Ionic boundary forces

If Eq. [35] is to be used in molecular simulations, methods must be devised to compute the contribution of each of the three terms to the forces on atoms. This problem is not particularly difficult for qE forces. 2-54 However, to date, computations of atomic forces based on the PB equation either have neglected dielectric and ionic boundary forces or have dealt with them by methods whose accuracy has not yet been examined.-52.54 As recently demonstrated, ionic boundary forces will usually be negligibly weak in comparison with dielectric boundary forces.5° However, dielearic boundary forces are strong,5o and the use of inaccurate methods to compute them can lead to rather large errors in the electrostatic forces on atoms. 

This is valid only in the case of an effectively infinite medium in which no walls limit the flow of charges. Conductors must be considered case-by-case under the limitations imposed by boundary surfaces. See, for example, the treatment of ionic solutions (Level 1, Ionic fluctuation forces Tables P.l.d, P.9.C, S.9, S.10, and C.5 Level 2, Sections L2.3.E L2.3.G and Level 3, Sections L3.6 and L3.7). 

The first term represents the forces due to the electrostatic field, the second describes forces that occur at the boundary between solute and solvent regime due to the change of dielectric constant, and the third term describes ionic forces due to the tendency of the ions in solution to move into regions of lower dielectric. Applications of the so-called PBSD method on small model systems and for the interaction of a stretch of DNA with a protein model have been discussed recently ([Elcock et al. 1997]). This simulation technique guarantees equilibrated solvent at each state of the simulation and may therefore avoid some of the problems mentioned in the previous section. Due to the smaller number of particles, the method may also speed up simulations potentially. Still, to be able to simulate long time scale protein motion, the method might ideally be combined with non-equilibrium techniques to enforce conformational transitions. 

It is seen that the symmetry of the non-coulombic non-local interaction in the bulk phase forces the symmetry of the localized interaction with the wall. If we omitted the surface Hamiltonian and set / = 0 we would still obtain the boundary condition setting the gradient of the overall ionic density to zero. The boundary condition due to electrostatics is given by... 

The other is AG g, at the potential of zero charge (PZC), where no direct electrostatic effect is expected. The former reflects the affinity to the interfacial region when the driving forces toward the interface from W and from O are balanced, notwithstanding that the surface activity at Aq phase-boundary potential as Aq 4>f is usually different from the PZC. AG g, values at the PZC are, however, useful in comparing the intrinsic or chemical surface activities of ionic compounds. 

Figure 11-6 defines the transport problem in a quasi-binary ionic system (A,B)X with a miscibility gap, if both chemical (V/i,) and electrical (Vp) driving forces act simultaneously (case 3)). If the chemical force is negligible, we are dealing with case 2) and the electrical drift flux of the cations shifts the boundary b in the direction of the flux. We can conclude that, in agreement with Figure 11-5 a, the boundary morphology is unstable if... 

The driving forces necessary to induce macroscopic fluxes were introduced in Chapter 3 and their connection to microscopic random walks and activated processes was discussed in Chapter 7. However, for diffusion to occur, it is necessary that kinetic mechanisms be available to permit atomic transitions between adjacent locations. These mechanisms are material-dependent. In this chapter, diffusion mechanisms in metallic and ionic crystals are addressed. In crystals that are free of line and planar defects, diffusion mechanisms often involve a point defect, which may be charged in the case of ionic crystals and will interact with electric fields. Additional diffusion mechanisms that occur in crystals with dislocations, free surfaces, and grain boundaries are treated in Chapter 9. 

These forces are the result of elastic stress fields that. exist near every impurity ion or aggregate and crystal imperfection like a dislocation line or grain boundary. These forces are very strong and are mainly responsible for the creation of second phase impurity aggregates in a host of ionic crystals. If the latent image is considered as a second phase formation of Ag° atoms in the silver halide crystal, then it seems that the elastic forces are those that cause the formation of this Ag aggregate. 

In this paper it is shown that the rate of deposition of Brownian particles on the collector can be calculated by solving the convective diffusion equation subject to a virtual first order chemical reaction as a boundary condition at the surface. The boundary condition concentrates the surface-particle interaction forces. When the interaction potential between the particle and the collector experiences a sufficiently high maximum (see f ig. 2) the apparent rate constant of the boundary condition has the Arrhenius form. Equations for the apparent activation energy and the apparent frequency factor are established for this case as functions of Hamaker s constant, dielectric constant, ionic strength, surface potentials and particle radius. The rate... 

Measurements of the rate of deposition of particles, suspended in a moving phase, onto a surface also change dramatically with ionic strength (Marshall and Kitchener, 1966 Hull and Kitchener, 1969 Fitzpatrick and Spiel-man, 1973 Clint et al., 1973). This indicates that repulsive double-layer forces are also of importance to the transport rates of particulate solutes. When the interactions act over distances that are small compared to the diffusion boundary-layer thickness, the rate of transport can be computed (Ruckenstein and Prieve, 1973 Spiel-man and Friedlander, 1974) by lumping the interactions into a boundary condition on the usual convective-diffusion equation. This takes die form of an irreversible, first-order reaction on tlie surface. A similar analysis has also been performed for the case of unsteady deposition from stagnant suspensions (Ruckenstein and Prieve, 1975). 

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