Redox reactions, “outer-sphere

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. 

Iwasita T, Schmickler W, Schultze JW. 1985. The influence of the metal on the kinetics of outer sphere redox reactions. Ber Bunsenges Phys Chem 89 138-140. 

Schmickler W. 1976. The effect of quantum vibrations on electrochemical outer sphere redox reactions. Electrochim Acta 21 161-168. 

Undoubtedly one of the most used LFER in transition metal chemistry involves electron transfer rate constants and associated equilibrium constants in outer sphere redox reactions. These are an unusual class of reactions in chemistry since bonds are only stretched or contracted in the formation of the activated complex. They therefore lend themselves well to theoretical treatment. We shall have more to say about these reactions in Chap. 5. It is sufficient here to state the simple form of the LFER with an example (Fig. 2.8). For the reaction... 

Negative or very small values of 7s.H are rare. They obviously cannot arise from a single step, and they give overwhelming evidence for a multistep process that includes a preequilibrium. Negative or near-zero values for AFT for a few inner-sphere and outer-sphere redox reactions indicate the occurrence of intermediates, and rule out a single step, with a single activated complex (Sec. 5.5). 

The transmission coefficient k is approximately 1 for reactions in which there is substantial (>4kJ) electronic coupling between the reactants (adiabatic reactions). Ar is calculable if necessary but is usually approximated by Z, the effective collision frequency in solution, and assumed to be 10" M s. Thus it is possible in principle to calculate the rate constant of an outer-sphere redox reaction from a set of nonkinetic parameters, including molecular size, bond length, vibration frequency and solvent parameters (see inset). This represents a remarkable step. Not surprisingly, exchange reactions of the type... 

If the reactants are oppositely charged, the collision complex in (5.18) takes the form of an outer-sphere complex with discernable stability. For the outer sphere redox reaction between Co(NH3)jL"+ and Fe(CN)g, L being a series of pyridine or carboxylate derivatives, saturation kinetics are observed, with the pseudo first-order rate constant (/ obs)> Fe(II) in excess, being given by... 

One might anticipate that there would be a rate difference for the reaction of enantiomers with a chiral compound. The first demonstration of stereoselectivity in an outer-sphere electron transfer was as recent as 1980. Since then such asymmetric induction has been established with a number of examples, nearly all involving outer-sphere redox reactions. Thus, consider the two reactions... 

The first group must be inner-sphere. The second group must involve a preequilibrium containing a CN ion, followed by an outer-sphere redox reaction. 

There has been some exploration of the mechanism of reduction of d transition metal complexes by M2+(aq) (M = Eu, Yb, Sm). Both inner- and outer-sphere mechanisms are believed to operate. Thus the ready reduction of [Co(en)3]3+ by Eu2+(aq) is necessarily outer-sphere. 2 However, the strong rate dependence on the nature of X when [Co(NH3)5X]2+ or [Cr(H20)5X]2+ (X = F, Cl, Br or I) are reduced by Eu2+(aq) possibly suggests an inner-sphere mechanism.653 The more vigorous reducing agent Yb2+ reacts with [Co(NH3)6]3+ and [Co(en)3]3+ by an outer-sphere route but with [Cr(H20)5X]2+ (X = halide) by the inner-sphere mechanism.654 Outer-sphere redox reactions are catalyzed by electron-transfer catalysts such as derivatives of isonicotinic acid, one of the most efficient of which is iV-phenyl-methylisonicotinate, as the free radical intermediate does not suffer attenuation through disproportionation. Using this catalyst, the outer-sphere reaction between Eu2+(aq) and [Co(py)(NH3)5]3+ proceeds as in reactions (18) and (19). Values found were ki = 5.8 x KFM-1 s 1 and k kx = 16.655... 

The mass transport rate coefficient, kd, for a RDE at the maximum practical rotation speed of 10000 per min"1 is approximately 2 x 10-2 cms-1 [28], which sets a limit of about 10 3 cms 1 for the electrode reaction kinetics. For the study of very fast electrode processes, such as some outer sphere redox reactions on noble metal electrodes under stationary conditions, higher mass transport rates in the solution adjacent to the electrode must be employed. 

The transmission coefficient k — 1 for weak overlap of electronic states of reactants and products in the transition state. It is strong enough to be adiabatic but yet weak enough for the free energy of activation not to have an appreciable contribution from the resonance energy. This condition is almost fulfilled by outer sphere redox reactions at electrodes. 

Only if the component processes I and II are independent of the electrode material, i.e. outer sphere redox reactions in the absence of double layer effects, is the mixed potential, EM, independent of the electrode. 

The Marcus therory provides an appropriate formalism for calculating the rate constant of an outer-sphere redox reaction from a set of nonkinetic parameters1139"1425. The simplest possible process is a self-exchange reaction, where AG = 0. In an outer-sphere electron self-exchange reaction the electron is transferred within the precursor complex (Eq. 10.4). 

Electron transfer rate constants of outer sphere redox reactions can be measured relatively easily at n-type semiconductor electrodes. This is because electrons are withdrawn from the surface under depletion conditions, so that their concentration is lower than in the bulk. Under ideal... 

Activated complex, bridged, redox reaction mechanisms and, 19-32 outer-sphere, redox reaction mechanisms and, 12-19... 

The reaction has also been examined in various solvent mixtures. In BuOH/H20 mixtures a plot of log k against the mole fraction of the alcohol shows a minimum at low values. The authors suggested that such minima are always shown by outer-sphere redox reactions (97). 

Iwasita T., Schmickler W. and Schultze J. W., (1985) The influence of metal adatoms deposited at underpotential on the kinetics of an outer-sphere redox reaction , J. Electroanal. Chem. 194, 355-359. 

EIS has been used to study the kineties of outer-sphere redox reactions at semiconductors in the dark (Meier et al., 1991 Meier et al., 1999). The reactions involve majority carriers (electrons for n-type materials), and the electrode behaves like a metal with a low and potential-dependent electron density. The EIS response can be modelled by the equivalent circuit shown in Eig. 12.1, where is interpreted as the faradaic resistance obtained by linearising the potential dependence of the current associated with electron transfer to the redox species. 

Second order rate constants, k, for some outer-sphere redox reactions at 298 K in aqueous solution. 

Several theories of outer-sphere redox reactions have been developed on the basis of the above oscillator model for the solvent, which make use of either the semiclassical activated complex theory or the quantum-mechanical perturbation theory /40,142,148/. The restrictions involved in both types of theories can be avoided by an application /37d,e/ of the general formulations of the.rate expression developed in Chapter III. 

On the basis of the above one-frequency oscillator model, the rate constant of outer-sphere redox-reactions can be computed using the equation... 

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