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$^4$ 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 0.1 Hz) using video microscopy to measure the displacement fluctuations, again without finding any deviations from the FDT.
We have directly observed short-time stress propagation in viscoelastic fluids using two optically trapped particles and a fast interferometric particle-tracking technique. We have done this both by recording correlations in the thermal motion of the
particles and by measuring the response of one particle to the actively oscillated second particle. Both methods detect the vortex-like flow patterns associated with stress propagation in fluids. This inertial vortex flow propagates diffusively for simple liquids, while for viscoelastic solutions the pattern spreads super-diffusively, dependent on the shear modulus of the medium.
We report measurements of the frequency-dependent shear moduli of aging colloidal systems that evolve from a purely low-viscosity liquid to a predominantly elastic glass or gel. Using microrheology, we measure the local complex shear modulus $G^{*}(o
mega)$ over a very wide range of frequencies (1 Hz- 100 kHz). The combined use of one- and two-particle microrheology allows us to differentiate between colloidal glasses and gels - the glass is homogenous, whereas the colloidal gel shows a considerable degree of heterogeneity on length scales larger than 0.5 micrometer. Despite this characteristic difference, both systems exhibit similar rheological behavior which evolve in time with aging, showing a crossover from a single power-law frequency dependence of the viscoelastic modulus to a sum of two power laws. The crossover occurs at a time $t_{0}$, which defines a mechanical transition point. We found that the data acquired during the aging of different samples can be collapsed onto a single master curve by scaling the aging time with $t_{0}$. This raises questions about the prior interpretation of two power laws in terms of a superposition of an elastic network embedded in a viscoelastic background. Keywords: Aging, colloidal glass, passive microrheology
