An analysis of radical diffusion in ionic liquids in terms of free volume theory

The Heisenberg spin exchange-dipole-dipole separation method was used to measure the translational diffusion coefficients of the ¹⁴N-labeled perdeuterated 2,2,6,6-tetramethyl-4-oxopiperidine-1-oxyl (¹⁴N-pDTEMPONE) nitroxide spin probe as a function of temperature in two methylimidazolium ionic liquid series, one based on the tetrafluoroborate (BF₄) anion and another one on the bis(trifluoromethane)sulfonimide (TFSI, Tf2N) anion. The obtained translational diffusion coefficients of ¹⁴N-pDTEMPONE were analyzed in terms of the Cohen-Turnbull free volume theory. It was found that the Cohen-Turnbull theory describes, exceptionally well, the translational diffusion of ¹⁴N-pDTEMPONE in all the ionic liquids in the measured temperature range. In addition, the Cohen-Turnbull theory was applied to the viscosity and self-diffusion coefficients of the cation and anion-taken from literature-in the same ionic liquids. The critical free volume for the self-diffusion of the cation and anion in a given ionic liquid is the same, which suggests that the diffusion of each ionic pair is coordinated. The critical free volumes for the ¹⁴N-pDTEMPONE diffusion, self-diffusion, and viscosity for a given cation were about 20% greater in the TFSI based ionic liquids than in the BF₄ based ionic liquids. It appears that the ratio of the critical free volumes for a given cation between the two series correlates with the ratio of their densities.