Nernst field

Ambipolar diffusion involves the transport of charged species, and in such cases overall electric charge neutrality must be maintained during diffusion. Moreover, during ambipolar diffusion the difference in the mobilities of the diffusing species sets up a field, the Nernst field, that influences the rates of motion of the particles. 

Doi and his coworkers have proposed a semiquantitative theory for the swelling behavior of PAANa gels in electric fields [14]. They have considered the effect of the diffusion of mobile ions due to concentration gradients in the gel. First of all, the changes in ion concentration profiles under an electric field have been calculated using the partial differential Equation 16 (Nernst-Planck equation [21]). 

Williams (1964) derived the relation T = kBTrQV3De2, where T is the recombination time for a geminate e-ion pair at an initial separation of rg, is the dielectric constant of the medium, and the other symbols have their usual meanings. This r-cubed rule is based on the use of the Nernst-Einstein relation in a coulom-bic field with the assumption of instantaneous limiting velocity. Mozumder (1968) criticized the rule, as it connects initial distance and recombination time uniquely without allowance for diffusional broadening and without allowing for an escape probability. Nevertheless, the r-cubed rule was used extensively in earlier studies of geminate ion recombination kinetics. 

The Hall Effect In the presence of an orthogonal magnetic field in the z-direction an x-directed electric current produces a y-directed gradient of the electrochemical potential. Similarly an x-directed thermal gradient produces a y-directed gradient of the electrochemical potential, known as the Nernst effect. 

The ideas of Overton are reflected in the classical solubility-diffusion model for transmembrane transport. In this model [125,126], the cell membrane and other membranes within the cell are considered as homogeneous phases with sharp boundaries. Transport phenomena are described by Fick s first law of diffusion, or, in the case of ion transport and a finite membrane potential, by the Nernst-Planck equation (see Chapter 3 of this volume). The driving force of the flux is the gradient of the (electro)chemical potential across the membrane. In the absence of electric fields, the chemical potential gradient is reduced to a concentration gradient. Since the membrane is assumed to be homogeneous, the... 

Turning back to field effects, they derive from the second terms on the right-hand sides of equations (4.22), (4.23), (4.25), and (4.26). It should be noted that they are different from the corresponding term in the Nernst-Planck equation, which depicts migration effects for free-moving ions as recalled in... 

Scientists who were trained primarily in physics soon disputed this claim. For Nernst and Perrin, physical chemistry was chemical physics.3 In his Introduction to Chemical Physics (1939), Slater made clear his view that it was a historical accident that physics and chemistry are separate sciences, that the field within which he situated his work was a unified chemistry and physics, and that it is called chemical physics "[for] want of a better name, since physical chemistry is already preempted."4... 

Such a mechanism is not incompatible with a Haven ratio between 0.3 and 0.6 which is usually found for mineral glasses (Haven and Verkerk, 1965 Terai and Hayami, 1975 Lim and Day, 1978). The Haven ratio, that is the ratio of the tracer diffusion coefficient D determined by radioactive tracer methods to D, the diffusion coefficient obtained from conductivity via the Nernst-Einstein relationship (defined in Chapter 3) can be measured with great accuracy. The simultaneous measurement of D and D by analysis of the diffusion profile obtained under an electrical field (Kant, Kaps and Offermann, 1988) allows the Haven ratio to be determined with an accuracy better than 5%. From random walk theory of ion hopping the conductivity diffusion coefficient D = (e /isotropic medium. Hence for an indirect interstitial mechanism, the corresponding mobility is expressed by... 

The ranges of Eh and pH over which a particular chemical species is thermodynamically expected to be dominant in a given aqueous system can be displayed graphically as stability fields in a Pourbaix diagram,10-14 These are constructed with the aid of the Nernst equation, together with the solubility products of any solid phases involved, for certain specified activities of the reactants. For example, the stability field of liquid water under standard conditions (partial pressures of H2 and 02 of 1 bar, at 25 °C) is delineated in Fig. 15.2 by... 

Figure 15.3 is constructed as follows. The boundary between the stability fields of solid iron and 1 x 10-3 mol L-1 Fe2+(aq) is given by the Nernst equation (15.52) for... 

This general equation covers charge transfer at electrified interfaces under conditions both of zero excess field, low excess fields, and high excess fields, and of the corresponding overpotentials. Thus the Butler-Volmer equation spans a large range of potentials. At equilibrium, it settles down into the Nernst equation. Near equilibrium it reduces to a linear / vs. T) (Ohm slaw for interfaces), whereas, if T) > (RT/fiF) (i.e., one is 50 mV or more from equilibrium at room temperature), it becomes an exponential /vs. T) relation, the logarithmic version ofwhich is called Tafel s equation. 

Similar statements can be made about holes. They, too, have to be transported to the interface to be available for the receipt of electrons there. These matters all come under the influence of the Nernst-Planck equation, which is dealt with in (Section 4.4.15). There it is shown that a charged particle can move under two influences. The one is the concentration gradient, so here one is back with Fick s law (Section 4.2.2). On the other hand, as the particles are changed, they will be influenced by the electric field, the gradient of the potential-distance relation inside the semiconductor. Electrons that feel a concentration gradient near the interface, encouraging them to move from the interior of the semiconductor to the surface, get seized by the electric field inside the semiconductor and accelerated further to the interface. 

This book treats a selection of topics in electro-diffusion—a nonlinear transport process whose essence is diffusion of charged particles, combined with their migration in a self-consistent electric field. Basic equations of electro-diffusion were formulated about 100 years ago by Nernst and Planck in the ionic context [1]—[3]. Sixty years later Van Roosbroeck applied these equations to treat the transport of holes and electrons in semiconductors [4]. Correspondingly, major applications of the theory of electro-diffusion still lie in the realms of chemical and electrical engineering, related to ion separation and semiconductor device technology. Some aspects of electrodiffusion are relevant for electrophysiology. 

In order to evaluate this expression, we need to know the force v / that is responsible for producing the molecular flux. It could be an external force such as an electric field acting on ions. Then evaluation of Eq. 18-48 would lead to the relationship between electric conductivity, viscosity, and diflusivity known as the Nernst-Einstein relation. 

Baird et al. [350]). In the following analysis, the functional forms, p(E), which have been proposed (see below) to represent the field-dependence of the drift mobility are used for electric fields up to 1010Vm 1. The diffusion coefficient of ions is related to the drift mobility. Mozumder [349] suggested that the escape probability of an ion-pair should be influenced by the electric field-dependence of both the drift mobility and diffusion coefficient. Baird et al. [350] pointed out that the Nernst— Einstein relationship is not strictly appropriate when the mobility is field-dependent instead, the diffusion coefficient is a tensor D [351]. Choosing one orthogonal coordinate to lie in the direction of the electric field forces the tensor to be diagonal, with two components perpendicular and one parallel to the electric field. 

This interface is also known as the perm-selective interface (Fig. 6.1a). It is found in ion-selective sensors, such as ion-selective electrodes and ion-selective field-effect transistors. It is the site of the Nernst potential, which we now derive from the thermodynamic point of view. Because the zero-current axis in Fig. 5.1 represents the electrochemical cell at equilibrium, the partitioning of charged species between the two phases is described by the Gibbs equation (A.20), from which it follows that the electrochemical potential of the species i in the sample phase (S) and in the electrode phase (m) must be equal. 

Symmetrical placement of the ion-selective membrane is typical for the conventional ISE. It helped us to define the operating principles of these sensors and most important, to highlight the importance of the interfaces. Although such electrodes are fundamentally sound and proven to be useful in practice, the future belongs to the miniaturized ion sensors. The reason for this is basic there is neither surface area nor size restriction implied in the Nernst or in the Nikolskij-Eisenman equations. Moreover, multivariate analysis (Chapter 10) enhances the information content in chemical sensing. It is predicated by the miniaturization of individual sensors. The miniaturization has led to the development of potentiometric sensors with solid internal contact. They include Coated Wire Electrodes (CWE), hybrid ion sensors, and ion-sensitive field-effect transistors. The internal contact can be a conductor, semiconductor, or even an insulator. The price to be paid for the convenience of these sensors is in the more restrictive design parameters. These must be followed in order to obtain sensors with performance comparable to the conventional symmetrical ion-selective electrodes. 

Also, in the late 1950s and 1960s some particularly seminal papers on ion exchange kinetics appeared by Helfferich (1962b, 1963, 1965) that are classics in the field. In this research it was definitively shown that the rate-limiting steps in ion exchange phenomena were film diffusion (FD) and/ or particle diffusion (PD). Additionally, the Nernst-Planck theories were explored and applied to an array of adsorbents (Chapter 5). 

W. Nernst and F. A. Lindemann, Berl. Ber., 1911, p. 494, discuss the deviations from Einstein s result. P. Ehrenfest, Welche Rolle spielt die Lichtquantenhypothese in der Theorie der W rme-strahlung Ann. d. Phys., 36 (1911), 91, studies the possibility of a generalization of Planck s assumption in the field of black-body radiation. 

The knowledge of the surface potential for the dispersed systems, such as metal oxide-aqueous electrolyte solution, is based on the model calculations or approximations derived from zeta potential measurements. The direct measurement of this potential with application of field-effect transistor (MOSFET) was proposed by Schenk [108]. These measurements showed that potential is changing far less, then the potential calculated from the Nernst equation with changes of the pH by unit. On the other hand, the pHpzc value obtained for this system, happened to be unexpectedly high for Si02. These experiments ought to be treated cautiously, as the flat structure of the transistor surface differs much from the structure of the surface of dispersed particle. The next problem may be caused by possible contaminants and the surface property changes made by their presence. 

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