Polyethylene unit cell dimensions

Use the unit cell dimensions cited above to determine the crystal density of polyethylene. Examine Fig. 4.10 to decide the number of repeat units per unit cell. 

Figure 8.3. Section through the ab plane in the orthorhombic polyethylene unit cell, a and b are the unit cell dimensions.

The unit cell dimensions calculated by these procedures for polyethylene are a = 0.740 nm, b = 0.493 nm and c = 0.254 nm and the density is (8.6 kg/m. Figure 8.3 shows the ab plane. The c-axis is parallel to the chain axis and its length of 0.254 nm is equal to the distance between alternate carbon atoms. This structure for polyethylene is identical with that determined for crystals of pure n-paraffins such as C32H66 - low molecular analogs of polyethylene. X-ray structures have been determined for many crystalline polymers. Miller [5] has published an extensive compilation of polymer unit cell data. 

The unit cell structure of polyethylene was first investigated by Bunn (20). A number of experiments were reviewed by Natta and Corradini (21). The unit cell is orthorhombic, with cell dimensions of a = 7.40, b = 4.93, and c = 2.534 A. The unit cell contains two mers (see Figure 6.5) (22). Not unexpectedly, the unit cell dimensions are substantially the same as those found for the normal paraffins of molecular weights in the range 300 to 600 g/mol.The chains are in the extended zigzag form that is, the carbon-carbon bonds are trans rather than gauche. The zigzag form may also be viewed as a twofold screw axis. 

Polyethylene terephthalate is known to crystallize in a triclinic crystal structure with unit-cell dimensions as follows [8] ... 

Unit cell dimensions for polyethylene may be assumed to be as follows ... 

The dimensions of the a, b, and c axes of an unperturbed polyethylene unit cell are reported to be 7.417,4.945, and 2.547 A respectively [7-9]. These values were measured for high density polyethylene at room temperature. The density of a unit cell with these dimensions is 1.00 g/cmh This value is widely accepted and is commonly used in the calculation of the degree of crystallinity from sample density. 

The crystal structures of C2Ht—CO copolymers with QH4/CO ratios of 1, 1.3, 2.2 and 3.5 have been determined49,50). For the 1 1 copolymer an orthorhombic unit cell of dimensions a = 7.97, b = 4.76, c (fiber axis) = 7.57 A was observed 49). The main chain had a planar zigzag form. For copolymers with higher C2Ht contents, the fiber periods were essentially identical with that of polyethylene (c 2.54 A) 50). Also, the higher the C2H content, the shorter the a axis and longer the b axis. 

X-Ray Studies. Lines in the x-ray, powder diffraction pattern of the terpolymer were similar to those found in polyethylene (PE). Since the terpolymer contains a majority of ethylene segments, we assumed that it crystallized in an orthorhombic unit cell as polyethylene does. The lattice parameters for the terpolymer were calculated to be a = 7.76 A, b = 5.06 A, and c = 2.56 A. These values are to be compared with the dimensions of PE unit cell a — 7.40 A, b = 4.93 A, and c = 2.54 A (8). Thus x-ray data suggest that the terpolymer crystallizes with an expanded PE unit cell. 

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