EQUATION OF STATE FOR LENNARD-JONES CHAINS

An equation of state for chains composed of tangent, freely jointed Lennard-Jones spheres is presented. The equation is based on a statistical mechanical description of polymerization that is based on Wertheim's theory of associating fluids. The Helmholtz free energy of a fluid of chains is expressed as the contribution from a monomeric reference fluid, which in this case is a fluid of Lennard-Jones spheres, plus a contribution due to bonding. The bonding term depends upon the number of monomers in a chain and the cavity correlation function of the reference fluid. We have performed molecular dynamics simulations of chain fluids composed of 2, 4, 12, 16, 18, 20, 50, and 100 spheres over the entire fluid density range at several temperatures and compared the results to the theory. The equation of state is found to be in good agreement with the simulation results, predicting pressures that are slightly too large overall. Internal energies are predicted well, except in the low-density region where the equation of state does not give the correct limiting value due to neglect of chain self-interaction.