Origin of glassy dynamics in a liquid crystal studied by broadband dielectric and specific heat spectroscopy

A combination of broadband dielectric $({10}^{-2}\mathrm{Hz}–{10}^9\mathrm{Hz})$ and specific heat $({10}^{-3}\mathrm{Hz}–2\times {10}^3\mathrm{Hz})$ spectroscopy is employed to study the molecular dynamics of the glass-forming nematic liquid crystal $E7$ in a wide temperature range. In the region of the nematic phase the dielectric spectra show two relaxation processes which are expected theoretically: The $\delta$ relaxation which corresponds to rotational fluctuations of the molecules around its short axis and the tumbling mode at higher frequencies than the former one. For both processes the temperature dependence of the relaxation rates follows the Vogel-Fulcher-Tammann formula which is characteristic for glassy dynamics. By applying a detailed data analysis, it is shown that close to the glass transition the tumbling mode has a much steeper temperature dependence than the $\delta$ process. The former has a Vogel temperature which is by $30\mathrm{K}$ higher than that of the $\delta$ relaxation. Specific heat spectroscopy gives one relaxation process in its temperature and frequency dependence which has to be assigned to the $\alpha$ relaxation (dynamic glass transition). The unique and detailed comparison of the temperature dependence of the dielectric and the thermal relaxation rates delivers unambiguously that the dielectric tumbling mode has to be related to the dynamic glass transition.

Figure 1

Dielectric loss vs frequency and temperature for an unaligned sample of $E7$ in the high frequency range.

Figure 2

Dielectric loss vs frequency for $E7$ at different temperatures and mesophases. Nematic state: $◻$, $T=214.2\mathrm{K}$; $엯$, $T=220.1\mathrm{K}$; $◇$, $T=252.2\mathrm{K}$; $▵$, $T=274.2\mathrm{K}$. Isotropic state: $☆$, $T=363.7\mathrm{K}$. Lines are guides to the eyes. Because the dielectric properties in the low and in the high frequency range are measured using different samples their order parameter can be also slightly different. The inset gives an example for the decomposition of the relaxation spectra at $T=320.1\mathrm{K}$ in to the $\delta$ and the tumbling mode by fitting three HN functions and one conductivity contribution to the data: Solid line, whole fit function; dashed line, contribution $\delta$ relaxation; dashed-dotted line, contribution tumbling relaxation; dotted line, contribution third relaxation process.

Figure 3

Relaxation rates $f_p$ versus inverse temperature obtained by dielectric spectroscopy for the different processes ($◻$, $\delta$ relaxation; $엯$, tumbling mode; $▵$, isotropic state) and specific heat spectroscopy $(☆)$. The inset compares the temperature dependence of the relaxation rates of the $\delta$ process reported here $(◻)$ with data taken from [39] $(∎)$. Note also that the relaxation rates measured for the both samples with the different orientation collapses into one chart with regard to its absolute values and its temperature dependence for both the $\delta$ and the tumbling mode.

Figure 4

$(d{\log }_{10}{f}_p∕dT{)}^{-1∕2}$ vs temperature for dielectric spectroscopy for the different processes ($◻$, $\delta$ relaxation; $엯$, tumbling mode) and specific heat spectroscopy $(\star )$. The lines are linear regressions to the dielectric data for the different processes. The inset shows $(d{\log }_{10}{f}_p∕dT{)}^{-1∕2}$ versus temperature for the dielectric data in the isotropic range for temperatures above the phase transition. The line is a linear regression to the data.

Figure 5

Real part of the complex heat capacity $C^{\prime }$ $(◻)$ and phase angle ${\delta }_{\mathrm{corr}}$ $(엯)$ versus temperature of an ac calorimetry measurement at $640\mathrm{Hz}$. The phase angle is corrected for heat transfer processes. The solid line is a guide for the eyes. The dashed line is a fit of a Gaussian to the data of the phase angle to estimate its maximum position.

Figure 6

Dielectric strength $\mathrm{\Delta }{\epsilon }_{\delta }$ of the $\delta$ relaxation vs reciprocal temperature: $◻$, parallel oriented sample; $엯$, perpendicular oriented sample at low frequencies scaled by a factor of 35; $▵$, perpendicular oriented sample at high frequencies scaled by a factor of 35; $☆$, isotropic state. Lines are guides for the eyes. The inset show the unscaled data: $◻$, parallel oriented sample; $엯$, perpendicular oriented sample at low frequencies; $▵$, perpendicular oriented sample at high frequencies. $\star$, isotropic state. Lines are guides for the eyes.

Figure 7

Dielectric strength $\mathrm{\Delta }{\epsilon }_{\mathrm{tumbling}}$ of the tumbling relaxation vs reciprocal temperature: $◻$, parallel oriented sample; $엯$, perpendicular oriented sample at low frequencies, $▵$, perpendicular oriented sample at high frequencies. $☆$, isotropic state. Lines are guides for the eyes.