Polyethylene chains, conformation defects

Note that individual chains pass through many unit cells. Note also that the polyethylene chains are in their minimum energy all-trans (zig-zag) conformation and are close packed to maximize intermolecnlar interactions. Branches could not be accommodated in this structure and such defects are generally-exclnded from crystalline domains. 

The study of the confoimational defects in polymethylene chains has been tackled some time ago in a systematic way by the school of Snyder by normal mode analysis of short-chain molecules (see, for example [104]) and by our group at Milano using NET [95, 101]. The results by both techniques are very similar. In the previous discussion in Figure 3-14 we have pointed out that a few peaks in the calculated g(v) for infinite trans polyethylene do not find corresponding infrared and/or Raman lines to be assigned to k = 0 motions. These additional experimental peaks are just an evidence of the existence of extra structures which we can identify as conformational defects using the theory we are presently discussing. 

The experiments were performed with a predominantly head-to-head, tail-to-tail chain that contained defects, arising from the 1,2 addition of 3 or 6% of the monomer units in the parent poly(2,3-dimethyl-1,3-butadiene). When short branches are present as defects in a polyethylene chain, they produce a decrease in Coo, by disrupting the preferred conformation consisting of short sequences of trans placements [23]. The defects present in the chains examined in the experiment, illustrated in Fig. 5, may play... 

Figure 1. Representative conformation defects in polyethylene chains, (a) Pech-hold kink, (b) Reneker twist, and (c) smooth twist.

Figure 2. Crystal packing in polyethylene (a, h projection), one coordination shell about a central chain is shown. Unit cell boundaries also are shown. In defect calculations, center chain (1) is replaced by one containing a conformational defect (see Figure 1). In the hybrid Newton-Raphson relaxation method, one chain at a time has its energy minimized with the other chains fixed. In the free chain, all internal degrees of freedom participate (torsional angles, etc.) as well as the position and orientation of the chain. After a cycle through all of the chains, the total energy of the assembly is computed. The cycles are repeated until the energy is stable.

PTHF chains have an a -trans conformation that is similar to polyethylene in the urea adduct or to -alkane complexes with urea. However, the stoichiometries of the adduct are uncertain and the diffraction patterns of the urea adducts even with /i-paraffin showed a high degree of disorder for the guest molecules. Some authors claim, particularly for the n-alkane adducts, that there may be some kind of conformational defects whereby some of the torsion angles could be gauche. Therefore, Chenite and Brisse reinvestigated the structures of PTHF-urea systems in more detail [15]. 

In addition, conformational disorder in polymer crystals may give rise to point and line defects which are tolerated in the crystal lattice at a low cost of free energy as kinks [104,105], jogs [106,107] and dislocations [108,109]. Such crystallographic defects arise whenever portions of chain adopt conformations different from the conformation assiuned by the chains in the crystal state [99], and have been widely discussed in the literature, in the case of polyethylene [108,109] and some aliphatic polyamides [99,106]. Point and... 

The theoretical tensile modulus of polyethylene is 180-340 GPa. [165, 166] The extremely high tensile modulus of polyethylene is due to the small cross-sectional area of the chain, no side groups, and the planar zig-zag conformation in the orthorhombic crystal lattice. The theoretical tensile strength calculated from the C-C bond energy is in the order of 20-60 GPa. These theoretical values for polyethylene can happen if all the C-C bonds fracture simultaneously. This requires defect free, chain-extended structure, and infinite polymer chains which is a completely different situation from which is encountered [167]. 

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