Crystalline Moduli of Polymers, Evaluated from Density Functional Theory Calculations under Periodic Boundary Conditions.

Taiga Kurita,Yuichiro Fukuda,Morihiro Takahashi,Yuji Sasanuma

doi:10.1021/acsomega.8b00506

Abstract

A theoretical methodology based on quantum chemistry to calculate mechanical properties of polymer crystals has been developed and applied to representative polymers. By density functional theory calculations including a dispersion force correction under three-dimensional periodic boundary conditions, crystal structures of poly(methylene oxide) (PMO), polyethylene (PE), poly(ethylene terephthalate) (PET), poly(trimethylene terephthalate) (PTT), and poly(butylene terephthalate) (PBT) were optimized and their mechanical properties, such as crystalline moduli and linear and volume compressibilities, were calculated. The optimized crystal structures were proved to be fully consistent with those determined by X-ray and neutron diffraction. The crystalline moduli (E∥) parallel to the chain axis were calculated to be 114 GPa (PMO), 333 GPa (PE), 182 GPa (PET), 7.1 GPa (PTT), and 20.8 GPa (PBT) and compared with those determined from X-ray diffraction, Raman spectroscopy, and neutron inelastic scattering experiments. Herein, the E∥ values thus determined are interpreted in terms of conformational characteristics of the polymeric chains and the validity of the homogeneous stress hypothesis adopted in the X-ray diffraction method is also discussed.

Highlights

Mechanical properties are crucial characteristics of polymeric materials, especially from a practical viewpoint
Polymer crystals exhibit the largest modulus in the chain axis direction; the crystalline modulus (E∥) parallel to the chain axis at 0 K may correspond to the ultimate hardness expected from the polymer
The poly(methylene oxide) (PMO) whisker is expected to give the true crystalline moduli directly; the whisker crystal itself is so small that it has to be embedded in resin matrices and undergo the mechanical measurements and Young’s modulus (E∥) of the whisker at room temperature was indirectly evaluated to be about 100 GPa.[34]

Summary

Introduction

Mechanical properties are crucial characteristics of polymeric materials, especially from a practical viewpoint. Solid polymers are composed of crystalline and amorphous regions, and the former is more rigid than the latter. By reference to the ultimate modulus, one can determine whether the polymer is suitable for one’s practical application and estimate how much the mechanical properties will be improved by processings such as stretching and annealing. It is of particular significance to determine the crystalline moduli of polymers as precisely as possible. The E∥ values of polymers have been estimated by experiments such as X-ray diffraction, Raman spectroscopy, and neutron inelastic scattering (NIS).[1,2] For example, the E∥ value of polyethylene (PE) has been reported as 150−254 GPa (Xray), 260−358 GPa (Raman), and 329 GPa (NIS)

Methods

Results

Conclusion