Chemistry Reference
In-Depth Information
with
α
and
β
from our simulations as input, yielded entropy as a function of tem-
perature that was quantitatively the same as that obtained using the one parameter
expression of Howe and Whitworth [146], because our model predicts that
α
and
β
are very close to each other. Howe and Whitworth's expression was used by
Lobban et al. [46] to determine the thermodynamic implications of their diffrac-
tion data. As seen from the inset, the entropy of the low temperature ice IX phase
calculated from our simulations is in very good agreement with the entropy pre-
dicted from Howe and Whitworth's expression. Nagle's expression overestimates
the entropy for partially disordered ice IX in agreement with previous analysis
[146]. Both models, however, when asked to estimate the entropy of partially or-
dered ice III based on occupational probabilities
α
and
β
, significantly overestimate
the configurational entropy. This test of the mean-field theories does not depend
on the quality of our effective Hamiltonian, unless our model is somehow grossly
atypical of the true Hamiltonian for this system (and we would argue, based on
its agreement with experiment, it is at least qualitatively accurate). The mean-field
theories are given the exact occupational probabilities for the model and should
return a value close to the exact simulations, if accurate.
We can also run the comparison in the opposite direction. Using the entropy
calculated from our simulations, we use the Howe and Whitworth's expression to
determine the occupational probability as a function of temperature. The parameter
α
would have to be 25%, significantly lower than the results of our simulations,
α
38%, and experiment [45, 46] to yield the true entropy. The transition entropy
obtained from our calculation is in better agreement with the value reported from
the calorimetric experiments of Nishibata and Whalley [142].
=
D.
Ice V/XIII
In 2006, the proton-ordered version of ice V, ice XIII, was first reported by Salz-
mann et al. [22] Unlike the ice Ih/XI transformation [8, 9, 58-60], where doping
with hydroxide enables formation of ice XI near 72 (76)K for H
2
O(D
2
O), ice
V reversibly transforms to ordered ice XIII in the presence of excess protons in
the form of HCl dopant [22-24]. In both cases, dopants presumably facilitate
H-bond rearrangements enabling a phase transition that otherwise has prohibitive
activation barriers. No ordering of ice V was observed when pure ice or samples
doped with hydroxide were cooled. Using Raman spectroscopy and monitoring
the change in lattice parameters, the ordering transition was found to be reversible
[22-24]. When cooling samples of ice V, the beginning of the ordering transition
occurred near 117 K and upon heating ice XIII, it started near 108 K [24]. The
unit cell of ice V, containing 28 water molecules, is a monoclinic, space group
A
2
/a
, as determined by X-ray and neutron diffraction techniques [46, 148, 149].
The unit cell of ice XIII, also containing 28 water molecules, is monoclinic with
space group
P
2
1
/a
, a reduction in symmetry from the ice V space group.
