Electric polarization equilibrium case

Relaxation processes are probably the most important of the interactions between electric fields and matter. Debye [6] extended the Langevin theory of dipole orientation in a constant field to the case of a varying field. He showed that the Boltzmann factor of the Langevin theory becomes a time-dependent weighting factor. When a steady electric field is applied to a dielectric the distortion polarization, PDisior, will be established very quickly - we can say instantaneously compared with time intervals of interest. But the remaining dipolar part of the polarization (orientation polarization, Porient) takes time to reach its equilibrium value. When the polarization becomes complex, the permittivity must also become complex, as shown by Eq. (5) ... 

In this section we shall consider the simplest model problem for the locally electro-neutral stationary concentration polarization at an ideally permselective uniform interface. The main features of CP will be traced through this example, including the breakdown of the local electro-neutrality approximation. Furthermore, we shall apply the scheme of 4.2 to investigate the effect of CP upon the counterion selectivity of an ion-exchange membrane in a way that is typical of many membrane studies. Finally, at the end of this section we shall consider briefly CP at an electrically inhomogeneous interface (the case relevant for many synthetic membranes). It will be shown that the concentration and the electric potential fields, developing in the course of CP at such an interface, are incompatible with mechanical equilibrium in the liquid electrolyte, that is, a convection (electroconvection) is bound to arise. 

We may attempt to make a rough quantitative statement about the bond type in these molecules by the use of the values of their electric dipole moments. For the hydrogen halogenides only very small electric dipole moments would be expected in case that the bonds were purely covalent. For the ionic structure H+X-, on the other hand, moments approximating the product of the electronic charge and the internuclear separations would be expected. (Some reduction would result from polarization of the anion by the cation this we neglect.) In Table 3-1 are given values of the equilibrium internuclear distances r0, the electric moments er0 calculated for the ionic structure H+X , the observed values of the electric moments /, and the ratios of these to the values of er0.ls These ratios may be interpreted in a simple... 

The reactions with which we are mostly concerned in chemistry take place in solution rather than in the gas phase. The majority of them moreover involve reactants, products, or transition states carrying electric charges. In such cases the entropies of solvation are extremely large, and these entropies cannot be estimated at present. This immediately rules out any possibility of estimating absolute values of equilibrium or rate constants for reactions of this kind. If we are concerned with absolute calculations of rates and equilibria, we must confine ourselves either to gas-phase reactions, or to reactions of non-polar type. Even here we will usually be forced to make estimates of entropies that are of dubious significance chemical theory has not yet progressed to a point where problems of this kind can usefully be discussed. 

Continuum solvation models consider the solvent as a homogeneous, isotropic, linear dielectric medium [104], The solute is considered to occupy a cavity in this medium. The ability of a bulk dielectric medium to be polarized and hence to exert an electric field back on the solute (this field is called the reaction field) is determined by the dielectric constant. The dielectric constant depends on the frequency of the applied field, and for equilibrium solvation we use the static dielectric constant that corresponds to a slowly changing field. In order to obtain accurate results, the solute charge distribution should be optimized in the presence of the field (the reaction field) exerted back on the solute by the dielectric medium. This is usually done by a quantum mechanical molecular orbital calculation called a self-consistent reaction field (SCRF) calculation, which is iterative since the reaction field depends on the distortion of the solute wave function and vice versa. While the assumption of linear homogeneous response is adequate for the solvent molecules at distant positions, it is a poor representation for the solute-solvent interaction in the first solvation shell. In this case, the solute sees the atomic-scale charge distribution of the solvent molecules and polarizes nonlinearly and system specifically on an atomic scale (see Figure 3.9). More generally, one could say that the breakdown of the linear response approximation is connected with the fact that the liquid medium is structured [105],... 

The model described allows the ions of the first n layers at the free j 100 J face of a hemScrystal with sodium chloride structure to relax in a direction normal to the face and to be polarized by the electric field in the surface region. The equilibrium configuration is determined by minimizing the energy of the system. Numerical results for sodium chloride are presented for the five cases 1 n < 5. A value of —107.4 erg cm.-2 is estimated for the total correction to the surface energy of this material due to surface distortion. 

As the existence of MChA can be deduced by very general symmetry arguments and the effect does not depend on the presence of a particular polarization, one may wonder if something like MChA can also exist outside optical phenomena, e.g. in electrical conduction or molecular diffusion. Time-reversal symmetry arguments cannot be applied directly to the case of diffusive transport, as diffusion inherently breaks this symmetry. Instead, one has to use the Onsager relation. (For a discussion see, e.g., Refs. 34 and 35.) For any generalized transport coefficient Gy (e.g., the electrical conductivity or molecular diffusion tensor) close to thermodynamic equilibrium, Onsager has shown that one can write... 

In the first part of this section we will illustrate the computer techniques used to repeat in this two-dimensional case the experiment of monitoring the polarization after sudden removal of an electric field (i.e., the two-dimensional counterpart of a key experimmt illustrated by Evans in Chapter V). In addition, we shall monitor several equilibrium properties which contrib-... 

One example of a dielectric material in which ionic motion is important is barium titanate BaTiOj, which is ferroelectric (i.e., the induced polarization does not decay npon the removal of the electric field), hi these structures, titanium ion displacement within its octahedral sites canses extremely large polarizations (2,000-3,000) [14]. In nonferroelectric materials snch as titanium dioxide, ions will return to equilibrium position npon removal of field. Electronic polarizabihty is greater for materials containing more electrons (i.e., heavy atoms, greater polarizability). The frequency range for electronic motion is np to 10 Hz. In the case of materials for organic... 

Physical origin of dielectric loss The foregoing conclusions correspond to a static description or cases for which the polarization can perfectly follow the oscillation of the electric field. Indeed, the electric field orientation depends on time with a frequency equal to 2.45 GHz (the electric field vector switches its orientation approximately every 10 s). The torque exercised by the electric field induces rotation of polar molecules, but they cannot always orient at this rate. The motion of the particles will not be sufficiently rapid to build up a time-dependent polarization P(t) that is in equilibrium with the electric field at any moment. This delay between electromagnetic stimulation and molecular response is the physical origin of the dielectric loss. 

Surfactant molecules are made up of two moieties that have antagonistic properties, a polar or electrically charged hydrophilic moiety and a hydrophobic moiety, most often an alkyl chain. In aqueous solution, most surfactants self-assemble and form micelles when their concentration becomes larger than the so-called critical micellization concentration (CMC). In micelles (fromthe Creek mica, which means "grain "), the alkyl chains are in contact and form an oily core that is coated by the polar head groups. The outer layer that contains head groups, counterions (in the case of ionic surfactants), water and the first methylene group of the alkyl chain is called the palisade layer. The formation o/micelles is a cooperative process that is spontaneous and reversible. Micelles are thermodynamically stable species that are in chemical equilibrium with free surfactants. 

It is possible, using an external energy source, to supply the system with electrical charges, which will push it towards a new equilibrium that, unlike the initial one, is not solely the result of the presence of donors and acceptors. The evolution of the equilibrium will depend on the nature of the introduced changes. The simplest case involves externally connecting the junction to a direct potential power supply. Positively polarizing the p-type material helps strengthen its p-type material characteristics. 

Of course, the equilibrium configurations of the molecule with and without an electric field differ. In a simple case, say the HCl molecule, the HCl distance increases. It has to increase since the cathode pulls the hydrogen atom and repels the chlorine atom, while the anode does the opposite. In more complex cases, like a flexible molecule, the field may change its conformation. This means that the polarizability results both from the electron cloud deformation and the displacement of the nuclei. It mrns out that the latter effect (called vibrational polarization) is of great importance. ... 

The reaction dipole moment zfM of a dipolar equilibrium may be obtained from the measurement of continuum properties such as the dielectric permittivity as well as from direct monitoring of concentration shifts produced by an externally applied electric field. In both approaches to reaction properties it is primarily the chemical part of the total polarization that is aimed at. However, the chemical processes are intimately connected with the physical processes of polarization and dipole rotation. In the case of small molecules the orientational relaxations are usually rapid compared to the diffusion limited chemical reactions. When, however, macromolecular structures are involved, the rotational processes of the macromolecular dipoles may control a major part of the chemical relaxations. Two types of processes may be involved if a vectorial perturbation like an external electric field is applied a chemical concentration change and a change in the orientation of the reaction partners. 

Outer vessel contains liquid of lower density while the inner vessel contains liquid of higher density. The system is intrinsically unstable and is naturally maintained far away from equilibrium. Up and down flow of liquid occurs through the capillary, which is reflected by the oscillatory movement of the fluid in the inner vessel. When the electrodes in the two chambers are connected to a voltage-measuring device, oscillations in electric potentials are also observed for the cases when aqueous solutions of electrolyte-water system or aqueous solution of polar non-electrolytes are used in the system. This type of hydrodynamic instability is different from Benard instability or Taylor instability [29]. 

In precisely the same way, a spontaneously splay-deformed structure must correspond to the equilibrium condition with finite coefficient fsTi 7 0 in tensor (8.13). The corresponding term should be added to the splay term with (divn). If the molecules have, e.g., pear shape they can pack as shown in Fig. 8.7b. In this case, the local symmetry is Coov (conical) with a polar rotation axis, which is compatible with existence of the spontaneous polarization. However, such packing is unstable, as seen in sketch (b), and the conventional nematic packing (a) is more probable. The splayed stmcture similar to that pictured in Fig. 8.7b can occur close to the interface with a solid substrate or when an external electric field reduces the overall symmetry (a flexoelectric ejfecf). 

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