Calculation of the Dielectric Constant of Water to 1000°C and Very High Pressures

Abstract

Measured data for the dielectric constant of water exist to 550°C and 5000 bar and to 400°C and 3000 bar (critical temperature: 374°C). The present calculations extend to 1000°C and a density of 1 g cm−3 (16000 bar). Results are given for densities between 0.1 and 1 g cm−3 and for temperatures to 1000°C. From 400 to 1000°C at densities of 0.1, 0.5 and 1.0 g cm−3 the dielectric constant varies from 2.04 to 1.50, from 10.45 to 4.69 and from 29.4 to 11.06 respectively. The calculation is based on a hard‐sphere with dipole moment molecular interaction model and an approximate equation of Patey et al. based on a linearized hypernetted chain procedure. The effective hard sphere diameter of 2.68 Å has been derived from fitting to existing PVT data to 1000°C by a suitable equation of state. The effective dipole moment of 2.33 D was obtained from fitting to existing experimental dielectric constant values to 550°C and high densities with the Patey equation. Analogous calculations of the dielectric constants of supercritical, dense HCl, NH3 and CH3F are presented.

Supercritical Water as a Solvent

“…Figure 6 shows the dielectric constant to 1273 K and 1 g cm À3 , based on experimental data to 823 K and 500 MPa [44] and model calculations for higher temperatures. [45] e decreases with increasing temperature and increases with increasing density. The familiar high value of effi80 occurs only in a small region at low temperatures.…”

Dielectric constant and density of water as a function of pressure at constant temperature

“…To circumvent this problem we optimized an equation with the same general form as the Bradley equation, for a restricted set of protein folding/unfolding suitable temperatures (273K, 298K, 323K, 348K). Therefore, an equation of the form EP S = EP S(T, 10) + a 0 ln((a 1 + P )/(a 1 + 10)) (3) was used to fit the data available from the International Association for the Properties of Water and Steam [28]. The fitting was performed using the program Xmgr v2.10 [29].…”

“…High temperature and pressure conditions are important for engineering processes and geothermal studies. For this reason, several equations have been proposed for different ranges of temperature and pressure [1][2][3][4][5]. Almost all of them are entirely empirical.…”

“…Their formula correlates well a selected set of data from a collection of experimental data assembled by the authors. Another approach [3] uses a hard sphere model for the water molecule and a modified Ornstein-Zernike equation, where the parameters are fit to the experimental data for water. One of the simplest but effective description of the dielectric constant dependence on the pressure and temperature, proposed by Bradley and Pitzer [5], uses an equation suggested by Tait in 1880 for volumetric data.…”

Dielectric properties of water under extreme conditions and transport of carbonates in the deep Earth

“…Several models correlating experimental data suggested extrapolations of e 0 to ∼1 GPa and ∼1,300 K (e.g., refs. [13][14][15], which corresponds to only very shallow mantle conditions under the oceans; however, deeper mantle conditions relevant to plate tectonic processes could not be reached and different extrapolations showed poor agreement with each other (1). The current lack of knowledge of the dielectric constant of water under the P and T of the mantle hampers our ability to model water-rock interactions, to study the solubility of minerals, and hence our understanding of geochemical processes involving aqueous fluids below the Earth's crust.…”