Dielectric response spatially varying

P.7.a.l. Spatially varying dielectric response in a finite layer, asymmetric, e(z) discontinuous at interfaces, with retardation... 

A similar approach to the boundary condition for the potential at the metal-solution interface has been applied by Biesheuvel et al., in consideration of diffuse charge effects in galvanic cells, desalination by porous electrodes, and transient response of electrochemical cells (Biesheuvel and Bazant, 2010 Biesheuvel et al., 2009 van Soestbergen et al., 2010). However, their treatment neglected the explicit effect of In principle, the PNP model could be modified to incorporate size-dependent and spatially varying dielectric constants in nanopores, as well as ion saturation effects at the interface. However, in a heuristic fashion, such variations could be accounted for in the Helmholtz capacitance of the Stern double layer model. 

The force fields used by scientists for simulations have been developed with distinct traditions, each appropriate for its own use. In computational chemistry, interest has been in bulk properties of solutions and proteins, in the thermodynamic limit in which boundary conditions do not appear explicitly and where equilibrium (i.e., zero flux of all species) is present. The thermodynamic limit of computational chemistry implies a spatial uniformity of bulk properties that can be analyzed with periodic boundary conditions if the period is longer than the spatial inhomogeneities of the bulk solution. Contrarily, in computational electronics, the interest has focused on electron devices, which exchange charge with their environment through geometrically and electrically complex boundaries and where internal dielectric discontinuities exist. Simulations are usually performed by varying the applied bias in order to reproduce transient nonequilibrium conditions and to obtain a record of the response of the simulated devices. 

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