Soft Report - Dipartimento di Fisica - Sapienza

Polarization Fluctuation and Dissipation in Out of EquilibriumSystemsSystems characterized by slow dynamics can bedriven to out of thermodynamic equilibrium states bymeans of a rapid change of appropriate externalvariables, for instance a temperature jump taking aliquid down to a glassy state. After such treatment,the system tends to relax to the thermodynamicequilibrium state, and the properties (dynamic,thermodynamic, mechanical) of the system dependon t w, the time elapsed after the achievement of theout of equilibrium state [1]. In an out-of-equilibriumsystem the response to a small externalperturbation, especially at long time, is not longerrelated, via the temperature of the thermal bath, tothe spontaneous fluctuations of the variable undertest, as predicted by the fluctuation-dissipationtheorem (FDT) [2], since both the fluctuations andFig. 1. (a) Normal probability plot and (b) voltagevs. time series at tw=30 min. after a quenching at278 K. (c) and (d) show the same plots atequilibrium after a slow cooling at 278 K. Crossesare the experimental values. Straight lines in (a)and (c) show the expected values for a Gaussiandistribution. Voltage values are amplified by the gainof the amplifier (factor 1800).the response depend on the thermal history of thesystem. In such situation the temperature of thesystem is not well defined any more, and it cannotbe used as an unique parameter able to describe thedynamic behaviour. Recently, the dynamics of outof-equilibriumsystems has been tentativelydescribed by introducing a temperature (fictive), T eff,defined by a generalization of the FDT [2]. Such aparameter should take into account the thermalhistory in the new thermodynamic description of outof-equilibriumsystems. Apart from the number ofsimulation works verifying the violation of the FDT inout-of-equilibrium systems, experimental worksconcerning glassy systems are almost missing. Wedeveloped an apparatus to measure simultaneouslythe complex permittivity (susceptibility) by dielectricspectroscopy and the polarization fluctuations(correlation function) observed via the voltage noise,produced by a capacitor cell filled with the glassformerunder test [3]. We performed measurementson an epoxy organic glass former both above andbelow the glass transition temperature. Thepolarization noise followed the predictions of the FDTwhen the material is at the thermodynamicequilibrium state or weakly out. In the out-ofequilibriumstate an intense polarization noise wasdetected, much more than that measured atequilibrium (Fig. (1b) and (1d)). A non-Gaussiandistribution of the probability density function of thepolarization fluctuations was observed immediatelyafter a rapid quenching of the sample below theglass transition temperature (Fig (1a) and (1c)). Thewidth of the distribution reduced during aging and itsshape tended towards a Gaussian distribution as theequilibrium state was approached [3]. T eff wascalculated for the dynamics properties in threedifferent frequency regions and for different valuesof the temperature of the thermal bath, T b (Fig. (2))[3]: (a) at the highest frequency (20 Hz) the FDTrelation holds above and below T g with T eff=T b (seeinset); (b) at the lowest frequency (0.2 Hz) a strongdeviation from the FDT prediction occurs just fewdegrees above T g and T eff reaches huge values (>105K) at lower temperatures; (c) at 2 Hz the deviationfrom FDT occurs below T g and the values of T eff areintermediate compared to the cases (a) and (b).References[1] Statistical Physics II, R. Kubo, M.Toda andN.Hashitsume (Springer Ser. on Solid-State Sci.,vol.31 Berlin, Heidelberg, 1992).[2] L.F.Cugliandolo, J.Kurchan, L.Peliti, Phys.Rev.E.55, 3898 (1997).[3] M. Lucchesi, A. Dominjon, S. Capaccioli, D.Prevosto, P.A. Rolla accepted on Journal of Non-Crystallyne Solids.Fig. 2. Effective temperature T eff calculated at threedifferent frequencies. Lines are guide for the eyes.Inset shows an enlarged view for the range aboveTg, straight line represents T eff=T.AuthorsS. Capaccioli (a), M. Lucchesi (b,c), A. Dominjon (b),D. Prevosto (b,c), P. Rolla (b,c)(a) CNR-INFM, CRS-Soft and Dip. Fisica “E. Fermi”Univ. Pisa. (b) Dip. Fisica “E. Fermi” Univ. Pisa and(c) CNR-INFM Polylab Largo B. Pontecorvo 3, Pisa.61SOFT Scientific Report 2004-06