Local deformation of polymer chains as reflected in proton dipole-dipole coupling distributions 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 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 tDQ DQ reconv. DQ exc. SSMQ/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

DQ spectroscopy for homonuclear dip. couplings tDQ DQ reconv. DQ exc. SSMQ/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 R. Graf et al., Phys. Rev. Lett. 80 (1998) 5783 KS, Progr. NMR Spectrosc. 51 (2007) 1-35

DQ spectroscopy and normalization tDQ DQ reconv. DQ exc. SSMQ/DQ determined by Dj = ±90° or n´180° spin pair calculation: longit. magn. (ZQ) DQ R. Graf et al., Phys. Rev. Lett. 80 (1998) 5783 KS, Progr. NMR Spectrosc. 51 (2007) 1-35

DQ spectroscopy and normalization longit. magn. (ZQ) DQ receiver Dj DQ ref 90° 0° 0° 180° 180° 0° 270° 0° 0° 0° 180° 0° Þ 4-step phase cycle, 2 complementary options: determined by Dj = ±90° or n´180° remove by tail fit (relaxes slowly) full echo, relaxation-only function! Þ normalized DQ signal, no relaxation: R. Graf et al., Phys. Rev. Lett. 80 (1998) 5783 KS, Progr. NMR Spectrosc. 51 (2007) 1-35

BaBa-xy16: distances in phosphates Q2a Q3a Q3b Q2b normalized DQ build-up curves: coupling constant estimates (2nd-moment approx.) expected: pair contact DPOP(2.9Å)/2p » 800 Hz rms-sum (dst. up to 5Å) (2/3)´(SD2)½/2p Q2A : 893 Hz Q2B : 800 Hz Q3C : 980 Hz Q3D : 920 Hz N tR / ms Q(2) Q(1) 1270 Hz 920 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: 0.0 0.2 0.4 0.6 0.8 1.0 1.2 SnDQ = SDQ/SSMQ DQ evolution time / ms peak D: 890 Hz peak C: 920 Hz peak B: 735 Hz peak A: 810 Hz Q(3) Q(2) 60 kHz MAS KS, F. Lange, K. Matyjaszewski, C.-F. Huang, R. Graf, J. Magn. Reson. 212 (2011), 204-215.

Empirical universal DQ build-up function model data: homogenous elastomer (dense 1H spin system with uniform Deff) <sin2f> powder avg. 2nd-moment approx. A-l function W. Chassé, J. López-Valentín, G.D. Genesky, C. Cohen, KS, J. Chem. Phys. 134 (2011) 044907 Þ enables D distribution analysis in inhomogeneous samples! 1.0 POST-C7: g encoding is no advantage! 0.8 0.6 norm. intensity 0.4 DQ SMQ nDQ 0.2 0.0 2 4 6 8 10 12 DQ evolution time / ms

Coupling and relaxation time distributions powder-averaged spin pair data SDQ = <sin2f> + s/2p = 200 Hz 200 400 600 800 1000 D/2p / Hz probability / a.u. s/2p = 200 Hz + diff. relaxation 2ms relax. 4ms relax. D/2p = 500 Hz SnDQ 0.6 0.5 0.4 DQ intensity 0.3 ® distribution changes build-up curve shape ® differential relaxation precludes normalization, gives only small bias at short times 0.2 0.1 0.0 0.0 0.4 0.8 1.2 1.6 2.0 tDQ / ms

Functional-group selectivity: MAS needed? model elastomer: natural rubber network 1H (400 MHz), 10 kHz MAS, BaBa-xy16 1 ppm 2 3 4 5 6 7 CH3 CH2 CH static low field (20 MHz, Baum-Pines seq.) is no disadvantage! nDQ stat fit 257 Hz 2 4 DQ evolution time / ms 0.0 0.2 0.4 0.6 norm. intensity CH3 SMQ CH3 DQ CH3 nDQ fit 250 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 CH nDQ CH2 nDQ KS, F. Lange, K. Matyjaszewski, C.-F. Huang, R. Graf, J. Magn. Reson. 212 (2011), 204-215.

A partial solution for dipolar truncation? CH3 CH2 CH 1 2 3 4 5 6 ppm 8 10 12 chemical shift d DQ shift (di+dj) 2 4 6 0.0 0.2 0.4 0.6 norm. intensity DQ evolution time / ms tDQ=0.8ms 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: 1 2 3 time evolution dominated by strong passive coupling! relative DQ intensities but: rel. int. reflects weak coupling! KS, F. Lange, K. Matyjaszewski, C.-F. Huang, R. Graf, J. Magn. Reson. 212 (2011), 204-215. KS, ChemPhysChem (2013) in press.

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 net70 best-fit (monomodal) net90 net100 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 DQ evolution time / 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 natural rubber different cure systems conventional: accelerator/sulphur (0.2/1) efficient: accelerator/sulphur (12/1) peroxide: dicumyl peroxide 0.0 0.2 0.4 0.6 0.8 1.0 5 10 15 20 25 30 conventional efficient peroxide rel. amplitude Dres/2p / kHz R· n … “zipping” reaction: J. López Valentín, P. Posadas, A. Fernández-Torres, M. A. Malmierca, L. González, W. Chassé, KS, Macromolecules 43 (2010) 4210.

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 Sb ~ Dres ~ R2 ~ F2 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” allows distribution analysis! l d d i i d d 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 probability orientation effect removed! Dres ~ 1/N Dres ~ R2 ~ F2 ® increased inhomogeneity, coexistence of almost unchanged and highly strained chains

Comparison with models of rubber elasticity R ^ F R || F classical affine model stretched l=2 R 2.0 unstretched 1.5 R tube model phantom model probabilty 1.0 0.5 0.0 1 2 3 4 5 Dres/Dres,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 nDQ,powder D res /D res,l=1 1.5 S 2.0 ò / 1.0 nDQ S 1.5 0.5 ò 0.0 1.0 20 40 60 80 100 5 10 15 20 W / ° l 2 -1 elongation - l ® nice confirmation of phantom behavior

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) €€€:

Beyond spin pairs: spin counting formally: DQ = all 2+4n, ref = all 4n coherence orders model for dense 1H spin system with uniform Deff: silicone elastomer experimental: 4-step DQ-filter O Si C a 0Q+LM 4Q 6Q 8Q 2Q ® build-up completely dominated by DQ coherences ® universal build-up curve shape! 1.0 2Q 2Q+6Q 4Q and 6Q ZQ+LM CH3-2Q 6-spin simulations: lines 0.8 nDQ intensity 0.6 0.4 0.2 0.0 2 4 6 8 10 DQ evolution time / ms KS, J.-U. Sommer, et al., J. Chem. Phys. 119 (2003), 3468

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 KS, F. Lange, K. Matyjaszewski, C.-F. Huang, R. Graf, J. Magn. Reson. 212 (2011), 204-215. 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 MgP4O11, 31P at 243 MHz (14.1 T) a b c Q2a Q3a Q3b Q2b dcswL/2p = 35 – 42 kHz * 8 kHz MAS (impurity) 100 –100 –200 ppm BaBa at 30 kHz MAS recoupling time 16 tR = 0.533 ms –50 –100 50 ppm “broadband BaBa” BaBa-xy16, DQ BaBa-xy16, ref (impurity) Q2 Q3 DQ build-up / SMQ curves 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 norm. intensity DQ evolution time / ms peak 4 peak 3 peak 2 peak 1 4 tR 8 tR “broadband BaBa” BaBa-xy16 SMQ DQ DQ ´3-4! KS, F. Lange, K. Matyjaszewski, C.-F. Huang, R. Graf, J. Magn. Reson. 212 (2011), 204-215.

BaBa-xy16 – truly broadband DQ MAS NMR offset and flip-angle stability (31P, phosphate sample) experimental: 60 kHz MAS, tDQ = 32 tR = 0.533 ms 5 10 15 20 25 30 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 DQ intensity resonance offset / kHz 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 relative rf nutation 60 kHz MAS 400 MHz 600 MHz 800 MHz 30 kHz simulation results: varying pulse length (90° º 1.3 ms) 0.8 1.0 1.2 1.4 1.6 1.8 ms varying offset –10 10 20 kHz KS, F. Lange, K. Matyjaszewski, C.-F. Huang, R. Graf, J. Magn. Reson. 212 (2011), 204-215.

Avoid “subensemble NMR” in constant-time exp.! DQ spinning sideband patterns [non g-encoded seq.] (Spiess et al.) constant-time DQ modulation (Schmedt a.d. Günne) + s/2p = 200 Hz 200 400 600 800 1000 D/2p / Hz probability / a.u. s/2p = 200 Hz x4 (!) + relaxation x4 2ms relax. 4ms relax. tDQ1 DQ rec. DQ exc. 2tDQ,max = cst. tDQ=cst. DQ rec. DQ exc. Dt1=tR/N 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 tDQ1= 2tDQmax-tDQ2 / ms D/2p = 500 Hz D/2p = 500 Hz tDQ = 2 ms -80 -40 40 kHz

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

Inhomogeneities in rubbers: defects 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: 100 200 300 400 500 600 5 10 15 20 25 30 peroxide efficient conventional non-coupled network defects / % Dres/2p / kHz SMQ DQ loops dangling ends sol mobile impurities tDQ

Inhomogeneities in natural rubber nDQ= DQ/(SMQ-tail) 0.5 initial slope reflects crosslink density (~ Dres ) and its distribution tDQ 0.0 0.2 0.4 0.6 0.8 1.0 5 10 15 20 25 30 conventional efficient peroxide rel. amplitude Dres/2p / kHz R· n … “zipping” reaction: J. López Valentín, P. Posadas, A. Fernández-Torres, M. A. Malmierca, L. González, W. Chassé, KS, Macromolecules 43 (2010) 4210.

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 (new, corrected model) 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 previous model new hydrodyn. model ® samples with aggregated filler have a more complex behavior ® a new, corrected hydrodynamic model is confirmed

DQ-DRENAR vs. nDQ analysis BaBa-xy16, 10 kHz MAS natural rubber 1 2 3 4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 norm. intensity tDQ = ½ ttot / ms CH2 2.4 ppm (on res.) SSMQ S0 = {C,iC’}n S0= {C, C’}n S0= {Cn, C’n} 2×SnDQ 1-S'/S0; S’ = {C, iC}n 1-S'/S0; S’ = {C, C}n 1-S'/S0; S’ = {Cn, Cn} º DQ-DRENAR Dapp/2p = 260 Hz 1 2 3 4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 norm. intensity tDQ = ½ ttot / ms CH 5.6 ppm (1.23 kHz off res.)