Electrode porous

Porous electrodes are used in numerous industrial applications because they have the advantage of an increased effective active area. A porous electrode can be obtained by such different techniques as pressing metal powder or dissolution. This type of porous electrode structure is also observed on some corroded elec-trodes. ° It is important to recognize that a porous electrode is not the same as a porous layer. The structure may be the same, but, while the pore walls are electroactive for a porous electrode, the pore walls are inert for a porous layer. 

In the general case, Zq and Rq are functions of the distance x. This dependence is due to the potential distribution or/and to the concentration distribution in the pore. The general solution can be obtained only by a numerical calculation of the corresponding transmission line. For example, the impedance of a porous elec- 

With the restrictive assumption that Zq and Rq are independent of the distance X, de Levie calculated analytically the impedance of one pore to be 

The derivation of the de Levie impedance, given in equation (13.66), is presented in Example 13.3. The impedance of the overall electrode is obtained by accoimting for the ensemble of n pores and for the electrolyte resistance outside the pore, i.e.. 

The set of equations (13.64)-(13.67) yields an expression for the impedance of the porous electrode Z that is a fimction of three geometrical peirameters , r, and n as 

The use of electrodes with highly enlarged specific surface area is favourable for the performance of, for example, batteries and fuel cells 

For porous electrodes, an additional frequency dispersion appears. First, it can be induced by a non-local effect when a dimension of a system (for example, pore length) is shorter than a characteristic length (for example, diffusion length), i.e. for diffusion in finite space. Second, the distribution characteristic may refer to various heterogeneities such as roughness, distribution of pores, surface disorder and anisotropic surface structures. De Levie used a transmission-line-equivalent circuit to simulate the frequency response in a pore where cylindrical pore shape, equal radius and length for all pores were assumed [14]. 

Double-layer charging of the pores only (non-faradaic process) and inclusion of a pore-size distribution leads to complex plane impedance plots, as in Fig. n.5.7, i.e. at high frequencies, a straight line results in an angle of 45° to the real axis and, at lower frequencies, the slope suddenly increases but does not change to a vertical line [16]. 

The two-dimensional simulation space for a porous electrode. The complete set of boundary conditions is 

This model differs from any previous two-dimensional model that we have studied in that the simulation space is not rectangular the zone defined by (re r rj, 0 2 Ze) is outside the bounds of the space. 

In terms of computational implementation, the container that stores the concentration grid may still be rectangular one simply sets the initial concentration of all species at all points in this exclusion zone to zero. In addition, any coefficients for the Thomas algorithm (ogj, fij) that refer to spatial points inside this zone are also set to zero, and the discretised boundary conditions derived from (10.42) are applied in the appropriate places. The current is calculated in exactly the same manner as for a microdisc electrode. 

The voltammetric behaviour of this system is controlled by the size of the diffusion layer V ) relative to the pore depth, z, and radius, r [29]. If the diffusion layer thickness is less than the pore depth, diffusion to the electrode surface is necessarily planar as the layer is confined to the interior of the pores and there is no possibility of radial diffusion, regardless of the size of rg. As a consequence, conventionally macroelectrode voltammetry is seen even if the radius of the pore is of micron-scale. If the size of the diffusion layer is greater than the depth of the pore then the voltammetric behaviour becomes sensitive to both rg and rj. 

The total current in layer x [by analogy with (18.9)] is given by 

Differentiating Eqs. (18.13) and (18.14), we find the general form of the differential equation in systems with concentration changes  

For a solution of differential equations (18.12) and (18.15) and for a quantitative calculation of the current distribution, we must know how the current density depends on polarization at constant reactant concentrations or on reactant concentrations at constant polarization. We must also formulate the boundary conditions. Examples of such calculations are reported below. 

In industrial electrochemical cells (electrolyzers, batteries, fuel cells, and many others), porous metallic or nonmetallic electrodes are often used instead of compact nonporous electrodes. Porous electrodes have large trae areas, S, of the inner surface compared to their external geometric surface area S [i.e., large values of the formal roughness factors y = S /S (parameters yand are related as y = yt()]. Using porous electrodes, one can realize large currents at relatively low values of polarization. 

In porous liquid-phase electrodes, all pores are hlled with liquid electrolyte (solution or melt). When part of the pores are gas hlled, the electrodes are called gas-liquid. When the electrode is nonconsumable and chemically inert, its pore structure will remain unchanged during operation (or change very slowly on account of secondary aging processes). The structure of an electrode that reacts changes continuously. 

Dibutyl phthalate is used in a method of preparing an electrode for a lithium based secondary cell. In this method, LiCoOz as active material, carbon or graphite as conductive agent, PVDF as binder and dibutyl phthalate as plasticizer are mixed in an organic solvent (NMP) to prepare an electrode material composition. 

The plasticizer is added to make perforations in the electrode. So, eventually the plasticizer is extracted by using an organic solvent 

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Fuel cells involve use of gaseous reactants to produce electricity - most often H2-O2 within a porous electrode. Secondary cells are rechargeable. The most important systems are... 

AC impedance spectroscopy is widely employed for the investigation of both solid- and liquid-phase phenomena. In particular, it has developed into a powerfiil tool m corrosion teclmology and in the study of porous electrodes for batteries [, and ]. Its usage has grown to include applications ranging from... 

The porous electrodes in PEFCs are bonded to the surface of the ion-exchange membranes which are 0.12- to 0.25-mm thick by pressure and at a temperature usually between the glass-transition temperature and the thermal degradation temperature of the membrane. These conditions provide the necessary environment to produce an intimate contact between the electrocatalyst and the membrane surface. The early PEFCs contained Nafton membranes and about 4 mg/cm of Pt black in both the cathode and anode. Such electrode/membrane combinations, using the appropriate current coUectors and supporting stmcture in PEFCs and water electrolysis ceUs, are capable of operating at pressures up to 20.7 MPa (3000 psi), differential pressures up to 3.5 MPa (500 psi), and current densities of 2000 m A/cm. ... 

Most battery electrodes are porous stmctures in which an interconnected matrix of soHd particles, consisting of both nonconductive and electronically conductive materials, is filled with electrolyte. When the active mass is nonconducting, conductive materials, usually carbon or metallic powders, are added to provide electronic contact to the active mass. The soHds occupy 50% to 70% of the volume of a typical porous battery electrode. Most battery electrode stmctures do not have a well defined planar surface but have a complex surface extending throughout the volume of the porous electrode. MacroscopicaHy, the porous electrode behaves as a homogeneous unit. 

When a battery produces current, the sites of current production are not uniformly distributed on the electrodes (45). The nonuniform current distribution lowers the expected performance from a battery system, and causes excessive heat evolution and low utilization of active materials. Two types of current distribution, primary and secondary, can be distinguished. The primary distribution is related to the current production based on the geometric surface area of the battery constmction. Secondary current distribution is related to current production sites inside the porous electrode itself. Most practical battery constmctions have nonuniform current distribution across the surface of the electrodes. This primary current distribution is governed by geometric factors such as height (or length) of the electrodes, the distance between the electrodes, the resistance of the anode and cathode stmctures by the resistance of the electrolyte and by the polarization resistance or hinderance of the electrode reaction processes. 

Fig. 8. Representation of the current distribution in porous electrodes showing the effect of conductivities of the electrolyte and electrodes where for (a)...

The effectiveness of a porous electrode over a plane surface electrode is given by the product of the active surface area S in cm /mL and the penetration depth Tp of the reaction process into the porous electrode. 

An effectiveness value greater than one indicates that the porous electrode is more effective than an electrode of the same geometric surface area, and that the reaction extends into the porous electrode stmcture. 

Methods for the Determination of the Real Surface Area of Rough and Porous Electrodes... 

Figure 15 shows a set of complex plane impedance plots for polypyr-rolein NaC104(aq).170 These data sets are all relatively simple because the electronic resistance of the film and the charge-transfer resistance are both negligible relative to the uncompensated solution resistance (Rs) and the film s ionic resistance (Rj). They can be approximated quite well by the transmission line circuit shown in Fig. 16, which can represent a variety of physical/chemical/morphological cases from redox polymers171 to porous electrodes.172... 

Two types of continuous flow solid oxide cell reactors are typically used in electrochemical promotion experiments. The single chamber reactor depicted in Fig. B.l is made of a quartz tube closed at one end. The open end of the tube is mounted on a stainless steel cap, which has provisions for the introduction of reactants and removal of products as well as for the insertion of a thermocouple and connecting wires to the electrodes of the cell. A solid electrolyte disk, with three porous electrodes deposited on it, is appropriately clamped inside the reactor. Au wires are normally used to connect the catalyst-working electrode as well as the two Au auxiliary electrodes with the external circuit. These wires are mechanically pressed onto the corresponding electrodes, using an appropriate ceramic holder. A thermocouple, inserted in a closed-end quartz tube is used to measure the temperature of the solid electrolyte pellet. 

FIG. 1 Geometries of electrolyte interfaces, (a) A planar electrode immersed in a solution with ions, and with the ion distrihution in the double layer, (b) Particles with permanent charges or adsorbed surface charges, (c) A porous electrode or membrane with internal structures, (d) A polyelectrolyte with flexible and dynamic structure in solution, (e) Organized amphophilic molecules, e.g., Langmuir-Blodgett film and microemulsion, (f) Organized polyelectrolytes with internal structures, e.g., membranes and vesicles. 

Porous electrodes are commonly used in fuel cells to achieve hi surface area which significantly increases the number of reaction sites. A critical part of most fuel cells is often referred to as the triple phase boundary (TPB). Thrae mostly microscopic regions, in which the actual electrochemical reactions take place, are found where reactant gas, electrolyte and electrode meet each other. For a site or area to be active, it must be exposed to the rractant, be in electrical contact with the electrode, be in ionic contact with the electrolyte, and contain sufficient electro-catalyst for the reaction to proceed at a desired rate. The density of these regions and the microstmcture of these interfaces play a critical role in the electrochemical performance of the fuel cells [1]. 

Many other opportunities exist due to the enormous flexibility of the preparative method, and the ability to incorporate many different species. Very recently, a great deal of work has been published concerning methods of producing these materials with specific physical forms, such as spheres, discs and fibres. Such possibilities will pave the way to new application areas such as molecular wires, where the silica fibre acts as an insulator, and the inside of the pore is filled with a metal or indeed a conducting polymer, such that nanoscale wires and electronic devices can be fabricated. Initial work on the production of highly porous electrodes has already been successfully carried out, and the extension to uni-directional bundles of wires will no doubt soon follow. 

This study Illustrates the use of situ MBS as applied to the Investigation of species Involved In redox processes In porous electrodes. It Is expected that a systematic utilization of this technique may enable the acquisition of microscopic level Information of difficult accessibility with other spectroscopic methods, although limited to only Mossbauer active nucleus. 

In situ analysis of the reaction products can also be carried out by mass spectrometry, using the differential electrochemical mass spectrometry (DBMS) technique.This technique permits the detection of gaseous products since they are produced and captured through a porous electrode. It has been confirmed that carbon dioxide is the main reaction product. With this technique, it is also possible to determine the production of CO2... 

It is of great value in efiforts to reduce polarization to raise the true working surface area by using strongly roughened or even porous electrodes instead of smooth... 

An appreciable increase in working area of the electrodes can be attained with porous electrodes (Section 18.4). Such electrodes are widely used in batteries, and in recent years they are also found in electrolyzers. Attempts are made to use particulate electrodes which consist of a rather thick bed of particulate electrode material into which the auxiliary electrode is immersed together with a separator. Other efforts concern fiuidized-bed reactors, where a finely divided electrode material is distributed over the full electrolyte volume by an ascending liquid or gas flow and collides continuously with special current collector electrodes (Section 18.5). 

Porous electrodes are systems with distributed parameters, and any loss of efficiency is dne to the fact that different points within the electrode are not equally accessible to the electrode reaction. Concentration gradients and ohmic potential drops are possible in the electrolyte present in the pores. Hence, the local current density, i (referred to the unit of true surface area), is different at different depths x of the porous electrode. It is largest close to the outer surface (x = 0) and falls with increasing depth inside the electrode. 

Mathematical calculations of the current-density distribution in a direction normal to the electrode are rather difficult hence, to discuss the major qualitative trends, we shall limit ourselves to reviewing the simplest cases. Consider the processes occurring in a porous electrode of thickness d operated unilaterally. The current density generated at depth x per unit volume will be designated as and it is obvious that iyj X ... 

FIGURE 18.5 Current density distribution inside a porous electrode [according to Eq. (18.18)] for two values of electrode thickness dj = 0.33L , jj and dj =... 

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