Probing the Fluctuation-Dissipation Theorem in a Perrin-like Experiment

In this Letter, we present a new experimental approach to investigate the effective temperature concept as a generalization of the fluctuation-dissipation theorem (FDT) for nonequilibrium systems. Simultaneous measurements of diffusion coefficient and sedimentation velocity of heavy colloids, embedded in a Laponite clay suspension, are performed with a fluorescence-recovery-based setup. This nonperturbative dual measurement, performed at a single time in a single sample, allows for a direct application of the FDT to the tracer velocity observable. It thus provides a well-defined derivation of the effective temperature in this ageing colloidal gel. For a wide range of concentrations and ageing times, we report no violation of the FDT, with effective temperature agreeing with bath temperature. This result is consistent with recent theoretical predictions on the coupling between the velocity observable and nonequilibrium gels dynamics.

Figure 1

Vertical intensity profiles emitted by fluorescent colloids in water, at time $t=8\mathrm{s}$ (black curve) and $t=239\mathrm{s}$ (blue curve) after a horizontal layer of $110\mu \mathrm{m}$ thickness has been photobleached. The Gaussian fits of the two intensity profiles are also plotted. Insert: Picture ($0.8\times 0.9\mathrm{mm}$) of the photobleached slab.

Figure 2

Evolution with time, for one experiment, of (a) the squared width and (b) the position of the mean of the Gaussian intensity profile allowing us to assess the diffusion coefficient $D$ and the sedimentation velocity $v_{\mathrm{s}}$ of the tracers.

Figure 3

Histograms of the temperatures measured in water (in light grey) and of those measured in the Laponite suspensions (in dark blue).

Figure 4

Evolution with time of the effective temperatures measured in Laponite suspensions of different concentrations (symbol, concentration in $\mathrm{wt}\%$): (▴, 1.6), (◆, 1.8), (▪, 2), (●, 2.2). Each symbol corresponds to the average of roughly 3 consecutive measurements in the same sample. The error bar corresponds to the standard deviation.