Reaction rates, heterogeneous electron transfer

We are currently carrying out further investigations with neutral ferrocene derivatives in an attempt to resolve the apparent disconnection between the effects of CB7 encapsulation on homogenous and heterogeneous electron transfer reactions rates. 

In a direct electrolysis, the electron is exchanged between the electrode and the substrate, and the rate of the reaction depends on the electrode potential and the rate constant of the heterogeneous electron-transfer reaction. In an indirect electrolysis, the electron is primarily exchanged with a substance (a mediator) that exchanges the electron with the substrate in a chemical reaction, and the rate does not depend on the ability of the substrate to exchange an electron with the electrode. 

The rate coefficient for a heterogeneous electron transfer reaction at an electrode can be written, according to the absolute rate theory [54], as... 

One of the simplest electrode reactions is the EC mechanism (also called a following chemical reaction) in which the electrogenerated species (R) rearranges or reacts with some other solution component (Z) at a rate characterized by the rate constant k. The EC mechanism is summarized by the following reaction sequence, in which the labels E and C identify the heterogeneous electron-transfer reaction (electrode reaction) and the subsequent homogeneous solution reaction (chemical reaction), respectively ... 

SEV is an effective means of probing homogeneous chemical reactions that are coupled to electrode reactions, especially when it is extended to cyclic voltammetry as described in the next section. Considerable information can be obtained from the dependence of ip and Ep on the rate of potential scan. Figure 3.20 illustrates the behavior of ip and Ep with variation in scan rate for a reversible heterogeneous electron transfer reaction that is coupled to various types of homogeneous chemical reactions. The current function j/p is proportional to ip according to the equation... 

There has been keen interest in determination of activation parameters for electrode reactions. The enthalpy of activation for a heterogeneous electron transfer reaction, AH X, is the quantity usually sought [3,4]. It is determined by measuring the temperature dependence of the rate constant for electron transfer at the formal potential, that is, the standard heterogeneous electron transfer rate constant, ks. The activation enthalpy is then computed by Equation 16.7 ... 

Activation volume — As in case of homogeneous chemical reactions, also the rate of heterogeneous electron transfer reactions at electrode interfaces can depend on pressure. The activation volume AVZ involved in electrochemical reactions can be determined by studying the pressure dependence of the heterogeneous -> standard rate constant ks AVa = -RT j (p is the molar - gas constant, T absolute temperature, and P the pressure inside the electrochemical cell). If AI4 is smaller than zero, i.e., when the volume of the activated complex is smaller than the volume of the reactant molecule, an increase of pressure will enhance the reaction rate and the opposite holds true when A14 is larger than zero. Refs. [i] Swaddle TW, Tregloan PA (1999) Coord Chem Rev 187 255 [ii] Dolidze TD, Khoshtariya DE, Waldeck DH, Macyk J, van Eldik R (2003) JPhys Chem B 107 7172... 

The above analysis also shows that for almost all applications of fast CV employing V > 1 kV s , the quasi-reversible or irreversible nature of heterogeneous electron transfer reactions must be considered. In particular, this becomes important when fast CV is used in a kinetic analysis of fast homogeneous follow-up reactions. The extraction of the relevant rate constants is complicated by the mixed kinetic control of the electrode process and the chemical reaction. As a result, the number of parameters involved in the fitting procedures is increased considerably and with it the possibility of introducing errors. 

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. 

The Marcus Theory can also be applied for heterogeneous electron transfer reaction at electrode surfaces [24 and references therein]. The electronic coupling between the protein and the electrode can be varied using different self-assembled monolayers controlling the orientation of the redox active protein on the surface and the distance between the redox active site of the protein and the electrode. The driving force is related to the appHed potential and the redox potential of the protein. In many cases the rate of electron transfer across the protein-electrode interface is limited by conformational reorganization. This has focussed the efforts of many groups on tailored interaction between proteins and enzymes and electrode surfaces. 

When spectroelectrochemistry is used as a tool in reaction kinetics, it is important to know accurately the rate of generation of reactive intermediates, that is, the accurate potential of the working electrode. This requirement becomes a particular problem when an OTE is the preferred electrode because of the ohmic drop in the electrode itself and the nonuniform current distributions often encountered. For the OTTLEs in particular, the accurate modeling of the diffusion in the cell also leads to rather complicated mathematical equations [346]. The most profitable way of operation is therefore to use a potential-step procedure where the potential is stepped to a value at which the heterogeneous electron transfer reaction proceeds at the diffusion-controlled rate. In transmission spectroscopy the absorbance, AB(t), of the initial electrode product B, in the absence of chemical follow-up reactions, is given by Eq. (99) [347,348], where b is the extinction coefficient of B. 

The opportunity of obtaining direct electrochemistry of cytochrome c and other metalloproteins at various electrode materials such as modified gold and pyrolytic graphite has led to numerous reports of heterogeneous electron transfer rates and mechanisms between the protein and the electrode. In all the reports, Nicholson s method (37) was employed to calculate rate constants, which were typically within the range of 10" -10 cm sec with scan rates varying between 1 and 500 mV sec This method is based on a macroscopic model of the electrode surface that assumes that mass transport of redox-active species to and from the electrode occurs via linear diffusion to a planar disk electrode and that the entire surface is uniformly electroactive, i.e., the heterogeneous electron transfer reaction can take place at any area. 

In the study of chemical kinetics, one can often simplify the prediction and analysis of behavior by recognizing that a single step of a mechanism is much more sluggish than all the others, so that it controls the rate of the overall reaction. If the mechanism is an electrode process, this rate-determining step (RDS) can be a heterogeneous electron-transfer reaction. 

Irreversible Case. A heterogeneous electron transfer reaction can be represented as in Eq. (1). Assuming that all of the sample is initially present as O, the absorption signals of R may be monitored in the SPS/ CA experiment. If the magnitude of the potential applied to the system is sufficient to cause the forward reaction to proceed at a rate governed only by kf, the rate-dependent absorbance of R then is given by ... 

Changes in Atir associated with the generation of TCNQ during a potential step were also employed for monitoring the rate of the heterogeneous electron transfer reaction. Following the development previously pubUshed by Kakiuchi et al. [12], it follows that for short times after the potential step... 

Temperature effects on were examined to evaluate enthalpic and entropic parameters for the heterogeneous electron transfer reaction. The effect of temperature on the standard heterogeneous rate constant is considered to obey the following relationship ... 

In the simplest cases, it is possible to compare rates for homogeneous and heterogeneous electron-transfer reactions. According to the Marcus theory for homogeneous outer-sphere reactions [10],... 

Clegg AD, Rees NV, Klymenko OV, Coles BA, Compton RG (2004) Marcus theory of outer-sphere heterogeneous electron transfer reactions dependence of the standard electrochemical rate constant on the hydrodynamic radius from high precision measurements of the oxidation of anthracene and its derivatives in nonaqueous solvents using the high-speed channel electrode. J Am Chem Soc 126(19) 6185-6192... 

Note that many steps are involved in an EC reaction, such as the electron transfer reaction, transport of molecules from the bulk solution to the electrode surface and chemical reactions coupled to the electron transfer reaction. As with any multi step reaction, the rate of the overall reaction is generally determined by the rate of the slowest step (the rate-limiting step), and it is important to identify this step. In the analytical electrochemistry of dissolved species, the limiting step is typically the transport of molecules to the electrode surface through the solution. However, there are many instances where this is not the case and where the rate of the heterogeneous electron transfer reaction is important, for example in corrosion electrochemistry. 

Two heterogeneous electron transfer reactions across the RuO /water interface are involved in the overall reaction. A decrease in the particle potential results in an increase of the rate of the cathodic electron transfer process, while that of the anodic reaction is retarded. Under steady state conditions, the RUO2 will assume a potential Ep which is given by the intersection of the two current-voltage c-urves. At this potential a current i will flow which defines the overall reaction rate. It appears that in the case of oxidizing agents such as Fe(bipy) 2 Ru(bipy) Ce, or ZnTMPyP a driving force of ca. I50 mV for the water oxidation... 

Activation volume — As in case of homogeneous chemical reactions, also the rate of heterogeneous electron transfer reactions at electrode interfaces can depend on pressure. The activation volume AV involved in electrochemical reactions can be determined by studying the pressure dependence of the heterogeneous standard rate constant ks AV = R is the molar... 

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