Effective dielectric polarization

We have shown in this paper the relationships between the fundamental electrical parameters, such as the dipole moment, polarizability and hyperpolarizability, and the conformations of flexible polymers which are manifested in a number of their electrooptic and dielectric properties. These include the Kerr effect, dielectric polarization and saturation, electric field induced light scattering and second harmonic generation. Our experimental and theoretical studies of the Kerr effect show that it is very useful for the characterization of polymer microstructure. Our theoretical studies of the NLDE, EFLS and EFSHG also show that these effects are potentially useful, but there are very few experimental results reported in the literature with which to test the calculations. More experimental studies are needed to further our understanding of the nonlinear electrooptic and dielectric properties of flexible polymers. 

Greater deviations which are occasionally observed between two reference electrodes in a medium are mostly due to stray electric fields or colloid chemical dielectric polarization effects of solid constituents of the medium (e.g., sand [3]) (see Section 3.3.1). Major changes in composition (e.g., in soils) do not lead to noticeable differences of diffusion potentials with reference electrodes in concentrated salt solutions. On the other hand, with simple metal electrodes which are sometimes used as probes for potential controlled rectifiers, certain changes are to be expected through the medium. In these cases the concern is not with reference electrodes, in principle, but metals that have a rest potential which is as constant as possible in the medium concerned. This is usually more constant the more active the metal is, which is the case, for example, for zinc but not stainless steel. 

These can be determined experimentally to very high accuracy from the Stark effect and molecular beam studies. The experimental accuracy is far beyond the capabilities of ab initio studies. At the other extreme, the original route to these quantities was through studies of the dielectric polarization of species in solution, and there is currently interest in collision-induced dipole moments. In either case, the quantities deduced depend critically on the model used to interpret the experiment. 

The effective dielectric constant can be included to model the effect of surrounding molecules (solvent) and the fact that interactions between distant sites may be through part of the same molecule, i.e. a polarization effect. A value of 1 for e... 

This is a reaction in which neutral molecules react to give a dipolar or ionic transition state, and some rate acceleration from the added neutral salt is to be expected53, since the added salt will increase the polarity or effective dielectric constant of the medium. Some of the rate increases due to added neutral salts are attributable to this cause, but it is doubtful that they are all thus explained. The set of data for constant initial chloride and initial salt concentrations and variable initial amine concentrations affords some insight into this aspect of the problem. 

Thermal effects (dielectric heating) can result from dipolar polarization as a consequence of dipole-dipole interactions of polar molecules with the electromagnetic field. They originate in dissipation of energy as heat, as an outcome of agitation and intermolecular friction of molecules when dipoles change their mutual orientation at each alternation of the electric field at a very high frequency (v = 2450 MHz) [10, 11] (Scheme 3.1). 

The effect of micelles on these spontaneous hydrolyses is difficult to explain in terms of kinetic solvent effects on these reactions. Mukerjee and his coworkers have refined earlier methods for estimating apparent dielectric constants or effective polarities at micellar surfaces. For cationic and zwitterionic betaine sulfonate micelles Def is lower by ca 15 from the value in anionic dodecyl sulfate micelles (Ramachandran et al., 1982). We do not know whether there is a direct connection between these differences in effective dielectric constant and the relation between reaction rates and micellar charge, but the possibility is intriguing. 

The validity of Equation (21) requires that the lattice must be treated as a continuum in the evaluation of the angular dependence of electric field gradients. It has also been. shown 97) that the proper factor to use in computing the electric field gradient produced by a point defect, taking into account the effect of polarization of the medium, is (2e + 3)/5 , where e is the dielectric constant of the medium. This result is based on the continuum approximation for the solid. 

Dielectric polarization is the polarized condition in a dielectric resulting from an applied AC or DC field. The polarizability is the electric dipole moment per unit volume induced by an applied field or unit effective intensity. The molar polarizability is a measure of the polarizability per molar volume thus it is related to the polarizability of the individual molecules or polymer repeat unit. 

Solvation Effects. Many previous accounts of the activity coefficients have considered the connections between the solvation of ions and deviations from the DH limiting-laws in a semi-empirical manner, e.g., the Robinson and Stokes equation (3). In the interpretation of results according to our model, the parameter a also relates to the physical reality of a solvated ion, and the effects of polarization on the interionic forces are closely related to the nature of this entity from an electrostatic viewpoint. Without recourse to specific numerical results, we briefly illustrate the usefulness of the model by defining a polarizable cosphere (or primary solvation shell) as that small region within which the solvent responds to the ionic field in nonlinear manner the solvent outside responds linearly through mild Born-type interactions, described adequately with the use of the dielectric constant of the pure solvent. (Our comments here refer largely to activity coefficients in aqueous solution, and we assume complete dissociation of the solute. The polarizability of cations in some solvents, e.g., DMF and acetonitrile, follows a different sequence, and there is probably some ion-association.)... 

A number of other polar monomers have been polymerized with butyllithium, nominally in hydrocarbon or aromatic solvents. In almost all cases the monomer concentration was so high that the effective dielectric constant was much greater than in a pure hydrocarbon. All show rather complex behaviour. The degree of polymerization of the polymer formed is always much higher than the initial monomer-catalyst ratio so that a simple scheme involving only initiation and propagation reactions is not applicable. Only precipitable polymer was isolated, so it is not sure if the low initiator efficiencies are due to low polymer formation or to side reactions of butyllithium with the monomer. In addition most systems studied stop before complete conversion of the monomer. Evidently the small fraction of active polymer chains formed... 

The SM2/AM1 model was used to examine anomeric and reverse anomeric effects and allowed to state that aqueous solvation tends to reduce anomeric stabilization [58]. Moreover, SM2/AM1 and SM3/PM3 models were accounted for in calculations of the aqueous solvation effects on the anomeric and conformational equilibria of D-glucopy-ranose. The solvation models put the relative ordering of the hydroxymethyl conformers in line with the experimentally determined ordering of populations. The calculations indicated that the anomeric equilibrium is controlled primarily by effects that the gauche/trans 0-C6-C5-0 hydroxymethyl conformational equilibrium is dominated by favorable solute-solvent hydrogen bonding interactions, and that the rotameric equilibria were controlled mainly by dielectric polarization of the solvent [59]. On the other hand, Monte Carlo results for the effects of solvation on the anomeric equilibrium for 2-methoxy-tetrahydropyran indicated that the AM1/SM2 method tends to underestimate the hydration effects for this compound [60]. 

By comparing with corresponding spectra of ion pairs in different solvents one obtains information on the local environment at the micellar surface73. (The polarity was expressed in terms of a so-called effective dielectric constant). Amphiphiles with a benzene ring also show an UV absorption74-76. UV spectra of solubilized species like benzene, naphthalene and pyrene have been extensively studied and compared with spectra of the compound in reference solvents to provide an estimate of the polarity in the vicinity of the solubilizate. 

In conclusion, we reported the investigation of inner and outer interfaces in pzt in order to quantity both the amount of effective ferroelectric polarization and change in dielectric properties. With pfm and kpfm we find a transition layer occurring at the Pt/PZT interface within... 

In order to formulate a theory for the evaluation of vibrational intensities within the framework of continuum solvation models, it is necessary to consider that formally the radiation electric field (static, Eloc and optical E[jc) acting on the molecule in the cavity differ from the corresponding Maxwell fields in the medium, E and Em. However, the response of the molecule to the external perturbation depends on the field locally acting on it. This problem, usually referred to as the local field effect, is normally solved by resorting to the Onsager-Lorentz theory of dielectric polarization [21,44], In such an approach the macroscopic quantities are related to the microscopic electric response of... 

M. Maroncelli, V. P. Kumar and A. Papazyan, A simple interpretation of polar solvation dynamics, J. Phys. Chem., 97 (1993) 13-17 E. W. Castner, Jr. and M. Maroncelli, Solvent dynamics derived from optical Kerr effect, dielectric dispersion, and time-resolved Stokes shift measurements an empirical comparison, J. Mol. Liq., 77 (1998) 1-36. 

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