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.