1. Local deformation of polymer chains as reflected in proton dipole-dipole coupling distributions
Kay Saalwächter
Martin-Luther-Universität
Halle-Wittenberg
Institut für Physik
NMR group

2. Dipole-dipole coupling constant distributions and local stress of polymer chains
Kay Saalwächter
Double-quantum (DQ) NMR
principles: normalization and distribution analysis
MAS (BaBa-xy16) vs. static low-field
elastomer applications
Chain stretching and orientation in strained elastomers
test of network elasticity theories
overstrain in nanoparticle-filled elastomers
tDQ
DQ reconv.
DQ exc.
SSMQ/DQ

3. Dipole-dipole couplings and time evolution
dipolar coupling tensor D µ gigj/rij3 B0 D zz xx yy
static powder
spectrum
Dstat = Dzz » 30 kHz! t
FID q
± wdip(q) w

4. DQ spectroscopy for homonuclear dip. couplings
tDQ
DQ reconv.
DQ exc.
SSMQ/DQ
1.0
SMQ
0.8 DQ
nDQ
0.6
fit
norm. intensity
0.4
0.2
0.0 2 4 6 8 10 12
DQ evolution time / ms
R. Graf et al., Phys. Rev. Lett. 80 (1998) 5783
KS, Progr. NMR Spectrosc. 51 (2007) 1-35

5. DQ spectroscopy and normalization
tDQ
DQ reconv.
DQ exc.
SSMQ/DQ
determined by Dj = ±90° or n´180°
spin pair calculation:
longit. magn. (ZQ) DQ
R. Graf et al., Phys. Rev. Lett. 80 (1998) 5783
KS, Progr. NMR Spectrosc. 51 (2007) 1-35

6. DQ spectroscopy and normalization
longit. magn. (ZQ) DQ
receiver
Dj DQ ref
90° 0° 0°
180° 180° 0°
270° 0° 0°
0° 180° 0°
Þ 4-step phase cycle, 2 complementary options:
determined by Dj = ±90° or n´180°
remove by tail fit
(relaxes slowly)
full echo, relaxation-only function!
Þ normalized DQ signal, no relaxation:
R. Graf et al., Phys. Rev. Lett. 80 (1998) 5783
KS, Progr. NMR Spectrosc. 51 (2007) 1-35

7. BaBa-xy16: distances in phosphates
Q2a
Q3a
Q3b
Q2b
normalized DQ build-up curves:
coupling constant estimates (2nd-moment approx.)
expected:
pair contact
DPOP(2.9Å)/2p » 800 Hz
rms-sum
(dst. up to 5Å)
(2/3)´(SD2)½/2p
Q2A : 893 Hz
Q2B : 800 Hz
Q3C : 980 Hz
Q3D : 920 Hz
N tR / ms
Q(2)
Q(1)
1270 Hz
920 Hz
J. Ren, H. Eckert, Angew. Chem. Int. Ed. 51 (2012)
KS, ChemPhysChem (2013) in press.
“homonuclear REDOR”
(S0 - S’)/S0
equivalent approach, new name:
0.0
0.2
0.4
0.6
0.8
1.0
1.2
SnDQ = SDQ/SSMQ
DQ evolution time / ms
peak D: 890 Hz
peak C: 920 Hz
peak B: 735 Hz
peak A: 810 Hz
Q(3)
Q(2)
60 kHz MAS
KS, F. Lange, K. Matyjaszewski, C.-F. Huang, R. Graf, J. Magn. Reson. 212 (2011),

8. Empirical universal DQ build-up function
model data: homogenous elastomer (dense 1H spin system with uniform Deff)
<sin2f> powder avg.
2nd-moment approx.
A-l function
W. Chassé, J. López-Valentín, G.D. Genesky, C. Cohen, KS, J. Chem. Phys. 134 (2011)
Þ enables D distribution analysis in inhomogeneous samples!
1.0
POST-C7: g encoding is no advantage!
0.8
0.6
norm. intensity
0.4 DQ
SMQ
nDQ
0.2
0.0 2 4 6 8 10 12
DQ evolution time / ms

9. Coupling and relaxation time distributions
powder-averaged spin pair data
SDQ = <sin2f>
+ s/2p = 200 Hz
200
400
600
800
1000
D/2p / Hz
probability / a.u.
s/2p = 200 Hz
+ diff. relaxation
2ms relax.
4ms relax.
D/2p = 500 Hz
SnDQ
0.6
0.5
0.4
DQ intensity
0.3
® distribution changes build-up curve shape
® differential relaxation precludes normalization, gives only small bias at short times
0.2
0.1
0.0
0.0
0.4
0.8
1.2
1.6
2.0
tDQ / ms

10. Functional-group selectivity: MAS needed?
model elastomer: natural rubber network 1H (400 MHz), kHz MAS,
BaBa-xy16
1 ppm 2 3 4 5 6 7
CH3
CH2 CH
static low field (20 MHz, Baum-Pines seq.)
is no disadvantage!
nDQ stat
fit 257 Hz 2 4
DQ evolution time / ms
0.0
0.2
0.4
0.6
norm. intensity
CH3 SMQ
CH3 DQ
CH3 nDQ
fit 250 Hz 2 4 6 8 10 12
0.0
0.2
0.4
0.6
0.8
1.0
norm. intensity
DQ evolution time / ms
CH nDQ
CH2 nDQ
KS, F. Lange, K. Matyjaszewski, C.-F. Huang, R. Graf, J. Magn. Reson. 212 (2011),

11. A partial solution for dipolar truncation?
CH3
CH2 CH 1 2 3 4 5 6
ppm 8 10 12
chemical shift d
DQ shift (di+dj) 2 4 6
0.0
0.2
0.4
0.6
norm. intensity
DQ evolution time / ms
tDQ=0.8ms
see: M. J. Bayro, M. Huber, R. Ramachandran, T. C. Davenport,
B. H. Meier, M. Ernst, and R. G. Griffin. J. Chem. Phys. 130 (2009)
DQ transfer in a 3-spin system: 1 2 3
time evolution dominated by strong passive coupling!
relative
DQ intensities
but:
rel. int. reflects weak coupling!
KS, F. Lange, K. Matyjaszewski, C.-F. Huang, R. Graf, J. Magn. Reson. 212 (2011),
KS, ChemPhysChem (2013) in press.

12. Constrained chain motion of polymers
NMR in entangled melts and networks (=rubbers) above Tg:
S = Dres/Dstat ~ 10-2
dynamic chain order parameter
b(t) R

13. fast-motion limit (rubber T >> Tg):
Dipole-dipole coupling and chain dynamics/statistics B0
Dstat » 30 kHz (!)
powder average (all b) R q
fast-motion limit (rubber T >> Tg):
wD ~ á P2(cos b) ñt ´ P2(cos q)
freq. w
Dres » 100 Hz
powder average (all q)
static limit (glass):
wD ~ P2(cos b)/rHH3 b2
± wD(b2) b1
± wD(b1)
freq. w H H
dyn. order parameter S = Dres/Dstat
= 3/(5N)
S and its distribution can be measured by time-domain (MQ) NMR
also accessible: isotropic fraction = sol, network defects chain ends
KS, Prog. Nucl. Magn. Reson. Spetrosc. 51 (2007), 1
network chain, N segments

14. Bimodal networks: test case for inhomogeneities
linear superpositions of
experimental data for net0 and net100
0.6
0.4
% short chains:
DQ intensity
net0 (monomodal)
net10
net20
net30
0.2
net50
PDMS precursors:
long chains: 47k
short chains: 0.8k
net70
best-fit
(monomodal)
net90
net100
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
DQ evolution time / ms
KS, J.-U. Sommer, et al., J. Chem. Phys. 119 (2003), 3468

15. Model-heterogeneous networks
residual coupling distributions in end-linked PDMS model networks
.008
100%
PDMS precursors:
long chains: 47k
short chains: 0.8k
90%
.006
70%
relative amplitude
KS, J. Am. Chem. Soc. 125 (2003), 14684
Bruker minispec mq20, 0.5 T cheap NMR! (~ € )
50%
.004
30%
% short chains
20%
.002
10% 0%
400
800
1200
1600
NMR crosslink density Dres (~ S ~ 1/N) / Hz
KS, J.-U. Sommer, et al., J. Chem. Phys. 119 (2003), 3468
W. Chassé, J. López-Valentín, G.D. Genesky, C. Cohen, KS, J. Chem. Phys. 134 (2011)

16. Inhomogeneities in natural rubber
different cure systems
conventional: accelerator/sulphur (0.2/1)
efficient: accelerator/sulphur (12/1)
peroxide: dicumyl peroxide
0.0
0.2
0.4
0.6
0.8
1.0 5 10 15 20 25 30
conventional
efficient
peroxide
rel. amplitude
Dres/2p / kHz R· n …
“zipping” reaction:
J. López Valentín, P. Posadas, A. Fernández-Torres, M. A. Malmierca, L. González, W. Chassé, KS, Macromolecules 43 (2010) 4210.

17. Unixaxial stretching of polymer networks
macroscopic z x ? R R
microscopic

18. Unixaxial stretching of polymer networks
macroscopic z x R R a
microscopic

19. Unixaxial stretching of polymer networks
Segmental (backbone) order parameter Sb
= second moment of time-averaged orientation distribution F b R
Sb ~ Dres ~ R2 ~ F2 F B0
® the residual dipolar interaction measures the local stress and strain
Sommer, J.-U. et al., Phys.
Rev. E 78 (2008)

20. DQ NMR on stretched networksf a
Bruker minispec mq20
0.5 T (20 MHz)

21. DQ NMR on stretched networks
average stretching: B W
remove orientation
effect!
“artifical powder” allows distribution analysis! l d d i i d d o R F a

22. Local stress/strain distributions in strained rubbers
vulcanized natural rubber
very homogeneous, low defect content
l=1.0
l=4.2
probability
orientation effect
removed!
Dres ~ 1/N
Dres ~ R2 ~ F2
® increased inhomogeneity, coexistence of almost unchanged and highly strained chains

23. Comparison with models of rubber elasticity
R ^ F
R || F
classical
affine model
stretched l=2 R
2.0
unstretched
1.5 R
tube model
phantom model
probabilty
1.0
0.5
0.0 1 2 3 4 5
Dres/Dres,l=1

24. Confirmation of models of rubber elasticity
rel. anisotropy from angle-dependent build-up curves
average local stretching from artificial powder
2.5
3.0
NR1B
NR3A
2.0
2.5
NR3B
nDQ,powder D
res /D
res,l=1
1.5 S
2.0 ò /
1.0
nDQ S
1.5
0.5 ò
0.0
1.0 20 40 60 80
100 5 10 15 20
W / ° l 2 -1
elongation - l
® nice confirmation of phantom behavior

25. Summary and Acknowledgement
Dipolar couplings and distributions from DQ spectroscopy
build-up signal normalization to remove relaxation effects is key
relative DQ intensities are not subject to dipolar truncation
universal build-up curve shape enables distribution analysis
avoid “subensemble NMR” in constant-time experiments!
BaBa-xy16: robust broadband homonuclear DQ MAS NMR
static low-field DQ spectroscopy reveals elastomer microstructure
Local chain stretching in strained elastomers
Dres distributions reflect complex local deformation mode
DQ NMR (in)validates rubber elasticity models
thanks to:
Frank Lange (U Halle), Robert Graf (MPI-P Mainz)
Maria Ott, Martin Schiewek, Horst Schneider (U Halle), Roberto Pérez Aparicio, Paul Sotta (CNRS-Rhodia, Lyon), Juan López Valentín (ICTP-CSIC, Madrid)
€€€:

26. Beyond spin pairs: spin counting
formally: DQ = all 2+4n, ref = all 4n coherence orders
model for dense 1H spin system with uniform Deff: silicone elastomer
experimental: step DQ-filter O Si C a
0Q+LM 4Q 6Q 8Q 2Q
® build-up completely dominated by DQ coherences
® universal build-up curve shape!
1.0 2Q
2Q+6Q
4Q and 6Q
ZQ+LM
CH3-2Q
6-spin simulations: lines
0.8
nDQ intensity
0.6
0.4
0.2
0.0 2 4 6 8 10
DQ evolution time / ms
KS, J.-U. Sommer, et al., J. Chem. Phys. 119 (2003), 3468

27. BaBa-xy16 – truly broadband DQ MAS NMR
(px)
(px py)
(py)
inverted
90°x
180°±x
virtual (composite) p pulses:
90°-x x x y y
original BaBa t t tR x x y y x x y y x x y y x x y y
“broadband” BaBa t t t t t t t t y t
(px)
(+ inverted) x
(py)
BaBa-xy16
KS, F. Lange, K. Matyjaszewski, C.-F. Huang, R. Graf, J. Magn. Reson. 212 (2011),
see: M. Feike, D. E. Demco, R. Graf, J. Gottwald, S. Hafner, H. W. Spiess
J. Magn. Reson. A 122 (1996) 214.

28. BaBa-xy16 – truly broadband DQ MAS NMR
MgP4O11, 31P at 243 MHz (14.1 T) a b c
Q2a
Q3a
Q3b
Q2b
dcswL/2p =
35 – 42 kHz *
8 kHz MAS
(impurity)
100
–100
–200
ppm
BaBa at 30 kHz MAS recoupling time 16 tR = ms
–50
–100 50
ppm
“broadband BaBa”
BaBa-xy16, DQ
BaBa-xy16, ref
(impurity) Q2 Q3
DQ build-up / SMQ curves
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
norm. intensity
DQ evolution time / ms
peak 4
peak 3
peak 2
peak 1
4 tR
8 tR
“broadband BaBa”
BaBa-xy16
SMQ DQ
DQ ´3-4!
KS, F. Lange, K. Matyjaszewski, C.-F. Huang, R. Graf, J. Magn. Reson. 212 (2011),

29. BaBa-xy16 – truly broadband DQ MAS NMR
offset and flip-angle stability (31P, phosphate sample)
experimental: 60 kHz MAS,
tDQ = 32 tR = ms 5 10 15 20 25 30
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
DQ intensity
resonance offset / kHz
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
relative rf nutation
60 kHz
MAS
400 MHz
600 MHz
800 MHz
30 kHz
simulation results:
varying pulse length
(90° º 1.3 ms)
0.8
1.0
1.2
1.4
1.6
1.8 ms
varying
offset
–10 10 20
kHz
KS, F. Lange, K. Matyjaszewski, C.-F. Huang, R. Graf, J. Magn. Reson. 212 (2011),

30. Avoid “subensemble NMR” in constant-time exp.!
DQ spinning sideband patterns
[non g-encoded seq.]
(Spiess et al.)
constant-time DQ modulation
(Schmedt a.d. Günne)
+ s/2p = 200 Hz
200
400
600
800
1000
D/2p / Hz
probability / a.u.
s/2p = 200 Hz
x4 (!)
+ relaxation x4
2ms relax.
4ms relax.
tDQ1
DQ rec.
DQ exc.
2tDQ,max = cst.
tDQ=cst.
DQ rec.
DQ exc.
Dt1=tR/N
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
3.6
4.0
tDQ1= 2tDQmax-tDQ2 / ms
D/2p = 500 Hz
D/2p = 500 Hz
tDQ =
2 ms
-80
-40 40
kHz

31. BaBa-xy16 – truly broadband DQ MAS NMRc
Q2a
Q3a
Q3b
Q2b
2D DQ corr., 30 kHz MAS recoupling time 16 tR = ms Q2 Q2 Q3 Q3 1 2 3 4
–115
–110
–105
single-quantum shift
double-quantum shift
–100
–95
–90
–85
–80
–75
–70
ppm
–35
–40
–45
–50
–55
KS, F. Lange, K. Matyjaszewski, C.-F. Huang, R. Graf, J. Magn. Reson. 212 (2011),

32. Inhomogeneities in rubbers: defects
J. López Valentín, P. Posadas, A. Fernández-Torres, M. A. Malmierca, L. González, W. Chassé, KS, Macromolecules 43 (2010) 4210.
conventional: accelerator/sulphur (0.2/1)
efficient: accelerator/sulphur (12/1)
peroxide: dicumyl peroxide
different cure systems:
100
200
300
400
500
600 5 10 15 20 25 30
peroxide
efficient
conventional
non-coupled network defects / %
Dres/2p / kHz
SMQ DQ
loops
dangling ends
sol
mobile
impurities
tDQ

33. Inhomogeneities in natural rubber
nDQ=
DQ/(SMQ-tail)
0.5
initial slope reflects crosslink density (~ Dres ) and its distribution
tDQ
0.0
0.2
0.4
0.6
0.8
1.0 5 10 15 20 25 30
conventional
efficient
peroxide
rel. amplitude
Dres/2p / kHz R· n …
“zipping” reaction:
J. López Valentín, P. Posadas, A. Fernández-Torres, M. A. Malmierca, L. González, W. Chassé, KS, Macromolecules 43 (2010) 4210.

34. º Local deformation in filled elastomers
hydrodynamic model of polydisperse and undeformable hard spheres:
matrix overstrain
R. Christensen, Mechanics of Composite Materials Wiley, New York,1979.
J. Domurath et al., J. Non-Newtonian Fluid Mech (2012) 8-16.
(new, corrected model)
macroscopic z x ?
microscopic

35. Local deformation in filled elastomers
vulcanized natural rubber with feff ~8…19 vol% silica filler
effective local stretching lloc ~ <Dres1/2>
homogeneous dispersion inhomogeneous dispersion
previous
model
new hydrodyn.
model
® samples with aggregated filler have a more complex behavior
® a new, corrected hydrodynamic model is confirmed

36. DQ-DRENAR vs. nDQ analysis
BaBa-xy16, 10 kHz MAS
natural rubber 1 2 3 4
0.0
0.2
0.4
0.6
0.8
1.0
1.2
norm. intensity
tDQ = ½ ttot / ms
CH2 2.4 ppm (on res.)
SSMQ
S0 = {C,iC’}n
S0= {C, C’}n
S0= {Cn, C’n}
2×SnDQ
1-S'/S0; S’ = {C, iC}n
1-S'/S0; S’ = {C, C}n
1-S'/S0; S’ = {Cn, Cn} º DQ-DRENAR
Dapp/2p = 260 Hz 1 2 3 4
0.0
0.2
0.4
0.6
0.8
1.0
1.2
norm. intensity
tDQ = ½ ttot / ms
CH 5.6 ppm (1.23 kHz off res.)