Length scale, electrode-electrolyte interface

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

The properties characteristic for electrochemical nonlinear phenomena are determined by the electrical properties of electrochemical systems, most importantly the potential drop across the electrochemical double layer at the working electrode (WE). Compared to the characteristic length scales of the patterns that develop, the extension of the double layer perpendicular to the electrode can be ignored.2 The potential drop across the double layer can therefore be lumped into one variable, DL, and the temporal evolution law of DL at every position r along the (in general two-dimensional) electrode electrolyte interface is the central equation of any electrochemical model describing pattern formation.3 It results from a local charge bal-... 

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. 

The PS layer thickness may show fluctuations over the electrode area on different length scales. The thickness variations may originate from a waviness of the bulk-PS interface, or the electrolyte-PS interface. The latter case, which is usually due to a dissolution of PS during anodization or a collapse of the PS microstructure due to capillary forces during drying, is discussed in Section 6.5. 

Going from planar to porous electrode introduces another length scale, the electrode thickness. In the case of a PEM fuel cell catalyst layer, the thickness lies in the range of IcL — 5-10 pm. The objective of porous electrode theory is to describe distributions of electrostatic potentials, concentrations of reactant and product species, and rates of electrochemical reactions at this scale. An accurate description of a potential distribution that accounts explicitly for the potential drop at the metal/electrolyte interface would require spatial resolution in the order of 1 A. This resolution is hardly feasible (and in most cases not necessary) in electrode modeling because of the huge disparity of length scales. The simplified description of a porous electrode as an effective medium with two continuous potential distributions for the metal and electrolyte phases appears to be a consistent and practicable option for modeling these stmctures. 

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