Effective temperatures from the fluctuation-dissipation measurements in soft glassy materials

We have investigated the validity of the fluctuation-dissipation theorem (FDT) and the applicability of the concept of effective temperature in a number of non-equilibrium soft glassy materials. Using a combination of passive and active microrheology to measure displacement fluctuations and the mechanical response function of probe particles embedded in the materials, we have directly tested the validity of the FDT. Our results show no violation of the FDT over several decades in frequency (1–10 Hz) for hard-sphere colloidal glasses and colloidal glasses and gels of Laponite. We further extended the bandwidth of our measurements to lower frequencies (down to 0.1Hz) using video microscopy to measure the displacement fluctuations, again without finding any deviations from the FDT. Copyright c © EPLA, 2008 Introduction. – While the foundations of equilibrium statistical mechanics are well established, non-equilibrium statistical physics is still being developed. One attempt in the direction of developing a statistical mechanical description of non-equilibrium, but slowly evolving systems is to extend the fluctuation dissipation theorem (FDT) to non-equilibrium situations [1]. The FDT relates the relaxation of spontaneous fluctuations to the response of an equilibrium system to a weak external perturbation. Specifically, the FDT states that the response function is proportional to the power spectral density of the thermal fluctuations, with a prefactor given by the temperature. To describe non-equilibrium systems, the idea is to (a)E-mail: [email protected] (b)Both authors have equally contributed to this work. relate the (non-equilibrium) fluctuations to the response function via a (possibly timeor frequency-dependent) effective temperature Teff [1]. Violations of the equilibrium FDT have recently been studied extensively in theory and simulations for various model systems such as structural glasses [2,3], spin glasses [1,4–6] and driven systems such as a fluid under shear [7] and aging critical systems [8]. The experimental situation, however, is less conclusive. Experiments have been reported on structural glasses [9], spin glasses [10], granular matter [11], hardsphere colloidal glasses [12,13] and the colloidal glass of Laponite [14–16], with sometimes contradictory results. For the “soft” systems considered here, the experimental situation is particularly confusing. For hard-sphere colloidal fluids there have been two reports on violation of FDT with very different results. Bonn et al. determined