Time scales electrode-electrolyte interface

II. Length and Time Scales at the Electrode-Electrolyte Interface HI. Static Structure of the Interface... 

In addition to the solvent contributions, the electrochemical potential can be modeled. Application of an external electric field within a metal/vacuum interface model has been used to investigate the impact of potential alteration on the adsorption process [111, 112]. Although this approach can model the effects of the electrical double layer, it does not consider the adsorbate-solvent, solvent-solvent, and solvent-metal interactions at the electrode-electrolyte interface. In another approach, N0rskov and co-workers model the electrochemical environment by changing the number of electrons and protons in a water bilayer on a Pt(lll) surface [113-115]. Jinnouchi and Anderson used the modified Poisson-Boltzmann theory and DFT to simulate the solute-solvent interaction to integrate a continuum approach to solvation and double layer affects within a DFT system [116-120]. These methods differ in the approximations made to represent the electrochemical interface, as the time and length scales needed for a fiilly quantum mechanical approach are unreachable. 

In these experiments, the potential distribution was measured under conditions where the interfacial current density was minimized by the use of an inert electrolyte. If the electron-transfer rate across the interface had truly been zero (Ret = °°), the whole 2 film would have eventually charged up to the applied potential it was the unavoidable leakage current across the interface and the relatively short time scale of our experiments that prevented this from happening. These experiments show that even when Rct is maximized, ion motion through the nanoporous film causes the applied potential to drop near the substrate electrode in nonilluminated DSSCs. As we showed earlier, decreasing Rct causes the applied potential to drop even closer to the substrate electrode. 

This is the kinetic equation for a simple A/AX interface model and illustrates the general approach. The critical quantity which will be discussed later in more detail is the disorder relaxation time, rR. Generally, the A/AX interface behaves under steady state conditions similar to electrodes which are studied in electrochemistry. However, in contrast to fluid electrolytes, the reaction steps in solids comprise inhomogeneous distributions of point defects, which build up stresses at the boundary on a small scale. Plastic deformation or even cracking may result, which in turn will influence drastically the further course of any interface reaction. 

Fig. 4.4 Scanning electron micrograph (left) of the edge of a porous electrode made from sintered Fc203 sols on a conducting cassiterite (Sn02) support (magnification 5,800 times). Absorption spectrum of the hematite electrode and quantum efficiency as a function of wavelength (right) obtained in 0.1 M NaOH at 1.4 V vs. RHE when illuminating the electrode through the substrate (SE) and directly onto the interface with the electrolyte (EE). Note that the scale of the IPCE values differs with a factor of 100 in the two cases. From [67] used with permission...

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