Determination of Mean Square Displacements of Polyethylene Molecules in Crystal Lattice

Abstract

X-Ray scattering intensities of bulk crystallized polyethylene were measured at temperatures from −165°C to 120°C. Mean square displacements of carbon atoms from their average locations were represented by the symmetric tensor U having four independent elements, Uaa, Ubb, Ucc, and Uab. These elements and the atomic coordinates were determined as a function of temperature by the least square method. The displacement of the carbon atom was a maximum in the direction perpendicular to the skeletal zigzag plane. The minimum displacement was found in the direction along the the molecular axis. The mean square displacements of atoms were separated into contributions from the molecular vibration and the lattice imperfection by extrapolating the elements of tensor U to the temperature of absolute zero. The amplitudes of molecular vibration obtained by X-ray measurements agreed fairly well with the theoretical values calculated on the assumption of the harmonic oscillator model by Kitagawa and Miyazawa at the temperatures below 0°C. The atomic coordinates did not change below 0°C. The skeletal plane of polyethylene molecule tended to deflect slightly toward the a axis above 0°C with increasing temperature.