Dielectric saturation in water as quantitative measure of formation of well-defined hydration shells of ions at various temperatures and pressures. Vapor–liquid equilibrium case I. Danielewicz-Ferchmin a , E.M. Banachowicz a , A.R. Ferchmin b, ⁎ a Faculty of Physics, A. Mickiewicz University, Umultowska 85, PL-61-614 Poznań, Poland b Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, PL-60-179 Poznań, Poland abstract article info Article history: Received 25 May 2013 Accepted 13 June 2013 Available online 9 July 2013 Keywords: Water High electric field Static electric permittivity Dielectric saturation Electrochemistry Static electric permittivity  of water at equilibrium saturated vapor pressures in electric field in the range 10 8 b E b 10 11 Vm −1 was calculated. A quantitative measure of the dielectric saturation phenomenon was introduced. It is found that, according to the definition of this measure, well-defined first hydration shells of numerous ions investigated by X-ray and neutron scattering methods described in literature are electrical- ly saturated, and that at various conditions. Calculations show that around some ions, including Ag + , whose hydration shells are not saturated at ambient conditions, dielectric saturation of water can be achieved by in- creasing temperature and pressure up to the values not far from the critical ones. This is compared with ex- tended X-ray absorption fine structure (EXAFS) and XAFS data for Ag + and Rb + found in literature. © 2013 Published by Elsevier B.V. 1. Introduction Studies of ion hydration at elevated temperature T and pressure P are of importance to geochemistry [1,2]. They are also valuable in elec- trochemistry, e. g., when one looks for partial molar volumes of ions in aqueous solutions [3]. On the other hand, our limited knowledge of the behavior of water in very high electric field E of the order of ~1 GV m −1 calls for such studies. At the same time, experimental works on that topic are scarce due to technical difficulties and it seems worthy to look more closely at the properties of ionic hydration shells in such conditions. It should be noted that the knowledge of static electric permittiv- ity  is needed for finding many physical parameters of water in high field E, for example entropy, the related electrocaloric effect, as well as local electrostriction and electrostriction pressure in hydration shells, to mention but a few. Some of the values of  in high E are available in literature: those at ambient conditions [4], under ambient pressure at varied temperature [4] and at ambient T but under varied P [5]. Also,  of water at equilibrium with vapor (at various T and P) was calculated [6]. Two main topics will be pursued. Firstly, the question is raised: what are the dielectric properties of water in the field of the ions at elevated temperature and pressure? In particular, what are the conditions of its dielectric saturation characterized as the state in which the H 2 O dipole moments point toward (or out of) the ion center? To answer these questions, some  data taken from the preliminary short account [6] will be recalled for consistency and used herein as a basis for further de- velopment devoted to finding conditions for dielectric saturation. A quantitative measure of the dielectric saturation will be introduced as a special value of 〈cosθ〉 — the mean cosine of the angle θ between the direction of the dipole moment μ of a H 2 O molecule and the direction of the electric field E. The dielectric saturation state of water corre- sponds to the values of 〈cosθ〉 very close to unity, to be precisely defined later. The discussion is based on the statistical approach [4,5] taking into account the dipoles of water molecules as well as the presence of hydro- gen bonds. This approach is applicable to static electric permittivity  of water in high electric field and in temperature and pressure ranges in which H 2 O is liquid. Secondly, the dielectric saturation phenomenon in the hydration shells of ions will be confronted with the knowledge, available in liter- ature, on the character of the shells obtained by methods using X-rays and neutrons. It will be noted that well-defined hydration shells around many ions are characterized, at the same time, by the dielectric satura- tion state of water. It will be argued that ions can be categorized on the one hand as cat- ions with two or three excess elementary charges, e.g., Ni 2+ or Cr 3+ , which form well-defined hydration shells characterized by two re- solved peaks in the radial distribution function [7,8], with addition of Li + ions and on the other hand by other cations and anions with one ex- cess elementary charge revealing no such shells. At ambient conditions, Journal of Molecular Liquids 187 (2013) 157–164 ⁎ Corresponding author. Tel.: +48 61 8695213; fax: +48 61 8684524. E-mail address: arfer@ifmpan.poznan.pl (A.R. Ferchmin). 0167-7322/$ – see front matter © 2013 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.molliq.2013.06.005 Contents lists available at SciVerse ScienceDirect Journal of Molecular Liquids journal homepage: www.elsevier.com/locate/molliq