Orthorhombic phase of crystalline polyethylene: A Monte Carlo study

Abstract

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 N pT 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 ther-1 modynamic 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.

Numerical calculation of the melting phase diagram of low molecular-weight polyethylene

“…20,25 A number of more sophisticated phenomenological and ab initio potential models are available 26 which give better agreement for certain quantities when compared to the ''Flexible Williams'' potential. For example, Martonák et al 27 find better estimates for the crystal phase density and the lattice parameters than obtained in our simulations. Their potential model uses off diagonal bond-bond, bond-angle, and various angle-angle terms.…”

Crystalline Polyethylene Nanofibers with the Theoretical Limit of Young's Modulus

“…that the fi ber has an axial ( z direction) Young's modulus of 343 GPa (obtained from Figure 3 c) and that the Young's moduli in x and y directions are 9 GPa and 9.5 GPa, as obtained from theoretical predictions. [ 23,47,48 ] For an anisotropic PE fi ber with a center load of 150nN (Figure 4 b), the maximum defl ection of the middle point is 62 nm, as shown in the FEA simulation result (Figure 4 b). For an isotropic PE fi ber with the same dimensions, the maximum defl ection from the FEA simulation is 54.2 nm (Figure 4 c), which agrees well with the analytical solution (54.1 nm) and the experimental result shown in Figure 3 c. We note that the anisotropic model gives a defl ection 10% higher than the isotropic model and the analytical solution.…”

A comparison of computer models for the simulation of crystalline polyethylene and the long n-alkanes.

“…However, they failed to reproduce the higher temperature hexagonal or rotator phases, and their model suffered from excessive longitudinal diffusion of the chain stems. Other simulations based on the infinite chain model have been presented more recently [31,33,34]. Although the infinite chain model might be considered a useful model for extended chain crystals, it appears that the tight constraints placed on the chains by the boundary conditions will tend to limit the formation of conformational defects: the contraction of one chain relative to its neighbours is strongly inhibited, because the periodic bonding prevents any one chain from being shorter in the c direction than the others.…”