(128d) On the Critical Properties of n-Alkanes At Long Chain Limit Using White's Renormalization Group Theory

An effective combination of Discontinuous Molecular Dynamics (DMD) and second order Thermodynamic perturbation Theory (TPT) can be employed to simulate the entire Equation of State (EOS) of pure components and also to offer a rigorous procedure to evaluate the perturbation contributions of any SAFT-like EOS. Based on DMD/TPT methodology, Elliott and Gray (The Journal of Chemical Physics, 123, 184902, 2005) proposed a correlation for n-alkanes viable at high packing fractions. Recently, Ghobadi and Elliott (Fluid Phase Equilibria, article in press, 2011) extended the application of this correlation to low density limit including the critical point region.

The improved correlation, named as SPEAD11, is used to study the effect of chain length on the critical properties of n-alkanes. Classically, it has been known for several years that at long chain limit, critical temperature and compressibility factor lean to a finite number while critical pressure and density tends to zero. But, the non-classical behavior at the long chain limit has remained as a mystery. To tackle this problem, White’s renormalization group theory is applied on SPEAD11 to calculate the critical properties as well as vapor pressure and binodal of pure n-alkanes. It is demonstrated that although the White’s method offers a physical and efficient tool to obtain the non-classical behavior of small molecules in the critical point vicinity, it would not be valid as the number of carbons exceeds 30. The binodal shape gets too flat in the critical region and the uncertainty of the predicted critical density becomes substantially large. These observations are partly attributed to the numerical nature of White’s method and the critical solver. Some corrections are suggested to improve these deficiencies and to broaden the applicability of White’s method to C₆₀H₁₂₂. By taking these results into consideration, a reasonable estimation for the critical properties and scaling trends of n-alkanes at the long chain limit are presented and compared to corresponding predictions available in the literature.