Electrical diffusion coefficient

The diffusion of metal ions in vitreous siUca has not been studied as extensively as that of the gaseous species. The alkaU metals have received the most attention because their behavior is important in electrical appHcations. The diffusion coefficients for various metal ions are Hsted in Table 5. The general trend is for the diffusion coefficient to increase with larger ionic sizes and higher valences. 

Electrically assisted transdermal dmg deflvery, ie, electrotransport or iontophoresis, involves the three key transport processes of passive diffusion, electromigration, and electro osmosis. In passive diffusion, which plays a relatively small role in the transport of ionic compounds, the permeation rate of a compound is deterrnined by its diffusion coefficient and the concentration gradient. Electromigration is the transport of electrically charged ions in an electrical field, that is, the movement of anions and cations toward the anode and cathode, respectively. Electro osmosis is the volume flow of solvent through an electrically charged membrane or tissue in the presence of an appHed electrical field. As the solvent moves, it carries dissolved solutes. 

These three terms represent contributions to the flux from migration, diffusion, and convection, respectively. The bulk fluid velocity is determined from the equations of motion. Equation 25, with the convection term neglected, is frequently referred to as the Nemst-Planck equation. In systems containing charged species, ions experience a force from the electric field. This effect is called migration. The charge number of the ion is Eis Faraday s constant, is the ionic mobiUty, and O is the electric potential. The ionic mobiUty and the diffusion coefficient are related ... 

First, when a large excess of inert elec trolyte is present, the electric field will be small and migration can be neglected for minor ionic components Eq. (22-19) then applies to these minor components, where D is the ionic-diffusion coefficient. Second, Eq. (22-19) apphes when the solution contains only one cationic and one anionic species. 

The mobilities of ions in molten salts, as reflected in their electrical conductivities, are an order of magnitude larger than Arose in Are conesponding solids. A typical value for diffusion coefficient of cations in molten salts is about 5 X lO cm s which is about one hundred times higher Aran in the solid near the melting point. The diffusion coefficients of cation and anion appear to be about the same in Are alkali halides, wiAr the cation being about 30% higher tlrair Are anion in the carbonates and nitrates. 

Why this large difference Well, whenever you consider an alloy rather than a pure material, the oxide layer - whatever its nature (NiO, Cr203, etc.) - has foreign elements contained in it, too. Some of these will greatly increase either the diffusion coefficients in, or electrical conductivity of, the layer, and make the rate of oxidation through the layer much more than it would be in the absence of foreign element contamination. 

The behavior of ionic liquids as electrolytes is strongly influenced by the transport properties of their ionic constituents. These transport properties relate to the rate of ion movement and to the manner in which the ions move (as individual ions, ion-pairs, or ion aggregates). Conductivity, for example, depends on the number and mobility of charge carriers. If an ionic liquid is dominated by highly mobile but neutral ion-pairs it will have a small number of available charge carriers and thus a low conductivity. The two quantities often used to evaluate the transport properties of electrolytes are the ion-diffusion coefficients and the ion-transport numbers. The diffusion coefficient is a measure of the rate of movement of an ion in a solution, and the transport number is a measure of the fraction of charge carried by that ion in the presence of an electric field. 

Following the general trend of looldng for a molecular description of the properties of matter, self-diffusion in liquids has become a key quantity for interpretation and modeling of transport in liquids [5]. Self-diffusion coefficients can be combined with other data, such as viscosities, electrical conductivities, densities, etc., in order to evaluate and improve solvodynamic models such as the Stokes-Einstein type [6-9]. From temperature-dependent measurements, activation energies can be calculated by the Arrhenius or the Vogel-Tamman-Fulcher equation (VTF), in order to evaluate models that treat the diffusion process similarly to diffusion in the solid state with jump or hole models [1, 2, 7]. 

The experimental value for Agl is 1.97 FT cirT1 [16, 3], which indicates that the silver ions in Agl are mobile with nearly a thermal velocity. Considerably higher ionic transport rates are even possible in electrodes, by chemical diffusion under the influence of internal electric fields. For Ag2S at 200 °C, a chemical diffusion coefficient of 0.4cm2s, which is as high as in gases, has been measured... 

This equation is identical to the Maxwell [236,237] solution originally derived for electrical conductivity in a dilute suspension of spheres. Hashin and Shtrikman [149] using variational theory showed that Maxwell s equation is in fact an upper bound for the relative diffusion coefficients in isotropic medium for any concentration of suspended spheres and even for cases where the solid portions of the medium are not spheres. However, they also noted that a reduced upper bound may be obtained if one includes additional statistical descriptions of the medium other than the void fraction. Weissberg [419] demonstrated that this was indeed true when additional geometrical parameters are included in the calculations. Batchelor and O Brien [34] further extended the Maxwell approach. 

Archie [23] examined electrical resistivity of various sand formations having pore spaces filled with saline solutions of different salt concentrations. Based upon his own experimental results, he obtained a simple relationship for the conductivity of beds of sand (assuming the sand itself is nonconductive) containing saline solution in terms of the porosity. In terms of diffusion coefficients his expression is... 

Trinh et al. [399] derived a number of similar expressions for mobility and diffusion coefficients in a similar unit cell. The cases considered by Trinh et al. were (1) electrophoretic transport with the same uniform electric field in the large pore and in the constriction, (2) hindered electrophoretic transport in the pore with uniform electric fields, (3) hydrodynamic flow in the pore, where the velocity in the second pore was related to the velocity in the first pore by the overall mass continuity equation, and (4) hindered hydrodynamic flow. All of these four cases were investigated with two different boundary condi-... 

The standard Rodbard-Ogston-Morris-Killander [326,327] model of electrophoresis which assumes that u alua = D nlDa is obtained only for special circumstances. See also Locke and Trinh [219] for further discussion of this relationship. With low electric fields the effective mobility equals the volume fraction. However, the dispersion coefficient reduces to the effective diffusion coefficient, as determined by Ryan et al. [337], which reduces to the volume fraction at low gel concentration but is not, in general, equal to the porosity for high gel concentrations. If no electrophoresis occurs, i.e., and Mp equal zero, the results reduce to the analysis of Nozad [264]. If the electrophoretic mobility is assumed to be much larger than the diffusion coefficients, the results reduce to that given by Locke and Carbonell [218]. 

Holz, M Lucas, O Muller, C, NMR in the Presence of an Electric Current, Simultaneous Measurements of Ionic Mobilities, Transference Numbers, and Self-Diffusion Coefficients Using an NMR Pulsed-Gradient Experiment, Journal of Magnetic Resonance 58, 294, 1984. Hooper, HH Baker, JP Blanch, HW Prausnitz, JM, Swelling Equilibria for Positively Ionized Polyacrylamide Hydrogels, Macromolecules 23, 1096, 1990. 

The EMD studies are performed without any external electric field. The applicability of the EMD results to useful situations is based on the validity of the Nemst-Planck equation, Eq. (10). From Eq. (10), the current can be computed from the diffusion coefficient obtained from EMD simulations. It is well known that Eq. (10) is valid only for a dilute concentration of ions, in the absence of significant ion-ion interactions, and a macroscopic theory can apply. Intuitively, the Nemst-Planck theory can be expected to fail when there is a significant confinement effect or ion-wall interaction and at high electric... 

Here, / is the electric field, k is the electrical conductivity or electrolytic conductivity in the Systeme International (SI) unit, X the thermal conductivity, and D the diffusion coefficient. is the electric current per unit area, J, is the heat flow per unit area per unit time, and Ji is the flow of component i in units of mass, or mole, per unit area per unit time. 

While electrical conductivity, diffusion coefficients, and shear viscosity are determined by weak perturbations of the fundamental diffu-sional motions, thermal conductivity is dominated by the vibrational motions of ions. Heat can be transmitted through material substances without any bulk flow or long-range diffusion occurring, simply by the exchange of momentum via collisions of particles. It is for this reason that in liquids in which the rate constants for viscous flow and electrical conductivity are highly temperature dependent, the thermal conductivity remains essentially the same at lower as at much higher temperatures and more fluid conditions. 

Some 30 years ago, transport properties of molten salts were reviewed by Janz and Reeves, who described classical experimental techniques for measuring density, electrical conductance, viscosity, transport number, and self-diffusion coefficient. 

Based on quite similar equilibria for the nitrate system (Li, K)N03, Lantelme and Chemla quantitatively estimated the existing species so that the experimental mobilities and self-diffusion coefficients could be obtained consistently. This could be successfully done. However, no direct evidence has been obtained yet that such species as [LiBrn] "and are really electrically conducting species. 

In order to calculate the rates for electron impact collisions and the electron transport coefficients (mobility He and diffusion coefficient De), the EEDF has to be known. This EEDF, f(r, v, t), specifies the number of electrons at position r with velocity v at time t. The evolution in space and time of the EEDF in the presence of an electric field is given by the Boltzmann equation [231] ... 

FIG. 9 Measured self-diffusion coefficients at 25°C for toluene (A), water ( ), acrylamide ( , and AOT ( ) in water, toluene, and AOT reverse microemulsions as a function of cosurfactant (acrylamide) concentration, f (wt%). The breakpoint at about 1.2% acrylamide approximately denotes, the onset of percolation in electrical conductivity. 

The electroneutrality condition decreases the number of independent variables in the system by one these variables correspond to components whose concentration can be varied independently. In general, however, a number of further conditions must be maintained (e.g. stoichiometry and the dissociation equilibrium condition). In addition, because of the electroneutrality condition, the contributions of the anion and cation to a number of solution properties of the electrolyte cannot be separated (e.g. electrical conductivity, diffusion coefficient and decrease in vapour pressure) without assumptions about individual particles. Consequently, mean values have been defined for a number of cases. 

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