Free volume in ionic liquids: a connection of experimentally accessible observables from PALS and PVT experiments with the molecular structure from XRD data

Abstract

In the current work, free volume concepts, primarily applied to glass formers in the literature, were transferred to ionic liquids (ILs). A series of 1-butyl-3-methylimidazolium ([C₄MIM]⁺) based ILs was investigated by Positron Annihilation Lifetime Spectroscopy (PALS). The phase transition and dynamic properties of the ILs [C₄MIM][X] with [X]⁻ = [Cl]⁻, [BF₄]⁻, [PF₆]⁻, [OTf]⁻, [NTf₂]⁻ and [B(hfip)₄]⁻ were reported recently (Yu et al., Phys. Chem. Chem. Phys., 2012, 14, 6856–6868). In this subsequent work, attention was paid to the connection of the free volume from PALS (here the mean hole volume, 〈v_h〉) with the molecular structure, represented by volumes derived from X-ray diffraction (XRD) data. These were the scaled molecular volume V_m,scaled and the van der Waals volume V_vdw. Linear correlations of 〈v_h〉 at the “knee” temperature (〈v_h〉(T_k)) with V_m,scaled and V_vdw gave good results for the [C₄MIM]⁺ series. Further relationships between volumes from XRD data with the occupied volume V_occ determined from PALS/PVT (Pressure Volume Temperature) measurements and from Sanchez–Lacombe Equation of State (SL-EOS) fits were elaborated (V_occ(SL-EOS) ≈ 1.63 V_vdw, R² = 0.981 and V_occ(SL-EOS) ≈ 1.12 V_m,scaled, R² = 0.980). Finally, the usability of V_m,scaled was justified in terms of the Cohen–Turnbull (CT) free volume theory. Empirical CT type plots of viscosity and electrical conductivity showed a systematic increase in the critical free volume with molecular size. Such correlations allow descriptions of IL properties with the easily accessible quantity V_m,scaled within the context of the free volume.