Heterogeneous electron transfer Marcus theory

Probably the most important outcome of the Marcus theory is the relationship between homogeneous homonuclear (fcs) and heterogeneous electron transfer rate coefficients (feei) after corrections for electrostatic work terms... 

Therefore, unlike the empirical Butler-Volmer theory, in the Marcus formulation the heterogeneous electron transfer rate constant is sensitive to both the structure of the redox center and the solvent. 

Figure 5.2 Tafel plots of In k versus overpotential for a mixed self-assembled monolayer containing HS(CH2)i600C-ferrocene and HS(CH2)isCH3 in 1.0 M HCIO4 at three different temperatures V, 1 °C O/ 25 °C , 47°C. The solid lines are the predictions of the Marcus theory for a standard heterogeneous electron transfer rate constant of 1.25 s-1 at 25 °C, and a reorganization energy of 0.85 eV (= 54.8 kj moh1). Reprinted with permission from C. E. D Chidsey, Free energy and temperature dependence of electron transfer at the metal-electrolyte interface, Science, 251, 919-922 (1991). Copyright (1991) American Association for the Advancement of Science...

Refs. [i] Born M (1920) Z Phys 1 45 [ii] Marcus Y (1997) Ion properties. Marcel Dekker, New York [iii] Rashin AA, Honig B (1985) ] Phys Chem 89 5588 [iv] Stilly WC, TempczykA, Hawley RC, Hendrickson TA (1990) ] Am Chem Soc 112 6127 [v] Rashin AA (1990) / Phys Chem 94 1725 [vi] Shoichet BK, Leach AR, Kuntz ID (1999) Proteins 34 4 [vii] Marcus RA (1977) Theory and application of electron transfer at electrodes and in solutions. In Rock PA (ed) Special topics in electrochemistry. Elsevier, Amsterdam, pp 61 [viii] Millery C/ (1995) Heterogeneous electron transfer kinetics at metallic electrodes. In Rubinstein I (ed) Physical electrochemistry. Marcel Dekker, New York, pp 46-47... 

The - Marcus theory [vi-vii] gives a unified treatment of both heterogeneous electron transfer at electrodes and homogeneous electron transfer in solutions. 

The Marcus Theory can also be applied for heterogeneous electron transfer reaction at electrode surfaces [24 and references therein]. The electronic coupling between the protein and the electrode can be varied using different self-assembled monolayers controlling the orientation of the redox active protein on the surface and the distance between the redox active site of the protein and the electrode. The driving force is related to the appHed potential and the redox potential of the protein. In many cases the rate of electron transfer across the protein-electrode interface is limited by conformational reorganization. This has focussed the efforts of many groups on tailored interaction between proteins and enzymes and electrode surfaces. 

Fig. 7.38 a) Single reduction wave, corrected for diffusion, for a 10 mM Mo(CN) solution at an Au electrode derivatized with a tetradecanethiol monolayer, b) Density of electronic states for Mo(CN)x calculated as the derivative of the heterogeneous electron transfer rate constant measured at the insulating layer on Au (Figs. 7,36 and 7.37). Solid curve, best fit to the experimental results dashed curve, the Gaussian distribution predicted by the Marcus theory. 

In the simplest cases, it is possible to compare rates for homogeneous and heterogeneous electron-transfer reactions. According to the Marcus theory for homogeneous outer-sphere reactions [10],... 

Clegg AD, Rees NV, Klymenko OV, Coles BA, Compton RG (2004) Marcus theory of outer-sphere heterogeneous electron transfer reactions dependence of the standard electrochemical rate constant on the hydrodynamic radius from high precision measurements of the oxidation of anthracene and its derivatives in nonaqueous solvents using the high-speed channel electrode. J Am Chem Soc 126(19) 6185-6192... 

The relationship between the standard heterogeneous electron transfer rate constant, k, h> and structural factors is expressed in terms of the Marcus-Hush theory applied to electrode reactions [2] ... 

Feldbeig SW (2010) Implications of Marcus-Hush theory for steady-state heterogeneous electron transfer at an inlaid disk electrode. Anal Chem 82 5176-5183... 

Electron Transfer Far From Equilibrium. We have shown how the Marcus Theory of electron transfer provides a quantitative means of analysis of outer-sphere mechanisms in both homogeneous and heterogeneous systems. It is particularly useful for predicting electron transfer rates near the equilibrium potential,... 

The Marcus theory is the most widely applied theory used to describe electron transfer reactions and is equally applicable to photoinduced, interfacial and thermally driven electron transfers. The fundamental difference between these processes lies primarily in the nature of the driving force. In the case of heterogeneous electron... 

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