Potential jumps

Fig. V-15. Volta potentials Galvani potentials 0, and surface potential jumps x in a two-phase system. (From Ref. 187.)...

Thus Pi, surface potential jump X, the chemical potential p, and the Galvani potential difference between two phases A0 = are not. While jl, is defined, there is a practical dif-... 

In fact, some care is needed with regard to this type of concentration cell, since the assumption implicit in the derivation of A2.4.126 that the potential in the solution is constant between the two electrodes, caimot be entirely correct. At the phase boundary between the two solutions, which is here a semi-pemieable membrane pemiitting the passage of water molecules but not ions between the two solutions, there will be a potential jump. This so-called liquid-junction potential will increase or decrease the measured EMF of the cell depending on its sign. Potential jumps at liquid-liquid junctions are in general rather small compared to nomial cell voltages, and can be minimized fiirther by suitable experimental modifications to the cell. 

Phosphoric acid esters are strong acids similar to orthophosphoric acid. Potentiometric titration of a 0.1 N aqueous solution of an acid phosphoric acid ester clearly shows two potential jumps which lie at pH values of 6.5 and 11.5. The pH value of diluted aqueous solutions of acid esters lies in the range of 1-3. Phosphoric acid esters are stable against hydrolysis, but adducts of free phosphoric acid esters with ethylene oxide are generally less stable. 

When a mixture of phosphoric acid and phosphoric acid esters is titrated with a sodium hydroxide solution two potential jumps can be observed. The first jump results from the acid group of the diester, the first neutralization step of the monoester, and the first neutralization step of free phosphoric acid. The second potential jump is caused by the second neutralization steps of the monoester and of the free phosphoric acid. The third step of neutralization of the free phosphoric acid cannot be covered by this method. Titration of acid esters can only be used for the determination of mono- and diesters of phosphoric acid when the amount of free phosphoric acid is separately ascertained. 

The possibility of measuring the Volta potential in the system metal-solid-state electrolyte and using the data obtained to determine ionic components of the free lattice energy has been shown in our papers. Earlier, Copeland and Seifert measured the Volta potential between Ag and solid AgNOj in the temperature range between 190 and 280 °C. They investigated the potential jump during the phase transition from solid to liquid salt. 

Yamakata, A., Uchida, T., Kubota, J. and Osawa, M. (2006) Laser-induced potential jump at the electrochemical interface probed by picosecond time-resolved surface-enhanced infrared absorption spectroscopy./. Phys. Chem. B, 110, 6423-6427. 

The above rate equations confirm the suggested explanation of dynamics of silver particles on the surface of zinc oxide. They account for their relatively fast migration and recombination, as well as formation of larger particles (clusters) not interacting with electronic subsystem of the semiconductor. Note, however, that at longer time intervals, the appearance of a new phase (formation of silver crystals on the surface) results in phase interactions, which are accompanied by the appearance of potential jumps influencing the electronic subsystem of a zinc oxide film. Such an interaction also modifies the adsorption capability of the areas of zinc oxide surface in the vicinity of electrodes [43]. 

In Fig. 4.6, the titration of p-hydroxybenzoic acid in pyridine shows that the COOH and OH groups can be clearly determined. However, in acetonitrile there is half-way the titration of the COOH group an additional potential jump this can be explained by a phenomenon which was already known for acetic acid23, viz., in the inert solvent acetonitrile intermolecular hydrogen-bridge... 

Conductometric titrations. Van Meurs and Dahmen25-30,31 showed that these titrations are theoretically of great value in understanding the ionics in non-aqueous solutions (see pp. 250-251) in practice they are of limited application compared with the more selective potentiometric titrations, as a consequence of the low mobilities and the mutually less different equivalent conductivities of the ions in the media concerned. The latter statement is illustrated by Table 4.7108, giving the equivalent conductivities at infinite dilution at 25° C of the H ion and of the other ions (see also Table 2.2 for aqueous solutions). However, in practice conductometric titrations can still be useful, e.g., (i) when a Lewis acid-base titration does not foresee a well defined potential jump at an indicator electrode, or (ii) when precipitations on the indicator electrode hamper its potentiometric functioning. 

Before finding the Laplace-transformed probability density wj(s, zo) of FPT for the potential, depicted in Fig. A 1(b), let us obtain the Laplace-transformed probability density wx s, zo) of transition time for the system whose potential is depicted in Fig. Al(c). This potential is transformed from the original profile [Fig. Al(a)] by the vertical shift of the right-hand part of the profile by step p which is arbitrary in value and sign. So far as in this case the derivative dpoints except z = 0, we can use again linear-independent solutions U(z) and V(z), and the potential jump that equals p at the point z = 0 may be taken into account by the new joint condition at z = 0. The probability current at this point is continuous as before, but the probability density W(z, t) has now the step, so the second condition of (9.4) is the same, but instead of the first one we should write Y (0) + v1 (0) = YiiOje f1. It gives new values of arbitrary constants C and C2 and a new value of the probability current at the point z = 0. Now the Laplace transformation of the probability current is... 

The formation of pores during anodization of an initially flat silicon electrode in HF affects the I-V characteristics. While this effect is small for p-type and highly doped n-type samples, it becomes dramatic for moderate and low doped n-type substrates anodized in the dark. In the latter case a reproducible I-V curve in the common sense does not exist. If, for example, a constant potential is applied to the electrode the current density usually increases monotonically with anodization time (Thl, Th2]. Therefore the I-V characteristic, as shown in Fig. 8.9, is sensitive to scan speed. The reverse is true for application of a certain current density. In this case the potential jumps to values close to the breakdown bias for the flat electrode and decreases to much lower values for prolonged anodization. These transient effects are caused by formation of pores in the initially flat surface. The lowering of the breakdown bias at the pore tips leads to local breakdown either by tunneling or by avalanche multiplication. The prior case will be discussed in this section while the next section focuses on the latter. 

Conduction of the action potential in myelinated axons is called saltatory conduction. Because ion flux only occurs at the nodes of Ranvier, the action potential jumps, in effect, from node to node. This provides two advantages, speeding the rate of conduction and reducing the metabolic cost of an action potential, because energy-dependent ion transporters are not needed along myelinated segments. 

We observe that the sign of A

additional potential jump on the surface of the semiconductor due to the electric double layer, which arises on the surface in adsorption and figures as one of the terms in the experimentally measured work fimction. Such an electric double layer may be the result of the polarization of the chemisorbed particles (when the dipole moments of the chemisorbed particles are directed normally to the surface). This can be the case, for example, in weak chemisorption (when the total charge of the surface remains unchanged). 

This may be why cells use electric signals because these are in principle highly efficient. Electrochemical machines (i.e., storage batteries) are just the type that enable large concentration gradients to be balanced by electrical potential jumps so as to preserve the continuity of the electrochemical potential, which is the requirement for reversibility. The concentration gradients of K+ and Na across cell membranes that... 

A terminological remark is due. An equilibrium between two media with different fixed charge density (e.g., an ion-exchanger in contact with an electrolyte solution) is occasionally termed the Donnan equilibrium. The corresponding potential drop between the bulks of the respective media is then termed the Donnan potential. By the same token, we speak of the local Donnan equilibrium and the local Donnan potential, referring, respectively, to the local equilibrium and the interface potential jump at the surface of discontinuity of the fixed charge density, considered in the framework of the LEN approximation. 

Equation (4.4.1b) expresses impermeability of the ideally cation-permselective interface under consideration for anions j is the unknown cationic flux (electric current density). Furthermore, (4.4.1d) asserts continuity of the electrochemical potential of cations at the interface, whereas (4.4. lg) states electro-neutrality of the interior of the interface, impenetrable for anions. Here N is a known positive constant, e.g., concentration of the fixed charges in an ion-exchanger (membrane), concentration of metal in an electrode, etc. E in (4.4.1h) is the equilibrium potential jump from the solution to the interior of the interface, given by the expression ... 

A countercharge of opposite sign to that at the metal surface accumulates at the electrolyte side, confined to a discrete region. The potential jump at the electrode—electrolyte interface occurs in a short finite distance given by the minimum approach distance of solvated ions due to their finite radius. 

The electric potential jump A

electrical charge. Thus, the interface corresponds to a capacitor for which we have (ps = surface charge density)... 

In general the diffusion of ions through a membrane is attended with the building-up of a potential jump across the membrane. The membrane potential is the potential difference which occurs between a point in the... 

In the second step the charge arrives at the internal phase passing through the interface. The associated potential is known as the surface potential jump (also called surface potential, surface electrical potential, etc.). It is determined by dipoles aligned at the interface and by surface charges. It is not identical with the Volta potential difference (also sometimes called the surface potential) that has so far been used for the description of the electrical double layer. For the treatment of the electrical double layer, dipoles did not play a role. In particular in water, however, the aligned water molecules contribute substantially to the surface potential jump x- The Galvani potential, Volta potential, and surface potential jump are related by... 

Fig. 3.8 Schematic showing both ohmic and activation losses, and the modeled discretized potential jump at the anode-electrolyte interface.

Figure 3.8 depicts a qualitative description of the resulting potential jump taking place at the anode-electrolyte interface. 

Additionally, the reaction at the cathode consumes electrons, thus a potential jump is also established between the cathode and the electrolyte. The ideal potential jump is provided by the Nemst equation, however, due to the activation loss, the real potential jump is lower than the ideal one, as reported in (3.41). 

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. 

Figure 16.2 Saltatory conduction. Myelin acts as an insulator to prevent current loss as the action potential travels down the axon. Sodium and potassium channels are clustered at the Nodes of Ranvier, where there is no myelin. Action potentials jump from one node to the next, reducing the overall membrane area involved in conduction, and speeding up electrical transmission.

The particular form of the charging current will depend on the potential perturbation. For the application of a potential jump from a rest potential to a constant value E, AE = E — restj it is given by [12] ... 

Note that, in agreement with Eq. (7.137), the non-faradaic contribution to the gsw — E curve is due only to the potential jump (equal to 2 sw). This behavior is due to the differential character of the gsw nf — E response. 

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