In this work, relationships between the free volume and various fundamental physical properties (density, surface tension and transport properties) of ionic liquids were investigated. Two imidazolium ionic liquids 1-butyl-3-methylimidazolium tris(pentafluoroethyl)trifluoro phosphate ([C4MIM][FPI]) and 1-butyl-3-methylimidazolium bis[bis(pentafluoroethyl)phosphinyl]imide ([C4MIM][FPI]) were measured by positron annihilation lifetime spectroscopy (PALS). Changes of the ortho-positronium lifetime (o-Ps) with different states (amorphous and crystalline) were depicted as completely as possible. The mean local free (hole) volume < v(h)> was calculated from the o-Ps lifetime in amorphous state for the samples. Comparison between < v(h)> and specific volume obtained from the temperature dependent mass density gave the specific hole densities N-f and the occupied volumes V-occ. Thermal expansion of hole volume was compared with molecular volume V-M of [C4MIM][FAP] and [C4MIM][FPI] as well as five other ionic liquids from our previous works, a monotonically increasing correlation between the two quantities was displayed. Hole volume of [C4MIM][FAP] sample from PALS experiment was compared with the result from surface tension according to Furth hole theory, good agreement exhibited. The free volume obtained from this work was applied to Cohen-Turnbull fitting of viscosity for [C4MIM][FPI] sample. The influence of the free volume to transport properties was investigated by the comparison of < v(h)>/V-M with the viscosity and conductivity for various ionic liquids. Correlation between the free volume and the molecular volume of ionic liquids was explained by a schematic free volume model. (C) 2013 Elsevier B.V. All rights reserved.