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Local chain deformation and stress distribution in strained elastomers

Local chain deformation and stress distribution in strained elastomers. Maria Ott, Horst Schneider, Kay Saalwächter Martin-Luther-Universität Halle-Wittenberg, Institut für Physik, Halle (Saale), Germany Roberto Pérez-Aparicio, Paul Sotta CNRS-Rhodia joint lab, Lyon, France.

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Local chain deformation and stress distribution in strained elastomers

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  1. Local chain deformation and stress distribution in strained elastomers Maria Ott, Horst Schneider, Kay Saalwächter Martin-Luther-Universität Halle-Wittenberg, Institut für Physik, Halle (Saale), Germany Roberto Pérez-Aparicio, Paul Sotta CNRS-Rhodia joint lab, Lyon, France

  2. Uniaxial stretching of polymer networks macroscopic z x R R ? microscopic

  3. Uniaxial stretching of polymer networks macroscopic z x R R a microscopic

  4. Segmental order parameter Segmental (backbone) order parameter Sb = second moment of orientation distribution function, time-averaged f r R R0: separation of closest constraints (x-links or entanglements) f Sommer, J.-U. et al., Phys. Rev. E, 2008, 78, 051803  The segmental oder parameter directly reports on local stretching and stress

  5. Segmental order parameter Anisotropic dipole-dipole interaction Segmental (backbone) order parameter Sb = second moment of orientation distribution function,time-averaged f H H B0 Multiple-quantum NMR experiment r R t = ms (… s) f B0 Sommer, J.-U. et al., Phys. Rev. E, 2008, 78, 051803 Saalwächter, K., Prog. Nucl. Mag. Res. Sp., 2007, 51, 1-35  The NMR residual dipolar interaction measures the local stress

  6. MQ NMR spectroscopy f R a f • MICROSCOPIC DEFORMATION: • Time-domain multiple-quantum NMR experiment, raw data: • Determination and removal of the DEFECT contribution(isotropic, Dres = 0) • Localstress distributions of the NETWORKafter processing

  7. MQ NMR spectroscopy di f da R a f • MACROSCOPIC DEFORMATION: remove orientation effect! B0  l Mean stretching: • MICROSCOPIC DEFORMATION: • Time-domain multiple-quantum NMR experiment, raw data: • Determination and removal of the DEFECT contribution(isotropic, Dres = 0) • Localstress distributions of the NETWORKafter processing

  8. MQ NMR spectroscopy f R a f Bruker minispec mq20 0.5 T (20 MHz) ~ € 75.000.-

  9. Natural Rubber Local stress distribution in the unstretched network: probability Vulcanized NR (Mc=1200kg/mol)  Low defect content (~5 vol%)  Very homogeneous network

  10. Uniaxially strained natural rubber Local stress distributions in strained networks: l=1.0 l=4.2 probability orientation effect removed!  Increased heterogeneity: appearance of highly strained polymer chains

  11. Uniaxially strained natural rubber Local stress distributions: Average local stress: l=1.0 l=4.2 probability • Mc • 1102 kg/mol • 1200 kg/mol • 2100 kg/mol Me ~3900 kg/mol  Increased heterogeneity: appearance of highly strained polymer chains  Increased average dipolar interaction (local stress)

  12. Uniaxial deformation of filled networks macroscopic z x microscopic ?

  13. Silica-filled natural rubber Effect of filler particles (silica,  =18 vol%): Local strain enhancement: filled unfilled  Local overstrain effects – NMR is the only method to detect this in real-life sampes!

  14. Silica-filled natural rubber Effect of filler particles (silica,  =18 vol%): Local strain enhancement: filled unfilled Model of a polydisperse system of hard spheres: R. Christensen, Mechanics of Composite Materials Wiley, New York,1979.  Local overstrain effects are in agreement with simple hydrodynamic prediction

  15. Silica-filled natural rubber Effect of filler particles (silica,  =18 vol%): Distribution widths: filled unfilled  Higher level of local stress inhomogeneity in filled rubber

  16. Network models fixed junction affine deformation Natural rubber Mc=1200 g/mol Mc=2100 g/mol 1  Experiments reveal a strongly sub-affine behaviour !

  17. Network models fixed junction [1] [2] Mc=1200 g/mol [3] Mc=2100 g/mol 1 [4] [1] Beltzung, M, et al., Macromolecules, 1984, 17, 663-669 [2] Ronca, G. , Allegra, G., J. Chem. Phys., 1975, 63, 4990-4997 [3] Pearson, D. S., Macromolecules, 1977, 10, 696-701 [4] Heinrich, G. & Straube, E., Acta Polym., 1984, 35, 115-119

  18. Comparison with literature Small-angle eutron scattering data (end-linked PDMS): R║/R0 R a R║ R┴ Beltzung, M. et al.; Macromolecules, 1984, 17, 663-669 • - Similar results for small netwok chain molecular weights • - Experimental difficulties: end-linked networks  high defect content • Experimental difficulties: • long deuterated chains  several crosslinkes per chain • end-linked network chains  high defect content • non-trivial scattering background

  19. Conclusions Local stress distributions of strained elastomeric networks: - Measured directly by low-field MQ NMR, after removal of low (!) defect contributions - Substantial stress inhomogeneity upon stretching • Local overstrain effects in filled elastomers: • - Average follows simple hydrodynamic predition • - More pronounced stress inhomogeneity • Deviations from the fixed-junction Gaussian chain model on the molecular level • - Junction fluctuations need to be allowed • Local constraints play a role at low stretching degrees • - Force equilibration may explain narrow distributions

  20. THANK YOU FOR YOUR ATTENTION ! DINaFil: Dynamics in the Interphase of Nanoscopic Fillers Maria Ott Horst Schneider Martin Schiewek Paul Sotta Roberto Pérez-Aparicio Juan López Valentín

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