Variational theory for Lennard-Jones chains

The Helmholtz energy and pressure for Lennard-Jones chains are derived using a variational first-order perturbation theory. The reference system, comprising freely jointed tangent hard-sphere chains is solved in the Percus-Yevick approximation. The optimal diameter of segments in the hard-sphere chain reference is determined by minimizing the free energy through the Gibbs-Bogoliubov inequality. Unlike previous perturbation theories for non-aggregated Lennard-Jones spheres, the resulting hard-sphere segment diameter depends on chain length in addition to density and temperature. The resulting theory exhibits excellent agreement with MC simulation, over a wide range of conditions, without adjustable parameters.