Solvation and Association of 3:1 Electrolytes in <i>N</i>,<i>N</i>‑Dimethylformamide

A detailed study has been made of the solvation and ion association of the trifluoromethanesulfonate (Tf^–) salts of aluminum­(III), scandium­(III), and lanthanum­(III) in <i>N</i>,<i>N</i>-dimethylformamide (DMF) at 25 °C using dielectric relaxation spectroscopy over the frequency range of 0.1 ≲ ν/GHz ≤ 89. The spectra of all solutions exhibited either two (for ScTf₃ and LaTf₃) or three (for AlTf₃) relaxation processes, a dominant mode centered at ∼15 GHz due to the solvent and one or (for AlTf₃ solutions) two solute-related processes at lower frequencies (ν_max ≲ 2 GHz). Effective solvation numbers, <i>Z</i>_ib, calculated from the solvent relaxation process indicated that all three cations were strongly solvated by DMF with <i>Z</i>_ib⁰ values at infinite dilution in the order (Al³⁺ ≈ Sc³⁺ ≈ 10) < (La³⁺ ≈ 13), consistent with at least partial formation of a second solvation shell around each cation. One solute-related mode for each set of salt solutions was assigned to the rotational diffusion of solvent-shared ion pairs (SIPs) of 1:1 stoicheometry; the additional slower process for AlTf₃ solutions in DMF was attributed to the presence of double-solvent-separated IPs. The overall association constants at infinite dilution for the 1:1 IPs, <i>K</i>_A°(MTf²⁺), were significant, but as expected from Debye–Hückel considerations, the <i>K</i>_A values decreased rapidly with increasing solute concentration