Mass-transfer overpotential, electrode reaction

Here we see that the mass-transfer-limited electrode reaction resembles an actual resistance element only at small overpotentials. 

In deriving eqn. (80), limitations due to mass transport at the interface were not considered. Strictly speaking, this is not realistic and as the reaction rate increases with overpotential in each direction a variation of the concentrations of reactant and product at the surface operates and concentration polarization becomes more important. Each exponential expression in eqn. (80) must be multiplied by the ratio of surface to bulk concentrations, ci s/ci b. The effect of mass transfer in electrode kinetics has been discussed in Sect. 2.4. 

Mass-transfer overpotential results from a finite mass-transfer rate from bulk electrolyte to electrode or vice versa. If the system is mass-transfer controlled, a limiting current density exists. The limiting current density is the maximum reaction rate under mass-transfer control. It increases as the concentration of the reacting species, their diffusion rate, temperature, or flow rate increase. In a system with limiting current density, the overpotential follows Eq. (12). The overpotential increases very rapidly when approaching the limiting current density. 

Each value of current density, j, is driven by a certain overpotential, 17. This overpotential can be considered as a sum of terms associated with the different reaction steps r/mt (the mass-transfer overpotential), (the charge-transfer overpotential), (the overpotential associated with a preceding reaction), etc. The electrode reaction can then be represented by a resistance, R, composed of a series of resistances (or more exactly, impedances) representing the various steps R i, R, etc. (Figure 1.3.7). A fast reaction step is characterized by a small resistance (or impedance), while a slow step is represented by a high resistance. However, except for very small current or potential perturbations, these impedances are functions of E (or /), unlike the analogous actual electrical elements. 

Two main contributions to the overpotential will be discussed in this book in some details. The first one is the charge (electron) transfer overpotential, which is due to a particular rate of the electrochemical reaction and takes place just at the electrodesolution interface. The second one is the mass transfer overpotential, which is due to delivering reactants to the electrochemical reaction interface or due to transporting products to the bulk solution. Other physicochemical processes taking place in the Nernst diffusion layer (e.g., chemical reactions and adsorption/desorption) can also contribute to the electrode overpotential, but they will not be discussed in this book. Note that chemical reactions occurring in the bulk solution should be taken into account to correctly estimate the concentration of the reduced, / buik nd oxidized, Obuik. species. 

It is convenient to distinguish three components of the overpotential, r. Two of these are associated respectively with mass-transfer restrictions in the electrolyte near the electrode (concentration overpotential, f/c), and with kinetic limitations of the reaction taking place at the electrode surface (surface overpotential, rjs) the third one is related to ohmic resistance. 

Therefore, criteria in the selection of an electrode reaction for mass-transfer studies are (1) sufficient difference between the standard electrode potential of the reaction that serves as a source or sink for mass transport and that of the succeeding reaction (e.g., hydrogen evolution following copper deposition in acidified solution), and (2) a sufficiently low surface overpotential and rate of increase of surface overpotential with current density, so that, as the current is increased, the potential will not reach the level required by the succeeding electrode process (e.g., H2 evolution) before the development of the limiting-current plateau is complete. 

It is an experimental fact that whenever mass transfer limitations are excluded, the rate of charge transfer for a given electrochemical reaction varies exponentially with the so-called overpotential rj, which is the potential difference between the equilibrium potential F0 and the actual electrode potential E (t) = E — Ed). Since for the electrode reaction Eq. (1) there exists a forward and back reaction, both of which are changed by the applied overpotential in exponential fashion but in an opposite sense, one obtains as the effective total current density the difference between anodic and cathodic partial current densities according to the generalized Butler-Volmer equation ... 

Although the kinetic variable in electrode reactions in the current density, extensive use of the overpotential concept has been made in the electrochemical literature to indicate the departure from equilibrium [7]. Depending on the particular rate-determining process, in the overall electrode kinetics ohmic, charge transfer, reaction, concentration or mass transport, and crystallization overpotentials are described in the literature. Vetter [7] distinguished the concept of overpotential from that of polarization in the case of mixed potentials when the zero current condition does not correspond to an equilibrium potential as will be discussed in Sect. 8. 

AE is the thermodynamic cell voltage depending on the nature of the electrode reactions, rj is the total overpotential and represents the surplus of electrical energy required to drive the process at a practical rate and to overcome mass transfer resistances. AFn = IR is the ohmic drop in the interelectrode gap, the electrode... 

Three dimensional electrode structures are used in several applications, where high current densities are required at relatively low electrode and cell polarisations, e g. water electrolysis and fuel cells. In these applications it is desirable to fully utilize all of the available electrode area in supporting high current densities at low polarisation. However conductivity limitations of three-dimensional electrodes generally cause current and overpotential to be non-uniform in the structure. In addition the reaction rate distribution may also be non-uniform due to the influence of mass transfer.1... 

Figure 12(a) shows the typical distributions in local current for a first order reaction with different values of v 2 and applied dimensionless overpotentials ° for the coupled anode model, including mass transfer parameter y. The values of °, in the range of 0.5 to 16 typically represent overpotentials in the approximate range of 25 to 800 mV. The total current flows fromX = 0 (anode fed plane) to X= 1 (membrane). Current is much higher at the face of the electrode adjacent to the membrane or free electrolyte solution and decreases towards the current collector. An increase in potential increases the local current density and thereby increases the overall variation in current density throughout the electrode. 

The transfer of reactants from the bulk solution to the electrode interface and in the reverse direction is an ordinary feature of all electrode reactions. As the oxidation-reduction reactions advance, the accessibility of the reactant species at the electrode/electrolyte interface changes. This is because of the concentration polarization effect, that is, r c, which arises due to the limited mass transport capabilities of the reactant species toward and from the electrode surface, to substitute the reacted material to sustain the reaction [6,8,10,66,124], This overpotential is usually established by the velocity of reactants flowing toward the electrolyte through the electrodes and the velocity of products flowing away from the electrolyte. The concentration overpotential, r c, due to mass transport restrictions, can be expressed as... 

The standard potentials are valid at "zero current"—that is, before any electrons are ever moved. In practical cells and when finite currents are passed, the cell potentials are affected by the finite resistance R of the electrolyte, which causes an "IR drop" across the cell, and also by "overpotentials," due to polarizations of the solution caused by (i) a finite mass transfer rate, (ii) a preceding reaction, or (iii) charge-transfer. If the "IR drop" is less than 0.002 V, then two-electrode cells are adequate for reproducible measurements (e.g., in polarography). 

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. 

To develop any electrochemical process, a voltage should be applied between anodes and cathodes of the cell. This voltage is the addition of several contributions, such as the reversible cell voltage, the overvoltages, and the ohmic drops, that are related to the current in different ways. One of these contributions, the overvoltage, controls the rate of the transfer of electrons to the electrochemically active species through the electrode-electrolyte interface when there is no limitation in the availability of these active species on the interface (no mass-transfer control and no control by a preceding reaction). In this case, the relationship between the current that flows between the anodes and the cathodes of a cell and the overpotential is... 

Chemical reactions can happen before or after the charge-transfer step. Any step can be rate determining, that is, the slowest one determines the total reaction rate. As the electrode polarizes, the resulting overpotential consists of several factors. The most important ones are activation, concentration, and resistance overpotentials. The activation overpotential results from the limited rate of a charge-transfer step, concentration overpotential from the mass-transfer step, and resistance overpotential is the result of ohmic resistances such as solution resistance. Depending on the nature of the slowest step, the reaction is activation, mass transfer, or resistance controlled. 

The thickness distribution of electrodeposits depends on the current distribution over the cathode, which determines the local current density on the surface. The current distribution is determined by the geometrical characteristics of the electrodes and the cell, the polarization at the electrode surface, and the mass transfer in the electrolyte. The primary current distribution depends only on the current and resistance of the electrolyte on the path from anode to cathode. The reaction overpotential (activation overpotential) and the concentration overpotential (diffusion overpotential) are neglected. The secondary... 

The reactions (20) to (22) form the copper equilibrium on the electrode surfaces. Concentration of Cu(I) on the cathode surface affects the deposition rate. The maximum net rate of Cu+ production is at about —50 mV versus Cu/CuSC>4 and at higher overpotentials it decreases. Disturbing the Cu(II)—Cu(I)—Cu equilibrium can cause the formation of copper powder, but this is more a problem on the anode. For the current densities commonly used in electrorefining, the cathode overpotential is between 50 and 100 mV. The system is mainly charge transfer controlled and the effect of mass-transfer polarization is small. If Cu(I) concentration on the cathode surface decreases, mass-transfer polarization will increase, causing more uneven deposit. 

The overpotential in the low current range is ascribed to the activation overpotential, which is caused by tlie slowness of the reactions taking place on the surface of the electrode. In the intermediate current range, tlie overpotential is mainly due to the ohmic losses of the system. The appearance of overpotential in the high current range is primarily ascribed to the mass transfer limitation of the involved species. 

Secondary current distribution [85, 86], Here, mass transfer effects are not controlling, bnt reaction kinetics are considered because of a non-negligible electrode polarization (i.e., electrode reactions that require an appreciable surface overpotential to sustain a high reaction rate). Once again, Laplace s Equation (Equation [26.120]) is solved for the potential distribution, but the boundary condition for O on the electrode surface (y = 0) is given by... 

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