Nonlocal Poisson equation

Spatial dispersion effects are usually considered separately from time dependences and correspond to static limit to = 0. Consequently s(k, 0) = s(k) and x(k, 0) = x(k) are basic susceptibility functions. Within the LRA the relation similar to Equation (1.131) is valid. It formally represents a solution to the nonlocal Poisson equation with a -dependent susceptibility. 

Let us consider the nonlocal Poisson equation V(sW) = -4irp in the uniform space. The singular boundary condition on the surface of the solute cavity is neglected. Note that this condition furnishes the mechanisms of the excluded volume effect. The solute is charged and spherical, i.e. p(r) = p(R). The solution T (A ) is obtained by using Fourier transform [6,16] it is valid outside the cavity (R > a),... 

Figure 3.31 As (due to orientational response of aqueous solvent) versus e, calculated for ET in a large binuclear transition metal complex (D (Ru2+/3+) and A (Co2+/3+) sites bridged by a tetraproline moiety) molecular-level results obtained from a nonlocal polarization response theory (NRFT, solid lines) continuum results are given by dashed lines, referring to numerical solution of the Poisson equation with vdW (cont./vdW) and SAS (cont./SAS) cavities, or as the limit of the NRFT results when the full k-dependent structure factor (5(k)) is replaced by 5(0) 5(k) for bulk water was obtained from a fluid model based on polarizable dipolar spheres (s = 1.8 refers to ambient water (square)). For an alternative model based on TIP3 water (where, nominally, 6 = ), ambient water corresponds to the diamond. (Reprinted from A. A. Milishuk and D. V. Matyushov, Chem Phys., 324, 172. Copyright (2006), with permission from Elsevier).

Gruen and Marcelja considered that the electric and polarization fields are not proportional in the vicinity of a surface and that while the electric field has the ion concentrations as its source, the source of the polarization field is provided by the Bjerrum defects. The coupled equations for the electric and polarization fields were derived through a variational method. Attard et al.14 contested the Gruen—Marcelja model because, to obtain an exponential decay of the repulsion, the nonlocal dielectric function was assumed to have a simple monotonic dependence upon the wavelength (eq 33 in ref 13). This was found to be inconsistent with the exact expression for multipolar models.14 In addition, the characteristic decay length for polarization (denoted in eq 18, ref 13) is inversely proportional to the square of the (unknown) concentration of Bjerrum defects in ice. While at large concentrations of Bjerrum defects the disordered ice becomes similar to water and the traditional Poisson—... 

A diffuse picture of the compact layer has been considered [19], According to this hypothesis, adsorbed ions can penetrate into the compact layer, which consists of solvent dipoles, analogous to nonlocalized electron gas penetration from a metal electrode to an aqueous electrolyte solution. Here, a penetrating ion can act as a hydrophobic anion in the organic phase and potential distribution (p(x) near to the point of zero charge can be calculated using the Poisson-Boltzmann equation ... 

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