Glass Transition Temperature and Density Scaling in Cumene at Very High Pressure

We present a new method that allows direct measurements of the glass transition temperature $T_g$ at pressures up to 4.55 GPa in the glass-forming liquid cumene (isopropylbenzene). This new method uses a diamond anvil cell and can measure $T_g$ at pressures of 10 GPa or greater. Measuring $T_g$ at the $\mathrm{glass}\to \mathrm{liquid}$ transition involves monitoring the disappearance of pressure gradients initially present in the glass, but also takes advantage of the large increase in the volume expansion coefficient ${\alpha }_p$ at $T_g$ as the supercooled or superpressed liquid is entered. Accurate $T_g(P)$ values in cumene allow us to show that density scaling holds along this isochronous line up to pressures much higher than any previous study, corresponding to a density increase of 29%. Our results for cumene over this huge compression range yield ${\rho }^{\gamma }/T=C$, where C is a constant and where $\gamma =4.77\pm 0.02$ for this nonassociated glass-forming system. Finally, high-pressure cumene viscosity data from the literature taken at much lower pressures and at several different temperatures, corresponding to a large dynamic range of nearly 13 orders of magnitude, are shown to superimpose on a plot of $\eta$ vs ${\rho }^{\gamma }/T$ for the same value of $\gamma$.

Figure 1

Schematic $\mathrm{glass}\to \mathrm{liquid}$ transition sequence showing possible initial pressure gradient lines in the DAC sample at low $T$ evolving upon heating until hydrostatic conditions are reached above $T_g$. Octagonal boundary represents diamond culets (tips of the diamonds), and the smaller circular region represents the sample contained within the steel gasket hole. Three shapes represent rubies at different locations.

Figure 2

Four representative $\mathrm{glass}\to \mathrm{liquid}$ transition heating runs. Pressure measurements were obtained from the three rubies arbitrarily designated 1, 2, and 3, as indicated in the legend in the lower right. Runs (a) and (b) were taken with one DAC loading, while (c) and (d) were obtained with a second DAC loading.

Figure 3

$T_g$ data obtained from 26 heating runs (circle). Atmospheric pressure value $T_g(1\mathrm{atm})=127\pm 2\mathrm{K}$ (upward filled triangle) is an average of measurements from several sources [39, 40, 41]. Atmospheric pressure melting temperature (filled square) is from Ref. [40]. Value of $P_g(348\mathrm{K})$ (filled diamond) was obtained from Ref. [43]. Value of $P_g(293\mathrm{K})$ (downward filled triangle) was obtained from Ref. [42]. Solid line shows fit to Eq. (3).

Figure 4

Plot of $T_g$ vs ${\rho }_g$ with fits to three models discussed in the text. Inset: Plot of ${\log }_{10}{T}_g$ vs ${\log }_{10}{\rho }_g$ with linear fit.

Figure 5

Plot of ${\log }_{10}\eta$ vs ${\rho }^{4.77}/T$ with atmospheric pressure viscosity data from Ref. [35] (filled circle) and Ref. [36] (filled downward triangle). High pressure isothermal data were obtained from Ref. [11] for 293 K (triangle), and from Ref. [47] for 253 K (diamond), 228 K (square), and 203 K (circle). Solid line is fit to Eq. (10) from Ref. [17].