Abstract
Periodic supercell models of electric double layers formed at the interface between a charged surface and an electrolyte are subject to serious finite size errors and require certain adjustments in the treatment of the long-range electrostatic interactions. In a previous publication Zhang and Sprik [Phys. Rev. B 94, 245309 (2016)], we have shown how this can be achieved using finite field methods. The test system was the familiar simple point charge model of a NaCl aqueous solution confined between two oppositely charged walls. Here this method is extended to the interface between the (111) polar surface of a NaCl crystal and a high concentration NaCl aqueous solution. The crystal is kept completely rigid and the compensating charge screening the polarization can only be provided by the electrolyte. We verify that the excess electrolyte ionic charge at the interface conforms to the Tasker 1/2 rule for compensating charge in the theory of polar rock salt (111) surfaces. The interface can be viewed as an electric double layer with a net charge. We define a generalized Helmholtz capacitance CH which can be computed by varying the applied electric field. We find CH=8.23 μF cm-2, which should be compared to the 4.23 μF cm-2 for the (100) non-polar surface of the same NaCl crystal. This is rationalized by the observation that compensating ions shed their first solvation shell adsorbing as contact ions pairs on the polar surface.
Highlights
Crystals exposing a face bearing a net charge are intrinsically unstable if, in addition, the unit cell has a net dipole moment perpendicular to the surface
While our procedure of a fractional increase of the charge of all ions of one species (Na+ or Cl) is nonphysical, we argue that the electrostatics of an electric double layer (EDL) formed by this system is similar to that of the “regular” EDL of Ref. 23
Our calculations show that the excess charge in a high concentration NaCl aqueous solution adjacent to a rigid NaCl (111) surface complies with the Tasker rule for a polar surface of this geometry
Summary
Crystals exposing a face bearing a net charge are intrinsically unstable if, in addition, the unit cell has a net dipole moment perpendicular to the surface. Such a termination is referred to as a type III polar surface in the classification by Tasker.[1] Tasker explained the instability of type III surfaces by showing that the energy diverges with increasing thickness of the crystal (polar catastrophe). The review of Ref. 2 is restricted to oxide materials It was updated in 2008 in collaboration with Goniakowski[3] and again in 2013, including nano-objects, such as thin films.[4]. Because of their small size, they can sustain the polarization field driving the instability in larger systems
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have