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Fluctuations and slow dynamics in an ageing polymer glass

Fluctuations and slow dynamics in an ageing polymer glass. D. Bagchi , S. Ciliberto, A. Naert, L. Bellon. Mechanical design: Fr édéric Arnould Electronics: Marius Tanase. UPoN 2008. June 2 - 6, 2008. Outline. Thermal fluctuations, non-equilibrium thermodynamics

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Fluctuations and slow dynamics in an ageing polymer glass

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  1. Fluctuations and slow dynamics in an ageing polymer glass D. Bagchi, S. Ciliberto, A. Naert, L. Bellon Mechanical design: Frédéric Arnould Electronics: Marius Tanase UPoN2008 June 2 - 6, 2008

  2. Outline • Thermal fluctuations, non-equilibrium thermodynamics • Fluctuations of a polymer glass and its response to thermal stress • More refined experiments • Results • Conclusions and unsolved aspects UPoN2008

  3. Fluctuations and Dissipation (Dynamics in Equilibrium) Examples: Colloidal particles in a fluid / Electrons in a resistor (Nyquist noise) F Dissipation Resistance R, Viscosity η Fluctuation Voltage V(t), Velocity v(t) Fluctuation Dissipation Theorem In general, if Sv(f) is the spectral density of Fluctuations and ϰ(t) the response, then

  4. Questions: How does a system respond when driven away from equilibrium? How does one develop a thermodynamic description for these systems? Answer: Derive useful information from fluctuations of a relevant variable.

  5. A typical off-equilibrium system E.g., a fluid coupled to a heat bath is quenched very fast • Increase in viscosity by many orders of magnitude • Physical properties depend on thermal history • Slow dynamics • Dynamic heterogeneities System: A glassy system, e.g. a polymer after a quench Study: How the Nyquist noise and response (dielectric losses) change as a polymer evolves after a quench

  6. Response C R Dissipation

  7. System thermally driven away from equilibrium Tg T Time evolution of the response (dielectric losses) tw

  8. Away from equilibrium Generalized FDT, Fluctuation Dissipation Ratio ϰ(t,tw) separated into short time part (obeys equilibrium FDT) Ageing part (obeys the following relation: The Effective Temperature Ref.: L. F. Cugliandolo, J. Kurchan, L. Peliti, Phys. Rev. E55 (1997) 3898.

  9. FDT for a dielectric C R Power spectral density of fluctuations Response

  10. Recent experiments Intermittent bursts in the noise voltage of polycarbonate L. Buisson, S. Ciliberto, Physica D 204 (2005)

  11. Optimization of the geometry of the sample Present geometry: 10 μm PVAc between two aluminium electrodes Buisson’s Sample 14 parallel capacitors with polycarbonate as dielectric • Advantages: • Higher mechanical rigidity • Higher dissipation • Less bulky (aids in efficient • thermal design of the setup). • 4. Good electrical contact

  12. Experimental Setup Thermal insulation Amplifier 1st Stage: Differential amplifier with Low noise JFET 2N6453 Peltiers 6GΩ Faraday Cage NI-PXI 4472 Polymer: Polyvinyl Acetate, Tg=45°C

  13. Minimisation of the influence of external sources of noise on the noise spectrum of the sample • The first stage of the amplifier is a differential amplifier made of JFET 2N6453, which has a very low input current noise (1 fA/Hz1/2) and input voltage noise (5 nV/Hz1/2) above 2 Hz. • The entire experimental setup was housed in a Faraday cage. • The current through the peltier was kept constant during the waiting time after a quench, so as to prevent the influence of magnetic fields due to changing currents.

  14. Thermal Cycles Tg Im[Z(f)] Re[Z(f)]

  15. Ageing As a function of Frequency and speed of the quench Tstop=22 °C, quench rate=6.8 °C/min. Tstop=23.5 °C, quench rate=3.25 °C/min. tw =0 when the system just crosses the glass transition temperature 45°C

  16. As a function of Frequency and depth of quench Tstop=35 °C. Tstop=23.5 °C.

  17. Z Ze Nyquist noise measurements ξ η Z G Current noise of Amplifier vZ vS Voltage noise of Amplifier In Fourier space

  18. A typical noise voltage signal and its power spectrum when the system is near equilibrium

  19. Effect of very slow quenches crossing the glass transition Effect of very slow quenches crossing the glass transition Evolution of the power spectrum of voltage noise for a very slow quench (rate = 0.15°C/min), Tstop= 32°C, for tw=57 mins., 65 mins., 200 mins., and 335 mins. Effective temperature (in Kelvins) for the same quench

  20. C Rx Vx Development of a DC polarisation voltage across the polymer film Equivalent Circuit • Follows temperature change • Insensitive to the presence of thermal gradients • Quite stable with time • Highest at high temperatures when the polymer molecules are more rubbery • Direction of polarization is constant

  21. Effect of fast quenches crossing the glass transition Quench rate: 7 °C/min.;Tstop= 21°C

  22. Time evolution of Teff Tf Effective temperature as a function of the waiting time Buisson’s slow quench

  23. Statistical analysis of the evolution of noise voltage after a quench Thermal voltage fluctuations in an ordinary impedance has a Gaussian distribution. What happens when the impedance ages with time?

  24. Deviations from the Gaussian shape

  25. Conclusions and Future Perspectives • The relaxation dynamics of the polymer depends on the quench rate. • There is a small violation of the FDT at low frequencies for the fastest quench studied. • The PDFs of the noise voltage after a quench are Gaussian. • No intermittent bursts are observed in the noise voltage. The understanding of intermittency still remains an open question. • It is crucial to minimise the 1/f noise of the amplifier in order to do a thorough study of the important low frequency regime.

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