A comparison of quasi-harmonic lattice dynamics and Monte Carlo simulation of polymeric crystals using orthorhombic polyethylene

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Abstract
The temperature dependence of lattice parameters,elastic constants and other physical properties of crystalline polyethylene at zero pressure in the orthorhombic phase is discussed. Two complementary approaches, self-consistent quasi-harmonic lattice dynamics and Monte Carlo simulation, both of which are predicated on the use of empirical force fields to describe the interatomic potentials, are critically compared. Both techniques are studied in their classical and quantum mechanical versions, to assess the accuracy and limitations of each method. Particular attention is paid to the classical approximation, the onset of anharmonicities in dynamical behavior which are not captured by the quasi-harmonic approximation, and finite size effects. It is shown that quantum effects are important throughout the range of temperatures 0⩽T⩽300 K. At temperatures below about 2 3 of the melting temperature (i.e., 250 K for polyethylene) the two approaches yield consistent results in both classical and quantum mechanical cases for a given empirical force field, provided that finite size effects are avoided. Above 300 K, anharmonic effects become quite pronounced. The combined treatment of these effects in the framework of path integral Monte Carlo (PIMC) pushes the limits of current computational feasibility, due to simulation sizes required. Guidelines are offered for choosing between classical simulations, quasi-harmonic methods, and full path integral Monte Carlo simulation.