Veronika Zinovyeva - Diffusional transport in ionic liquids: Stokes-Einstein relation or "sliding sphere" model? Ferrocene (Fc) in imidazolium liquids

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      Electrochimica   Acta   2010, 55, 5063-5070

      Vorotyntsev   Mikhail A., Zinovyeva Veronika A., Picquet Michel


      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 =   kBT/4πηa. 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 =   kBT/6πηa, 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][BF4]. 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][NTf2] and numerous molecular organic solvents.   The value of the diffusion coefficient of Fc in   [BMIM][BF4], (8.8 ± 0.85) 10−8  cm2/s, is about two times smaller than that in   [BMIM][NTf2], (1.7 ± 0.2) × 10−7  cm2/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,   kBT/4πa, 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 =   kBT/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).

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