Diffusion effects, electron-transfer bulk reaction

DNA mediated photoelectron transfer reactions have been demonstrated60 . Binding to DNA assists the electron transfer between the metal-centered donor-acceptor pairs. The increase in rate in the presence of DNA illustrates that reactions at a macromolecular surface may be faster than those in bulk homogeneous phase. These systems can provide models for the diffusion of molecules bound on biological macromolecular surfaces, for protein diffusion along DNA helices, and in considering the effect of medium, orientation and diffusion on electron transfer on macromolecular surfaces. 

Kinetic studies of ECE processes (sometimes called a DISP mechanism when the second electron transfer occurs in bulk solution) [3] are often best performed using a constant-potential technique such as chronoamperometry. The advantages of this method include (1) relative freedom from double-layer and uncompensated iR effects, and (2) a new value of the rate constant each time the current is sampled. However, unlike certain large-amplitude relaxation techniques, an accurately known, diffusion-controlled value of it1/2/CA is required of each solution before a determination of the rate constant can be made. In the present case, diffusion-controlled values of it1/2/CA corresponding to n = 2 and n = 4 are obtained in strongly acidic media (i.e., when kt can be made small) and in solutions of intermediate pH (i.e., when kt can be made large), respectively. The experimental rate constant is then determined from a dimensionless working curve for the proposed reaction scheme in which the apparent value of n (napp) is plotted as a function of kt. 

Note that it may be surprising that a chemical term is considered in Eq. (3), whereas we have supposed that no chemical reaction term was involved within the stagnant layer. As explained in Chapter 1, this stems from the fact that the effect of any chemical reaction within the diffusion layer depends on the relative magnitude of k5 /D versus unity. For usual laboratory conditions, 8 10 cm and D 5 x IC cm s and then 5 /D is of the order of 0.2 s. Thus, provided k is less than approximately 1 s it has no tangible effect on the concentration profiles of the species, whereas it has a definite effect in the bulk solution due to the long reaction times (usually longer or comparable to half an hour). In practice it is important to decide when the simplification in Eq. (2) or (3) applies to a given experimental situation. The discussion just presented affords a simple answer to the problem. Indeed, consider the electron transfer reaction in Eq. (5), possibly followed by a chemical step in Eq. (6). 

There are features of these reactions which have attracted a great deal of attention to the problem of the coupling between outer-sphere electron transfer processes and solvent relaxation processes (a) the electron-transfer potential-energy surface is presumably somewhat cusp-like in the surface-crossing region, and this makes the reactions unusually sensitive to solvent fluctuations (b) the electron transfer step is often very fast and the bulk solvent translational diffusion properties are often not pertinent to the observed frictional effects. 

FIGURE 11.11 Calculated free energy diagram for the full ORR over a Pt(lll) surface at C/=0.9V. The different elementary reaction steps included are as follows, in order from left to right diffusion of from the bulk electrolyte to the region (double layer) just outside the surface (the effective free energy barrier shown is deduced from the diffusion rate) adsorption of Oj (note that this involves electron transfer to the molecule, but not a whole electron, and the electron transfer is there also in the absence of the potential since a metal surface has a large pool of electrons available at the Fermi level), followed by four coupled electron-proton transfers to form water and recreation of the adsorption site A. Adapted from Hansen et al. (2014). 

---