Renormalization Group Adaptation to Equations of State From Molecular Simulation

• Published in: Industrial & engineering chemistry research 2013-05, Vol.52 (21), p.7030-7043
• Main Authors: Ghobadi, Ahmadreza F, Elliott, J. Richard
• Format: Article
• Language: English
• Subjects: Adaptation; Asymptotic properties; Chains; Density; Mathematical models; Methodology; Molecular weight; Simulation
• ISSN: 0888-5885; 1520-5045
• DOI: 10.1021/ie400500j

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 Z c = 0.2. Where experimental data for T c are available, deviations of the RG correlations are roughly 4 K, compared to 20 K for the classical implementation of TPT. Although White’s RG theory has a robust physical background, a number of limitations were noted during its adaptation to DMD/TPT, some of which are inherent in the method and unavoidable. To begin, the methodology is not readily adapted to the transferable site-based perspective implicit in molecular simulation models. Therefore, a procedure for translating from a site-based perspective to a segment-based perspective was developed. Second, it was noted that previous implementations resulted in binodal curves that were excessively “flat” in the critical region as chain length increased. An adaptation was made in the “t” exponent to eliminate anomalous behavior of long chains in the transition from the critical to the liquid regime. Regarding the implicit limitations, we note that White’s method alters the van der Waals loop inside the binodal in a destructive way, it requires at least three adjustable parameters that must be predicted for its implementation when experimental data are not available and it suffers from numerical limitations that hinder its application to compounds with relatively low critical pressure and density such as long chain n-alkanes.