Electrochemical potential, ions interface

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. 

When the Gibbs equation is used for an electrode-electrolyte interface, the charged species (electrons, ions) are characterized by their electrochemical potentials, while the interface is regarded as electroneutral that is, the surface density, 2, of excess charges in the metal caused by positive or negative adsorption of electrons ... 

Figure 29.4 shows an example, the energy diagram of a cell where n-type cadmium sulfide CdS is used as a photoanode, a metal that is corrosion resistant and catalytically active is used as the (dark) cathode, and an alkaline solution with S and S2 ions between which the redox equilibrium S + 2e 2S exists is used as the electrolyte. In this system, equilibrium is practically established, not only at the metal-solution interface but also at the semiconductor-solution interface. Hence, in the dark, the electrochemical potentials of the electrons in all three phases are identical. 

Kakiuchi [41] has examined the transport mechanism in some detail. He considers the interface as a region of thickness k in which friction is considerably larger than in the bulk. The transferring ion has different electrochemical potentials = 1, 2) in the two bulk phases as usual, they can be decomposed into their chemical and their electrostatic parts /x,- = /x,- -t-zeo, where z is the charge number of the ion. When the system is in equilibrium, and the concentration of the ion is the same in the two solutions, then the difference in the inner potential is given by ... 

The first controversial point in this mechanism is the nature of the reaction planes where the precursor formation and the ET reaction take place. Samec assumed that the ET step occurs across an ion-free layer composed of oriented solvent molecules [1]. By contrast, Girault and Schiffrin considered a mixed solvent region where electrochemical potentials are dependent on the position of the reactants at the interface [60]. From a general perspective, the phenomenological ET rate constant can be expressed in terms of... 

The metal ions Mz+, the atoms M, and the electrons at the interface are in equilibrium with the metal so we may use the electrochemical potentials of these species in the metal instead of the interfacial quantities, and split them into the chemical part and the electrostatic part ... 

The only potential that varies significantly is the phase boundary potential at the membrane/sample interface EPB-. This potential arises from an unequal equilibrium distribution of ions between the aqueous sample and organic membrane phases. The phase transfer equilibrium reaction at the interface is very rapid relative to the diffusion of ions across the aqueous sample and organic membrane phases. A separation of charge occurs at the interface where the ions partition between the two phases, which results in a buildup of potential at the sample/mem-brane interface that can be described thermodynamically in terms of the electrochemical potential. At interfacial equilibrium, the electrochemical potentials in the two phases are equal. The phase boundary potential is a result of an equilibrium distribution of ions between phases. The phase boundary potentials can be described by the following equation ... 

For ion adsoiption in equilibrium on the electrode interface, the electrochemical potential Pi.., of hydrated adsorbate ions in aqueous solution equals the electrochemical potential Pi..d of adsorbed ions as shown in Eqn. 5-20 ... 

We now consider a transfer reaction of charged particles across the interface of electrodes. For a hydrated particle in aqueous solution, the electrochemical potential of the particle is independent of the electrode potential, though it depend on the activity of the partide (the concentration of the partide), regardless of whether the partide is charged (ion) or noncharged (neutral partide). In contrast, for a charged particle (electron or ion) in the electrode, the electrochemical potential of the particle depends on both the electrode potential E and the absolute activity Xk Pk = A7 lnXk-i-zeE. From Eqn. 7-34 we then obtain Eqn. 7-35 for the reaction order, Ck, with respect to a charged particle k in the electrode if the activity of k is constant ... 

Fig. 9-1. Potential energy profile for transferring metal ions across an interface of metal electrode M/S py. = metal ion level (electrochemical potential) x = distance fiom an interface au. = real potential of interfacial metal ions = real potential of hydrated metal ions - compact layer (Helmholtz layer) V = outer potential of solution S, curve 1 = potential energy of interfadal metallic ions curve 2 = potential energy of hydrated metal ions.

Equality (1.20) is of primary importance because of the following reason. It is customary in most ionic transport theories to use the local electroneutrality (LEN) approximation, that is, to set formally e = 0 in (1.9c). This reduces the order of the system (1.9), (l.lld) and makes overdetermined the boundary value problems (b.v.p.s) which were well posed for (1.9). In particular, in terms of LEN approximation, the continuity of Ci and ip is not preserved at the interfaces of discontinuity of N, such as those at the ion-exchange membrane/solution contact or at the contact of two ion-exchange membranes or ion-exchangers, etc. Physically this amounts to replacing the thin internal (boundary) layers, associated with N discontinuities, by jumps. On the other hand, according to (1-20) at local equilibrium the electrochemical potential of a species remains continuous across the interface. (Discontinuity of Cj, ip follows from continuity of p2 and preservation of the LEN condition (1.13) on both sides of the interface.)... 

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 ... 

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. 

Each phase is charged and has electrostatic potential cp, which is called the Gal-vani potential. The profiles of the ion activity, of the Galvani potential, and of the electrochemical potential across the sample/electrode interface are shown in Fig. 6.2. 

It is important to note that the electrode potential is related to activity and not to concentration. This is because the partitioning equilibria are governed by the chemical (or electrochemical) potentials, which must be expressed in activities. The multiplier in front of the logarithmic term is known as the Nernst slope . At 25°C it has a value of 59.16mV/z/. Why did we switch from n to z when deriving the Nernst equation in thermodynamic terms Symbol n is typically used for the number of electrons, that is, for redox reactions, whereas symbol z describes the number of charges per ion. Symbol z is more appropriate when we talk about transfer of any charged species, especially ions across the interface, such as in ion-selective potentiometric sensors. For example, consider the redox reaction Fe3+ + e = Fe2+ at the Pt electrode. Here, the n = 1. However, if the ferric ion is transferred to the ion-selective membrane, z = 3 for the ferrous ion, z = 2. 

Although the equilibrium principle was available (equality of electrochemical potential of each ion that reversibly equilibrates across an immiscible liquid/liquid interface), the elementary theory and consequences were not explored until recently (6). To develop an interfacial potential difference (pd) at a liquid interface, two ions M, X that partition are required. However,... 

The interfacial potential difference (pd) for the partition equilibrium interface is given by the equality of electrochemical potential in terms of all ions in equilibrium, equation (4). 

For the thermodynamic study of the mercury-solution interface, the electrochemical potential will be used in Gibbs s isotherm instead of the chemical potential, due to the presence of charged species. In the metal side of the interface, the components are the electrons in excess and the mercury metal whereas in solution the two ions of the electrolyte and the solvent must be considered in the sum,... 

Any surface (typically a piece of metal) on which an electrochemical reaction takes place will produce an electrochemical potential when in contact with an electrolyte (typically water containing dissolved ions). The unit of the electrochemical potential is volt (TV = 1JC1 s 1 in SI units).The metal, or strictly speaking the metal-electrolyte interface, is called an electrode and the electrochemical reaction taking place is called the electrode reaction. The electrochemical potential of a metal in a solution, or the electrode potential, cannot be determined absolutely. It is referred to as a potential relative to a fixed and known electrode potential set up by a reference electrode in the same electrolyte. In other words, an electrode potential is the potential of an electrode measured against a reference electrode. The standard hydrogen electrode (SHE) is universally adopted as the primary standard reference electrode with which all other electrodes are compared. By definition, the SHE potential is OV, i.e. the zero-point on the electrochemical potential scale. Electrode potentials may be more positive or more negative than the SHE. 

Two aspects of Table 1 are important. The standard conditions are 298 K and all reactants and products are at unity activity. The second key is the selection of the hydrogen reaction as having a standard reversible potential of 0.0 V. The table allows the first use of thermodynamics in corrosion. For a metal in a 1 M solution of its salt, the table allows one to predict the electrochemical potential below (i.e., more negative) which net dissolution is impossible. For example, at +0.337 V(NHE), copper will not dissolve to cuprous ion if the solution is 1 M in Cu2+. In fact, at more negative potentials, there will be a tendency at the metal/solution interface to reduce the cuprous ions to copper metal on the surface. 

Distribution (Nernst) potential — Multi-ion partition equilibria at the -> interface between two immiscible electrolyte solutions give rise to a -> Galvanipotential difference, Af(j> = (j>w- 0°, where 0wand cj>°are the -> inner potentials of phases w and o. This potential difference is called the distribution potential [i]. The theory was developed for the system of N ionic species i (i = 1,2..N) in each phase on the basis of the -> Nernst equation, the -> electroneutrality condition, and the mass-conservation law [ii]. At equilibrium, the equality of the - electrochemical potentials of the ions in the adjacent phases yields the Nernst equation for the ion-transfer potential,... 

Non-linear phenomena accompanied by periodic changes of electrochemical potential have been the subject of many research activities since Dupeyrat and Nakache [39] reported on periodic macroscopic movements of an oil/water interface and generation of electrochemical potential in 1978. These authors found such non-linear behaviour at a W/NB interface with positively charged cationic surfactants. They explained the nonlinear behaviour on the basis of formation of ion pairs between the positively charged cationic surfactants in the aqueous phase and negatively charged picrate anions dissolved in the oil phase. The ion pairs formed at a W/NB interface were assumed to be removed from the interface by a phase transfer process and oscillatory behaviour was explained in terms of the Marangoni effect. 

This ion interaction retention model of IPC emphasized the role played by the electrical double layer in enhancing analyte retention even if retention modeling was only qualitatively attempted. It was soon realized that the analyte transfer through an electrified interface could not be properly described without dealing with electrochemical potentials. An important drawback shared by all stoichiometric models was neglecting the establishment of the stationary phase electrostatic potential. It is important to note that not even the most recent stoichiometric comprehensive models for both classical [17] and neoteric [18] IPRs can give a true description of the retention mechanism because stoichiometric constants are not actually constant in the presence of a stationary phase-bulk eluent electrified interface [19,20], These observations led to the development of non-stoichiometric models of IPC. Since stoichiometric models are not well founded in physical chemistry, in the interest of brevity they will not be described in more depth. 

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