Electrode-solution interface model

Measurement of the differential capacitance C = d /dE of the electrode/solution interface as a function of the electrode potential E results in a curve representing the influence of E on the value of C. The curves show an absolute minimum at E indicating a maximum in the effective thickness of the double layer as assumed in the simple model of a condenser [39Fru]. C is related to the electrocapillary curve and the surface tension according to C = d y/dE. Certain conditions have to be met in order to allow the measured capacity of the electrochemical double to be identified with the differential capacity (see [69Per]). In dilute electrolyte solutions this is generally the case. 

The question arises of the extent to which the build-up of an electrode potential may significantly alter the original concentration of the solution in which the electrode is placed. Let us take the example of a silver electrode. Once the electrode has been immersed in an Ag+ solution, part of the Ag+ ions will be discharged by precipitation of the corresponding amount of Ag and to an extent such that the Nemst potential has been reached. In fact, a double layer at the electrode/solution interface has been formed whose structure cannot be as precisely described as has appeared from the model proposed by... 

Similar to those observed with the cysteine-modified electrode in Cu, Zn-SOD solution [98], CVs obtained at the MPA-modified Au electrode in phosphate buffer containing Fe-SOD or Mn-SOD at different potential scan rates (v) clearly show that the peak currents obtained for each SOD are linear with v (not v 1/2) over the potential scan range from 10 to 1000 mVs-1. This observation reveals that the electron transfer of the SODs is a surface-confined process and not a diffusion-controlled one. The previously observed cysteine-promoted surface-confined electron transfer process of Cu, Zn-SOD has been primarily elucidated based on the formation of a cysteine-bridged SOD-electrode complex oriented at an electrode-solution interface, which is expected to sufficiently facilitate a direct electron transfer between the metal active site in SOD and Au electrodes. Such a model appears to be also suitable for the SODs (i.e. Cu, Zn-SOD, Fe-SOD, and Mn-SOD) with MPA promoter. The so-called... 

In addition to the universal concern for catalytic selectivity, the following reasons could be advanced to argue why an electrochemical scheme would be preferred over a thermal approach (i) There are experimental parameters (pH, solvent, electrolyte, potential) unique only to the electrode-solution interface which can be manipulated to dictate a certain reaction pathway, (ii) The presence of solvent and supporting electrolyte may sufficiently passivate the electrode surface to minimize catalytic fragmentation of starting materials. (iii) Catalyst poisons due to reagent decomposition may form less readily at ambient temperatures, (iv) The chemical behavior of surface intermediates formed in electrolytic solutions can be closely modelled after analogous well-characterized molecular or cluster complexes (1-8). (v)... 

Figure 2.5 Schematic representation of the Au/MPS/PAH-Os/solution interface modeled in Refs. [118-120] using the molecular theory for modified polyelectrolyte electrodes described in Section 2.5. The red arrows indicate the chemical equilibria considered by the theory. The redox polymer, PAH-Os (see Figure 2.4), is divided into the poly(allyl-amine) backbone (depicted as blue and light blue solid lines) and the pyridine-bipyridine osmium complexes. Each osmium complex is in redox equilibrium with the gold substrate and, dependingon its potential, can be in an oxidized Os(lll) (red spheres) or in a reduced Os(ll) (blue sphere) state. The allyl-amine units can be in a positively charged protonated state (plus signs on the polymer...

Fig. 2. Simplified schematic model of ionic distribution at the electrode—solution interface with (a) and without (b) specific anion adsorption and the corresponding potential distributions at the interface (c) and (d).

Figure 2.12 Simple capacitor model of electrode-solution interface as a charged double layer (original Helmholtz model). Negatively charged surface. Positively charged ions are attracted to the surface, forming an electrically neutral interphase.

The electrode/solution interface, in the simpler case (no passive layer on the electrode surface) can be modeled using the following equivalent circuit (Figure 1.18), where Rel stands for the electrolyte resistance, CDL for the double layer capacitance, and ZF the faradic impedance. 

The only models that exist for double layer structure in ionic liquids suggest a Helmholz layer at the electrode/solution interface [103, 104], If the reduction potential is below the point of zero charge (pzc) then this would result in a layer of cations approximately 5 A thick across which most of the potential would be dropped, making it difficult to reduce an anionic metal complex. Hence, the double layer models must be incorrect. 

S. Trasatti. The Electrode Potential, in Comprehensive Treatise of Electrochemistry, Vol. 1, J. O M. Bockris, B.E. Conway and E. Veager. Eds. Plenum (1980), chapter 2 B.E. Conway, The State of Water and Hydrated Ions at Interfaces, Adv. Colloid Interface Sci. 8 (1977) 91 W.R. Fawcett, Molecular Models for Solvent Structure at Polarizable Interfaces. Isr. J. Chem. 18 (1979) 3 M.A. Habib, Solvent Dipoles at the Electrode-Solution Interface. in Modem Aspects of Electrochemistry, Vol. 12, J. O M. Bockris and B.E. Conway. Eds. Plenum (1977) 131 S. Trasatti, Solvent Adsorption and Double Layer Potential Drop at Electrodes, in Modem Aspects of Electrochemistry, B.E. Conway and J. O M. Bockris, Eds. Vol. 13 Plenum (1979) chapter 2 J. O M. Bockris. K-T. Jeng, Water Structure at Interfaces The Present Situation. Adv. Colloid Interface Set 33 (1990) 1. 

The electrical behavior of the electrode-solution interface and the processes which can take place at it, due to an electrochemical reaction, can be treated in terms of an electrical equivalent circuit. Such an equivalent circuit must represent the time-dependent behavior of the mechanism of the reaction but usually it is possible that more than one equivalent circuit can model the reaction behavior. The simplest equivalent circuit is (Cl) for a charge-transfer process not involving the production of an adsorbed intermediate, for example, for the case of an ionic redox reaction such as Fe(CN)e3- +e-- Fe(CN)6 - ... 

M Although our model is oversimplified, it provides a reasonably accurate picture of the processes occurring at the electrode/solution interface. 

The development of microscopic models of the double layer began over 100 years ago with work of Helmholtz [20]. He assumed that the charge on the polarizable metal electrode is exactly compensated by a layer of ionic charge in solution located at a constant distance from the geometrical electrode solution interface. The separation distance was assumed to have molecular dimensions. This simple model which gave rise to the term double layer is the equivalent of a parallel-plate capacitor with a capacitance given by... 

Fig. 10.23 Models of the solvent monolayer at the electrode solution interface according to (a) the two-state model with spherical solvent dipoles in either the up (f) or down orientations ( ) (b) the three-state model in which a third state with solvent dipoles parallel ( ) to the interface has been added (c) the cluster model with clusters in the up (/ / ) and down ( / ) orientations, and single molecules up (t) and down (f,).

This research evaluates the measurement of the "master" Eh of solutions in terms of heterogeneous electron-transfer kinetics between aqueous species and the surface of a polished platinum electrode. A preliminary model is proposed in which the electrode/solution interface is assumed to behave as a fixed-value capacitor, and the rate of equilibration depends on the net current at the interface. Heterogeneous kinetics at bright platinum in 0.1 m KCl were measured for the redox couples Fe(III)/Fe(II), Fe(CN)53-/Fe(CN)6, Se(VI)/Se(IV), and As(V)/As(Iin. Of the couples considered, only Fe(III)/Fe(II) at pH 3 and Fe(CN)g37Fe(CN)g at pH 6.0 were capable of imposing a Nemstian potential on the platinum electrode. 

This paper attempts to model and define the conditions under which platinum Eh measurements are likely to reflect the true electrical potential of aqueous solutions. The double layer at the surface of the electrode is modeled as a fixed capacitor (C jj), and the rate at which an electrode equilibrates with a solution (i.e. the rate at which C jj is charged) is assumed to be proportional to the electrical current at this interface. The current across the electrode/solution interface can be calculated from classical electrochemical theory, in which the current is linearly proportional to the concentration and electron-transfer rate constant of the aqueous species, and is exponentially proportional to the potential across the interface. 

Fig. 1. Three-phase model of electrode-solution interface.

With modern computerized frequency-analysis instrumentation and software, it is possible to acquire impedance data on cells and extract the values for all components of the circuit models of Figure 2.>7, This type of analysis, w hich is called electrochemical impedance spectroscopy, reveals the nature t>f the faradaic processes and often aids in the investigation of the mechanisms of electron-transfer reactions. In the section that follows, we explore the processes at the electrode-solution interface that give rise to the faradaic impedance. 

In this equation )/m s is the diffusion coefficient of the analyte, c/mol the analyte concentration, A/m the electrode area, and S/m the thickness of the electrical double layer. We shall take this up in greater detail (1.5.2) but it is sufficient here that the significance of 6 alters for each model of the electrode/solution interface. Having considered the electron transfer and mass transport process separately, let us now consider them together. 

The basic optical theory of reflection for a soHd surface covered with a thin film has already been well established. We do not intend to review it here in full detail. Instead, readers can refer to the textbook of optics [12] or review articles on UV-visible reflection spectroscopy at electrode surfaces [2, 6-8]. It must be noted that for some electrode/solution interfaces it is stiU an extremely difficult task to establish the modeling of the interface through the use of classical light reflection theory, as described in the later sections. 

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