Crystal Poisson's Ratios of Polyethylene and Poly(vinylalcohol) Estimated by X-ray Diffraction Using the Ultradrawn Films

Abstract

The elastic compliances of polyethylene (PE) and poly(vinylalcohol) (PVA) crystals were measured by X-ray diffraction using the films prepared by gelation/crystallization from dilute solutions. The measurements were carried out at 20 °C for the PE and PVA films with elongation ratios of 60 and 11, respectively. For the PE films, the measurable compliances, and , were (−0.013 to −0.017) × 10-2 GPa-1 and (−0.040 to 0.043) × 10-2 GPa-1, respectively, while for the PVA films, they were −0.012 × 10-2 and (−0.037 to −0.038) × 10-2 GPa-1, respectively. From the above values, the corresponding Poisson's ratios, and , of PE crystals were estimated to be 0.029−0.038 and 0.090−0.096, respectively, while and , for PVA crystals are 0.026 and 0.081−0.083, respectively. A question can be arisen as to whether the crystal elastic compliance and Poisson's ratio as measured by X-ray diffraction are equal to the corresponding intrinsic values. To check this, a mathematical representation based on a linear elastic theory was proposed by which one may investigate the dependence of the crystal Poisson's ratios on molecular orientation and crystallinity. The mathematical description indicated that the crystal Poisson's ratio as estimated by X-ray diffraction are essentially different from the intrinsic crystal Poisson's ratios. Even so, the numerical calculations indicated that the values as measured by X-ray diffraction are equal to the intrinsic values, if the morphology of test specimens can be represented as a parallel model for composite of the crystal and amorphous phases, approximately.

Effects of Finite Lengths of Chains on the Structural and Mechanical Properties of Polyethylene Fibers

“…The unit cell strain of b decreased faster than that of a . This is consistent with the relative magnitudes of Poisson’s ratios in two different directions estimated from the experiment . Profiles of unit cell strains of a and b with the PE fiber model with finite chains are also shown in Figure a.…”

“…This is consistent with the relative magnitudes of Poisson's ratios in two different directions estimated from the experiment. 30 Profiles of unit cell strains of a and b with the PE fiber model with finite chains are also shown in Figure 4a. Before the yield strain, unit cell strains of a and b with the PE fiber model followed similar patterns observed in the crystalline PE without chain ends.…”

Multiscale Structure and Microscopic Deformation Mechanisms of Gel-Spun Ultrahigh-Molecular-Weight Polyethylene Fibers

“…Among others, Tashiro et al reports lattice direction-dependent estimations: ν ac i = 0.06 and ν bc i = 0.20. However, as pointed out by Xu and Matsuo, these intrinsic values do not reflect the deformation behavior of the actual crystals (examined in an X-ray experiment). In fact, in reality, crystals have finite dimensions and, most importantly, their deformation is impaired by the connections (tie molecules) to the surrounding amorphous phase.…”

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.…”