Equations of state for orthorhombic and triclinic lattices of polyethylene

P, V, T equations of state were theoretically constructed for the orthorhombic (o-PE) and triclinic modifications of polyethylene (t-PE). Helmholtz free energies A at arbitrary temperatures were calculated for the lattices with various unit cell dimensions. Contribution of the zero-point energy (for T=0 K) as well as of the phonon free energy (T〉 0 K) was evaluated directly from the density of states obtained by means of the normal coordinate treatment of the crystal lattices. The isotherms were obtained for various temperatures by numerical differentiation of A with respect to the unit cell dimensions. For the o-PE lattice the calculated volume thermal expansion at atmospheric pressure and the theoretical isotherms at room temperature agree well with the experimental results. The predicted anisotropy in linear thermal expansion as well as in linear compressibility, on the contrary, does not reproduce the experimental data. The calculated elastic moduli in the directions perpendicular to the c axis are in a good agreement with the values measured by x-ray diffraction method. The calculated Gibbs free energies of o-PE and t-PE were compared with each other for various temperatures and pressures, concluding that at atmospheric pressure o-PE is favored over t-PE in the temperature range higher than 130 K, and that the effect of hydrostatic pressure on the thermodynamic stability is not significant up to 10 kbar.