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

Phys Chem Chem Phys. 2013 Jun 14;15(22):8821-30. doi: 10.1039/c3cp43306d. Epub 2013 May 2.

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 Vm,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 Vocc 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), R(2) = 0.981 and V(occ)(SL-EOS) ≈ 1.12 V(m,scaled), R(2) = 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.