Diffusional transport in ionic liquids: Stokes–Einstein relation or “sliding sphere” model? Ferrocene (Fc) in imidazolium liquids

Abstract

Our theoretical analysis of the transport of an “inert” (without specific interactions with the solvent) species inside a very viscous medium has led to the conclusion that the classical Stokes–Einstein description is not valid for these systems. Instead of it, the model of a perfectly sliding sphere was proposed for such systems, which results in the Sutherland formula for the diffusion coefficient, D = k B T/4 πηa. It is assumed that “the hydrodynamic radius”, a, in this expression for very viscous ionic liquids (ILs) may be identified with the crystallographic radius of the species, as it is valid for the Stokes–Einstein relation, D = k B T/6 πηa, for the ferrocene (Fc) transport in “normal” (molecular) organic solvents. For experimental verification of these predictions the procedure based on combination of electrochemical and spectral measurements proposed in our previous paper [M.A, Vorotyntsev, V.A. Zinovyeva, D.V. Konev, M. Picquet, L. Gaillon, C. Rizzi, J. Phys. Chem. B 113 (2009) 1085] has been applied to study Fc properties for a set of its solutions in another ionic liquid (IL), [BMIM][BF 4]. Both the Fc oxidation current in voltammetry and the maximum absorption in the visible range (at 440 nm) have found to be proportional to the concentration of the solute Fc. The extinction coefficient of the Fc + IL solution at 440 nm, 88.1 ± 3.2 M −1 cm −1, is within the same narrow range of the values for Fc solutions in [BMIM][NTf 2] and numerous molecular organic solvents. The value of the diffusion coefficient of Fc in [BMIM][BF 4], (8.8 ± 0.85) 10 −8 cm 2/s, is about two times smaller than that in [BMIM][NTf 2], (1.7 ± 0.2) × 10 −7 cm 2/s. The values of the product of the diffusion coefficient and the dynamic viscosity of the medium are close to one another for these two ILs and to the theoretical value of the product for the perfectly sliding sphere, k B T/4 πa, thus confirming this model for Fc in ILs as well as that the Stokes-Einstein formula is not applicable for these systems. It has been proposed to calculate “the Sutherland coefficient”, θ = k B T/ πDηa, as the criterion of the compatibility of the experimental value of D with predictions of the general theory of “the partially sticking sphere” (including its particular cases of the sticking and sliding spheres).