martin-luther-universität halle-wittenberg institut für physik nmr group bias-free determination...

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


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


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


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


IMQ/DQ

DQ


NMR group

DQ spectroscopy and normalization

determined by = ±90° or n180°

DQ


IMQ/DQ

DQ


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


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 )


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


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


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


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


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


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


0.0

0.2

0.4

0.6

no

rm.

inte

nsi

ty


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


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.


–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


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


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


NMR group


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


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


BaBa-xy16

DQ 3-4!

4 tR

8 tR


NMR group


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


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


NMR group

x

z

zz

macroscopic

microscopic?R R

xx

Unixaxial stretching of polymer networks


NMR group

xx

macroscopic

microscopic

x

z

zz

RR



NMR group


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


NMR group

DQ NMR on stretched networks

xx

zz

R

f

f Bruker minispec mq20

0.5 T (20 MHz)


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!


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


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


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


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.


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


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)

martin-luther-universität halle-wittenberg institut für physik nmr group bias-free determination...

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