Electrostriction compression

The electrostriction volnme, V around ions in nonaqneons solvents and the electrostrictive compression per mole of solvent, was dealt with by Marcus... 

Electrostrictive materials are materials that exhibit a quadratic relationship between mechanical stress and the square of the electric polari2ation (14,15). Electrostriction can occur in any material. Whenever an electric field is appHed, the induced charges attract each other, thus, causing a compressive force. This attraction is independent of the sign of the electric field and can be approximated by... 

Initially the effect of applied voltage on membrane capacitance was attributed to the uniform electrostriction, in the manner of the elastic capacitor model [1,103], The effect of undulations was first considered by Leikin [78], In Ref. 89 the combined effect of undulations and uniform compression is studied, including the possible influence of nonlocality. The differential capacitance C is presented as... 

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. 

Here, V refers to the molar volume of the nonelectrolyte, V and Vs° are the intrinsic3 and apparent molar volume of the salt, respectively, and /3 is the isothermic compressibility coefficient of the solution. Although this equation is strictly valid in the limit of Vi - 0 and ca - 0, it works quite satisfactorily for small nonpolar solutes. The equation shows that the effect is greatest for nonelectrolytes of large molar volume Vi, and for salts that cause the largest electrostriction, Vs - Vs°. A difficulty with this expression is that it is not always easy to evaluate the intrinsic volume of a salt (the mere volume, without... 

Values range from + 22 cm /mol for m-xylene to —27 cm /mol for 1-pentene. This depends on the relative magnitude of two large volume terms that make up Vg. One is the cavity volume, a positive term, and the other is the electrostriction of the solvent around the trapped electron. Whereas the electrostriction term varies considerably depending on the compressibility of the solvent, the cavity volume does not change much and the average value for the hydrocarbons is 96 cm /mol, corresponding to a cavity radius of 0.34 nm. 

These changes in /td led to values of AFtr equal to -22 and -27 cm /mol for n-hexane and 1-pentene, respectively. The negative volume changes are due to the role of electrostriction [160] of the solvent around the trapped electron, and the electrostriction volume, Fei, is a function of the isothermal compressibility Xt of the liquid. 

Electrostriction process in which water molecules aggregate in higher densities than predicted near salt ions (e.g., Na" ") these pockets of water molecules have higher densities than the bulk water, resulting in a compression or reduction of the solvent. 

Additional difficulties beyond that of dielectric saturation already mentioned (page 527) have to do with the enormous electrostrictive pressures in the neighborhoods of ions. These can amount to some 10 to 10 atm and lead to serious changes in the properties of the solvent (unpublished work by the author). Note that these lead to an increase in dielectric constant due to compression of solvent and tend to cancel the effects of saturation. For some detailed discussion, see paper by H. S. Frank, J. Chem, Phys.j 23, 2023 (1966). 

Taking into account a finite compressibility of the hydration waters led Onori to suggest solvation numbers that differed from those of Passynski with his assumption of zero compressibility of the inner region of the solvation shell. For example, for a 1.5 M solution, Onori has the value 19 for the sum of the solvation numbers of Na and cr, whereas the Passynski at 0.05 M solution is 6 However, later on (Section 2.22), when electrostriction is discussed in detail, Onori s estimate will be shown to be unlikely. 

Effects of this kind are shown in Fig. 2.75. However, electrostriction has its limits. As seen in Fig. 2.75, the value of the compressibility itself is reduced as the electric field (and hence the local pressure) increases. Some details of this are worked out in the next section. 

Fig. 2.75. (a) Local compressibility fi of water as afunctbn of log(field) near an bn. (b) Electrostriction, AW, in water as a function of bg(fielcl) near an bn. (Reprinted from B. E. Conway, Ionic Hydration in Chemistry and Biophysics, Elsevier, New Yoik, 1981.)... 

This deaease in compressibility with inaease in pressure explains the overlarge deaease in volume (44%) due to electrostriction calculated earlier, assuming fi to be independent of pressure. It also supports Passynski s approximation Off)hyd sheii =... 

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. 

It is important to be aware of clustering caused by electrostriction in order to understand reactions of ions in supercritical rare gases. If a classical continuum model is used to calculate clustering, the magnitude of the volume change due to electrostriction would be overestimated because such a model ignores the density build-up around the ion. Because of this density augmentation, the compressibility of the fluid near the ion is less and, since electrostriction is proportional to compressibility, the actual electrostriction will be less... 

---