Current-limiting diffusion polarization

As the polarization (the overvoltage t) ) increases of a redox reaction that requires the transport of minority charge carriers towards the electrode interface (anodic hole transfer at n-type and cathodic electron transfer at p-type electrodes), the transport overvoltage, t)t, increases from zero at low reaction currents to infinity at high reaction current at this condition the reaction current is controlled by the limiting diffusion current (iu.)tm or ip.um) of minority charge carriers as shown in Fig. 8-25. 

The second type of polarization, concentration polarization, results from the depletion of ions at the electrode surface as the reaction proceeds. A concentration gradient builds up between the electrode surface and the bulk solution, and the reaction rate is controlled by the rate of diffusion of ions from the bulk to the electrode surface. Hence, the limiting current under concentration polarization, ii, is proportional to the diffusion coefficient for the reacting ion, D (see Section 4.0 and 4.3 for more information on the diffusion coefficient) ... 

Equations (3.105)-(3.107) point out the existence of three different polarization causes. So, 7km is a kinetically controlled current which is independent of the diffusion coefficient and of the geometry of the diffusion field, i.e., it is a pure kinetic current. The other two currents have a diffusive character, and, therefore, depend on the geometry of the diffusion field. I((((s corresponds to the maximum current achieved for very negative potentials and I N is a current controlled by diffusion and by the applied potential which has no physical meaning since it exceeds the limiting diffusion current 7 ss when the applied potential is lower than the formal potential (E < Ef"). This behavior is indicated by Oldham in the case of spherical microelectrodes [15, 20, 25]. 

An ideal unpolarized cell would have R = 0 and infinite current an ideal polarized cell would have a fixed R independent of and thus a constant current. Reality is somewhere in between There are several sources of "polarization" that can be considered as finite contributions to the overall resistance R > 0 (or better, the impedance Z). The IR drop, from whatever source, is also called the overpotential t] (i.e., IR > 0), which always decreases the overall E remember that R is always a function of time and E. The causes of polarization are (1) diffusion-limited mass transfer of ions from bulk to electrode (2) chemical side reactions (if any), and (3) slow electron transfer at the electrode between the adsorbed species to be oxidized and the adsorbed species to be reduced. 

In the case under consideration, complete Ohmic control of the deposition process can be expected for 70//L > 100 up to a current density about 0.95yh (Fig. 7) and for yo/yh = 10 up to 0.6yh (Fig. 9). It is obvious from Figs. 7-10 that, regardless of the shape of the polarization curve, which depends on the jo/jh ratio and /c, a limiting diffusion current density plateau is present in all cases. 

It can be noted that before the increase of the current density, over the value of the limiting diffusion one, the first part of the polarization curve for silver deposition from nitrate solution7 has practically the same shape as that from Fig. 7 and that those from Fig. 8 are very similar to the ones for Cd and Cu deposition.26 The value of yb for Ag deposition is very large.27 In the cases of both Cd28 and Cu29 deposition, yo is considerably lower than in the case of Ag deposition. 

The initiation of dendritic growth is followed by an increase of the deposition current density, and the overall current density will be larger than the limiting diffusion current on a flat active electrode. Based on the above discussion, the polarization curve equation in the Ohmic-controlled electrodeposition of metals can be determined now by 9... 

It is interesting to note that (67c) describes qualitatively the increase of the apparent current density over the value of the limiting diffusion current density after initiation of dendritic growth, since the quantitative treatment of the polarization characteristics in the presence of dendrite growth is simply impossible. This is because dendrites can have a variety of unpredictable structures. In this way, the results of Ibl and Schadegg,59 Diggle et al.,12 and Popov et al.,21 as well as the Ohmic-controlled deposition of tin,57 silver,7 and lead,58 could be explained qualitatively. 

Thus, instead of a limiting diffusion current density plateau, a curve inflection point or a short inclined plateau can be expected on the polarization curve in Ohmic-controlled electrodeposition of metals, as observed in the case of silver electrodeposition from nitrate solutions. The exchange current density of the silver reaction in nitrate electrolytes is sufficiently large to permit Ohmic-controlled deposition as well as dendritic growth at low overpotentials.27 After a linear increase of the deposition current density with increasing overpotential, an exponential increase after the inflection point appears, meaning the elimination of mass-transfer limitations due to the initiation of dendritic growth. 

Since both the exchange current density and the limiting diffusion current density are included in the general cathodic polarization curve equation given by (7), it is necessary to standardize them in the same way, hence, to the apparent surface area. In that case, the exchange current density has some effective value, y o,eff, given by (68)... 

Electrocatalysts are produced in different ways, on different substrates, and for different purposes,10,64-72 but almost in all cases the electrochemical characterization was performed by using the cyclic voltammetry observations. In this way, it was not possible to analyze the effects of the mass-transfer limitations on the polarization characteristics of electrochemical processes. As shown recently,7,9 the influence of both kinetic parameters and mass-transfer limitations can be taken into account using the exchange current density to the limiting diffusion current density ratio, jo/ju for the process under consideration. Increased value of this ratio leads to the decrease of the overpotential at one and the same current density and, hence, to the energy savings. 

The polarization curves for copper deposition on the electrodes whose surfaces are shown in Fig. 24a and 26a are given in Fig. 27. It is obvious that the noticeable increase of the exchange current density attained by the application of the PO regime ( /o.eff = 3.3 mAcm-2 /r = 23.5) is followed by the minimal increase of limiting diffusion current density, relative to the one corresponding to the substrate from Fig. 24a. 

Second, as it was recently shown,2,9 the ratio of the exchange current density and the limiting diffusion current density, jo/ju determines the polarization characteristics of an electrochemical processes. Increased value of this ratio leads to a decrease of the... 

Several newer techniques, such as cyclic voltammetry (CV) are now used to identify a proper choice of an antioxidant. CV is an electrolytic method that uses microelectrodes and an unstirred solution, so that the measured current is limited by analyte diffusion at the electrode surface. The electrode potential is ramped linearly to a more negative potential, and then ramped in reverse back to the starting voltage. The forward scan produces a current peak for any analyte that can be reduced through the range of the potential scan. The current will increase as the potential reaches the reduction potential of the analyte, but then falls off as the concentration of the analyte is depleted close to the electrode surface. As the applied potential is reversed, it wiU reach a potential that will reoxidize the product formed in the first reduction reaction, and produce a current of reverse polarity from the forward scan. This oxidation peak will usually have a similar shape to the reduction peak. The peak current, ip, is described by the Randles-Sevcik equation ... 

The sequence of reactions involved in the overall reduction of nitric acid is complex, but direct measurements confirm that the acid has a high oxidation/reduction potential, -940 mV (SHE), a high exchange current density, and a high limiting diffusion current density (Ref 38). The cathodic polarization curves for dilute and concentrated nitric acid in Fig. 5.42 show these thermodynamic and kinetic properties. Their position relative to the anodic curves indicate that all four metals should be passivated by concentrated nitric acid, and this is observed. In fact, iron appears almost inert in concentrated nitric acid with a corrosion rate of about 25 pm/year (1 mpy) (Ref 8). Slight dilution causes a violent iron reaction with corrosion rates >25 x 1()6 pm/year (106 mpy). Nickel also corrodes rapidly in the dilute acid. In contrast, both chromium and titanium are easily passivated in dilute nitric acid and corrode with low corrosion rates. 

Concentration polarization as reflected by the limiting diffusion current is observed for protein-free solutions at U s slightly negative to the corrosion potential, and at potentials lower than about —0.5 V for both protein-free and protein-containing solutions. The activation polarization region with a Tafel slope of beta = 0.22 V is higher by almost a factor of 2 from the beta = 0.12... 

Figure 2. Partial polarization curves for (a) hydrogen evolution and (b) metal dissolution (c) polarization curve due to superposition of the two processes. The limiting diffusion current for curve b is influenced by stirring with hydrogen.

When the electrode has become polarized, a fresh supply of M" " ions to its surface is controlled by the diffusion of such ions from the bulk of the solution, through the zone depleted of M" ". In other words, the current flowing is dependent on the diffusion of ions from the bulk liquid. This current is called the diffusion current and the plateau region of the curve can be used to measure the limiting diffusion current jl. It is usual to extrapolate the residual current background and to construct a parallel line through the diffusion current plateau to correct for the residual current contribution to j l. ... 

Mixed potential theory and the Levich equation are used to construct the anodic and cathodic polarization curve of the active-passive alloy and to estimate the value of the oxygen limiting diffusion current when a spontaneous passive film is formed on the surface. Figure 4.11 correlates the relationship between potential and current for the... 

---