Electrochemical potential, ions

Electrochemical Potential Ion-selective electrodes Gas selective electrodes Field effect transistors (ISFET, semiconductors)... 

Membrane Potentials Ion-selective electrodes, such as the glass pH electrode, function by using a membrane that reacts selectively with a single ion. figure 11.10 shows a generic diagram for a potentiometric electrochemical cell equipped with an ion-selective electrode. The shorthand notation for this cell is... 

Attack associated with nonuniformity of the aqueous environments at a surface is called concentration cell corrosion. Corrosion occurs when the environment near the metal surface differs from region to region. These differences create anodes and cathodes (regions differing in electrochemical potential). Local-action corrosion cells are established, and anodic areas lose metal by corrosion. Shielded areas are particularly susceptible to attack, as they often act as anodes (Fig. 2.1). Differences in concentration of dissolved ions such as hydrogen, oxygen, chloride, sulfate, etc. eventually develop between shielded and nearby regions. 

Consider a phospholipid vesicle containing 10 mMNa ions. The vesicle is bathed in a solution that contains 52 mMNa ions, and the electrical potential difference across the vesicle membrane Ai/t = i/toutskie / inside = —30 mV. What is the electrochemical potential at 25°C for Na ions ... 

If a diffusion potential occurs inside the membrane, the relation between mass transport and electrochemical potential gradient — as the driving force for the diffusion of ions — has to be examined in more detail. This can be done by three different approaches ... 

The most important quantity that determines the instability in pitting dissolution is the fluctuation of the electrochemical potential of dissolved metal ions in the electric double layer. In the presence of a large amount of supporting electrolyte, the fluctuation can be formulated with the fluctuations of the potential x, y, ff of the Helmholtz layer and the concentration cm (, y, Cfl.0a as follows,... 

Substituting Eqs. (35) and (36) into Eq. (34), the electrochemical potential fluctuation of dissolved metal ions at OHP is deduced. Then, disregarding the fluctuation of the chemical potential due to surface deformation, the local equilibrium of reaction is expressed as fi% = 0. With the approximation cm x, y, 0, if cm(x, y, (a, tf, we can thus derive the following equation,... 

As shown in Fig. 24, the mechanism of the instability is elucidated as follows At the portion where dissolution is accidentally accelerated and is accompanied by an increase in the concentration of dissolved metal ions, pit formation proceeds. If the specific adsorption is strong, the electric potential at the OHP of the recessed part decreases. Because of the local equilibrium of reaction, the fluctuation of the electrochemical potential must be kept at zero. As a result, the concentration component of the fluctuation must increase to compensate for the decrease in the potential component. This means that local dissolution is promoted more at the recessed portion. Thus these processes form a kind of positive feedback cycle. After several cycles, pits develop on the surface macroscopically through initial fluctuations. 

The symmetrical fluctuation of the electrochemical potential of metal ions is given in the form... 

As shown in Fig. 33, the decreasing mechanism of this fluctuation is summarized as follows At a place on the electrode surface where metal dissolution happens to occur, the surface concentration of the metal ions simultaneously increases. Then the dissolved part continues to grow. Consequently, as the concentration gradient of the diffusion layer takes a negative value, the electrochemical potential component contributed by the concentration gradient increases. Here it should be noted that the electrochemical potential is composed of two components one comes from the concentration gradient and the other from the surface concentration. Then from the reaction equilibrium at the electrode surface, the electrochemical potential must be kept constant, so that the surface concentration component acts to compensate for the increment of the concen-... 

Figure 5.20. Left Schematic of an O2 conducting solid electrolyte cell with fixed P02 and PO2 values at the porous working (W) and reference (R ) electrodes without (top) and with (bottom) ion backspillover on the gas exposed electrodes surfaces, showing also the range of spatial constancy of the electrochemical potential, PQ2-, of O2. Right Corresponding spatial variation in the electrochemical potential of electrons, ]Ie(= Ef) UWR is fixed in both cases to the value (RT/4F)ln( P02 /pc>2 ) also shown in the relative position of the valence band, Ev, and of the bottom of the conduction band, Ec, in the solid electrolyte (SE) numerical values correspond to 8 mol% Y203-stabilized-Zr02, pc>2=10 6 bar, po2=l bar and T=673 K.32 Reproduced by permission of The Electrochemical Society.

Very simply these equations are valid as long as ion backspillover from the solid electrolyte onto the gas-exposed electrode surfaces is fast relative to other processes involving these ionic species (desorption, reaction) and thus spillover-backspillover is at equilibrium, so that the electrochemical potential of these ionic species is the same in the solid electrolyte and on the gas exposed electrode surface. As long as this is the case, equation (5.29) and its consequent Eqs. (5.18) and (5.19) simply reflect the fact that an overall neutral double layer is established at the metal/gas interface. 

Now eUWR is still fixed by the Nemst Eq. 7.16 but w are variables. They can change due to the spillover of ions which can now establish a constant electrochemical potential not only in the solid electrolyte but on the gas exposed electrode surfaces as well. They will change in such a way as to minimize the excess electrostatic energy of the system... 

Figure 8.21. (a) Effect of the rate, I/2F, of electrochemical oxygen ion removal (I<0) on the induced increase in the rate of propylene oxidation on Pt/YSZ.28 (b) Effect of catalyst potential and work function change on the rate enhancement ratio p (=r/r0) at a fixed gaseous composition. Reprinted with permission from Academic Press. 

The common underlying principle was shown in Figure 11.2. The electrochemical potential of electrons jl e(=Ep, the Fermi level) in the metal catalyst is fixed at that of the Fermi level of the support.37 This is valid both for electrochemically promoted model catalysts (left) and for seminconducting or ion-conducting-supported metal nanoparticles (right). 

On the other hand, the electrochemical potentials of electrons, pe, oxygen ions, jIo2, and gaseous oxygen, po2 are related via the charge transfer equilibrium at the three-phase-boundaries (tpb) metal-support-gas38"40 ... 

Mitchell s chemiosmotic theory postulates that the energy from oxidation of components in the respiratory chain is coupled to the translocation of hydrogen ions (protons, H+) from the inside to the outside of the inner mitochondrial membrane. The electrochemical potential difference resulting from the asymmetric dis-... 

Each of the respiratory chain complexes I, III, and IV (Figures 12-7 and 12-8) acts as a proton pump. The inner membrane is impermeable to ions in general but particularly to protons, which accumulate outside the membrane, creating an electrochemical potential difference across the membrane (A iH )-This consists of a chemical potential (difference in pH) and an electrical potential. 

For diffusion in liquid electrolytes such as molten salts, two forces acting on an ion of interest should be taken into account the gradient of the chemical potential and the charge neutrality. Thus the electrochemical potential rather than the chemical potential should be the driving force for diffusion. 

The energy of an ion in a given medium depends not only on chemical forces but also on the electrostatic held hence the chemical potential of an ion j customarily is called its electrochemical potential and labeled fi. The electrostatic potential energy of an ion j when reckoned per mole is given by ZjF, where / is the electrostatic (inner) potential of the phase containing the ion a plus sign for cations and a minus sign for anions. Hence, the electrochemical potential can be written as the sum of two terms ... 

The Gibbs energy of an electroneutral system is independent of the electrostatic potential. In fact, when substituting into Eq. (3.7) the electrochemical potentials of the ions contained in the system and allowing for the electroneutrality condition, we can readily see that the sum of aU terms jZjF f is zero. The same is true for any electroneutral subsystem consisting of the two sorts of ion and (particularly when these are produced by dissociation of a molecule of the original compound k into x+ cations and x anions), for which... 

The electrochemical potential of single ionic species cannot be determined. In systems with charged components, all energy effects and all thermodynamic properties are associated not with ions of a single type but with combinations of different ions. Hence, the electrochemical potential of an individual ionic species is an experimentally undefined parameter, in contrast to the chemical potential of uncharged species. From the experimental data, only the combined values for electroneutral ensembles of ions can be found. Equally inaccessible to measurements is the electrochemical potential, of free electrons in metals, whereas the chemical potential, p, of the electrons coincides with the Fermi energy and can be calculated very approximately. 

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