Charged spheres electrostatic factors

The thermodynamics of an outer-sphere electron-transfer reaction is represented by the Weller equation that provides the free enthalpy AG° as a function of the standard redox potentials of the donor and the acceptor and an electrostatic factor containing the sum d of the radiuses of the donor and acceptor, their charges Zd and Za, the dielectric constant e of the medium and the ionic strength factor f (often approximated to one). 

Diffuse layer metal retention and outer sphere complex formation involve electrostatic attractive forces, which are characteristically weaker than co-ordinative interactions leading to inner sphere surface complex formation. A number of factors influence metal interactions with surfaces, including the chemical composition of the surface, surface charge, and the nature and speciation of the metal ion. The importance of the pH of the aqueous phase in these interactions will be discussed further in Section 3.2.4.1. 

For inner sphere complexes with the entire charge at the surface plane Uxi x = Zx and the Boltzmann factor becomes simply exp(—ZxFV s/RT). For outer sphere complexes nx = 0 and both activities are determined by ipd only. Assuming that, except for the electrostatic interactions, the surface phase behaves ideal, the ratios of the surface group activities in Eqs. (46), (51) and (52) can be replaced by ratios of site fractions, 6x = SX/Nj where is the total density of surface sites ... 

The first term in Equation 1.4 was retained from Debye s colliding sphere model the electron-donor and electron-acceptor species were viewed as spheres of radii r-i and r2 that possessed charges of z, and z2, respectively. This term is associated with the electrostatic energy (Coulombic work) required to bring the two spheres from an infinite distance to the center-to-center separation distance, ri2 G + G, which is also known as the distance of closest approach (formation of the precursor complex [Dn—Am] in Scheme 1.1). The magnitude of the Coulombic term is modified by a factor exp(—yr12), which accounts for the effects of the dielectric medium (of dielectric constant D) and of the total ionic strength /a. 

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