Diffusion controlled electrode process

From Equations 3.92 and 3.93, we can see that the frequency dependence at low frequencies comes from Warburg impedance terms hence, the linear correlation of Zm versus Zre features a diffusion-controlled electrode process. As the frequency rises, the presupposition for Equation 3.94 will not exist. The linear correlation will deviate with increasing frequencies. 

Nagy G, Sugimoto Y, Denuault G (1997) Three-dimensional random walk simulation of diffusion controlled electrode processes (I) a hemisphere, disc and growing hemisphere. J Electroanal Chem 433 167-173... 

Using the Berzins and Delahay equation for the case in which a single substance undergoes two consecutive charge transfer reactions (diffusion-controlled electrode processes) at sufficiently different potentials [19] ... 

The limiting current of reaction sequence XI and XII is less than the corresponding diffusion limiting current had species Q been oxidized directly. This will serve as a good criterion to distinguish between reaction and diffusion controlled electrode processes. This limiting current will be constant even... 

As expected for reversible processes, values obtained from the cyclic voltammograms are independent of the scan rates (0.1-0.7 V s . Fig. 3.8) and concentrations (3. 5 mmol/kg) studied. The peak current for the reduction of DmCc varies linearly with the square root of the scan rate (0.1-0.7 V s ), characteristic of diffusion-controlled electrode processes [65]. 

This system can be taken as an example of so-called reversible, diffusion-controlled electrochemical processes. In short, during the initial anodic scan, an electron-transfer process between the ferrocyanide (or hexacyanoferrate(II)) ions, [Fe(CN)6] ", and the working electrode occurs. This can be represented by means of the equation (here, aq denotes species in aqueous solution) ... 

When a ferrocene derivative loaded Pt/Nafion-GOD electrode is transferred to a phosphate buffer solution containing no ferrocene derivatives, the observed redox waves reflect their electrochemical behavior in the film. The scan rate dependence of the cyclic voltammetry for the Pt/Nafion-GOD incorporated with different ferrocene derivatives was studied. A linear plot of the anodic peak current against the square root of the scan rate was obtained in all cases, which is indicative of diffusion controlled redox process. Typical chronoamperometric... 

This equation is often used to determine the formal potential of a given redox system with the help of cyclic voltammetry. However, the assumption that mid-peak potential is equal to formal potential holds only for a reversible electrode reaction. The diagnostic criteria and characteristics of cyclic voltammetric responses for solution systems undergoing reversible, quasi-reversible, or irreversible heterogeneous electron-transfer process are discussed, for example in Ref [9c]. An electro-chemically reversible process implies that the anodic to cathodic peak current ratio, lpa/- pc equal to 1 and fipc — pa is 2.218RT/nF, which at 298 K is equal to 57/n mV and is independent of the scan rate. For a diffusion-controlled reduction process, Ip should be proportional to the square root of the scan rate v, according to the Randles-Sevcik equation [10] ... 

The principle of the electrochemical measurement of oxygen diffusion in a metal consists in bringing the metal from a well-defined state into another well-defined state and following the diffusion-controlled relaxation process electrochemically. For example, the metal sample is placed on one side of the solid electrolyte ZrOa and functions as one electrode of a galvanic cell. On the other side of the electrolyte there is a practically unpolarizable electrode such as porous platinum in contact with air, or an Fe/FeO electrode, which has a fixed oxygen partial pressure of about 10 atm at 800°C. The following cell may be used ... 

In simple diffusion-controlled electrode reactions. deviations between + 1.5 and + 2.2 %/ °C occur. For kinetic and catalytic currents, the temperature coefficients can be up to -i- 70 %/ °C, Currents that are based on adsorption processes can... 

A general transport phenomenon in the intercalation electrode with a fractal surface under the constraint of diffusion mixed with interfadal charge transfer has been modelled by using the kinetic Monte Carlo method based upon random walk approach (Lee Pyim, 2005). Go and Pyun (Go Pyun, 2007) reviewed anomalous diffusion towards and from fractal interface. They have explained both the diffusion-controlled and non-diffusion-controlled transfer processes. For the diffusion coupled with facile charge-transfer reaction the... 

A single homogeneous phase representation, where a combination of double-layer capacitance and diffusion-controlled Faradaic process is responsible for oxidation reduction of the polymer, resulting in appearance of "transmission line" in the equivalent circuit model. The large capacitances exhibited by conducting polymer electrodes are usually attributed to the double-layer capacitance and pseudocapacitance originating from the redox process of the polymer. 

Similarly to the response at hydrodynamic electrodes, linear and cyclic potential sweeps for simple electrode reactions will yield steady-state voltammograms with forward and reverse scans retracing one another, provided the scan rate is slow enough to maintain the steady state [28, 35, 36, 37 and 38]. The limiting current will be detemiined by the slowest step in the overall process, but if the kinetics are fast, then the current will be under diffusion control and hence obey the above equation for a disc. The slope of the wave in the absence of IR drop will, once again, depend on the degree of reversibility of the electrode process. 

In contrast to the influence of velocity, whose primary effect is to increase the corrosion rates of electrode processes that are controlled by the diffusion of reactants, temperature changes have the greatest effect when the rate determining step is the activation process. In general, if diffusion rates are doubled for a certain increase in temperature, activation processes may be increased by 10-100 times, depending on the magnitude of the activation energy. 

It has been seen from the above simple examples that the concentration of the substrate has a profound effect on the rate of the electrode process. It must be remembered, however, that the process may show different reaction orders in the different potential regions of the i-E curve. Thus, electron transfer is commonly the slow step in the Tafel region and diffusion control in the plateau region and these processes may have different reaction orders. Even at one potential the reaction order may vary with the substrate concentration as, for example, in the case discussed above where the electrode reaction requires adsorption of the starting material. 

In such systems the researcher can electrochemically clean and precondition the metal electrode before each run to provide an identical surface for the anodic and the cathodic half-reactions as well as for the catalytic reaction between them. Use of a rotating disk electrode/ckatalyst also allows surface- and diffusion-controlled processes to be easily distin-guished. ... 

In order to obtain a definite breakthrough of current across an electrode, a potential in excess of its equilibrium potential must be applied any such excess potential is called an overpotential. If it concerns an ideal polarizable electrode, i.e., an electrode whose surface acts as an ideal catalyst in the electrolytic process, then the overpotential can be considered merely as a diffusion overpotential (nD) and yields (cf., Section 3.1) a real diffusion current. Often, however, the electrode surface is not ideal, which means that the purely chemical reaction concerned has a free enthalpy barrier especially at low current density, where the ion diffusion control of the electrolytic conversion becomes less pronounced, the thermal activation energy (AG°) plays an appreciable role, so that, once the activated complex is reached at the maximum of the enthalpy barrier, only a fraction a (the transfer coefficient) of the electrical energy difference nF(E ml - E ) = nFtjt is used for conversion. 

Again returning to the diffusion-controlled limiting current, we often meet a considerable influence on its height by catalysis, adsorption or other surface phenomena, so that we have to deal with irreversible electrode processes. For instance, when to a polarographic system with a diffusion-controlled limiting... 

Mohamed [63] investigated the complexation behavior of amodiaquine and primaquine with Cu(II) by a polarographic method. The reduction process at dropping mercury electrode in aqueous medium is reversible and diffusion controlled, giving well-defined peaks. The cathodic shift in the peak potential (Ep) with increasing ligand concentrations and the trend of the plot of EVl versus log Cx indicate complex formation, probably more than one complex species. The composition and stability constants of the simple complexes formed were determined. The logarithmic stability constants are log Bi = 3.56 log B2 = 3.38, and log B3 = 3.32 [Cu(II)-primaquine at 25 °C]. 

Similar to those observed with the cysteine-modified electrode in Cu, Zn-SOD solution [98], CVs obtained at the MPA-modified Au electrode in phosphate buffer containing Fe-SOD or Mn-SOD at different potential scan rates (v) clearly show that the peak currents obtained for each SOD are linear with v (not v 1/2) over the potential scan range from 10 to 1000 mVs-1. This observation reveals that the electron transfer of the SODs is a surface-confined process and not a diffusion-controlled one. The previously observed cysteine-promoted surface-confined electron transfer process of Cu, Zn-SOD has been primarily elucidated based on the formation of a cysteine-bridged SOD-electrode complex oriented at an electrode-solution interface, which is expected to sufficiently facilitate a direct electron transfer between the metal active site in SOD and Au electrodes. Such a model appears to be also suitable for the SODs (i.e. Cu, Zn-SOD, Fe-SOD, and Mn-SOD) with MPA promoter. The so-called... 

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