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The Helmholtz free energy,  A , and the Gibbs free energy,  G , of polyethylene (PE) were determined based on its empirical pressure–volume–temperature–entropy equation of state,  P-V-T-S  Eos, and the empirical partition function, which we reported previously. The  P A -V A -T A -S AEos for the iso-Helmholtz free energy, iso- A , was determined based on the  P-V-T-S  Eos where the pressure ( P A), volume ( V A), temperature ( T A), and entropy ( S A) satisfied the condition that  A  is constant. The  P G -V G -T G -S GEos for the  G  being constant was also determined based on the  P-V-T-S  Eos. The three-dimensional (3D) plots, 3D plot, with the three axes,  x = T A , y = P A , z = V Aexpressed by the 3D ( T A,  P A,  V A) and the 3D ( T A , V A,  S A) at constant  A  in PE were determined, where the iso- A  processes were characterized assuming that the volume and the entropy in the iso- A  process decreased with increasing pressure and temperature, while in the 3D ( T G , P G,  V G) and  3 D ( T G , V G,  S G) plots at constant  G  in PE, the volume and the entropy in the iso- G  process were increasing with increasing pressure and temperature. The empirical partition function for the Helmholtz free energy was expressed by the summation of the terms of  T ,  T2 , and  T4, the Boltzmann factorswith  i  = 1, 2, 3, and 6 andand the  U ( V , T  = 0 K) term for the zero Kelvin internal energy where the  T4  term and the Boltzmann factorswith  i  = 6 and 3 were dominant negative factors in the  A - T  relation at the constant  V  = 1.04 cm 3 /g. In case of the Gibbs free energy where the partition function was expressed by the summation of the terms of  T ,  T2 , and  T4, the Boltzmann factorswith  i  = 1, 2, 3, and 6, the  U ( V , T  = 0 K) term,  PV  and  PV ( T  = 0) terms, the T 2  term and the Boltzmann factorswith  i  = 6 and 3 were dominant negative factors in the  G - T  relation at 1 atm (1.01 × 10 −4  GPa), while at high pressure, 1.0 GPa, the  PV  and  PV ( T  = 0) terms were dominant positive factors.

journal of macromolecular science, part b

Empirical Determination of the Helmholtz Free Energy and the Gibbs Free Energy of Polyethylene Based on the Pressure–Volume–Temperature–Entropy Equation of State and the Partition Function