Water Clusters: Overview
Plato thought that water could be represented by
So do I. Read on and decide if we may be correct.
Cluster and hydrogen-bond lifetimes are independent
Icosahedral water clusters
'...we may ask why all trees and
bushes - or at least most of them - unfold a flower in a five-sided
pattern, with five petals.... Some botanist might well examine
the sap of plants to see if any difference there corresponds
to the shapes of their flowers.'
Johannes Keplar (1611) 
It is clear that life on Earth depends on the unusual structure
and anomalous nature of liquid water.
Organisms consist mostly of liquid water. This water performs many
functions and it can never be considered simply as an inert diluent;
it transports, lubricates, reacts, stabilizes, signals, structures
and partitions. The living world should be thought of as an equal
partnership between the biological molecules and water. Both short-range (< 1nm) and long range (> 100 nm)  organization of the water molecules has been detected.
In spite of much work, many of the properties of water are
puzzling. Enlightenment comes from an understanding that water
molecules form an infinite dynamic hydrogen-bonded network with localized
and structured clustering . The middling strength of the connecting
hydrogen bonds seems ideally suited to life processes, being
easily formed but not too difficult to break. An important
concept, often overlooked, is that liquid water is not homogeneous
at the nanoscopic level (e.g. see ).
Small clusters of four water molecules may
come together to form water bicyclo-octamers. The molecular
arrangement (A) also occurs in high-density ice-seven whereas, with 60°
relative twist, (B) is found in low density hexagonal ice; (see
animated gif, 129 kB). Structures similar to A have greater numbers of 3-hydrogen bonded and 5-coordinated water molecules as found at higher temperatures in liquid water, whereas structures similar to B have greater numbers of 4-hydrogen bonded and 4-coordinated water molecules as found at lower temperatures in liquid water . Such equilibria are balanced
due to the existence of two minima in the potential energy
(U) - molecular separation (r) diagram below, which shows
the approach of the water tetramers. It has been found using recent high energy x-ray diffraction experiments that the number of water nearest neighbors does not vary over the range 254.2 – 365.9 K with neighboring molecules switching between strong hydrogen bonded and weak or non-hydrogen bonded , in agreement with this model .
This competition between maximizing van-der Waals interactions
(A, yielding higher orientation entropy,
higher density and individually weaker but more numerous water-water
binding energies) and maximizing hydrogen bonding (B,
yielding more ordered structuring, lower density and fewer
but stronger water-water binding energies) is finely balanced,
easily shifted with changed physical conditions, solutes and
surfaces. The potential energy barrier between these states
(see below left) ensures that water molecules prefer either
structure A or B with little
time spent on intermediate structures. An individual water
molecule may be in state A with respect to
some neighbors whilst being in state B with
respect to others (for example, ice-seven).
Certainly, recent simulations using ab initio van der Waals interactions support this mechanism for the density fluctuations in liquid water .
The shallow minimum (a),
due to non-bonded interactions, lies up to 20% inside
the deeper minimum (b) due to hydrogen
bonding (even allowing for a 15% closer approach
of individual hydrogen bonded water molecules). In
spatial terms, minimum (a) is far
more extensive as the hydrogen-bonded minimum (b)
is restricted in its geometry, being highly directional.
At lower temperatures (particularly below the temperature
of maximum density) and pressures, the less dense
structure with more extensive hydrogen bonding at
the lower minimum (b) will be preferred
even though it involves a more ordered (lower entropy)
structure. At higher temperatures, non-bonded interactions
dominate causing breakdown of the clustering (Figure inspired by ).
The hydrogen bonding, although cohesive in nature,
is thus holding the water molecules apart. It is the conflict
between these two effects, and how it varies with conditions,
which endows water with many of its unusual properties.
These bicyclo-octamers may cluster
further, with only themselves, to form highly symmetric 280-molecule
icosahedral water clusters that are able to interlink and tessellate
throughout space. A mixture of water cyclic
pentamers and tricyclo-decamers can bring about the same resultant
As all three of these small clusters are relatively stable quasi-polyhedra found , it
is likely that their interaction will produce these larger icosahedral
clusters (and the latter two are the lowest energy structures out of those found by simulating supercooled water ). Such clusters can dynamically form a continuous network
of both open, low-density, and condensed structures.
It is important to recognize that whenever there is a cluster of water molecules in liquid water, there will be a large number of 'decorating' water molecules on their periphery. Thus the linear H2O chain, cyclic pentamer, bicyclo-octamer, tricyclo-decamer, (H2O)20 dodecahedron, (H2O)100 (from ES), (H2O)280 ( ES) clusters form only ~33%, ~33%, ~36%, ~38%, ~50%, ~63%, ~70% respectively of their cluster+'decorating' H2O assemblage. These 'decorating' H2O molecules necessarily have different properties than the internal clusters and naturally form a second 'state' of water molecule present.
[Back to Top ]
Cluster and hydrogen-bond lifetimes are independent
On the right is a cartoon to aid the understanding of how the lifetimes of clusters are independent of the lifetime of individual linkages. The cartoon shows a two-dimensional representation of a three-dimensional phenomenon. The actual clusters of water molecules are not represented. It is supposed (opposite) that the star clusters (shown yellow filled) may reform around key structures (shown as rhombuses, sometimes red, but closed ring oligomers of H2O in water). For each shifting cluster a few units move to break up the existing cluster and help create a new cluster. The new clusters are identical to the old ones but only contain a proportion of the units. Thus. dynamic clusters may reform around any of the star arms. One mechanism for such cluster reorientation involves a proton cascade leading to cluster reorientation . Movement of such clusters may involve ther travelling as a wave form through the medium as well as flickering on and off unpredictably. b
Although the hydrogen bonds between water molecules in ice have equally short lifetimes to those in water, ice cubes, which can be considered as enormous ice clusters, can last forever at 0 °C in water.
Similarly but on a macro-scale on addition of solutes, water retains its integrity as liquid water with the hydrogen bond network connected throughout the entire bulk (percolating) and yet the local hydrogen bonds are known to be fleetingly breaking and forming . Cluster formation and lifetime are both increased by the highly cooperative nature of hydrogen bonding. Whenever low density clusters are formed they are surrounded by about the same number of 'decorating' water molecules with intermediate density.
There is a similarity, in principle, with John Conway's game "life" b in the persistence of some of its structures . [Back to Top ]
Icosahedral water clusters
Such a dynamic fluctuating self-replicating network of water molecules,
with localized and overlapping icosahedral
symmetry, was first proposed to exist in liquid water
in 1998  and the structure
subsequently independently found, by X-ray diffraction, in
water nanodrops in 2001 .
The clusters formed can interconvert between lower and higher
density forms by bending, but not breaking, some of the hydrogen
bonds. Structuring may also flicker between statistically and topographically equivalent
clusters but involving different molecules by shifting their cluster
centers. These polyhedral structures are idealized as given, and are considerably distorted and fragmented by thermal effects, but the existence of long-lived ring fragments is nevertheless considered to be well-founded . The cluster size required for ice formation has been estimated at about 400 molecules (one further layer of water around the icosahedral water core), although the structure of this core structure was indeterminable . As the temperature increases the average cluster
size, the cluster integrity and the proportion in the low-density
form all decrease. This structuring accommodates explanation of many of the anomalous properties
of water including its temperature-density and pressure-viscosity behavior, the radial distribution
pattern, the presence of both cyclic pentamers and hexamers,
the change in properties on supercooling a and the solvation and hydration properties of ions, hydrophobic molecules, carbohydrates and macromolecules. The model described
here offers a "two-state" structural model on to
which large molecules can be mapped in order to offer insights
into their interactions. [Back to Top ]
a As the temperature of supercooled water
drops further below 0 °C, the density, self-diffusion, thermal
conductivity, enthalpy and entropy all decrease whereas compressibility, viscosity, thermal convection, specific heat (CP) and gas solubility all increase. As the
pressure increases on supercooled water, viscosity and freezing point decrease whereas
entropy and self-diffusion increases.
b The Game of Life is 'played' on an infinite two-dimensional grid of squares, each of which is in one of two possible states, alive or dead (see right for an example). Every cell interacts with its eight adjacent neighbors using the four rules:
- Any live cell with fewer than two live neighbors dies, as if caused by under-population.
- Any live cell with two or three live neighbors lives on to the next generation.
- Any live cell with more than three live neighbors dies, as if by overcrowding.
- Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction.