Liquid-vapour coexistence curve

Figure A2.5.29. Peak positions of the liquid-vapour heat capacity as a fiinction of methane coverages on graphite. These points trace out the liquid-vapour coexistence curve. The frill curve is drawn for p = 0.127. Reproduced from [31] Kim H K and Chan M H W Phys. Rev. Lett. 53 171 (1984) figure 2. Copyright (1984) by the American Physical Society.

Recently, Orkoulas and Panagiotopoulos [161] have shown that it is possible to use histogram reweighting and multicanonical simulations, starting with individual simulations near the critical point, to map out the liquid-vapour coexistence curve in a very efficient way. 

For a multicomponent system, it is possible to simulate at constant pressure rather than constant volume, as separation into phases of different compositions is still allowed. The method allows one to study straightforwardly phase equilibria in confined systems such as pores [166]. Configuration-biased MC methods can be used in combination with the Gibbs ensemble. An impressive demonstration of this has been the detennination by Siepmaim et al [167] and Smit et al [168] of liquid-vapour coexistence curves for n-alkane chain molecules as long as 48 atoms. 

FIGURE 5.1. Liquid/vapour coexistence curves of SPC water (solid line) and OPLS methanol (dashed line) following hrom the RISM-KH theory. Molecular simulation results for water [45] and methanol [46] (open circles and squares, respectively) and critical point extrapolations (filled symbols). 

FIGURE 5.8. Liquid/vapour coexistence curve of the Lennard-Jones fluid predicted by the lOZ/LMBW theory in the KHM, KH and VM approximation (solid, short-dash and long-dash lines, respectively). Monte Carlo (MC) simulations are shown by the open circles. 

FIGURE 5.2. Liquid/vapour coexistence curves of hydrogen fluoride (solid line), methanol (short-dashed line), water (long-dashed line) and dimethylsulfoxide (dash-dotted line) following from theRISM-KH theory. Experimental data for their critical points (filled triangle, square, circle and rhomb, respectively), and at ambient conditions (corresponding open symbols). 

Figure 4 Distribution of the tetrahedricity measure 6 in liquid water along the liquid-vapour coexistence curve (from 100 to 450 K). Thick lines indicate two coexisting liquid phases. Left panel - total distributions right panel -distributions for four-coordinated molecules.

The obtained distributions of the tetrahedricity measure were used for estimation of the concentration C of the four-coordinated tetrahedrally ordered water molecules. Temperature dependence of this concentration along the liquid-vapour coexistence curve is shown in the upper panel of Fig.5. There is only slight increase of C upon cooling from the liquid-vapour critical temperature to about 350 K (due to the temperature mismatch of ST2 water and real water, about 30 to 35° lower temperature should be expected for real water). The drastic increase of C is evident at lower temperatures, when approaching the liquid-liquid phase transition. At 7 = 270 K, concentrations of the tetrahedrally ordered four-coordinated water molecules in two coexisting phases was found to be about 28% and 46.5%. Such step increase of C is related to a step decrease of density from 0.97 to 0.91 g/cm ... 

Figure 5 Temperature dependence of the concentration C of the tetrahedrally ordered four-coordinated water molecules (upper panel) and of the liquid water density (lower panel) along the liquid-vapour coexistence curve. Vertical dashed line indicates the temperature of the liquid-liquid transition. Dotted lines indicate the densities and concentrations of the coexisting phases. Stars indicate percolation transition of the tetrahedrally ordered four-coordinated molecules.

As we have mentioned in the Introduction, the location of the critical point of the lowest density liquid-liquid transition of real water is unknown and both scenarios (critical point at positive or at negative pressure) can qualitatively explain water anomalies. Recent simulation studies of confined water show the way, how to locate the liquid-liquid critical point of water. Confinement in hydrophobic pores shifts the temperature of the liquid-liquid transition to lower temperatures (at the same pressure), whereas effect of confinement in hydrophilic pores is opposite. If the liquid-liquid critical point in real water is located at positive pressure, in hydrophobic pores it may be shifted to negative pressures. Alternatively, if the liquid-liquid critical point in real water is located at negative pressure, it may be shifted to positive pressures by confinement in hydrophilic pores. Interestingly, that it may be possible in both cases to place the liquid-liquid critical point at the liquid-vapour coexistence curve by tuning the pore hydrophilicity. We expect, that the experiments with confined supercooled water should finally answer the questions, concerning existence of the liquid-liquid phase transition in supercoleed water and its location. 

Gruff ES, Koch SA (1989) A trigonal planar [Zn(SR)3] " complex - A possible new coordination mode for zinc cysteine centers. J Am Chem Soc 111 8762-8763 Guissani Y, Guillot B (1993) A computer simulation study of the liquid-vapour coexistence curve of water. J Chem Phys 98 8221-8235... 

Figure 15.11 Temperature-dependence of the Debye factor /d (eqn (15.7)) for the charged reactants in water along the liquid-vapour coexistence curve. An encounter distance of 0.5 nm has been assumed.

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