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

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

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

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

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

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

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

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

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! (~ € 75.000.-) 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) 044907

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.

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.

Functional-group selectivity: DQ MAS NMR natural rubber network (very homogeneous) 1H (400 MHz), 10 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

BaBa-xy16 – truly broadband DQ MAS NMR (px) (px py) (py) inverted 90°x 180°±x virtual (composite) p pulses: º 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.

BaBa-xy16 – truly broadband DQ MAS NMR c 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 = 0.533 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.

BaBa-xy16 – truly broadband DQ MAS NMR c Q2a Q3a Q3b Q2b 2D DQ corr., 30 kHz MAS recoupling time 16 tR = 0.533 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

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

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

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

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

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) 051803

DQ NMR on stretched networks f a Bruker minispec mq20 0.5 T (20 MHz)

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

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

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

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

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. 171-172 (2012) 8-16. º macroscopic z x ? microscopic

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

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) €€€: