Polyethylene chain configuration

Probabilities of configurations conducive to the intramolecular back-biting abstraction of a hydrogen atom are evaluated for growing unperturbed PVAc chains. A realistic RIS model is used for the chain statistics, Probabilities are found to be smaller than those seen in an earlier treatment of the polyethylene chain. The smaller probabilities of PVAc contribute to the virtual absence of short branches. The present study therefore provides support for the validity of the Roedel mechanism for the formation of short branches in the free radical initiated polymerization of ethylene. 

Formation of complex branches, which might arise from two intramolecular rearrangements of the Roedel type, are investigated in polyethylene. An RIS model is used for the polyethylene chain statistics, with inclusion of the effect of a trifunctional branch point on weighting of all configurations. 

First, it is necessary to define the structure. The structure of a planar zig-zag polyethylene chain is shown in Fig. 2, together with its symmetry elements. These are C2 — a two-fold rotation axis, C — a two-fold screw axis, i — a center of inversion, a — a mirror plane, and og — a glide plane. Not shown are the indentity operation, E, and the infinite number of translations by multiples of the repeat (or unit cell) distance along the chain axis. All of these symmetry operations, but no others, leave the configuration of the molecule unchanged. 

Polytetrafluoroethylene (PTFE) has a chemical structure which can be designated by (CF2)k. From its resemblance to the chemical structure of polyethylene it might be thought that the spectra of these two polymers should be quite similar. They do in fact resemble each other, but there are also important differences. This is a consequence of the fact that the PTFE chain configuration is quite different from that of polyethylene, and also the intramolecular forces are undoubtedly significantly different in the two cases. As we shall see, the spectrum is moderately well understood, but not in quite as great detail as that of polyethylene. This is primarily a result of the lack of Raman data on the polymer and certain key polarization data in the infrared. 

Fig. 14.10 Chain configurations from a nonisothermal deformation simulation. From top to bottom, the images were taken at 374, 368, 364, 360 K, and 290K, corresponding to 7.6, 8.2, 8.6, 9.0, and 16.0 ns. [Reprinted by permission from M. C. Levine, N. Waheed, and G. C. Rutledge, Molecular Dynamics Simulation of Orientation and Crystallization of Polyethylene during Uniaxial Extension, Polymer, 44, 1771-1779, (2003).]...

However, problems frequently arise in the comparison of calculated frequencies with optical spectra. Since infrared and Raman measurements are subject to optical selection rules, only frequencies associated with certain active phases of a phase-frequency curve are observed. In certain cases, a mode may have frequencies that lie outside the range of optical measurements, or it may have no optically active phases. For exainple, the skeletal deformation and torsional modes for an infinite and isolated polyethylene chain in the trans-configuration have optically active phases that correspond to zero frequency (36). 

Fig. 15-19. Scheme of a polyethylene chain zigzag configuration in one plane. 

Fig. 2.3 Spatial structure of a polyethylene chain segment in the most energetically favorable configuration.

Mark, J. E. Curro, J. G., A Non-Gaussian Theory of Rubberlike Elasticity Based on Rotational Isomeric State Simulations of Network Chain Configurations. I. Polyethylene and Polydimethylsiloxane Short-Chain Unimodal Networks. J. Chem. Phys. 1983, 79, 5705-5709. 

Consider now what this implies for a really long polyethylene chain with, say, 50,000 carbon atoms. If each successive pair of carbon atoms has a choice of three configurations, then the total number of possible chain configurations would be 3 x 3x3x3 x3, reaching S o.ooo number too monstrous to... 

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