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Water's Two-State Cluster History

'Because of the importance of water in the theoretical speculations as well as the practical routine of chemists,

a review of the theories concerning its structure is pertinent.'

Harris Marshal Chadwell 1927    

 

V Two state theories

V Are the icosahedral clustering model and the outer structure two-state mixture models related?

Two state theories

The anomalous properties of water have excited chemists to attempt explanation for many years. These hypotheses have mainly involved consideration of the existence of different water clusters within liquid water. Generally two states are hypothesized. Such clusters are either low-density (similar in density to that of hexagonal ice) or of higher density; their changing relative concentrations determining the changes in physical properties. Thus the properties of water are shown to follow those of a more typical liquid at higher temperatures (~> 50 °C) based on the higher density form, and follow those of a very different liquid at lower temperatures (~< 0 °C) based on the lower density form with about equal amounts of the two forms present at about 0 °C.


Ice Ih cell cluster

Low-density ice-like particles

 Dense liquid water

Higher-density liquid matrix

1884

The first reported suggestion for clusters being responsible for water's anomalous density maximum was by Whiting in 1884 [764]. Melting ice was proposed to release solid low-density ice crystals (left) which remained within the higher density matrix (right). Whiting proposed that the concentrations of these solid particles changed with temperature and pressure. Chadwell [765] reviewed the first 40 years in the development of this idea.


Ice Ih cell cluster

Low-density ice-like clusters

 

 

 

 

 

=

 Walrafen pentamer;  'quartz-like' cluster

Higher-density clusters

1933

In 1933, Bernal and Fowler developed this model in two important respects [1177]. Firstly the denser matrix was proposed to be made up of 'quartz-like' clusters (right) that may pack closer together. Secondly, and significantly, they introduced the idea of equilibration of water molecules interconverting between the clusters [766].


Ice Ih cell cluster

Low-density ice-like clusters

Ice Ih cell cluster, with an interstitial water molecule

Cluster plus an interstitial molecule

1946

An interesting idea, based on interstitial water molecules within the ice hexagonal box (right) was put forward in 1946 [767]. Such clusters are not now generally thought to be present in significant quantities, although some researchers still make use of this hypothesis [2009].


Dodecahedral water cluster

Low-density clathrate clusters

Dodecahedral water cluster, with an interstitial water molecule

Cluster plus an interstitial molecule

1959

Pauling suggested another interstitial arrangement in 1959, making use of his interest in clathrate structures [8b]. These clusters were quickly dismissed, however, for being unable to explain the available diffraction data if the main constituents in liquid water.


Ice Ih cell cluster

Low-density ice-like particles

Dense water shown as 2 water tetramers

Close packed hexagons

1965

Davis and Litovitz proposed a variation on Whiting's hypothesis [2160]. The high-density state consists of almost close packed water hexagon rings. The fraction of ice-like particles was about 0.6 at 0 °C.


Ice Ih cell cluster

Low-density ice-like particles

Dense liquid water

 

Higher-density liquid of

unbonded monomers

1969

Arakawa and Sasaki also proposed a variation on Whiting's hypothesis [2161]. The high-density state consists of close packed unbonded molecules. The fraction of ice-like particles was 0.52 at 0 °C.


   4-membered cyclic water cluster     5-membered cyclic water cluster    6-membered cyclic water cluster      7-membered cyclic water cluster  8-membered cyclic water cluster

1975

A random network model of water, also introduced by Bernal [1177] and published in 1975 [19], contained a mixture of water clusters including 4-, 5-, 6-, 7- and 8-membered rings. Some success has been had using this model but its homogeneous nature is not universally applicable or productive.


Ice Ih cell cluster

An ice Ih cluster

1987

Wilse Robinson's research group introduced the outer structure two-state mixture model in 1987, b which involved a mixture of water clusters related to ices 1h, II and III. The group went on to produce a number of papers using the model to successfully and quantitatively explain many of water's anomalies (for example, [23, 56, 57, 60, 69, 73, 148, 826, 1354]).

 

 

A cluster from ice-two

 

An ice II cluster

A cluster from ice-three

An ice III cluster

 

 

The only difficulty with this model concerned whether such clusters could exist for significant time in liquid water and so the clusters were more realistically considered as rapidly fluctuating 'indicative' structures [1354c].


Dodecahedral water cluster

 

 

 

 

 

=
5-membered cyclic water cluster6-membered cyclic water cluster

1998

In 1998 Dougherty and Howard proposed an equilibrium model for water [15] involving dodecahedra, 5- and 6-membered clusters based on several of water's anomalous properties.


Dense water shown as 2 water tetramers

Dense cluster

 

 

 

=
8-molecule open water cluster

Low-density cluster

2000

These water cluster models lead logically on to the icosahedral water cluster model , published in 2000 [55] and described at this site. This model is based on dense and less dense clusters equivalent to an equilibrium opposite (see animated gif). The less-dense bicyclo(2,2,2) structures (right) occur when the hydrogen bonding is strongest and the dense structures occur when the weaker but more numerous van der Waals interactions predominate.


 

 

 

 

 

  8-molecule open water cluster

 

Low-density cluster

 

 

 

 

 

 

 

=

280-molecule icosahedral open water cluster

Icosahedral cluster

 

 

When conditions arise (such as on supercooling at low temperatures) when there is a high concentration of the expanded 8-membered bicyclo clusters, partial to complete icosahedral clusters (right) may arise. A full description of this is given elsewhere on this site. This cluster contains the dodecahedral, ice Ih cell, 5-, 6-membered and 8-membered bicyclo(2,2,2) subclusters included in the historical survey of models, above. It fits well with and extends the general theory of water two-state clustering.

 

Later publications have described two-state systems with a low-density state and a high-density state but without using explicit structures. Thus Maréchal describes them entirely from their infrared spectra [1738] (with the low-density form having peaks at 744 cm-1, 1669 cm-1 and 3356 cm-1 whereas the high-density form has peaks at 518 cm-1, 1639 cm-1 and 3519 cm-1), Taschin et al describes them as tetrahedrally hydrogen bonded (associated with a Raman peak at 225 cm-1) and disordered (associated with a Raman peak at 180 cm-1) [2019], and Nilsson et al describes them as tetrahedrally hydrogen bonded (low-density liquid-like) and closely packed disordered with distorted hydrogen bonds (high-density liquid-like) [1899].

 

The meaning of the term 'cluster' has evolved during this time as well. In the beginning, water clusters were thought of as discrete entities, like crystals, with long (e.g. > seconds) individual lifetimes where the same molecules were involved, within the cluster, throughout. Nowadays, we know that molecules may leave or add to clusters a with frequencies that depend on their situation and obey statistical laws with clusters appearing, evolving and disappearing with involvement of physically different molecular constituents (that is, the water molecules come and go). The aqueous environment is heterogeneous with more than one type of environment present and with the relative preponderance of these environments changing with temperature, pressure, solutes and surfaces. Clusters are now thought of as dynamic entities offering a simplified view into a complex, broken and rapidly shifting environment. As such they reveal water's underlying, if elusive, nature.


Footnotes

a   Some authors prefer the term 'dynamic heterogeneities' to 'clusters', but this site does not. The same type of structuring is meant in both cases although 'dynamic heterogeneities' may include the scenario where their is a gradual change in cluster type with temperature (a single cluster form under a set of conditions) whereas 'cluster' is more easily understood in two state systems (a mixture of cluster forms in equilibrium with each other). [Back]

b Are the icosahedral clustering model and the outer structure two-state mixture models related?

The outer structure two-state mixture model has been successfully used to explain many of the anomalous properties of water (for example, [23, 56, 57, 60, 69, 73, 148, 826, 1354]). Although this model explicitly includes ice Ih (hexagonal ice) and ice-two (ice II) substructures, these may be thought of as representing fully tetrahedral open low-density structures (ice Ih equivalent in the icosahedral network model to ES) and tetrahedral structures with close second neighbors, giving a higher density 'collapsed' structure (ice-two equivalent in the icosahedral network model to CS). This equivalence can best be envisioned by examining the behavior of a 'c'-type water molecule. They are the most numerous water molecules in icosahedral water clusters (120/280 = 43%) and they are the least affected by the movements due to the ESreversible arrowCS equilibrium. These water molecules are tetrahedrally hydrogen-bonded to the surrounding four (2 'b' and 2 'c' type) water molecules in both ES and CS. In ES the next 'outer' structure (including 2 'a' type) water molecules are also tetrahedrally positioned but in CS the two 'a' type water molecules in this 'outer' structure are flexible and collapsed, allowing close second neighbors. It may be noted that the outer structure two-state mixture model does not depend on the explicit structures of ice Ih and ice-two in order to explain water's anomalous properties; in fact the existence of such explicit structures is unlikely as shown by many of the other properties of water (for example, see earlier). This means that arguments using this model can also be used in support of the icosahedral cluster model (but not explicitly vice versa). [Back]

 

 

 

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This page was established in 2005 and last updated by Martin Chaplin on 30 June, 2016


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