Electrical polarizability difference

In order to obtain a definite breakthrough of current across an electrode, a potential in excess of its equilibrium potential must be applied any such excess potential is called an overpotential. If it concerns an ideal polarizable electrode, i.e., an electrode whose surface acts as an ideal catalyst in the electrolytic process, then the overpotential can be considered merely as a diffusion overpotential (nD) and yields (cf., Section 3.1) a real diffusion current. Often, however, the electrode surface is not ideal, which means that the purely chemical reaction concerned has a free enthalpy barrier especially at low current density, where the ion diffusion control of the electrolytic conversion becomes less pronounced, the thermal activation energy (AG°) plays an appreciable role, so that, once the activated complex is reached at the maximum of the enthalpy barrier, only a fraction a (the transfer coefficient) of the electrical energy difference nF(E ml - E ) = nFtjt is used for conversion. 

The discussion above has been more or less empirical and descriptive. However, considerable effort has been made to interpret 3-SCS on a more physical basis. Electric-field effects (71-75) were invoked to explain signal shifts of 3-carbon atoms induced by protonation of amines (157,158) (cf. Section II-B-3). This approach was later extended to other functionalities by Schneider and coworkers, who assumed that the SEF component (E2) rather than inductive properties of the substituents should be responsible for 3-SCS (113). They found fairly linear correlations of 3-SCS(X ) and 3-SCS(X ) in cyclohexyl derivatives (76) and attributed the difference between these for a given X to a widening of the C -Cp-Cv bond angle by 2.2° in the axial conformer (114,159). The decrease of 3-SCS in the order primary Cp —> secondary Cp — tertiary Cp — quaternary Cp was explained by electron-charge polarization in the Cp-C" bond(s) induced by the LEF component of the C -X dipole, which is already of significance at this distance, though ( 2) still dominates (160). Such an electron flow toward the 3 carbon is expected to be much more pronounced in C-C than in C-H bonds because of the polarizability difference (aCH = 0.79 acc = 1.12) (150,151,160). 

Identify different types of electrical polarizability, and determine if they are relevant to a given chemical structure. 

Dielectrophoresis is the translational motion of neutral matter owing to polarization effects in a non-uniform electric field. Depending on matter or electric parameters, different particle populations can exhibit different behavior, e.g. following attractive or repulsive forces. DEP can be used for mixing of charged or polarizable particles by electrokinetic forces [48], In particular, dielectric particles are mixed by dielectrophoretic forces induced by AC electric fields, which are periodically switched on and off. 

Induced polarizabilities differ from zero for a variety of reasons. A most important influence is the deviation of the local electric field from the externally applied laser field if another polarized atom or molecule is in close proximity. The classical dipole-induced dipole (DID) model considers the interacting pair as point dipoles [135, 136] and leads to separation-dependent invariants of the incremental polarizabilities [51, 62, 87, 115]. For the more highly polarizable particles, the DID anisotropy model is fairly accurate. Even for the less polarizable atoms such as helium and neon, at most separations of interest, the DID component of the anisotropy is known to be... 

The set of excitation energies consistent with the SCF parameterization of the wave function are those given by the random-phase approximation (RPA), in the sense that these are the locations of poles in the dynamic electric polarizability. The eigenvalues of A are not the RPA energy differences, and they often deviate significantly from them. 

Fig. II.3. Effect of fluorine substitutions on the out-of-plane minus average in-plane component of the magnetic susceptibility are shown for several aromatic rings. The difference between the Cotton-Mouton and the rotational Zeeman effect data is probably due to the neglect of the field dependence of the electric polarizability in the analysis of the Cotton-Mouton data. Note that the difference in the results for 1,2- and 1,3-difluorobenzene indicates that the ring current quenching effects of substituents strongly depend on their position...

The difference between the Cotton-Mouton curves and the curves connecting the rotational Zeeman results may be partly due to the neglect of a possible field dependence of the electric polarizabilities in the analysis of the Cotton-Mouton data. 

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. ... 

For light ions (i.e., not in the Rayleigh limit), fi depends on m and a change of M multiplies K of nonisobaric ions by different factors, which could materially affect the separation. However, the choice of gas matters in other cases too the value of fl always depends on such properties of gas molecules as size, shape, electrical polarizability (ap), and dipole moment (pm) The interplay of those dependences is complex, but qualitatively many trends are understood. With respect to size, for... 

Born then decided to neglect the explicitly detailed structure of water molecules and replace them with a continuous electrically polarizable medium. This approximation is the same as that made in any Poisson-Boltzmann calculation, but unlike the Debye-Hiickel approximation, the ions in Born s calculation retained finite size. Thus, the Born treatment had the possibility of seeing chemically relevant differences due to ionic size. It should be remarked that Fajans was also looking for the chemically interesting dependence on ionic size in his less successful calculations. 

N is the Loschmidt number while 0i and 02 are complex functions of the dipole moments and polarizabilities belonging to the molecule. The Kerr constant itself can be split into two terms of which one (Ki) merely expresses the anisotropy of the optical and electrical polarizability and is named the anisotropy term K, while the other represents the effect of possibly existing electric moments. This is called the dipole term K2. The two terms differ from each other in their dependence upon temperature the Kerr effect of dipole-free molecules is proportional to 1/T, that of dipole molecules is proportional to 1/T. ... 

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