Dielectric constant effective

In this model of electrostatic in teraction s, two atoms (i and j) have poin t charges tq and qj. The magnitude of the electrostatic energy (V[. , [ ) varies inversely with the distance between the atoms, Rjj. fh e effective dielectric constant is . For in vacuo simulations or simulation s with explicit water rn olecules, the den om in a tor equals uRjj, In some force fields, a distance-dependent dielectric, where the denominator is uRjj Rjj, represen is solvent implicitly. 

If this electrostatic treatment of the substituent effect of poles is sound, the effect of a pole upon the Gibbs function of activation at a particular position should be inversely proportional to the effective dielectric constant, and the longer the methylene chain the more closely should the effective dielectric constant approach the dielectric constant of the medium. Surprisingly, competitive nitrations of phenpropyl trimethyl ammonium perchlorate and benzene in acetic anhydride and tri-fluoroacetic acid showed the relative rate not to decrease markedly with the dielectric constant of the solvent. It was suggested that the expected decrease in reactivity of the cation was obscured by the faster nitration of ion pairs. 

A variety of experimental techniques have been employed to research the material of this chapter, many of which we shall not even mention. For example, pressure as well as temperature has been used as an experimental variable to study volume effects. Dielectric constants, indices of refraction, and nuclear magnetic resonsance (NMR) spectra are used, as well as mechanical relaxations, to monitor the onset of the glassy state. X-ray, electron, and neutron diffraction are used to elucidate structure along with electron microscopy. It would take us too far afield to trace all these different techniques and the results obtained from each, so we restrict ourselves to discussing only a few types of experimental data. Our failure to mention all sources of data does not imply that these other techniques have not been employed to good advantage in the study of the topics contained herein. 

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... 

Manning s theory does not take the local effective dielectric constant into consideration, but simply uses the a value of bulk water for the calculation of E,. However, since counterion condensation is supposed to take place on the surface of polyions. Manning s 2, should be modified to E, by replacing a with aeff. The modified parameters E, is compared with E, in Table 1, which leads to the conclusion that the linear charge density parameter calculated with the bulk dielectric constant considerably underestimates the correct one corresponding to the interfacial dielectric constant. 

It is clear from Table 1 that pKobs decreases systematically as the charge density of the polyanion decreases, and pK shows a slight increase with a decrease in the charge density. The latter arises from a decrease in the effective dielectric constant with decreasing charge density. The electrostatic potential systematically decreases as the charge density decreases. 

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. 

The greater than unit value of Kf in pure solvents is the result expected by the field effect model (33) on a distance basis. The lower than unit value ofKj in the mixed aqueous organic solvents appears to be related to preferential hydration of the reaction center, which results in an increased effective dielectric constant from the m- compared to the p- position. The fact that values fall into two separate categories for pure organic and mixed aqueous organic solvents does not support the treatments of Exner (20) or Yukawa and Tsuno (16). 

Here, R is the average distance between two neighbouring doubly ionized monomeric units and is the effective dielectric constant. 

It is, of course, usual in discussing the electrochemical interface to use a dielectric constant, which is the ratio of the electric displacement to the electric field. By Fourier transforming the dielectric function e(k), one would obtain an effective dielectric constant, which would, however, depend on position. In fact,48 the screening... 

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. 

Metal ion-catalyzed hydrolytic processes have been studied for a long time, and many interesting systems have been explored which give valuable information about catalysis. However, with very few exceptions the catalysis afforded by these systems in water is disappointing when compared with enzymatic systems where a metal ion cofactor activates a substrate and a nucleophilic or basic group in an acyl or phos-phoryl transfer process. It has been noted that bulk water may not be a good medium to approximate the medium inside the active site of an enzyme where it is now known that the effective dielectric constants resemble those of organic solvents rather than water. 

A subject not treated here is the use of distance-dependent effective dielectric constants as a way to take account of the structure in the dielectric medium when a solute is present. This subject has recently been reviewed [120], In the approaches covered in the present chapter, deviations of the effective dielectric constant from the bulk value may be included in terms of physical effects in the first solvation shell, as discussed in Section 2.2. 

Predicted ionic radii r, experimental ionic radii n, central charge Q and RF potential Ok in atomic units. Electrostatic free energies of solvation, 8pel, in kcal/mol. Experimental values from reference [16]. Electrostatic potential for anions from reference [19]. For all calculations done, the effective dielectric constant reported in [16] was used. 

In a recent upsurge of studies on electron transfer kinetics, importance was placed on the outer shell solvent continuum, and the solvent was replaced by an effective model potential or a continuum medium with an effective dielectric constant. Studies in which the electronic and molecular structure of the solvent molecules are explicitly considered are still very rare. No further modem quantum mechanical studies were made to advance the original molecular and quantum mechanical approach of Gurney on electron and proton (ion) transfer reactions at an electrode. 

Clearly, if one takes a smaller value of D, one gets a higher value of IVj j, for a given distance Rufj. Kirkwood and Westheimer (1938), Westheimer and Kirkwood (1938), and Westiieimer and Shookhoff (1939) indeed argued that one should take a much smaller dielectric constant, since the intervening medium between the two protons more closely resembles a hydrocarbon liquid rather than water. In fact, for any dicarboxylic acid one can define an effective dielectric constant to fit the experimental value of W, by an equation of the form (4.8.13), with Dg being dependent on the proton-proton distance, the type and size of the acid and the solvent. 

A through-space electrostatic effect (field effect) due to the charge on X. This model was developed by Kirkwood and Westheimer who applied classical electrostatics to the problem. They showed that this model, the classical field effect (CFE), depended on the distance d between X and Y, the cosine of the angle 6 between d and the X—G bond, the effective dielectric constant and the bond moment of X. 

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