Ionic potential barriers

The presence of the large repulsive potential barrier between the secondary minimum and contact prevents flocculation. One can thus see why increasing ionic strength of a solution promotes flocculation. The net potential per unit area between two planar surfaces is given approximately by the combination of Eqs. V-31 and VI-22 ... 

For an ion to move through the lattice, there must be an empty equivalent vacancy or interstitial site available, and it must possess sufficient energy to overcome the potential barrier between the two sites. Ionic conductivity, or the transport of charge by mobile ions, is a diffusion and activated process. From Fick s Law, J = —D dn/dx), for diffusion of a species in a concentration gradient, the diffusion coefficient D is given by... 

The theoretical treatment of ionic conductivity in solids is very similar to that of diffusion, the main difference is the superimposition of the potential field upon the potential barrier to migration (Fig. 3). 

A single-particle effect that adds features in the X-ray absorption spectrum of molecules not present in that of atoms is the shape resonance (74, 75). (In the case of solids this effect, caused by a modification of the density of states due to the presence of the other atoms in the molecule, is automatically accounted for in band calculations.) Localization of the excited electron inside the molecule in states resulting from an effective potential barrier located near the electronegative atoms in the molecule causes strong absorption bands in free molecules and near the inner-shell ionization limits of positive ions in ionic crystals (74). Consequently, molecular inner-shell spectra depart markedly from the corresponding atomic spectra. The type of structure of an inner-shell photoabsorption spectrum depends on the geometry of the molecule, the nature of its ligands, etc., and can sometimes be used to determine the structure of the molecule. 

With potential barrier chromatography, the double layer is suppressed by the use of high ionic strength and the van de Waal s attractive force predominates. Large particles, due to their greater attraction to the packing, are retarded more than small ones and elute later. 

Often a rather slow adsorption at the air-water interface has been observed. Whether this is due to electrical potential barriers, or whether a particular orientation is required of the arriving molecule before it can enter the monolayer has not yet been clearly demonstrated. For small ions taking part in reactions at interfaces, such as hydroxyl and permanganate, the latter effect has never been observed, although Alexander (29) claims that ion exchange below monolayers of amines is a slow process. The present author considers that this may be explained in terms of a slow desorption of one ionic species rather than as a slow approach of the other. A gradual change in the structure of the amine film is also a possibility. 

In PBFFF, the variation of the potential energy of interaction between the colloidal particles and the channel wall can be succeeded, except for the variation of the ionic strength, by changing also the pH and the nature of the suspending medium. Polydisperse, irregular supramicron colloidal particles of the mixed sulfides Cuj,Zni j,S (0 < x < 1) were used as model samples to verify the applicability of the potential barrier gravitational field-flow fractionation (PBGFFF), based on the variation of the above parameters, to fractionate colloidal particles. 

Second, being quasibound Inside a potential barrier on the perimeter of the molecule, such resonances are localized, have enhanced electron density In the molecular core, and are uncoupled from the external environment of the molecule. This localization often produces Intense, easily studied spectral features, while suppressing non-resonant and/or Rydberg structure and, as discussed more fully below, has a marked Influence on vibrational motion. In addition, localization causes much of the conceptual framework developed for shape resonances In free molecules to apply equally well to photolonlzatlon and electron scattering and to other states of matter such as adsorbed molecules, molecular crystals, and Ionic solids. 

In order to describe the stability of fine disperse systems stabilized by diffuse ionic layers, one has to use the total free energy of interaction between particles, instead of the energy per unit film area, and compare the barrier height,, to the thermal energy, kT. For us to be able to use the solution derived for the case of plane-parallel surfaces, let us introduce some effective area of particle contact, Se[. Then the potential barrier height for the particles can be expressed as = A5 max St(. When diffuse part of electrical double... 

A model has been proposed by us for this behaviour in which the compensation of a polymer-dopant system occurs in four stages. In the first stage, the counter-ion present in the outer monolayer of the polymer-dopant system, is compensated. This is a very fast ionic reaction without any potential barrier to overcome because diffusion is not involved. The monolayer becomes an insulator instantaneously but its thickness is negligible compared to the film thickness and the conductivity loss would be very small at this stage. In the second stage, the affected monolayer skin expands into the polymer-dopant system from both sides, at a rate controlled by the diflusion of compensant which may further be influenced by the rate of chemical... 

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