Marcus theory¹ of electron transfer is the dominant theory to describe the rate constant of electron transfer reactions both in chemistry and biology during last several decades. The general treatment on the solvation free energy of reactants is largely based on Born model² that the solvent is assumed as a dielectric continuum and each reactant is treated as a sphere where the first solvation layer is dielectrically saturated. However, these assumptions could shield the fact of non-covalent interactions within the solvation shell of reactants, including reactant nuclei-solvent, reactant nuclei-inert ion, inert ion-solvent interactions and hydrogen bonding of solvent molecules. The entropy change of an electron transfer reactions, , is the difference of standard molar entropy between the reduced and oxidized forms of a redox couple. The reaction entropy of outer sphere self-exchange can be qualitatively described by Born model even though the Born prediction differs from the experimental data of some redox couples, according to previous studies³. It was shown that the reaction entropy of a given redox couple increases with decreasing in solvent acceptor number. This dependence of upon the solvent nature could be associated with the degree of “internal order” of solvent molecules. Besides solvent-solvent molecule interaction, the “internal order” of solvent could be disrupted by dissolved charged species, including the reactant nuclei of redox couples and inert ions either from the counter-ion of redox couples or from the supporting electrolyte. Depending on its effects on water structure and vice versa, ions are usually categorized in either “structure maker” or “structure breaker”⁴, which could affect surrounding hydrogen bonds and water molecular arrangement around itself⁵. In addition to solvent-solvent and ion-solvent interactions, the coulombic interaction between the redox couples and the ions with opposite sign of charge to those of redox couples has been suggested⁶. It could form an ionic atmosphere and, thereby affects to the reaction entropy of redox couples. In aqueous electrolyte, a simple description of this coulombic interaction by an electrostatic energy necessary for forming an ionic atmosphere by surrounding the species with the counter ions seems not to be prudent due to the fact of ternary interactions of redox nuclei, counter ions and solvent molecules. However, the non-covalent interactions have not, to the best of our knowledge, previously been considered in terms of the entropy change of outer sphere self-exchange electron transfer reactions, and it is the impact of structure making/breaking ions on the structure of the solvation shell of the reactant nuclei that constitutes the focus of this work.

Here, we studied reaction entropy of two outer sphere reactions: [Fe⁽H₂O)₆]^2+/3+ and [Fe(CN)₆]^3-/4- upon the nature and the concentration of anions and cations, respectively. For both positively and negatively charged redox couples, it was shown that structure maker ions enhance the “order” in vicinity of redox nuclei while structure breaker ions promote “disorder”. We suggest also molecular level models for redox nuclei solvation by taking into account reactant nuclei-solvent, reactant nuclei-inert ion, inert ion-solvent interactions and hydrogen bonding of solvent molecules.

 References

(1) Marcus, R. A. J. Chem. Phys. 1956, 24, 966.

(2) Born, M. Z. Für Phys. 1920, 1 (1), 45–48.

(3) Hupp, J. T.; Weaver, M. J. Inorg. Chem. 1984, 23 (22), 3639–3644.

(4) Marcus, Y. Chem. Rev. 2009, 109 (3), 1346–1370.

(5) Miller, D. J.; Lisy, J. M. J. Am. Chem. Soc. 2008, 130 (46), 15381–15392.

(6) Yamato, Y.; Katayama, Y.; Miura, T. J. Electrochem. Soc. 2013, 160 (6), H309–H314.