The ability of simple potential functions to reproduce accurately the density of liquid water from −37 to 100 °C at 1 to 10 000 atm has been further explored. The result is the five-site TIP5P model, which yields significantly improved results; the average error in the density over the 100° temperature range from −37.5 to 62.5 °C at 1 atm is only 0.006 g cm−3. Classical Monte Carlo statistical mechanics calculations have been performed to optimize the parameters, especially the position of the negative charges along the lone-pair directions. Initial calculations with 216 molecules in the NPT ensemble at 1 atm focused on finding a model that reproduced the shape of the liquid density curve as a function of temperature. Calculations performed for 512 molecules with the final TIP5P model demonstrate that the density maximum near 4 °C at 1 atm is reproduced, while high-quality structural and thermodynamic results are maintained. Attainment of high precision for the low-temperature runs required sampling for more than 1 billion Monte Carlo configurations. In addition, the dielectric constant was computed from the response to an applied electric field; the result is 81.5±1.5 at 25 °C and the experimental curve is mirrored from 0–100 °C at 1 atm. The TIP5P model is also found to perform well as a function of pressure; the density of liquid water at 25 °C is reproduced with an average error of ∼2% over the range from 1 to 10 000 atm, and the shift of the temperature of maximum density to lower temperature with increasing pressure is also obtained.

/pdf/a-five-site-model-for-liquid-water-and-the-reproduction-of-4waghhehgx.pdf

A five-site model for liquid water and the reproduction of the density anomaly by rigid, nonpolarizable potential functions

The vapour pressures of ice and supercooled water are reviewed with an emphasis on atmospheric applications. Parametrizations are given for the vapour pressure, molar heat capacity, and latent heat of vaporization of both ice and liquid water. For ice, the experimental vapour pressure data are in agreement with a derivation from the Clapeyron equation. Below 200 K cubic ice may affect the vapour pressure of ice both in the atmosphere and in the laboratory. All of the commonly used parametrizations for the vapour pressure of supercooled water are extrapolations that were not originally intended for use below the freezing point. In addition, the World Meteorological Organization definition of the vapour pressure of supercooled water contains an easily overlooked typographical error. Recent data on the molar heat capacity of supercooled water are used to derive its vapour pressure. Nevertheless, the uncertainty is such that measurements of the deliquescence and freezing behaviour of aerosol particles are beginning to be limited by uncertainties in the thermodynamics of supercooled water. Copyright © 2005 Royal Meteorological Society

/pdf/review-of-the-vapour-pressures-of-ice-and-supercooled-water-3m0zwl6nnb.pdf

Review of the vapour pressures of ice and supercooled water for atmospheric applications

In the 1960’s an industrial formulation for the thermodynamic properties of water and steam was developed called “The 1967 IFC Formulation for Industrial Use” (IFC-67) [1]. Since 1967 IFC-67 has been formally recognized to calculate thermodynamic properties of water and steam for any official use such as performance guarantee calculations of power cycles. In addition to this, IFC-67 has been used for innumerable other industrial applications. However, during the last few years a number of weaknesses of IFC-67 have appeared. This fact and the progress that has been achieved in mathematical methods to develop accurate equations of state led to the development of a new industrial formulation in an international research project initiated and coordinated by the International Association for the Properties of Water and Steam (IAPWS).

The IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam

Over the last forty years many computer simulations of water have been performed using rigid non-polarizable models. Since these models describe water interactions in an approximate way it is evident that they cannot reproduce all of the properties of water. By now many properties for these kinds of models have been determined and it seems useful to compile some of these results and provide a critical view of the successes and failures. In this paper a test is proposed in which 17 properties of water, from the vapour and liquid to the solid phases, are taken into account to evaluate the performance of a water model. A certain number of points between zero (bad agreement) and ten (good agreement) are given for the predictions of each model and property. We applied the test to five rigid non-polarizable models, TIP3P, TIP5P, TIP4P, SPC/E and TIP4P/2005, obtaining an average score of 2.7, 3.7, 4.7, 5.1, and 7.2 respectively. Thus although no model reproduces all properties, some models perform better than others. It is clear that there are limitations for rigid non-polarizable models. Neglecting polarizability prevents an accurate description of virial coefficients, vapour pressures, critical pressure and dielectric constant. Neglecting nuclear quantum effects prevents an accurate description of the structure, the properties of water below 120 K and the heat capacity. It is likely that for rigid non-polarizable models it may not be possible to increase the score in the test proposed here beyond 7.6. To get closer to experiment, incorporating polarization and nuclear quantum effects is absolutely required even though a substantial increase in computer time should be expected. The test proposed here, being quantitative and selecting properties from all phases of water can be useful in the future to identify progress in the modelling of water.

/pdf/simulating-water-with-rigid-non-polarizable-models-a-general-4316yz77p3.pdf

Simulating water with rigid non-polarizable models: a general perspective

Properties of aqueous solutions of lithium and calcium chlorides: formulations for use in air conditioning equipment design

Consistent with the latest experimental data and the recent internationally recommended values for the critical parameters, we have developed compact and accurate representative equations for the following properties on the saturation line of ordinary (light) water substance: vapor pressure, density, enthalpy and entropy of both the saturated liquid and the saturated vapor. These equations form the basis of a ‘‘Supplementary Release on Saturation Properties of Ordinary Water Substance’’ issued by the International Association for the Properties of Steam (IAPS).

International Equations for the Saturation Properties of Ordinary Water Substance

In order to define the phase boundary between the solid phase (ice) and the fluid phase (liquid and gas) of ordinary (light) water substance in pressure‐temperature coordinates, correlation equations for the pressure along the melting curve of the various modifications of ice as well as for the pressure along the sublimation curve are presented. The five equations for the melting pressure of the ice phases, ice I, ice III, ice V, ice VI, and ice VII, which only contain one to three fitted coefficients, cover the pressure range from the ‘‘normal’’ triple point to 20000 MPa. In this entire range the equations represent the selected measurements of the melting pressure within their experimental uncertainty. The 2‐coefficient equation for the sublimation pressure covers the temperature range from 190 K to the triple point (273.16 K). The equations correspond to the new International Temperature Scale of 1990 (ITS‐90). All these equations form the basis of the revised release on the pressure along the melting and sublimation curves of ordinary water substance. A verbatium copy of this release is presented in the Appendix of this paper. §

International Equations for the Pressure Along the Melting and Along the Sublimation Curve of Ordinary Water Substance

The current knowledge of thermodynamic properties of ordinary water substance is summarized in a condensed form of a set of skeleton steam tables, where the most probable values with the reliabilities on specific volume and enthalpy are provided in the range of temperatures from 273 to 1073 K and pressures from 101.325 kPa to 1 GPa and at the saturation state from the triple point to the critical point. These tables have been accepted as the IAPS Skeleton Tables 1985 for the Thermodynamic Properties of Ordinary Water Substance(IST‐85) by the International Association for the Properties of Steam(IAPS). The former International Skeleton Steam Tables, October 1963(IST‐63), have been withdrawn by IAPS. About 17 000 experimental thermodynamic data were assessed and classified previously by Working Group 1 of IAPS. About 10 000 experimental data were collected and evaluated in detail and especially about 7000 specific‐volume data among them were critically analyzed with respect to their errors using the statistical method originally developed at Keio University by the first three authors. As a result, specific‐volume and enthalpy values with associated reliabilities were determined at 1455 grid points of 24 isotherms and 61 isobars in the single‐fluid phase state and at 54 temperatures along the saturation curve. The background, analytical procedure, and reliability of IST‐85 as well as the assessment of the existing experimental data and equations of state are also discussed in this paper.

A. Saul

Papers

International Equations for the Saturation Properties of Ordinary Water Substance

International Equations for the Pressure Along the Melting and Along the Sublimation Curve of Ordinary Water Substance

New International Skeleton Tables for the Thermodynamic Properties of Ordinary Water Substance

Correlation Equations for the Vapour Pressure and for the Orthobaric Densities of Water Substance