Continuum models electrode-electrolyte interface

In this article, a brief discussion will be given on the relevance of continuum theory in explaining the rate of electron transfer and the activation of species in solution we will concentrate in particular on molecular and quantum mechanical models of ET reactions at the electrode/electrolyte interface that are needed to replace those based on the continuum approach. ... 

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. 

Cell-level models solve the species [Eq. (26.1)], momentum [Eq. (26.5)], and energy [Eq. (26.7)] conservation equations using the effective properties of the electrodes and can include the electrochemistry using a continuum-scale (Section 26.2.4.1) or a mesoscale (Section 26.2.4.2) approach. Traditionally, cell-level models use a continuum-scale electrochemistry approach, which includes the electrochemistry as a boundary condition at the electrode-electrolyte interface [17, 51, 54] or over a specified reaction zone near the interface. The electrochemistry is modeled via the Nernst equation [Eq. (26.12)] using a prescribed current density and assumptions for the polarizations in the cell. The continuum-scale electrochemistry is then coupled to the species conservation equation [Eq. (26.1)] using Faraday s law ... 

The good electrical conductivity of the solid makes more sizeable and evident the occurrence of phenomena related to the presence of electric potentials at the interface (similar phenomena also occur at interfaces of different type, however" ). A well-known example is the double layer at the liquid side of an electrolyte/electrode surface. For the double layer, actually there is no need of interaction potentials of special type the changes in the modelling mainly regard the boundary conditions in the simulation or in the application of other models, of continuum or integral equation type. 

In SOFC modeling, the electrochemistry of the fuel cell can be included in the model at various levels of detail. In a continuum-scale approach, empirical current-potential (f-V) relations are typically used to model the electrochemistry of the SOFC. In a mesoscale approach, the electrochemical reactions and the transport of electrons and ions in the SOFC can be modeled explicitly. The continuum-scale approach allows for a quick evaluation of the I-V performance of the SOFC by assuming that the electrochemistry occurs only at the interface of the electrode and electrolyte. In the mesoscale approach, the electrochemistry of the SOFC is resolved through the thickness of the electrodes based on the local conditions in the cell. In this section, we discuss the details of both approaches. 

One of the most fundamental problems in electrochemical surface science is distribution of the electric potential and the particles at the interface. The classical model which prevailed until about 1980 treated the electrode surface as a perfect and structureless conductor and did not take into account the surface electronic structure. The electrolyte was considered as an ensemble of hard, point ions immersed in a dielectric continuum. This approximation neglected the fine structure of the solvent molecules and the solute as well as their discrete interactions. In recent years, much progress has been made in providing a more realistic model of the solid-liquid electrochemical interface by applying quantum mechanical theories to model the metal... 

The processes occurring at the interface between the catalyst and electrolyte are manifold and strongly influenced by the surrounding environment and the external parameters (temperature, pressure and electrode potential). In addition, these external parameters can affect the morphology and composition of the CL, especially in cases where nanoparticles are used as catalyst materials. A consistent theoretical description of such complex catalytic systems is a real challenge. We have proposed a novel model within a continuum framework to describe in a detailed way the electrochemical interface at the vicinity of the catalyst under non-equilibrium conditions.This nanoscale model, which is a key part of MEMEPhys , comprises a ID-dififiise layer sub-model and a ID-inner layer submodel, as represented in Fig. 11.13. 

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