Electron transfer work terms

The electrochemical reaction of interest takes place at the working electrode (WE). Electrical current at the WE due to electron transfer is termed faradaic current. An auxiliary, or counter electrode (AE) is driven by the potentiostatic circuit to balance the faradaic process at the WE with an electron transfer of opposite direction (e.g, if reduction takes place at the WE, oxidation takes place at the AE). The process at the AE is typically not of interest, and in most experiments the small currents observed mean that the electrolytic products at the AE have no influence on the processes at the WE. 

The common example of real potential is the electronic work ftmction of the condensed phase, which is a negative value of af. This term, which is usually used for electrons in metals and semiconductors, is defined as the work of electron transfer from the condensed phase x to a point in a vacuum in close proximity to the surface of the phase, hut heyond the action range of purely surface forces, including image interactions. This point just outside of the phase is about 1 pm in a vacuum. In other dielectric media, it is nearer to the phase by e times, where e is the dielectric constant. 

Gibbs energy of electron transfer (AGe ) and the work terms for precursor formation (Wp) and successor dissociation (ws),... 

Mechanistic Formulation of Electron Transfer. The Importance of the Work Term. Accordingly, the electron transfer mechanism can be considered in the light of the standard potentials E° for each redox couple, i.e., E x for the oxidation of the donor (D D+ + e ) and E ed for the reduction of the acceptor (A + e" A"). Thus the general reaction scheme for an irreversible process is represented by (20) ... 

Evaluation of the Work Term from Charge Transfer Spectral Data. The intermolecular interaction leading to the precursor complex in Scheme IV is reminiscent of the electron donor-acceptor or EDA complexes formed between electron donors and acceptors (21). The latter is characterized by the presence of a new absorption band in the electronic spectrum. According to the Mulliken charge transfer (CT) theory for weak EDA complexes, the absorption maximum hv rp corresponds to the vertical (Franck-Condon) transition from the neutral ground state to the polar excited state (22). 

The charge transfer Scheme V is akin to the adiabatic electron transfer cycle in Scheme IV. In this case the work term Wp required to bring the products D+ and A together to the mean separation rp in the CT excited state is given by ... 

Figure 18, Relationship between the activation free energy AG including the work term Awp and the driving force for electron transfer AG° to TCNE (left) and IrClt (right) following Equation 30,...

Comparison with the case of a purely repulsive product profile [equation (3.17)] vs. equations (3.3) and (3.4) reveals that the effect of an attractive interaction between the fragments in the product cluster is not merely described by the introduction of a work term in the classical theory of dissociative electron transfer. Such a work term appears under the form of —AG p, but there is also a modification of the intrinsic barrier. With the same Ap, the change in the intrinsic barrier would simply be obtained by replacement of Dr by /Dr — /D )2. It is noteworthy that small values of DP produce rather strong effects of the intrinsic barrier. For example, if DP is 4% of Dr, a decrease of 20% of the intrinsic barrier follows. The fact that a relatively small interaction leads to a substantial decrease of the activation barrier is depicted in Figure 3.4. 

We have investigated the ferrocene/ferrocenium ion exchange to determine the effects of different solvents on electron-transfer rates. There is probably only a very small work term and very little internal rearrangement in this system. Thus the rates should reflect mostly the solvent reorganization about the reactants, the outer-sphere effect. We measured the exchange rates in a number of different solvents and did not find the dependence on the macroscopic dielectric constants predicted by the simple model [Yang, E. S. Chan, M.-S. Wahl, A. C. J. Phys. Chem. 1980, 84, 3094]. Very little difference was found for different solvents, indicating either that the formalism is incorrect or that the microscopic values of the dielectric constants are not the same as the macroscopic ones. 

At 25°C and p = 0.1 M, the values of are 10 -10 M and those of k are 10 -10 s depending on the identity of L. The internal electron transfer rate in an outer-sphere complex can thus be analyzedwithout considering work terms or, what is equivalent, the equilibrium controlling the formation of precursor complex. This favorable situation is even improved when the metal centers are directly bridged. The relative orientation of the two metal centers in a well-established geometry can be better treated than in the outer-sphere complex (Sec. 5.8). 

Early attempts at observing electron transfer in metalloproteins utilized redox-active metal complexes as external partners. The reactions were usually second-order and approaches based on the Marcus expression allowed, for example, conjectures as to the character and accessibility of the metal site. xhe agreement of the observed and calculated rate constants for cytochrome c reactions for example is particularly good, even ignoring work terms. The observations of deviation from second-order kinetics ( saturation kinetics) allowed the dissection of the observed rate constant into the components, namely adduct stability and first-order electron transfer rate constant (see however Sec. 1.6.4). Now it was a little easier to comment on the possible site of attack on the proteins, particularly when a number of modifications of the proteins became available. 

The investigation of electron ionization is clearly in the early stages in comparison with the electron transfer studies, and additional work on the influence of orientation on Augmentation will be required before a coherent pattern emerges and a model for fragmentation can be attempted. However, a simple model that considers ionization in terms of the Coulomb potential developed between the electron and the polar molecule, taking the electron transition probability into account, reproduces the main experimental features. This model accounts qualitatively for the steric effect measured and leads to simple, generally applicable, expressions for the maximum (70 eV) ionization cross section. 

When a gas is adsorbed at a metal surface, the observed change in work function is brought about by electronic interaction between the metal and the adsorbate. Most chemisorptions involve electron transfer, the nature of which is related to the electronic structure and the surface properties of the metal. At the outset, therefore, it is desirable to consider the adsorption process and the formation of chemical bonds at metal surfaces in general terms. 

Finally, we must consider the contribution of the electrostatic work required to transfer one electron into free space. After overcoming the short range chemical forces, the electron must be moved a certain distance against the electric field in the surface. Under the assumption that the lines of force of the electric field are located between the ion defects in the boundary layer and the surface charges represented by the chemisorbed gas atom, we obtain the expression afi for this electrostatic work term. is the boundary field strength represented in Equation (11), and a is the distance between the surface of the oxide and the centers of charge of the chemisorbed atoms in the a-phase. 

Electron transfer is a fast reaction ( 10-12s) and obeys the Franck-Condon Principle of energy conservation. To describe the transfer of electron between an electrolyte in solution and a semiconductor electrode, the energy levels of both the systems at electrode-electrolyte interface must be described in terms of a common energy scale. The absolute scale of redox potential is defined with reference to free electron in vacuum where E=0. The energy levels of an electron donor and an electron acceptor are directly related to the gas phase electronic work function of the donor and to the electron affinity of the acceptor respectively. In solution, the energetics of donor-acceptor property can be described as in Figure 9.6. 

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