Electron-transfer reactions constants

The radical cation of 1 (T ) is produced by a photo-induced electron transfer reaction with an excited electron acceptor, chloranil. The major product observed in the CIDNP spectrum is the regenerated electron donor, 1. The parameters for Kaptein s net effect rule in this case are that the RP is from a triplet precursor (p. is +), the recombination product is that which is under consideration (e is +) and Ag is negative. This leaves the sign of the hyperfine coupling constant as the only unknown in the expression for the polarization phase. Roth et aJ [10] used the phase and intensity of each signal to detemiine the relative signs and magnitudes of the... 

A number of different types of experiment can be designed, in which disc and ring can either be swept to investigate the potential region at which the electron transfer reactions occur, or held at constant potential (under mass-transport control), depending on the infomiation sought. 

Because of the unique nature of electron-transfer reactions, these have been of great theoretical interest. More recently, research has centered on a microscopic picture of the electron-transfer reactions and predicting reaction rate constants (5,6). 

Among the dynamical properties the ones most frequently studied are the lateral diffusion coefficient for water motion parallel to the interface, re-orientational motion near the interface, and the residence time of water molecules near the interface. Occasionally the single particle dynamics is further analyzed on the basis of the spectral densities of motion. Benjamin studied the dynamics of ion transfer across liquid/liquid interfaces and calculated the parameters of a kinetic model for these processes [10]. Reaction rate constants for electron transfer reactions were also derived for electron transfer reactions [11-19]. More recently, systematic studies were performed concerning water and ion transport through cylindrical pores [20-24] and water mobility in disordered polymers [25,26]. 

Use die activated complex theory for explaining clearly how the applied potential affects the rate constant of an electron-transfer reaction. Draw free energy curves and use proper equations for your explanation. 

Packer, J.E., Willson, R.L., Hahnemann, D. and Asmus, K.-D. (1980). Electron transfer reactions of halogenated aliphatic peroxyl radicals measurements of absolute rate constants by pulse radiolysis. J. Chem. Soc. Perkins Transact. II, 296-299. 

Early studies of ET dynamics at externally biased interfaces were based on conventional cyclic voltammetry employing four-electrode potentiostats [62,67 70,79]. The formal pseudo-first-order electron-transfer rate constants [ket(cms )] were measured on the basis of the Nicholson method [99] and convolution potential sweep voltammetry [79,100] in the presence of an excess of one of the reactant species. The constant composition approximation allows expression of the ET rate constant with the same units as in heterogeneous reaction on solid electrodes. However, any comparison with the expression described in Section II.B requires the transformation to bimolecular units, i.e., M cms . Values of of the order of 1-2 x lO cms (0.05 to O.IM cms ) were reported for Fe(CN)g in the aqueous phase and the redox species Lu(PC)2, Sn(PC)2, TCNQ, and RuTPP(Py)2 in DCE [62,70]. Despite the fact that large potential perturbations across the interface introduce interferences in kinetic analysis [101], these early estimations allowed some preliminary comparisons to established ET models in heterogeneous media. 

Eqns. 3.71-3.74 show the possibility of checking the mechanism of the respective electrode reactions on the basis of their logarithmic term containing <1/2 and r1/2 in all the instances the product ir1 2 is constant as a function of the constant i chosen however, when a chemical reaction necessarily precedes the electron transfer reaction, i.e. in a CE system, it11 2 decreases with increasing i. 

The donor-acceptor complexes [Ir(/r-dmpz)(CO)(PPh2 0(CH2)2R )]2 exhibit photo-induced electron-transfer rate constants of 1012s—1 and charge recombination rates slower than 2 x 10los-1 when R = pyridine and 4-phenylpyridine.534 Further studies on these complexes revealed that recombination reactions were temperature dependent and slower for the deuterated acceptors.535... 

From Table 14.6 it can be seen that, with the exception of astaxanthin (ASTA), the rate constants for the electron transfer reactions decrease for each carotenoid in the order 9-phenanthryl peroxyl > 1-naphthyl peroxyl > 2-naphthyl peroxyl. This order of reactivity should be related to the reduction potentials of the radicals, with 9-phenanthryl peroxyl having the highest reduction potential. The same order of reactivity for these three arylperoxyl radicals reacting with Trolox was shown by Neta and coworkers (Alfassi et al. 1995). The reactivities of all the carotenoids studied are similar... 

Thus, if the lifetime of a spin state is 81, the energy level is broadened by an amount H/81, with consequences for ESR line widths. Ward and Weissman1 added some unreduced naphthalene to a solution of the radical anion, and, from the observed broadening, computed 81, and from 8/ the rate constant for the electron transfer reaction ... 

In summary, to apply the Marcus theory of electron transfer, it is necessary to see if the temperature dependence of the electron transfer rate constant can be described by a function of the Arrhenius form. When this is valid, one can then determine the activation energy AEa only under this condition can we use AEa to determine if the parabolic dependence on AG/ is valid and if the reaction coordinate is defined. 

Our problem now is to determine the functional form of this experimental free energy curve for the intrinsic rate constant ki for electron transfer. In addition to the Marcus eq 4, two other relationships are currently in use to relate the activation free energy to the free energy change in electron transfer reactions (15, JL6). 

One striking prediction of the energy gap law and eq. 11 and 14 is that in the inverted region, the electron transfer rate constant (kjjj. = ket) should decrease as the reaction becomes more favorable (lnknr -AE). Some evidence has been obtained for a fall-off in rate constants with increasing -AE (or -AG) for intermolecular reactions (21). Perhaps most notable is the pulse radiolysis data of Beitz and Miller (22). Nonetheless, the applicability of the energy gap law to intermolecular electron transfer in a detailed way has yet to be proven. 

Rate Constants and Reactivity. Electron-transfer reactions of plastocyanin (and other metalloproteins) are so efficient that only a narrow range of redox partners (having small driving force) can be employed. Rates are invariably in the stopped-flow range, Table I. Unless otherwise stated parsley plastocyanin... 

Cyclic chain termination with aromatic amines also occurs in the oxidation of tertiary aliphatic amines (see Table 16.1). To explain this fact, a mechanism of the conversion of the aminyl radical into AmH involving the (3-C—H bonds was suggested [30]. However, its realization is hampered because this reaction due to high triplet repulsion should have high activation energy and low rate constant. Since tertiary amines have low ionization potentials and readily participate in electron transfer reactions, the cyclic mechanism in systems of this type is realized apparently as a sequence of such reactions, similar to that occurring in the systems containing transition metal complexes (see below). 

Photosensitization of diaryliodonium salts by anthracene occurs by a photoredox reaction in which an electron is transferred from an excited singlet or triplet state of the anthracene to the diaryliodonium initiator.13"15,17 The lifetimes of the anthracene singlet and triplet states are on the order of nanoseconds and microseconds respectively, and the bimolecular electron transfer reactions between the anthracene and the initiator are limited by the rate of diffusion of reactants, which in turn depends upon the system viscosity. In this contribution, we have studied the effects of viscosity on the rate of the photosensitization reaction of diaryliodonium salts by anthracene. Using steady-state fluorescence spectroscopy, we have characterized the photosensitization rate in propanol/glycerol solutions of varying viscosities. The results were analyzed using numerical solutions of the photophysical kinetic equations in conjunction with the mathematical relationships provided by the Smoluchowski16 theory for the rate constants of the diffusion-controlled bimolecular reactions. 

The Smoluchowski theory for diffusion-controlled reactions, when combined with the Stokes-Einstein equation for the diffusion coefficient, predicts that the rate constant for a diffusion-controlled reaction will be inversely proportional to the solution viscosity.16 Therefore, the literature values for the bimolecular electron transfer reactions (measured for a solution viscosity of r ) were adjusted by multiplying by the factor r 1/r 2 to obtain the adjusted value of the kinetic constant... 

Denote the forward and backward rate constants of this reaction by ka and kb- When the reaction proceeds under stationary conditions, the rates of the chemical and of the electron-transfer reaction are equal. Derive the current-potential relationship for this case. Assume that the concentrations of A and of the oxidized species are constant. 

Therefore the electron-transfer reaction from Fe2+ to Fe3+ proceeds along a reaction path like the one indicated in the figure. Note that the electron-transfer step itself occurs practically at a constant distance from the metal surface the reaction coordinate is given by the solvent coordinate. This is the reason why the simple treatment presented in Chapter 6 is valid. 

The first term is the intrinsic electronic energy of the adsorbate eo is the energy required to take away an electron from the atom. The second term is the potential energy part of the ensemble of harmonic oscillators we do not need the kinetic part since we are interested in static properties only. The last term denotes the interaction of the adsorbate with the solvent the are the coupling constants. By a transformation of coordinates the last two terms can be combined into the same form that was used in Chapter 6 in the theory of electron-transfer reactions. 

Let us summarize the results obtained. The theory is restricted to nonadiabatic electron-transfer reactions. If only classical modes are reorganized during the transition, the rate constant for the oxidation is ... 

A significant technical development is the pulsed-accelerated-flow (PAF) method, which is similar to the stopped-flow method but allows much more rapid reactions to be observed (1). Margerum s group has been the principal exponent of the method, and they have recently refined the technique to enable temperature-dependent studies. They have reported on the use of the method to obtain activation parameters for the outer-sphere electron transfer reaction between [Ti Clf ] and [W(CN)8]4. This reaction has a rate constant of 1x108M 1s 1 at 25°C, which is too fast for conventional stopped-flow methods. Since the reaction has a large driving force it is also unsuitable for observation by rapid relaxation methods. 

Here, i is the faradaic current, n is the number of electrons transferred per molecule, F is the Faraday constant, A is the electrode surface area, k is the rate constant, and Cr is the bulk concentration of the reactant in units of mol cm-3. In general, the rate constant depends on the applied potential, and an important parameter is ke, the standard rate constant (more typically designated as k°), which is the forward rate constant when the applied potential equals the formal potential. Since there is zero driving force at the formal potential, the standard rate constant is analogous to the self-exchange rate constant of a homogeneous electron-transfer reaction. 

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