Sharp dielectric boundaries

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,... 

The permeation rate of ions across membranes can be estimated using a continuum dielectric model of a water-membrane system. In this model, both water and membrane are represented as homogeneous, isotropic media, characterized by dielectric constants and ej, respectively, and separated by a sharp planar boundary. If the ion is represented as a point charge q located at the center of a cavity of radius a, the change in the excess chemical potential associated with the transfer of the ion from bulk water to the center of the membrane (the free energy barrier), is expressed in this model as [58,59] ... 

The next question to be discussed was already mentioned in Section 2.1, namely, since the electrostatic problem, with its sharp boundary and its homogeneous solvent dielectric constant, already represents a somewhat unrealistic idealization of the true molecular situation, how important is it to solve that problem by exact electrostatics We would answer that this is not essential. Although it presumably can t hurt to solve the electrostatics accurately, except perhaps by raising the computer time, it may be unnecessary to do so in order to represent the most essential physics, and a simpler model may be more manageable, more numerically stable, and even more interpretable. This is the motivation for the GB approximation and COSMO. 

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). 

The Rate Constant of Electron Transfer We shall commence by assuming that the liquid liquid interface can be described in terms of a sharp boundary between water and a lower dielectric medium. The single ET process of Eq. (1) involves the approaching of the reactants to the interface as schematically represented in Eig. 3. The observed rate of ET is given by... 

It should be noticed that this expression is obtained for a sharp boundary between the dielectric therefore it may not be directly applicable in the mixed-solvent region model. The equivalent expression for the successor complex (w°) can be easily obtained by replacing the charges of the reactants by the corresponding products. For the sake of comparison, if we introduce the parameters employed earlier for estimating it can be obtained that... 

Before closing this section on the three-phase system and the evaluation of film optical properties, a word of caution seems appropriate. Some 15 years ago, when we started to evaluate monolayer optical constants by the three-phase model with sharp boundaries, I was much more optimistic than I am today. The model discussed above (which still seems to be the only one around) has a number of severe drawbacks. For example, the validity of the concept of a macroscopic (continuum) theory for monolayer and submonolayer adsorbates was questioned quite early, although it was hoped that the model would yield an effective film dielectric constant which represents at least average values of the absorptive and refractive properties of the thin film. Application of the continuum theory is especially critical for the direction normal to the... 

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