Question 16.7: Impact Resistant Polyethylene A new grade of flexible, impac......
Impact Resistant Polyethylene
A new grade of flexible, impact-resistant polyethylene for use as a thin film requires a density of 0.88 to 0.915 g/cm³. Design the polyethylene required to produce these properties. The density of amorphous polyethylene is about 0.87 g/cm³.
To produce the required properties and density, we must control the percent crystallinity of the polyethylene. We can use Equation 16-4
% Crystalline = \frac{ρ_{c}(ρ \ – \ ρ_{a})}{ρ (ρ_{c} \ – \ ρ_{a})}× 100 (16-4)
to determine the crystallinity that corresponds to the required density range. To do so, however, we must know the density of completely crystalline polyethylene. We can use the data in Figure 16-15 and Table 16-6 to calculate this density if we recognize that there are two polyethylene repeat units in each unit cell.
ρ_{c} = \frac{ (4 \ C \ atoms)(12 \ g/mol) \ + \ (8 \ H \ atoms)(1 \ g/mol)}{(7.41 × 10^{-8} \ cm)(4.95 × 10^{-8} \ cm)(2.55 × 10^{-8} \ cm)(6.022 × 10^{23} \ atoms/mol)}
= 0.9942 g/cm³
We know that ρ_{a} = 0.87 g/cm³ and that r varies from 0.88 to 0.915 g/cm³. The required crystallinity then varies from
% crystalline = \frac{(0.9942)(0.88 \ – \ 0.87)}{(0.88)(0.9942 \ – \ 0.87)}× 100 = 9.1
% crystalline = \frac{(0.9942)(0.915 \ – \ 0.87)}{(0.915)(0.9942 \ – \ 0.87)} × 100 = 39.4
Therefore, we must be able to process the polyethylene to produce a range of crystallinity between 9.1 and 39.4%.
| Table 16-6 Crystal structures of several polymers | ||
| Polymer | Crystal Structure | Lattice Parameters (nm) |
| Polyethylene | Orthorhombic | a_{0} = 0.741 \ b_{0} = 0.495 \ c_{0} = 0.255 |
| Polypropylene | Orthorhombic | a_{0} = 1.450 \ b_{0} = 0.569 \ c_{0} = 0.740 |
| Polyvinyl chloride | Orthorhombic | a_{0} = 1.040 \ b_{0} = 0.530 \ c_{0} = 0.510 |
| Polyisoprene (cis) | Orthorhombic | a_{0} = 1.246 \ b_{0} = 0.886 \ c_{0} = 0.810 |
