Entropy of attractive forces and molecular nonsphericity in real liquids: A measure of structural ordering

Attempts are made to unravel the entropy of real liquids into its component parts, a topic of general interest in liquid chemistry. The method is based on a comparison of the experimentally-determined entropies of vaporization of a liquid with the entropies of vaporization calculated using three different models for the reference systems: (I) hard spheres, (II) dipolar hard spheres, and (III) dipolar-polarizable hard spheres. For the first and second reference systems, accurate equations of state are known. In the third case, a somewhat less accurate expression based on the mean spherical approximation (MSA) is available. The calculations are performed on a set of 87 liquids covering most of the chemically relevant solvent classes. The excess entropies thus calculated are a measure of the degree of order in real liquids, above that in the corresponding reference system. This excess order is the result of attractive forces (as in the case of strongly dipolar or associated liquids) as well as more efficient packing of elongated molecules, relative to hard spheres (as is the case for compounds containing longer hydrocarbon chains). The appreciable excess entropy of the longer-chain hydrocarbons, however, cannot be explained solely in terms of nonsphericity of the repulsive core. Other effects have to be invoked such as the intertwining of the chains. The numerical values of all the excess entropies are critically dependent on the choice of the hard sphere diameter σ, given that the molecules to be modeled are neither hard nor spherical. A method that uses the liquid isothermal compressibility as the parameter probing intermolecular repulsion as a route to the determination of σ is employed and found to be consistent with an independent route based on inert gas solubilities.