Equilibrium structural model of liquid water: Evidence from heat capacity, spectra, density, and other properties
Authors: Dougherty Ralph C. , Howard Louis N. 
Published: July 2002

Hydrogen bond strength depends on both temperature and pressure. The gradient for hydrogen bond strength with temperature, or pressure, depends upon the hydrogen bonded structure. These features create an intimate connection between quantum mechanics and thermodynamics in the structure of liquid water. The equilibrium structural model of liquid water developed from analysis of the heat capacity at constant pressure is complex. The model is based on the assumptions that: (i) the hydrogen bond length and molecular packing density of water both vary with temperature; (ii) the number of different geometries for hydrogen bonding is limited to a small set; (iii) water molecules that possess these hydrogen bonding geometries are in equilibrium with each other under static conditions; (iv) significant changes in the slope of the heat capacity, Cp, and to a lesser extent other properties of the liquid, reflect the onset of significant changes in the chemical structure of the liquid; (v) the partial molal enthalpies and entropies of the different water arrays generated from these building blocks differ from each other in their dependence upon temperature; and (vi) the structure of the liquid is a random structural network of the structural components. The equilibrium structural model for liquid water uses four structural components and the assumptions listed above. At the extrapolated-homogeneous nucleation temperature, 221 K, a disordered hexagonal-diamond lattice (tetrahedrally hydrogen bonded water clusters) is the structure of liquid water. At the homogeneous nucleation temperature, ∼238 K, liquid water is a mixture of disordered tetrahedral water arrays and pentagonal water arrays. The abundance of tetrahedral water structures at this temperature causes the system to self-nucleate. As the temperature increases to 266 K the proportion of disordered pentagonal water clusters in the equilibrium mixture increases. At 256 K, the temperature of the previously unrecognized maximum in the heat of fusion of water, “planar”-hexagonal water arrays appear in the liquid. At 273 K the concentration of tetrahedral hydrogen bonded water approaches zero. At the temperature of maximum density, 277 K, the liquid consists of a disordered dodecahedral-water lattice. The equivalence point between pentagonal and “planar”-hexagonal water arrays occurs near 291 K, the approximate temperature of minimum solubility of large hydrocarbons in water. At temperatures above 307.6 K, the minimum in Cp, square water arrays first appear in significant concentrations. Pentagonal water arrays become insignificant in the liquid at the temperature of minimum isothermal compressibility, ∼319 K. The equilibrium point between “planar”-hexagonal and square water arrays occurs near 337 K. As the temperature increases the liquid structure becomes dominated by disordered cubic arrays of water molecules. Structures with fewer than four hydrogen bonds per water molecule appear in the liquid near 433 K. “Planar”-hexagonal clusters are no longer present in the liquid at the temperature of the maximum dissociation constant for water, 513 K. These views are certainly oversimplified. Simple models for density are introduced. A model for viscoscosity based on the variation of hydrogen bond strength with temperature is introduced. Attempts to model density, heat capacity, or other thermodynamic properties of liquid water, using only two functions will not capture the subtle complexity of the equilibrium process. The equilibrium structural model of water has the potential to provide a basis for quantitative descriptions of the liquid’s seeming anomalies.