A One-Dimensional Model for Water

A one-dimensional (1-D) model for water may sound like an extremely unrealistic model for such a complex liquid. Indeed, it is If the aim is to calculate thermodynamic quantities and to compare them to the corresponding experimental quantities of 

It has long been recognized that the unique properties of water are related to the open structure or the ice-like character of liquid water. The idea that water contains some kind of structure related to the structure of ice is very old (see Sec. 2.1). This idea was the underlying motivation for constructing various mixture models for water. 

In all of these models, the hydrogen bonds, or the structure of liquid water, were traditionally emphasized as the main molecular reasons for the anomalous behavior exhibited by liquid water. However, underlying this relatively ill-defined concept of structure (which was much later defined in statistical mechanical terms see Sec. 2.7) lies a more fundamental principle which can be defined in molecular terms, and which does not explicitly mention the concept of structure yet is responsible for the unusual properties of liquid water. This principle was first formulated in terms of generalized molecular distribution functions in 1973. It states that there exists a range of temperatures and pressures at which the water-water interactions produce a unique correlation between high local density and a weak binding energy. Clearly, this principle does not mention structure. As will be demonstrated in this section, it is this principle, not the structure per se, which is responsible for the unique properties of water as well as of aqueous solutions.  

A simpler version of the same principle uses the language of the mixture-model approach to liquid water. Within this approach, the principle states that there exists a range of temperatures and pressures at which there are non-negligible concentrations of two species one characterized by large partial molar volume and large absolute value of the partial molar enthalpy, and a second characterized by a smaller partial molar volume and smaller absolute value of the partial molar enthalpy. In order to obtain the outstanding properties of water, one also needs to assume that the concentrations of these two species are of comparable magnitude (see Sec. 2.3 for details). 

This principle was first used implicitly in the construction of the first successful pair potential for water molecules. Later, it was used explicitly in constructing pair potentials that exhibit 

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