Interfacial potential jump

Issues (vi) and (vil) both deal with the nature of the solvent they are also related to (v). Considering water, the spatial distribution of the molecules is in a very complicated way determined by solvent-solvent, solvent-countercharge and solvent-surface charge interactions. A detailed knowledge of this structure is required to quantify ion-ion correlations, ion-ion and ion-surface solvent structure-originated interactions and the local dielectric permittivity. Polarization of the solvent also contributes to the interfacial potential Jump or X POtential (secs. 1.5.5a and 3.9), which does not occur in Poisson-BoltzmEmn theory. 

Relative Galvanl potentials cannot be made absolute because there is no way to establish the conditions under which there is no potential difference across the boundary between dissimilar phases. For lack of better knowledge, i/° is therefore usually referred to the point of zero charge which, although not thermodynamically defined, can often be established with some confidence, see below and sec. 3.8. However, the point of zero charge is not necessarily identical to the point of zero potential because even at cr = 0 the interfacial potential Jump X, caused by preferential orientation of solvent (water) dipoles and polarization of the particle is non-zero. Anticipating sec. 3.9 it is realized that x may change with [Pg.334]

Potentials of zero charge are not necessarily identlced to "potentials of zero potential" because, as a rule, the interfacial potential Jump X 3.9). As... 

The (unmeasurable) total, or Galvanl, potential difference consists of the (measurable) Volta potential difference between the two phases and the (unmeasurable) interfacial potential Jump (see I.5.5.3 and 4)) and Is given by... 

The S02 oxidation process is kinetically limited, inducing a non-negligible anodic overvoltage, given by a Tafel electrokinetic law [11], In order to account for the secondary potential distribution prevailing in the domain, potential jumps are calculated at the anode/fluid interface thanks to the interfacial-type elements provided within the solver. These zero-width finite elements allow electrical potential discontinuities to be managed, as described in ref. [7], The same formalism is used at the cathode/fluid interface as well to model the proton reduction overvoltage. 

The Cottrell equation predicts an infinite current for f = 0, immediately following the potential jump. In practice, several factors limit the current and prevent such a situation from ever occurring the limited rise time and current output of the potentiostat, the ohmic drop in the solution that prevents the potential to instantly reach the prefixed value, and the kinetic limitations of the interfacial reaction. In potentiostatic step experiments, the current therefore attains the theoretical value given by the Cottrell equation only after a certain time lag. Figure 5.10 shows schematically the typical shape of the current transients observed in potential step experiments. 

In practice, the changeover can be achieved by adding a surfactant to the water/oil or water/air interface. It enhances both interfacial surface potentials and tends to make them equal (i.e. n(D) for similar surfaces > n(D) for dissimilar surfaces) and it lowers the surface tension of the drop. This type of behaviour has been observed in a variety of systems (see Figure 4.4), including oil/water [54,56,62,63] systems where the addition of surfactant prevented jump-in and in air/water systems where the addition of surfactant decreased (and sometimes eliminated) jump-in distances [5,46,48,49]. 

The objective of a temperature-jump method applied to the study of interfacial kinetics is to effect, as closely as possible, an instantaneous step change in the interfacial temperature. The change in the interfacial temperature will disturb the extant interfacial electronic equilibrium, and the open circuit potential will readjust as the interface establishes a new equilibrium at the new temperature (see Sec. IV). In this section we will focus solely on how best to change the interfacial temperature in a manner that will be conducive to the study of interfacial kinetics. 

Figure 3.1 shows the structure of an interfacial region between two distinct phases, the particle and the solution. As discussed in Section 2.4, it is strictly a region and not a plane, because the properties cannot vary abruptly, but must show some transition for example, the electrical potential cannot jump at the hypothetical plane of the interface between two phases which, in the general case, will have different potential values, because a jump would imply an infinitely high electric field. 

Computation of density can be avoided if one assumes that it changes abruptly across the interphase boundary, i.e. jumps between both equilibrium values p/,Pv over a molecular-scale distance d. This is the sharp interface approximation. The interfacial energy is contributed then only by the second term in Eq. (9). We consider a flat boundary at 2 = 0 and neglect the vapor density compared to the liquid density, i.e. set p = pi = const at 2 < 0 and p = 0 at 2 > 0. Then a short computation using the hard- core interaction potential (5) yields the interfacial energy per unit area... 

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