Concentration polarization electrode

As the Nemst equation suggests, concentration variations in the electrolyte lead to potential differences between electrodes of the same kind. These potential differences are concentration polarizations or concentration overpotentials. Concentration polarizations can also affect the current distribution. Predicting these is considerably more difficult. If concentration gradients exist, equations 25 and 27 through 29 must generally be solved simultaneously. 

Further, as the current density of the fuel cell increases, a point is inevitably reached where the transport of reactants to or products from the surface of the electrode becomes limited by diffusion. A concentration polarization is estabhshed at the elec trode, which diminishes the cell operating potential. The magnitude of this effect depends on many design and operating variables, and its value must be obtained empirically. 

Chronopotentiometry has been widely used to determine diffusion coefficients in molten salts. Chronopotentiometry is an experimental procedure in which the potential of an electrode is observed as a function of time during the passage of a constant current sufficiently large to produce concentration polarization with respect to the species undergoing electrochemical reaction. 

Electrode reactions are heterogeneous since they occur at interfaces between dissimilar phases. During current flow the surface concentrations Cg j of the substances involved in the reaction change relative to the initial (bulk) concentrations Cy p Hence, the value of the equilibrium potential is defined by the Nemst equation changes, and a special type of polarization arises where the shift of electrode potential is due to a change in equilibrium potential of the electrode. The surface concentrations that are established are determined by the balance between electrode reaction rates and the supply or elimination of each substance by diffusion [Eq. (4.9)]. Hence, this type of polarization, is called diffusional concentration polarization or simply concentration polarization. (Here we must take into account that another type of concentration polarization exists which is not tied to diffusion processes see Section 13.5.)... 

The polarization equation describes polarization as a fnnction of current density. In the case of concentration polarization, the form of the polarization eqnation is nnre-lated to the natnre of reaction or electrode. In the case of activation polarization, the parameters of the polarization eqnations depend decisively on the natnre of the reaction. At identical values of current density and otherwise identical conditions, the values of polarization for different reactions will vary within wide limits, from less than 1 mV to more than 2 or 3 V. However, these equations still have common features. A relatively simple set of equations is obtained for simple redox reactions of the type... 

Under the effect of pure concentration polarization, when activation polarization is absent, the electrode potential retains an equilibrium value, but this is a value tied to the variable nonequilibrium values of surface concentrations... 

The surface concentrations that are attained as a result of balance between the electrode reaction rates and the rates of supply or escape of components by diffusion and migration are given by Eqs. (4.11) and (4.12). Hence, the overall expression for concentration polarization becomes... 

Transient measnrements (relaxation measurements) are made before transitory processes have ended, hence the current in the system consists of faradaic and non-faradaic components. Such measurements are made to determine the kinetic parameters of fast electrochemical reactions (by measuring the kinetic currents under conditions when the contribution of concentration polarization still is small) and also to determine the properties of electrode surfaces, in particular the EDL capacitance (by measuring the nonfaradaic current). In 1940, A. N. Frumkin, B. V. Ershler, and P. I. Dolin were the first to use a relaxation method for the study of fast kinetics when they used impedance measurements to study the kinetics of the hydrogen discharge on a platinum electrode. 

Consider the case when the equilibrium concentration of substance Red, and hence its limiting CD due to diffusion from the bulk solution, is low. In this case the reactant species Red can be supplied to the reaction zone only as a result of the chemical step. When the electrochemical step is sufficiently fast and activation polarization is low, the overall behavior of the reaction will be determined precisely by the special features of the chemical step concentration polarization will be observed for the reaction at the electrode, not because of slow diffusion of the substance but because of a slow chemical step. We shall assume that the concentrations of substance A and of the reaction components are high enough so that they will remain practically unchanged when the chemical reaction proceeds. We shall assume, moreover, that reaction (13.37) follows first-order kinetics with respect to Red and A. We shall write Cg for the equilibrium (bulk) concentration of substance Red, and we shall write Cg and c for the surface concentration and the instantaneous concentration (to simplify the equations, we shall not use the subscript red ). 

In an electrochemical system, gas supersaturation of the solution layer next to the electrode will produce a shift of equilibrium potential (as in diffusional concentration polarization). In the cathodic evolution of hydrogen, the shift is in the negative direction, in the anodic evolution of chlorine it is in the positive direction. When this step is rate determining and other causes of polarization do not exist, the value of electrode polarization will be related to solution supersaturation by... 

The formation of new nuclei and of a fine-crystalline deposit will also be promoted when a high concentration of the metal ions undergoing discharge is maintained in the solution layer next to the electrode. Therefore, concentration polarization will have effects opposite those of activation polarization. Rather highly concentrated electrolyte solutions, vigorous stirring, and other means are employed to reduce concentration polarization. Sometimes, special electrolysis modes are employed for the same purposes currents that are intermittent, reversed (i.e., with periodic inverted, anodic pulses), or asymmetric (an ac component superimposed on the dc). 

When only taking into account the concentration polarization in the pores (disregarding ohmic potential gradients), we must use an equation of the type (18.15). Solving this equation for a first-order reaction = nFhjtj leads to equations exactly like (18.18) for the distribution of the process inside the electrode, and like (18.20) for the total current. The rate of attenuation depends on the characteristic length of the diffusion process ... 

For isolating the overpotential of the working electrode, it is common practice to admit hydrogen to the counter-electrode (the anode in a PEMFC the cathode in a direct methanol fuel cell, DMFC) and create a so-called dynamic reference electrode. Furthermore, the overpotential comprises losses associated with sluggish electrochemical kinetics, as well as a concentration polarization related to hindered mass transport ... 

In addition to this, one distinguishes that there are two other sources of voltage difference. One has its origin within the electrolyte of the cell, and the other is referred to rate processes taking place at the electrodes. The former is called concentration polarization, while the latter is called overvoltage. 

In fact, the occurrence of iresiduai represents an electrochemical polarization and that of iUmiting a concentration polarization the term depolarization should be used only if a polarizing agent occurring at an electrode is eliminated, e.g., Cl2 (and/or 02) at an anode is reduced by a reductant, or Zn (and/or H2) at a cathode oxidized by an oxidant. 

In the practice of electrolysis one mostly deals with altering and even exhausting redox concentrations at the electrode interface, so-called concentration polarization this has been considered already on pp. 100-102 for exhaustion counteracted by mere diffusion. The equations given for partial and full exhaustion (eqns. 3.3 and 3.4) can be extended to the current densities ... 

Polarization is produced by the slow rate of at least one of the partial processes in the overall electrode process. If this rate-controlling step is a transport process, then concentration polarization is involved if it is the charge transfer reaction, then it is termed charge transfer polarization, etc. Electrode processes are often classified on this basis. 

Conductance of a solution is a measure of its ionic composition. When potentials are applied to a pair of electrodes, electrical charge can be carried through solutions by the ions and redox processes at the electrode surfaces. Direct currents will result in concentration polarization at the electrodes and may result in a significant change in the composition of the solution if allowed to exist for a significant amount of time. Conductance measurements are therefore made using alternating currents to avoid the polarization effects and reduce the effect of redox processes if they are reversible. 

Concentration Polarization As a reactant is consumed at the electrode by electrochemical reaction, there is a loss of potential due to the inability of the surrounding material to maintain the initial concentration of the bulk fluid. That is, a concentration gradient is formed. Several processes may contribute to concentration polarization slow diffusion in the gas phase in the electrode pores, solution/dissolution of reactants/products into/out of the electrolyte, or diffusion of reactants/products through the electrolyte to/from the electrochemical reaction site. At practical current densities, slow transport of reactants/products to/from the electrochemical reaction site is a major contributor to concentration polarization ... 

Summing of Electrode Polarization Activation and concentration polarization can exist at both the positive (cathode) and negative (anode) electrodes in fuel cells. The total polarization at these electrodes is the sum of r act and riconc, or... 

Concentration Polarization The rate of mass transport to an electrode surface in many cases can be described by Pick s first law of diffusion ... 

The potential difference (AE) produced by a concentration change at the electrode is called the concentration polarization ... 

As the redox reactions proceed, the availability of the active species at the electrode/electrolyte interface changes. Concentration polarization arises from limited mass transport capabilities, for example, limited diffusion of active species to and from the electrode surface to replace the reacted material to sustain the reaction. Diffusion limitations are relatively slow, and the buildup and decay take >10 s to appear. For limited diffusion the electrolyte solution, the concentration polarization, can be expressed as... 

Figure 7. (A, top) Simple battery circuit diagram, where Cdl represents the capacitance of the electrical double layer at the electrode—solution interface (cf. discussion of supercapacitors below), W depicts the Warburg impedance for diffusion processes, Rj is the internal resistance, and Zanode and Zcathode are the impedances of the electrode reactions. These are sometimes represented as a series resistance capacitance network with values derived from the Argand diagram. This reaction capacitance can be 10 times the size of the double-layer capacitance. The reaction resistance component of Z is related to the exchange current for the kinetics of the reaction. (B, bottom) Corresponding Argand diagram of the behavior of impedance with frequency, f, for an idealized battery system, where the characteristic behaviors of ohmic, activation, and diffusion or concentration polarizations are depicted.

A lithium ion transference number significantly less than 1 is certainly an undesired property, because the resultant overwhelming anion movement and enrichment near electrode surfaces would cause concentration polarization during battery operation, especially when the local viscosity is high (such as in polymer electrolytes), and extra impedance to the ion transport would occur as a consequence at the interfaces. Fortunately, in liquid electrolytes, this polarization factor is not seriously pronounced. 

This approach was coupled to a system of three NAD+-dependent enzymes comprised of alcohol dehydrogenase (EC 1.1.1.1), aldehyde dehydrogenase (EC 1.2.1.3), and formate dehydrogenase (EC 1.2.1.2) to create an electrode theoretically capable of complete oxidation of methanol to carbon dioxide, as shown in Eigure 5. The anode was, in turn, coupled to a platinum-catalyzed oxygen cathode to produce a complete fuel cell operating at pH 7.5. With no externally applied convection, the cell produced power densities of 0.67 mW/cm at 0.49 V for periods of less than 1 min, before the onset of concentration polarization. 

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