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A new analytic equation of state for liquid water
Christopher A. Jeffery and Philip H. Austin
Journal of Chemical Physics , 1999, 110, 484-496.
Abstract
We develop a new analytical equation of state for water
based on the Song, Mason and Ihm equation of state and Poole \textit{et al.}'s
simple model of the free energy of strong tetrahedral hydrogen bonds.
Repulsive and attractive forces are modelled using
a modification of the Weeks-Chandler-Anderson decomposition of the pair potential,
with closed tetrahedral hydrogen bonds
contributing both internal energy and entropy to the free energy of water.
Strong tetrahedral hydrogen bonds are modelled explicitly using a
simplified partition function. The resulting equation of state is 20
to 30 times more accurate than equivalent simple cubic equations of
state over a wide range of pressures $(0.1 \rightarrow 3000 \un{\
bar})$ and temperatures $(-34 \rightarrow 1200\ \degc)$ including the
supercooled region. The new equation of state predicts a second
liquid-liquid critical point at $p_{C^{\prime}}=0.954$ kbar,
$\rho_{C^\prime}=1.045\ \un{g\ cm^{-3}}$ and $T_{C^{\prime}}=228.3$ K.
The temperature of this second critical point is above the homogeneous
freezing temperature at 1 kbar, thus this region of the phase diagram
may be experimentally accessible.
The phase diagram also suggests that the homogeneous nucleation temperature
above $1.2 \un{\ kbar}$ may be determined by a phase transition from
high density water to low density water.
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