Existence of a liquid-liquid phase transition in methanol

A simple model is constructed to study the phase diagram and thermodynamic properties of methanol, which is described as a dimer of an apolar sphere mimicking the methyl group and a sphere with core-softened potential as the hydroxyl group. Performing classical Monte Carlo simulations, we obtained the phase diagram, showing a second critical point between two different liquid phases. Evaluating systems with a different number of particles, we extrapolate to infinite size in accordance with Ising universality class to obtain bulk values for critical temperature, pressure, and density. Strong evidence that the structure of the liquid changes upon transition from high- to low-density phase was provided. From the experimentally determined hydrogen bond strength and length in methanol and water, we propose where the second critical point of methanol should be.

Figure 1

Methanol is modeled with two pseudoatoms (OH and ${\mathrm{CH}}_3$) in a fixed position. Interaction between type 1 particles is described by the CSW potential, while other interactions behave like a 24-6 Lennard-Jones potential.

Figure 2

Isotherms ($p^{*}$ vs ${\rho }^{*}$) for the model of methanol studied. Symbols (triangles $T^{*}=1.30$, squares $T^{*}=1.09$, stars $T^{*}=0.9$, crosses $T^{*}=0.7$, circles $T^{*}=0.54$, and diamonds $T^{*}=0.52$) are results of MC simulations; numerical error is smaller than the symbol size. Black full circles represent gas-liquid and liquid-liquid critical point. Connecting lines are a guide for the eye.

Figure 3

Size dependence of the critical temperature and density for the modeled systems. (a) Critical density for gas-liquid transition. (b) Critical temperature for gas-liquid transition. (c) Critical density for liquid-liquid transition. (d) Critical temperature for liquid-liquid transition. Dashed lines represent best linear fits.

Figure 4

Site-site radial distribution functions between (a), (b) type 1 [(b) shows derivative], (c) type 1 and 2, and (d) type 2 particles show the difference in ordering of low-density and high-density liquid phases. In high-density phase (blue, solid line) ordering is higher than in low-density phase (purple, dotted line). Green (dot-dashed) line depicts ordering in the liquid-liquid critical point.

Figure 5

Average displacement per particle as a function of simulation cycles (left). Densities shown (from top to bottom line): ${\rho }^{*}=0.22$, 0.23, 0.24, 0.25, 0.26, 0.27, and 0.28. (Right) Diffusion coefficient shown as a function of density of methanol.

Figure 6

Free energy as a function of density, ${\rho }^{*}$, and bond-orientational order parameter, $Q_6$, in the vicinity of the liquid-liquid critical point. At $p^{*}=0.200$ and $T^{*}=0.52$, two basins of minimum free energy are visible.