Renormalization Group Adaptation to Equations of State From Molecular Simulation

Abstract

We have previously demonstrated how combination of Discontinuous Molecular Dynamics (DMD) and Thermodynamic Perturbation Theory (TPT) can be employed to characterize the entire phase diagram from molecular simulations. Nevertheless, the precision of that characterization in the (nonanalytic) critical region is unavoidably limited by the analytic behavior inherent in TPT. In the present work, we adapt White’s Renormalization Group (RG) methodology to address this deficiency. We applied the DMD/TPT/RG methodology to n-alkanes ranging in molecular weight to 1122 (C80) with emphases on the asymptotic behavior in the long chain limit. Critical properties were estimated in the approach to the long chain limit whereas experimental measurements become sparse at molecular weights above 506 (C36). For example, the critical temperature of polyethylene is estimated at roughly 1300 K and we are able to speculate that the critical compressibility factor is lower than previous estimates of Zc = 0.2. Where experimental d...