martin-luther-universität halle-wittenberg institut für physik nmr group bias-free determination...
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Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
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 PhysikNMR group
Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
Dipole-dipole coupling constant distributions
and local stress of polymer chainsKay 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
DQ
DQ reconversionDQ excitation
IMQ/DQ
DQ
Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
dip(
B0
Dipole-dipole couplings and time evolution
dipolar coupling tensor D
ij/rij3
Dzz
Dxx
Dyy static powderspectrum
Dstat = Dzz 30 kHz!
t
FID
R. Graf et al., Phys. Rev. Lett. 80 (1998) 5783
KS, Progr. NMR Spectrosc. 51 (2007) 1-35
Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
DQMQ
nDQ
0 2 4 6 8 10 120.0
0.2
0.4
0.6
0.8
1.0n
orm
. in
ten
sity
DQ evolution time / ms
DQ spectroscopy for homonocular dip. couplings
fit
DQ
DQ reconversionDQ excitation
IMQ/DQ
DQ
Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
DQ spectroscopy and normalization
determined by = ±90° or n180°
DQ
DQ reconversionDQ excitation
IMQ/DQ
DQ
Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
NMR in entangled melts and networks (=rubbers) above Tg:
Constrained chain motion of polymers
S = Dres/Dstat ~ 10-2
dynamic chain order parameter
b(t)
R
Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
2
D
Dipole-dipole coupling and chain dynamics/statistics
B0
HH
static limit (glass):D ~ P2(cos )/rHH
3
1
D
freq.
Dstat 30 kHz (!)
powder
average (all
)
network chain, N segmentsdyn. 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
R
fast-motion limit (rubber T >> Tg):
D ~ P2(cos )tP2(cos )
freq.
Dres 100 Hz
powder average (all )
Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
Bimodal networks: test case for inhomogeneities
best-fit (monomodal)
0.0 0.5 1.0 1.5 2.0 2.5 3.00.0
0.2
0.4
0.6
3.5
net0 (monomodal) net10 net20 net30 net50 net70 net90 net100
DQ
inte
nsi
ty
% short chains:
linear superpositions of experimental data for net0 and net100
PDMS precursors:long chains: 47k
short chains: 0.8k
excitation time DQ / ms
KS, J.-U. Sommer, et al., J. Chem. Phys. 119 (2003), 3468
Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
Model-heterogeneous networks
0 400 800 1200 16000
.002
.004
.006
.008
rela
tive a
mplit
ude
NMR crosslink density Dres (~ S ~ 1/N) / Hz
0%
10%
20%
30%
50%
70%
90%
100%
% s
hort c
hain
sKS, 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) 044907
KS, J. Am. Chem. Soc. 125 (2003), 14684
Bruker minispec mq20, 0.5 T
cheap NMR! (~ € 75.000.-)
PDMS precursors:long chains: 47k
short chains: 0.8k
residual coupling distributions in end-linked PDMS model networks
Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
Inhomogeneities in rubbers: defects
MQDQ
loops
dangling ends
sol
mobileimpurities
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 6000
5
10
15
20
25
30
Peroxide Efficient Conventional
Non
-cou
pled
net
wor
k de
fect
s (%
)
Dres/2 / Hz
DQ
Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
Inhomogeneities in natural rubber
0.5
nDQ=DQ/(MQ-tail)
R
n
n
n
…
“zipping” reaction:
J. López Valentín, P. Posadas, A. Fernández-Torres, M. A. Malmierca, L. González, W. Chassé, KS, Macromolecules 43 (2010) 4210.
0.0 0.2 0.4 0.6 0.8 1.00
5
10
15
20
25
30 Peroxide (D
res/2 = 191 Hz)
Conventional (Dres
/2 = 204 Hz) Efficient (D
res/2 = 205 Hz)
rel.
ampl
itude
Dres
/2 / kHz
initial slope reflects crosslink density (~ Dres ) and its distribution DQ
Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
CH3 MQCH3 DQCH3 nDQfit 205 Hz
0 2 4 6 8 10 120.0
0.2
0.4
0.6
0.8
1.0
no
rm.
inte
nsi
ty
DQ evolution time / ms
CH nDQCH2 nDQ
Functional-group selectivity: DQ MAS NMR
natural rubber network (very homogeneous) 1H (400 MHz), 10 kHz MAS
H
CH2
C CH3CH2
C
H2Cn
H
CH2
C CH3CH2
C
H2Cn
1 ppm234567
CH3
CH2
CHstatic(implies single Dres!)
nDQ statfit 281 Hz
0 2 4
DQ evolution time / ms
0.0
0.2
0.4
0.6
no
rm.
inte
nsi
ty
Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
BaBa-xy16 – truly broadband DQ MAS NMR
yyy
x yx y
x y y
t t
t t
x x y
t t
x y y
t t
x x
t t
x xtR
original BaBa
see: M. Feike, D. E. Demco, R. Graf, J. Gottwald, S. Hafner, H.
W. SpiessJ. Magn. Reson. A 122 (1996)
214.
“broadband” BaBa
yyyy
t t
y
t t(px)
y
t t t t (+ inverted)
x xy x x x xy x x
(px)(py) (py) (py) (px) (px)(py)
BaBa-xy16
(px) (px py) (py)
inverted
90°x 180°±x
virtual (composite) p pulses:
º
90°-x
Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
MgP4O11, 31P at 243 MHz (14.1 T)
see: M. Feike, D. E. Demco, R. Graf, J. Gottwald, S. Hafner, H.
W. SpiessJ. Magn. Reson. A 122 (1996)
214.
BaBa-xy16 – truly broadband DQ MAS NMR
–1000 –200100 ppm
8 kHz MAS
(impurity)
*
–10 0 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° 1.6 s)
csL/2 = 35 – 42 kHz
0 –50 –10050 ppm
“broadband BaBa”
BaBa-xy16, DQ
BaBa-xy16, ref(impurity)
BaBa at 30 kHz MASrecoupling time 16 R = 0.533 ms
Q2 Q3
ab
c
Q2a
Q2a
Q3a
Q3a
Q3b Q3
b
Q2b
Q3b
Q3b
Q3a
Q2b
Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
–35 –40 –45 –50 –55ppm
–70
–75
–80
–85
–90
–95
–100
–105
–110
–115
single-quantum shift
do
ub
le-q
ua
ntu
m sh
ift
Q2 Q3 Q3Q2
BaBa-xy16 – truly broadband DQ MAS NMR
2D DQ corr., 30 kHz MASrecoupling time 16 R = 0.533 ms
1 2 3 4
ab
c
Q2a
Q2a
Q3a
Q3a
Q3b Q3
b
Q2b
Q3b
Q3b
Q3a
Q2b
Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
BaBa-xy16 – truly broadband DQ MAS NMR
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.0
0.2
0.4
0.6
0.8
1.0
norm
. in
tens
ity
DQ evolution time / ms
peak 4
peak 3
peak 2
peak 1
DQ build-up / MQ curves
norm
. in
tens
ity
MQ
DQ
“broadband BaBa”
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.0
0.2
0.4
0.6
0.8
1.0
DQ evolution time / ms
BaBa-xy16
DQ 3-4!
4 tR
8 tR
Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
BaBa-xy16 – truly broadband DQ MAS NMR
normalized DQ build-up curves: coupling constant estimates (2nd-moment approx.)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60.0
0.2
0.4
0.6
0.8
1.0
norm
. in
tens
ity
DQ evolution time / ms
peak 4: 750 Hz
peak 3: 780 Hz
peak 2: 670 Hz
peak 1: 770 Hz
expected:
DPOP(2.9Å)/2 800 Hz
rms-sum: (D2)½/2 (dst. up to 5 Å)
Q2a : 1.34 kHz
Q3a : 1.47 kHz
Q3b : 1.38 kHz
Q2b : 1.20 kHz
Q3
Q2
Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
x
z
zz
macroscopic
microscopic?R R
xx
Unixaxial stretching of polymer networks
Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
xx
macroscopic
microscopic
x
z
zz
RR
Unixaxial stretching of polymer networks
Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
Unixaxial stretching of polymer networks
Sommer, J.-U. et al., Phys. Rev. E 78 (2008) 051803
R
f
f
Segmental (backbone) order parameter Sb
= second moment of time-averaged orientation distribution
b
res
B0
20
2
5
3
R
R
NSb
the residual dipolar interaction measures the local stress and
strain
Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
DQ NMR on stretched networks
xx
zz
R
f
f Bruker minispec mq20
0.5 T (20 MHz)
Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
DQ NMR on stretched networks
xx
zz
R
f
f
di
da
di
do
l
average stretching:
B0
remove orientation effect!
“artifical powder”
response allows distribution analysis!
Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
Local stress/strain distributions in strained rubbers
probabilit
y
vulcanized natural rubbervery homogeneous, low defect content
=1.0=4.2
orientation effect
removed!
increased inhomogeneity, coexistence of almost unchanged and highly strained chains
Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
Comparison with models of rubber elasticity
2.5
2.0
1.5
1.0
0.5
0.0
pro
bab
ilty
6543210Dres/Dres,=1
unstretched
tube model
phantom model
R F R || F
R
classical affine model
stretched R
Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
Confirmation of models of rubber elasticity
3.0
2.5
2.0
1.5
1.0
Dre
s/D
res,
=1
20151050
elongation 2-
-1
NR1B NR3A NR3B
2.5
2.0
1.5
1.0
0.5
0.0
n
I DQ/
nI D
Q,p
ow
de
r
100806040200 / °
rel. anisotropy from angle-dependent build-
up curves
average local stretching from artificial powder
nice confirmation of phantom behavior
Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
xx
x
z
zz
macroscopic
microscopic ?
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. 171-172 (2012) 8-16.
Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
samples with aggregated filler have a more complex behavior
Local deformation in filled elastomers
new hydrodyn
.model
vulcanized natural rubber with eff ~8-19 vol% silica fillereffective local stretching loc ~ <Dres
1/2>
homogeneous dispersion inhomogeneous dispersion
a new, corrected hydrodynamic model is confirmed
Martin-Luther-Universität Halle-Wittenberg Institut für Physik
NMR group
Summary and Acknowledgement
Dipolar couplings as a probe for molecular dynamics:
• local dynamics in elastomers, [structure of phosphates] 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)