Orthorhombic Phase of Crystalline Polyethylene: A Monte Carlo Study

In this paper we present a classical Monte Carlo simulation of the orthorhombic phase of crystalline polyethylene, using an explicit atom force field with unconstrained bond lengths and angles and periodic boundary conditions. We used a recently developed algorithm which apart from standard Metropolis local moves employs also global moves consisting of displacements of the center of mass of the whole chains in all three spatial directions as well as rotations of the chains around an axis parallel to the crystallographic c-direction. Our simulations are performed in the NpT ensemble, at zero pressure, and extend over the whole range of temperatures in which the orthorhombic phase is experimentally known to be stable (10 - 450 K). In order to investigate the finite-size effects in this extremely anisotropic crystal, we used different system sizes and different chain lengths, ranging from C_12 to C_96 chains, the total number of atoms in the super-cell being between 432 and 3456. We show here the results for structural parameters, such as the orthorhombic cell parameters a,b,c, and the setting angle of the chains, as well as internal parameters of the chains, such as the bond lengths and angles. Among thermodynamic quantities, we present results for thermal expansion coefficients, elastic constants and specific heat. We discuss the temperature dependence of the measured quantities as well as the related finite-size effects. In case of lattice parameters and thermal expansion coefficients, we compare our results to those obtained from other theoretical approaches as well as to some available experimental data. We also suggest some possible ways of extending this study.Comment: 27 pages, RevTex, 24 figures, submitted to Journal of Chemical Physic

Orthorhombic Phase of Crystalline Polyethylene: A Constant Pressure Path Integral Monte Carlo Study

In this paper we present a Path Integral Monte Carlo (PIMC) simulation of the orthorhombic phase of crystalline polyethylene, using an explicit atom force field with unconstrained bond lengths and angles. This work represents a quantum extension of our recent classical simulation (J. Chem. Phys. 106, 8918 (1997)). It is aimed both at exploring the applicability of the PIMC method on such polymer crystal systems, as well as on a detailed assessment of the importance of quantum effects on different quantities. We used the $NpT$ ensemble and simulated the system at zero pressure in the temperature range 25 - 300 K, using Trotter numbers between 12 and 144. In order to investigate finite-size effects, we used chains of two different lengths, C_12 and C_24, corresponding to the total number of atoms in the super-cell being 432 and 864, respectively. We show here the results for structural parameters, like the orthorhombic lattice constants a,b,c, and also fluctuations of internal parameters of the chains, such as bond lengths and bond and torsional angles. We have also determined the internal energy and diagonal elastic constants c_11, c_22 and c_33. We discuss the temperature dependence of the measured quantities and compare to that obtained from the classical simulation. For some quantities, we discuss the way they are related to the torsional angle fluctuation. In case of the lattice parameters we compare our results to those obtained from other theoretical approaches as well as to some available experimental data. In order to study isotope effects, we simulated also a deuterated polyethylene crystal at a low temperature. We also suggest possible ways of extending this study and present some general considerations concerning modeling of polymer crystals.Comment: 18 pages, RevTex, 18 figures, 3 tables, submitted to Phys. Rev.