Electron transfer macroscopic electrode

By tradition, electrochemistry has been considered a branch of physical chemistry devoted to macroscopic models and theories. We measure macroscopic currents, electrodic potentials, consumed charges, conductivities, admittance, etc. All of these take place on a macroscopic scale and are the result of multiple molecular, atomic, or ionic events taking place at the electrode/electrolyte interface. Great efforts are being made by electrochemists to show that in a century where the most brilliant star of physical chemistry has been quantum chemistry, electrodes can be studied at an atomic level and elemental electron transfers measured.1 The problem is that elemental electrochemical steps and their kinetics and structural consequences cannot be extrapolated to macroscopic and industrial events without including the structure of the surface electrode. 

The field of modified electrodes spans a wide area of novel and promising research. The work dted in this article covers fundamental experimental aspects of electrochemistry such as the rate of electron transfer reactions and charge propagation within threedimensional arrays of redox centers and the distances over which electrons can be transferred in outer sphere redox reactions. Questions of polymer chemistry such as the study of permeability of membranes and the diffusion of ions and neutrals in solvent swollen polymers are accessible by new experimental techniques. There is hope of new solutions of macroscopic as well as microscopic electrochemical phenomena the selective and kinetically facile production of substances at square meters of modified electrodes and the detection of trace levels of substances in wastes or in biological material. Technical applications of electronic devices based on molecular chemistry, even those that mimic biological systems of impulse transmission appear feasible and the construction of organic polymer batteries and color displays is close to industrial use. 

The theory on the level of the electrode and on the electrochemical cell is sufficiently advanced [4-7]. In this connection, it is necessary to mention the works of J.Newman and R.White s group [8-12], In the majority of publications, the macroscopical approach is used. The authors take into account the transport process and material balance within the system in a proper way. The analysis of the flows in the porous matrix or in the cell takes generally into consideration the diffusion, migration and convection processes. While computing transport processes in the concentrated electrolytes the Stefan-Maxwell equations are used. To calculate electron transfer in a solid phase the Ohm s law in its differential form is used. The electrochemical transformations within the electrodes are described by the Batler-Volmer equation. The internal surface of the electrode, where electrochemical process runs, is frequently presented as a certain function of the porosity or as a certain state of the reagents transformation. To describe this function, various modeling or empirical equations are offered, and they... 

The electron transfer (ET) at the interface between electrode and electrolyte is central to an electrode reaction. Electrons pass through the interface. Macroscopically we observe a current i. 

The Butler-Volmer formulation of electrode kinetics [16,17] is the oldest and least complicated model constructed to describe heterogeneous electron transfer. However, this is a macroscopic model which does not explicitly consider the individual steps described above. Consider the following reaction in which an oxidized species, Ox, e.g. a ferricenium center bound to an alkanethiol tether, [Fe(Cp)2]+, is converted to the reduced form, Red, e.g. [Fe(Cp)2], by adding a single electron ... 

An important macroscopic structural aspect concerns the arrangement and the contact design of the current collector, which has to supply the electrons from/to an external electrical circuit. These electrons are due to the driving redox reactions at or within the electrodes. Direct electron transfer between dissolved redox partners, e.g., in the... 

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. 

The previous sections dealt with a generalized theory of heterogeneous electron-transfer kinetics based on macroscopic concepts, in which the rate of the reaction was expressed in terms of the phenomenological parameters, and a. While useful in helping to organize the results of experimental studies and in providing information about reaction mechanisms, such an approach cannot be employed to predict how the kinetics are affected by such factors as the nature and structure of the reacting species, the solvent, the electrode material, and adsorbed layers on the electrode. To obtain such information, one needs a microscopic theory that describes how molecular structure and environment affect the electron-transfer process. 

Electrochemical microsystem technology can be scaled down from macroscopic science to micro and further to nanoscale through EMST to ENT [1]. In ENT, electrochemistry involves in the production process to realize nanoproducts and systems which must have reproducible capability. The size of the products and systems must be in the submicron range. It considers electrochemical process for nanostructures formation by deposition, dissolution and modification. Electrochemical reactions combining ion transfer reactions (ITR) and electron transfer reactions (ETR) as applicable in EMST are also applied in ENT. Molecular motions play an important role in ENT as compared with EMST. Hence, mechanical driven system has to be changed to piezo-driven system to achieve nanoscale motions in ENT. Due to the molecular dimension of ENT, quantum effects are always present which is not important in the case of EMST. The double layer acts as an interface phenomenon between electrode and electrolyte in EMST, however, double layer in the order of few nanometers even in dilute electrolyte interferes with the nanostmcture in ENT. 

Note that the reorganization energy that appears in Eq. (7) is associated with the change in the redox state of the molecular species only. The nominal change in the oxidation state of the macroscopic electrode does not affect the polarization state of the surrounding solvent because the transferred electron or hole does not stay localized. 

In deriving the latter expression we assumed that R R- Equation 196 is very fundamental, and it provides a relationship between the macroscopic rate constant k and the macroscopic processes of substrate electrode kinetics and spherical diffusion at the catalytic particle. On the rhs of Eqn. 196 the first term describes the effect of heterogeneous kinetics of the substrate at the particle surface. This rate constant k is a strong function of electrode potential. The second term describes the spherical diffusion of substrate to the catalytic particle. When ks DsIR the mass transport of S to the particle surface is rate-determining. Alternatively when k E DsiR then the electron transfer process at the particle surface is rate-determining. 

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