Electron-Exchange Reaction

However, the probability of electron transfer (tunneling) depends critically on the distance between the species participating in the electron exchange reactioa A reaction can take place between two molecules when they meet each other. It follows that the rate-determining step can be either the mass transport (mostly diffusion is considered, but effect of migration cannot be excluded) or the reaction (the actual rate of electron transfer in our case). For an electron exchange process coupled to isothermal diffusion, the following kinetic scheme may be considered  

If the reaction has a small energy of activation, so k is high (kg kd), the rate-determining step is the approach of the reactants. Under these conditions it holds that k= ki. The kinetics ate activation-controlled for reactions with large activation 

Since A d/ d is the equihbrium constant, K for the formation of the precursor complex k can be expressed as 

The rate of the colhsion, ki, can be estimated using Smoluchowski s equation  

It follows that diffusion control is more frequently operative in polymeric systems than that in ordinary solution reactions, because and k are more likely to be comparable due to the low D values [9-16], If the election exchange reaction occurs between ionic species (charged polymer sites), the coulombic forces may reduce or enhance both the probability of the ions encoimtering each other and the rate of electron transfer. For the activation-controlled case, kg can be obtained as follows [17]  

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The Nemst equation above for the dependence of the equilibrium potential of redox electrodes on the activity of solution species is also valid for uncharged species in the gas phase that take part in electron exchange reactions at the electrode-electrolyte interface. For the specific equilibrium process involved in the reduction of chlorine ... 

A schematic diagram of the free energy changes in an electron exchange reaction, showing the intersection of two parabolas. The lighter curve represents n,c the darker one, eng, ncg. 

The above statements are valid for monomolecular layers only. In the case of polymer films with layer thickness into the p-range, as are usually produced by electropolymerization, account must also be taken of the fact that the charge transport is dependent on both the electron exchange reactions between neighbouring oxidized and reduced sites and the flux of counterions in keeping with the principle of electroneutrality Although the molecular mechanisms of these processes... 

Similar films are obtained from powdered molecular sieves loaded with organic molecules Zeolite Y microparticles embedded into a polystyrene film and loaded with appropriately sized transition metal complexes allow selective electron exchange reactions between trapped and mobile species in the film... 

The rate of the path involving Fe(H20)5CF as a reactant is 3000 times faster than the alternative (outer-sphere) path. Table 4 summarises results on this reaction and the corresponding electron exchange reactions in terms of relative rate coefficients. 

In this reaction, an electron is transferred from Cr2+ to Fe3+, and such reactions are usually called electron transfer or electron exchange reactions. Electron transfer reactions may also occur in cases where only one type of metal ion is involved. For example, the reaction... 

Fig. 23 Entropy effects on intramolecular reactions of polymethylene chains. Plot of 9AS (e.u.) against number of single bonds for (O) nucleophilic substitutions at saturated carbon ( ) electron-exchange reactions (A) quenching of benzophenone phosphorescence. The straight line has intercept +30 e.u. and slope —4.0 e.u. per rotor. The right-hand ordinate reports the purely entropic EM s calculated as exp(0AS /J )...

Electron exchange reactions, 13 445-447 Electron field emission, 17 49-50 Electron guns, 24 102 Electron-hole pairs... 

A recently proposed semiclassical model, in which an electronic transmission coefficient and a nuclear tunneling factor are introduced as corrections to the classical activated-complex expression, is described. The nuclear tunneling corrections are shown to be important only at low temperatures or when the electron transfer is very exothermic. By contrast, corrections for nonadiabaticity may be significant for most outer-sphere reactions of metal complexes. The rate constants for the Fe(H20)6 +-Fe(H20)6 +> Ru(NH3)62+-Ru(NH3)63+ and Ru(bpy)32+-Ru(bpy)33+ electron exchange reactions predicted by the semiclassical model are in very good agreement with the observed values. The implications of the model for optically-induced electron transfer in mixed-valence systems are noted. 

The rate constant for the aqueous Fe -Fe electron exchange reaction is calculated as 2... 

In this paper we demonstrate the feasibility of applying the techniques of ab initio molecular quantum mechanics in a determination of matrix elements and other electronic properties which give insight into the mechanism of electron exchange reactions. In addition, general kinetic formalisms are adopted which permit the overall rate constant to be calculated for bimolecular electron exchange reactions in polar solvents. Initial accounts of some of this work are given in refs (11) and (13). 

The hexacyanoferrate(II)/(III) electron exchange reaction is strongly catalyzed by cations such as K" ". However if the K" " is complexed by, e.g., 18-crown-6 or the cryptand [2.2.2] then the rate constant for the uncatalyzed reaction can be determined. Carbon-13 NMR spectroscopy has established that is 240 s (at 298 K), with AVyyJ = —11.3 cm mol Pressure effects on... 

Accordingly, evaluation of k from line-width measurements gives a bimolecular rate constant of 0.5 X 1081 sec-1 M-1. This is one of the fastest electron exchange reactions studied in aqueous solution. Transfer rate here may not describe direct electron transfer between Cu1 and Cu11 Stranks has suggested (129) that the rate may refer to transfer within a bridged activated complex, e.g.,... 

While there is a long history of using parameterized force fields to study minerals (5), molecular modeling of reactive processes, involving coupled ligand, proton, and electron-exchange reactions... 

Consider a z electron exchange reaction occurring at an interface of an electrode in solution. It can be written ... 

Fig. 7.69. In a multistep electron-exchange reaction, each step produces its individual current density. At a steady state, all these currents must be equal.

In order to calculate equilibrium electrode potential, we assume that in the part of the cell where a semiconductor electrode is placed, the electrolyte solution contains a redox couple, the equilibrium between the electrode and solution being established due to the reversible electron exchange reaction... 

Fig. 5. Relation between log A and AE values for electron exchange reactions in solutions measurements from Huizenga and Magnusson (24), Gryder, Silvermann, and Dodson (25,26), Meyer and Kahn (27).

The ICoCHjOVl "electron exchange reaction proceeds It) limes taster than prcdMCd hy ihe Marcus equation. Whal docs this suggest. ibwit Hie mechanism of electron transfer ... 

Electron tunneling between organic species was first detected, by direct kinetic experiments, for reactions of the biphenyl anion radical with naphthalene and pyrene [11] and triphenylethylene [12], As is known, upon irradiating vitreous solutions containing biphenyl or pyrene, Py, these acceptors react with electrons to form Ph2 and Py with characteristic optical spectra [13]. Ph2 particles have been found [11] to enter into the electron exchange reactions at 77 K with naphthalene, Nh, and pyrene molecules in mixtures of ethyl alcohol and diethyl ether (2 1). 

The important functionality of Equation 29.20 is that the sensitivity is less for broad lines. We describe in a later section how electron exchange reactions cause lines to broaden when the electrochemical reaction is incomplete (see Sec. VI.F). 

In homogeneous electron exchange reactions between two species differing only in their valence states, AF is given by Equation 10 with X equal to 2X2 and (AF0,int — w) replaced by AFot — uf + wp (5). (uf... 

Limited space also will be devoted to the many instances of qualitative experimental evidence for substituent-exchange equilibria between two kinds of central moieties in favor of quantitative studies of this type. Excluded from the scope of this review will be isotope-exchange equilibria and electron-exchange reactions. 

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