Electrical opposites, theory

We shall now briefly illustrate the ideas which have been developed about the nature of the induced alternating polarity by a few examples. The first step towards a theory was made by Vor-lander, who called it the theory of electrical opposites. Vorlander assumes that in substituted benzenes the individual atoms carry charges whose sign is determined by the nature of the substituents, e.g. ... 

The Dehye-Hbckel theory of electrolytes based on the electric field surrounding each ion forms the basis for modern concepts of electrolyte behavior (16,17). The two components of the theory are the relaxation and the electrophoretic effect. Each ion has an ion atmosphere of equal opposite charge surrounding it. During movement the ion may not be exacdy in the center of its ion atmosphere, thereby producing a retarding electrical force on the ion. 

A finite time is required to reestabUsh the ion atmosphere at any new location. Thus the ion atmosphere produces a drag on the ions in motion and restricts their freedom of movement. This is termed a relaxation effect. When a negative ion moves under the influence of an electric field, it travels against the flow of positive ions and solvent moving in the opposite direction. This is termed an electrophoretic effect. The Debye-Huckel theory combines both effects to calculate the behavior of electrolytes. The theory predicts the behavior of dilute (<0.05 molal) solutions but does not portray accurately the behavior of concentrated solutions found in practical batteries. 

The theory outlined above is adequate for the description of a system of noninteracting bosons of mass m and spin 0 that are electrically neutral and that have no other quantum numbers to characterize them, for example, the neutral pions. It is, however, observed in nature that for particles with spin 0 that do have other quantum numbers specifying them, such as charge and strangeness, there always exist two kinds of particles with the same mass and spin but opposite additive quantum numbers such as charge and strangeness. By additive we mean that the quantum number for a system of such particles is the algebraic sum of the quantum numbers for the individual particles. 

The theory of Debye and Hiickel started from the assumption that strong electrolytes are completely dissociated into ions, which results, however, in electrical interactions between the ions in such a manner that a given ion is surrounded by a spherically symmetrical distribution of other ions mainly of opposite charges, the ionic atmosphere. The nearer to the central ions the higher will be the potential U and the charge density the limit of approach to the central ion is its radius r = a. 

The Schottky-Mott theory predicts a current / = (4 7t e m kB2/h3) T2 exp (—e A/kB 7) exp (e n V/kB T)— 1], where e is the electronic charge, m is the effective mass of the carrier, kB is Boltzmann s constant, T is the absolute temperature, n is a filling factor, A is the Schottky barrier height (see Fig. 1), and V is the applied voltage [31]. In Schottky-Mott theory, A should be the difference between the Fermi level of the metal and the conduction band minimum (for an n-type semiconductor-to-metal interface) or the valence band maximum (for a p-type semiconductor-metal interface) [32, 33]. Certain experimentally observed variations of A were for decades ascribed to pinning of states, but can now be attributed to local inhomogeneities of the interface, so the Schottky-Mott theory is secure. The opposite of a Schottky barrier is an ohmic contact, where there is only an added electrical resistance at the junction, typically between two metals. 

The surface sites and complexes lie in a layer on the mineral surface which, because of the charged complexes, has a net electrical charge that can be either positive or negative. A second layer, the diffuse layer, separates the surface layer from the bulk fluid. The role of the diffuse layer is to achieve local charge balance with the surface hence, its net charge is opposite that of the sorbing surface. Double layer theory, applied to a mixed ionic solution, does not specify which ions make up the diffuse layer. 

This idea is elegant for its simplicity and also for its usefulness. While often in phenomenological theories of materials, control of parameters with molecular structure would provide useful properties, but the parameters are not related in any obvious way to controllable molecular structural features. Meyer s idea, however, is just the opposite. Chemists have the ability to control enantiomeric purity and thus can easily create an LC phase lacking reflection symmetry. In the case of the SmC, the macroscopic polar symmetry of this fluid phase can lead to a macroscopic electric dipole, and such a dipole was indeed detected by Meyer and his collaborators in a SmC material, as reported in 1975.2... 

What appears to be new in the theory developed here is that the strength of the electrical field on each side depends on the nature of what is occupying the other site on the opposite side. This explains the marked differences between the reactions in polar and non-polar solvents. 

The conversion came at a time when the Newtonian program of explanation had lost ground in several fields of laboratory studies, including physical optics, electricity, and heat. Intellectually, this loss of influence was epitomized by the publication in 1826 of Augustin Fresnel s 1819 prize memoir on the diffraction of light, in which he abandoned the Newtonian corpuscular theory. Institutionally, the decline was registered by the 1822 election of Fourier to the office of permanent secretary of the Academy of Sciences, despite the opposition of Laplace, who along with Berthollet had earlier personified the Newtonian tradition in France.37... 

The existence of a correlation between the catalytic activity and the electrical conductivity which follows from the theory was indicated by us back in 1950 (37, 6S), when there were as yet no measurements available that could either corroborate or refute this theoretical prediction. To date we have already a whole series of experimental work in which such a correlation has been observed (e.g., 36, 56, 66-70). A number of authors have measured the electrical conductivity and the catalytic activity of various samples of a semiconductor which differed in the method of preparation and have discovered that these two properties of the semiconductor vary in the same or in opposite directions from one sample to another. The results of some of these experiments are presented in Table II. 

In addition to the interphase potential difference V there exists another potential difference of fundamental importance in the theory of the electrical properties of colloids namely the electro-kinetic potential, of Freundlich. As we shall note in subsequent sections the electrokinetic potential is a calculated value based upon certain assumptions for the potential difference between the aqueous bulk phase and some apparently immobile part of the boundary layer at the interface. Thus represents a part of V but there is no method yet available for determining how far we must penetrate into the boundary layer before the potential has risen to the value of the electrokinetic potential whether in fact f represents part of, all or more than the diffuse boundary layer. It is clear from the above diagram that bears no relation to V, the former may be in fact either of the same or opposite sign, a conclusion experimentally verified by Freundlich and Rona. 

However, the intra-atomic Coulomb interaction Uf.f affects the dynamics of f spin and f charge in different ways while the spin fluctuation propagator x(q, co) is enhanced by a factor (1 - U fX°(q, co)) which may exhibit a phase transition as Uy is increased, the charge fluctuation propagator C(q, co) is depressed by a factor (1 -H UffC°(q, co)) In the case of light actinide materials no evidence of charge fluctuation has been found. Most of the theoretical effort for the concentrated case (by opposition to the dilute one-impurity limit) has been done within the Fermi hquid theory Main practical results are a T term in electrical resistivity, scaled to order T/T f where T f is the characteristic spin fluctuation temperature (which is of the order - Tp/S where S is the Stoner enhancement factor (S = 1/1 — IN((iF)) and Tp A/ks is the Fermi temperature of the narrow band). 

As the electrode surface will, in general, be electrically charged, there will be a surplus of ionic charge with opposite sign in the electrolyte phase in a layer of a certain thickness. The distribution of jons in the electrical double layer so formed is usually described by the Gouy— Chapman—Stern theory [20], which essentially considers the electrostatic interaction between the smeared-out charge on the surface and the positive and negative ions (non-specific adsorption). An extension to this theory is necessary when ions have a more specific interaction with the electrode, i.e. when there is specific adsorption of ions. 

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