Diffusion overpotential equations

By combining the Nernst equation with the expressions for charge-transfer overpotential (r CT) and diffusion overpotential (r D), equations can be written for the total experimental polarization behavior, E(iex ox) and E(iex red), of a single half-cell reaction ... 

The contribution of diffusion overpotential to the total overpotential can be achieved by an increase of convection near the electrode surface. In a very controlled manner this is possible with the rotating disc electrode. In the Koutecky—Levich equation the separation of diffusion contributions and charge transfer contributions to the overpotential was achieved. A general charge transfer reaction with exchange of n electrons was chosen. The Koutecky-Levich equation is... 

Impedance spectroscopy in the high-frequency region is another way of eliminating diffusion overpotential. The equations were given in Chapter 5. The combination of the double-layer equivalent circuit with the diffusion impedance was described in Section 5.23 and examples for the determination of the charge transfer resistance at high frequencies were given. 

Concentration Polarization (Diffusion Overpotential). If copper is made cathode in a solution of dilute CUSO4 in which the activity of cupric ion is represented by (Cu ), then the potential ( )i, in absence of external current, is given by the Nernst equation... 

Concerning the diffusion overpotential, the main relation with the fuel utilization is present at the anode side. The model equations and hypothesis are assumed by literature [21,25,26]. Transport of gaseous species usually occurs by binary diffusion, where the effective binary diffusivity is a function of the fundamental binary diffusivity and the... 

The parameters used for solving the equations of the contribution of the diffusion overpotential to the analytical expression of the sensitivity of the cell voltage to the fuel utilization are been listed in Table 4 ... 

The diffusion overpotentials are described according to equations (32) and (36). The fundamental binary diffusivities have been calculated using the previously described Brokaw model and the values of microscopic parameters have been assumed by literature and are listed in Table 4. 

In the Rotating Disk Electrode (RDE) technique, the current-potential curves on smooth platinum exhibit an anodic limiting current density, which depends on rotation rate in both acidic and alkaline media [46]. These plots are well described by equation (19), which holds for a diffusion overpotential alone. Similar relationships have been observed in acidic solutions for Ir, Rh, and Pd, and well-characterized Pt-Ru, Pt-Rh, Pt-Sn [53], and Pt-Au [51] alloys, and also for Ni in alkaline solutions. In the case of platinum, a evolution of the limiting diffusion current density to a limiting reaction current density ( x) independent of rotation rate, is observed as a consequence of the rate-determining H2 adsorption. 

The analysis of electrode reactions composed of diffusion and electrode transfer kinetics is only possible after suitable models have been formulated. Here the scheme (1) is used. The reactions involving the two higher oxidation states are reversible. According to [11] the reaction involving the metallic phase is irreversible. The current intensity of the reaction obeys the current overpotential equation... 

In order to derive the equation for pure reaction overpotential we assume that jo is high, i.e., an equilibrium exists at the electrode metal surface in respect of the surface concentrations of O and R. All other steps including diffusion are fast enough, i.e., much faster than reaction (2). (In general, rj is a. sum of different contributions activation overpotential, diffusion overpotential etc.] which might be interdependent.)... 

If mass transfer is presented by the diffusion overpotential and electron transfer is described using the Butler-Vohner theory, these two approaches can be combined and the generalized Butler-Vohner equation can be obtained. 

In general, the charge transfer and diffusion overpotential add to each other according to T = t ct + i1d/ arid the measured current density is limited by both effects. At small values, X is determined by the Butler-Volmer equation due to a dominating charge transfer reaction and becomes diffusion limited at larger overpotentials as shown in Figure 1.22 by the dashed line. 

In the chemical desorption step the adsorbed H atoms diffuse about on the metal surface, either by threading their way through adsorbed water molecules or by pushing them aside, until two collide to form an Hj molecule which escapes into the solution. This chemical step will be independent of overpotential, since charge transfer is not involved, and the rate will be proportional to the concentration or coverage of adsorbed H,, (see equation 20.39) and may occur at coverages that range from very small to almost complete. 

Equations (37) and (38), along with Eqs. (29) and (30), define the electrochemical oxidation process of a conducting polymer film controlled by conformational relaxation and diffusion processes in the polymeric structure. It must be remarked that if the initial potential is more anodic than Es, then the term depending on the cathodic overpotential vanishes and the oxidation process becomes only diffusion controlled. So the most usual oxidation processes studied in conducting polymers, which are controlled by diffusion of counter-ions in the polymer, can be considered as a particular case of a more general model of oxidation under conformational relaxation control. The addition of relaxation and diffusion components provides a complete description of the shapes of chronocoulograms and chronoamperograms in any experimental condition ... 

In an earlier note (p. 9) we mentioned the occurrence of overvoltage in an electrolytic cell (and overpotentials at single electrodes), which means that often the breakthrough of current requires an Uappl = Eiecomp r] V higher than Ehack calculated by the Nernst equation as this phenomenon is connected with activation energy and/or sluggishness of diffusion we shall treat the subject under the kinetic treatment of the theory of electrolysis (Section 3.2). 

A related technique is the current-step method The current is zero for t < 0, and then a constant current density j is applied for a certain time, and the transient of the overpotential 77(f) is recorded. The correction for the IRq drop is trivial, since I is constant, but the charging of the double layer takes longer than in the potential step method, and is never complete because 77 increases continuously. The superposition of the charge-transfer reaction and double-layer charging creates rather complex boundary conditions for the diffusion equation only for the case of a simple redox reaction and the range of small overpotentials 77 [Pg.177]

At extreme overpotentials, the current is independent of potential. This maximum current is said to be limiting, that is, current a Cbuik- It is termed the diffusion current, /j. The dependence of la on concentration, drop speed, etc., is described by the Ilkovic equation (equation (6.5)), although calibration graphs or standard addition methods (Gran plots) are preferred for more accurate analyses. 

With the evaluated site coverage and pore blockage correlations for the effective ECA and oxygen diffusivity, respectively, and the intrinsic active area available from the reconstructed CL microstructure, the electrochemistry coupled species and charge transport equations can be solved with different liquid water saturation levels within the 1-D macrohomogeneous modeling framework,25,27 and the cathode overpotential, q can be estimated. 

Because the kinetic and mass-transport phenomena occur in a thin region adjacent to the electrode surface, this area is treated separately from the bulk solution region. Since kinetic effects are manifested within 100 A of the electrode surface, the resulting overpotential is invariably incorporated in the boundary conditions of the problem. Mass transport in the boundary layer is often treated by a separate solution of the convective diffusion equation in this region. Continuity of the current can then be imposed as a matching condition between the boundary layer solution and the solution in the bulk electrolyte. Frequently, Laplace s equation can be used to describe the potential distribution in the bulk electrolyte and provide the basis for determining the current distribution in the bulk electrolyte. 

---