Dahms-Ruff theory

Homogeneous charge transfer can take place between chemically similar redox species of one redox couple, e.g., Fe3+ and Fe2+ ions in solution or ferrice-nium and ferrocene moieties in poly(vinylferrocene) films, the electron transfer (- electron hopping or electron exchange reaction) can be described in terms of second-order kinetics and according to the - Dahms-Ruff theory [viii-x] it may be coupled to the isothermal diffusion ... 

Dahms-Ruff theory — For fast electron exchange processes coupled to isothermal diffusion in solution, the theoretical description and its experimental verification were given by Dahms [i] and by Ruff and co-workers [ii—v]. Ruff and co-workers studied the displacement of the centers of mass particles, which is brought about by both common migrational motion and chemical exchange reaction of the type... 

If the hydroxonium ions migrated only hydrodynam-ically A° 85 cm2 would be expected, which value can easily be derived by using the -> Stokes law and the known values of the -+ self-diffusion coefficient of water, the radius of the ion and the - viscosity. (See also proton, - Eigen complexes, - Zundel complexes, charge transfer, - Dahms-Ruff theory.)... 

According to the Dahms-Ruff theory of electron diffusion [9-12]... 

As the concentration of enzyme in the film is increased from 0 to 65 wt%, the diffusion constant falls by 2 orders of magnitude with a function that is close to exponential. Simplistic application of the Dahms-Ruff theory (which implicitly requires that a "mean-field" approximation holds) would predict a linear dependence on concentration. The latter approximation would require that physical diffusion of the Os sites be rapid compart to electron hopping, which is clearly not the case here. Theory based on rigorously fixed site redox molecules and extended electron transfer (ie. static percolation), would indeed predict an exponential decrease in electron hopping with concentration.(25) However, simulations by Blauch and Saveant for the case of tethered redox sites also leads to a behavior part-way between that predicted by "static percolation" and "mean-field" approximations, resulting in a functional form of close to that seen in the inset of Figure 6. (See Figure 3B of reference 15 where tjtp=0.1). It must be pointed out that the weak dependence of the film thickness, r, on enzyme content (Table I), leads to little electrochemically measurable decrease in site concentration as enzyme is increased. This of course makes a quantitative application of any of the models mentioned above rather difficult. 

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