Correlation between surface tension and void fraction in ionic liquids

An effort to systematize published and new data on the surface tension gamma of ionic liquids (ILs) is based on the hypothesis that the dimensionless surface tension parameter gamma V-v(2/3)/kT is a function of the void fraction x(v) = V-v/V-m. The void volume V-v is defined as the difference between the liquid volume V-m occupied by an ion pair (known from cationic and anionic masses and liquid density measurements) and the sum V+ + V- of the cationic and anionic volumes (known from crystal structures), while kT is the thermal energy. Our hypothesis that gamma V-m(2/3)/kT = G(x(v)) is initially based on cavity theory. It is then refined based on periodic lattice modeling, which reveals that the number N of voids per unit cell (hence the dimensionless surface tension) must depend on xv. Testing our hypothesis against data for the five ILs for which surface tension and density data are available over a wide range of temperatures collapses all of these data almost on a single curve G(x(v)), provided that slight (4%) self-consistent modifications are introduced on published crystallographic data for V+ and V-. An attempt to correlate the surface tension vs temperature data available for inorganic molten salts is similarly successful, but at the expense of larger shifts on the published ionic radii (8.8% for K; 3.3% for I). The collapsed G(x(v)) curves for ILs and inorganic salts do not overlap anywhere on x(v) space, and appear to be different from each other. The existence of a relation between gamma and x(v) is rationalized with a simple capillary model minimizing the energy. Our success in correlating surface tension to void fraction may apply also to other liquid properties.