Polyethylene elastic stiffness constants

Table 8.3 Elastic stiffness constants for crystaJline polyethylene (CPa).

The results of such calculations for semi-crystalline polyethylene have been reviewed elsewhere [37]. A rather wide range of predicted values is obtained, due to the choice of force constants and also to sensitivity to detailed assumptions on the unit cell structure. In spite of these limitations the principal predictions for the elastic anisotropy are clear. These include the anticipated high values for C33 and the very low values for the shear stiffnesses C44, C55 and cee, which reflect the major differences between bond stretching and bond bending forces that control C33 and the intermolecular dispersion forces that determine the shear stiffnesses. It is therefore of value to compare such theoretical results with those obtained experimentally. Table 7.3 shows results for polyethylene where data for the orthorhombic unit cell at 300 K are used to calculate these constants for an equivalent fibre (Voigt averaging procedure see Section 7.5.2 below) compared with ultrasonic data for a solid sheet made by hot compaction. It can be seen that... 

It can be seen that a rather wide range of predicted values is obtained that is partly due to choice of different force constants. The results are also sensitive to the details of the assumed crystal unit cell structure, especially the angle made by the plane of the planar zigzag polyethylene chain with the b-axis of the orthorhombic unit cell. The overall pattern of elastic anisotropy is however clear. The stiffness in the chain axis direction C33 is by far the greatest value, and the shear stiffnesses C44, C55 and Cee are the lowest values. This reflects the major differences between the intramolecular bond stretching and valence bond bending forces and the intermolecular dispersion forces, which determine the shear stiffnesses. The lateral stiffnesses also relate primarily to dispersion forces and are correspondingly low. 

Finally, it is of interest to compare the theoretical values for a uniaxially oriented sheet (calculated by averaging the stiffness values using the Voigt averaging scheme) with those obtained for a die-drawn rod and a sheet made by hot compaction of high modulus polyethylene fibres (Table 8.4). It can be seen that although, as expected, these materials have not reached full axial orientation so that the experimental values of C33 are much less than the theoretical value, the patterns of anisotropy are very similar, and some of the values for the other elastic constants are surprisingly close. 

The high axial elastic modulus of polyethylene and polyamide 6 is due to the fact that these polymers have a preferred conformation that is fully extended, i.e. all-trans. The elastic deformation is caused by the deformation of bond angles and by bond stretching, both showing high elastic constants. Isotactic polypropylene and polyoxymethylene crystallize in helical conformations and therefore exhibit a maximum stiffness which is only 20% of the maximum stiffness of the all-trans polymers. The elastic deformation of a helical chain involves, in addition to the deformation of bond angles and bond stretching, deformation by torsion about the G bonds. The latter... 

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