Modeling of the n–alkane homologous series in the range of C6 to C20 using linear Yukawa isotherm regularity (LYIR)

Abstract

The linear Yukawa isotherm regularity (LYIR) equation of state (EoS) was used to model the p–v–T behavior of n–alkane homologous series CnH2n+2 (6≤n≤20) in the dense fluid region. A molecular model was proposed and the LYIR EoS was modified based on this model to take the effects of segments of the chain molecule into account. In the proposed model, each n–alkane molecule was assumed as an n–fold tangentially one–center spherical segments. In the other word, the n–alkane fluid was considered as a hypothetical mixture of methyl and methylene groups. The average effective pair potential (AEPP) between two segments was modeled by the hard–core Yukawa (HCY) potential in the framework of liquid's thermodynamic perturbation theory (TPT). The experimental p–v–T data of the selected n–alkanes were used to evaluate the validity of the modified LYIR EoS (MLYIR). Four important conclusions were obtained in this work: (a) The average coordination number (z) in the hypothetical mixture depends on n as well as temperature (T) and molar density (ρ) so that its value increases and decreases for the odd and even values of n, respectively. (b) the effective HS diameter (σeff) of segment increases and decreases with the chain length for the n–alkanes with odd and even value of n, respectively, and become independent of the chain length for n>20. (c) The σeff of the n–alkanes with the even number of carbon atoms is greater than that of the molecules with the odd value of n for n<18. (d) The MLYIR EoS showed that the εeff and λeff of Yukawa AEPP for the segment–segment interaction are independent of the chain length. Moreover, the results demonstrated the relationship between the symmetry of chain structure and the value of σeff.