Comment on “Negative effective Li transference numbers in Li salt/ionic liquid mixtures: does Li drift in the “Wrong” direction?” by M. Gouverneur, F. Schmidt and M. Schönhoff, Phys. Chem. Chem. Phys., 2018, 20, 7470

Gouverneur et al. have recently reported “effective transport numbers” for mixtures of lithium and 1-ethyl-3-methylimidazolium salts with common (fluorinated) anions using 7Li, 1H and 19F and electrophoretic NMR to determine the electrophoretic mobilities of all three ionic species. The “effective transport number” for lithium is small, but negative. From this they deduce that the Li+ ions are each associated with two or more anions to form negatively charged complexes. However this interpretation may be incorrect: only a single independent transport number can be measured in such a system as the three ion fluxes are not independent. One ion flow must define the reference frame and then the transport numbers for the other two ions must sum to unity. Electrophoretic NMR appears to produce what are called “external” ion mobilities and transport numbers in the notation used by Klemm and Haase for molten salts. These are defined in the laboratory frame of reference and can depend on the boundary conditions of the experiment. Simple relations exist for their conversion to “internal” transport numbers where ion mobilities for two ions are given relative to that of the third, analogous to the more familiar Hittorf transport numbers of ions in electrolyte solutions which are given in the “solvent-fixed” frame of reference, i.e. relative to the flow of solvent. It is not unusual for a cation external transport number to be negative in molten salt mixtures, e.g. (LiNO3 + AgNO3) in a Hittorf experiment employing nitrate electrodes whereas true ion association would produce negative internal transport numbers. In the examples studied by Gouverneur et al. the cation internal transport numbers are both positive. Those for Li+ are also very small, and close to zero within experimental error. This may simply reflect that the mixtures employed are dilute in lithium ions.