Structural changes in the Lennard-Jones supercooled liquid and ideal glass: an improved integral equation for the replica method

TL;DR

The paper addresses whether an equilibrium ideal glass can exist in a simple liquid and how its structure differs from the deeply supercooled liquid. It employs a replicated HMSA integral-equation approach with an Optimized Division Scheme to study the Lennard-Jones fluid at very low $T^\ast$, accessing both the supercooled liquid and ideal-glass regimes. The authors identify a dynamical transition at $T_D^\ast$ and a lower critical temperature $T_{\rm cr}^\ast$ where the ideal glass becomes thermodynamically stable, along with a density-dependent onset $T_0^\ast$ where the radial distribution develops a mid-peak indicative of quasi-fcc short-range order; they show a close structural similarity between liquid and glass in pair correlations at comparable conditions. The results demonstrate that structural changes accompany thermodynamic transitions and provide a thermodynamically grounded framework for exploring glass formation in LJ and other model systems.

Abstract

Framing the glass formation within standard statistical mechanics is an outstanding problem of condensed matter theory. To provide new insight, we investigate the structural properties of the Lennard-Jones fluid in the very-low temperature regime, by using a replicated version of the refined HMSA theory of the liquid state, combined with an appropriate split of the pair potential [Bomont and Bretonnet, J. Chem. Phys. 114, 4141 (2001)]. Our scheme allows one to reach an unprecedented low-temperature domain within both the supercooled liquid and the ideal-glass phase. Therein, a density-dependent temperature is identified, whereupon the radial distribution function experiences clear-cut structural changes, insofar as an additional peak develops in between the main and the second peaks. Such a structural feature points to a local structure of the Lennard-Jones ideal glass with an fcc-like short-range order, in the absence of any long-range order.

Figures (8)

• Figure 1: LJ potential in units of $\varepsilon$ (black), as split according to either the WCA (blue) or ODS (red) schemes. Inset: $u_{12}(r)$ in the same units, as drawn with $c=0.6\sigma$ and $\varepsilon_{12}=\varepsilon$.
• Figure 2: A: dependence of the order parameter $Q$ on the inter-replicas coupling $\varepsilon_{12}$, along several isotherms (in the legend) for $\rho^\ast=1$. A discontinuous jump of $Q$ is observed at $T^\ast=0.88$, indicating the occurrence of the expected "precursor transition". In this representation, the behavior is reminiscent of isotherms in a liquid-vapor system. B: behavior of the order parameter $g_{\mathrm{12}}(r=0)$ for $\rho^\ast=0.9$ upon cooling, under condition $\varepsilon_{12}=\varepsilon$ (dashed line) and after extinction of $\varepsilon_{12}$ at $T^\ast=0.2$ (full line). The inset shows the overlap $Q$ for $T^\ast<0.2$.
• Figure 3: Predicted values of $T^\ast_{\rm D}$ (crosses) $T^\ast_{\rm cr}$ (pluses) and $T^\ast_{\mathrm{0}}$ (stars), together with the liquid branch of liquid-vapor coexistence (circles), and liquid-solid coexistence (squares) LJwiki. The horizontal line indicates the triple-point isotherm. In between crosses and pluses, the supercooled liquid is stable; below $T^\ast_{\rm cr}$, a weak first-order phase transition makes the ideal glass stable. Note the logarithmic vertical scale to enhance the visibility of the low-temperature portion.
• Figure 4: Excess free energies $f_{\rm ex}^{\ast\rm L}$ (blue lines) and $f_{\rm ex}^{\ast\rm G}$ (red lines) as functions of $T^\ast$ along the isochores $\rho^\ast=0.85$ and 0.90. Along each isochore, $f_{\rm ex}^{\ast\rm L}$ and $f_{\rm ex}^{\ast\rm G}$ cross at the temperature $T_{\mathrm{cr}}^\ast(\rho^\ast)$.
• Figure 5: Comparison between $g(r)$ in the liquid (blue) and $g_{11}(r)$ in the ideal glass (red) phases for $\rho^\ast=0.9$ at $T^\ast=0.2$ (full lines) and $T^\ast=0.1$ (dashed lines, shifted by one along the vertical axis, for clarity)