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

Thermal fluctuations, non-equilibrium thermodynamics Fluctuations of a polymer glass and its response to thermal stress More refined experiments Results Conclusions and unsolved aspects UPoN 2008 Outline

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

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

A typical off-equilibrium system 1.Increase in viscosity by many orders of magnitude 2.Physical properties depend on thermal history 3.Slow dynamics 4.Dynamic heterogeneities E.g., a fluid coupled to a heat bath is quenched very fast 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

R C Dissipation Response

T twtw TgTg System thermally driven away from equilibrium Time evolution of the response (dielectric losses)

ϰ(t,t w ) separated into short time part (obeys equilibrium FDT) Ageing part (obeys the following relation: Away from equilibrium Generalized FDT, Fluctuation Dissipation Ratio Ref.: L. F. Cugliandolo, J. Kurchan, L. Peliti, Phys. Rev. E 55 (1997) The Effective Temperature

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

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

Optimization of the geometry of the sample Buissons Sample 14 parallel capacitors with polycarbonate as dielectric Present geometry: 10 μm PVAc between two aluminium electrodes Advantages: 1.Higher mechanical rigidity 2.Higher dissipation 3.Less bulky (aids in efficient thermal design of the setup). 4.Good electrical contact

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

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/Hz 1/2 ) and input voltage noise (5 nV/Hz 1/2 ) 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.

Re[Z(f)] TgTg Im[Z(f)] Thermal Cycles

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

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

ZZ ZeZe vSvS vZvZ G ξ η Nyquist noise measurements Current noise of Amplifier Voltage noise of Amplifier In Fourier space

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

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

Development of a DC polarisation voltage across the polymer film 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 VxVx RxRx C Equivalent Circuit

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

Effective temperature as a function of the waiting time Time evolution of Teff TfTf Buissons slow quench

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?

Deviations from the Gaussian shape

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.