DIFFUSION AND MIGRATION

With respect to a coupled diffusion and migration mass transfer case, eq. (4.2) reduces to 

Solving this ordinary deferential equation gives a theoretical definition of the potential gradient as 

---

Although the h.e.r. involves transport of HjO ions (or HjO molecules) to the metal surface by diffusion and migration, the activation energy for... 

Fig. 12.2 Ion distortion by the field in the vicinity of a negative cathode, (a) Diffusion of anion to cathode, (b) diffusion and migration of distorted complex and (c) release of CN ions and incorporation of Ag into the lattice...

Trai brt. of Ions . the, combined mottoh. of ions in an electrOIyte, (solid Or liquid) under, diffusion and migration. ... 

The surface concentrations that are attained as a result of balance between the electrode reaction rates and the rates of supply or escape of components by diffusion and migration are given by Eqs. (4.11) and (4.12). Hence, the overall expression for concentration polarization becomes... 

Thus, the ideas above do not suffice for an interpretation of all experimental results. These ideas include the assumption that the ions move in the membrane only under the effect of concentration and potential gradients (diffusion and migration), and that transport of one sort of ions is independent of the transport of other sorts of ions. This transport of ions under the effect of external forces has been named passive ionic transport. 

The mobility of a species ut is a parameter connecting diffusion and migration processes. This section will be concerned primarily with the qualitative theory of mobility, which has characteristic properties for... 

Diffusion and migration in solid crystalline electrolytes depend on the presence of defects in the crystal lattice (Fig. 2.16). Frenkel defects originate from some ions leaving the regular lattice positions and coming to interstitial positions. In this way empty sites (holes or vacancies) are formed, somewhat analogous to the holes appearing in the band theory of electronic conductors (see Section 2.4.1). 

According to Faraday s law, the current passing through the electrode is equivalent to the material flux of electroactive substances. The disappearance of electroactive substances in the electrode reaction is considered as their transport through the electrode surface. Consequently, only diffusion and migration but not convection flux need be considered at the electrode surface, as the electrode is impenetrable to the solution components. 

The second factor is the type and concentration of chemicals in soil. Soils with low initial ionic strengths favor high EO efficiencies. A lower initial ionic strength is responsible for a higher conductivity of the specimen, which in turn results in a decrease in the resistance offered to current flow, and hence the ion flow is governed more by diffusion and migration. 

Equivalent Diffusion and Migration Laws for Electron Hopping Between Fixed Sites... 

Planck s solution for the liquid junction potential [30, 31] is based on the assumption of stationary state transport, through diffusion and migration, and... 

Figure 3.38. Principle of the photorefractive effect By photoexcitation, charges are generated that have different mobilities, (a) The holographic irradiation intensity proHle. Due to the different diffusion and migration velocity of negative and positive charge carriers, a space-charge modulation is formed, (b) The charge density proHle. The space-charge modulation creates an electric Held that is phase shifted by 7t/2. (c) The electric field profile. The refractive index modulation follows the electric field by electrooptic response, (d) The refractive index profile.

Convection plays an important part in electrochemical systems and it is of interest here to state a few of its properties. The transport processes that have been dealt with so far are diffusion and migration. In diffusion, it is found that the movement of the dissolved entities follows (dc/dx)y z, i.e., they follow the concentration gradient in the one direction, usually that perpendicular to the electrode. In migration, it is the movement of ions only that is being discussed and they travel at the bidding of, and hence in the direction of, the electric field in the region of the solution being considered. 

Equation (52) contains right-hand terms representing diffusion and migration. The overall effects of these two transport processes may be separated in the following way. Write eqn. (52) for j = 1, = 2,. . . 7 = N and then sum these equations. The summation generates a migratory term with a factor 2z -c,-(x, t) which eqn. (50) shows to be zero. Hence... 

In order to be able to describe quantitatively the flux of electrons at an electrode, we first have to know the flux of material reaching the electrode which can result from convection, diffusion, and migration processes. In general, we may write for a species ... 

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... 

---