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 [R. Marto\ifmmode \check{n}\else \v{n}\fi{}\'ak et al., 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 $\mathrm{NpT}$ ensemble and simulated the system at zero pressure in the temperature range 25\char21{}300 K, using Trotter numbers between 12 and 144. In order to investigate finite-size effects, we used chains of two different lengths, ${\mathrm{C}}_{12}$ and ${\mathrm{C}}_{24},$ corresponding to the total number of atoms in the supercell 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 the 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 low temperature. We also suggest possible ways to extend this study and present some general considerations concerning modeling of polymer crystals.