Critique of the Free Volume Theory of the Liquid State

A deduction of the free volume theory of the liquid state from the general principle of statistical mechanics and certain well-defined approximations is undertaken. The Gibbs configuration integral is expressed as a sum of integrals corresponding to single and multiple occupancy of the cells of a reference lattice. The integral corresponding to single occupancy is evaluated with the approximate probability density, expressed as a product of functions of the coordinates of individual molecules, which leads to minimum free energy under the restraints of constant temperature and volume. The minimization of the free energy gives an integral equation for the probability density within each cell of the lattice. A first approximation of the solution of this equation yields a partition function identical with that of the Lennard-Jones-Devonshire free volume theory.