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polymer dynamics & field cycling NMR

polymer dynamics & field cycling NMR. - glass transition - dynamics in polymer melts analyzing T 1 relaxation. E.A. Rössler Experimentalphysik II, Universität Bayreuth, Germany. a rheological crossover in the viscosity of polymer melts. M < M c :   M 1

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polymer dynamics & field cycling NMR

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  1. polymer dynamics & field cycling NMR - glass transition - dynamics in polymer melts analyzing T1 relaxation E.A. Rössler Experimentalphysik II, Universität Bayreuth, Germany

  2. a rheological crossover in the viscosity of polymer melts M < Mc:   M1 M > Mc:   M(3.4-3.7 Mc: „entanglement M“ Berry and Fox 1968

  3. two microscopic theories for explaining two rheological regimes rheological behavior changes at entanglement molecular weight Mc M < Mc: Rouse theory (1953) M > Mc: tube reptation theory (deGennes 1979, Doi/Edwards 1987)

  4. Rouse model (M < Mc): bead & spring model in a viscous medium entropic force constant:

  5. Rouse model II: calculating correlation function of normal mode coordinates neglecting inertia effects, (overdamped oscillations due to viscous medium) and continuous chain decoupled relaxation („breathing“) modes

  6. Rouse -1/2 1 <R2> lgt 1/2 lgt Rouse model III – results a.) mean square segment displacement b.) correlation function of tangent vector b

  7. Rouse modell IVscaling arguments yielding more and more segments are dragged cf. T. Springer, IFF-Ferienkurs 1994

  8. Rouse glassy & Rouse dynamics mean square segmental displacement <r2(t)> = g1(t) MD simulations (Binder et al. 2003) - ballistic regime:  t2 - cage regime  to - sub-diffusive Rouse regime:  t1/2 - hydrodynamic regime: (t  ): <r2> = 6 D t

  9. accounting for entanglement effects: deGennes´ idea: tupe-reptation model forecast:  M3(exp.: M3.60.2) D  M-2 (exp.: D M-2.2)

  10. from Rouse to entanglement dynamics hierachy of power-laws is expected mean square rank-two displacementorientational correlation function (courtesy K. Saalwächter) regime II and III:

  11. shear modulus lg G(t) lg t What mechanical relaxations do we expect in polymers? Rouse entanglement simple liquid = „glassy dynamics“ (-process) M <MRM >MRM >Me

  12. bead-and-spring model JCP evidence of tube

  13. coming from short times: neutron scattering

  14. coming from long times: field gradient NMR

  15. fast or electronic field cycling NMR:powerful tool for investigating polymer dynamics since 2005 in Bayreuth (EPII) Doi, M.; Edwards, S.F. The Theory of Polymer Dynamics; Oxford 1986. Binder, K., Baschnagel, J., Paul, W. Progr. Polym. Sci. 28, 115 (2003) Kimmich, R., Fatkullin, N. Adv. Polym. Sci. 170, 1 (2004) Greassley, W.W. Polymer Liquids & Ntworks: Dynamics and Rheology, Garland 2008 Kruk D.; Herrmann, A.; Rössler, E.A.Progr..NMR Spectroscopy 63,33 (2012) Bayreuth (EP II; FFC NMR and DS): Kariyo et al. Phys. Rev. Lett.97, 207803 (2006) Kariyo et al. Macromolecules41, 5313 dito 41, 5322 (2008) Herrmann et al. Macromolecules42, 2063 dito 42, 5236 (2009) Abou Elfadl et al. Macromolecules42, 6816 (2009) dito 43, 3340 (2010) Herrman et al. Macromolecules45, 1408 dito 45, 6516 (2012) Hofmann et al. Macromoleces45, 2390 (2012) Kruk, Meier, Rössler, J. Phys. Chem. B115, 951 (2011) Meier, Kruk, Rössler, J. Chem. Phys.136, 034508 (2012) Kruk, Meier, Rössler, PRE 85, 020201 (2012) Meier et al. ACS MacroLetters 2, 96 (2013)

  16. short introduction to field cycling NMR

  17. N-0 N+0 nuclear spin in external magnetic field B0

  18. nuclear magnetization (in therm. eq.)

  19. impact of pulses RF probe pulse (B1 field) turns Mz into x,y-planeafter pulse: magnetization precesses with Land decays freely: free induction decay (FID) FID amplitude M0

  20. signal detection precessing magnetization induces NMR signal S(t) in RF coil perpendicular to Bz=B0

  21. Mz M0 M0 (1- e-1) t T1 spin-lattice relaxation What re-establishes Mz and Boltzmann distribution of Ni? no spontaneous emission relevance of internal relaxation processes due to coupling of spins with “lattice”

  22. source of spin-lattice interaction: dipolarly coupled spins simplest case: pair of spins fixed by distance r fluctuation of orientation () produces Bloc(t) driving transitions in 4-level-system of spin pairs T1 relevant: intensity of fluctuations at L and 2L

  23. Bloembergen, Purcell, Pound theory (BPP) isotropic liquid: 1/T1 probes spectral densityJi() at L=B0and2L a noise probing experiment

  24. correlation function CAA(t)describes equilibrium fluctuations of the quantity A stationary process:

  25. correlation function, spectral density, susceptibility a measure of the fluctuation of A with frequency 

  26. What is a susceptibilty? relaxation experiment: equilibrium disturbed by applying AC field and response measured

  27. fluctuation-dissipation theorem linear response theory dissipation fluctuations in equilibrium (with exciting field) (without field)

  28. some important properties „normalized“ „time constant“

  29. simplest case: „Debye relaxation“ solution of rotational diffusion equation

  30. dielectric spectroscopy probing susceptibility related to reorientational correlation function C1(t)

  31. frequency-temperature superposition (FTS) spectral shape is independent of  or T feature commonly observed for glassy and polymer dynamics

  32. 1H NMR in polymers: probing fluctuation of bond vector segmental correlation function C2(t)

  33. Mz T1 Mz polarization Mz detection T1 relaxation Mz T1 t T1 relaxation T1 frequency principle of field cycling NMR Larmor frequency becomes variable  =  Bo t

  34. Mz() = M0(Br) + [M0(Bp) – M0(Br)] exp {-  /T1(Br)}

  35. Bd Bp Br 90o Tx Acq basic FFC sequence switching time of Bo ~ 1.5 ms Bo/2 =  = 10 kHz – 20 MHz FFC 2000 relaxometer (STELAR) operating in Bayreuth since 2005

  36. transforming to susceptibility representation

  37. similar relaxation behavior as revealed by dielectric spectroscopy DS behavior typical of glass formers

  38. applying FTS yields master curves 5 - 6 decades in amplitude & frequency accessible at  << 1 „simple liquid limit“

  39. FFC NMR: 10-11s – 10-6 s NMR master curve yields time constant (T) agreement with results from other techniques non-Arrhenius behavior typical of glass transition

  40. crossover from simple liquid to polymer melt master curves of a series of polybutadienes

  41. crossover from simple liquid to polymer melt

  42. crossover from simple liquid to polymer melt PB355 and PB466 show no polymer effect (like OTP)

  43. crossover from simple liquid to polymer melt first polymer effect for PB777

  44. crossover from simple liquid to polymer melt

  45. crossover from simple liquid to polymer melt

  46. crossover from simple liquid to polymer melt note:  s(segmental time)assumed

  47. crossover from simple liquid to polymer melt

  48. crossover from simple liquid to polymer melt increasing contribution at low frequencies (<<1)

  49. crossover from simple liquid to polymer melt saturation due to entanglement (M >> Me)

  50. crossover from simple liquid to polymer melt

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