dynamics as probed by lowresolution NMR A Mordvinkin Kay Saalwächter NMR approaches for complex anisotropic rotational diffusion Chain dynamics in polymer melts and ID: 759391
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Slide1
Details of polymer chain
dynamics as probed by low-resolution NMRA. Mordvinkin, Kay Saalwächter
NMR approaches for complex (anisotropic) rotational diffusionChain dynamics in polymer melts and supramolecular networks
Slide2“Simple NMR”: the potential of integrated 1H signal
Fourier
transformation
HO–CH
2
–CH
3
frequencyspectrum
N
S
spin-1/2
free induction decay
acquisition time
inhom
. low field:
no spectral resolution
couplings, broadening and relaxation...
...encoded in
time-domain
(echo)
decay
Slide3intermediate
t
c
»
1/Dzz
t
c
(T)
Rotations and averaging of dipolar couplings
static
spectrum
dipolar coupling tensor
D
µ gigj/rij3
Dstat = Dzz » 30 kHz!
fast-limit
spectrum
D
res
µ S (order param.)
q
±
D
(
q
)
B
0
D
zz
D
xx
D
yy
Slide4Rotational diffusion from relaxation times/rates
isotropic Brownian tumbling removes orientation-dependent interacations from spectra (Dres = 0)but: relaxation times (T1, T2) depend on the timescale of these fast (tr ~ ns) orientation fluctuations
H
H
e.g. dipole-dipole coupling
q
(
t
)
B
0
t
r
described in terms of
orientation autocorrelation functions, e.g. C2,0(t) = <P2[cos q(t)]P2[cos q(t+t)]>t ~ exp{-t/tr}internal motions: Lipari-Szabo (LSz) “model-free” approachC2,0(t) := [(1-S2)exp{-t/tint} + S2]exp{-t/tr}BPP/Redfied theory predicts, e.g., where the spectral density Jr(w) = FT{C(t)} (LSz: just sum of Lorentzians!)
spectral density and
R
i
high-field
R
1
, NOE range
t
r
-1
t
int
-1
log
w
log
J
(
w
)
R
2
(
J
(0))
FT
log-log scale
t
w
S
2
Slide5Beyond Lipari-Szabo?
log
w
log
J
(
w
)
log
C(t)
log
t
“normal”
Brownian tumbling
correlation function
C
2,0
(
t
) =
C
(
t
)
Þ
spectral density
J
(
w)
power laws?
Slide6Rouse t <
t
e
(locally unrestricted)
entanglements
or crosslinks
t
e
< t <
t
R
(tube restriction)
reptation
t
R
< t <
t
d
(tube renewal)
Structure and dynamics in polymers: concepts
multi-timescale
dynamics
single-chain (!)
bead-spring
models
l
0
Slide7Tube model prediction for NMR observable C(t)
see: de Gennes, J. Chem. Phys. 1971!
0
I
II
III
IV
t
1/2
log
<
r
(
t
)
-
r
(0)
2
>
log
t
10
-6
m
t
s
ns
ns –
m
s
m
s – ms
ms – d
ps
t
e
t
R
t
d
10
-8
m
10
-10
m
C
C
C
f
sub-
segmental
free
Rouse
constrained
Rouse
reptation
free
diffusion
t
1/4
t
1/2
t
1
log
C
(
t) ~ S
b
2
1
10
-4
10
-8
t
–
1
t
–
1/4
t
–
1/2
R. C. Ball, P. T. Callaghan,
E. T.
Samulski
,
J. Chem. Phys.
106
(1997) 7352.
Slide8R. Graf et al.,
Phys. Rev. Lett. 80 (1998) 5783KS, Progr. NMR Spectrosc. 51 (2007) 1-35
spectrum
FID/Hahn echo
dipolar time evolution (coupling changes with time!)
freq.
t
echo
FT
convoluted
signal decay,
ambiguous
analysis
MQ vs
T
2
: more meaningful signal functions!
Transverse relaxation vs. MQ spectroscopy
½
t
echo
½
t
echo
p
I
echo
separated effects:
S
MQ – segmental
dynamics (
a
=
f
(
t
<
t
e
) )
D
Q –
local order
(
D
res
,
b
)
and reptation (
b
=
f
(
t>
t
e
))
MQ experiment
mobile
parts (ends)
t
DQ
t
DQ
t
DQ
DQ
reconversion
DQ
excitation
I
S
MQ
/
DQ
vs.
Slide9MQ time-domain NMR: networks vs. melts
KS, A. Heuer, Macromolecules 39 (2006) 3291-3303
normalized DQ build-up in networks C(t) plateau due to crosslinks C(t) ~ Sb2 ~ Dres2 ~ 1/Mc2
0.5
S
MQ relaxation:
incoherent
dynamics
DQ
nDQ =
DQ
/
S
MQ
:
local order µ C(tDQ)
example: natural rubber
0
2
4
6
8
10
0.0
0.2
0.4
0.6
0.8
1.0
norm. intensity
DQ evolution time / ms
S
MQ
DQ
nDQ
0
2
4
6
DQ evolution time / ms
vulcanized (3 phr sulfur)
403K
285K
340K
10
-
5
10
-
4
10
-
3
10
-
2
10
-
1
10
0
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
-
6
10
-
5
10
-
4
10
-
3
10
-
2
10
-
1
10
0
C
(
t
/
t
e
)
t
/
t
e
(
T
)
nDQ
0
2
4
6
DQ evolution time / ms
0
2
4
6
8
10
DQ evolution time / ms
S
MQ
DQ
403K
285K
340K
linear precursor polymer
segmental dynamics!
tube constraint, reptation!
segmental dynamics!
network chain structure (
S
) !
Slide10Scaling analysis of MQ NMR observable and TTS
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
0.0
0.1
0.2
0.3
0.4
0.5
PB2000k (
Z
=1100)
t
2
DQ
C
(
t
)
absolute-value fit
243 K
303 K
363 K
norm. DQ intensity
validity limit
t
DQ
/ ms
TTS
–0.29
TTS
other temperatures
TTS
initial
nDQ signal
10
0
10
1
10
2
10
3
10
4
10
5
10
-6
10
-5
10
-4
10
-3
0.1
1
10
-4
10
-3
C
(
t
/
t
e
)
243 K
303 K
363 K
t
DQ
[ms]
C
(
t
DQ
) ~
I
nDQ
/
t
DQ
2
t
/
t
e
PB2000k (
Z
=1100)
use
time-temperature
superposition
to obtain
C
(
t
/
t
e
,
T
ref
):
see: R. Graf et al.,
Phys. Rev. Lett.
80
(1998) 5783
Slide11t
-
0.85
I
0
PB2.8k (
Z
=1.5)
PB4.6k (
Z
=3)
PB9.5k (
Z
=5)
PB11.4k (
Z
=8)
PB18k (
Z
=10)
T
1
field
cycling
(Herrmann
et al
.)
A. Herrmann, V. N. Novikov, E. A. Rössler,
Macromolecules
42
(2009) 2063.
field cycling NMR
Full time range by NMR
10
-4
10
-3
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
10
-8
10
-7
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
10
1
t
/
t
e
C
(
t
/
t
e
)
PB23k (
Z
=12)
PB35k (
Z
=19)
PB87k (
Z
=47)
PB2000k (
Z
=1100)
low-field
MQ NMR
(our
work)
II
III,IV
F. V. Chavez, KS,
Phys. Rev. Lett.
104
(2010) 198305.
Slide12Analytical treatment and MQ data fitting
KS, A. Heuer,
Macromolecules 39 (2006) 3291-3303F.V. Chavez, KS, Macromolecules 44 (2011) 1560-1569.
use the second-moment (Anderson-Weiss) approximationto calculate signal functions, e.g.
averages
over
phase factors reduce to integrals over C(t), e.g.
time
0
frequency
FT
assumption
:
Gaussian
freq. distribution
Þ
not valid
at
long
times!
½
t
echo
½
t
echo
p
I
echo
t
DQ
t
DQ
2: DQ reconv.
1: DQ exc.
I
S
MQ/DQ
vs.
Slide13Analytical predictions based upon full (known) C(t)
0
2
4
6
8
10
12
14
16
18
20
0.0
0.2
0.4
0.6
0.8
1.0
273 K
PB 87 kDa
353 K
0
2
4
6
8
10
12
14
16
18
20
0.0
0.2
0.4
0.6
0.8
1.0
normalized intensity
PB 35 kDa
0
2
4
6
8
10
12
14
16
18
20
0.0
0.2
0.4
0.6
0.8
1.0
normalized intensity
t
DQ
[ms]
PB 441 kDa
0
2
4
6
8
10
12
14
16
18
20
0.0
0.2
0.4
0.6
0.8
1.0
PB 2000 kDa
t
DQ
[ms]
S
MQ
DQ
273 K
363 K
343 K
273 K
353 K
273 K
MQ data
F.V. Chavez, KS,
Macromolecules
44
(2011) 1560-1569.
0
2
4
6
8
10
0.0
0.2
0.4
0.6
0.8
1.0
normalized Hahn echo intensity
0
2
4
6
8
10
0.0
0.2
0.4
0.6
0.8
1.0
normalized Hahn echo intensity
t
echo
[ms]
273 K
363 K
PB 2000 kDa
PB 35 kDa
273 K
343 K
Hahn echo
data
no
free
parameters
!
clearly
non-
exponential
!
Slide14just an
exponential
T2 term for dynamics at t < t0=tDQmin!
Minimal fitting model
A.
Mordvinkin, KS, J. Chem. Phys. 146 (2017) 094902;Erratum: 148 (2018) 089901
*KS, A. Heuer,
Macromolecules 39 (2006) 3291-3303
analytical result (AW approx.):*
simple power-law decay
to 0:
t
0
/ ms
k
app
10
-7
~0
10
-6
0.03
10
-5
0.18
10
-4
0.61
10
-3
0.89
fitted
t
DQ
time region:
imposed plateau changes
apparent power law
testing the model on analytical metadata:
fitted
:
0
0.01
0.11
0.64
0.92
Slide15Test on MQ-NMR data of polymer melts
A. Mordvinkin, KS, J. Chem. Phys. 146 (2017) 094902.
earlier approaches
new: joint
data fitting
many samples, many temperatures
Þ
new, powerful multi-purpose fitting approach!
Slide16Supramolecular self-healing rubbers (ionomers)
n
n
n
n
n
n
A. Das, A.
Sallat
, F.
Böhme
, M.
Suckow
, D.
Basu
, S.
Wiesner
, K.W.
Stöckelhuber
, B.
Voit
, G. Heinrich,
ACS Appl. Mater.
Interf
.
7
, 20623-20630
(
2015);
Slide17A true engineering material
SEM micrograph oft the
c
utting
line
after
24 h
healing at 20°C
room-temperature healing 1 …
192 h
100
°C for the first
10
min
(red)uncut sample (green)
A. Das, A.
Sallat
, F.
Böhme
, M.
Suckow
, D.
Basu
, S.
Wiesner
, K.W.
Stöckelhuber
, B.
Voit
, G. Heinrich,
ACS Appl. Mater.
Interf
.
7
, 20623-20630
(
2015);
Slide18R:
methyl butyl hexyl nonyl
Sample variations
Stress at break / MPa
MI
BI
HI
NI
Self-healing
degree
/ %
pristine
healed
Slide19NMR
results
Slide20NMR
vs
DMA
shift
factors
:
ionic
cluster
activation
Slide21Summary
and Acknowledgment
beyond Lipari-Szabo: ”simple” bi/multi-exponential C(t) is too simplistic for polymers (also proteins…?)power-law C(t) in entangled polymer melts: anisotropic chain motion on the “spectral” timescale intermediate-motional effects (“true T2”), T-dependent residual couplings1H MQ NMR as a suitable tool to extract details of C(t)new fitting approach to characterize power-law C(t)application to study “sticky chain dynamics” in self-healing rubbers
Anton
Mordvinkin, Fabián Vaca Chávez, Filipe Furtado, Marie-Luise Trutschel (U Halle)Andreas Heuer (U Münster) Axel Herrmann, Ernst Rössler (U Bayreuth)Markus Suckow, Frank Böhme et al. (IPF Dresden)
€€€:
Slide22Why 1H multiple-quantum spectroscopy?
D
res
~ Sb
-4
-2
6
4
2
0
ppm
-4
-2
6
4
2
0
ppm
vs.
~ 1/
T
2
*
T
2
*
subject to
•
non-dipolar effects
•
multi-spin couplings
•
slow dynamics
•
order distributions...
Þ
more specific experiment!
real system
static
dipolar multiple-
quantum spectroscopy
t
DQ
t
DQ
DQ reconversion
DQ excitation
Slide23True “molecular rheology”
10
-5
10
-4
10-3
10-2
10-1
100
101
102
103
104
105
106
107
10-6
10-5
10-4
10-3
10-2
10-1
10 0
C
(
t
/
t
e
)
t
/
t
e
G
(
t
)
t
/ h
entangled polymer melt
vs. elastomer (no reptation)
“time-temperature
superposition” (
TTS
)
Slide24NMR: segmental dynamics and entanglements
n
entangled chains,
N
segments
each
time-dependent orientation
autocorrelation function
C
a
(
t
) = <
P
2
(cos
a
0
)
P
2
(cos
a
t
)
>
t,n,N
log
C
a
log
time
a
(
t
)
reference
direction
reptation, cooperative
processes (ms
-
s)
polymer melt far above
T
g
:
fast segmental
motions (ns
-m
s)
residual average orientation
~ semilocal backbone order parameter
dependent on
N
e
-1
(~
n
e
~ 1/
M
e
)
NMR-observable
dipolar coupling
w
D
~
S
e
~ line width ~ 1/
T
2
!
~1%
H
H
network:
S
2
plateau
Slide25NMR: segmental dynamics and entanglements
n
entangled chains,
N
segments
each
time-dependent orientation
autocorrelation function
C
a
(
t
) = <
P
2
(cos
a
0
)
P
2
(cos
a
t
)
>
t,n,N
log
C
a
log
time
a
(
t
)
reference
direction (
B
0
)
polymer melt far above
T
g
:
fast segmental
motions (ns
-m
s)
residual average orientation
~ semilocal backbone order parameter
S
b,e
=
C
(
t
e
)
1/2
dependent on
N
e
-1
(~
n
e
~ 1/
M
e
)
NMR-observable dipolar coupling
D
res
~ line width ~ 1/
T
2
!
~1%
reptation, cooperative
processes (ms
-
s)
b
(
t
)
Slide260.0
0.5
1.0
1.5
2.0
-7
-6
-5
-4
-3
-2
-1
0
log
C
(
t
) + cst.
log
t
t
-
1/2
t
-
3/2
III IV
t
d
~ t
d
/3
Correlation function in regimes III and IV
C
(
t
)
~
y
(
t
)
t
-1/2
,
y
(
t
) =
tube survival probability
(de Gennes: 1D random walk along tube)
t
1
t
2
t
3
loss of orientation correlation due to probing of adjacent primitive-path segments
Slide27Analysis of the correlation function
10
0
10
1
10
2
10
3
10
4
10
5
10
-
6
10
-
5
10
-
4
10
-
3
10
-
2
PB196k (
Z
=106)
PB87k (
Z
=47)
PB35k (
Z
=19)
fits
t
/
t
e
C
(
t
/
t
e
)
t
R
t
-
0.5
t
-
e
Z
=47
t
d
t
-
1.5
R. C. Ball, P. T. Callaghan, E. T. Samulski,
J. Chem. Phys.
106
(1997) 7352.
Slide28M
rept
»
200
M
e
M
c
»
2.5
M
e
constraint release!
t
/
t
e
(
M
e) = 1
10
4
10
4
10
5
10
6
t
d
t
R
log
t
/
t
e
M
w
/
Da
e
1
2
3
4
5
6
7
0.0
0.2
0.4
0.6
0.8
1.0
0.85
0.25?
3.42
±
0.07
2.16
±
0.25
II
III
IV
0
Results overview
F. V. Chavez, KS,
Phys. Rev. Lett.
104
(2010) 198305.
Slide29Sample variations: DMA results
BIIR+MI
BIIR+BI
BIIR+HI
BIIR+NI
Slide30GN, MPa Dres2, kHz2 theor. 0.7 BIIR+MI 1.9 0.112BIIR+BI 2.2 0.114BIIR+HI 2.4 0.106BIIR+NI 3.0 0.097
DMA vs. NMR master curves
reinforcement effects by variable ionic cluster sizes…?
10
-4
10
-3
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
10
-2
10
-1
BIIR-S 0.5 phr
BIIR+MI
BIIR+BI
BIIR+HI
BIIR+NI
BIIR
(D
eff
/2
p
)
2
*C(t) / kHz
2
a
T
*t / ms
10
-8
10
-6
10
-4
10
-2
10
0
10
2
10
4
10
6
10
8
10
-1
10
0
10
1
10
2
10
3
BIIR-S 0.5
phr
BIIR+MI
BIIR+BI
BIIR+HI
BIIR+NI
E' / MPa
a
T
w
/ Hz