniaxial motion, e.g., motion such as

isotropic rotational diffusion in a cone

d

d¼

3 cos2 Dbj � 1D E

2¼ 1� 3

2sin2 Dbj

D E(6)

According to Equation (6), the fractional motional narrowing f

(‘‘narrowingby f¼15%’’, etc.) is directly related to the square ofDbrms

f ¼ 1� d

d¼ 3

2sin2 Db� �

<3

2Db2rms (7)

with Dbrms in radian.

Other definitions of motional amplitude may also be mean-

ingful. For motions within a restricted angular range Dbmax, this

angular range can be considered as the motional amplitude. The

most pronounced averaging bymotion of amplitudeDb, according

to this definition, is produced by a two-site jump by 2Db, since any

intermediate steps will result in smaller angular displacement

and less strong averaging [only half of the jump angle 2Db is the

amplitude Db, since by definition, Equation (5), the amplitude is

the distance from the average orientation between the two sites].

In otherwords, for a given d/d, the amplitude is smallest for a jump

motion of jump angle 2Dbj

DQmax � Dbmax � Dbj (8)

Note that NMR can only detect changes by Db� 908. The aver-

aged value d can be calculated easily for such a jump motion,[16]

if h¼ 0

d

d¼

3 cos2 Dbj � 1

2¼ 1� 3

2sin2 Dbj (9)

While strictly valid only for h¼0, Equation (9) is a good

approximation up to h¼0.5. Equation (9) also applies to rotations

on (but not in) a conewith an angle ofDbj between the cone and its

axis. Equation (9) can again be rewritten as

f ¼ 1� d

d¼ 3

2sin2 Dbj <

3

2Db2

j(10)



2194 �

Equation (5) and (7), or (8) and (10), can be combined to give a

lower limit

Macrom

2007

DQ � ð2=3f Þ1=2180�=p ðin degreesÞ (11)

An analogous result was given by Hentschel, Sillescu, and

Spiess for librational motions in crystalline PE.[38]

For f> 0.5, a more stringent lower limit is obtained from the

equality in Equation (10)

DQ � arcsin½ð2=3f Þ1=2� 180�=p (12)

For instance, for f¼1, this yields DQ�548, for f¼1.5, DQ� 908.

Figure 4.Measurement of 19F-13C dipolar coupling constants from2D SLF spectra, acquired without sample rotation at ambienttemperature. (a) 2D SLF spectrum of PTFE, recorded with 40 t1increments and 16 scans for each increment, with a 5-s recycle

Results and Discussion

Overview

We will first present and discuss 19F-13C and 19F experi-

mentswithout sample spinning,which help us characterize

fast backbone motions in PTFE and Nafion. Subsequently,

we show 1D and 2D 19F MAS experiments that resolve the

small signals of side-branch sites and allow us to assess the

amplitude of their dynamics, for instance as a function of

hydration.
delay. The 19F decoupling frequency was set to the peak in the19F CSA powder pattern. The experiment took 1 h. (b) Correspond-ing spectrum of Nafion, recorded with 32 t1 increments and 1 024scans for each increment with a 1.5-s recycle delay. Experimenttime: 14 h. 1D slices along v1 extracted at the maximum in v2 for(c) PTFE and (d) Nafion. The rigid-limit splitting is indicated bydashed lines. The central peak can be attributed to long-range19F-13C couplings. The PTFE helix shown as an inset was takenfrom ref.[19]
19F-13C Dipolar Splitting

Separated local field spectra for chemical shift-dipolar

coupling correlation are shown in Figure 4(a) and 4(c), and

the corresponding extracted 19F-13C dipolar coupling

spectra in Figure 4(b) and 4(d), for PTFE and Nafion, res-

pectively. The extracted 19F-13C dipolar coupling splitting,

corrected for the MREV-8 scaling factor, is 5.9 kHz for PTFE,

which is about two-fold reduced from the rigid limit of19F-13C dipolar coupling constant, 11.5 kHz, at the one-

bond C–F distance of 1.35 A.[39–42] This is close to the

expected motionally averaged dipolar coupling with the

C–F bond almost perpendicular to backbone [uCF¼ 908 inEquation (1)], d ¼ d=2 ð3 cos2 90� � 1Þ ¼ �d=2. The 19F-13C

dipolar coupling spectrum extracted from the Nafion 2D

spectrum [Figure 4(d)] shows a similar reduction in split-

ting. However, the 19F-13C dipolar spectrum clearly exhib-

its a broader distribution of motionally averaged dipolar

couplings in Nafion than in PTFE. This indicates a limi-

tation of rotation amplitude for a significant fraction of

backbone segments in Nafion, most likely due to the

branch points.[20] In contrast, Gruger and coauthors inter-

preted their IR results in terms of unperturbed PTFE back-

bones plus straight extended side branches.[43] Compo-

nents with smaller 19F-13C dipolar splittings observed

for Nafion could be due to different orientations of the19F-13C internuclear vector relative to the rotation axis, or

ol. Chem. Phys. 2007, 208, 2189–2203


due tomotions of the backbone axis. Evidence for the latter

will be presented below.

19F CSA Powder Patterns

The SLF experiment just discussed is technically demand-

ing and requires knowledge of the 13C CSA pattern in the

v2 dimension. In order to fully characterize the dynamics

and NMR of Nafion and PTFE, we have measured the 19F

and 13C chemical shift powder patterns, which can provide

useful information on fast segmental rotations.

The �40 kHz chemical shift dispersion of 19F in our

spectrometer is so large that direct detection of the 19F

signal in the windows of a multiple-pulse sequence is not

possible. Therefore, we probed the chemical shift evolution

under homonuclear decoupling in the first dimension of a

2D experiment, which allows us to minimize the windows

between pulses and thus the cycle time, maximizing the

DOI: 10.1002/macp.200700200


Figure 5. 19F and 13C chemical shift powder patterns of PTFE and Nafion, obtained withoutsample rotation. (a) Indirectly detected 19F NMR spectrum of PTFE, 64 t1 increments and 16 scansper increment with a recycle delay of 2 s. The spectrum is the sum projection onto the v1dimension of the 2D spectrum measured with the pulse sequence of Figure 1(b). (b) Corre-sponding 19F NMR spectrum of Nafion, with 50 t1 increments, 16 scans per increment, and arecycle delay of 1.5 s. (c) Fit of the 19F chemical shift powder pattern of PTFE based on anundistorted ‘‘uniaxial’’ powder pattern with a pulse excitation function (dashed line) andGaussian broadening of s¼ 3.4 ppm. (d) 13C NMR spectra of PTFE, each acquired with 256 scansand a recycle delay of 7 s. The decoupling-pulse offsets ranged from 22 to �13 kHz in steps of5 kHz relative to the isotropic chemical shift. For reference, a spectrum at 2.3 kHz MAS is alsoshown (lower trace), acquired with 16 scans at the reduced CP time of 200ms. (e) Corresponding13C NMR spectra of Nafion, each acquired with 2 048 scans and a recycle delay of 2 s. The19F decoupling-pulse offsets ranged from 22 to �18 kHz in steps of 5 kHz. Bottom trace: 2.3-kHzMAS spectrum, acquired with 160 scans. (f) Fit of the skyline of the 13C spectra of PTFE by apowder pattern for h¼0 and with Gaussian broadening of s¼ 1.9 ppm.

spectral width. This evolution

modulates the strong 19F signal

detected without dipolar decoup-

ling in the second dimension. The

projection onto the v1 dimension

gives the 19F chemical shift pow-

der pattern. A similar approach

has been used in 1Hmultiple-pulse

NMR.[44]

The static 19F chemical shift

powder pattern of PTFE obtained

in this way is shown in Figure 5(a).

It exhibits the shape characteristic

of a uniaxial interaction (h¼ 0),

compare Figure 3(b). The static19F chemical shift spectrum of

Nafion, see Figure 5(b), shows an

overall similar, almost ‘‘uniaxial’’

powder pattern. The ‘‘hump’’

around�95 ppm can be attributed

to the side-branch sites with an

isotropic shift at �78 ppm and an

intensity maximum at the upfield

end of their powder patterns; this

is confirmed in the MAS spectrum

of Figure 7(b). The isotropic chem-

ical shifts of the center bands in

that MAS spectrumwere also used

to determine the MREV-8 scaling

factor. A close comparison with

the spectrum of PTFE shows that

the Nafion spectrum exhibits

more motional narrowing, with

the right edge shifted by�10 ppm,

and the peak by ��7 ppm. This

could result from a slight differ-

ence in the chain conformation of

Nafion compared to PTFE, or, more

likely, from additional motions of

the chain axis.

In Figure 5(c), the PTFE chemical

shift powder pattern is fitted

with an h¼ 0 powder pattern

with an isotropic chemical shift

of �122 ppm and an averaged

anisotropy parameter d¼ 66 ppm. Gaussian broadening as

well as a symmetric sixth-order polynomial-pulse ex-

citation profile were included in the simulation. The

anisotropy is 8% smaller than that reported by Vega and

English[18] based on similar multiple-pulse spectra. We

will present two further, independent measurements

that confirm the smaller CSA value. The CSA para-

meter of Nafion, �56 ppm, is about 15% smaller than

that of PTFE.



13C CSA Powder Patterns

The 13C CSA also providesmotional information. Due to the

wide range of the isotropic (�30 kHz) and anisotropic19F chemical shifts (�35 kHz), even with broad-band

COMARO2[30] 19F decoupling, only part of the 13C spectrum

can be obtained in one experiment.We, therefore, recorded

a series of static 13C CP spectra with systematically

incremented 19F decoupling frequency for COMARO2. In



2196 �

general, for obtaining the 13C chemical shift powder spec-

trum of fluoropolymers, a series of spectra obtained with

equally spaced 19F decoupling frequencies should be added

up; this corresponds to a sum projection of the 19F-13C

pseudo-2D spectrum onto thev2 axis. In the case of parallel

uniaxial tensors, the ‘‘skyline’’ projection of the 2D spec-

trum onto the v2 axis is also the 1D powder pattern,

but with much improved sensitivity compared to a sum

projection. The skyline projection is equivalent to the top

outline of all the 1D 13C spectra with different 19F

decoupling frequencies. Thus, the top outline of all the13C spectra traces out the full 13C chemical shift powder

pattern.

Figure 5(d) shows the superimposed 1D 13C spectra of

PTFE with the 19F decoupling frequency during COMARO2

ranging from 22 to �13 kHz relative to the isotropic

chemical shift 19F frequency, in steps of 5 kHz. The top

outline profiles a 13C chemical shift powder pattern for

h¼ 0. The bottom spectrum in Figure 5(d) is the 2.3 kHz

MAS 13C spectrum of PTFE under the same experimental

conditions. The simulated powder pattern shown in

Figure 5(f) gives a 13C anisotropy parameter dc ¼ 15 ppm.

To the best of our knowledge, this is the first measurement

of the PTFE 13C CSA, which had been hampered mostly by

the difficulty of effective broad-band 19F decoupling. Com-

pared with the anisotropies of sp3 hybridized CH2 groups,

�30 ppm,[45] the CSA of CF2 is quite small. This can be

attributed to the motional narrowing by the backbone

rotation. The positive sign of dc shows that the frequency

for the principal axis approximately perpendicular to the

F–C–F plane, which is �358 from the chain axis, is

downfield from the isotropic chemical shift in PTFE and

Nafion. This is different from the tensor orientation in CH2

groups.[46]

The 13C CSA powder spectrum of Nafion obtained by

similarly incremented decoupling, Figure 5(e), is compar-

able in breadth and overall shape to that of PTFE. The

differences, such as a 2 ppm (15%) reduced width and the

hump near the main side branch isotropic-shift position,[47]

are similar to the differences of the Nafion and PTFE19F spectra. This suggests that these features are produced

by similar dynamic processes, namely rotation of backbone

segments around the helix axis, restricted motions of that

axis, and mobile side branches, respectively.

19F-13C CSA Correlation

In the discussion of the 19F and 13C CSAs of Nafion and

PTFE, it was concluded that the ‘‘uniaxial’’ static powder

patterns are due to fast uniaxial rotation around the local

chain axis. Therefore, we expect to observe a straight ridge

in the pseudo-2D 19F-13C correlation spectra due to the

linear correlation of 19F and 13C chemical shift, Equation (4)



and Figure 3(b). As a reference without such fast uniaxial

motions, Figure 6(a) shows the pseudo-2D 19F-13C correla-

tion spectra for PCTFE, a perfluorinated polymer without

fast large-amplitude dynamics at ambient temperature.

The broad chemical shift patterns in both 19F and13C dimensions are characteristic of rigid fluoropolymers.

The spread of 13C frequencies over�60 ppm is comparable

to that of C–CH2–C groups in polyethylene (range of Ds¼40 ppm) and of O–CH2–O in polyoxymethylene (Ds¼42 ppm).[46]

The pseudo-2D chemical shift correlation spectrum of

PTFE, Figure 6(b), exhibits the prominent straight ridge

predicted for uniaxial motional averaging. The Nafion

spectrum shown in Figure 6(c) is dominated by a similar

straight ridge, confirming fast uniaxial motions of many

backbone segments. Besides the straight ridge, a broad

background is also observed in the Nafion spectrum, pre-

sumably due to segments near the branch points whose

mobility is restricted. After a longer T2 filter, only the

rotating PTFE-like components are retained, see Figure 6(d).

The pseudo-2D 19F-13C correlation spectra thus confirm

that less mobile segments near the branch points coexist

with the PTFE-like rotating component in Nafion.

The v1 dimension of the pseudo-2D 19F-13C spectrum

also yields thewidth of the 19F CSA powder pattern of PTFE,

without any scaling factor. It yields principal values of 60,

153, and 153 ppm (d¼ 62 ppm), and is clearly inconsistent

with previously proposed principal values of 49, 156, and

156 ppm.[18]

Site-Resolved Dynamics Measurements

The backbone in Nafion provides the dominant signal in

static NMR spectra, but the dynamics of the side-branch

segments are also of interest and can be studied using 19F

MAS NMR, where four side-branch peaks are resolved.[20]

The CSAs, possibly with an admixture of 19F–19F dipolar

couplings, are the most accessible observables reflecting

the amplitude of motion. We had previously determined

the widths of the 19F and 13C peaks under MAS; they give

an indication of the extent of conformational averaging,

which was found to be most restricted near the branch

point.[20]

Figure 7(a) and 7(b) compares the 19F chemical shift

side band spectra of PTFE and Nafion at 2.3 kHz MAS.

The envelope of the PTFE side-band pattern resembles the

static spectrum of Figure 5(a), with some modulation due

to MAS. For Nafion, a similar set of backbone side bands

dominates the spectrum. Two additional sets of side bands

due to side-branch sites are recognized. The one centered

near �79 ppm and spreading from approximately �50 to

�100 ppm confirms that the hump near �95 ppm in the

spectrum of Figure 5(b) is due to side-branch sites. With

an isotropic shift of �79 ppm and a peak at �95 ppm, it

DOI: 10.1002/macp.200700200


Figure 6. Pseudo-2D 19F-13C NMR spectra obtained by plotting the 13C spectrum as a function of the 19F cw-decoupling carrier frequency [seeFigure 1(d)]. (a) Spectrum of PCTFE [Kel-F, –(CClF–CF2)n–]. The 19F decoupling, with gB1/2p¼ 55 kHz, was applied at positions ranging from10.6 to �255 ppm in steps of 10.6 ppm. For each 1D spectrum, 160 scans with a recycle delay of 14 s were added. The T2 filter time 2t was0.6 ms. The experiment took 17 h. (b) Spectrum of PTFE. The 19F decoupling, with gB1/2p¼ 51 kHz, was applied at positions ranging from�26.6 to �207 ppm in steps of 5.3 ppm. At every 19F decoupling frequency, 64 scans were coadded, with a recycle delay of 6 s. The T2 filtertime 2t was 1.2 ms. Experiment time: 3.9 h. (c) Spectrum of Nafion. The 19F decoupling, with gB1/2p¼42 kHz, was applied at positionsranging from�26.6 to�186 ppm in steps of 10.6 ppm. At every 19F decoupling frequency, 768 scans were coadded, with a recycle delay of 2.5s. T2 filter time 2t: 0.6 ms; experiment time: 19 h. (d) Spectrum of Nafion. Same as (c), except that the T2 filter time was set to 3 ms.Experiment time: 27 h.

appears to be associated with a positive d¼ 32 ppm. The

pattern centered near �116 ppm is more difficult to

evaluate, but the larger side band to the right of the iso-

tropic chemical shift again points to a positive d.

The motional difference can also be seen without

multiple-pulse decoupling. In this case, homonuclear di-

polar couplings also contribute and produce a wider range

of significant side bands. Nevertheless, motional narrow-

ing of the side band envelope still occurs. In 12-kHz MAS

spectra, Figure 7(c) and 7(d), the difference in backbone and

side-branch CSAs is easy to see: the backbone fluorines

show a wide side-band pattern, centered at �122 ppm,

the CF3 and OCF2 branch sites a pronounced center band at

�79 ppm with small side bands.

The overlapping 19F chemical shift side-band patterns

can be better resolved in a 2D isotropic–anisotropic sepa-

ration spectrum where they are separated according to

their isotropic chemical shifts, see Figure 8. For compar-

ison, the 1D spectra of Nafion [Figure 7(d)] and PTFE

[Figure 7(c)] at 12 kHz MAS are also shown in Figure 8(a)



and 8(c), respectively. The site-specific chemical shift

side-band patterns extracted from the 2D spectrum at the

given isotropic-shift positions are displayed in Figure 8(b)

and 8(c). Visual inspection shows that backbone CF2 groups

have a bigger anisotropy than the side-branch sites. The

pattern centered at �116 ppm shows a similar envelope

as that of the backbone fluorines, confirming that the CSA

of the backbone CF2 sites flanking the branch point[20] is

positive. Almost identical chemical shift spinning side-

band patterns are observed for the backbone CF2 of Nafion

and PTFE, as expected. Comparison of Figure 8(c) and 8(d)

for PTFE shows slight distortions of the side-band pattern

in the 2D experiment, due to the eight 1808 pulses in the

TOSS–deTOSS sequence.

19F CSA Recoupling

The anisotropies of the smaller signals in the slices from

the 2D spectrum of Figure 8 are still difficult to assess. More



Figure 7. 19F NMR spinning side-bands patterns at ambient temperature. (a) Indirectly detected pure chemical shift side-band pattern at2.5 kHz MAS for PTFE. 16 scans with a recycle delay of 2.5 s for each t1 increment. The experiment took 1 h. (b) Same for Nafion, with 64 scansand a recycle delay of 1.5 s for each t1 increment. Experiment time: 5.5 h. (c) Regular 19F 12-kHzMAS spectrum of PTFE with a 2-s recycle delay.(d) Same for Nafion. Center- and side bands of the backbone (–CF2–)n resonance are marked by asterisks, those of the main side-branchresonance by ‘‘s’’, and others by circles.

2198 �

accurate values of the motionally averaged anisotropy

parameters can be obtained by recording and fitting exper-

imental CSA dephasing curves. Significant dephasing by

the CSA alone can be achieved, even at high spinning

frequencies, via recoupling of the CSA[33,34] at 30 kHz MAS,

using the pulse sequence of Figure 2(b). Here, the CSAs

even of the small CF peaks are easy to measure reli-

ably, since they are not near any side bands of the large

peaks. CF3 signals were obtained selectively after T2filtering.[20]

Curves were simulated for h¼ 0. This is the correct asym-

metry parameter for the backbone fluorines. For other

sites, the value of h is not known, but it has been shown

that the dephasing curves for I(tCSA)/I(0)> 0.3 depend only

weakly on the asymmetry parameter.[34] The relative

values of the anisotropy parameters required for calculat-

ing the motional narrowing factor f¼ 1� d/d will be

affected even less by the h values.

The original d value for PTFE derived from the fit of the

dephasing curve shown in Figure 9(a) is 22 kHz

or 58.5 ppm. This is slightly smaller than the values of

62 and 66 ppm derived above from the static spectra, but

within the expected uncertainty range given the finite



length of the CSA recoupling pulses. In the following, we

report all d values corrected by a scaling factor of 62 ppm/

58.5 ppm¼ 1.06. Note that the motional narrowing factors

f¼ 1� d/d used for estimating motional amplitudes are

unaffected by the scaling factor.

The d¼ 62-ppm value from PTFE can serve as the refer-

ence for additionalmotional-averaging effects of backbone

fluorines in Nafion. As a reference for CSAs of CF groups in

Nafion, the dephasing of immobile CF groups was mea-

sured in dry Nafion with TMA counterions, where strong

electrostatic crosslinks restrict mobility.[23] Figure 9(a)

shows that the backbone and side-branch CF dephasing

coincides nicely, with an anisotropy parameter of 45 ppm.

The fits of Nafion CSA dephasing curves, Figure 9(b), give

anisotropy parameters in the ascending order of CF3<

CF(s)<CF(b)<OCF2< (CF2)n, mostly due to motional

averaging effects. The 58-ppm d value of (CF2)n in Nafion

is reduced by f¼ 7% compared to that in PTFE, which is in

fair agreement with the static spectra of Figure 5(a)

and 5(b). According to Equation (11), the f values of 7 and

15% from CSA-dephasing curves and static spectra,

respectively, correspond to a minimal motional amplitude

of the chain axis between 128 and 188.

DOI: 10.1002/macp.200700200


Figure 8. Spinning side-bands patterns from 2D isotropic–anisotropic separation 19F NMRspectra at 12 kHz MAS. (a) 1D 19F spectrum of Nafion for comparison. (b) Spinning sidebands of different chemical groups in Nafion. Slices were taken from the 2D spectrum atthe chemical shift values in v1 indicated on the right. The 19F 908 pulse length was 2.8 ms.The experiment, with 128 t1 increments and 256 scans with a 1.5-s recycle delay perincrement, took 13.7 h. (c) 1D 19F spectrum of PTFE for reference. (d) Spinning side bands ofPTFE in a 1D slice from the 2D spectrum at 122 ppm. The 2D experiment was taken with 64t1 increments and 128 scans with a recycle delay of 1.5 s per increment. The 19F 908 pulselength was 2.2 ms and the experiment took 3.5 h.

The d values clearly show that the amplitude of motion

of the CF group in the side branch, CF(s), is larger than

that of the CF at the branch point, CF(b). Compared to the

45-ppm CSA in Nafion-TMA, motional narrowing by f¼24% indicates a motional amplitude �238 of the CF site

in the side branch. Even for the branch point in the

backbone, motional narrowing is observed, with f¼ 9%

indicating motions with an amplitude �148, according to

Equation (11).

At �79 ppm in the 19F spectrum, the signals of the CF3and two OCF2 groups overlap. After a T2 filter, the

dephasing of the CF3 group can be observed selectively.[20]

This signal is known to contribute 3/7 of the total intensity

around �79 ppm and can be subtracted on that basis,

leaving the signal of the two OCF2 groups. We can infer

that the CSA of the OCF2 group near the end of the branch

point must be more strongly motionally narrowed than

that of the CF(s), which has fewer degrees of freedom. The

observation that the average d of the two OCF2 fluorines[20]

is much larger than that of CF(s) indicates that the OCF2



group near the branch point has a large

d value, possibly even larger than that

of the (CF2)n. This is expected given the

large MAS line width of the OCF2(b) site

in our previous study[20] and the large-

amplitude motions of many of the

(CF2)n sites around the chain axes. Note

that the relative size of the CSA of

different types of sites, e.g., CF(b) versus

OCF2(b), does not directly translate into

their relative motional amplitudes,

because there may be differences in

rigid-limit CSA parameters, as seen for

CF versus (CF2)n in Figure 9(a)

Mobility Change due to Hydration

Figure 9(c) shows the effect of absorbed

water on the mobilities of different

groups in Nafion. Water in the film is a

must for Nafion to function as the

polymeric-electrolyte membrane in fuel

cells or as the separator membrane in

chloride electrolysis. The absorbed

water is seen to increase the segmental

mobility in Nafion, and the effects are

different for different groups.

The CSAs of the side branches are

narrowed most prominently. The

motional narrowing of f¼ 52% for

CF(s) corresponds to an amplitude

�338. The 45% narrowing for the CF3group upon hydration indicates a simi-

lar motional amplitude. This confirms that the mobile side

branch is most strongly affected by the absorbed water,

which is consistent with all Nafion hydration models,

where most of the absorbed water is located in the

hydrophilic ionic cluster region.[2,7]

Interestingly, backbone sites also show additional

motional narrowing in the wet sample. The anisotropy

parameter for CF2 in wet Nafion is narrowed by an addi-

tional 10% compared to dried Nafion, to f¼ 18%. Similarly,

the CSA of the branch point, CF(b), in wet Nafion is nar-

rowed by an additional 15%, to f¼ 24%. The overall

motional amplitude of the chain axis in the wet sample is

�238.

Temperature Dependence of Side Bands

No obvious difference is observed in the side-band

patterns of backbone signals in 19F spectra of Nafion at

different temperatures from 291 to 353 K, see Figure 10.



Figure 9. Recoupled 19F CSA dephasing curves at 30 kHz MAS ofresolved peaks in the spectra of (a) PTFE, (b) Nafion, and (c) wetNafion. Signals of CF3 groups were separated from overlappingOCF2 bands by a T2 filter. Fit curves and corresponding values ofthe (motionally averaged) CSA parameters d, after correction forfinite pulse length, are also shown. Experiments were performedwith 32 scans, a recycle delay of 2.5 s, and a dwell time of 0.5 ms.The dephasing time was corrected for finite pulse length (3.9 msfor a 1808 pulse), to be the time between pulse centers.

2200 �

This is in agreement with the findings in ref.[23] Therefore,

temperature does not greatly affect Nafion backbone dy-

namics in the range where the frictional heating due to

high-speed MAS is a concern. The lack of temperature

dependence also confirms our assumption that the back-

bone motion in Nafion is in the fast-motion limit.

Synopsis of Backbone and Side-Chain Motion

In summary, a large fraction of Nafion backbone segments

are similar to PTFE backbones, undergoing fast uniaxial

rotation around the local chain axis. The 19F-13C dipolar

coupling is averaged by a factor of close to 2, and the static19F and 13C chemical shifts exhibit motionally averaged



uniaxial powder patterns and are linearly correlated. Based

on the 19F CSA without motion, �50 kHz,[18] the rotation

rate must be above 100 kHz. How the large-angle rotation

around the chain axis can occur with the ends of relatively

short backbone sections fixed by branch points is not

obvious. This is reminiscent of the surprising uniaxial

rotation of significantly curved backbones in PEMA above

the glass transition.[17]

The motional narrowing of the 19F CSA due to the

uniaxial rotation is only about 16%, as shown by Vega and

English in their variable-temperature experiments on

PTFE.[18] This must be attributed to the rotation axis

almost (within 168) coinciding with the 19F CSA principal

axis associated with the principal value of largest magni-

tude.[18] The narrowing of the 13C CSA appears to be more

pronounced, by an estimated factor of 15 ppm/

30 ppm¼ 50%.

In Nafion, the broadening of the 19F-13C dipolar splitting

indicates a distribution ofmotional amplitudes around the

helix axis. This is expected, since segments near the branch

point have amore restrictedmobility, as pointed out in our

previous paper.[20] In terms of dynamics around the chain

axis, the backbone in Nafion can be roughly divided into

two components but it is important to note that these do

not correspond to crystalline and noncrystalline regions.

Rather, there are (i) segments far from branch points

undergoing large- amplitude rotations around the chain

axis and (ii) others near a branch point with restricted

dynamics. The former include segments in both the

crystalline and the noncrystalline regions. It is interesting

to note that the amplitude of motion around the backbone

axis in the crystallites is larger than that of some of the

backbone segments in the noncrystalline regions, namely

those near the branch points.

The additional averaging of both 19F and 13C CSAs in

Nafion relative to PTFE strongly suggests that the back-

bone axis in Nafion undergoes significant (�158) motions.

In the CSA dephasing experiment, this motion is also

detected at the CF branch points in the backbone. With

hydration, the amplitude of this motion increases to �238.The analysis of motional amplitudes assumed implicitly

that all segments of a given type undergo the same

motional process. While small MAS line widths indicate

that this is a good approximation for the ends of the hy-

drated side branches, it does not hold for the backbone. In

addition to a gradient of mobility between branch points

and long (–CF2–)n segments, there will be a difference in

the amplitude of chain-axis motions between crystallites

and noncrystalline regions. The volume crystallinity is ca.

14%;[2,7] given that the backbone accounts for 62 wt.-%

of Nafion 117 and that water clusters take �20% of the

volume, the backbone crystallinity is �14%/(62%�0.8)¼28%. Since large-amplitude motions of chain axes in the

crystallites are unlikely, the motional amplitude of chain

DOI: 10.1002/macp.200700200


Figure 10. 19F NMR spectra at 12 kHzMAS of Nafion as a function of temperature: (a) 291, (b) 313, (c) 333,and (d) 353 K. The spectra were obtained with a 19F 908 pulse of 3.7 ms, 64 scans, and a recycle delay of3 s. The center band and side bands of the backbone (–CF2–)n resonance are marked by asterisks.

axes in the noncrystalline regions must be somewhat

larger than the 158 and 238 values given above for regular

and wet Nafion, respectively.

The side branches in Nafion are more mobile than

the backbone when water is present. The CSA values, in

agreement with our MAS line width measurements,[20]

indicate that groups near the end of the side branch

are more mobile than those near the branch point, where

the mobilities are restricted. Motional amplitudes for the

middle of the side branch in wet Nafion exceed 348.In summary, the results obtained here show that

not only side branches but also backbones undergo fast

motions in strongly and in lightly hydrated Nafion. The

motional amplitude around the chain axis is>1808, that ofthe chain axis smaller but still significant, �208. Swelling

of Nafion by water is likely to be facilitated by the chain

dynamics. That the polymer does not simply disperse

in water can mostly be attributed to the presence of

crystallites acting as physical crosslinks.

Assignment of Motions to Relaxation Processes

At least three relaxation processes, labeled a, b, and g , have

been observed in Nafion by dynamic-mechanical, di-

electric, and NMR relaxation measurements.[48–50]

The a-relaxation occurs at >100 8C[48] and is, therefore,



irrelevant for the motions

near ambient temperature

investigated in this work. In

the Nafion Hþ form studied

here, the b-relaxation process

occurs at 25 8C with rates

>10 Hz in a dry sample and

shifts to much lower tempera-

tures with hydration.[48] In

Nafion with tetraalkylammo-

nium counterions, it occurs at

higher temperatures.[23] Thus,

it appears to be associatedwith

the side-branch motions

observed here by NMR, which

increase with hydration and

are suppressed in Nafion with

TMA counterions. The fast

backbone rotations cannot be

responsible for the b-relaxation

since we have observed such

motions far below the b-relaxa-

tion maximum (unpublished

results). Whether the low-tem-

perature g-relaxation is related

to the backbone rotations is

hard to judge without low-

temperature experiments. The

robust static pseudo-2D 19F-13C experiment introduced in

this work should be useful in such a study.

Implications of Dynamicsfor Nafion Chain Conformation

Based on crystal lattice spacings from electron diffraction,

it has been proposed that the backbone of Nafion adopts a

polyethylene-like zig–zag structure.[51] The chain rotation

observed here strictly excludes packing of planar zig–zag

chains in a polyethylene-like fish-bone pattern, since the

time-averaged shape of the chain is clearly a cylinder,

not a plane. The identical isotropic and similar anisotropic

chemical shifts of PTFE and Nafion backbone sites in

both 13C and 19F NMR[20,21] also indicate that the

conformation in Nafion resembles the helix of PTFE. Given

the small (�1/3 ppm) line width in the 13C MAS NMR

spectrum,[21] any conformational difference would be

detected easily.

The backbone helices must be quite stiff; indeed, the

persistence length of PTFE near ambient temperature is

2–5 nm.[41,52–54] This backbone stiffness can be attributed

at least in part to the steric crowding of fluorine atoms,

which are larger than the hydrogen atoms in polyethylene.

The two energy minima near the trans–trans conforma-



2202 �

tion, which produce the left- or right-handed PTFE helices,

are much deeper than the corresponding single minimum

in polyethylene; gauche conformations, which produce

kinks in the chain, have a probability of 20% or less in PTFE

at 300 K.[53,54]

Implications of Chain Stiffness for Models of Nafion

The stiff backbones will stabilize the long crystallites and

cylindrical inverted micelles formed by side branches

and backbone in hydrated Nafion according to our recent

quantitative analysis of small-angle scattering data.[7]

Another model that takes into account the chain stiffness

is that of Ioselevitch et al., which attempts to form multi-

faceted clusters from straight chains.[55] However, the

finite thickness of the chains was disregarded in this

model; in reality, each of the four or more ‘‘points’’ where

three chains ‘‘intersect’’ would have a diameter of >2 nm.

Together, these intersection regions wouldmake the cluster

significantly larger than the size indicated by SAXS. The

polymer-bundle model[6,56,57] also features straight Nafion

backbones, but again there is problemwith volume filling:

the small volume fraction of the ‘‘water matrix’’ does not

allow for sufficient disorder to match the ionomer scat-

tering peak.[7]

Other models of Nafion are inconsistent with the

observed chain stiffness. For instance, the backbone

stiffness was not properly taken into account in recent

molecular dynamics simulations of Nafion.[58] These

yielded small spacings of sulfonate groups that showed

that ‘‘the equilibrated Nafion chains fold.’’[58] Some other

Figure 11. Schematic representations of Nafion structural modelswith sharply folded chains, which are inconsistent with relativelystiff helical, rotating chain segments detected by NMR. The chainbackbones are highlighted as thick lines. (a) A lamellar model(ref.[5]) and (b) Litt’s chain-folded crystal model (ref.[22]).



models do not explicitly consider the backbone conforma-

tion, but several exhibit small branch-point spacings or

other features that require sharp turns of the backbone.

Figure 11 displays two examples[5,22] with sharp hairpin

turns; again, such chain flexibility is inconsistent with the

2–5 nm persistence length of PTFE and the backbone

stiffness deduced from our NMR experiments.

Conclusion

Sections of the backbone of Nafion between branch points

undergo fast uniaxial rotation around the local chain axis

similarly as in PTFE, at ambient temperature. This motion

reduces the 19F-13C dipolar splitting by a factor of ca. two,

and results in uniaxial 19F and 13C CSAs that are parallel to

each other. The results underline the stiffness of the helical

Nafion backbone and make models of Nafion with sharp

hairpin turns highly unlikely. The backbone axis in Nafion

at ambient humidity moves with an amplitude �158. Thesites in the Nafion side branch have motional amplitudes

increasing with distance from the branch point, e.g., �258in the center of the side branch, as indicated bymotionally

averaged 19F CSA parametersmeasured by a CSA dephasing

technique. Absorbed water not only significantly increa-

ses the amplitudes of the side-branch motions, which are

apparently associated with the b-relaxation, but also

results in increased mobility of the backbone axes, to�238in fully hydrated Nafion.

Acknowledgements: Work at the Ames Laboratorywas supportedby the Department of Energy-Basic Energy Sciences (MaterialsChemistry and Biomolecular Materials Program) under contractno. DE-AC02-07CH11358. The authors thank Kirt Page and Dr.Robert B. Moore (University of Southern Mississippi) for providingthe Nafion-TMA sample.

Received: April 4, 2007; Revised: July 12, 2007; Accepted: July 13,2007; DOI: 10.1002/macp.200700200

Keywords: b-relaxation; Nafion; NMR; perfluorosulfonate iono-mer (PFSI); poly(tetrafluoroethylene) (PTFE)

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Backbone Dynamics of the Nafion Ionomer Studied by 19F-13C Solid-State NMR