Diffusion layer through-plane

Consider the structure of an interface layer between a metal electrode and an electrolyte solution kept under a potential difference electrostatic adsorption) and the dipolar molecules are oriented along the lines of the electric force. They can also be physically or chemically adsorbed specifically adsorbed) on the electrode. In the case of electrostatic adsorption alone, ions can approach the electrode to a distance given by their primary solvation shells. The plane parallel to the electrode surface through the centers of elecfrostatically adsorbed ions at their maximum approach to the electrode is called the outer Helmholtz plane (OFIP) and the solution region between the OHP and the electrode surface is called the Helmholtz or compact layer. Due to thermal motion the ions are not confined within the compact layer, but are distributed over the so-called diffuse layer. The plane through the centers of specifically adsorbed ions is referred to as the inner Helmholtz plane (IHP) (Fig. 2.21). 

One of the main parameters that would improve the overall performance of a fuel cell is better mass transport of reactants through the diffusion layer toward the active catalyst zones. In order to quantify and characterize how well the gas mass transport is in a specific DL material and design, it is important to measure the in-plane and through-plane permeabilities. Most of the published permeability results report the viscous permeability... 

Although in-plane permeability is critical in order to understand in detail the transport mechanisms of fluids inside diffusion layers, it has not been as commonly used (and measured) as through-plane permeability. The following are a few examples of how in-plane permeability can be determined... 

In order to determine the viscous and inert through-plane gas permeabilities of diffusion layers at varied compression pressures, Gostick et al. [212] designed a simple method in which a circular specimen was sandwiched between two plates that have orifices in the middle, aligned with the location of the material. Pressurized air entered the upper plate, flowed through the DL, and exited the lower plate. The pressure drop between the inlet and the outlet was recorded for at least ten different flow rates for each sample. The inert and viscous permeabilities were then determined by fitting the Forchheimer equation to the pressure drop versus flow rate data as explained earlier. 

Park, Lee, and Popov [136] used a similar technique to determine the liquid permeation in different diffusion layers. Feser, Prasad, and Advani [214] used the same method explained in Section 4.4.S.2 to measure the liquid in-plane permeability of DLs. When water was used, flow was forced from a pressurized tank (0-200 kPa) through the apparatus (and the sample), and the outlet water was then collected with a graduated cylinder. 

The following subsection will briefly discuss the main methods used to measure in-plane and through-plane electrical conductivity for diffusion layer materials. This parameter is critical for optimal fuel cell performance. 

The most typical way to measure the in-plane electrical conductivity of a diffusion layer is through the use of the four-point probe method. A small current is applied across the sample material a separate set of voltage measuring probes that are in touch with the material are used to measure the resulting voltage drop in order to calculate the resistance. With these values, the in-plane resistivity, p, can be calculated with the following equation [9,233] ... 

Regarding the electrode as a giant ion, the solvent molecules form its first solvation layer the IHP is the plane that passes through the centre of these dipoles and specifically adsorbed ions. In a similar fashion, OHP refers to adsorption of solvated ions that could be identified with a second solvation layer. Outside this comes the diffuse layer. Note that the actual profile of electrostatic potential variation with distance (Fig. 3.9b) is the same in qualitative terms as in the Grahame model (Fig. 3.8b). 

Figure 3.37. Computed velocity fields (m/s) for flows in adjacent interdigitated oxygen channels (with gas diffusion layer on the left side) of a PEM fuel cell (A inlet, C outlet, in x-y plane). In the middle (B), the flow from one gas channel through the gas diffusion layer to the adjacent gas channel is shown in the z-y plane, for the midpoint of the cell extension in the z-direction. The flows in A and C are for the midpoint value of z. (From S. Um and C. Wang (2004). Three-dimensional analysis of transport and electrochemical reactions in polymer electrolyte fuel cells. /. Power Sources 125, 40-51. Used with permission from Elsevier.)...

Aqueous radionuclide species and other solutes can sorb to mineral surfaces by forming chemical bonds directly with the amphoteric sites or may be separated from the surface by a layer of water molecules and be bound through longer-range electrostatic interactions. In the TLM, complexes of the former type are often called inner-sphere complexes those of the latter type are called outer-sphere complexes (Davis and Kent, 1990). The TLM includes an inner plane (o-plane), an outer plane (/8-plane), and a diffuse layer that extends from the /8-plane to the bulk solution. Sorption via formation of inner-sphere complexes is often referred to chemisorption or specific... 

The structure of the double layer and the specific surface adsorption can affect the reaction kinetics. In the absence of specific adsorption, copper ions position of the closest approach to the electrode surface is the Outer Helmholtz Plane (OHP). The potential at the OHP, potential drop through the diffuse layer and possibly because some ions are specifically adsorbed. These potential differences in the double layer, as known, can affect the electrode reaction kinetics [5]. 

The triple layer model attempts to take into account inner sphere complex formation and electrostatic adsorption simultaneously by considering "specifically adsorbed" ions which are supposed to be maintained very close to the surface, whether it be through the formation of covalent bonds with some surface groups, or of some outer sphere complex. No specific interpretation of the bonding is required, provided one can define a plane of specific adsorption, located a few A from the surface and containing those ions this is called the Stem layer. The theory distinguishes then between three successive parallel layers the surface plane proper, the Stem layer, and the diffuse layer. 

Fig. 3. Thin-film flow-through cell with plane electrode. 6, diffusion layer thickness, d, film thickness s, length (A) perpendicular to the plane of the paper, width of the electrode and liquid film. Shaded bands in (B) indicate concentration functions. (Note the parabolic flow profile makes the real situation more complicated.)...

A schematic representation of the inner region of the double layer model is shown in Fig. 1. Figure lb describes the distribution of counterions and the potential profile /(a ) from a positively charged surface. The potential decay is caused by the presence of counterions in the solution side (mobile phase) of the double layer. The inner Helmholtz plane (IHP) or the inner Stem plane (ISP) is the plane through the centers of ions that are chemically adsorbed (if any) on the solid surface. The outer Helmholtz plane (OHP) or the outer Stem plane (OSP) is the plane of closest approach of hydrated ions (which do not adsorb chemically) in the diffuse layer. Therefore, the plane that corresponds to x = 0 in Eq. (4) coincides with the OHP in the GCSG model. The doublelayer charge and potential are defined in such a way that ao and /o, op and Tp, and <5d and /rf are the charge densities and mean potentials of the surface plane, the Stem layer (IHP), and the diffuse layer, respectively (Fig. 1). 

Between the diffuse layer and the interface lies the Stern layer, i.e., layer of ions, which are not subjected to Brownian motion. Two levels are identified within it the internal with unhydrated ions and external with hydrated ions. Most of ions in the Stern layer are hydrated, so they caimot approach too closely the mineral surface. Because of this Helmholtz plane is drawn through the centers of immobile hydrated ions, and the thickness of Stern layer 8 is assumed equal to half of the median radius of hydrated ions (about 2 A). Electrostatic field in such layer is defined by the charge of mineral s surface, on the one hand, and by the charge of Helmholtz plane, on the other. It characterizes the density of electric permittance, which, according to equation (2.98), is equal to... 

These rates are associated with different processes, which operate simultaneously but different distance from the separation surface, i.e., in different portions of the mass transfer flow. Thus, the following zones are identified in this flow 1) zone of kinetic reactions in the inner Stern layer, 2) zone of migration through diffuse layer of immobile water, 3) zone of active mixing with gravity water behind the slip plane (Figure 2.32). 

The thermal dilTusivity of CVD diamond has been measured over the temperature range 200-425 K using the thermal flash technique which measures the thermal diffusivity perpendicular to the plane of the layer (through-the-plane) [1,3],... 

Two planes are usually associated with the double layer. The first one, the inner Helmholtz plane (IHP), passes through the centers of specifically adsorbed ions (compact layer in the Helmholtz model), or is simply located just behind the layer of adsorbed water. The second plane is called the outer Helmholtz plane (OHP) and passes through the centers of the hydrated ions that are in contact with the metal surface. The electric potentials linked to the IHP and OHP are usually written as 4 2 and 4f, respectively The diffuse layer develops outside the OHP. The concentration of cations in the diffuse layer decreases exponentially vs. the distance from the electrode surface. The hydrated ions in the solution are most often octahedral complexes however, in Fig. 1.1.2. they are shown as tetrahedral structures for simplification. 

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