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

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,V-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,V-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) approximate to 1.63 V-vdw, R-2 = 0.981 and V-occ(SL-EOS) approximate to 1.12 V-m,V-scaled, R-2 = 0.980). Finally, the usability of V-m,V-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,V-scaled within the context of the free volume.