Water phases under high electric field and pressure applied simultaneously I. Danielewicz-Ferchmin a , E. 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 Received 24 January 2006; accepted 25 October 2006 Available online 28 February 2007 Abstract The rigorous equation of state of an open system containing water in an electric field above 10 8 Vm - 1 under pressure applied in the range 10 - 4 ≤ P o ≤ 0.8 GPa leads to phase diagrams with two possible kinds of phase transitions at 293 K. The first one is the discontinuous phase transition under pressure applied in the range 10 - 4 ≤ P o ≤ 0.05 GPa in the Π, σ coordinates (Π is the electrostriction pressure and σ denotes the surface charge density at an adjacent charged surface). The second one represents the continuous phase transition under pressure applied in the range 10 - 4 ≤ P o ≤ 0.8 GPa; it occurs at higher values of σ than the former one. © 2007 Published by Elsevier B.V. PACS: 05.70.Np; 68.35.Rh; 77.22.-d; 77.22.Ch Keywords: Water; Electrochemistry; Phase diagram; Thermodynamics 1. Introduction Water is known for its rich phase diagram in the P , V , T variables. However, our knowledge of H 2 O phases under the action of high electric fields E >10 8 Vm - 1 seems to remain still in its infancy and only a few isolated experimental facts are known [1–7] accompanied by a number of theoretical approaches to the question. Thus, any attempt to clarify the situation seems substantiated. The electric fields above 10 8 Vm - 1 can be encountered, e.g., in hydration layers arising when charged surfaces with surface (free) charge density σ o ≥ 10 - 3 Cm - 2 are immersed in water. Such charge densities can exist at the surfaces of flat [4] or spherical (mercury droplets) [1,2] metallic electrodes, oxides, for instance TiO 2 [3] and RuO 2 [6], at surfaces of proteins [8–12] and micelles as well as at internal surfaces of reverse micelles [13]. High local electric fields exist also around ions in solutions. In this paper the properties of water in a high electric field above 10 8 Vm - 1 in various conditions specified by temperature and pressure applied are discussed. Our earlier effort has been concentrated on establishing the effect of high electric field on the properties of water (at that time solely under atmospheric pressure), and in particular the coexistence of its different phases [14,15]. The most striking earlier result was the finding of a region of coexistence of two water phases (B and A) under various temperatures together with a corresponding “electric” critical point. A literature experiment apparently confirmed the existence of the latter [1,2]. Herein, we discuss what happens to the same system under the action of externally applied pressure of the order of tens or hundreds of MPa. It will be shown that at ambient temperature under various moderate pressures of several tens of MPa one also finds a region of coexistence of two phases (related to a first-order, discontinuous phase transition) and a corresponding critical point. The discussion is based on the statistical and thermodynamic approach [15] taking into account the dipoles of water molecules. The current analysis leads to predictions of some new effects in water in the electric field under pressure. We find a discontinuous transition induced by electric field at various pressures. The knowledge of the permittivity ϵ is needed to evaluate the local electrostriction pressure Π [16] under the pressure P o applied. The approach of Refs. [17,18] is applicable to ϵ of water in high electric fields and in the temperature and pressure range in which H 2 O is liquid. The electrostriction pressure coefficient is introduced, defined by the slope γ of the Π vs. σ isotherms. Yet another possible second order (continuous) phase transition with the related order parameter hcoshi (mean cosine between the electric field and Journal of Molecular Liquids 135 (2007) 75 – 85 www.elsevier.com/locate/molliq ⁎ Corresponding author. Tel.: +48 61 8695123; fax: +48 61 8684524. E-mail address: arfer@ifmpan.poznan.pl (A.R. Ferchmin). 0167-7322/$ - see front matter © 2007 Published by Elsevier B.V. doi:10.1016/j.molliq.2006.10.006