An adaptive model is developed here for the liquid water density fluctuations as momentary dense clusters with helices of hydrogen bonds and nondense tetrahedral clusters of ice. This model can be useful for explanation of liquid water structural anomalies including the high quantity of hydrogen bonds with quasitetrahedral orientation in the nonordered liquid water. The topology of such clusters is essentially differed from the one of the crystalline ice. From this and only this point of view, the liquid water can be considered as a two-structural fluid by dynamic forming the two topological kinds of clusters as a consequence of condensed-matter density fluctuations. Another feature of the dense-water-part clusters is helical ordering of protons which can realize coherent vibrations. A spectral series of such vibrations is determined as a function of the number of molecules into the helical cluster.

Although the liquid water is all around us, we still do not understand how it behaves on a microscopic level. Its dynamic hydrogen bonds (HB) structure has been the subject of intense debate for decades. Ice with well-established HB structure forms a tight tetrahedral lattice of water molecules each binding to four others. The prevailing model of the liquid water holds that the molecules loosen their grip but remain generally arranged in the same tetrahedral groups [

However, the majority of water molecules in the liquid are found in higher density regions [

The conclusion that a dominant fraction of molecules in the liquid water is very asymmetrically hydrogen bonded with only two well-defined H bonds (one donating and one accepting) is in a strong contrast to the accepted picture of four quasitetrahedral H bonds.

Very recently, also X-ray emission spectroscopy (XES) is applied at high resolution to the liquid water [

The controversy about the microstructure of liquid water pits a new model involving water molecules in a relatively stable “rings-and-chains” structure against the standard model that considers water molecules in the distorted tetrahedral coordination. An analysis [

At the same time, it is known that a topological density-fluctuations structure of liquids is ramified clusters of almost regular Delaunay simplexes (tetrahedrons) built on the fours of densely packed particles and connected in pairs by faces in tetrahedral Bernal chains [

For identifying the dense-part structure of liquids, they have selected those Delaunay simplexes which have a tetrahedral factor more than or equal to the some given one,

Opposite, a topological criterion offered in [

These data may be useful for creating an analytical model of the cluster statistics for calculating the configuration entropy of any condensed matter and estimating its thermodynamic properties using only a pair potential of particles [

Precise experimental techniques for determining the local structure of the liquid water are lacking since each water molecule undergoes a quick rearrangement (during femtoseconds). The need for better understanding the liquid water at the microscopic level has forced developing computational methods that describe the individual and cooperative dynamics and structure of water molecules. Many investigations are carried out using these techniques. They show that locally HB-ordered clusters of water molecules are formed and broken uninterruptedly [

MD studying density fluctuations of the liquid water have shown [

The dense-part cluster in MD model of water at 300 K and its frame (broken red line); blue points are the molecules and red points are centers of the cluster tetrahedrons.

One can expect that water molecules have enough time for rebuilding hydrogen bonds in the dense part of water density fluctuations due to fast librations and rotations of them. From this, we will build a model for tetrahedral clusters of the dense part of liquid water provided that each water molecule in such cluster is hydrogen bonded with three molecules of this cluster and all angles between these bonds are equal to each other.

It turned out that such cluster represents “nanotube” of water molecules and geometric parameters of this tube are defined strictly. For illustration, Figure

The diagram of angular shift,

These parameters are defined under the assumption of helix edges equality as the distance between oxygen atoms of nearest water molecules:

From the equality of angles,

Solutions of this task for

Using these parameters, it is easy to find the value of

Now, one can estimate a packing factor of water molecules into the helix provided that all particles are inside the cylinder in radius of

In using the cubic model of ice shown in Figure

The cubic model of ice.

The elementary ice cell contains 7.5 molecules of water. The edge length of such cell is equal to

One can estimate a volume portion ^{3} and the water one is equal to 1.0 g/cm^{3} at 4°C. From here, we obtain an upper bound of this portion as helical clusters

These clusters having higher molecular density provide, in principle, four hydrogen bonds for each molecule of water: three of them are internal and one is external for connecting ice crystallites with less density. However, if protons are ordered in the helix (see Figure

The dense part of water density fluctuations with the coherent exchange of protons (red balls) between oxygen atoms (blue balls) along the helical hydrogen bonds (black lines) and HB bridges (pink balls); the projections of oxygen atoms in the (

One assumes that the motion of all protons in helical circuit (coin), as shown in Figure

For describing such coherent vibrations, we can use equation [^{10} cm/s. From defining

In substituting these values in formula (

Finally, from (

The spectral absorption modes of the coherent proton vibrations as a function of the water-molecules number in the helix,

Spectral modes | Spectral modes | ||||
---|---|---|---|---|---|

THz | cm^{−1} | THz | cm^{−1} | ||

6 | 8.2 | 273 | 20 | 4.8 | 160 |

10 | 6.6 | 220 | 25 | 4.3 | 144 |

15 | 5.5 | 183 | 30 | 3.9 | 132 |

The topology of the dense liquid water part as helices of hydrogen bonds differs from the one for tetrahedral crystalline-ice clusters as a nondense part of liquid water. Therefore, one can tell about water as a two-structural liquid though this is a dynamic distinction having only statistical sense because such clusters arise and disappear as density fluctuations of the liquid water.

At the same time, possible coherent proton vibrations by external impact at their resonant frequencies can selectively amplify some modes and, thus, strengthen water microheterogeneity far from its equilibrium. In this connection, studying the electromagnetic absorption spectra in this range of frequencies can be interested both for revealing spectral lines (

Moreover, any additives can be concentrated in the expected ramified border between two dynamic structures of water solution that, in turn, can cause fluctuation-induced clustering and impurity [

Thus, the helices of hydrogen bonds in water density fluctuations and the high resonant mobility of proton in them as a catalytic stimulator for chemical reactions can create templates for building macromolecules and structural blocks of biosystems.

The model of hydrogen bond helix is built for the dense part of the liquid water density fluctuations. This model allows providing the high quantity of tetrahedral hydrogen bonds in the nonordered liquid matrix and explaining the density anomaly of liquid water.

The topology of such helical clusters is essentially differed from the one of the crystalline ice. From this and only this point of view, the liquid water can be considered as the two-structural liquid because the formation and decay of such clusters has dynamic character and is natural consequence of water density fluctuations.

The other interesting feature of these clusters is possible helical ordering protons in them which can have coherent vibrations. A spectral series of such resonances is defined.

The authors are pleased to acknowledge Dr. A. S. Kolokol for giving some data on molecular dynamic simulation of water structure and discussing this work which is supported by the Russian Foundation of Basic Research (RFBR) (Grant no. 10-08-00217a).