Concentration interface worked example

The solution for a diffusion couple in which two semi-infinite ternary alloys are bonded initially at a planar interface is worked out in Exercise 6.1 by the same basic method. Because each component has step-function initial conditions, the solution is a sum of error-function solutions (see Section 4.2.2). Such diffusion couples are used widely in experimental studies of ternary diffusion. In Fig. 6.2 the diffusion profiles of Ni and Co are shown for a ternary diffusion couple fabricated by bonding together two Fe-Ni-Co alloys of differing compositions. The Ni, which was initially uniform throughout the couple, develops transient concentration gradients. This example of uphill diffusion results from interactions with the other components in the alloy. Coupling of the concentration profiles during diffusion in this ternary case illustrates the complexities that are present in multicomponent diffusion but absent from the binary case. 

The second example, a blend sample consists of 80% PA 6.6, 18% PTFE and 2% silicone oil. From the relative concentrations, it can be seen that PA forms the matrix and provides the necessary stability to the bearing. PTFE acts as an incorporated lubricant. The two main components are not chemically linked. Therefore, silicone oil has been added to work as a boundary lubricant during the break-in phase of the bearing. Due to its liquid nature, it quickly migrates to the surface when pressure is applied and prevents abrasion at the first stage. Shortly after, a thin film of PTFE forms at the interface between the thermoplastic bearing and the counter part. 

Figure 10. Kleitz s reaction pathway model for solid-state gas-diffusion electrodes. Traditionally, losses in reversible work at an electrochemical interface can be described as a series of contiguous drops in electrical state along a current pathway, for example. A—E—B. However, if charge transfer at point E is limited by the availability of a neutral electroactive intermediate (in this case ad (b) sorbed oxygen at the interface), a thermodynamic (Nernstian) step in electrical state [d/j) develops, related to the displacement in concentration of that intermediate from equilibrium. In this way it is possible for irreversibilities along a current-independent pathway (in this case formation and transport of electroactive oxygen) to manifest themselves as electrical resistance. This type of chemical valve , as Kleitz calls it, may also involve a significant reservoir of intermediates that appears as a capacitance in transient measurements such as impedance. Portions of this image are adapted from ref 46. (Adapted with permission from ref 46. Copyright 1993 Rise National Laboratory, Denmark.)...

The cell potential is simply the work that can be accomplished by the electrons produced in the SOFC, and this potential decreases from the equilibrium value due to losses in the electrodes and the electrolyte. For YSZ electrolytes, the losses are purely ohmic and are equal to the product of the current and the electrolyte resistance. Within the electrodes, the losses are more complex. While there can be an ohmic component, most of the losses are associated with diffusion (both of gas-phase molecules to the TPB and of ions within the electrode) and slow surface kinetics. For example, concentration gradients for either O2 (in the cathode) or H2 (in the anode) can change the concentrations at the electrolyte interface,which in turn establish the cell potential. Similarly, slow surface kinetics could result in the surface at the electrolyte interface not being in equilibrium with the gas phase. 

However, there is another kind of influence on current distribution that may even the score. This is called secondary current distribution and describes the resistances set up at the interface of the working electrodes in a cell in which the interface tends to be polarizable. For example, it was shown [Eq. (7.36)] that when f) < RT/F, the interfacial resistance per unit area is RT/igF. If i0 is very small (e.g., 10-10 A cm-2, hence, an interfacial resistance cm-2 of 2.6 x 10 ohms), it is this interfacial resistance and not the ohmic resistance in the bulk solution that detennines the current distribution. Thus, in an extreme case of high solution concentration (low solution resistance) and low i q, a substantial fraction of the length of the pores in a porous electrode remains active.34 Considerations such as these, together with resistance effects at edges, all count in cell design. 

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