Effect of Electric Field Orientation on the Mechanical and Electrical Properties of Water Ices: An Ab-initio Study Giuseppe Cassone, †,‡,§,∥,⊥ Paolo V. Giaquinta, †,# Franz Saija,* ,‡ and A. Marco Saitta §,∥,¶ † Dipartimento di Fisica e di Scienze della Terra, Universita ̀ degli Studi di Messina, Contrada Papardo, 98166 Messina, Italy ‡ CNR-IPCF, Viale Ferdinando Stagno d’Alcontres 37, 98158 Messina, Italy § UMR 7590, IMPMC, UPMC Univ Paris 06, Sorbonne Universite ́ s, F-75005 Paris, France ∥ UMR 7590, IMPMC, CNRS, F-75005 Paris, France ABSTRACT: We present a first-principles study of the properties of ordinary hexagonal ice (phase I h ) and of its proton-ordered version (phase XI) under the action of static electric fields. We compute the mechanical response to the field in addition to the ionic current−voltage diagrams; we also analyze several other microscopic aspects of the proton transfer mechanism, with particular emphasis on the role played by the oxygen sublattice in driving molecular dissociation. We further study the topological aspects of the mechanical and electrical responses by orienting the external field along two different crystalline directions in both ice samples. At variance with ice I h , ice XI displays an anisotropic behavior in the range of explored field intensities. In fact, when the direction of the field coincides with the ferroelectric axis, sustained molecular dissociation and proton transfer events are both observed just beyond a given field intensity; instead, the two processes exhibit different activation thresholds when the field is oriented along another symmetry axis. The underlying mechanism of molecular dissociation appears to be the same in solid and liquid water independently of the direction of the field. I. INTRODUCTION Water is for some aspects one of the simplest molecules in nature but several of its properties are not yet fully understood, mainly because of the subtle role played by hydrogen bonds (H-bonds). In addition to the vast and still highly debated phenomenology exhibited by stable and metastable liquid water, 1 even the thermodynamics of its solid forms is rather baroque in that the phase diagram includes at least 16 crystalline structures. 2 At ambient conditions the stable solid phase is ice I h , in which molecules are located on the sites of a hexagonal lattice while being orientationally disordered (i.e., the proton sublattice is randomly distributed). By cooling KOH- doped ice I h down to a temperature of 72 K, one obtains ice XI, the proton-ordered counterpart of ice I h , 3,4 in which the dipole moment of each molecule is mainly oriented along the c-axis, its z-component thus being everywhere positive in the standard lattice. In the ice I h to ice XI first-order phase transition the hydroxide ions of KOH catalyze the rearrangement of H-bonds via the formation of defects which lead to an improved molecular mobility. In this way the molecules find a more stable arrangement by reducing the symmetry of the phase from P6 3 / mmc to Cmc2 1 , thus giving rise to the ferroelectric phase known as ice XI. The ordering of the proton sublattice also affects many important properties of the material, such as its electrical polarizability and conductivity. Actually, ice can be described as a “protonic semiconductor” and the understanding of its electrical behavior is highly relevant for even more complex systems and materials in which proton transfer (PT) takes place along H-bonded chains. In liquid water the process through which a H 2 O molecule dissociates, thus setting the acid or basic character (pH) of an aqueous solution, is known as protolysis and occurs according to the reaction ⇌ + − + 2HO OH HO 2 3 (1) in which, formally, a PT occurs between two water molecules. This is an extremely rare event at standard conditions, both in liquid and in solid water, as can be argued from their respective pH values. However, by applying an external electric field, it is possible to stimulate in a systematic fashion the molecular dissociation process and, eventually, to obtain an effective protonic current via correlated proton jumps which take place along H-bonded chains. In ice phases, hydronium and hydroxide ionic defects are responsible, together with Bjerrum (i.e., orientational) defects, for electrical transport processes. 2 Although the underlying microscopic motions that lead to the fast transport rate of H 3 O + have been known since the 1800s as the Grotthuss mechanism, 5 a satisfactory and coherent theoretical framework which may explain the complex processes associated with PT through point defects in aqueous systems is still missing. Recently, great effort has been made to fill the gap between theory and experimental observations, 6−10 also in relation to the transformation of proton-disordered systems into proton- Received: July 23, 2014 Revised: September 23, 2014 Published: September 29, 2014 Article pubs.acs.org/JPCB © 2014 American Chemical Society 12717 dx.doi.org/10.1021/jp507376v | J. Phys. Chem. B 2014, 118, 12717−12724