Dielectric Domains-Electrostatic Fields

In contrast to conductive material with the ability to accommodate electric flow fields, dielectric matter, as well as vacuum, may exhibit electrostatic fields. Although the physical condition of the examined dielectric domain is not limited to solid state, it may be described in analogy with deformable structures as a continuum. In comparison to the mechanical fields, the tensors characterizing the electrostatic fields will be one order lower. A comprehensive description of electrical engineering is given by Paul [140], while electromagnetic fields are detailed by Fischer [74], Lehner [120], and Reitz et al. [153]. 

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This fundamental principle of physics is given by the axiom of Remark 3.1 in its most general formulation, where SW is the total virtual work of the system. For mechanical fields in deformable structures as well as for electrostatic fields in dielectric domains, it can be restated by the equality of internal 51A and external 6V contributions. 

Electric systems may be treated like mechanical ones the quantities appearing in electricity have a lower tensorial order the mechanical displacement is a vector field, the electric potential is a scalar field. The electrostatic equilibrium of an infinitesimal volume element of a dielectric domain, given by Eq. (3.34), may be multiplied by the scalar field of a virtual electric potential 6(p and integrated over the Volume A, yielding... 

The membrane/protein interface with the bulk is dominated by the discontinuity of the physical chemical properties of the reaction space. On one side of the borderline there is a low viscosity, high dielectric constant matrix where rapid proton diffusion can take place. On the other side of the boundary, there is a low dielectric matrix that is covered by a large number of rigidly fixed charged residues. The dielectric boundary amplifies the electrostatic potential of the fixed charges and, due to their organization on the surface of proteins, a complex pattern of electrostatic potentials is formed. These local fields determine the specific reactivity of the domain, either with free proton or with buffer molecules. In this chapter we shall discuss both the general properties of the interface and the manner in which they affect the kinetics of defined domains. 

A comparative study of ultrathin dielectric (an azo-compound) and ferroelectric (copolymer P(VDF-TrFE)) Langmuir-Blodgett (LB) films has been carried out by Electrostatic Force Microscopy (EFM). Films were poled locally by a strong d.c. field applied between a conductive tip of an Atomic Force Microscope (AFM) and the bottom A1 electrode. The electrically poled domain was studied by EFM using a weak a.c. electric field and a lock-in amplifier technique. Two modes, a contact and non-contact ones, allowed for the measurement of field a in the air gap between the film and the tip and the piezoelectric distortion of the film due to the d.c. field aligned spontaneous polarization. Simultaneously the topographic relief of the same area was imaged. The results confirm unequivocally a possibility to switch ferroelectric LB film locally by an AFM tip. 

Given a molecular or supra-molecular system embedded in a solvent charge distribution, the solute-solvent interaction can be modelled using a mean field (MF) approach [21-24], which treats the solvent as a continuum fully defined by a dielectric constant (s) and by a shape function, uniquely identifying the space regions where the solute and the solvent are placed. The boundary between the two domains is a compact cavity S, which in Fig. 17.2 has been represented as a spherical boundary surface including the explicit molecules. Then, the major issue related to such a scheme is how to model the interactions between the continuum and the explicit molecules placed inside the cavity. In a static picture, such interactions are of two types, electrostatic and non-electrostatic, whereas when such a model is used in MD simulations, an additional potential is included, in order to ensure that all the molecules remain confined inside the cavity during the simulation with a correct density up to the boundary [21]. 

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