Local electrical potential

In a simple electron transfer reaction, the reactant is situated in front of the electrode, and the electron is transferred when there is a favorable solvent fluctuation. In contrast, during ion transfer, the reactant itself moves from the bulk of the solution to the double layer, and then becomes adsorbed on, or incorporated into, the electrode. Despite these differences, ion transfer can be described by essentially the same formalism [Schmickler, 1995], but the interactions both with the solvent and with the metal depend on the position of the ion. In addition, the electronic level on the reactant depends on the local electric potential in the double layer, which also varies with the distance. These complications make it difficult to perform quantitative calculations. 

Here (r, 6) are polar coordinates, < (r, 9) is the normalized local electric potential, and integration is carried Over the region accessible for counterions. If the singularity in

positive line charge indeed were of... 

The amount of adsorbed hydrogen decreases in the presence of halide ions [395, 396]. This is due to a decrease in the M-H adsorption energy induced by ion-specific adsorption with partial charge transfer. The decrease in M-H bond strength results in an increase of overpotential. The effect is lower for Cl and higher for I -. However two joint effects are operative one due to electronic modifications, and the other one of an electrostatic nature related to a change in the local electric potential... 

Piezoresponse force microscopy (pfm) [11] and Kelvin probe force microscopy (kpfm) [9] were applied to deduce the polarization and local electric potential distribution over the whole cross section of the pzt sample (see Figure 12.3 and Figure 12.4) under static conditions as well as after switching. The details of our setup are described elsewhere [9,11],... 

The sex attractants of Bombyx and Porthetria (and probably those of most Lepidoptera as well as of insects of other orders) are received by olfactory receptors of the male antennae 38), Removal of one male antenna does not prevent detection of the sex scent, but complete removal of both antennae results in loss of such reception. Schneider and coworkers 35, 36) have taken advantage of this antennal reception in developing an electrophysiological method for the bioassay of insect sex attractants which is approximately 1000 times more sensitive than any known behavioral method. They found that stimulation of the sensory cells in the male antenna by exposure to the female sex scent set up a local electrical potential (receptor potential) %hose amplitude is dependent upon the intensity of the stimulant. The... 

A further spatially resolved method, also based on work function contrast, is scanning Kelvin probe microscopy (SKPM). As an extended version of atomic force microscopy (AFM), additional information on the local surface potential is revealed by a second feedback circuit. The method delivers information depending on the value (p (p(x) + A x). Here, A(zS(x) is the difference in work function between the sample and the AFM tip and cp(x) is the local electric potential [12]. (p x) itself gives information on additional surface charges due to... 

Boltzmann Equation A fundamental equation giving the local concentrations of ions in terms of the local electric potential in an electric double layer. See also Poisson-Boltzmann Equation. 

The bulk transport of ions in electrochemical systems without the contribution of advection is described by Poisson-Nernst-Planck (PNP) equations (Rubinstein, 1990).The well-known Nernst-Planck equation describes the processes of the process that drives the ions from regions of higher concentration to regions of lower concentration, and electromigration (also referred to as migration), the process that launches the ions in the direction of the electric field (Bard and Faulkner, 1980). Since the ions themselves contribute to the local electric potential, Poisson s equation that relates the electrostatic potential to local ion concentrations is solved simultaneously to describe this effect. The electroneutrality assumption simplifies the mathematical treatise of bulk transport in most electrochemical systems. Nevertheless, this no charge density accumulation assumption does not hold true at the interphase regions of the electric double layer between the solid and the Uquid, hence the cause of most electrokinetic phenomena in clay-electrolyte systems. 

In summary, the modeling of the electroosmotic component of the electrochemical transport is dependent on the electroosmotic velocity of the fluid flow. The classical H-S equation expresses this parameter as a function of the held gradient. Due to the tight coupling between the ion concentrations and electric potential—as the ions contribute to the local electric potential themselves—the use of H-S electroosmotic velocity in transport determination in clay soils may result in nonlinear predictions (Ravina and Zaslavsky, 1967 Chu, 2005). Hence, uncoupling this parameter from the electric potential using the surface conductivity C7s, and the resulting proportion of the current transferred over the solid-liquid interface 4, should provide an intrinsic electroosmotic velocity dependent on clay surface properties only, as first introduced by Khan (1991) in Equation 2.8. 

Moreover, local electrical potentials are known to adversely affect the performance of pH electrodes. 

The local electric potential is governed by the Poisson equation... 

Here nie is electron mass and h is Planck s constant. Hence, for electron energy W = 1 eV-10 keV, the wavelength is X 10-0.1 A. From this diffraction experiment we can find the distribution of the electric potential correlated to some extent with the distribution of the mass density. Another technique for mapping the local electric potential is Atomic Force Microscopy [3]. 

J c and Z are, respectively, the ion flux vector, diffusion coefficient, concentration, and charge of species i in solution and u are the local electric potential and fluid velocity while F, R, and T are Faraday s constant, the gas constant, and the absolute temperature, respectively... 

Here x is the distance from a reference plane, corresponding to the distance of closest approach of hydrated ions z. and C are the charge number and unperturbed concentration of the i" ionic species is the local electric potential and R, F, and T are the gas constant, Faraday s constant, and the absolute temperature. The situation is quite analogous to the junction between a semiconductor and a metal, except that, in an electrolyte, the density of ionic states close to the interface is large compared with the electronic density of states, and therefore an ionic rather than an electronic space charge forms. This perturbation in concentration extends into the electrolyte for a characteristic distance known as the Debye length ... 

The potential generated outside the sphere contains two contributions, i.e., one from the incident field (first term) and another from the field of an electric dipole located at the center of the sphere with polarizability ga oriented in the direction of the incident field (second term). Thus the local electric potential at position r, in the small-sphere approximation, is equivalent to that generated by the applied incident field and a reflected field produced by the metal sphere. 

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