Redox electron

As described in the introduction, certain cosurfactants appear able to drive percolation transitions. Variations in the cosurfactant chemical potential, RT n (where is cosurfactant concentration or activity), holding other compositional features constant, provide the driving force for these percolation transitions. A water, toluene, and AOT microemulsion system using acrylamide as cosurfactant exhibited percolation type behavior for a variety of redox electron-transfer processes. The corresponding low-frequency electrical conductivity data for such a system is illustrated in Fig. 8, where the water, toluene, and AOT mole ratio (11.2 19.2 1.00) is held approximately constant, and the acrylamide concentration, is varied from 0 to 6% (w/w). At about = 1.2%, the arrow labeled in Fig. 8 indicates the onset of percolation in electrical conductivity. 

The dielectric response of a solvated protein to a perturbing charge, such as a redox electron or a titrating proton, is related to the equilibrium fluctuations of the unperturbed system through linear response theory [49, 50]. In the spirit of free energy... 

Metal oxides possess multiple functional properties, such as acid-base, redox, electron transfer and transport, chemisorption by a and 71-bonding of hydrocarbons, O-insertion and H-abstract, etc. which make them very suitable in heterogeneous catalysis, particularly in allowing multistep transformations of hydrocarbons1-8 and other catalytic applications (NO, conversion, for example9,10). They are also widely used as supports for other active components (metal particles or other metal oxides), but it is known that they do not act often as a simple supports. Rather, they participate as co-catalysts in the reaction mechanism (in bifunctional catalysts, for example).11,12... 

The value of xh o is important for estimating theoretically the energy levels of hydrated ions and redox electrons in aqueous solutions. 

Fig. 2-39. Gaussian normal distri bution of the probabili density of redox electron levels due to thermal fluctuation of hydrate structures epd)Bx>X) = standard Fermi level of redox electrons.

As the localized electron level of hydrated redox particles distributes itself in a rather wide range, we may assume the presence of energy bands in which the redox electron level fluctuates the reductant particles form a donor band, and the oxidant particles form an acceptor band. The donor and acceptor bands overlap in the tailing of their probability densities as shown in Fig. 2-39. 

Fig. 2-40. Distribution of electron state density of hydrated redox particles (a) oxidant concentration JVox equal to reductant concentrationNRED. (b) oxidant concentration iVox greater than reductant concentration NgEo cnsEDox) = Fermi level of redox electrons.

In the fluctuation band of electron energy of hydrated redox particles, the donor band of the reductant is an occupied band, and the acceptor band of the oxidant is a vacant band. The level erotsDcno at which the donor state density equals the acceptor state density (Aai/e) = Dox(e)) is called the Fermi level of the redox electron by analogy with the Fermi level e, of metal electrons [Gerischer, 1961]. From Eqns. 2—48 and 2—49 with f BED(e) =-DoxCe), we obtain the Fermi level Tiixxox.) (the redox electron level) as shown in Eqn. 2-51 ... 

The most probable donor level, ered, the most probable acceptor level, eox, and the standard Fermi level, e redox) of redox electrons are characteristic of individual redox particles but the Fermi level, e m dox), of redox electrons depends on the concentration ratio of the reductant to the oxidant, which fact is similar to the Fermi level of extrinsic semiconductors depending on the concentration ratio of the donor to the acceptor. 

The Fermi level ekredox) (= P.(redox)) of redox electrons may also be obtained thermodynamically from the reaction equUibriiun (RED = OX , + edanox)), i.e. p(REDox) = P.(iaD0X) = Pred Pox, as shown in Eqn. 2—53 ... 

In the foregoing reaction steps, , nhe) is the real potential of an equilibrium redox electron of the reaction of normal hydrogen electrode (NHE), which is the energy required for transferring a standard gaseous electron Ccstd) at the outer... 

The energy balance in the foregoing reaction cyde gives the real potential a<(NHE) of the equilibrium redox electron in the reaction of normal hydrogen electrode as shown in Fig. 2-44 represents the Fermi level croniB) of the... 

As some numerical energy values such as given in the foregoing involve a certain degree of inaccuracy, there have been several values reported for the Fermi level of the equilibrium redox electron of NHE. For instance, the value of a NHE) = ewNHE)= -4.44 eV has been reported in the International Union of Pure and Applied Chemistry (lUPAC) [Trasatti, 1986]. 

Electrodes may be classified into the following two categories as shown in Fig. 4-3 one is the electronic electrode at which the transfer of electrons takes place, and the other is the ionic electrode at which the transfer of ions takes place. The electronic electrode corresponds, for instance, to the case in which the transfer of redox electrons in reduction-oxidation reactions, such as Fe = Fe + e,occurs and the ionic electrode corresponds to the case in which the transfer of ions, such as Fe , , = Fe, occiirs across the electrode interface. Usually, the former is found with insoluble electrodes such as platinum electrodes in aqueous solution containing redox particles and the latter is found with soluble metal electrodes such as iron and nickel. In practice, both electron transfer and ion transfer can take place simultaneously across the electrode interface. 

Next, we consider the interface M/S of a nonpolarizable electrode where electron or ion transfer is in equilibrium between a solid metal M and an aqueous solution S. Here, the interfadal potential is determined by the charge transfer equilibrium. As shown in Fig. 4-9, the electron transfer equilibrium equates the Fermi level, Enn) (= P (M)), of electrons in the metal with the Fermi level, erredox) (= P s)), of redox electrons in hydrated redox particles in the solution this gives rise to the inner and the outer potential differences, and respectively, as shown in Eqn. 4-10 ... 

For an electronic electrode at which the transfer of redox electrons is in equilibrimn (OX i + e(jj) = RED q), as shown in Fig. 4-17, the Fermi level EpdUEDoxs) of redox electrons e(REDox., s in hydrated redox particles equals the Fermi level cp(M) of electrons e,io in the electrode the energy for the electron transfer across the electrode interface is, then, zero (a M/s) = 0). Consequently, the electron level u M/aAo in the electrode equals the electron level a, s/v) in the aqueous solution, i.e. the redox electron level a KEoax s) of hydrated redox particles. 

Fig. 4-17. Electronic electrode in equilibrium of electron transfer OX = hydrated oxidant particles RED = hydrated reductant partides FWEDQx, s) = Fermi level of redox electrons in hydrated redox partides in solution S p. = electrochemical potential of electrons.

The electrode potential, E, represented by the real potential hydrated redox particles in aqueous solution as shown in Fig. 4-18 and defined in Eqn. 4-19 ... 

Fig. 4-18. Electron levels of an electronic electrode in equilibrium of redox electron transfer eojenox s> = redox electron at equilibrium e ) = electrons in metal electrode .q = electrode potential in equilibrium of electron transfer.

It, thus, follows that the electrode potential in electron transfer equilibriiun represents the redox electron level of the redox particles in aqueous electrolyte solution. Further, it follows from Eqn. 4-19 that the electrode potential in the transfer equilibrium of redox electrons is characteristic of individual redox reactions but independent of the nature of the electrode materials. 

The electrode potential in the equilibrium of redox electron transfer may also be defined by the free enthalpy change in the reaction of the hydrated redox particles with the standard gaseous electron eisro) as shown in Eqn. 4—20 ... 

The chemical potential h,(redoxs) of redox electrons (OX + (redoxs) = RED ) in the state of redox equilibrium is given by u,(redoxs) = 1 rbixs) - licws). We hence obtain from Eqn. 4-19 the expression in Eqn. 4-21 ... 

Fig. 4-22. Electron energy levels of the hydrogen electrode in electron-and-ion transfer equilibrium Hjiju) = gaseous hydrogen molecule on electrode eaj>/H2, u) = gaseous redox electron in equilibrium with the hydrogen reaction, + 2e(H-/H p,) Hp, =...

In adsorption equUibrimn, the Fermi level c m) of electrons in the metal electrode equals the Fermi level ep(HyH ) oi redox electrons in the adsorbed redox particles the state density of the occupied electron level equals the state density of the vacant electron level at the Fermi level ( >b = Da). Assuming the Langmuir adsorption isotherm at low adsorption coverages and the Gaussian distribution for the state density, we obtain Eqn. 5-55 for the Fermi level ... 

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