Application of Cell Theory to Liquid Hydrocarbons

The cell theory in the formulation of Prigogine, Trappeniers, and Mathot and their assumptions are examined. The molecular volumes of n-paraffins of high molecular weight are well represented in terms of an energy and volume parameter characteristic of the repeating unit. Fairly good agreement for branched systems is also found on making the proper modifications in the equation of state. The resulting low temperature heats of vaporization seem reasonable. One can show that the theory leads to the Kurtz-Lipkin-Sankin relations and interprets, so far, for paraffins their K1 and K5. Isotherms up to about 1000 bars can be represented fairly satisfactorily, 80–90% of the total compression observed being accounted for. This applies to n-paraffins as well as polyethylene and, in a semiempirical manner, to polystyrene. The physical significance of the constants in the empirical Tait equation is explored. For large chain lengths C is a pure numeric and independent of structure and molecular weight, in qualitative conformity with experimental results. B is related to the ratio of characteristic energy and volume of the submolecule, or to the above parameter K1. These results argue in favor of extending the theory, so as to permit handling of a wider range of variables, and other types of molecules.