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

Martin-Luther-UniversitätHalle-Wittenberg Institut für Physik

NMR group

Local deformation of polymer chains as reflected in proton dipole-dipole

coupling distributions

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

- 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

DQ

DQ reconv.DQ exc.SMQ/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


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 homonuclear dip. couplings

fit

R. Graf et al., Phys. Rev. Lett. 80 (1998) 5783

KS, Progr. NMR Spectrosc. 51 (2007) 1-35

DQ


DQ


NMR group

DQ spectroscopy and normalization

determined by = ±90° or n180°

longit. magn. (ZQ) DQ

spin pair calculation:



DQ


DQ


NMR group

DQ spectroscopy and normalization

determined by = ±90° or n180°

longit. magn. (ZQ) DQ

receiver DQ ref 90° 0° 0°180° 180° 0°270° 0° 0° 0° 180° 0°

4-step phase cycle, 2 complementary options:

remove by tail fit (relaxes slowly)

full echo, relaxation-only function! normalized DQ signal, no relaxation:




NMR group

BaBa-xy16: distances in phosphates

normalized DQ build-up curves: coupling constant estimates (2nd-moment approx.)

expected:

pair contactDPOP(2.9Å)/2 800 Hz

rms-sum(dst. up to 5Å)(2/3)(D2)½/2 Q2

A : 893 HzQ2

B : 800 HzQ3

C : 980 HzQ3

D : 920 Hz

KS, F. Lange, K. Matyjaszewski, C.-F. Huang, R. Graf, J. Magn. Reson. 212 (2011), 204-215.

0.0 0.2 0.4 0.6 0.8 1.0 1.20.0

0.2

0.4

0.6

0.8

1.0S

nD

Q =

SD

Q/S

MQ


peak D: 890 Hz

peak C: 920 Hz

peak B: 735 Hz

peak A: 810 Hz

Q(3)

Q(2)

60 kHz MAS

ab

c

Q2a

Q2a

Q3a

Q3a

Q3b Q3

b

Q2b

Q3b

Q3b

Q3a

Q2b

N R / ms

Q(2)

Q(1)

1270 Hz920 Hz

J. Ren, H. Eckert, Angew. Chem. Int. Ed. 51 (2012) 12888.

KS, ChemPhysChem (2013) in press.

“homonuclear REDOR”

(S0 -

S’)/

S0

equivalent approach, new name:


NMR group

Empirical universal DQ build-up function

DQMQ

nDQ

0 2 4 6 8 10 120.0

0.2

0.4

0.6

0.8

1.0

no

rm.

inte

nsi

ty


POST-C7: encoding is no

advantage!

2nd-moment approx.

<sin2>powder avg.model data: homogenous elastomer (dense 1H spin system with uniform Deff)

A-l function

W. Chassé, J. López-Valentín, G.D. Genesky, C. Cohen, KS, J. Chem. Phys. 134 (2011) 044907

enables D distribution analysis in

inhomogeneous samples!


NMR group

SnDQ

Coupling and relaxation time distributions

0.0 0.4 0.8 1.2 1.6 2.00.0

0.1

0.2

0.3

0.4

0.5

0.6

DQ

inte

nsi

ty

DQ / ms

powder-averaged spin pair dataSDQ = <sin2>

D/2= 500 Hz

distribution changesbuild-up curve shape

differential relaxation

precludes normalization,

gives only small bias at

short times

/2= 200 Hz

0 200 400 600 800 1000D/2 / Hz

pro

bab

ility

/

a.u

.

/2 = 200 Hz

diff. relaxation

2ms relax.4ms relax.


NMR group

CH3 MQCH3 DQCH3 nDQfit 250 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: MAS needed?

model elastomer: natural rubber network 1H (400 MHz),

10 kHz MAS, BaBa-xy16

H

CH2

C CH3CH2

C

H2Cn

H

CH2

C CH3CH2

C

H2Cn

1 ppm234567

CH3

CH2

CHstatic low field

(20 MHz, Baum-Pines

seq.)is no

disadvantage!

nDQ statfit 257 Hz

0 2 4


0.0

0.2

0.4

0.6

no

rm.

inte

nsi

ty



NMR group

CH3CH2CH

123456 ppm

2

4

6

8

10

12

chemical shift

DQ

sh

ift

(i+

j)

A partial solution for dipolar truncation?


KS, ChemPhysChem (2013) in press.

H

CH2

C CH3CH2

C

H2Cn

H

CH2

C CH3CH2

C

H2Cn

0 2 4 60.0

0.2

0.4

0.6

norm

. in

ten

sity


DQ=0.8ms

relativeDQ

intensities

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)

114506.

DQ transfer in a 3-spin system:

12 3

time evolution dominated by strong

passive coupling!but:

rel. int. reflects weak coupling!


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(2)

Dipole-dipole coupling and chain dynamics/statistics

B0

HH

static limit (glass):D ~ P2(cos )/rHH

3

1

± D(1)

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 ) P2(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

in

ten

sity

% short chains:

linear superpositions of experimental data for net0 and net100

PDMS precursors:long chains: 47k

short chains: 0.8k


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 natural rubber

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.

conventional: accelerator/sulphur (0.2/1)

efficient: accelerator/sulphur (12/1)

peroxide: dicumyl peroxide

different cure systems

0.0 0.2 0.4 0.6 0.8 1.00

5

10

15

20

25

30 conventional efficient peroxide

rel.

am

plitu

de

Dres/2 / kHz


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

Sb Dres ~ R2 F2


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

do

di

d

l

average stretching:

B0

remove orientation effect!

“artifical powder” allows

distribution analysis!


NMR group

Local stress/strain distributions in strained rubbers

vulcanized natural rubbervery homogeneous, low defect content

=1.0=4.2

orientation effect

removed!

increased inhomogeneity, coexistence of almost unchanged and highly strained chains

probabilit

y

Dres ~ R2 F2

Dres ~ 1/N


NMR group

Comparison with models of rubber elasticity

unstretched

R F R || F

R

2.0

1.5

1.0

0.5

0.0

pro

bab

ilty

543210Dres/Dres,=1

classical affine model

phantom model

tube model

stretched =2R


NMR group

Confirmation of models of rubber elasticity

3.0

2.5

2.0

1.5

1.0

Dre

s/D r

es,

=1

20151050

elongation 2-

-1

NR1B NR3A NR3B

2.5

2.0

1.5

1.0

0.5

0.0

S

nDQ/

S

nD

Q,p

ow

der

100806040200 / °

rel. anisotropy from angle-dependent build-

up curves

average local stretching from artificial powder

nice confirmation of phantom behavior


NMR group

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)


NMR group

2Q

build-up completely dominated by DQ coherences

universal build-up curve shape!

2Q2Q+6Q

4Q and 6Q

ZQ+LM

CH 3-2Q

6-spin simulations: lines

0Q+LM

4Q 6Q 8Q

Beyond spin pairs: spin counting

0 2 4 6 8 100.0

0.2

0.4

0.6

0.8

1.0


nDQ

inte

nsity

experimental: 4-step DQ-filter

KS, J.-U. Sommer, et al., J. Chem. Phys. 119 (2003), 3468

formally: DQ = all 2+4n, ref = all 4n coherence ordersmodel for dense 1H spin system with uniform Deff: silicone elastomer

OSi

C

O

C


NMR group

BaBa-xy16 – truly broadband DQ MAS NMR

yyy

x yx y

x y y

x x y

x y y

x x

x xR

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

(x) (x y)(y)

inverted

90°x180°±x

virtual (composite) pulses:

90°-x

yyyy

y

(x)

y

(+ inverted)x xy x x x xy x x

(x)(y) (y) (y) (x) (x)(y)

BaBa-xy16



NMR group

MgP4O11, 31P at 243 MHz (14.1 T)


–1000 –200100 ppm

8 kHz MAS

(impurity)

* csL/2 = 35 – 42 kHz

BaBa at 30 kHz MASrecoupling time 16 R = 0.533 ms

0 –50 –10050 ppm

“broadband BaBa”

BaBa-xy16, DQ

BaBa-xy16, ref(impurity)

Q2 Q3

ab

c

Q2a

Q2a

Q3a

Q3a

Q3b Q3

b

Q2b

Q3b

Q3b

Q3a

Q2b


DQ build-up / MQ curves

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

ten

sity


peak 4

peak 3

peak 2

peak 1

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6DQ evolution time / ms

4 tR

8 tR

“broadband BaBa”

BaBa-xy16

MQ

DQDQ 3-4!


NMR group

varying pulse length (90° 1.3 ms)



offset and flip-angle stability (31P, phosphate sample)

experimental: 60 kHz MAS, DQ = 32 R = 0.533 ms

varyingoffset

–10 0 10 20 kHz

1.0 1.2 1.4 1.6 1.8 ms0.8

0 5 10 15 20 25 300.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

DQ

in

ten

sity

resonance offset / kHz

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.50.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

DQ

in

ten

sity

relative rf nutation

60 kHz MAS

400 MHz 600 MHz 800 MHz 400 MHz 600 MHz 800 MHz

30 kHz MAS

simulation results:


NMR group

Avoid “subensemble NMR” in constant-time exp.!

0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0DQ1= 2DQmaxDQ2 / ms

D/2 = 500 Hz

D/2 = 500 Hz

-80 -40 0 40 kHz

DQ = 2 ms

/2 = 200 Hz

/2 = 200 Hz

0 200 400 600 800 1000D/2 / Hz

pro

bab

ility

/

a.u

.

/2 = 200 Hz

x4 (!)

relaxation

relaxationx4

2ms relax.4ms relax.

constant-time DQ modulation

(Schmedt a.d. Günne)

DQ spinning sideband patterns

[non -encoded seq.]

(Spiess et al.)

DQ1

DQ rec.DQ exc.

2DQ,max = cst.

DQ=cst.

DQ rec.DQ exc.

DQ=cst.

t1=R/N


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

Inhomogeneities in rubbers: defects

MQDQ

loops

dangling ends

sol

mobileimpurities DQ


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-

coup

led

netw

ork

defe

cts

/ %

Dres/2 / kHz


NMR group

Inhomogeneities in natural rubber

0.5

nDQ=DQ/(MQ-tail)

R

n

n

n

…

“zipping” reaction:


initial slope reflects crosslink density (~ Dres ) and its distribution DQ

0.0 0.2 0.4 0.6 0.8 1.00

5

10

15

20

25

30 conventional efficient peroxide

rel.

am

plitu

de

Dres/2 / kHz


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.

(new, corrected model)


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

previous

model


NMR group

0 1 2 3 40.0

0.2

0.4

0.6

0.8

1.0

1.2

norm

. in

tens

ity

DQ = ½ tot / ms

CH2 2.4 ppm (on res.)

SMQ

S0 = {C,iC’}n

S0= {C, C’}n

S0= {Cn, C’n}

2×SnDQ

1S'/S0; S’ = {C, iC}n

1S'/S0; S’ = {C, C}n

1S'/S0; S’ = {Cn, Cn} DQ-DRENAR

Dapp/2 = 260 Hz

0 1 2 3 40.0

0.2

0.4

0.6

0.8

1.0

1.2

norm

. in

tens

ity

DQ = ½ tot / ms

CH 5.6 ppm (1.23 kHz off res.)

DQ-DRENAR vs. nDQ analysis

BaBa-xy16, 10 kHz MASnatural rubber

Documents

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