Electrical potential Nemst

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 ... 

The movement of solute across a semipermeable membrane depends upon the chemical concentration gradient and the electrical gradient. Movement occurs down the concentration gradient until a significant opposing electrical potential has developed. This prevents further movement of ions and the Gibbs-Donnan equilibrium is reached. This is electrochemical equilibrium and the potential difference across the cell is the equilibrium potential. It can be calculated using the Nemst equation. 

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 ... 

Schofield Phil. Mag. March, 1926) has recently verified this relation by direct experiment. In order to appreciate the significance of this result, it is necessary to consider in more detail the electrical potential difference V and the manner in which it arises. Instead of regarding the phenomenon from the point of view of the Gibbs equation, it has been, until recently, more usual to discuss the subject of electro-capillarity from the conceptions developed by Helmholtz and Lippmann. These views, together with the theory of electrolytic solution pressure advanced by Nemst, are not in reality incompatible with the principles of adsorption at interfaces as laid down by Gibbs. 

Based on the previous description of the double layer, it is logical to assume that a direct relationship between the absolute charge at the interface and the concentration of ions in the vicinity of the interface exists. Indeed, several models have been developed in the past that describe the ion concentration as a function of the actual surface charge at a specific distance jc from the interface. Furthermore, the famous Nemst equation, which is the basis for understanding many electrochemical reactions, proves to be helpful as it relates the ion concentration to a quantity called the electrical potential ( j/). The electrical potential is the work (W) required to move a unit charge (q) through the electrical field ... 

The conversion of the reaction at the specific temperature, pressure and initial gas compositions is governed by its thermodynamic equilibrium. According to Equation (2.16), the maximum available work of the fuel cell can be determined by the Nemst potential, which represents the electrical potential of the reaction. 

The electric potential ip is assumed to be continuous throughout the electrodes and electrolyte except at the electrode/electrolyte interfaces. These discontinuities are usually modeled by Nemst s law. The model to calculate the potential jumps at each electrolyte/electrode interface is described in Celik et al. (2005). The source term in Equation (5.24) is non-zero only near the electrode/electrolyte interfaces to account for the potential jumps. 

The unequal distribution of K+ and Na+ across plasma membranes gives rise to an electrical potential difference AE. It can be calculated by the Nemst equation (see Chapter 2) ... 

On dissociation of a salt, ions start to diffuse in a solution. Without an electric potential effect, however, the diffusion of a single salt is treated as molecular diffusion. For dilute solutions of a salt, the Nemst-Haskell equation is used to estimate the dilfusivity coefficient... 

The Nemst equation applies (if we neglect the activity coefficients of the ions, in keeping with PB theory) to the emf (electromotive force) of an electrochemical cell. The emf of such a cell and the surface potential of a colloidal particle are quantities of quite different kinds. It is not possible to measure colloidal particle with a potentiometer (where would we place the electrodes ), and even if we could, we have no reason to expect that it would obey the Nemst equation. We have been at pains to point out that all the experimental evidence on the n-butylam-monium vermiculite system is consistent with the surface potential being roughly constant over two decades of salt concentration. This is clearly incompatible with the Nemst equation, and so are results on the smectite clays [28], Furthermore, if the zeta potential can be related to the electrical potential difference deviations from Nemst behavior, as discussed by Hunter... 

Figure 3-3. Equilibrium of K+ across a membrane. When K+ is in equilibrium across some membrane, the side with the higher concentration must be at a lower electrical potential for its chemical potential to be unchanged (ju = /aJJ in crossing the membrane is the same on the two sides of the membrane). The electrical potential difference across the membrane is then the Nemst potential for K+, /vKNote that E° and El must be expressed relative to some arbitrary baseline for electrical potentials.

The Nemst-Planck equation is conventionally applied to measure iontophoretic flux and arises from the theoretical development of Eq. 1 to define the flux of an ionic solute /, across a membrane (a) by simple diffusion due to the solute concentration gradient and (b) as a result of the electric potential difference across the membrane (electrochemical transport) [68-70]. 

The diffusion of charged ions is more complicated because of the law of electroneutrality, which states that the sum of the positive charges on each side of the membrane must equal the sum of the negative charges. In addition to the concentration gradient, the electrical potential difference determines the Bnal equilibrium of a substance across the membrane. Therefore at equilibrium, the concentration of an ionic species may be unequal across the membrane and this gradient will balance the electrical difference across the membrane. The driving force for transport in this situation is defined as the electrochemical potential. The Nemst equation describes the equilibrium situation for ions... 

To calculate the electric potential, we ll use the Nemst equation (Equation 23.13) ... 

Although the DDL theory was initially applied to clays of permanent charge, it was later used to describe the electrical potential at variable-charge (e.g., oxide) surfaces. This application required that the Nemst equation be first used to determine the surface electrical potential, as a function of the solution pH ... 

If the SE and RE of the zirconia-based sensor are exposed to different oxygen partial pressures, P02 (gas) and 7 02 (reference), this induces different chemical potentials of oxygen ions in zirconia at the interfaces with gas phases. In order that the electrochemical potential remains constant, the electrical potential has to be different. Therefore, the output emf of the electrochemical cell (3.2), represented as a difference between potentials on the RE and SE, obeys the well-known Nemst s law ... 

A biological cell can be compared to a concentration cell for the purpose of calculating its membrane potential. Membrane potential is the electrical potential that exists across the membrane of various kinds of cells, including muscle cells and nerve cells. It is responsible for the propagation of nerve impulses and heart beat. A membrane potential is established whenever there are unequal concentrations of the same type of ion in the interior and exterior of a cell. For example, the concentrations of ions in the interior and exterior of a nerve cell are 400 mM and 15 mM, respectively. Treating the situation as a concentration cell and applying the Nemst equation, we can write... 

If there is a difference in ion concentrations across a membrane, an electrical potential difference will arise. To compute the magnitude of that potential difference, we start with the Nemst equation, Eq. 14.6-5, which can be applied, to any one of the ions that can pass through the membrane ... 

Figure 4. The dependence of the ellipticity of bacteriorhodopsin reconstituted in vesicles on the electric diffusion potentials. The ordinate is the decrease of the CD signal at 210 nm induced by 10 7-M valinomycin. The abscissa is the electrical potentials calculated by the Nemst equation. The sign indicates the polarity inside the vesicle.

Cells create potential differences by pumping ions across membranes. The Nemst equation defines the electrical potential arising from differences in ionic concentration created by the various pumps. It relates the membrane resting potential to the charge and concentration of ions on either side of a membrane. 

Since these first reports, Iwahara and other investigators have studied the conductivities (both ionic and electronic), conduction mechanism, deuterium isotope effect, and thermodynamic stability of these materials. The motivation for most of this work derives from the desire to utilize these materials for high temperature, hydrogen-fiieled solid oxide fuel cells. In a reverse operation mode, if metal or metal oxide electrodes are deposited onto a dense pellet of this material and heated to temperature T, the application of an electric potential to the electrodes will cause a hydrogen partial pressure difference across the pellet according to the Nemst equation ... 

UF and RO models may all apply to some extent to NF. Charge, however, appears to play a more important role than for other pressure driven membrane processes. The Extended-Nemst Planck Equation (equation (3.28)) is a means of describing NF behaviour. The extended Nernst Planck equation, proposed by Deen et al. (1980), includes the Donnan expression, which describes the partitioning of solutes between solution and membrane. The model can be used to calculate an effective pore size (which does not necessarily mean that pores exist), and to determine thickness and effective charge of the membrane. This information can then be used to predict the separation of mixtures (Bowen and Mukhtar (1996)). No assumptions regarding membrane morphology ate required (Peeters (1997)). The terms represent transport due to diffusion, electric field gradient and convection respectively. Jsi is the flux of an ion i, Di,i> is the ion diffusivity in the membane, R the gas constant, F the Faraday constant, y the electrical potential and Ki,c the convective hindrance factor in the membrane. 

Wagner s theory is valid only for the growth of relatively thick films. The Nemst-Einstein relationship and the equation for transport by gradients of chemical and electrical potential (66) are valid only for small electric fields, whereas according to Eqs. (77 and 78) the voltage between the two interfaces of a film... 

Equation (5.2) implies that when summation of all the fluxes (Ji) of charged species (Zi) across the membrane leading to charging of the membrane capacity has concluded a quasi-equilibrium with a (approximately) constant Vm or Aij/ is attained. Its value depends on the difference in chemical potential Afj, ) of all transported species and on the affinities of coupled chemical reactions. This is embodied in the so-called Goldman diffusion equation but these relations are essentially transcendental with their explicit solution tractable only under defined conditions. If only one species permeates through the membrane, for example, a true equilibrium state is reached and the resulting transmembrane electrical potential difference is described by an expression known as the Nemst equation... 

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