At ambient temperatures,
the icosahedral cluster equilibrium in water is shown rather idealistically
in the equation (ESCS).
Clearly complete clusters, without any pendant hydrogen bonding,
are likely to be rarely, if ever, found. It should be noted that
such a five or six (complete) shell cluster has 86% or 89% hydrogen bonding (respectively), approximately
in line with that estimated by some in water [465a].
A dynamic range of partial structures (reducing the % hydrogen bonding)
is expected together with extensive links to pendant molecules and
other clusters (increasing the hydrogen bonding). A model, using
the significant liquid structure theory, estimates an average of
20 water molecules per flickering cluster gives the best fit over
a range of temperatures (0-100 °C) .
As the hydrogen bonding flickers between arrangements, the stability
of the expanded water dodecahedra (see below)
will vary . An
effectively-infinite number of arrangements (even a dodecahedral
(H2O)20 cluster has 30026 symmetry-distinct
hydrogen bond arrangements differing in energy by up to the equivalent
of 40% of the hydrogen bond energies )
will be found with an extraordinarily complex potential energy surface;
lower energy (more symmetrically arranged with smallest net overall
and partial-cluster dipoles being more stable )d arrangements tending to expand whereas higher energy forms (more
asymmetric with largest net dipoles being least stable) will pucker,
so leading to the cluster flickering phenomena. If the range of
energies for the dodecahedral (H2O)20 cluster
 is used for calculating the range
of energies for the icosahedral (H2O)280 cluster,
it is expected that differences in energy by up to the equivalent
of 8% (40% x 60/20 x 20/280) of the hydrogen bond energies will
be possible for differing hydrogen bond arrangements. As the temperature
is lowered towards 0 °C and below, it is expected that a greater
degree of cluster completion is to be found, flickering between
structural forms (see animated gifs, 379 KB).
There is likely to be a continuum of structures present. It is also
possible that clusters can fuse together to form cylindrical clusters
and cover surfaces.
The agreement of the CS structure with the radial distribution
function indicates that it is by far the major contributor at
4 °C. Under pressure the collapsed structure (CS)
may collapse further because only the one dodecahedron at the center
has collapsed in the cluster model (CS),
leaving three (12 quarters, icosahedrally arranged) mostly uncollapsed
on the periphery. As the density of ES is 0.94 g cm-3 and that of CS (with a quarter of the dodecahedral voids collapsed) is 1.00 g cm-3 then the collapse of these other three (equivalent) dodecahedral
voids (under pressure) will give a density of about 1.18 g cm-3;
similar to that of high-density amorphous ice when returned to ambient
pressure; so offering explanation of the continuous nature of the
LDAHDA process that occurs without breaking
the hydrogen bonds .
There are a number of changes to the structure
of water that occur with increasing temperature. The water
molecules gain energy, which is used to bend and break the
hydrogen bonds. Due to the multiple nature of the hydrogen
bonding around water molecules, central molecules in clusters
are likely to resume unchanged hydrogen bonding after such
breakage but peripheral molecules will be preferentially lost
to other clusters, less structured environments and interstitial
sites. On raising the temperature, the size of ordered clusters
decreases, the number of smaller clusters increases, the number
of hydrogen bonds decreases and the average distance between
the water molecules increases.
(H2O)m (H2O)n + (H2O)m-n
There is always considerable hydrogen bonding, however, and
it is likely that almost all molecules will be linked to almost
all others by at least one intact chain of hydrogen bonds.
Some hydrogen bonding, of the order of 1-2 hydrogen bonds
per molecule dependent on the density, is evident even in supercritical water (>374 °C)
Interesting phenomena, in the (interfacial) vicinal water that occurs at
solid surfaces, are the apparent transitions in physical properties
at the 'Drost-Hansen' temperatures (~15 °C, ~30 °C,
~45 °C, ~60 °C and ~75 °C) .
It is possible that these transitions are caused by the breakage
of hydrogen bonds due to the increasing difference between
the potential of the ordered vicinal and disordered bulk phases.
This would then cause an incremental loss of order and restructuring
of the water clusters and explain the pronounced thermal hysteresis
in the effects. Note that the properties of bulk water have
similar turning points (for example, complex permittivity analysis shows a discontinuity at about 30 °C , specific
heat has a minimum at about 36 °C, compressibility has a minimum at about 46.5 °C and the speed
of sound has a maximum at about 73 °C) and gaseous
solutes can create other turning points (for example, the
presence of equilibrated air creates a turning point at 44 °C
for the proton spin-lattice relaxation time in water, T1 ), so it is not
unreasonable that the changes in the clustering of water creates
these transitions within the interfaces.c Other transitions occur in many ionic solutions on increasing
their concentration to about molal concentrations ,
when the preferred (low concentration) water clustering starts
to overlap at higher concentrations and indicating that at
least 20 water molecules are associated with each ion's cluster.
Dodecahedral (H2O)20 clusters are at the center of the icosahedral water clusters. These
are expanded when the hydrogen bonding is dominant and collapsed
when the van der Waals dispersion interactions dominate. Under normal
conditions there will be equilibrium between these forms.
The central (H2O)20 dodecahedron of water molecules (a) in a water cluster can
collapse in a number of ways.a Their oxygen atoms are depicted above showing a collapse
with 8 (b), 4 (c) or 6 (d) inner molecules (shown as yellow)
producing cubic, tetrahedral or octahedral cavities respectively.
Other collapsed structures are also possible
(for example, with two inner molecules similar to that
occurring with the oxygen atoms in CO2 clusters).
The connectivity map of the convex dodecahedron
(a) is shown below with the most-stable positioning (red or blue circles) of
outwards-oriented donor hydrogen atoms in an isolated clusterb,
having just three nearest neighbor double-donor and double-acceptor
pairs . The favored directions of (one set of) the hydrogen-bonded hydrogen atoms are also shown as short red lines .
Also shown are the connectivity maps of the dodecahedra showing
the collapsed positions (red or blue circles) for 2 (e), 4
(c), 6 (d) and 8 (b) molecules. Alternative structures (with
redundancy in map b) may be formed from all of these connectivity
maps by rotation and reflection.
In water it is expected that the more-central water
molecules will be constantly changing and there will be a range
of collapsed structures although some may clearly be more stable
than others; structure (b) was favored by molecular modeling. The
figures (above) show the maximum amount of puckering
that occurs when the non-bonded distance between the inner molecules
(the edges of the holes) is the same as the bonded distance between
two neighbors. In practice a lesser degree of puckering is expected.
With this maximal puckering the central cavities have radii 1.71
Å, 2.01 Å, and 2.42 Å for tetrahedral, octahedral
and cubic cavities respectively. Interactive structures are available
The cavities may be occupied by ions which interact with the puckered water molecules in some cases forming magic
number cluster ions.
a It is also possible that
dodecahedra can fuse together to form tubes and cover surfaces.
b Although the difference
in stability between hydrogen-bonding arrangements of the water
central dodecahedron ((H2O)20) within an icosahedral
structure ((H2O)280) will be much smaller
than for the isolated water dodecahedron, modeling studies show
that a similar order of relative stability against puckering remains. The least stable hydrogen bond arrangement in the central dodecahedron is that with the greatest symmetry (S10), where the ten outward-facing hydrogen bonds are contributed by two oppositely-positioned cyclic pentamers.
c An interesting,
if not fully convincing, alternative explanation involves
thermal quantum effects depending on the effective size of
the molecules and the free volume space .
d This can also be visualized as the form with the least number possible of free (non-hydrogen bonded) H atoms on adjacent (hydrogen-bonded) water molecules. Of the ten free H-atoms in the most stable dodecahedral water cluster, (H2O)20 isomer, four are isolated and six are contained in three isolated pairs of adjacent (hydrogen-bonded) water molecules, as shown above (a).