Dielectric boundary pressure

The second force component, the dielectric boundary pressure, results from the tendency of a high dielectric medium to displace a low dielectric constant medium if an electrical field is present. This force is always directed along the gradient of the dielectric constant, which means that it constitutes a pure pressure at the solute-solvent interface. The dielectric boundary pressure is the force component that balances the reaction field component of the qE force. For example, in the case of an isolated charge inside a low dielectric cavity, the dielectric boundary pressure provides the equal and opposite force to the qE force urging the charge toward the solvent. It is therefore evident that the dielectric boundary force is quantitatively as important as the reaction field force and that its neglect will lead to a violation of Newton s third law of motion. 

The forces so far discussed are those associated with the Poisson equation. It is not surprising that the situation is somewhat more complex when an electrolytic solvent is treated by using the Poisson-Boltzmann equation. However, it can be shown O i that the force density expression in this case is identical to that for the Poisson equation, except for the addition of an ion boundary pressure term. Like the dielectric boundary term, this represents a pure pressure acting at the ion exclusion boundary of the solute. It results from... 

Electrolysis can occur only at the boundary between an electrode and a medium that conducts the electric current, and the nature of the solvent is important for the course of electrolytic reactions. Such factors as proton activity, usable potential range, dielectric constant, ability to dissolve electrolytes and substrates, ion pair formation, accessible temperature range, vapor pressure, viscosity, toxicity, and price must be taken into consideration when the choice of solvent is made. 

Materials Analysis. The next level of complexity involves the measurement of dielectric properties for the determination of composition and microstructure as well as thicknesses. Thin films are typically microscopically inhomogeneous with substantial fractions of grain boundaries and voids, so their dielectric properties are rarely equal to those of the corresponding materials in bulk form. As an example, the pseudodielactric function <(> film deposited by low pressure... 

The effective electric field pressure in Eq. 12 causes the dielectric material to deform according to its elasticity. The amount of deformation depends on the film s boimdary conditions. For free boundary conditions (zero external force on the film s boimdaries), the deformation or strain in z can be written as... 

Most soft elastomers are nearly incompressible and the adoption of the hypothesis of incompressibility in the constitutive equations allows for some simplifications in the analytical calculations. However, this choice has some shortcomings (i) die constraint/ = 1 poses difficulties in the convergence of computational algorithms when numerical solutions are sought and (ii) the stmcture of die constitutive electroelastic equations are not completely revealed because of die presence of the hydrostatic pressure. Therefore, aiming at elucidating the latter item, we prefer to formulate the constitutive equations and solve a relevant boundary-value problem, for a soft dielectric beginning from the compressible case. 

It should be noted that the force described by equation (8) includes solute/solvent boundary force contributions from the dielectric and ion pressures (second and third terms) in addition to the familiar direct force on a charge in an electrostatic field (first term). With expressions for the potential distribution, the electrostatic free energy, and the electrostatic force, the PB treatment of solvent effects can be applied to a variety of macromolecular properties, including pATa shifts, redox potential shifts, binding energies, association rates, folding and stabilization. 

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