Slow dynamics of salol: A pressure- and temperature-dependent light scattering study

We study the slow dynamics of salol by varying both temperature and pressure using photon correlation spectroscopy and pressure-volume-temperature measurements, and compare the behavior of the structural relaxation time with equations derived within the Adam-Gibbs entropy theory and the Cohen-Grest free volume theory. We find that pressure-dependent data are crucial to assess the validity of these model equations. Our analysis supports the entropy-based equation, and estimates the configurational entropy of salol at ambient pressure $\sim 70\%$ of the excess entropy. Finally, we investigate the evolution of the shape of the structural relaxation process, and find that a time-temperature-pressure superposition principle holds over the range investigated.

Figure 1

Temperature dependence of the volume of salol in the crystal and liquid state at different pressures. The pressures are, from top to bottom, from 0.1 to $200\mathrm{MPa}$ in steps of $10\mathrm{MPa}$. In the inset the melting temperature versus pressure deduced from the $PVT$ measurements here reported.

Figure 2

Temperature dependence of the volume of salol in the liquid state. The solid lines through symbols are the best fit with the Tait equation of state, Eq. (6), with $V^{\mathit{liquid}}(T,0)=V_0\exp \left(\alpha T\right)$ and $B\left(T\right)=b_1\exp (-b_{2}T)$.

Figure 3

Temperature dependence of the excess entropy over crystal, $S_{exc}=S^{melt}-S^{\mathit{crystal}}$, calculated from the calorimetric data. The solid line represents the fit of the experimental data according to $S_{\infty }-k∕T$.

Figure 4

Normalized photon correlation functions collected at a constant temperature of $267.1\mathrm{K}$. Pressures from left to right are 88, 95, 102.5, 110.5, 119, 125, 132.5, 141, 148.5, 156.5, 163.5, 171, 181, and $189.5\mathrm{MPa}$. The solid lines represent the fits to the data using the KWW function. The isothermal spectra at $267.1\mathrm{K}$ taken at different pressures rescale on a master curve as shown in the inset.

Figure 5

Temperature and pressure-dependent structural relaxation times of salol from photon-correlation measurements. The solid lines represent the simultaneous fit with the $\mathrm{PEAG}$ equation [Eq. (8)] of all the experimental data, including the ones from Ref. 49 shown in Fig. 6. As explained in the text, four parameters are adjusted by the fitting procedure, in particular giving.${\left(\partial V∕\partial T\right)}_0^{\mathit{nonstruct}}=(3.8\pm 0.7)\times {10}^{-8}{\mathrm{m}}^3{\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}$ and $\Phi =0.68\pm 0.08$.

Figure 6

Structural relaxation time of salol from depolarized light-scattering measurements at atmospheric pressure: $(◻)$ depolarized photon-correlation data from Ref. 49; $(•)$ depolarized Brillouin and Raman light-scattering data from Ref. 11. The solid line is the fit with the $\mathrm{PEAG}$ equation [Eq. (8)] through the square symbols, i.e., in the region where some cooperativity is expected. The dash line is the fit of all the data with the temperature-dependent $\mathrm{CG}$ equation [Eq. (10)]. The dotted line is the fit with the pressure-extended $\mathrm{CG}$ equation [Eq. (11)]; see also the solid lines in Fig. 7.

Figure 7

Temperature- and pressure-dependent structural relaxation times of salol from depolarized light-scattering measurements. The solid lines represent the simultaneous fit with the pressure-extended $\mathrm{CG}$ equation [Eq. (11)] of all the experimental data, including the ones at atmospheric pressure from Refs. 49 and [11] shown in Fig. 6; see text for details.