Fluctuation-dissipation
relation in a colloidal glass: frequency and aging time dependence
2, place Jussieu, CC 7056, 75251 Paris Cedex
05
Glassy systems are characterized by slow relaxation processes; they therefore remain far from equilibrium on long time scales. Recently, there have been serious attempts to approach and understand aging phenomena on a theoretical level. Many efforts have been devoted to apply statistical physics description - in particular fluctuation-dissipation relations (FDR) to such out-of-equilibrium systems. At thermodynamic equilibrium, FDR relate the response function of the system to its autocorrelation function, involving a single thermodynamic parameter, the equilibrium temperature. However, FDR apply only to ergodic systems at equilibrium, and is not expected to hold in out-of-equilibrium systems. The idea that a timescale dependent nonequilibrium temperature or effective temperature could describe the slow relaxation modes has received a lot of attention.
We present an experimental investigation of the Generalized Einstein Relation (GER), a particular form of a fluctuation-dissipation relation, in an out-of-equilibrium complex fluid. Micrometer beads used as thermometers are immersed in an aging colloidal glass to provide both fluctuation and dissipation measurements. At a given aging time of the system, we measure the fluctuating motion of a micrometric tracer bead immersed in the glass, leading to the direct measurement of the mean square displacement of the bead. At the same aging time, we apply an oscillatory or step force on the tracer bead with an optical tweezer, and measure its mobility. From these measurements, the fluctuation-dissipation ratio also expressed in terms of an effective temperature is derived as a function of frequency and aging time. The deviations from the GER, observed during the glass formation process, suggest that the effective temperature can be directly related to the relaxation times of the glass.
B. Abou & F. Gallet, Phys. Rev. Lett. 93 160603 (2004)
N. Pottier, Physica A 317,
371 (2003)