Polarizing effect, expression

When a bulk material is subjected to an oscillating external electric field produced by an incident radiation, there is a polarization effect, expressed by... 

That these expressions do combine resonance and polarity effects can be seen as follows ... 

Different surfactants are usually characterised by the solubility behaviour of their hydrophilic and hydrophobic molecule fraction in polar solvents, expressed by the HLB-value (hydrophilic-lipophilic-balance) of the surfactant. The HLB-value of a specific surfactant is often listed by the producer or can be easily calculated from listed increments [67]. If the water in a microemulsion contains electrolytes, the solubility of the surfactant in the water changes. It can be increased or decreased, depending on the kind of electrolyte [68,69]. The effect of electrolytes is explained by the HSAB principle (hard-soft-acid-base). For example, salts of hard acids and hard bases reduce the solubility of the surfactant in water. The solubility is increased by salts of soft acids and hard bases or by salts of hard acids and soft bases. Correspondingly, the solubility of the surfactant in water is increased by sodium alkyl sulfonates and decreased by sodium chloride or sodium sulfate. In the meantime, the physical interactions of the surfactant molecules and other components in microemulsions is well understood and the HSAB-principle was verified. The salts in water mainly influence the curvature of the surfactant film in a microemulsion. The curvature of the surfactant film can be expressed, analogous to the HLB-value, by the packing parameter Sp. The packing parameter is the ratio between the hydrophilic and lipophilic surfactant molecule part [70] ... 

Leo et al. indicated that the van der Waals volume is linearly related to hydro-phobicity for non-polar compounds expressed in terms of log P (octanol/water)66). Moriguchi et al. showed that the log P value is generally factored into two components attributable to hydrophilic effect of polar group and hydrophobic effect due to the net molar volume 67). Thus, the van der Waals volume could be a parameter related to solute-solvent interactions and partition coefficient. 

From the results already given, it can be seen that the ease of polarographic reduction depends on the ring position of the reducible group and also on the positions and electronic nature of other substituents. It was readily shown that the polar effects of the substituents on the half-wave reduction potentials could be expressed in the general form of the Hammett equation. 

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. 

Anode reaction. The expression inert electrode is often used to indicate that we may neglect reaction of the electrode itself. This can be due to the high value of its electrode potential or because of polarization effects related to the preparation of the electrode surface. The remaining possible anode reactions are the reverses of the following ... 

The transfer of reactants from the bulk solution to the electrode interface and in the reverse direction is an ordinary feature of all electrode reactions. As the oxidation-reduction reactions advance, the accessibility of the reactant species at the electrode/electrolyte interface changes. This is because of the concentration polarization effect, that is, r c, which arises due to the limited mass transport capabilities of the reactant species toward and from the electrode surface, to substitute the reacted material to sustain the reaction [6,8,10,66,124], This overpotential is usually established by the velocity of reactants flowing toward the electrolyte through the electrodes and the velocity of products flowing away from the electrolyte. The concentration overpotential, r c, due to mass transport restrictions, can be expressed as... 

In the early 1960s, Fowkes [88,89] introduced the concept of the surface free energy of a solid. The surface free energy is expressed by the sum two components a dispersive component, attributable to London attraction, and a specific (or polar) component, y p, owing to all other types of interactions (Debye, Keesom, hydrogen bonding, and other polar effects, as similarly described before in Sec. II. C... 

If the coions and counterions have an identical diffusivity, the above expression will reduce to that derived by Dukhin and Derjaguin [6]. The polarization effect of thick double layer on the electrophoretic mobility of... 

We move now from qualitative considerations to a more quantitative approach. It has become clear that a simple molecular mechanical energy expression can represent noncovalent interactions surprisingly well (16). Such energy expressions contain only the first three terms mentioned above electrostatic, exchange repulsion, and dispersion. By a suitable choice of parameters, change transfer and polarization effects are implicitly included in such an expression, which is simple and easy to evaluate, along with its derivatives, for... 

Non-additive terms effects of polarization in the potential function. Polarization effects induced by the ionic presence on the ion-molecule system have been investigated. We use the expression by Lybrand and Kollman24 that includes in the potential function a self-consistent field (SCF) polarization energy Upoi based on classical electrostatics, given by ... 

In particular, called resonance polar effect [Taft, 1956] is defined for any benzene derivative where there is no direct conjugation between substituent and reactive it can be considered constant for a particular solvent, therefore expressing resonance interactions between substituent and skeletal group. 6r is usually referred to as the effective resonance constant and of hold for electrophilic and nucleophilic reaction series, respectively. 

The dielectric constant of the solvent does not include the polarization effect from the ion pairs and can be found from Adelman expression [74], Thus, in... 

The differentiation between the polar and the stcric effects of the substituents in the glycosyl moiety (and the aliphatic compounds in general) is more complicated. However, it appears that the glycosides are stabilized by virtue of the polar effect of the hydroxyl groups. Much light has been thrown on this subject by the recent work of Kreevoy and Taft, especially with regard to the hydrolysis of diethyl acetals. Their results are expressed... 

In practice, (f) can be calculated by inserting experimental copolymerization rates into Eq. (7.64). The values of (j> thus obtained are frequently greater than unity, and these deviations are ascribed to polar effects that favor cross-termination over homotermination. However, this is not always unambiguous, since the apparent cross-termination factor may vary with monomer feed composition in a given system [25,26]. It is clear also that termination reactions are at least partially diffusion controlled [27,28]. A dependence of segmental diffusivity on the structure of macroradicals is to be expected and dependence of diffusion controlled termination on copolymer composition seems reasonable. It is therefore plausible that the value of the overall termination rate constant ku in copolymerizations should be functions of fractions F and Fi) of the comonomers incorporated in the copolymer. An empirical expression for ku has thus been proposed [27] ... 

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