Porous electrode geometry

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. 

Keiser et al.164 first showed that the more occluded the shape of the pore, the more distorted the impedance locus from the ideal capacitive behavior. However, the pore shapes in real system turn out to be much complicated and thus a straightforward analytical calculation is not usually possible of the overall impedance for those complicated pores. In connection with this problem, the fractal geometry has given a powerful tool for the analysis of the CPE behavior of the porous electrode. A number of theoretical papers166,179 191 have devoted to investigate the relationship between the fractal geometry of the electrode and the CPE impedance on the basis of the electrolytic resistive distribution due to the surface irregularity. 

In the case of well-known electrochemical reactions, as well as for electrolyses where larger scales are involved, two-electrode cells (connected to a galvanostat) can be used with continuous feed of the reactant to the working electrode. This type of electrolysis is suitable for industrial purposes where specific devices and cells are utilized. Since electrodes of large areas are necessary, the distance between the anode and the cathode is small and determines the cell geometry (e.g. capillary-gap cell or filter-press cell). The use of cells equipped of porous electrodes (materials like graphite or carbon moss, platinum, nickel) have also been developed to perform electrocatalytic reactions at very large surfaces. Some typical cells used in the laboratory and in industry are presented at the end of this review. 

At porous electrodes, diffusion will be conditioned by the electrode geometry and pore-size distribution, so that under several conditions, semi-infinite diffusion holds however, under several other conditions, the porous electrode can be treated as an array of microelectrodes (Rolison, 1994). 

The cylindrical pore model is an idealization of a real porous electrode. Other pore geometries were also studied. De Levie [413] obtained an analytical solution for the impedance of V-grooved pores. Such pores might be obtained, for example, by scratching the electrode surface. A cross section of such a groove is displayed in Fig. 9.8. Its impedance per unit of groove length is... 

In the preceding sections the impedance of a single pore or the distribution of simple pores of known geometry was treated. However, in real cases of porous electrodes used in, for example, lithium or hydrogen storage batteries or fuel cells, one does not... 

Porous Electrode. Most battery electrodes comprise an open stmcture consisting of small particles compressed together, as shown in Figure 4.5.6. This structure does not have well-defined pores (such as cylindrical) but rather an irregular network of interconnected space between particles filled with electrolyte. The absence of well-defined pores complicates ab initio deduction of electrolyte impedance however, the frequency dependence of the impedance of porous materials is well described by the ladder-network approach originally proposed by de Levie [1963] for cylindrical pores. See also Section 2.1.6 for treatment of various geometries of porous electrodes. 

A brush of many thin wires, oriented in a parallel way and constrained to be in lateral contact, provides a useful and geometrically weU-deflned model of a porous electrode. Of course, the model pores are linear and of anticyUndrical cross section while pores in a real powder electrode, or an electrode made from unoriented carbon fibers, are of random size and geometry. 

In addition to these features of a porous electrode, there is another factor that can introduce electrical losses which a-rises from the fact that a porous electrode is not in continuous contact with the electrolyte The result of this discrete contact is that ions and electrons will be restricted in their flow to regions of electrode/electrolyte/gas phase contact, the so-called triple-point contact (T P C ). This introduces a resistive loss which is termed a constriction resistance and is additional to the cell resistance that would be expected on the basis of bulk resistivities and geometry. This type of polarisation will be discussed further in section 3. 

The functions of porous electrodes in fuel cells are 1) to provide a surface site for gas ionization or de-ionization reactions, 2) to provide a pathway for gases and ions to reach the catalyst surface, 3) to conduct water away from the interface once these are formed, and 4) to allow current flow. A membrane electrode assembly (MEA) forms the core of a fuel cell and the key electrochemical reactions take place in the MEA. MEA performance is severely affected by electrode composition, structure, and geometry, and especially by cathode structure and composition, due to poor oxygen reduction kinetics and transport liniitations of the reactants in the cathode catalyst layer. 

In the published work on CDI, the water usually flows through a sUt in between the two parallel porous electrodes, from one side to the other. This slit can be an open channel, typically at least 1 nun in thickness, or can be constructed from a spacer material, being a porous thin layer, of thickness typically between 100 and 300 pm. The geometry is normally not such that a purely one-dimensional flow pattern arises, but instead water flows from one edge of a square channel to an exit point at the opposite corner, or water flows from a hole in the center of a square cell and then radially outward to leave the cell on all four sides the direction of this flow pattern can also be reversed. 

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