Surfaces of ionic solids interacting with an ionic solution can build upcharge by exchange of ions. The surface charge is compensated by a strip ofexcess charge at the border of the electrolyte forming an electric doublelayer. These electric double layers are very hard to model using the supercellsmethods of computational condensed phase science. The problem arises when thesolid is an electric insulator (as most ionic solids are) permitting a finiteinterior electric field over the width of the slab representing the solid inthe supercell. The slab acts as a capacitor. The stored charge is a deficit inthe solution failing to compensate fully for the solid surface charge. Here weshow how these problems can be overcome using the finite field methodsdeveloped by Stengel, Spaldin and Vanderbilt [Nat. Phys. {\bf 5}, 304, (2009)].We also show how the capacitance of the double layer can be computed onceoverall electric neutrality of the double layer is restored by application of afinite macroscopic field $\mathbf{E}$ or alternatively by zero electricdisplacement $\mathbf{D}$. The method is validated for a classical model of asolid-electrolyte interface using the finite temperature molecular dynamicsadaptation of the constant field method presented previously [Phys. Rev. B,2016, 93, 144201]. Because ions in electrolytes can diffuse across supercellboundaries, this application turns out to be a critical illustration of themultivaluedness of polarization in periodic systems.
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