Electrostriction theory

Long and McDevit s thermodynamic electrostriction theory [44] tries to calculate it from the excess work necessary to put an element of volume of the neutral... 

Equations of this type are most often used by experimentalists to fit their data to theory,52"54 as indications of an exponential 7(E) dependence are numerous. Vervey55 has used a similar approach to consider the volume-limited processes of ionic migration and obtained the same equation. In order to explain deviations of experimental behavior from that predicted by Eq. (40), Vermilyea56 has also taken into consideration the effect of electrostriction modifying the activation distance for migrating ions and obtained the following equation for the ionic current flow ... 

Marshall s extensive review (16) concentrates mainly on conductance and solubility studies of simple (non-transition metal) electrolytes and the application of extended Debye-Huckel equations in describing the ionic strength dependence of equilibrium constants. The conductance studies covered conditions to 4 kbar and 800 C while the solubility studies were mostly at SVP up to 350 C. In the latter studies above 300°C deviations from Debye-Huckel behaviour were found. This is not surprising since the Debye-Huckel theory treats the solvent as incompressible and, as seen in Fig. 3, water rapidly becomes more compressible above 300 C. Until a theory which accounts for electrostriction in a compressible fluid becomes available, extrapolation to infinite dilution at temperatures much above 300 C must be considered untrustworthy. Since water becomes infinitely compressible at the critical point, the standard entropy of an ion becomes infinitely negative, so that the concept of a standard ionic free energy becomes meaningless. 

To account for the difference between experiment and theory, Schwarz suggested that electrostriction includes the formation of a glassy shell of 7 to 9 solvent molecules around the ion [102]. This phase transition provides a substantial density increase, and the observed volume changes can then be accounted for. 

As will be shown in the theory, the electrostriction effect plays an important role in the piezoelectric effect of polymer films. Moreover, a knowledge of the complex electrostriction constant as a function of frequency reveals a new aspect of the relaxational behavior of polymers. In this review a new method for measuring complex electrostriction constant with varying frequency will be presented with some results for poly(vinylidene fluoride). 

Electrostriction is the study of the effects of squeezing of ions and moiecuies by the electrical forces that are exerted upon them by the ions we have been deaiing with (Section 2.22). It is only recently that modelers have begun to take into account the shapes formed by these compressed bodies. In fact, they do become lenshke in shape (not spheres) and when this is taken into account, agreement between theory and experiment is improved. 

Values of V are generally small except near 62 bar where V reaches a minimum value of -9 L/mol. This is approximately one-third of that expected theoretically for electrostriction by Oj. Clearly there is a volume decrease in the reaction but the lack of agreement with theory indicates either that the hill volume change is not obtained until the reaction is complete, or that Oj has a significant cluster around it i.e. the partial molar volume of neutral O2 in xenon is negative. 

Frank, his theory of electrostriction, 190 Free eneigies of hydration dependence on radius. 54 how to get them, described, 53 Free eneigies of solvation, described, 53 Friedman... 

Electrostriction is important in solvation, but has not ever been properly incorporated in any detail into electrolyte theory. 

Nernst made numerous other important contributions to physical chemistry. For example, his distribution law described the concentration distribution of a solute in two immiscible liquids and allowed the calculation of extraction processes. He also formulated several significant theories, such as those on the electrostriction of ions, the diffusion layer at electrodes, and the solubility product. In addition, he established new methods to measure dielectric constants and to synthesize ammonia, on which the German chemist Fritz Haber later successfully followed up. see also Electrochemistry Haber, Fritz Ostwald, Friedrich Wilhelm Physical Chemistry. 

When reaction involves the approach of opposite charges, the result is a positive contribution to the entropy of activation, and an abnormally high frequency factor. The situation is represented in Figure 9.16b. The activated complex now has a lower charge than either of the reactants and there is less electrostriction in the activated state. There is some release of bound water molecules and a resulting increase in entropy. This simple theory leads to the result that this gain in entropy will be approximately... 

Equation (14-50) is the formula for electrostriction at constant T and p. In general, 8eldp)j is positive so that a system will contract when put into an electric field at constant T and p. It is interesting to note that this theory, when applied on the molecular scale in the consideration of electrostriction of solvent in the field of an ion, qualitatively accounts for the decrease in volume resulting when some solutions are mixed. 

In this paper, we report experimental results of the Poisson s ratio and electrostriction constant of PVDF and discuss the role of their constants to the piezoelectric effect by using the theory developed by Wada and Hayakawa. 

There is at present no general theory that permits the estimation of the salting properties, even of the limiting A ne values, for given salts and nonelectrolytes that relates them to readily available measurable properties of the salt and the solute. The electrostriction, scaled particle, and the Kirk-wood-Buff theories do not answer this requirement, and research to meet this need should be forthcoming. In particular, direct attractive interactions between the ions of the salt and the solute that could lead to salting-in are not well understood so far. Extension of any theory to higher salt and solute concentrations should also be attempted. 

The electrostrictive coefficient Q links the field-induced strain x and the polarization P by a parabolic relationship, and should not be confused with the general order parameter Q in Landau theory. 

Starting with the Landau theory, Trebin and coworkers [122], [124] have calculated the electrostriction coefficients by allowing both the wave vectors and scalar amplitudes of the Fourier components to distort. Good agreement with the data is achieved, except for the case of anomalous electrostriction in BPI. The authors therefore conclude that the explanation for this behavior is beyond the capability of the Landau theory. As described earlier, the same group has also proposed a model of the blue phases incorporating bond-orientational order [45], [46]. However, a calculation of the anomalous electrostriction from this model [123] has had only limited success. 

---