The Vibrational Spectrum and Ultimate Modulus of Polyethylene

• Published in: Macromolecules Vol. 39; no. 7; pp. 2683 - 2690
• Main Authors: Barrera, Gustavo D, Parker, Stewart F, Ramirez-Cuesta, Anibal J, Mitchell, Philip C. H
• Format: Journal Article
• Language: English
• Published: Washington, DC American Chemical Society 04.04.2006
• Subjects: Applied sciences; Exact sciences and technology; Mechanical properties; Organic polymers; Physicochemistry of polymers; Properties and characterization; Vibrational transition; Elastic modulus; Polyethylene; Crystalline polymer; Lattice dynamics; Mechanical properties; Theoretical study; Density functional method; Generalized gradient approximation; Ab initio calculations; Orthorhombic crystals; Local density approximation
• ISSN: 0024-9297; 1520-5835
• DOI: 10.1021/ma052602e

We have performed the first completely ab initio lattice dynamics calculation of the full orthorhombic cell of polyethylene using periodic density functional theory in the local density approximation (LDA) and the generalized gradient approximation (GGA). Contrary to current perceptions, we show that LDA accurately describes the structure whereas GGA fails. We emphasize that there is no parametrization of the results. We then rigorously tested our calculation by computing the phonon dispersion curves across the entire Brillouin zone and comparing them to the vibrational spectra, in particular the inelastic neutron scattering (INS) spectra, of polyethylene (both polycrystalline and aligned) and perdeuteriopolyethylene. The Γ-point frequencies (where the infrared and Raman active modes occur) are in good agreement with the latest low temperature data. The near-perfect reproduction of the INS spectra, gives confidence in the results and allows us to deduce a number of physical properties including the elastic moduli, parallel and perpendicular to the chain. We find that the Young's modulus for an infinitely long, perfectly crystalline polyethylene is 360.2 GPa at 0 K. The highest experimental value is 324 GPa, indicating that current high modulus fibers are ∼90% of their maximum possible strength.