Ion-transfer potential

A relative scale of the standard Gibbs energies of ion transfer or the standard ion transfer potentials can be established based on partition and solubility measurements. The partition eqnilibrium of the electrolyte can be characterized by a measnrable parameter, the partition coefficient P x-... 

The standard Gibbs energy of electrolyte transfer is then obtained as the difference AG° x ° = AG° ° - AG° x. To estabfish the absolute scale of the standard Gibbs energies of ion transfer or ion transfer potentials, an extrathermodynamic hypothesis must be introduced. For example, for the salt tetraphenylarsonium tetraphenyl-borate (TPAs TPB ) it is assumed that the standard Gibbs energies of transfer of its ions are equal. 

TABLE 32.2 Standard Gibbs Energy of Transfer and Standard Ion Transfer Potentials for Ion Transfer Between Water and Nitrobenzene Derived from Partition Measurements... 

FIGURE 32.4 Potential dependence of the interfacial tension J and the capacity C for the interface between solutions of 5mM tetrabutylammonium tetraphenylborate in 1,2-dichloroethane and lOOmM LiCl in water. The potential scale E represents the Galvani potential difference relative to the standard ion transfer potential for tetraethylammonium ion, cP o EA+ = 0.02 V. 

Previously, Osaka and coworkers [29-31] employed ion-transfer voltammetry to determine the standard ion-transfer potentials (Aq 4> ) of heteropoly- and isopolyoxome-talate anions (in short, polyanions) at the nitrobenzene (NB)/W and 1,2-dichloroethane (1,2-DCE)/W interfaces is directly related to the transfer energy by... 

Accordingly, the contribution of the CT interaction to the ion-transfer potential [being given by Eq. (7)] can be expressed as... 

Calculated from the standard ion-transfer potentials compiled previously [33]. 

Thus, the HLB of an ionic surface-active substance is balanced at the standard ion-transfer potential. This is simply a reinterpretation of the definition of Aq P, but is a very important relation, which is valid no matter what the actual form of the adsorption... 

Aq ° is the standard ion-transfer potential (these values for some ions can be found in Ref. 74), z is the number of the charge of the potential-determining ion, and are the activities of the potential-determining ion in the oil and water phases, respectively. 

Electrode reactions may include elementary steps involving electron transfer, ion transfer, potential-independent or chemical steps, etc. Since electrochemical reactions are heterogeneous processes, the reaction rate coefficients have units of m s 1... 

A potential difference across the NB/water interface (Ao 0) is determined by the concentrations of TBA+ dissolved in both phases, and calculated to be —131 mV on the basis of Eq. 4. A standard ion transfer potential of ferrocene has been reported to be -75 mV [96]. Therefore, FeCp-EtOH+ is likely to exit quickly to the water phase across the droplet/water interface at the present Ao . Diffusion of FeCp-EtOH + in the NB and water phases is thus concluded to be the rate-determining step of MT from GE to CE across the droplet/water interface. If the Ao value is higher than the ion transfer potential of FeCp-EtOH+ in the NB/water system, a slow MT process, such as migration of the compound across the interface, will be detected. A combination of laser trapping with the microelectrode array methods is highly useful for studying directly MT processes between a droplet and the surrounding solution phase. 

Table 2.1 Standard ion transfer potentials of different A/yV-alkylimidazolium and l-butyl-4-methylpyridinium ionic liquid cations [29]...

Eoutj and Emnj are the individual potential drops at each interface caused by the application of the first and second potential steps. Am / x1 and A f+ are the formal ion transfer potentials for the target ion X+ and for the membrane electrolyte cation R+, respectively, c + is the concentration of the membrane electrolyte cation, R+, and Dy1 and D)) are the diffusion coefficients of X+ in the membrane (M phase) and R+ in the inner aqueous solution (w2 phase), respectively. 

Interface between two liquid solvents — Two liquid solvents can be miscible (e.g., water and ethanol) partially miscible (e.g., water and propylene carbonate), or immiscible (e.g., water and nitrobenzene). Mutual miscibility of the two solvents is connected with the energy of interaction between the solvent molecules, which also determines the width of the phase boundary where the composition varies (Figure) [i]. Molecular dynamic simulation [ii], neutron reflection [iii], vibrational sum frequency spectroscopy [iv], and synchrotron X-ray reflectivity [v] studies have demonstrated that the width of the boundary between two immiscible solvents comprises a contribution from thermally excited capillary waves and intrinsic interfacial structure. Computer calculations and experimental data support the view that the interface between two solvents of very low miscibility is molecularly sharp but with rough protrusions of one solvent into the other (capillary waves), while increasing solvent miscibility leads to the formation of a mixed solvent layer (Figure). In the presence of an electrolyte in both solvent phases, an electrical potential difference can be established at the interface. In the case of two electrolytes with different but constant composition and dissolved in the same solvent, a liquid junction potential is temporarily formed. Equilibrium partition of ions at the - interface between two immiscible electrolyte solutions gives rise to the ion transfer potential, or to the distribution potential, which can be described by the equivalent two-phase Nernst relationship. See also - ion transfer at liquid-liquid interfaces. 

Cyclic voltammetry has been used mainly for the determination of the standard ion-transfer potential Aq (or the standard Gibbs energy of ion transfer A ttx °), and e ion diffusion coefficient. The Figure shows an example of the cyclic voltammogram for the Cs+ ion-transfer reaction at ITIES in the electrochemical cell... 

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,... 

For ion-pair extraction, a cation is extracted with an anion into oil. In this case, individual ions or the ion pair species transfer across a microdroplet/water interface and the extraction rate is expected to depend on the Galvani potential between the microdroplet and water, the ion transfer potentials across the liquid/liquid interface, the association constant of the ions in the solution and so forth [46-54]. Therefore, the mass transfer processes are complicated even in the absence of adsorption of an ion at the microdroplet/water interface. In this section, the kinetic analysis of a simple ion-pair extraction without adsorption is described and the extraction mechanism is discussed on the basis of the single microdroplet technique. 

Aw G° and Aq 0° are not experimentally accessible quantities, e.g., the standard ion transfer potential can be measured with respect to the potential difference between the two terminals of an electrochemical cell using two appropriate reference electrodes. The values of these quantities have been compiled for several organic solvent-water systems on the basis of a nonthermodynamic assumption [4, 11]. In general, the values of the Gibbs energy of transfer of an ion in Eq. (2) differ from those for the transfer from one pure solvent to another pure solvent. 

Hung derived a general expression for calculating the distribution potential from the initial concentrations of ionic species, their standard ion transfer potentials, and the volumes of the two phases [19]. When all ionic species in W and O are completely dissociated, and the condition of electroneutrality holds in both phases, the combination of Nernst equations for all ionic species with the conservation of mass leads to... 

In Eq. (3), summations are taken for all ionic species. The only unknown in Eq. (3) is Aq 0- By knowing initial concentrations of ionic species and their standard ion transfer potentials, together with the volumes of W and O phases, the distribution potential can be calculated by solving Eq. (3). The concentration of each ionic component at a distribution equilibrium can then be obtained through Aq 0 using the relation... 

The treatment of partition equilibrium was further generalized to the cases in the presence of ion-pair formation [19] and ion-ionophore complex formation [21]. An important corollary of this theory of partition equilibrium based on standard ion transfer potentials of single ions is to give a new interpretation to liquid extraction processes. Kakutani et al. analyzed the extraction of anions with tris(l,10-phenan-throline) iron(II) cation from the aqueous phase to nitrobenzene [22], which demonstrated the effectiveness of the theory and gave a theoretical backbone for ion-pair extraction from an electrochemical point of view. 

First, when only one ionic species can be distributed between the phases, there is a contact equilibrium [23] at the interface and the potential difference is completely determined by the standard ion transfer potential of this potential-determining ion. In actual cases, however, this contact equilibrium is seldom achieved at the ITIES, since the transfer of counter ions of the potential-determining ion across the interface is not always negligible. If a distribution equilibrium is established t the reference ITIES, the degree of interference can be estimated using Eq. (3). However, the distribution equilibrium is not usually realized in an actual reference ITIES. Rather, the final equilibrium, if achieved, would nullify the potential difference between the two aqueous phases. Consider the following example ... 

On the one hand, the thermodynamic realities of the ITIES, e.g., electrocapillarity and standard ion transfer potential, have been well established. On the other hand, our knowledge of charge transfer kinetics is less solid. Although traditional macroscopic concepts appear to be applicable at least as a first approximation, there is still a rift between macroscopic views and microscopic understanding. 

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