Dielectric constant definition

Debye-Falkenhagen-type forces do not suffer from the vanishing of the rotationally averaged interaction since they arise from a force due to induction which can track the rotation of the particle. Unlike the Keesom force in which, in principle, the interaction of distributed point charges are considered, induction forces are dependent upon a collective molecular or material property, the static dielectric constant. Definition of the domain of validity for the classical calculation is required and has been given in the case of metals [5.17]. Those authors pointed out that if the surface of the metal were taken at the center of mass of the surface charge distribution, then classical electrostatic calculations would be valid. 

Aqueous titrations of amines are amply discussed elsewhere d. Nonaqueous titrations. Three main purposes may be served by carrying out titrations in nonaqueous solvents increased solubility, change of the pH scale, and resolution of mixtures. The prediction of a potentiometric titration curve in an arbitrary solvent is a difficult task, in which many factors intervene, such as dielectric constant, definition of acid and base in relation to the solvent, electrodes, actual structure of conjugate acids and bases, etc. Acetic acid, sulphuric acid, acetonitrile, and alcohol-water mixtures have been extensively studied and were reviewed elsewhere Some solvents will be treated here briefly ... 

In a medium where the relative dielectric constant is e, the force between fixed chages at a definite separation is decreased by the dimensionless factor e. This is true regardless of the system of units and is incorporated into Eqs. (10.101) and (10.102) by dividing the right-hand side of each by e. ... 

If we now transfer our two interacting particles from the vacuum (whose dielectric constant is unity by definition) to a hypothetical continuous isotropic medium of dielectric constant e > 1, the electrostatic attractive forces will be attenuated because of the medium s capability of separating charge. Quantitative theories of this effect tend to be approximate, in part because the medium is not a structureless continuum and also because the bulk dielectric constant may be an inappropriate measure on the molecular scale. Eurther discussion of the influence of dielectric constant is given in Section 8.3. 

Such a mechanism is open to serious objections both on theoretical and experimental grounds. Cationic polymerizations usually are conducted in media of low dielectric constant in which the indicated separation of charge, and its subsequent increase as monomer adds to the chain, would require a considerable energy. Moreover, termination of chains growing in this manner would be a second-order process involving two independent centers such as occurs in free radical polymerizations. Experimental evidence indicates a termination process of lower order (see below). Finally, it appears doubtful that a halide catalyst is effective without a co-catalyst such as water, alcohol, or acetic acid. This is quite definitely true for isobutylene, and it may hold also for other monomers as well. 

With the proper definitions of ex and k0, this equation is applicable to the metal as well as to the electrolyte in the electrochemical interface.24 Kornyshev et al109 used this approach to calculate the capacitance of the metal-electrolyte interface. In applying Eq. (45) to the electrolyte phase, ex is the dielectric function of the solvent, x extends from 0 to oo, and x extends from L, the distance of closest approach of an ion to the metal (whose surface is at x = 0), to oo, so that kq is replaced by kIo(x — L). Here k0 is the inverse Debye length for an electrolyte with dielectric constant of unity, since the dielectric constant is being taken into account on the left side of Eq. (45). For the metal phase (x < 0) one takes ex as the dielectric function of the metal and limits the integration over x ... 

There are basically two semicontinuum models one owing to Copeland, Kestner, andjortner (1970) (CKJ) and another to Fueki, Feng, and Kevan (1970, 1973 Fueki et al, 1971) (FFK). The calculations were designed for eh and eam,but have been extended to other polar media (Fueki et al., 1973 Jou and Dorfman, 1973). In these four or six solvent molecules form the first solvation layer in definite arrangement. Beyond that, the medium is taken as a continuum with two dielectric constants and a value of VQ, the lowest electron energy in the conduction state. 

The paired cation Pn+A The relative concentrations of the paired and unpaired cations are governed by an Ostwald-type equilibrium with dissociation constant KD. The magnitude of this is governed by the size and shape of the ions and the dielectric constant of the solvent. In contrast to anionic polymerisations, there is no definite evidence for distinguishing between tight and solvent-separated ion-pairs. 

An ion adsorbed on the surface of a suspension will draw near to it an ion of opposite sign in the solution these ions in the double layer are thus hound and can only escape if their kinetic energy exceeds a definite critical value W. If the chemically adsorbed ions have a valency % and n is the valency of the opposite charged ions in the liquid of dielectric constant K in contact with the solid and separated from the former by a distance x, we obtain... 

This definition for K holds only for monovalent ions and depends on the aqueous dielectric constant (c), Boltzmann s energy (k T), and the electronic charge (e). The Debye length varies inversely with the ionic strength of the solution and thus measures the ability of the ions to screen the protein/interface interactions. 

We could point to several reasons why the model fails to predict reality. For one, it neglects ion-ion interactions, which definitely become important at high concentrations. A second error, and perhaps the most important, is the assumption of point-charge ions. Finally comes the value of the dielectric constant, which was taken as a constant in the region between the electrode and the bulk of the solution. 

This equation, together with the definition of the dielectric constant (Equation IX-2), leads at once to the equation... 

However, in contrast to the cases of complex elastic modulus G and dielectric constant e, the imaginary part of the piezoelectric constant, e", does not necessarily imply an energy loss (Holland, 1967). In the former two, G"/G and e"/e express the ratio of energy dissipation per cycle to the total stored energy, but e"/e does not have such a meaning because the piezoelectric effect is a cross-coupling effect between elastic and electric freedoms. As a consequence, e" is not a positive definite quantity in contrast to G" and e". In a similar way to e, however, the Kramers-Kronig relations (Landau and Lifshitz, 1958) hold for e ... 

The first property of solvents to be considered is the dielectric constant, e. The dielectric constant of a substance measures the reduction of the strength of the electric field surrounding a charged particle immersed in the substance, compared to the field strength around the same particle in a vacuum. The dielectric constant is a macroscopic property that is, its definition and measurement... 

---