Overview of NMR of Bulk Polymers

Overview of NMR of Bulk Polymers 

Hans Wolfgang Spiess 

Max-Planck-Institut für Polymerforschung 

Mainz, Germany 

“NMR Spectroscopy of Polymers” 

Tutorial 

ACS National Meeting 

New Orleans, April 6, 2008


Introduction • 

Configuration, Conformation • 

Local Structure & Dynamics • 

Phase Behavior • 

Supramolecular Organization • 

Conclusions • 

Basics 

Chain Branching 

Amorphous & Crystalline Polymers 

Core Shell Structures 

Functional Polymeric Systems 

Scattering and NMR

Chemical Shift Ranges for Organic Compounds 

Isotropic Anisotropic ( 13 C) 

Analogous for 2 H quadrupole coupling

Structure and Dynamics from Solid-State NMR 

Dipole-Dipole Coupling 

i 

B 0 γ 

iγ j 1 

∝ ⋅ ( 3 cos 2 θ -1) 

θ ij 

r ij 

j 

D 

3 2 

ij 

rij 

Structure 

Distance between nuclei 

Orientation of internuclear vector 

Dynamics 

Typical pairs of nuclei 

1 

H- 13 1 

H- 1 13 

C H 

1 

H- 15 N 

C- 13 C 

25 

20 15 10 5 0 

2 

H quadrupole 

coupling strength [kHz] 

coupling

Solid State NMR Spectra 

static 

2 

H static spectra 

2 

H quadrupole coupling 

Spinning frequency 

1 kHz 

2 kHz 

4 kHz 

8 kHz 

13 

C MAS spectra 

15 kHz 

0 1 2 3 4 5 6 7 

time [ms] 

-16 

-12 -8 -4 0 4 8 12 

frequency [kHz] 

16

Magic-angle spinning (MAS) 

How does MAS work ? 

B 0 

B 0 B 0 B 0 

θ m 

θ 

θ m 

ω R 

ω R 

ω R 

rotor is spun around 

an axis inclined at 

an angle of 

θ m 

=54.7° with 

respect to B 0 

. 

spatial part of 

interaction tensor 

averaging by 

fast rotation 

resulting average tensor 

in terms of coordinate transformations: 

1 2 

2 (3cos θ −1) 

sin β cos(2ω t−2 γ) − sin(2 β)cos( ω t−γ) 

1 2 

1 

2 R 

2 

R 

rotor modulations with frequencies 2ω R 

and ω R

Polyolefin Branching 

Short (SCB)< 30 C 

pronounced effect on 

viscosity & 

melt processability 

Long (LCB) > Me ≈ 270 C

MAS-NMR in Melts: Very Low Branch Contents 

∗ 

∗B2 α α 

α 

‘Linear’ PE 

Site SNR Content 

per 1000 C 

∗B2 

∗ 

α 

*B2 4.5 0.07 

* 3.7 0.05 

α 9.4 0.08 

Sample: 

R.H. Grubbs, Caltech 

Quantification of 7–8 branches per 10 000 C 

Optimised solution NMR: 

50,000 to 2,000,000 scans (up to 60 days!) 

Optimised melt-state NMR: 21,500 scans (13 h) 

Macromolecules 37, 813 (2004), Macromol. Chem. Phys. 207, 382 (2006).

13 

C – NMR: Conformational Effects 

Potential 

Energy 

Polymer 

Chain 

13 

C NMR spectrum of PE 

Crystalline 

regions: 

all-trans 

Non-crystalline 

regions: gauche 

Sensitivity of 13 C Chemical Shifts 

on Conformation : 

42 40 38 36 34 32 30 28 26 24 22 

Gamma - gauche effect: 

- 5,2 ppm in alkanes

Conformational Effects on 13 C Chemical Shifts

Self-Assembly and Molecular Dynamics of Peptide- 

Functionalized Polyphenylene Dendrimers 

X-ray Scattering: 

columnar order 

13 

C=O 

α - helix β - sheet 

176.3 ppm 172.4 ppm 

PLys 

Solid state NMR: 

Peptide conformation 

G 2 

F 16 

N 16 

G 2 

F 16 

N 58 

Short polypeptides (n < 16) 

High order of columns, 

Low order of peptide chains 

Long polypeptides (n > 20) 

Low order of columns, 

High order of peptide chains 

(α-helices)



Configuration, Conformations • 





Basics 






Motional averaging effects 

H 

CS 

= δ ⋅ θ − −η θ ϕ ⋅ I 

1 2 2 

2 

(3cos 1 sin cos(2 )) 

Z 

Anisotropic Chemical Shift 

H = D ⋅ (3cos θ −1)(3 I I −I I ) 

( ij ) 1 2 ( i ) ( j ) ( i ) ( j ) 

D ij 2 Z Z 

Dipole-Diplole Coupling 

π 2π 

∫∫ 

0 0 

1 

2 

2 

eqQ 

HQ 

= ⋅ − I I −I⋅I 

2 I(2I 

−1) 

⋅h 

Motional averaging: 

! 

2 

(3cos θ − 1) dϕsinθdθ 

= 0 

1 2 

2 

(3cos θ 1)(3 

Z Z 

) 

Quadrupole Coupling 

Solid crystal 

order parameter S ij : 

S 

ij 

= 

1 

2 

(3cos 

2 

θ −1) 

Liquid crystal 

Plastic crystal

Motional averaging effects 

Basics: Two site jumps 

fast 

(analogous to chemical exchange) 

intermediate 

slow 

Calculated NMR line shapes 

resulting from 

interchange between 

two NMR frequencies. 

Δ : coupling strength 

Ω : exchange rate 

The numerical values apply to 

2 

H NMR 

of deuterons in C-H bonds 

ultraslow

Two-site jumps: CSA 

δ 

1 

H powder spectrum 

of H 2 O molecules 

in crystalline CaSO 4 ·2H 2 O 

m 

k 

jump 

= = 

δ 

1 

δ ⋅τ 

jump 

m 

m 

m 

Two-site jump in solid: 

Different frequencies depending on orientation. 

Result in fast motion limit: 

Averaged interaction tensor 

Line shape analysis yields both: 

Timescale and geometry of motion 

m 

m 

m

Two-site jumps: CSA, DDC and QC 

Single transition 

Pake pattern 

Anisotropic 

Chemical Shift 

Quadrupole 

Coupling 

Example: Phenyl 

180° ring flip: 

Reorientation C-H bonds 

by β = 120° 

Averaged principal 

axes (1), (2) and (3) 

δ = 5/8 δ ; η = 0.6

The “solid echo” experiment 

x 

dead 

time 

x 

x 

Large spectral width (> 250 kHz) 

requires short dwell and dead 

times (< 4 µs). 

-1 

-0.5 

0 0.5 1 

ω/δ 

sampling 

(“dwell”) time 

Overcoming the dead-time problem by echo experiments: 

spin (“Hahn”) echo 

solid (“Solomon”) echo 

x y 

refocuses “linear-spin” interactions 

refocuses “bilinear-spin” interactions

Motions in the “solid echo” experiment: 

Increased dynamic range 

Absorption 

spectra: 

Line shape 

changes 

within one 

order of 

magnitude 

Solid echo spectra: 

Line shape changes 

over several orders 

of magnitude, 

But: loss of signal!

NMR line shapes conveniently calculated by 

NMR Weblab 

http://weblab.mpip-mainz.mpg.de/weblab/weblab.html

NMR Weblab: How to use it 


NMR Weblab: Example phenyl flip 


Inhomogeneous and homogeneous line broadening 

... 

Similar distinction if 

whole line shapes are 

superimposed due to 

a distribution of 

• different structures, or 

• different rates, or 

• different geometry of 

motion 

Overall resonance consists of 

indiviual sharp lines and 

represents the sum over all 

different orientations 

Inhomogeneous: 

CSA, quadrupolar, 

dipolar two-spin 

Due to spin-spin couplings the energy 

levels of single transitions (resonance 

lines) are no longer degenerate, but 

split into a multitude of levels 

Homogeneous: 

dipolar multi-spin

Example of heterogeneous rate distribution 

rigid limit 

narrow 

distribution 

broad 

rapid exchange 

Superposition of line shapes for different rates

2D-Exchange-Spectroscopy: Simplicity 

Determine geometry and time scale of motions 

directly and in real time 

Pulse Sequence 

Spectra

Geometry of Chain Motion in Polymers 

POM (crystalline) PEO(disordered) PVAc (amorphous) 

13 

C 2D Exchange NMR Spectra of Polymers 

with Different Degrees of Disorder

Helical jumps in polymer crystallites: POM 

Timescale and Geometry of Motion

Chain Folding, Chain Diffusion and Drawability 

Sample: 

UHMW-PE 

(M w 

=3.4 M) 

Drawability 

Solution Crystallized: 

Drawable 

Melt Crystallized: 

Not Drawable 

Morphology 

Chain motion 

Chain diffusion 

Ordered 

Disordered 

Solution 

Crystallized 

Melt 

Crystallized 

Local 

Collective

Timescales of Molecular Dynamics Accessible by NMR 

Spin-lattice 

relaxation: 

dipole-dipole coupling, 

quadrupole coupling, 

anisotropic chemical 

shift 

Averaging of dipole-dipole couplings, 

as detected by spinning sideband experiments: 

C-H, N-H: REREDOR, REPT-HDOR 

H-H: double-quantum 

Destructive interference effects: 

reduction and loss of NMR signal 

Change of anisotropic interactions 

during experimental “mixing time”: 

exchange NMR experiments 

2 

H, 13 C, 15 N: 2D, CODEX etc. 

very fast 

fast intermediate 

slow 

10 -9 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 

motional correlation time [seconds] 

10 -1 

10 0

Conformational Dynamics at the Glass Transition 

Polymer Chain 

Potential Energy 

Sensitivity of 13 C Chemical Shifts 

on Conformation : 

Gamma - gauche effect: 

- 5,2 ppm in alkanes

Chain Dynamics of Atactic Poly(propylene) 

at the Glass Transition 

Conformational 

dynamics from 

2D 13 C MAS NMR 

Rotational 

dynamics from 

2D 2 H NMR 

Geometry: 

Reorientational 

Angle Distribution 

All data fit 

on a single 

WLF - curve 

Conformational transitions, 

but no defined geometry 

Correlation Times of Chain Motion 

from different NMR experiments

Structure Schemes of Syndiotactic and 

Isotactic Poly-(Methyl-Methacrylate) 

n-alkyl-methacrylates contain extended chain segments 

schematic 

structure 

syndiotactic 

isotactic 

schematic 

structure 

Example: 

PMMA 

NMR probes 

local chain-axis 

through ω ω 33 

ω 33 

33 

local 

chain-axis 

local 

chain-axis 

crystal structures

a-PEMA: Two-step Randomization of Chain Motion 

+ randomization 

of chain motion 

+ anisotropic 

chain motion 

rigid + fractional 

sidegroup flips 

T g 

= 354 K 

s-PEMA: Conformation and Conformational Dynamics 

s-PEMA 

CH 3 

(main chain) 

(rr) 

(mm) 

(mr) 

(rr) 

(mr) 

CD 3 

(side chain) 

T g 

+ 65 K 

T = 418 K 

(mm) 

13 

C MAS NMR 

t.g / g.t 

g.g / g.g 

t.t 

t.g / g.t 

g.g 

temperature 

[ g.g 

[ 

T g 

-50 K 

T = 303 K 

T g = 354 K 

T = 353 K 

35 30 25 20 15 10 ppm 

35 30 25 20 15 10 ppm

Separation of Dynamic Timescales in PEMA-Melts 

Correlation Times from NMR, PCS, Dielectrics 

T g = 338K 

10 0 

NMR: confromational 

relaxation 

time [s] 

10 2 2.0 

10 -2 

10 -4 

NMR: spatial 

randomisation 

(t I 

, WLF) 

β-relaxation 

(Arrhenius) 

T c 

10 -6 

10 -8 

α-Relaxation 

(WLF) 

NMR 

PCS 

Dielectric 

2.2 2.4 2.6 2.8 3.0 3.2 3.4 

1000 / T [K -1 ] 

Difference in time scale (factor 50): 

consistent with length scale 7 repeat units

Intersegmental Order in Poly(methacrylates): WAXS 

X-Ray Scattering 

Bragg distances d [nm] 

Intensity [a.u.] 

1.6 

1.2 

0.8 

0.4 

0 

(LVDW) 

III 

II 

? 

II/I 

(VDW) 

WAXS-Data 

I 

0 10 20 

q [nm -1 ] 

Bragg-Distance 

PHMA 

PBMA 

PEMA 

PMMA 

III 

(LVDW) 

0 2 4 6 8 10 12 

# sidechain carbon atoms 

II 

I 

(VDW) 

d 0 

d III 

inter layer 

inter chain 

intra chain 

syndiotactic 

PEMA 

main chain 

side chains 

d I 

isotactic 

PEMA 

side chains 

main chains 

X-Ray patterns 

reminiscent of 

stiff macromolecules 

with 

flexible sidechains 

monolayer 

bilayer 

d II 

d 

III 

„layered 

nano aggregates"

2D DECODER NMR for Ordered Systems 

Example: Biaxially stretched PET 

2D exchange with sample flip 

rather than molecular motion

Recoupling CSA: CODEX 

CODEX: Centreband-Only Detection of Exchange 

Approach: Recoupling the chemical-shift anisotropy (CSA) under MAS 

B 0 

CP 

DD 

DD 

DD 

θ m 

CP 

t m 

+ - + - 

- + - + 

AQ 

ω R 

[ ] N/2-1 [ ] N/2-1 

nτ R 

~ 

0 1 N/2 

N/2+n 

exchange during t m 

? 

Complete refocusing of 

CSA only if there is 

no exchange during t m 

! 

Advantages: 

High spectral resolution, short measuring time 

compared to 2D exchange NMR

CODEX: reorientation angle 

t m 

t m 

0,6 

50°/130° 

Exchange intensity 

0,5 

0,4 

0,3 

0,2 

0,1 

60°/120° 

70°-110° 

40°/140° 

30°/150° 

20°/160° 

0,0 

0 1 2 3 4 5 6 7 8 9 10 11 12 

δ N τ R / π 

10°/170° 

DMS 

T = 288 K 

CODEX build-up curves 

exchange intensity 

for a given mixing 

time depends on the 

overall duration of 

recoupling 

shape of the 

curves depends 

significantly on the 

reorientation angle








Basics 






Phase Separation Probed by Spin diffusion 

selection spin diffusion 

M 

Morphology and Z 

1 

H magnetization 

A B A 

x 

NMR spectra 

A B A 

A 

B 

A 

B 

A 

B 

intensity 

ω CS 

NMR spin diffusion experiment 

selection 

spin diffusion time t m 

diffusion 

t m 

Chemical shift filters (e.g. DANTE): spectral selection 

Dipolar filters (e.g. SR-12): motional selection

Domain Sizes in Phase Separated Polymers 

Rigid and Mobile Components 

Both Components Rigid

Spin Diffusion in 2D Wideline Separation Spectra 

Interface 

spin diffusion

Investigating core-shell particles 

1.0 

0.8 

1.0 

0.8 

0.6 

d Particle = 

38 nm 

76 nm 

113 nm 

I/I 0 

0.6 

0.4 

I/I 0 

0.4 

0.2 

0.0 

(t m 

s 

) 1/2 

0 10 20 30 40 50 

0.2 

initial slope 

magnetization source 

magnetization drain 

0.5 

t m [ms 0.5 ] 

contact surface: S 

source volume: V 

0.0 

0 5 10 15 20 25 

0.5 

t m 

[ms 0.5 ] 

S/V 

= 

π 

D eff t 

S 

m 

with 

D 

eff 

= 

2 

D A 

D A D B 

+ D B 

structure and particle size can be determined








Basics 






C 1 2 H 2 5 

C 1 2 

H 2 5 

C 1 2 

H 2 5 

C 1 2 

H 2 5 

Key Elements of Supramolecular Assemblies 

C H 

H a 

13 27 

H d 

O N 

N N N O 

H c H b H b H c 

O N N N 

N 

H a O 

H d C H 13 27 

n 

H-bonds 

surfaces 

C 1 2 

H 2 5 

C 1 2 H 2 5 

π−π stacking 

shape 

Challenge: Elucidate Noncrystalline Structures

Scattering 

Scattering Diagram / (Reflections) 

Double Quantum NMR 

NMR Spectrum 

1/d 

r 

1/r 3 

Incident Scattered 

r 

Wave 

Double 

Quantum 

Coherence 

X-ray- or neutron-scattering 

Analogy: 

In both cases: coherent superposition 

of signals from spatially separated centers 

rf- irradiation

1 

H NMR spectra in solid and liquid state 

static 

dipolar 

broadening 

60 40 20 0 -20 -40 -60 kHz 

30 kHz MAS 

rigid 

solid 

θ m 

high magnetic 

field: 700 MHz 

20 10 0 kHz 

ω R 

Magic-Angle 

Spinning (MAS) 

HRMAS 

4 

3 kHz 

partial 

mobility 

increasing spectral 

resolution 

solution 

5 0 kHz 

rapid isotropic 

tumbling

Dipolar DQ Spectroscopy of a Spin-Pair under MAS 

Excitation 

Evolution 

Reconversion 

Detection 

x -x 

y -y 

x -x y -y 

n exc 

n rec =n exc 

x τ R 

t exc = n exc 

t R 

Recoupling 

t 1 

t rec = n rec t R 

Recoupling 

t 2 

B 0 

r ij 

θ m Dipole-Dipole Coupling: 

H$ = R$ ⋅ $ 

ω 2, 0 

T2 , 0 

R 

Space Spin 

i 

θ ij 

j

Line Narrowing in Solid-State NMR 

Hamiltonian of Dipole-Dipole Coupling: 

H$ = R$ ⋅ T$ 

2, 0 2, 

0 

B 0 

θ ij 

Space Spin 

1 

$ 1 

H ∝ ( 3cos 2 

θ −1) γ γ ( 3$ I $ I − $ I ⋅ $ I ) 

r 

j 

i 

Magic Angle Spinning: 

θ m 

3 

ij 

2 

θ 

ij i j Z, i Z, 

j i j 

B 0 B 0 B 0 B 0 

θ m 

R$ 2, 

0 

0 

ω R 

ω R 

ω R 

RF Irradiation: 

0 

T$ 2, 

0 

(CRAMPS) 

τ 

-x y -y x 

τ 

0 

t C 

x -xy -y 

τ 

τ 

H D,eff. 

(Recoupling) 

-x y -y x -x y -y 

2τ τ τ τ τ 2τ τ τ τ τ 2τ τ 

t C 

x -xy -y 

τ 

τ 

x 

τ 

-xy 

t 

t 

0 

t 

R 

t 

R

Signal build-up versus rotor-encoding 

Two alternative concepts for measuring recoupled interactions: 

• following the signal intensity as a function of the recoupling time 

(resulting in build-up or dephasing curves) 

• recording rotor-encoded signal (resulting in MAS sideband patterns) 

REDOR 

scheme 

I 

S 

t rcpl 

Rotorencoded 

REDOR 

scheme 

I 

S 

t rcpl 

t 1 

t rcpl

Rotor-encoding of dipolar Hamitonians 

Recoupled dipolar Hamiltonian: 

with dipolar “phases” for 

first recoupling period: 

and for “rotor-encoded” 

second recoupling period: 

D 

2 2 sin 2 sin 

Φ 

IS 

0 =− β γ 

ωR 

D Φ =− 2 2 sin 2βsin( ω t + γ) 

IS 

t1 R 1 

ωR 

1 st recoupling 

period 

t 1 

2 nd recoupling 

period 

ω R 

Φ 0 

0 

Φ 0 

ω R 

Φ 

Φ t1 

Leads to Amplitude 

Modulation of Signal 

and hence, Sidebands

REDOR-type curves and sideband patterns 

(i) 

(ii) (iii) 

(i) 

0.5 

Intensity (a.u.) 

0.4 

0.3 

0.2 

Multispin effects 

and relaxation 

(ii) 

(iii) 

0.1 

Build-up curves decay 

0 

0 1 2 3 

-5 

-3 -1 1 3 5 

ω/ω R 

D IS 

t rcpl 

/ 2π 

HDOR sideband patterns 

robust: 

Multispin effects: 

additional sidebands

Multiple-quantum NMR methods: 

investigating (supra)molecular structure 

internuclear proximities, 

chemical shifts and π-shifts 

internuclear distances 

molecular dynamics 

1 H- 

1 H homonuclear 

H'' 

H 

H' 

H 

H' 

H'' 

H 

0.21 nm 

0.24 nm 

0.27 nm 

9 7 5 3 1 –1 –3 –5 -7 -9 

1 H- 

13 C/ 

15 N heteronuclear 

H' 

H 

π 

CH 2 

O 

O 

CH' CH CH 2 

r HH 

H' 

H 

H' 

0.16 nm 

0.18 nm 

0.20 nm 

9 7 -7 -9 

r NH 

5 3 1 –1 –3 –5

Multiple Hydrogen Bonds 

in Natural and Synthetic Systems 

DNA 

Watson-Crick 

base pairs 

Supramolecular polymers via hydrogen bonds 

R.P. Sijbesma, E.W. Meijer et al., Science, 1997: 

Thermoreversible linkages through quadruple hydrogen bonding 

Keto form 

Enol form 

DQ NMR 

spectrum 

C H 

H a 

13 27 

H d 

O N 

N N N O 

H c H b H b H c 

O N N N 

N 

H d H a O 

C H 13 27 

n 

N 

O 

H a 

O 

H d 

C H 13 27 

H c 

H d 

N 

N N O 

H b H b H a 

N N O 

N N 

H c 

C H 13 27 

n 

DQ NMR 

spectrum

Heat-Induced Tautomeric Rearrangement: 

1 

H- 1 H DQ Spectra of Quadruple Hydrogen Bonds 

before heating: keto form 

after heating: enol form 

13 

a 

d 

O 

N N N O 

N a O 

C H 27 

13 

N 

C H 27 

c b b c 

O N N N 

d 

n 

Heating 

N 

O 

O 

d 

a 

N 

N 

c 

C H 27 

C 13 H 27 

d 

N 

N O 

b b a 

N O 

N c N 

13 

n 

a b c d 

a b c d 

ω 1 [ppm] 

ω 1 [ppm] 

10 

10 

15 

15 

b 

- 

c 

b 

- 

b 

20 

25 

b 

- 

b 

a 

- 

b 

20 

25 

15 10 

single quantum ω 2 [ppm] 

5 

30 

15 10 

single quantum ω 2 [ppm] 

5 

30

Kinetics of the Tautomeric Rearrangement 

enol fraction 

1 

0.8 

0.6 

0.4 

0.2 

0 

310 330 350 370 390 410 430 

Temperature 

Dependence 

Temperature [K] 

enol form 

keto form 

-10 

T [K] 

enol fraction 

0.6 

0.5 

0.4 

T = 375 K 

375 365 355 

0 5 10 15 20 25 

Time [h] 

enol form 

keto form 

Time 

Dependence 

transition rate 

ln k 

-11 

-12 

E A = (145± 15) kJ/mol 

Arrhenius 

Plot 

-13 

0 2.70 2.75 2.80 

10 -3 /T [K]

Multiple N-H Distances in the Pyrimidinone Form 

1 

H{ 15 N} recoupling: 1 H-detection 

106 107 

REREDOR 8/8 

107 pm 

-8 -4 0 4 8 ω/ω R 

107.5 

~180° 

201 

240 

107.5 

~65° 

201 

280 

REREDOR 6/6 

107.5 pm 

201 pm 

~ 180° 

-8 -4 0 4 8 ω/ω R 

REREDOR 24/24 

240 pm 

280 pm 

~ 65° 

-8 -4 0 4 8 ω/ω R

Separator Membranes and NMR 

reveal details of proton conductivity 

on molecular level 

(site-selective & non-destructive) 

provide structural constraints 

(proton transfer mechanism ?)

31 

P NMR 

PVPA: poly(vinyl phosphonic acid) 

High proton conductivity under dry conditions 

at elevated temperatures 

NMR probes for local structure 

& dynamics 

1 


2 


1 

H- 13 C NMR 

phosphonic acid units, local dynamics 

backbone as well as mobile protons (local dynamics) 

primary process: orientation-dependent rate of movement: 

time scale and geometry (multi-site jumps) 

segment mobilities of alkyl chains, polyvinyl backbone 

1 

H -31 P and 1 H- 1 H NMR 

hydrogen bonding at phosphonic acid units

PVPA: VT NMR motional narrowing 

mobile 

OH groups 

backbone 

unaffected 

condensation 

1 

H MAS NMR 

31 

P MAS NMR 

very narrow lines in both 1 H and 31 P spectra

Poly(vinyl phosphonic acid): PVPA 

P-OH : mobile proton, hydrogen bonded 

Dynamics of motion involved in proton conduction 

P-OH proton: mobile 

318 K 

1 

H - 1 H DQ Spectra 

Log (T2 * ) 

-5 

-6 

-7 

-8 

E A 

= 25 kJ/mol 

mobile 

-9 

2.2 2.4 2.6 2.8 3.0 3.2 

* 

n 

1000/T (K -1 14 12 10 8 6 4 2 0 -2 -4 

) 

413 K 

394 K 

2 

H solid echo spectra 

393 K 

O 

P 

OD 

* 

OD 

281 K 

ppm 

-5 

0 

5 

10 

15 

20 

25 

ppm 

375 K 

356 K 

318 K 

20 10 0 -10 

ppm 

1 

H MAS spectra 

353 K 

297 K 

253 K 

230 K 

150 100 50 0 -50 -100 -150 

kHz 

motion 

frozen 

16 12 8 4 0 

ppm 

-5 

0 

5 

10 

15 

20 

25 

30 

-4 

ppm

PVPA: ab initio structure (model geometry) 

P 

O 

H-bonding 

along the 

chains 

H-bonding 

between the 

chains 

Ab initio calculation based on model geometry (CPMD): 

* Elucidation of hydrogen bondings and 1 H chemical shift calculation: 

H-bonding between phosphonic acids on the same chains and between two 

parallel chains 

MD: Proton hopping occurs along chains as well as between chains 

mediated by hydrogen bonds. 

calculated δ(P-OH) = 9.7 ppm (exp.: 10.6 ppm)

PVPA: Averaging of Deuteron Quadrupole Coupling 

Broad distribution of angles between 

instantaneous O-H and C-P directions, 

yet 

Quadrupole coupling reduced 

by factor 10 after CPMD run of 15 ps








Basics 






Scattering and NMR in Bulk Polymers 

SCATTERING 

NMR 

incoherent coherent single 

quantum 

double 

quantum 

D 

Y 

N 

A 

M 

I 

C 

S 

Molecular n-quasielastic n-quasielastic 2D-, 3D-, 4Dexchange 

sidebands 

Collective n-spin-echo 2D-exchange decay of DQC 

S 

T 

R 

U 

C 

T 

U 

R 

E 

Molecular WAXS, WANS chemical 

shift, 

sidebands 

Collective 

(packing) 

X-ray pole figures, 

SAXS, SANS 

DECODER 

chemical shift 

2D pattern, 

sidebands 

2D signal 

pattern


Advantages of NMR: 

- Selectivity, Versatility 

- Detailed information on geometry 

and time scale of dynamics 

- Large range of length- and time 

scales accessible 

- Elucidation of supramolecular 

organization 

- Relation between structure, 

dynamics and functional behavior 

- Limits not reached, e.g. microcoils

References 

K. Schmidt-Rohr, H.W. Spiess, Multidimensional NMR and 

Polymers, Academic Press, London, 1994 

H. W. Spiess, Advanced Solid-State Nuclear Magnetic Resonance 

for Polymer Science; 

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