The Stokes-Einstein equation and the diffusion of ferrocene in imidazolium-based ionic liquids studied by cyclic voltammetry: Effects of cation ion symmetry and alkyl chain length

The diffusion of ferrocene (Fc) molecules in ionic liquids (ILs) was studied using cyclic voltammetry. The symmetric ILs 1,3-dialkylimidazolium bis[(trifluoromethane)sulfonyl]amide ([(C_N/2)₂im][NTf₂] with N = 4, 6, 8, and 10) and non-symmetric ILs 1-alkyl-3-methylimidazolium bis[(trifluoromethane)sulfonyl]amide ([C_N−1C₁im][NTf₂] with N = 3, 4, 6, 8, and 10) were used to examine the effect of the symmetry of alkyl substitution on the cation and the role of alkyl chain length on the diffusion of Fc. The diffusion coefficient D of Fc was determined by applying the Randles-Sevcik equation to the peak current in the cyclic voltammograms. The diffusion coefficient was found to be higher in a symmetric IL than in a non-symmetric IL with the same number of alkyl carbon atoms N, with the difference decreasing with increasing N. The diffusion of Fc in these ILs is well described by the Stokes-Einstein equation with slip boundary conditions, but with an effective hydrodynamic radius of 0.23 ± 0.01 nm, which is less than the 0.27 nm crystallographic radius of Fc, in agreement with previous studies of the diffusion of solutes in ILs that show the hydrodynamic radius to be less than the van der Waals radius of the solute.