Electrochemical interface, modeling

W. Schmickler, D. Henderson. New models for the electrochemical interface. Prog SurfSci 22 323-420, 1986. 

Specific aspects examined here include insights and conclusions derived from the most recently performed density functional theory (DFT) calculations, which have been based on a comprehensive model of the electrochemical interface, and the strong disagreements (which seem to defy all recent theoretical efforts) that remain regarding proper interpretation of experimental ORR results and proper identihcation of the ORR mechanism in a PEFC cathode employing Pt catalysts. 

Accordingly, Neurock and co-workers have developed models for the electrochemical interface that retain this concept of hexagonal stmcture over close-packed metal surfaces [FiUiol and Neurock, 2006 Taylor et al., 2006c]. With the use of a screening charge as described in Section 4.3, the sensitivity of the stmctural parameters of water with respect to the electrochemical environment were explored [Taylor et al., 2006a]. The predominant effect stems from the polar nature of the water molecule, in which the water molecules are observed to rotate as a function of the applied potential. 

Taylor CD, Wasileski SA, Filhol JS, Neurock M. 2006b. First principles reaction modeling of the electrochemical interface Consideration and calculation of a tunable surface potential fi om atomic and electronic structure. Phys Rev B, 73. 

The term G T, a,, A/, ) is the Gibbs free energy of the full electrochemical system x < x < X2 in Fig. 5.4). It includes the electrode surface, which is influenced by possible reconstructions, adsorption, and charging, and the part of the electrolyte that deviates from the uniform ion distribution of the bulk electrolyte. The importance of these requirements becomes evident if we consider the theoretical modeling. If the interface model is chosen too small, then the excess charges on the electrode are not fuUy considered and/or, within the interface only part of the total potential drop is included, resulting in an electrostatic potential value at X = X2 that differs from the requited bulk electrolyte value < s-However, if we constrain such a model to reproduce the electrostatic potential... 

Halley JW, ScheUing P, Duan Y. 2000. Simulation methods for chemically specific modeling of electrochemical interfaces. Electrochim Acta 46 239-245. 

Villegas I, Weaver MJ. 1996. Infrared spectroscopy of model electrochemical interfaces in ultra-high vacuum Evidence for coupled cation-anion hydration in the Pt(lll)/K, Cl system. J Phys Chem 100 19502-19511. 

This chapter is devoted to the behavior of double layers and inclusion-free membranes. Section II treats two simple models, the elastic dimer and the elastic capacitor. They help to demonstrate the origin of electroelastic instabilities. Section III considers electrochemical interfaces. We discuss theoretical predictions of negative capacitance and how they may be related to reality. For this purpose we introduce three sorts of electrical control and show that this anomaly is most likely to arise in models which assume that the charge density on the electrode is uniform and can be controlled. This real applications only the total charge or the applied voltage can be fixed. We then show that predictions of C < 0 under a-control may indicate that in reality the symmetry breaks. Such interfaces undergo a transition to a nonuniform state the initial uniformity assumption is erroneous. Most... 

For the metal in the electrochemical interface, one requires a model for the interaction between metal and electrolyte species. Most important in such a model are the terms which are responsible for establishing the metal-electrolyte distance, so that this distance can be calculated as a function of surface charge density. The most important such term is the repulsive pseudopotential interaction of metal electrons with the cores of solvent species, which affects the distribution of these electrons and how this distribution reacts to charging, as well as the metal-electrolyte distance. Although most calculations have used parameterized simple functional forms for this term, it can now be calculated correctly ab initio. 

The second stage of modeling is the introduction of solvated ionic species into the model double layer. Coadsorption of HF and water yields adsorbed HgO ions the solvation stoichiometries of ions in the first monolayer and in subsequent layers are determined. The third stage of modeling is establishment of potential control in UHV. Hydrogen coadsorption is used to deflect the effective potential of the water monolayer below the potential of zero charge. The unique ways in which UHV models can contribute to an improved molecular-scale understanding of electrochemical interfaces are discussed. 

With the work still in the infant stages, there is no accepted method of modeling electrode reactions with DFT. A few recent studies have attempted to include both electrostatic and solvent effects in DFT models of electrochemical reactions using different approaches.84-89 However, the lack of surface techniques available for in situ study of electrochemical cells hinders validation of models by experimental data. Results can only offer qualitative information at best. Despite the challenges, DFT modeling of electrochemical reactions offers promise as a method for providing insights into the electrochemical interface in cases where experiments are difficult. 

The approach to the mathematical definition of the interface model is very simple. For every layer in the interface, the charge is defined once as a function of chemical parameters and once as a function of electrostatic parameters. The functions for charge are set equal to each other and solved for the unknown electrochemical potentials. Mathematical techniques for solving the equations have been worked out and described in detail (9). 

One of the important electrochemical interfaces is that between water and liquid mercury. The potential energy functions for modeling liquid metals are, in general, more complex than those suitable for modeling sohds or simple molecular liquids, because the electronic structure of the metal plays an important role in the determination of its structure." However, based on the X-ray structure of liquid mercury, which shows a similarity with the solid a-mercury structure, Heinzinger and co-workers presented a water/Hg potential that is similar in form to the water/Pt potential described earlier. This potential was based on quantum mechanical calculations of the adsorption of a water molecule on a cluster of mercury atoms. ... 

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 electrochemical interface is the site where electrode reactions take place. At equilibrium, differences of chemical potential in the electrode and electrolyte bring about differences in electrical potential across the interface. The structure and models of such an electrochemical interface will be discussed in Sect. 2.3. 

Protein function at solid-liquid interfaces holds a structural and a dynamic perspective [31]. The structural perspective addresses macroscopic adsorption, molecular interactions between the protein and the surface, collective interactions between the individual adsorbed protein molecules, and changes in the conformational and hydration states of the protein molecules induced by these physical interactions. Interactions caused by protein adsorption are mostly non-covalent but strong enough to cause drastic functional transformations. All these features are, moreover, affected by the double layer and the electrode potential at electrochemical interfaces. Factors that determine protein adsorption patterns have been discussed in detail recently, both in the broad context of solute proteins at solid surfaces [31], and in specific contexts of interfacial metalloprotein electrochemistry [34]. Some important elements that can also be modelled in suitable detail would be ... 

To model the water-splitting reaction and any electrochemical reaction, it is necessary to include the potential or bias. As long as only reaction energies are considered, it is possible to avoid explicit modeling of the electrochemical interface. With this approach, barriers for charge transfer reactions cannot be treated. In this section, the reference for the potential will be introduced. 

The complications and sources of error associated with the polarization resistance method are more readily explained and understood after introducing electrical equivalent circuit parameters to represent and simulate the corroding electrochemical interface (1,16-20). The impedance method is a straightforward approach for analyzing such a circuit. The electrochemical impedance method is conducted in the frequency domain. However, insight is provided into complications with time domain methods given the duality of frequency and time domain phenomena. The simplest form of such a model is shown in Fig. 3a. The three parameters (Rp, Rs, and C d,) that approximate a corroding electrochemical inter-... 

Figure 3 Electrical equivalent circuit model commonly used to represent an electrochemical interface undergoing corrosion. Rp is the polarization resistance, Cd] is the double layer capacitance, Rct is the charge transfer resistance in the absence of mass transport and reaction intermediates, RD is the diffusional resistance, and Rs is the solution resistance, (a) Rp = Rct when there are no mass transport limitations and electrochemical reactions involve no absorbed intermediates and nearly instantaneous charge transfer control prevails, (b) Rp = Rd + Rct in the case of mass transport limitations.

The simplest and most common model of an electrochemical interface is a Randles circuit. The equivalent circuit and Nyquist and Bode plots for a Randles cell are all shown in Figure 2.39. The circuit includes an electrolyte resistance (sometimes solution resistance), a double-layer capacitance, and a charge-transfer resistance. As seen in Figure 2.39a, Rct is the charge-transfer resistance of the electrode process, Cdl is the capacitance of the double layer, and Rd is the resistance of the electrolyte. The double-layer capacitance is in parallel with the charge-transfer resistance. 

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