Fluctuation-Dissipation Theorem in Liquid and Glassy Glycerol: Frequency-Dependent Dielectric Permittivity and Dielectric Polarization Fluctuation Measurements

We show frequency-dependent dielectric permittivity and dielectric polarization fluctuation measurements of liquid and glassy glycerol. This allows a direct comparison of both quantities determined independently. After cooling the glycerol sample to 179 K with a cooling rate of $0.85\mathrm{K}/\min$ we studied the aging time dependence of the dielectric permittivity and the polarization fluctuations using the identical glycerol sample. A cross-correlation technique allows measurements of noise levels below the amplifier noise. In the frequency range between 0.3 and 300 Hz we find the measured data to be in agreement with the fluctuation-dissipation theorem for the liquid and glassy state not depending on the aging time.

Figure 1

Essentials of the electrical circuit used: The voltage fluctuations across the sample-filled capacitor are read out by two preamplifiers in parallel [25, 26]. A subsequent cross-correlation analysis and Fourier transform give us voltage power spectral density spectra. Hereby the cross-correlation technique suppresses the amplifier noise and allows measurements of noise 1 order of magnitude lower than the intrinsic amplifier noise.

Figure 2

Imaginary part ${ϵ}^{\prime \prime }$ (open black circles, right $y$ axis) of the dielectric permittivity measured using a dielectric responses analyzer and voltage power spectral density in comparison: The gray (red) filled circles are directly measured voltage noise, and the black filled circles are based on the dielectric permittivity measurement. The sample temperature was $205.0\pm 0.6\mathrm{K}$.

Figure 3

The imaginary part ${ϵ}^{\prime \prime }$ of the dielectric function is shown as a function of frequency at $179.0\pm 0.6\mathrm{K}$ after 10 min (black filled circles), 1 h [light gray (red) filled circles], and 8 h [dark gray (blue) filled circles] waiting time. During aging ${ϵ}^{\prime \prime }$ decreases.

Figure 4

The voltage power spectral density $S_V$ at $179.0\pm 0.6\mathrm{K}$ is shown after 10 min (black filled circles), 1 h [light gray (red) filled circles], and 8 h [dark gray (blue) filled circles] waiting time as a function of frequency. Upon waiting the sample ages. The voltage power spectral density decreases. The relative temperature accuracy was better than 0.1 K.

Figure 5

The product of voltage power spectral density $S_V$ and frequency $\nu$ at $179.0\pm 0.6\mathrm{K}$ is shown after 10 min (black filled circles), 1 h [light gray (red) filled circles], and 8 h [dark gray (blue) filled circles] waiting time. The multiplication of $S_V$ by frequency makes the aging fingerprint better visible. Upon waiting the sample ages. The relative temperature accuracy was better than 0.05 K. In addition we show the predicted aging behavior of $\nu S_V$ on the basis of the corresponding dielectric permittivity measurements carried out under identical conditions (smooth lines). In this data set no fitting procedures are involved and no adjustments made.