Standard rate constant surface

Sodium-silicate glass, 151 Sol-gel films, 120, 173 Solid electrodes, 110 Solid state devices, 160 Solvents, 102 Speciation, 84 Spectroelectrochenristry, 40 Spherical electrode, 6, 8, 9, 61 Square-wave voltammetry, 72, 92 Staircase voltammetry, 74 Standard potential, 3 Standard rate constant, 12, 18 Stripping analysis, 75, 79, 110 Supporting electrolyte, 102 Surface-active agents, 79... 

When the solution is not quite inert, ac techniques are widely used to investigate the capacitance and other surface properties of platinum electrodes as well as of various other electrodes. Their chief advantage is the possibility to apply them in the case of electrodes passing some faradaic current. It is shown in Section 12.5.1 that in this case the electrode s capacitance can be determined by extrapolating results obtained at different ac frequencies to the region of high frequencies. This extrapolation can be used for electrodes where electrode reactions occur that have standard rate constants, of up to 1 cm/s. 

Here, i is the faradaic current, n is the number of electrons transferred per molecule, F is the Faraday constant, A is the electrode surface area, k is the rate constant, and Cr is the bulk concentration of the reactant in units of mol cm-3. In general, the rate constant depends on the applied potential, and an important parameter is ke, the standard rate constant (more typically designated as k°), which is the forward rate constant when the applied potential equals the formal potential. Since there is zero driving force at the formal potential, the standard rate constant is analogous to the self-exchange rate constant of a homogeneous electron-transfer reaction. 

Here sur is the surface standard rate constant in units of s. By substitution (2.93) and (2.94) into (2.95), one obtains an integral equation, which is a general solution for a surface electrode reaction ... 

This equation is of particular importance since it enables estimation of both the interaction product a and the standard rate constant sur, provided the relative surface coverage is known. For this, the quasireversible maximum is to be determined by varying the frequency for various values of the surface coverage 0. Plotting ln(/)... 

The theory for the reaction of an adsorbed redox couple (2.146) has been exemplified by experiments with methylene blue [92], and azobenzene [79], Both redox couples, methylene blue/leucomethylene, and azobenzene/hydrazobenzene adsorb strongly on the mercury electrode surface. The reduction of methlylene blue involves a very fast two-step redox reaction with a standard rate constants of 3000 s and 6000 s for the first and second step, respectively. Thus, for / < 50 Hz, the kinetic parameter for the first electron transfer is log(m) > 1.8, implying that the reaction appears reversible. Therefore, regardless of the adsorptive accumulation, the net response of methylene blue is a small peak, the peak current of which depends linearly on /J. Increasing the frequency above 50 Hz, the electrochemical... 

Here, cp = (E —E ) is a dimensionless potential and rs = 1 cm is an auxiliary constant. Recall that in units of cm s is heterogeneous standard rate constant typical for all electrode processes of dissolved redox couples (Sect. 2.2 to 2.4), whereas the standard rate constant ur in units of s is typical for surface electrode processes (Sect. 2.5). This results from the inherent nature of reaction (2.204) in which the reactant HgL(g) is present only immobilized on the electrode surface, whereas the product is dissolved in the solution. For these reasons the cathodic stripping reaction (2.204) is considered as an intermediate form between the electrode reaction of a dissolved redox couple and the genuine surface electrode reaction [135]. The same holds true for the cathodic stripping reaction of a second order (2.205). Using the standard rate constant in units of cms , the kinetic equation for reaction (2.205) has the following form ... 

Figure 3.12 shows the forward and backward components of square-wave voltam-mograms of mercury(ll)-ferron complex adsorbed on the surface of static mercuiy drop electrode [208]. The ratio of the current and the corresponding SW frequency is reported. At pH 3.5 the electrode reaction involves the direct transfer of two electrons, whereas at pH 5.8 only one electron is exchanged. The simulated responses are presented by symbols. The best fit was achieved by using the following standard rate constants and the transfer coefficients k. = 1550 50 s and a = 0.5 (at pH 3.5), and = 1900 400s and a = 0.55 (at pH 5.8) [208]. 

Cd(II) reduction at the mercury electrode from aqueous 1 M NaCl04 in the presence of sucrose was described [49] by CEE mechanism. An attempt was made to correlate the individual standard rate constants that became lower with increasing concentration of sucrose, with (1) the surface coverage by sucrose, and (2) the viscosity of the solution layer adjacent to the electrode surface. 

Similar SECM experiments can be performed using a simple (unassisted) IT process [41]. In this case, both the top and the bottom phases contain the same ion at equilibrium. The micropipet tip is used to deplete concentration of this common ion in the top solvent near the ITIES. The depletion results in the IT across the ITIES, which produces positive feedback. Any solid surface (or a liquid phase containing no specific ion) acts as an insulator in this experiment. The mass transfer rate for IT measurements by SECM is similar to that for heterogeneous ET measurements, and the standard rate constants in excess of 1 cms-1 should be measurable. 

The measurement of ket for single electron-transfer reactions is of particular fundamental interest since it provides direct information on the energetics of the elementary electron-transfer step (Sect. 3.1). As for solution reactants, standard rate constants, k t, can be defined as those measured at the standard potential, E, for the adsorbed redox couple. The free energy of activation, AG, at E°a is equal to the intrinsic barrier, AG t, since no correction for work terms is required [contrast eqn. (7) for solution reactants] [3]. Similarly, activation parameters for surface-attached reactants are related directly to the enthalpic and entropic barriers for the elementary electron-transfer step [3],... 

Fig. 15. The dependence of the logarithm of the standard rate constant of the Eu(III)/Eu(II) system on acetonitrile concentration in its mixtures with water. The upper panel shows the surface coverage and the change in the free energy of transfer for the system studied. AAGf = AG gudu)...

Fig. 16. Variation of the standard rate constant of the V(III)/V(II) system (upper panel) and the absorption spectra of V(III) (lower panel) with mixed solvent composition in terms the surface coverage of the electrode by the organic component. Solvent system curve 1, H2O-DMF curve 2, HjO-DMPU curve 3, HjO-HMPA curve 4, H2O-AN.

Studies on the electrochemical behavior of ferrocene encapsulated in the hemi-carcerands 61 and 62, indicated that encapsulation induces substantial changes in the oxidation behavior of the ferrocene subunit [98]. In particular, encapsulated ferrocene exhibits a positive shift of the oxidation potential of c. 120 mV, probably because of the poor solvation of ferrocenium inside the apolar guest cavity. Lower apparent standard rate constants were found for the heterogeneous electron transfer reactions, compared to those found in the uncomplexed ferrocene under identical experimental conditions. This effect may be due to two main contributions (i) the increased effective molecular mass of the electroactive species and (ii) the increased distance of maximum approach of the redox active center to the electrode surface. 

One of the most important phenomenological aspects of electrocatalysis is the dependence of standard rate constants or exchange current densities, Iq (see Section III), for the reaction concerned on the properties and chemical identity of the electrode metal (Fig. 15) and/or the state and orientation of its surface. In fact, this is the basis of the good deffnition of electrocatalysis proposed by Busing and Kauzmann (12). 

In this equation, and represent the surface concentrations of the oxidized and reduced forms of the electroactive species, respectively k° is the standard rate constant for the heterogeneous electron transfer process at the standard potential (cm/sec) and oc is the symmetry factor, a parameter characterizing the symmetry of the energy barrier that has to be surpassed during charge transfer. In Equation (1.2), E represents the applied potential and E° is the formal electrode potential, usually close to the standard electrode potential. The difference E-E° represents the overvoltage, a measure of the extra energy imparted to the electrode beyond the equilibrium potential for the reaction. Note that the Butler-Volmer equation reduces to the Nernst equation when the current is equal to zero (i.e., under equilibrium conditions) and when the reaction is very fast (i.e., when k° tends to approach oo). The latter is the condition of reversibility (Oldham and Myland, 1994 Rolison, 1995). 

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