Scaling laws for the equation of state of flexible and linear tangent hard sphere chains

The influence that molecular flexibility has on the phase diagram and equation of state of hard sphere chains is examined. In the isotropic phase the equation of state is insensitive to flexibility; rigid chains display the same equation of state as flexible chains. However, with the onset of liquid crystalline phases for rigid molecules this similarity disappears. Differences are also apparent between the rigid and flexible models in the solid phase. Wertheim's thermodynamic perturbation theory has been extended to describe the solid phase of fully flexible chains and excellent agreement with simulation results is seen. A scaling is proposed that, when applied to the fully flexible model, reproduces simulation results for a linear rigid model. It is shown that for the fully flexible model the compressibility factor for the fluid and solid phases scale with the number of monomers m. The compressibility factor for the linear model scales with m in the isotropic fluid, and becomes independent of m in the nematic, smectic, and solid phases.