1. Applications to study local stress of polymer chains
Bias-free determination of homonuclear dipole-dipole coupling constant distributions
and
Applications to study local stress of polymer chains
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
elastomer applications
static low-field vs. MAS (BaBa-xy16)
structure of phosphates
Chain stretching and orientation in strained elastomers
tDQ
DQ reconversion
DQ excitation I
SMQ / 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
R. Graf et al., Phys. Rev. Lett. 80 (1998) 5783
KS, Progr. NMR Spectrosc. 51 (2007) 1-35

4. DQ spectroscopy for homonocular dip. couplings
tDQ
DQ reconversion
DQ excitation I
SMQ / 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

5. DQ spectroscopy and normalization
tDQ
DQ reconversion
DQ excitation I
SMQ / DQ
determined by Dj = ±90° or n´180°

6. 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

7. 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

8. 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
best-fit
(monomodal)
net70
net90
net100
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
excitation time tDQ / ms
KS, J.-U. Sommer, et al., J. Chem. Phys. 119 (2003), 3468

9. 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)

10. Inhomogeneities in rubbers: defects
Conventional: accelerator/sulphur (0.2/1)
Efficient: accelerator/sulphur (12/1)
Peroxide: dicumyl peroxide
different cure systems:
SMQ DQ
loops
dangling ends
sol
mobile
impurities
tDQ
J. López Valentín, P. Posadas, A. Fernández-Torres, M. A. Malmierca, L. González, W. Chassé, KS, Macromolecules 43 (2010) 4210.

11. Inhomogeneities in natural rubber
nDQ=
DQ/(SMQ-tail)
0.5
initial slope reflects crosslink density (~ Dres ) and its distribution
tDQ R· n …
“zipping” reaction:
J. López Valentín, P. Posadas, A. Fernández-Torres, M. A. Malmierca, L. González, W. Chassé, KS, Macromolecules 43 (2010) 4210.

12. Functional-group selectivity: DQ MAS NMR
natural rubber network
(very homogeneous) H (400 MHz), kHz MAS
1 ppm 2 3 4 5 6 7
CH3
CH2 CH
static
(implies single Dres!)
CH3 SMQ
CH3 DQ
CH3 nDQ
fit 205 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
0.6
CH nDQ
CH2 nDQ
0.4
norm. intensity
0.2
nDQ stat
fit 281 Hz
0.0 2 4
DQ evolution time / ms

13. 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
see: M. Feike, D. E. Demco, R. Graf, J. Gottwald, S. Hafner, H. W. Spiess
J. Magn. Reson. A 122 (1996) 214.

14. BaBa-xy16 – truly broadband DQ MAS NMRc
Q2a
Q3a
Q3b
Q2b
MgP4O11, 31P at 243 MHz (14.1 T)
dcswL/2p =
35 – 42 kHz *
8 kHz MAS
(impurity)
100
–100
–200
ppm
–10 10 20
kHz
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6 ms *
offset
variation
pulse length
(90° º 1.6 ms)
–50
–100 50
ppm
“broadband BaBa”
BaBa-xy16, DQ
BaBa-xy16, ref
(impurity)
BaBa at 30 kHz MAS recoupling time 16 tR = ms Q2 Q3
see: M. Feike, D. E. Demco, R. Graf, J. Gottwald, S. Hafner, H. W. Spiess
J. Magn. Reson. A 122 (1996) 214.

15. 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

16. BaBa-xy16 – truly broadband DQ MAS NMR
DQ build-up / SMQ curves
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
DQ evolution time / ms
BaBa-xy16
DQ ´3-4!
4 tR
8 tR
“broadband BaBa”
1.0
peak 4
0.8
peak 3
peak 2
0.6
peak 1
norm. intensity
norm. intensity
SMQ
0.4
0.2 DQ
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
DQ evolution time / ms

17. BaBa-xy16 – truly broadband DQ MAS NMR
normalized DQ build-up curves:
coupling constant estimates (2nd-moment approx.)
expected:
DPOP(2.9Å)/2p » 800 Hz
rms-sum: (SD2)½/2p
(dst. up to 5 Å)
Q2a : 1.34 kHz
Q3a : 1.47 kHz
Q3b : 1.38 kHz
Q2b : 1.20 kHz
1.0
peak 4: 750 Hz Q3
peak 3: 780 Hz
0.8
peak 2: 670 Hz Q2
0.6
peak 1: 770 Hz
norm. intensity
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
DQ evolution time / ms

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

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

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

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

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

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

24. Comparison with models of rubber elasticity
classical
affine model
R ^ F
R || F
stretched R
2.5
unstretched
2.0 R
1.5
probabilty
tube model
1.0
phantom model
0.5
0.0 1 2 3 4 5 6 D /D
res
res,
l=1

25. 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
DQ,powder D
res /D
res,l=1
1.5 nI
2.0 ò /
1.0 DQ
1.5 nI
0.5 ò
0.0
1.0 20 40 60 80
100 5 10 15 20
W / ° l 2 l -1
elongation -
® nice confirmation of phantom behavior

26. 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.
macroscopic z x ?
microscopic

27. 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
new hydrodyn.
model
® a new, corrected hydrodynamic model is confirmed
® samples with aggregated filler have a more complex behavior

28. Summary and Acknowledgement
Dipolar couplings as a probe for molecular dynamics:
local dynamics in elastomers, [structure of phosphates] Þ BaBa-xy16: robust broadband homonuclear DQ MAS NMR
DIPSHIFT: site-resolved fast-limit and intermediate motions
crystallinity and complexity in P3HT
slow protein dynamics
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)
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