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Hans Wolfgang Spiess
Max-Planck-Institut für PolymerforschungMainz, Germany
“NMR Spectroscopy of Polymers”Tutorial
ACS National Meeting
New Orleans, April 6, 2008
Overview of NMR of Bulk Polymers
Overview of NMR of Bulk Polymers
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 (13C)
Analogous for 2H quadrupole coupling
Structure and Dynamics from Solid-State NMR
Dipole-Dipole
Coupling
i
jθij
rij
B0 ( cos )Drij
iji j∝ -3 13
12
2θγ γ
⋅
Orientation of internuclear vectorDistance between nuclei
1H-1H1H-13C 13C-13C1H-15N
20 15 10 5 025
coupling strength [kHz]
Typical
pairs
of nuclei
Structure
Dynamics
2H quadrupolecoupling
static
1 kHz
2 kHz
4 kHz
8 kHz
15 kHz0 4 8-12 -4 12-16
frequency [kHz]16-80 1 2 3 4 5 6 7
time [ms]
Solid State NMR Spectra
2H static spectra
13C MAS spectraSpin
nin
g f
requen
cy
2H quadrupole coupling
Magic-angle spinning (MAS)
rotor is spun around an axis inclined at an angle of θm =54.7° with respect to B0 .
spatial part of interaction tensor averaging by
fast rotationresulting average tensor
How does MAS work ?
in terms of coordinate transformations:
212 (3cos 1)θ − 21 1
2 2sin cos(2 2 ) sin(2 ) cos( )R Rt tβ ω γ β ω γ− − −
rotor modulations with frequencies 2ωR and ωR
θm
ωR
B0
ωR
θ
θmωR
B0 B0 B0
Polyolefin Branching
Short (SCB)< 30 C
Long (LCB) > Me ≈
270 C
pronounced effect on viscosity &
melt processability
MAS-NMR in Melts: Very Low Branch Contents
‘Linear’
PE
∗ α∗B2
∗
α
∗B2 α α
Quantification of 7–8 branches per 10 000 COptimised solution
NMR:
50,000 to 2,000,000 scans (up to 60 days!)Optimised melt-state NMR: 21,500 scans (13 h)
Site SNR Content
per 1000 C
*B2 4.5 0.07
* 3.7 0.05
α 9.4 0.08
Sample:R.H. Grubbs, Caltech
Macromolecules 37, 813 (2004), Macromol. Chem. Phys. 207, 382 (2006).
13 C –
NMR: Conformational Effects
Potential Energy
Polymer Chain
Gamma -
gauche effect:-
5,2 ppm in alkanes
Sensitivity of
13C Chemical Shifts
on Conformation
:
42 40 38 36 34 32 30 28 26 24 22
13C NMR spectrum of PE
Crystalline regions:all-trans
Non-crystallineregions: gauche
Conformational Effects on 13C Chemical Shifts
Self-Assembly and Molecular Dynamics of Peptide- Functionalized Polyphenylene Dendrimers
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)
X-ray Scattering:columnar order
Solid state NMR:Peptide conformation
176.3 ppm 172.4 ppm
13C=O
PLys
G2
F16
N16
G2
F16
N58
α -
helix β -
sheet
Overview of NMR of Bulk Polymers
Introduction
•
Configuration, Conformations •
Local Structure & Dynamics
•
Phase Behavior •
Supramolecular Organization •
Conclusions •
Basics
Chain Branching
Amorphous & Crystalline Polymers
Core Shell Structures
Functional Polymeric Systems
Scattering and NMR
Motional averaging effects
( ) 2 ( ) ( ) ( ) ( )12 (3cos 1)(3 )ij i j i j
ijD θ= ⋅ − −D Z ZH I I I I
Motional averaging:2 !21
20 0
(3cos 1) sin 0d dπ π
θ ϕ θ θ− =∫ ∫
221
2 (3cos 1)(3 )2 (2 1)Q
e qQI I
θ= ⋅ − − ⋅− ⋅ Z ZH I I I I
h
2 212 (3cos 1 sin cos(2 ))δ θ η θ ϕ= ⋅ − − ⋅CS ZH I
Solid crystal
Plastic crystalLiquid crystal
Anisotropic Chemical Shift
Dipole-Diplole Coupling
Quadrupole Coupling
order parameter Sij :
)1cos3(S 221
ij −θ=
Motional averaging effects
Basics: Two site jumps
(analogous to chemical exchange)
Calculated NMR line shapes resulting from interchange between two NMR frequencies.
Δ
: coupling strengthΩ
: exchange rate
The numerical values apply to 2H NMR of deuterons in C-H bonds
fast
intermediate
slow
ultraslow
Two-site jumps: CSA
1H powder spectrumof H2 O molecules
in crystalline CaSO4 ·2H2 O
δ
1jump
jump
kδ δ τ= = ⋅m
m
m
m
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
Two-site jumps: CSA, DDC and QC
Example: Phenyl180° ring flip:
Reorientation C-H bondsby β
= 120°
Averaged principal axes (1), (2) and (3)
δ = 5/8 δ ; η
= 0.6
Single transition Pake pattern
Anisotropic Chemical Shift
QuadrupoleCoupling
The “solid echo”
experiment
0 0.5 1-0.5-1ω/δ
x
xx
sampling (“dwell”) time
deadtime
Large spectral width (> 250 kHz) requires short dwell and dead times (< 4 µs).
x y
Overcoming the dead-time problem by echo experiments:
spin (“Hahn”) echo solid (“Solomon”) echo
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
http://weblab.mpip-mainz.mpg.de/weblab/weblab.html
NMR Weblab: Example phenyl flip
http://weblab.mpip-mainz.mpg.de/weblab/weblab.html
Inhomogeneous and homogeneous line broadening
...
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
Overall resonance consists of indiviual sharp lines and
represents the sum over all different orientations
Homogeneous:dipolar multi-spin
Similar distinction ifwhole line shapes are superimposed due to a distribution of
• different structures, or• different rates, or • different geometry of
motion
Example of heterogeneous rate distribution
narrow broad
distribution
rigid limit
rapid exchange
Superposition of line shapes for different rates
2D-Exchange-Spectroscopy:
Simplicity
Pulse Sequence Spectra
Determine geometry and time scale of motions directly and in real time
Geometry
of Chain Motion in Polymers
POM (crystalline) PEO(disordered) PVAc
(amorphous)
13C 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
Chain motionMorphology Chain diffusion
Local Collective
Ordered Disordered
SolutionCrystallized
MeltCrystallized
DrawabilitySample:
UHMW-PE (Mw =3.4 M)
Solution
Crystallized:
Drawable
Melt
Crystallized:
Not
Drawable
Timescales of Molecular Dynamics Accessible by NMR
Averaging of dipole-dipole couplings, as detected by spinning sideband experiments: C-H, N-H: REREDOR, REPT-HDORH-H: double-quantum
Destructive interference effects: reduction and loss
of NMR signal
Change of anisotropic interactionsduring experimental “mixing time”:exchange NMR
experiments2H, 13C, 15N: 2D, CODEX etc.
Spin-lattice relaxation:dipole-dipole coupling, quadrupole coupling,anisotropic chemical shift
fast
10010-110-210-310-410-510-610-710-810-9
slowvery fast intermediate
motional correlation time [seconds]
Conformational Dynamics at the Glass Transition
Potential Energy
Gamma - gauche effect:- 5,2 ppm in alkanes
Polymer Chain
Sensitivity of 13C Chemical Shifts
on Conformation :
Chain Dynamics of Atactic Poly(propylene) at the Glass Transition
Correlation Times of Chain Motionfrom different NMR experiments
All data fit on a singleWLF - curve
Conformational dynamics from 2D 13C MAS NMR
Rotational dynamics from 2D 2H NMR
Geometry: ReorientationalAngle Distribution
Conformational transitions,but no defined geometry
Structure Schemes of Syndiotactic
and
Isotactic
Poly-(Methyl-Methacrylate)
syndiotactic isotactic
ω33ω33
localchain-axis
localchain-axis
schematicstructure
crystal structures
schematicstructure
NMR probes local chain-axis
through ω33
n-alkyl-methacrylates contain extended chain segments
Example:PMMA
a-PEMA: Two-step Randomization of Chain Motion
180°
CO
13
ω33<10°
ω22
ω11
180°C
O13
0°
-
180°
180°
CO
13 ω
50°ω
400 K
405 K
411 K
433 K
472 K
394 K
250 200 150 100
298 K
ω
ω
ω22
ω33
ω11
1D 13C NMR: experimentsimulation
melt
melt
melt
gla
ss
Tgrigid + fractionalsidegroup flips
+ anisotropicchain motion
+ randomizationof chain motion
Tg = 354 K
tem
pera
ture
s-PEMA: Conformation and Conformational Dynamics
(mr)
(rr)
CH3 (main chain)
CD3(side chain)
(mm)
T = 303 K
t.tt.g / g.t
g.g
t.g / g.tg.g / g.g
g.g
35 30 25 20 15 10 ppm
[ [
Tg - 50 K
s-PEMA
T = 353 K
Tg + 65 K
Tg = 354 K
T = 418 K
35 30 25 20 15 10 ppm
(mm)(mr)
(rr)
13C MAS NMR
Separation of Dynamic Timescales in PEMA-Melts
Correlation Times from NMR, PCS, Dielectrics
Tg = 338K
α-Relaxation(WLF)
β-relaxation(Arrhenius)
NMR: spatial randomisation
(tI, WLF)
NMR: confromational relaxation
NMRPCSDielectric
2.2 2.4 2.6 2.8 3.0 3.2 3.410-8
10-6
10-4
10-2
100
102
2.0
1000 / T [K-1]
time
[s]
Difference in time scale (factor 50):consistent with length scale 7 repeat units
Tc
Intersegmental
Order in Poly(methacrylates): WAXS(LVDW)
PMMA
PEMA
PBMA
PHMA
Inte
nsity
[a.u
.]
q [nm-1]0 10 20
II/I
WAXS-DataIII
(VDW)
III
?syndiotactic
PEMA
main chain
side chains
dI
dIII
d0
IIId
dII
„layered nano aggregates"
isotacticPEMA
main chains
side chains
monolayer
bilayer
X-Ray patternsreminiscent of
stiff macromoleculeswith
flexible sidechains
X-R
aySca
tter
ing
0
0.4
0.8
1.2
1.6
0 2 4 6 8 10 12# sidechain carbon atoms
Brag
gdi
stan
ces
d [n
m]
I
II
III
(VDW)
(LVDW)
Bragg-Distance
intra chain
inter chain
inter layer
2D DECODER NMR for Ordered Systems
Example: Biaxially stretched PET
2D exchange with sample fliprather than molecular motion
Recoupling CSA: CODEX
CODEX: Centreband-Only Detection of ExchangeApproach: Recoupling the chemical-shift anisotropy (CSA) under MAS
0 1 N/2
~ ~
N/2+n
CP
DD DD
[ ]N/2-1 [ ]N/2-1
tm AQ
nτR
+ + + +- - --
CP DD
exchange during tm ?Complete refocusing of CSA only if there is no exchange during tm !
Advantages:High spectral resolution, short measuring time compared to 2D exchange NMR
θm
ωR
B0
0 1 2 3 4 5 6 7 8 9 10 11 120,0
0,1
0,2
0,3
0,4
0,5
0,6
δ N τR / π
10°/170°
20°/160°
30°/150°
40°/140°
50°/130°
70°-110°
60°/120°
DMST = 288 K
Exc
hang
e in
tens
ity
tmtm
CODEX: reorientation angle
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
Overview of NMR of Bulk Polymers
Introduction
•
Configuration, Conformations •
Local Structure & Dynamics •
Phase Behavior •
Supramolecular Organization
•
Conclusions •
Basics
Chain Branching
Amorphous & Crystalline Polymers
Core Shell Structures
Functional Polymeric Systems
Scattering and NMR
Phase Separation Probed by Spin diffusion
NMR spectra
Morphology and1H magnetization
MZ
selection spin diffusion
x
A B A
inte
nsi
ty
ωCS
spin diffusion time tm
A B A
B
AA
BA B
NMR spin diffusion experiment
selection diffusion
tm
Chemical shift filters (e.g. DANTE): spectral selection
Dipolar filters (e.g. SR-12): motional selection
Domain Sizes in Phase Separated Polymers
Both Components RigidRigid and Mobile Components
Spin Diffusion in 2D Wideline
Separation Spectra
Interface
spin diffusion
Investigating core-shell particles
structure and particle size can be determined
0 10 20 30 40 50
1.0
0.8
0.6
0.4
0.2
0.0
tm [ms 0.5 ]0.5
I/I0
38 nm76 nm113 nm
(t ms)1/2
d Particle =
contact surface: S source volume: V
withS/V Deff tmSπ
= 2eff
DA DBDDA
=+ DB
magnetization source
magnetization drain
initial slope
I/ I0
1.0
0.8
0.6
0.4
0.2
0.00 5 10 15 20 25
tm [ms0.5 ]0.5
Overview of NMR of Bulk Polymers
Introduction
•
Configuration, Conformations •
Local Structure & Dynamics •
Phase Behavior
•
Supramolecular Organization
•
Conclusions •
Basics
Chain Branching
Amorphous & Crystalline Polymers
Core Shell Structures
Functional Polymeric Systems
Scattering and NMR
Key Elements of Supramolecular Assemblies
shapeπ−π
stac
king
C 1 2 H 2 5
C 1 2 H 2 5
C 1 2 H 2 5
C 1 2 H 2 5
C 1 2 H 2 5
C 1 2 H 2 5
H-bonds
C H2713
N
N
HaO
N
C H27Hd
ON
Hc Hb Hb Hc
O N
NHa
O
N N
Hd
13
n
surfac
es
Challenge: Elucidate Noncrystalline
Structures
Scattering
X-ray- or neutron-scattering
Incident Scattered
Wave
Scattering Diagram / (Reflections)
1/d
r
r
rf- irradiation
DoubleQuantumCoherence
NMR Spectrum
1/r3
Double Quantum NMR
Analogy:In both cases: coherent superposition
of signals from spatially separated centers
1H NMR spectra in solid and liquid state
60 40 20 0 -20 -40 kHz-60
5 0 kHz
20 10 0 kHz
static
30 kHz MAS
solution
θm
ωR
Magic-AngleSpinning (MAS)
rapid isotropictumbling
3 kHz4HRMAS
partialmobility
increasing
spectral
resolution
rigidsolid
dipolarbroadening
high magneticfield: 700 MHz
Dipolar DQ Spectroscopy of a Spin-Pair under MAS
Reconversion DetectionEvolution
t1
Excitation
texc = nexctR
y -yx -x
nexc
y -yx -x
nrec=nexc
x τR
trec = nrectR
θm
ωR
i
j
θij
B0
rij
Dipole-Dipole Coupling:
$ $ $, ,H R T= ⋅2 0 2 0
Space Spin
t2Recoupling Recoupling
Line Narrowing in Solid-State NMR
Hamiltonian of Dipole-Dipole Coupling:
i
j
θij
B0
$ ( cos ) ( $ $ $ $ ), ,Hr
I I I Iij
ij i j Z i Z j i j∝ − − ⋅1
3 1 3312
2 θ γ γ
$ $ $, ,H R T= ⋅2 0 2 0
Space Spin
Magic Angle Spinning:
$,R2 0 0 ωR
θ
θm
ωR
θm
ωR
B0 B0 B0 B0
R R
RF Irradiation:
$,T2 0
00 tC
-x y -y x
tτ ττ τ2τ τ ττ τ2τ τ ττ 2τ
-x y -y x -x y -y
tC
0 t
t
t
(CRAMPS)
(Recoupling)HD,eff.
x y -y-x
τ τ
x y -y-x
τ τ
x y-x
τ
Signal build-up versus rotor-encoding
I
S
REDOR scheme
I
S
t1
Rotor-
encoded
REDOR scheme
trcpl
trcpl trcpl
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)
Rotor-encoding of dipolar Hamitonians
IS0
R
D 2 2 sin 2 sinΦ = − β γω
Recoupled
dipolar Hamiltonian:
with dipolar “phases” for first recoupling period:
IS1 R 1t
R
D 2 2 sin 2 sin( t )Φ = − β ω + γω
and for “rotor-encoded”second recoupling period:
t1 2nd recouplingperiod
1st recouplingperiod
ωR
ωR
0Φ0Φ
0Φt1Φ
Leads to Amplitude
Modulation
of Signal
and hence, Sidebands
REDOR-type curves and sideband patterns
ω/ωR
-3 3-1 1 5-5
(i)
(ii)
(iii)
0 1 2 3
DISt rcpl
/ 2π
Inte
nsi
ty (
a.u.)
0.5
0.4
0.3
0.2
0.1
0
(i)(ii)
(iii)
Build-up curves decay
HDOR sideband patternsrobust:
Multispin effects: additional sidebands
Multispin effects and relaxation
Multiple-quantum NMR methods: investigating (supra)molecular
structure
H H''H'
H
H'H''
CH' CH2CH
O
OCH2
H'H
H
H'
rHH
H
H'
rNH
5 3 1 –1 –3 –5
1 H-1 H
hom
onuc
lear
1 H-13
C/15
N h
eter
onuc
lear
internuclear proximities,chemical
shifts
and π-shiftsinternuclear distances
π
7 -79 -9
5 3 1 –1 –3 –57 -79 -9
0.21 nm
0.24 nm
0.27 nm
0.16 nm
0.18 nm
0.20 nm
molecular
dynamics
Multiple Hydrogen Bonds in Natural and Synthetic Systems
DNA
Supramolecular polymers via hydrogen bonds
C H2713
C H2713
N
NN
Hd
Hb Hb Ha
N
N N
N O
Hd
O
HaO
Hc
N
O
Hc
n
R.P. Sijbesma, E.W. Meijer et al., Science, 1997:Thermoreversible linkages through quadruple hydrogen bonding
C H2713
N
N
HaO
N
C H27Hd
ON
Hc Hb Hb Hc
O N
NHa O
N N
Hd
13
n
Keto form Enol form
Watson-Crickbase pairs
DQ NMRspectrum
DQ NMRspectrum
Heat-Induced Tautomeric
Rearrangement: 1H-1H DQ Spectra of Quadruple Hydrogen Bonds
Heating
51015single quantum ω2 [ppm]
10
15
20
25
30
ω1 [p
pm]
a b c d
b- c
b- b
C H2713
N
N
a
O
N
C H27d
ONc b b c
O N
N a O
N N
d
13
n
before heating: keto form
51015single quantum ω2 [ppm]
10
15
20
25
30
ω1
[ppm
]
a b c d
b- b
a- b
C H2713
C H2713
N
NN
d
b b a
N
N N
N O
d
O
aO
c
N
O
c
n
after heating: enol form
Kinetics
of the
Tautomeric
Rearrangement
0
0.2
0.4
0.6
0.8
1
Temperature [K]
keto form
enol form
310 330 350 370 390 410 430
enol
frac
tion
TemperatureDependence
T [K]
10-3/T [K]Plot 0 2.70 2.75 2.80
-13
-12
-11
-10
lnk
375 365 355
EA = (145± 15) kJ/mol
tran
sitio
n ra
te
Arrhenius
TimeDependence
0 5 10 15 20 25
0.4
0.5
0.6
Time [h]
T = 375 Kenol form
keto form
enol
frac
tion
Multiple N-H Distances in the Pyrimidinone
Form
REREDOR 24/24240 pm280 pm~ 65°
107.5REREDOR 6/6107.5 pm201 pm~ 180°
106
201
1H{15N}
recoupling: 1H - detection
-8 -4 0 4 8 ω/ωR
201
107.5
~180°
-8 -4 0 4 8 ω/ωR
280
240
~65°
REREDOR 8/8107 pm
-8 -4 0 4 8 ω/ωR
107
Separator Membranes and NMR
reveal details of proton conductivityon molecular level(site-selective & non-destructive)
provide structural constraints(proton transfer mechanism ?)
PVPA: poly(vinyl
phosphonic
acid)
31P NMR
phosphonic
acid units, local dynamics
1H-31P and 1H-1H NMR
hydrogen bonding
at phosphonic acid units
1H-13C NMR
segment mobilities of alkyl chains, polyvinyl backbone
1H NMR
backbone as well as mobile protons
(local dynamics)
2H NMR
primary process: orientation-dependent rate of movement:time scale and geometry (multi-site jumps)
NMR probes for local structure & dynamics
High proton conductivity under dry conditions at elevated temperatures
PVPA: VT NMR motional narrowing
condensationbackbone unaffected
mobileOH groups
31P
MAS NMR1H
MAS NMR
very narrow
lines in both 1H and 31P spectra
Poly(vinyl phosphonic
acid): PVPA
EA
= 25 kJ/mol2.2 2.4 2.6 2.8 3.0 3.2
-9
-8
-7
-6
-5
Log
(T2* )
1000/T (K-1) -414 12 8 4 0ppm
10 6 2 -2
2015105
-5
ppm
25
0mobile
1H -
1H DQ Spectra
281 K
-416 12 8 4 0ppm
2015105
-5
ppm
2530
0
318 K
motion frozen
**
n
POO
ODD
P-OH proton: mobile
P-OH : mobile proton, hydrogen bondedDynamics of motion involved in proton conduction
20 10 0 -10
413 K
394 K
375 K
356 K
318 K
ppm150 100 50 0 -50 -100 -150
297 K
393 K
353 K
253 K
kHz
230 K
1H MAS spectra
2H solid echo spectra
PVPA: ab initio structure
(model
geometry)
Ab initio calculation based on model geometry (CPMD):
* Elucidation of hydrogen bondings and 1H chemical shift calculation:H-bonding between phosphonic acids on the same chains and between two parallel chainsMD: 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)
H-bonding between the chains
H-bonding along the chains
PO
PVPA: Averaging of Deuteron Quadrupole
Coupling
Broad distribution of angles betweeninstantaneous O-H and C-P directions,yetQuadrupole coupling reduced by factor 10 after CPMD run of 15 ps
Overview of NMR of Bulk Polymers
Introduction
•
Configuration, Conformations •
Local Structure & Dynamics •
Phase Behavior •
Supramolecular Organization •
Conclusions •
Basics
Chain Branching
Amorphous & Crystalline Polymers
Core Shell Structures
Functional Polymeric Systems
Scattering and NMR
Scattering and NMR in Bulk Polymers
incoherent coherent single quantum
double quantum
D
Y
N
A
M
I
C
S
Molecular n-quasielastic n-quasielastic 2D-, 3D-, 4D- exchange
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
2D pattern,sidebands
Collective
(packing)
X-ray pole figures, SAXS, SANS
DECODER chemical shift
2D signal pattern
SCATTERING NMR
Advantages of NMR:
- Selectivity, Versatility
- Detailed information on geometryand time scale of dynamics
- Large range of length- and timescales accessible
- Elucidation of supramolecularorganization
- Relation between structure, dynamics and functional behavior
- Limits not reached, e.g. microcoils
Overview of NMR of Bulk Polymers
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;J. Polym. Sci. A 42, 5031–5044 (2004).
H.W. Spiess, NMR Spectroscopy, in Macromolecular Engineering, edited by K. Matyjaszewski, Y.Gnanou, L. Leibler, WILEY-VCH, Weinheim, Vol. 3, 1937-1965 (2007).
H. W. Spiess, NMR Spectroscopy: Pushing the Limits of SensitivityAngew. Chem. Int. Ed. 47, 639-642 (2008).
References