Electrode reaction rate constant conventional

Additional information on the rates of these (and other) coupled chemical reactions can be achieved by changing the scan rate (i.e., adjusting the experimental time scale). In particular, the scan rate controls the tune spent between the switching potential and the peak potential (during which the chemical reaction occurs). Hence, as illustrated in Figure 2-6, i is the ratio of the rate constant (of the chemical step) to die scan rate, which controls the peak ratio. Most useful information is obtained when the reaction time lies within the experimental tune scale. For scan rates between 0.02 and 200 V s-1 (common with conventional electrodes), the accessible... 

The combination of photocurrent measurements with photoinduced microwave conductivity measurements yields, as we have seen [Eqs. (11), (12), and (13)], the interfacial rate constants for minority carrier reactions (kn sr) as well as the surface concentration of photoinduced minority carriers (Aps) (and a series of solid-state parameters of the electrode material). Since light intensity modulation spectroscopy measurements give information on kinetic constants of electrode processes, a combination of this technique with light intensity-modulated microwave measurements should lead to information on kinetic mechanisms, especially very fast ones, which would not be accessible with conventional electrochemical techniques owing to RC restraints. Also, more specific kinetic information may become accessible for example, a distinction between different recombination processes. Potential-modulation MC techniques may, in parallel with potential-modulation electrochemical impedance measurements, provide more detailed information relevant for the interpretation and measurement of interfacial capacitance (see later discus-... 

Early studies of ET dynamics at externally biased interfaces were based on conventional cyclic voltammetry employing four-electrode potentiostats [62,67 70,79]. The formal pseudo-first-order electron-transfer rate constants [ket(cms )] were measured on the basis of the Nicholson method [99] and convolution potential sweep voltammetry [79,100] in the presence of an excess of one of the reactant species. The constant composition approximation allows expression of the ET rate constant with the same units as in heterogeneous reaction on solid electrodes. However, any comparison with the expression described in Section II.B requires the transformation to bimolecular units, i.e., M cms . Values of of the order of 1-2 x lO cms (0.05 to O.IM cms ) were reported for Fe(CN)g in the aqueous phase and the redox species Lu(PC)2, Sn(PC)2, TCNQ, and RuTPP(Py)2 in DCE [62,70]. Despite the fact that large potential perturbations across the interface introduce interferences in kinetic analysis [101], these early estimations allowed some preliminary comparisons to established ET models in heterogeneous media. 

The quantity kconv = exp (anFE0,/RT) is the value of the rate constant of the electrode reaction at the potential of the standard reference electrode and will be termed the conventional rate constant of the electrode reaction. It can be found, for example, by extrapolation of the dependence (5.2.36) to E = 0, as... 

The overall charge number of the electrode reaction is then n, while the exponential term in the rate constant of the electrode reaction has a form corresponding to a one-electron reaction. If the value of E0f is not known, then the conventional rate constant of the electrode reaction is introduced, kcony- kT exp (ffiFE /RT), so that Eq. (5.2.48) can be expressed in the form... 

Should any iron(II) reach the anode, it also would be oxidized and thus not require the chemical reaction of Eq. (4.13) to bring about oxidation, but this would not in any way cause an error in the titration. This method is equivalent to the constant-rate addition of titrants from a burette. However, in place of a burette the titrant is electrochemically generated in the solution at a constant rate that is directly proportional to the constant current. For accurate results to be obtained the electrode reaction must occur with 100% current efficiency (i.e., without any side reactions that involve solvent or other materials that would not be effective in the secondary reaction). In the method of coulometric titrations the material that chemically reacts with the sample system is referred to as an electrochemical intermediate [the cerium(III)/cerium(IV) couple is the electrochemical intermediate for the titration of iron(II)]. Because one faraday of electrolysis current is equivalent to one gram-equivalent (g-equiv) of titrant, the coulometric titration method is extremely sensitive relative to conventional titration procedures. This becomes obvious when it is recognized that there are 96,485 coulombs (C) per faraday. Thus, 1 mA of current flowing for 1 second represents approximately 10-8 g-equiv of titrant. 

Relatively little attention has been given in the literature to the electronic transmission coefficient for electrochemical reactions. On the basis of the conventional collisional treatment of the pre-exponential factor for outer-sphere reactions, Kel has commonly been assumed to equal unity, i.e. adiabatic reaction pathways are followed. Nevertheless, as noted above, the dependence of xei upon the spatial position of the transition state is of key significance in the "encounter pre-equilibrium treatment embodied in eqns. (13) and (14). Thus, the manner in which Kel varies with the reactant-electrode separation for outer-sphere reactions will influence the integral of reaction sites that effectively contribute to the overall measured rate constant and hence the effective electron-tunneling distance, Srx, in eqn. (14). 

An obvious application of high sweep rates is the determination of E° values for A/B couples where B undergoes a chemical reaction so fast that it cannot to be outrun by the sweep rates applicable to conventional electrodes [94,100,189]. Once E is known, the rate constant may be determined from LSV relations of the type already given, as in Eqs. (45)-(46). 

The influence of varying the electrode material upon proton electroreduction has been the subject of extensive study . This reaction can be regarded as inner-sphere in that it often involves a rate-limiting, proton-transfer step to form an adsorbed hydrogen atom . Although superficially different, the conventional treatment of substrate effects upon such reactions is similar to that presented here. Thus the marked increase in the rate constants seen for Hj evolution as the metal-hydrogen atom bond energy... 

Conventional cyclic voltammetry s greatest utility is in the diagnosis of electrode reactions involving chemical complications, and the ac variant is also useful in meeting this kind of problem. The ratio /p,r//p,f is a sensitive indicator of product stability, just as the dc voltammetric ratio l/p,r/ p,f I is. However, the ac ratio is easier to measure precisely, and it lends itself well to quantitative evaluation of homogeneous rate constants. 

In above two equations, rrij is an integer constant which takes values of -1, +1, and 0 for species R(z-i) Os and inert electrolyte species respectively if the reduction current is considered positive p refers to the thickness of the compact EDL Fq refers to the radius of electrode y is the ratio between the standard rate constant of ET reaction and the mass transport coefficient of the electroactive species. It can be seen that the current density, which is given in a dimensionless form through normalization with the limiting diffusion current density (i, and the electrostatic potential distribution appear simultaneously in the two equations. Equation 2.2 could be approximated to the PB equation at low current density, while Equation 2.3 would reduce to Eq. 2.4, which is the diffusion-corrected Butler-Volmer equation and has been used to perform voltammetric analysis in conventional electrochemistry, as exp(-Zj/ rcp/F)=1, that is, electrostatic potentials in CDL are close to zero. These conditions are approximately satisfied in large electrode systems, suggesting that the voltammetric behaviour and the EDL structure can be treated separately at large electrode interface ... 

Voltammetric simulations for ET reactions of various fe and X at electrodes of various sizes have shown that, for ET reactions with fe near 0.1 cm/s, the BV theory could predict voltammetric responses visibly deviating from that expected by the MHC model as the electrode radii are smaller than 50 mn, while this occurs as Tq approaches 10 nm for ET reactions with fe around 1.0 cm/s. According to the half-wave-potential difference in the polarization curves predicted by the BV and MHC models, the BV-based voltammetric analysis would give standard rate constants of ca. 0.6 and 0.5fe , respectively, for a reaction of 0.1 cm/s kP and 100 kJ/mol X at electrodes with radii of 20 and 10 nm. For the ET reaction with k° of 1.0 cm/s, apparent standard rate constants of 0.8fe and 0.6fe will be obtained by BV-based analysis at an electrode with radii of 10 and 5 nm. Considering that the EDL effect would result in enhanced apparent ET kinetics for cation reduction or anion oxidation (Table 2.1), the measured polarization curves at nanoelectrodes would be closer to that predicted by the BV formalism without including the EDL effect. For anion reduction or cation oxidation, the EDL effect and the MHC formalism both predict inhibited ET kinetics as compared with the conventional BV model combined with the diffusion-based MT theory. In this case, the measured polarization would significantly deviate from the prediction of conventional voltammetric theory. Therefore, BV-based voltammetric analysis would result in apparent rate constants that are significantly lower than the real fc . 

It is convenient at this juncture to introduce a concept that, in electro analytical chemistry, sometimes is referred to as the reaction order approach. Consider first the half-life-time, t1/2> which in conventional homogeneous kinetics refers to the time for the conversion of half of the substrate into product(s). From basic kinetics, it is well known that t /2 is independent of the substrate concentration for a reaction that follows a first-order rate law and that 1/t j2 is proportional to the initial concentration of the substrate for a reaction that follows a second-order rate law. Similarly, in electro analytical chemistry it is convenient to introduce a parameter that reflects a certain constant conversion of the primary electrode intermediate. In DPSCA, it is customary to use ti/2 (or to.s), which is the value of (f required to keep the value of Ri equal to 0.5. The reaction orders (see Equation 6.30) are then given by Equations 6.35 and 6.36, where Ra/b = a + b, and Rx = x (in reversal techniques such as DPSCA, in which O and R are in equilibrium at the electrode surface, it is not possible to separate the... 

As in all potentiostatic techniques, the double layer charging is a parallel process to the faradaic reaction that can substantially attenuate the photocurrent signal at short-time scale (see Section 5.3)" . This element introduces another important difference between fully spectroscopic and electrochemical techniques. Commercially available optical instrumentation can currently deliver time resolution of 50 fs or less for conventional techniques such as transient absorption. On the other hand, the resistance between the two reference electrodes commonly employed in electrochemical measurements at the liquid/liquid interfaces and the interfacial double layer capacitance provide time constants of the order of hundreds of microseconds. Consequently, direct information on the rate of heterogeneous electron injection from/to the excited state is not accessible from photocurrent measurements. These techniques do allow sensitive measurements of the ratio between electron injection and decay of the excited state under pho-tostationary conditions. Other approaches such as photopotential measurements, i.e. relative changes in the Fermi levels in both phases, can provide kinetic information in the nanosecond regime. 

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