Second virial coefficient of rod-shaped molecules and molecular dynamics simulations of the isotropic phase

The second virial coefficient, B(2) is computed of linear rigid rods composed of m equally spaced sites interacting with sites on other rods via the hard-sphere or Weeks-Chandler-Andersen (WCA) pair potentials. The dependence of B(2) on a wide range of separation distance between the sites L and m for both types of potential is computed. Molecular dynamics simulations were carried out of the thermodynamic, static, and percolation properties of the WCA rigid rods in the isotropic phase as a function of rod number density ρ. Simple scaling relationships are discovered between thermodynamic and other static properties as a function of ρ and m, which extend well into the semidilute density range. The percolation threshold distance (PTD) between the centers of mass of the rods complies well with a mean-field random orientation approximation from low density well into the semidilute regime. The corresponding site-site PTD proved more problematic to represent by simple functions, but at high rod density, scales better with the number of sites density rather than the rod number density.