Ions in glass-forming glycerol: Close correlation of primary and fast $\beta$ relaxation

We provide broadband dielectric loss spectra of glass-forming glycerol with varying additions of LiCl. The measurements covering frequencies up to 10 THz extend well into the region of the fast β process, commonly ascribed to caged molecular dynamics. Aside from the known variation of the structural α relaxation time and a modification of the excess wing with ion content, we also find a clear influence on the shallow loss minimum arising from the fast β relaxation. Within the framework of mode-coupling theory, the detected significant broadening of this minimum is in reasonable accord with the found variation of the α-relaxation dynamics. A correlation between α-relaxation rate and minimum position holds for all ion concentrations and temperatures, even below the critical temperature defined by mode-coupling theory.

Figure 1

Comparison of broadband dielectric loss spectra of glycerol-salt mixtures with various LiCl concentrations, shown for three typical temperatures. For better readability, in the boson-peak region (ν > 1 THz) the results are shown for 252 K, only. The lines are guides to the eyes. The data for pure glycerol were previously published in [2, 3, 7, 12] and were taken at 213, 252, and 295 K.

Figure 2

Dielectric loss spectra including the α-peak and excess-wing region for different concentrations. Temperatures have been chosen that lead to identical α-peak positions at 50 Hz (a) and 16 kHz (b). The loss has been scaled to the peak values ${\varepsilon }_{\max }^{\prime \prime }$. The lines are guides to the eyes.

Figure 3

Dielectric loss spectra in the minimum region of pure glycerol and of glycerol with 20$\%$ LiCl, shown for various temperatures. Same temperatures are denoted by identical symbols. The lines are guides to the eyes.

Figure 4

Dielectric loss spectra of glycerol-salt mixtures with various LiCl concentrations at frequencies beyond 10 MHz (data for pure glycerol taken from [2, 3]). Curves for six different temperatures are shown as indicated in the figure legend. The solid lines are fits with MCT, Eqs. (1) and (2). In (b), a curve calculated by the sum of two power laws is shown (dash-dotted line) assuming a linear increase of ${\varepsilon }^{\prime \prime }$(ν) at the low-frequency flank of the boson peak. It demonstrates the presence of additional intensity in the minimum region. The dashed lines correspond to power laws with exponents between 1.5 and 1.8, indicating the steep increase at the left flank of the boson peak. The inset shows the dependence of the MCT system parameter on ion concentration. The line in the inset indicates a linear fit.

Figure 5

Critical temperature dependence of the amplitude (first row) and position (second row) of the ${\varepsilon }^{\prime \prime }$(ν) minimum and of the α-relaxation rate (third row). Data for pure glycerol (first column; [7]) and for glycerol with three concentrations of LiCl are shown. Representations have been chosen that should result in a linear behavior according to the predictions of idealized MCT [17]. The solid lines correspond to the critical laws of MCT and should extrapolate to the critical temperature (indicated by the dashed lines) for ordinate values of zero.

Figure 6

Minimum frequency (read off from the experimental spectra) vs α-peak frequencies, estimated by ${\nu }_p\approx {\nu }_{\alpha }=1/\left(2\pi \langle {\tau }_{\mathrm{CD}}\rangle \right)$ with $\langle {\tau }_{\mathrm{CD}}\rangle ={\tau }_{\mathrm{CD}}{\beta }_{\mathrm{CD}}$, where ${\tau }_{\mathrm{CD}}$ and ${\beta }_{\mathrm{CD}}$ were obtained from fits with the Cole-Davidson function [5]. Results are shown for all concentrations and temperatures investigated. The dashed line corresponds to a power law with an exponent 0.28. The dotted line shows a power law with exponent 0.65 as expected from MCT (see text).