Flux of charges

During motion of the solution, excess charges are transported which are present in the slip layer. This flux of charges is equivalent to the electrical current in the solution. Taking into account that the perimeter of the slip layer is close to 2jrr, we find for the current... 

As mentioned above, the distribution of the various species in the two adjacent phases changes during a potential sweep which induces the transfer of an ion I across the interface when the potential approaches its standard transfer potential. This flux of charges across the interface leads to a measurable current which is recorded as a function of the applied potential. Such curves are called voltammograms and a typical example for the transfer of pilocarpine [229] is shown in Fig. 6, illustrating that cyclic voltammograms produced by reversible ion transfer reactions are similar to those obtained for electron transfer reactions at a metal-electrolyte solution interface. 

The flux of charge, connected with the mass flux of the electrically charged species, is given by Faraday s law for the equivalence of the current density and the material fluxes ... 

The fluxes of charged solutes depend on the diffusion potential arising from differences in the mobihties of individual ions, as well as on an ion s own concentration gradient (Equation 2.21). The effect of diffusion potentials will be important if the carbonate species are a large part of the total ion concentration, as they often will be. Therefore we have for the net flux of ion B... 

The role of gas phase initiation processes was further explored by Tibbitt et al. . These authors proposed that the polymerization of unsaturated hydrocarbons in a 13.56 MHz plasma is initiated by free radicals formed in the gas by electron-monomer collisions, the initiation reactions listed in Table 6. Moreover, it was assumed that the formation of free radicals on the polymer surface due to the impact of charged particles could be neglected. This assumption is supported by the fact that at 13.56 MHz and pressures near one torr the discharge frequency is significantly greater than either f, or f and that as a result the fluxes of charged particles to the electrode surfaces are quite small. 

Again, for the process Mn+ (aq) + ne —> M(s) and assuming first that diffusion is the only mechanism of transport across the stationary layer, in the steady state, the flux of electroactive species across the layer must be balanced by the flux of charge at the electrode surface. For a linear concentration gradient across a stationary layer of thickness 8, application of Fick s first law gives... 

However, if A>/, = 0 across a stationary interface, a flux of charged species i results, which can be written in a linear theory as... 

Consider an ionic material that contains a dilute concentration of positively charged ions that diffuse interstitially (interstitial diffusion is described in Section 8.1.4). D is the interdiffusivity of these ions in the absence of any field. As shown in Sections 2.2.2 and 2.2.3, if an electric field, E = —V, is applied, the diffusion potential will be the electrochemical potential given by Eq. 2.41. According to Eq. 2.21, the flux of charged interstitials is... 

In the absence of a significant concentration gradient, the corresponding flux of charge is then... 

The charge mobility of an ion represents the speed that acquires the ion per unit of electric field. The electric migration current corresponding to the ionic movement of a single kind of charge is equal to the flux of charge, i.e., to the rate at which the charge cross any plane normal to the flow (see Eq. 1.141) [56]... 

Fig. 9. Energy spectrum of the calculated flux of charge exchange neutrals which escape from TFTR immediately after neutral beam heating23 ...

It has been shown that the impact of any electric potential gradient on the flux of ions may be disregarded under flue gas desulfurization conditions, as long as the mass flux equations are combined with a flux charge equation [99]. Therefore, the mass balances must be combined with a flux of charge balance as the potential gradient is neglected [70]. 

Here C is the specific differential double layer capacitance. The two terms on the left side of Eq. (4) describe the capacitive and faradaic current densities at a position r at the electrode electrolyte interface. The sum of these two terms is equal to the current density due to all fluxes of charged species that flow into the double layer from the electrolyte side, z ei,z (r, z = WE), where z is the direction perpendicular to the electrode, and z = WE is at the working electrode, more precisely, at the transition from the charged double layer region to the electroneutral electrolyte. 4i,z is composed of diffusion and migration fluxes, which, in the Nernst-Planck approximation, are given by... 

The current, /, that passes between two parallel electrodes of area A is related to the flux of charge j, and to the potential difference between them, A0, by... 

Nernst-Planck equation — This equation describes the flux of charged particles by diffusion and electrostatic forces. When the ion with charge ze is distributed at concentration c in the potential, cp, it has a one-dimensional flux of the ion, / = -Ddc/dx - (zF/RT) Dcdcp/dx [i]. This can be derived from the concept that the force caused by the gradient of the electrochemical potential is balanced with frictional force by viscosity, t], of the medium. When a spherical ion with radius ro is in the inner potential, cp, the gradient of the electrochemical potential per ion is given by... 

Wagner equation — denotes usually one of two equations derived by -> Wagner for the flux of charged species Bz under an -> electrochemical potential gradient, and for the - electromotive force of a -> galvanic cell with a mixed ionic-electronic -> conductor [i-v] ... 

The first equation shows that the flux of -> charge carriers in an electrochemical system is proportional to the partial conductivity and thermodynamic driving force, namely the electrochemical potential gradient (see Onsager equation). When the chemical potential of... 

Show that the molar flux of charged particles obeys... 

As emphasized earlier [see Eq. (6.2.15), for example], any flux of charged particles (on a per mole basis) arises in response to the establishment of a gradient Vf in... 

In this chapter we turn our attention to the properties of solutes. We will compare chemical potentials in the aqueous phases on the two sides of a membrane or across some other region to predict the direction of passive solute fluxes as well as the driving forces leading to such motion. We will also show how the fluxes of charged species can account for the electrical potential differences across biological membranes. 

The fundamental equation for the current density (flux of charge) as a function of the drift velocity has been shown to be... 

As emphasized earlier (see Eq. (6.1.27), for example), any flux of charged particles /+ (on a per mole basis) arises in response to the establishment of a gradient Vf in electrochemical potential. For one-dimensional flow we may write J+ = LVt = L(V/x- -Z -FV(/)) = L(V+VP-1-Z+FV0), where the contribution —SdT has been dropped because constant-temperature conditions were adopted similarly, Jq = L VqVP. 

The single particle flux of charge carriers, with neglect of cross terms between fluxes, is given by... 

Bockris Reddy (1970) describes the Butler-Volmer-equation as the "central equation of electrode kinetics . In equilibrium the adsorption and desorption fluxes of charges at the interface are equal. There are common principles for the kinetics of charge exchange at the polarisable mercury/water interface and the adsorption kinetics of charged surfactants at the liquid/fluid interface. Theoretical considerations about the electrostatic retardation for the adsorption kinetics of ions were first introduced by Dukhin et al. (1973). 

Mechanism and Kinetics of Piasma Poiymerization. Using kinetic relation (9-66), find the plasma polymerization regimes (derive criteria for the regimes) when the polymer film deposition rate depends on and is proportional to (1) only the flux of charged particles, (2) only the flux of relevant neutral species, and (3) fluxes of both active neutral and charged particles. 

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