Anomalous Features in the Potential Energy Landscape of a Waterlike Monatomic Model with Liquid and Glass Polymorphism

We study the potential energy landscape (PEL) of a waterlike monatomic liquid that exhibits a liquid-liquid phase transition (LLPT) and glass-glass transformation (GGT). We identify two anomalous features of the PEL that give origin to both phenomena. Specifically, during the pressure-induced LLPT and GGT, (i) the inherent structures (IS) energy becomes a concave function of volume, and (ii) the IS pressure exhibits a van der Waals–like loop. We argue that features (i) and (ii) imply that the GGT is a (nonequilibrium) first-order phase transition, analogous to the LLPT. Interestingly, contrary to the case of the classical ST2 model for water, (a) we do not find two separate PEL megabasins (one for the low-density glass and liquid, and another for the high-density glass and liquid), and (b) features (i)–(ii) persist at temperatures well above the LLPT.

Figure 1

(a) Pressure $P_{\mathrm{IS}}(v)$, (b) energy per particle $E_{\mathrm{IS}}(v)$, and (c) basin shape function ${\mathcal{S}}_{\mathrm{IS}}(v)$ of the IS sampled by the equilibrium liquid at constant temperatures (open symbols). Also included are $P_{\mathrm{IS}}(v)$, $E_{\mathrm{IS}}(v)$, and ${\mathcal{S}}_{\mathrm{IS}}(v)$ during the isothermal compression of ten independent LDA configurations at $T=0.01$ (solid dark green circles) and the corresponding decompression of the resulting HDA from $P=1.5$ (solid blue and red circles; blue circles represent the two trajectories that crystallize rapidly after LDA is formed). In panels (b) and (c), $E_{\mathrm{IS}}(v)$ and ${\mathcal{S}}_{\mathrm{IS}}(v)$ for the LDA-HDA transformations are shifted by $\mathrm{\Delta }{E}_{\mathrm{IS}}=-0.1$ and $\mathrm{\Delta }{\mathcal{S}}_{\mathrm{IS}}(v)=-0.5$. The inset in (a) shows the FJ pair interaction potential $U(r)$ characterized by a hard-core radius $r\approx a$, a core-softened part at $a\le r\le b\approx 2a$, and a weak attractive part; a Lennard-Jones (LJ) pair potential with same minimum depth and location is included for comparison.

Figure 2

(a) Vibrational energy $E_{\mathrm{vib}}(v)$ as function of volume for different isotherms (bottom to top: $T=0.14$, 0.16, 0.18, 0.20, 0.22, 0.26, 0.30, 0.34, 0.38, 0.43, 0.50). $E_{\mathrm{vib}}(v)$ is a weak, nonmonotonic function of $v$ and exhibits a minimum at $v=2.8–3.0$ for all temperatures. (b) Pressure $P(v)$ (solid symbols) and IS pressure $P_{\mathrm{IS}}(v)$ (empty symbols) at $T=0.16$ (up triangles), $T=T_c=0.18$ (diamonds), $T=0.20$ (squares), and $T=0.22$ (circles). (c) Vibrational pressure $P_{\mathrm{vib}}(v)$ compared to $P_{\mathrm{IS}}(v)$ for the same temperatures included in (b). In panels (b) and (c), isotherms of $P(v)$ and $P_{\mathrm{vib}}(v)$ are shifted by $\mathrm{\Delta }P=-0.1$, 0.0, 0.1, 0.2 for $T=0.16$, 0.18, 0.20, 0.22, respectively. The volumes where the liquid is unstable correspond to ${(\partial P/\partial v)}_T>0$. At these volumes (approximately $2.4\le v\le 3.4$), ${(\partial P_{\mathrm{IS}}/\partial v)}_T>0$ but ${(\partial P_{\mathrm{vib}}/\partial v)}_T<0$, and $E_{\mathrm{vib}}(v)$ has a positive curvature.

Figure 3

(a) $P_{\mathrm{IS}}(E_{\mathrm{IS}})$ and (b) ${\mathcal{S}}_{\mathrm{IS}}(E_{\mathrm{IS}})$ during the LDA-to-HDA (solid dark green circles) and HDA-to-LDA transformation (solid red and blue circles; blue circles represent the two trajectories that crystallized) at $T=0.01$. The corresponding $P_{\mathrm{IS}}(E_{\mathrm{IS}})$ and ${\mathcal{S}}_{\mathrm{IS}}(E_{\mathrm{IS}})$ for the equilibrium liquid is also included (open symbols). During the LDA-HDA transformations, the system samples IS never explored by the equilibrium liquid. Data are taken from Fig. 1.