Idealized Glass Transitions under Pressure: Dynamics versus Thermodynamics

The interplay of slow dynamics and thermodynamic features of dense liquids is studied by examining how the glass transition changes depending on the presence or absence of Lennard-Jones-like attractions. Quite different thermodynamic behavior leaves the dynamics unchanged, with important consequences for high-pressure experiments on glassy liquids. Numerical results are obtained within mode-coupling theory (MCT), but the qualitative features are argued to hold more generally. A simple square-well model can be used to explain generic features found in experiment.

Figure 1

Glass-transition lines for the Lennard-Jones system with and without attractions: MCT results for both coincide (solid line). Triangles are glass-transition points from simulations [40, 41]. Dash-dotted line: soft-sphere asymptote, $T_c^{*}(\varrho )\approx (\pi /6{\phi }_{\mathrm{eff}}^c{)}^4{\varrho }^4$, ${\phi }_{\mathrm{eff}}^c=0.564$. The dotted line indicates a gas-liquid spinodal. Inset: LJ (solid line), LJR (dashed), and square-well ($\delta =0.12$; dash-dotted) potentials.

Figure 2

Lennard-Jones glass transitions with (thick line) and without (dashed) attractions in a pressure-vs-temperature representation, from MCT. Triangles: simulation data from Refs. 40, 45 (filled: LJ; open: purely repulsive; inverted: truncated LJ). Dash-dotted line: LJ transition as $P_{\mathrm{eff}}^{*}=P^{*}{T}^{-1/4}$. Thin solid line: square-well model transition ($\delta =0.12$, shifted as $T^{*}\mapsto 1.5T^{*}$); dotted: square-well model spinodal with critical point (cross). Diamonds: experimental data for glycerol (Refs. 28, 49), see text. Arrows indicate isobars and isotherms used in Fig. 3.

Figure 3

Typical relaxation times $\tau$ as functions of density: MCT results for the SW system ($\delta =0.12$; bottom and left axes), along the isobar $P^{*}=0.316$ (solid line) and the isotherm $T^{*}=0.3$ (dashed), marked by thick arrows in Fig. 2. Symbols (upper/right axes) are viscosity data for isopropylbenzene [17] for the isobar $P=0.1\mathrm{MPa}$ (filled) and the isotherm $T=293\mathrm{K}$ (open). Inset: MCT results for $P^{*}=8.91$ (solid line) and $T^{*}=0.775$ (dashed line); thin arrows in Fig. 2.