Interpretation of the unusual behavior of H2O and D2O at low temperatures: Tests of a percolation model

Abstract

The unusual low-temperature behavior of liquid water is interpreted using a simple model based upon connectivity concepts from correlated-site percolation theory. Emphasis is placed on examining the physical implications of the continuous hydrogen-bonded network (or ’’gel’’) formed by water molecules. Each water molecule A is assigned to one of five species based on the number of ’’intact bonds’’ (the number of other molecules whose interaction energy with A is stronger than some cutoff VHB). It is demonstrated that in the present model the spatial positions of the various species are not randomly distributed but rather are correlated. In particular, it is seen that the infinite hydrogen-bonded network contains tiny ’’patches’’ of four-bonded molecules. Well-defined predictions based upon the putative presence of these tiny patches are developed. In particular, we predict the detailed dependence upon (a) temperature, (b) dilution with the isotope D2O, (c) hydrostatic pressure greater than atmospheric, and (d) ’’patch-breaking impurities’’—for four separate response functions, (i) the isothermal compressibility KT, (ii) the constant-pressure specific heat CP, (iii) the constant-volume specific heat CV, and (iv) the thermal expansivity αP, as well as for dynamic properties such as (v) the transport coefficients self-diffusivity Ds and shear viscosity η, (vi) the characteristic rotational relaxation time τch, and (vii) the Angell singularity temperature Ts. The experimentally observed dependence of these seven quantities upon the four parameters (a)–(d) is found in all cases to agree with the predicted behavior. The paradoxical behavior associated with the absence of a glass transition in pure liquid water is also resolved. Finally, we propose certain experiments and computer simulations—some of which are underway—designed to put the proposed percolation model to better tests than presently possible using available information.

Is there a second critical point in liquid water?

“…Also the data do not predict any "real" critical behavior in Kr or Ce at atmospheric pressure, but rather a maximum in Kr and Ce for pressures lower than the critical pressure. The high density structure (defective tetrahedral network) that smoothly transforms into the low density structure (random tetrahedral network) on lowering the temperature is reminiscent of the progressive growth of four-bonded clusters implied by the model of Stanley and Teixeira [15 ]. The temperature at which KT is maximum, which indicates the point of smooth transition between the two structures in the ST2 system, is similar to the percolation point of low density tetrahedrally coordinated molecules in the Stanley-Teixeira model.…”

“…Since then, many static and dynamic quantities have been studied and shown to satisfy a power law relation at the lowest temperatures, as expected for such quantities near a spinodal [8][9][10][11][12][13][14]. However, theories which are not based on the existence of critical behavior in the supercooled region are also able to reproduce the experimental data with functional forms other than a power law [15].…”

Water Structure from Scattering Experiments and Simulation

“…There is now consensus that the space-filling percolating hydrogen-bonding network of the liquid (a model proposed by Stanley and Teixeira based upon connectivity concepts from correlated-site percolation theory 176 ) present under ambient conditions collapses 162 , although local hydrogen-bonding is still present near the critical temperature and density. Figure 7 shows a comparison of the partial radial distribution functions from x-ray scattering 169 , neutron scattering 103 , and simulations using the TIP4P water model at the subcritical state T=573K and ρ=0.72g/ml, and supercritical state of T=673K and ρ=0.66g/ml (further detail can be found in [177].…”

The puzzling unsolved mysteries of liquid water: Some recent progress

“…This work, supported by the NSF Chemistry Division, has been carried out with many collaborators and has been heavily influenced by a number of experimentalists including S.-H. Chen [44,50,77,82], L. Liu [39,40], F. Mallamace [85,86], O. Mishima [13,87,88], J. Teixeira [89][90][91], M.-C. Bellissent [92][93][94][95], and H. Reichert [96].…”