Empirical Determination of the Pressure–Volume– Temperature–Entropy Equation of State of Polyethylene in Isothermal, Isobaric and Isochoric Ensembles: II. Correlation Between the Equations of State in the Various Ensembles

Abstract

The pressure–volume–temperature–entropy equations of state, P–V–T–S Eos, of polyethylene (PE) for its isothermal, isobaric and isochoric ensembles were reported in our previous report (Part 1). In this report the correlation between the P–V–T–S Eos in the various ensembles was analyzed quantitatively where it was found that the three dimensional P–T–V plane for the P_T–T–V_T Eos in the isothermal ensemble was almost the same as that for the P–T_P–V_P Eos in the isobaric ensemble, while the 3D T–P–S plane for the T–P_T–S_T Eos in the isothermal ensemble was almost the same as that for the T_P–P–S_P Eos in the isobaric ensemble where the subscript of _T and _P mean isothermal and isobaric ensembles, respectively. The isothermal bulk modulus, ${\kappa }_T,$ and its first and second pressure derivatives ${(\frac{\partial {\kappa }_T}{\partial P})}_T,$ and ${(\frac{{\partial }^2{\kappa }_T}{\partial P^2})}_T,$ were calculated and it was found that the 3D T–P_T–${\kappa }_T$ plane in the isothermal ensemble was almost the same as that for the T_P–P–${\kappa }_T$ in the isobaric ensemble, and the 3D T–P_T–${(\frac{\partial K_T}{\partial P})}_T$ plane in the isothermal ensemble was different only slightly from the 3D T_P–P–${(\frac{\partial K_T}{\partial P})}_T$ plane in the isobaric ensemble, while a considerable difference was observed between the 3D T–P–${(\frac{{\partial }^2{K}_T}{\partial P^2})}_T$ planes for the isothermal and isobaric ensembles.

Keywords:

• equation of state
• isobaric
• isochoric
• isothermal
• polyethylene