Electric potential gradient diffusion

However, in interdiffusion of ions of different mobilities, Fick s law fluxes would be unequal and disturb electroneutrality. Here, the first, minute deviation from local electroneutrality generates an electric potential gradient (diffusion potential) that produces electric transference of ions superimposed on diffusion. This is the mechanism by which the system manages to balance the fluxes so as to maintain electroneutrality (Schlogl and Helfferich, 1957 Helfferich, 1962a Helfferich and Hwang, 1988). The flux now obeys the Nernst-Planck equation (Nernst, 1888 1889 Planck, 1890)... 

Nonporous Dense Membranes. Nonporous, dense membranes consist of a dense film through which permeants are transported by diffusion under the driving force of a pressure, concentration, or electrical potential gradient. The separation of various components of a solution is related directiy to their relative transport rate within the membrane, which is determined by their diffusivity and solubiUty ia the membrane material. An important property of nonporous, dense membranes is that even permeants of similar size may be separated when their concentration ia the membrane material (ie, their solubiUty) differs significantly. Most gas separation, pervaporation, and reverse osmosis membranes use dense membranes to perform the separation. However, these membranes usually have an asymmetric stmcture to improve the flux. 

The first of these is the ohmic potential gradient, characteristic for charge transfer in an arbitrary medium. It is formed only when an electric current passes through the medium. The second expression is that for the diffusion potential gradient, formed when various charged species in the electrolyte have different mobilities. If their mobilities were identical, the diffusion electric potential would not be formed. In contrast to the ohmic electric potential, the diffusion electric potential does not depend directly on the passage of electric current through the electrolyte (it does not disappear in the absence of current flow). 

As demonstrated in the preceding section, an electric potential gradient is formed in electrolyte solutions as a result of diffusion alone. Let us assume that no electric current passes through the solution and convection is absent. The Nernst-Planck equation (2.5.24) then has the form ... 

The analysis of oxidation processes to which diffusion control and interfacial equilibrium applied has been analysed by Wagner (1933) who used the Einstein mobility equation as a starting point. To describe the oxidation for example of nickel to the monoxide NiO, consideration must be given to the respective fluxes of cations, anions and positive holes. These fluxes must be balanced to preserve local electroneutrality throughout the growing oxide. The flux equation for each species includes a term due to a chemical potential gradient plus a term due to the electric potential gradient... 

However, in bulk diffusion, ions cannot move independently of each other because electrical neutrality must be maintained. Consequently there is an electric potential between diffusing ions such that the faster ions tend to be slowed down by the slower ones and vice versa. The flux of a particular ion is therefore the sum of the diffusion due to its own concentration gradient and that due to the gradient of the diffusion potential arising from differences in the mobilities of the ions present. This is expressed by the Nemst-Planck equation along the x-axis ... 

The only process occurring in a Hquid junction is the diffusion of various components of the two solutions in contact with it. The various mobilities of the ions present in the Hquid junction lead to the formation of an electric potential gradient, termed the diffusion potential gradient. A potential difference, termed the liquid-junction potential, A0x,. is formed between two solutions whose composition is assumed to be constant outside the Hquid junction. 

The sulfonamide diuretics cause problems through excessive excretion of potassium which diffuses into the urine as Na+ is removed in the distal tubule. This cation exchange is prevented by a different type of diuretic, triamterene (198), which was developed by following the observation that xanthopterin (199) affects renal function. The pyrazine amiloride (200) also increases Na+ output and spares K+, and is used in conjunction with chlorothiazide. It has been shown to reduce the electrical potential gradient along which K+ migrates into the lumen of the tubule. 

The mobility, u, of an ion expresses the ease with which it responds to a gradient of electric potential. The diffusion coefficient, D, of an ion expresses the ease with which it responds to a gradient of its concentration. One might well imagine that a relationship exists between u and D. This is indeed the case the relation is... 

An applied electrical potential gradient can induce diffusion (electromigration) in metals due to a cross effect between the diffusing species and the flux of conduction electrons that will be present. When an electric field is applied to a dilute solution of interstitial atoms in a metal, there are two fluxes in the system a flux of conduction electrons, Jq, and a flux of the interstitials, J. For a system maintained at constant temperature with Fq = -V = E, Eq. 2.21 gives... 

Both thermal gradients and electrical-potential gradients can induce mass diffusion. In a system containing a thermal gradient where both heat flow and mass diffusion of a dilute interstitial component 1 can occur, Eq. 2.21 predicts the interstitial flux... 

Action potentials are waves of depolarization and repolarization of the plasma membrane. In a resting nerve cell, the electric potential gradient (At//) across the plasma membrane is about —70 mV, inside negative. This potential difference is generated mainly by the unequal rates of diffusion of K+ and Na+ ions down concentration gradients maintained by the Na+-K+ ATPase. 

The Nernst-Planck equation constitutes the starting point for the electrotransport models [55-57], The overall flux of the ionic species i (/,) comprises the diffusion term driven by the chemical potential gradient (dc,/dx) and the electric transference term due to the electrical potential gradient (d /dx) ... 

The reductive dissolution of metal oxides such as Mn(III/IV) oxides by organic reductants occurs by the following sequential steps (Stone, 1986) (1) diffusion of reductant molecules to the oxide surface, (2) surface chemical reaction, and (3) diffusion of reaction products from the oxide surface. Steps (1) and (3), which are transport steps, are influenced by both the interfacial concentration gradient and the electrical potential gradient due to the net charge of the oxide surface. 

In the sedimentation-equilibrium method a lower centrifugal field is applied and the processes of sedimentation and diffusion are brought to equilibrium [13]. In this case the governing equation contains sedimentation equilibrium concentrations of species at different positions from the axis of rotation, but one does not need to know D. It should be pointed out that sedimentation and diffusion are more complicated when the species are electrically charged. This is because the smaller counterions sediment at a slower rate than do the colloidal-sized species. This creates an electric potential gradient that tends to speed up the counter-ions and to drag the colloidal species. The reverse effect occurs for diffusion. 

Example 10.5 Diffusion cell and transference numbers The diffusion cell shown in Figure 10.2 has NaCl mixtures in the two chambers with concentrations c1A = lOOmmol/L and c1B = lOmmol/L. The mobilities of Na+ and Cl- ions are different and their ratio yields their transference numbers b+lb = t+/t = 0.39/0.61 (NaCl). The transference number t for an ion is the fraction of the total electric current carried by the ion when the mixture is subjected to an electric potential gradient. For monovalent ions, we have t+lt = 1. Estimate the diffusion potential of the cell at steady-state conditions at 298 K. Assume that activity coefficients are equal in the two reservoirs (Garby and Larsen, 1995). 

Surface tension gradient effects add to the better known phenomena of density-gradient-driven convection, concentration-gradient-driven diffusion and electrical-potential-gradient-driven ion migration, which appear in the existing theory of cells and electrodes. The potential difference of a working cell is affected by all the near electrode effects mentioned here. The experimental and analytical difficulty is to separate the variables. Indeed the fluid mechanical effects stir the electrochemical reaction, and make cause and effect difficult to discern. 

The basic principle of electrodialysis for desalination is to drive the cations and anions from saline water feeds under the influence of an electric potential gradient through cation- and anion-selective membranes. The electric potential prevents diffusion of oppositely charged ions in the other direction. A schematic of the process is shown in Figure 29.7. In a typical electrodialysis cell to deionize a salt solution, anion- and cation-exchange membranes are arranged alternatively in a... 

The overall flux /, of an arbitrary species i is composed of three additive terms the diffusion flux (/i)difr caused by the chemical potential gradient of the species (Fig. 7), the electric transference (y,)ei caused by the electric potential gradient, and the transfer (yi)con caused by convection. The diffusion flux is... 

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