Sharp dielectric surfaces

The sharp dielectric surface was implemented for the Polarizable Continuum Model (PCM) for the first time by Bonaccorsi et al. [9] and further developed by Hoshi etal. [10] The only requirements for the employment of the PCM is a knowledge of the constitutive parameters of the system geometry of the dielectrics and corresponding dielectric constants. The same model has been subsequently revisited in 2000 [11] supplemented with the modelling of nonelectrostatic interactions (see later). 

Corona discharge is the simplest type of plasma generator. A feature of the corona discharge, which differentiates it from the other discharges, is that no dielectric is involved. Instead, an electron avalanche is initiated from a sharp metallic surface where the radius of curvature is small. The electric field has to be pulsed in order to prevent the plasma from going into the thermal mode and forming an arc. The electric field in corona reactors is about 50 kV/cm. 

In the special case of sharp dielectric boundaries the dielectrics is separated into domains of uniform dielectric coefficients. The dielectric coefficient jumps from one value to another along a boundary. Let us denote the surface of the dielectric boundaries by B. Then the induced charge is a surface charge on the dielectric interfaces (if the induced charges around the source charges are not considered), and the volume integral in Eq. (15) becomes a surface integral over the surface B,... 

Although often small, ICEO flows at dielectric surfaces need not be negligible in microfluidic devices, due to large local fields. For example, an electric field passing around a sharp comer in a dielectric microchannel can drive a strong nonlinear electrokinetic jet of ICEO flow due to the comer field singularity [5], as shown in Fig. lb. In very simple terms, this phenomenon can be understood as half of the quadmpolar flow around a polarizable particle, where the jet corresponds to the outward flow at the equator in Fig. 2c. 

It is well known that the SPR may be registered as the sharp minimum of the reflection coefficient for the plane-parallel light which depends on the incidence angle. The position of the resonance angle and the minimum depth of the incidence are determined by the parameters of the metal layer, and the optical constants of the external medium. As molecules adsorb and interact at the gold surface, the dielectric properties of the formed layer change, which leads to the transformation of the resonance curve and to the displacement of the resonance angle [7, 9, 15]. 

The advantage of the IEF-PCM formulation in this respect is that the surface between the two dielectrics is hidden within the Green s function and only the explicit description of the molecular cavity is needed as for bulk IEF-PCM. Although the IEF-PCM implementation was able to overcome several numerical problems as a result of the explicit description of the dielectric interface, the BEM discretization technique for those tesserae in close proximity of the sharp interface could still potentially lead to unphysical divergences. 

In the planar geometry we consider a dielectric slab shown in Fig. 1. Two semi-infinite dielectrics of dielectric coefficients S and 3 are separated by a dielectric slab of thickness D and with a dielectric coefficient 2. The boundaries of the slab are flat, sharp, and parallel. This can be regarded as a simple model of a membrane. This case has been studied in our previous paper [58] where MC simulation results have been shown for the distribution of hard sphere ions around a slab. Nevertheless, in our previous work, we did not use the SC approximation. In the following, we will show that it is necessary only if the width of the slab is small compared to the width of the surface elements. 

In the preceding derivation of the frequencies of surface polaritons and surface excitons the boundary conditions were applied at a sharp boundary without surface currents and charges. In this simplest version of the theory the so-called transition subsurface layer has been ignored however, this layer is always present at the interface between two media, and its dielectric properties differ from the dielectric properties of the bulk. Transition layers may be of various origins, even created artificially, e.g. by means of particular treatment of surfaces or by deposition of thin films of thickness dphenomenological theory it is rather easy to take account of their effects on surface wave spectra in an approximation linear in k (15). 

The continuum model of the solvent in the BE method ignores all the solvent-specific interactions and assumes that there is a sharp boundary between the dielectric constants of the solute and the solvent. These are very serious approximations, but the method works and gives accurate estimates of the total solvation energies [5,19,23]. Parameters of the method include the vdW radii of the solute atoms, which are necessary to compute the cavity surface, and the dielectric constant of the solute (ss). 

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