(563f) Trends of Perturbation Terms for Polymers in the Critical Region

In this work, we have interpolated the results of discontinuous molecular dynamic (DMD) simulation at individual state points with a form that is applicable in the critical region. These results take the form of contributions to the Helmholtz energy expressed by thermodynamic perturbation theory (TPT). In performing the interpolation, a new functional form for second order perturbation term has been introduced and constraints on the first order term have been identified. The new form is tested using simulations of n-alkanes by means of transferable step potential of Unlu et al (2004) over a range of chain lengths from C3 (propane) to C80. The results can qualitatively reproduce the simulation results at small packing fractions (η) including critical packing fraction. Furthermore, it is consistent with the functional form applied to polyethylene by Elliott et al., 2005, whereas the older form was viable only at packing fractions higher than 0.3. With this result in hand, the generalized equation of state (EOS) is used to obtain analyze trends for critical temperature (Tc), critical pressure (Pc), and critical compressibility factor (Zc) of n-alkanes as a function of carbon number. These trends are analyzed relative to non-classical effects in the critical region and how experimental observations can be correlated quantitatively with molecular simulations of finite systems.