Dielectric constant terms

The first term represents the forces due to the electrostatic field, the second describes forces that occur at the boundary between solute and solvent regime due to the change of dielectric constant, and the third term describes ionic forces due to the tendency of the ions in solution to move into regions of lower dielectric. Applications of the so-called PBSD method on small model systems and for the interaction of a stretch of DNA with a protein model have been discussed recently ([Elcock et al. 1997]). This simulation technique guarantees equilibrated solvent at each state of the simulation and may therefore avoid some of the problems mentioned in the previous section. Due to the smaller number of particles, the method may also speed up simulations potentially. Still, to be able to simulate long time scale protein motion, the method might ideally be combined with non-equilibrium techniques to enforce conformational transitions. 

The energy of solvation can be further broken down into terms that are a function of the bulk solvent and terms that are specifically associated with the first solvation shell. The bulk solvent contribution is primarily the result of dielectric shielding of electrostatic charge interactions. In the simplest form, this can be included in electrostatic interactions by including a dielectric constant k, as in the following Coulombic interaction equation ... 

This result, called the Clausius-Mosotti equation, gives the relationship between the relative dielectric constant of a substance and its polarizability, and thus enables us to express the latter in terms of measurable quantities. The following additional comments will connect these ideas with the electric field associated with electromagnetic radiation ... 

The capacitance of a condenser ia terms of its physical dimensions and the dielectric constant of the iasulation is given by the foUowiag equatioa, where C = capacitance ia microfarads, K = dielectric coastant of the iasulatioa, A = area of plates ia square centimeters, and t = thickness of the iasulation ia centimeters. 

Principles in Processing Materials. In most practical apphcations of microwave power, the material to be processed is adequately specified in terms of its dielectric permittivity and conductivity. The permittivity is generally taken as complex to reflect loss mechanisms of the dielectric polarization process the conductivity may be specified separately to designate free carriers. Eor simplicity, it is common to lump ah. loss or absorption processes under one constitutive parameter (20) which can be alternatively labeled a conductivity, <7, or an imaginary part of the complex dielectric constant, S, as expressed in the foUowing equations for complex permittivity ... 

Relative Permittivity lEC 250. The term relative permittivity is currently more commonly used than the term dielectric constant used by the author and most of the references quoted in this chapter. As explained in this chapter, it is a ratio and thus dimensionless. 

Wetting and capillarity can be expressed in terms of dielectric polarisabilities when van der Waals forces dominate the interface interaction (no chemical bond or charge transfer) [37]. For an arbitrary material, polarisabilities can be derived from the dielectric constants (e) using the Clausius-Mossotti expression [38]. Within this approximation, the contact angle can be expressed as ... 

Ultimately physical theories should be expressed in quantitative terms for testing and use, but because of the eomplexity of liquid systems this can only be accomplished by making severe approximations. For example, it is often neeessary to treat the solvent as a continuous homogeneous medium eharaeterized by bulk properties such as dielectric constant and density, whereas we know that the solvent is a molecular assemblage with short-range structure. This is the basis of the current inability of physical theories to account satisfactorily for the full scope of solvent effects on rates, although they certainly can provide valuable insights and they undoubtedly capture some of the essential features and even cause-effect relationships in solution kinetics. Section 8.3 discusses physical theories in more detail. 

The charge density on the surface of the hole, cr(rs), is given by standard electrostatics in terms of the dielectric constant, e, and the electric field perpendicular to the surface, F, generated by the charge distribution within the cavity. 

The Amount of Free Energy Lost by a Dielectric. The above considerations apply to fields of any intensity. When we are dealing only with ordinary weak fields, for which the polarization is proportional to the field (the straight part of the curve in Fig. 5), the substance under discussion is said to possess a dielectric constant. This will be denoted by t. In a vacuum e is set equal to unity and in a dielectric the polarization is proportional to (t — 1). The loss of free energy by the dielectric may be expressed in terms of e. In Note 1 of the Appendix at the end of this book it is shown that, when a homogeneous slab is introduced into a uniform field of initial intensity X, the free energy lost per unit volume amounts to... 

The satisfactory result shown in Table 12 suggests that one might give a more detailed and quantitative discussion of the variation with temperature. If we are to do this, we need some standard of comparison with which to compare the experimental results. Just as wq compare an imperfect gas with a perfect gas, and compare a non-ideal solution with an ideal solution, so we need a simple standard behavior with which to compare the observed behavior. We obtain this standard behavior if, supposing that. /e is almost entirely electrostatic in origin, we take J,np to vary with temperature as demanded by the macroscopic dielectric constant t of the medium 1 that is to say, we assume that Jen, as a function of temperature is inversely proportional to . For this standard electrostatic term we may use the notation, instead of... 

Places the Langevin dipoles at grid points. I The (1 +r0) term is a distance dependent I dielectric constant for the non iterative LD I procedure ( See references 4). 

As we have shown, the polarization force depends not only on the topography [through the f(R z) term] and dielectric constant e, but also on the local contact potential 4). As we shall see now, ac bias modulation and lock-in detection allow these contributions to be separated. 

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