Stationary current-voltage

Figure 24. (a) Experimental cyclic voltammogram of formic acid oxidation on Pt (111) with external resistance430 1. Electrolyte 0.05 M HCOOH, lO M HCIO4. Scan rate 5 mV/s. (After Strasser et al. (b) Calculated cyclic voltammogram and stationary current-voltage curve for the formic acid model [Eq. (15)]. A smaller trppjggjjWas chosen than the one used in Fig. 22(a). The anodic and cathodic scans are indicated by arrows. The dashed line shows the portion of the stationary state curve that corresponds to unstable steady states. (After Strasser et al. with permission of the authors.)... 

The bubble growth on an electrode can be followed by considering the mean stationary current—voltage characteristics obtained by measuring the mean... 

An interesting consequence of these calculations is that the normalised mean stationary current—voltage characteristics are similar for different electrodes and electrolytes. An example is shown in Fig. 3.19 where the normalised mean current—voltage characteristics for a sodium hydroxide solution with different concentrations is depicted. 

We start from the stationary current-voltage curve (6.10.2) for a solution that contains one oxidizable electroactive species (so that i = 0), which we write in dimensionless form as... 

In its semi-differentiation mode, the macro instead converts a stationary current-voltage curve into the corresponding linear sweep or cyclic voltammogram. 

Fig. 7.18 Stationary current voltage characteristics for the symmetrical cell Pt, 02 ceria Pt,02 (ceria is CaO-do-ped) [579]. The transfer reaction determines the overall kinetics and makes for a markedly nonlinear behaviour. The fitting reveals Sz = az = 1. In the model z=2 and the symmetry factor 1/2. From Ref. [579].

The proposed model for the so-called sodium-potassium pump should be regarded as a first tentative attempt to stimulate the well-informed specialists in that field to investigate the details, i.e., the exact form of the sodium and potassium current-voltage curves at the inner and outer membrane surfaces to demonstrate the excitability (e.g. N, S or Z shaped) connected with changes in the conductance and ion fluxes with this model. To date, the latter is explained by the theory of Hodgkin and Huxley U1) which does not take into account the possibility of solid-state conduction and the fact that a fraction of Na+ in nerves is complexed as indicated by NMR-studies 124). As shown by Iljuschenko and Mirkin 106), the stationary-state approach also considers electron transfer reactions at semiconductors like those of ionselective membranes. It is hoped that this article may facilitate the translation of concepts from the domain of electrodes in corrosion research to membrane research. 

The rotating disc electrode is constructed from a solid material, usually glassy carbon, platinum or gold. It is rotated at constant speed to maintain the hydrodynamic characteristics of the electrode-solution interface. The counter electrode and reference electrode are both stationary. A slow linear potential sweep is applied and the current response registered. Both oxidation and reduction processes can be examined. The curve of current response versus electrode potential is equivalent to a polarographic wave. The plateau current is proportional to substrate concentration and also depends on the rotation speed, which governs the substrate mass transport coefficient. The current-voltage response for a reversible process follows Equation 1.17. For an irreversible process this follows Equation 1.18 where the mass transfer coefficient is proportional to the square root of the disc rotation speed. 

It is further important to note that all the current/voltage characteristics depicted in Fig. 6 are unchanged by the presence of liquid fuels such as methanol, formaldehyde, formic acid, or hydrazine. The phthalocyanine electrode remains completely inert toward such substances. For this reason, no mixed potential can be formed at a phthalocyanine electrode, as for example can occur at a platinum electrode, when it is used as cathode in a methanol cell containing sulfuric acid. This is shown by a comparison (see Fig. 7) of the stationary characteristics of the platinum alloy we found to be the most active in the presence of methanol, namely a Raney ruthenium—rhodium electrode, with an iron phthalocyanine electrode, both measured in 4.5 N H2SO4+2M CH3OH. 

Stirred-solution voltammetry utilizes current-voltage relationships that are obtained at a stationary electrode immersed in a stirred solution. In order to understand this aspect of electrochemistry, it is extremely useful to consider a typical current-voltage curve (voltammogram) in terms of the concept of concentration-distance profiles presented in the preceding section. The discussion will consider the potential, rather than the current, as the controlled variable. 

Using the faradaic current derived from a redox reaction at an electrode a versatile chemical analytical method can be established. Applying a distinct potentiostatically controlled voltage between a working electrode and the electrolyte, with the redox species electrochemically converted only at the electrodes, results in a stationary current following Eq. 3. In this case, a diffusion controlled measurement of redox species can be obtained. 

Originally, polarography was defined as a method making use of current-voltage curves obtained in the electrolysis at a dropping mercury electrode of the solutions to be analyzed. Later, the application of solid electrodes [8] which may be stationary, rotated or vibrated was introduced. Polarography with solid electrodes is often called voltammetry. 

Following the idea of Yu. Volfkovich, a model of stationary water flows in the membrane with account of porous structure-related aspects and inhomogeneous water distribution was developed [16,83]. This model will be presented in some detail below. Its implications on water-content profiles and current-voltage performance under fuel cell operation conditions will be compared to the effective diffusion models. 

Upon specification of the functions w(r), n(w), ae (w) for a specific PEM sample, the given set of equations provides analytical or numerical solutions for stationary water-content profiles and current-voltage performance. Analytical expressions, which help to rationalize the relevant asymptotic cases (i.e., nonohmic corrections at low current densities, asymptotic behavior near /pc), have been studied in detail [16]. 

By combining these relations, one gets the normalised mean stationary current characteristics for terminal voltages lower than the critical voltage (i.e. U < 1) ... 

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