Thermodynamic perturbation theory coefficients for hard spherocylinders and cylinders

Thermodynamic perturbation theories are indispensable in the development of equations of state based on Statistical Mechanics. Recently, a new statistical thermodynamic model has been proposed in which molecules are represented as cylindrically symmetric hard bodies (ellipsoids of revolution, spherocylinders, and cylinders) interacting with identical neighboring molecules through a spherically symmetric square-well potential. This novel equation of state embeds at least two approximations to the Onsager's second virial theory: one restrains the equation of state to systems with an isotropic (disordered) orientation distribution, while the other decouples the translational and orientational degrees of freedom, being only valid at low densities. Using canonical Monte Carlo simulations, we investigated the feasibility of such approximations by determining the uniaxial nematic order parameter of the systems and calculating the first- and second-order perturbation coefficients of the hightemperature series expansion (HTSE) of the Helmholtz free energy. Our results indicate that both approximations are reasonable for a certain range of packing fractions and molecular anisotropies. We have also calculated the full Helmholtz free energy of the perturbed system, which can be used for determining high-order perturbation terms to improve the predictive capability of the equation of state.