Polyethylene chains, conformation

The picture presented so far of the polyethylene chain being of a linear zig-zag geometry is an idealised one. The conformation of a molecular chain is in fact random provided that the bond tetrahedral angle remains fixed. This is best illustrated by considering a piece of wire with one bend at an angle of 109° 28 as shown in Fig. A.5a. 

One modification of polyethylene (PE), which appears to be stable at high temperatures and pressures (see Sect. 3.2), also presents a pseudohexagonal packing and a disorderd chain conformation [59],... 

Figure 15 (A) Polyethylene chain in planar zig-zag conformation. (B) Energy diagram of...

Snyder, R.G, Vibrational study of the chain conformation of the liquid n-paraffins and molten polyethylene, J. Chem. Phys., 47, 1316, 1967. 

The most relevant property of stereoregular polymers is their ability to crystallize. This fact became evident through the work of Natta and his school, as the result of the simultaneous development of new synthetic methods and of extensive stractural investigations. Previously, the presence of crystalline order had been ascertained only in a few natural polymers (cellulose, natural rubber, bal-ata, etc.) and in synthetic polymers devoid of stereogenic centers (polyethylene, polytetrafluoroethylene, polyamids, polyesters, etc.). After the pioneering work of Meyer and Mark (70), important theoretical and experimental contributions to the study of crystalline polymers were made by Bunn (159-161), who predicted the most probable chain conformation of linear polymers and determined the crystalline structure of several macromolecular compounds. 

To elucidate the phase structure in detail it is necessary to characterize the molecular chain conformation and dynamics in each phase. However, it is rather difficult to obtain such molecular information, particularly of the noncrystalline component, because it is substantially amorphous. In early research in this field, broad-line H NMR analysis showed that linear polyethylene crystallized from the melt comprises three components with different molecular mobilities solid, liquid-like and intermediate molecular mobility [13-16]. The solid component was attributed to molecules in the crystalline region, the liquid component to... 

Rather recently, we have studied the solid-state structure of various polymers, such as polyethylene crystallized under different conditions [17-21], poly (tetramethylene oxide) [22], polyvinyl alcohol [23], isotactic and syndiotactic polypropylene [24,25],cellulose [26-30],and amylose [31] with solid-state high-resolution X3C NMR with supplementary use of other methods, such as X-ray diffraction and IR spectroscopy. Through these studies, the high resolution solid-state X3C NMR has proved very powerful for elucidating the solid-state structure of polymers in order of molecules, that is, in terms of molecular chain conformation and dynamics, not only on the crystalline component but also on the noncrystalline components via the chemical shift and magnetic relaxation. In this chapter we will review briefly these studies, focusing particular attention on the molecular chain conformation and dynamics in the crystalline-amorphous interfacial region. 

In this section we will discuss the molecular structure of this polymer based on our results mainly from the solid-state 13C NMR, paying particular attention to the phase structure [24]. This polymer has somewhat different character when compared to the crystalline polymers such as polyethylene and poly(tetrameth-ylene) oxide discussed previously. Isotactic polypropylene has a helical molecular chain conformation as the most stable conformation and its amorphous component is in a glassy state at room temperature, while the most stable molecular chain conformation of the polymers examined in the previous sections is planar zig-zag form and their amorphous phase is in the rubbery state at room temperature. This difference will reflect on their phase structure. 

As pointed out above with relation to the data at 87 °C, the Tic of the crystalline-amorphous interphase is appreciably longer than that of the amorphous phase, suggesting the retention of the helical molecular chain conformation in the interphase. We also note that a Tic of 65-70 s for the crystalline phase is significantly shorter than that for other crystalline polymers such as polyethylene and poly-(tetramethylene oxide), whose crystalline structure is comprised of planar zig-zag molecular-chain sequences. In the crystalline region composed of helical molecular chains, there may be a minor molecular motion in the TiC frame, with no influence on the crystalline molecular alignment that is detected by X-ray diffraction analyses. Such a relatively short TiC of the crystalline phase may be a character of the crystalline structure that is formed by helical molecular chain sequences. 

First, let s revisit chain conformations. We ve mentioned that although there is a minimum energy conformation, one where all the bonds are trans in polyethylene, for example, a statistical distribution of conformations will be found in the melt. Upon cooling, however, ordered structures are formed as a result of crystallization (for reasons we consider later). So, the initial questions we want to answer are first, what is the shape or conformation of the chains in the crystal and second, how are they arranged relative to one another ... 

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. 

Tb get a better feel for this, let s look at a polymer example that will be relevant to our discussion of crystallization. Essentially, we would like to know what would be the probability that a polyethylene chain in the melt would spontaneously adopt an all-trans extended conformation. Now this is a difficult problem to tackle, in the sense that we would need a precise knowledge not only of the potential function describing bond rotations, but also the calculations would have to... 

Considerations of minimum overlap of radii of nonbonded substituents on the polymer chain are useful in understanding the preferred conformations of macromolecules in crystallites. The simplest example for our purposes is the polyethylene (1-3) chain in which the energy barriers to rotation can be expected to be similar to those in /i-butane. Figure 4-2 shows sawhorse projections of the conformational isomers of two adjacent carbon atoms in the polyethylene chain and the corresponding rotational energy barriers (not to scale). The angle of rotation is that between the polymer chain substitutents and is taken here to be zero when the two chain segments are as far as possible from each other. 

Yoon, Smith, and Matsuda, on the other hand, compared two approaches, using a united-atom model and a fully atomistic model.Stochastic dynamics and MD simulations of w-tridecane (C13H28) were used to study polyethylene. Besides studying the bulk melt, the authors examined confined melts between solid surfaces. Chain conformations, chain packing orientational correlations, and self-diffusion were among the properties studied. In regard to chain confer-... 

This review has summarize the applications of neutron inelastic scattering to the study of pol3uners. The technique has proven useful for measuring and characterizii low-frequency intramolecular and inter-molecular vibrations, particularly for three systems, such as polyethylene and the n-paraffins, for which theoretical calculations of phase-frequency relations are available. More calculations of this type, and extension of them to include the effects of departures of chain conformations from their ideal transplanar or helical configurations, are needed for an optimum application of the method. 

Finally, we note that Schmidt-Rohr and co-workers have elegantly demonstrated that 2D 13C-13C DQ spectra recorded for static samples can identify the chain conformation statistics for 13C-labeled polymer samples.112 Remembering that the frequency of a given 13C resonance depends on the orientation of the CSA tensor, the method relies on the fact that the adoption of a particular torsional angle along the chain results in DQ peaks for only specific pairs of 13C frequencies. In particular, it was shown that trans and gauche conformations lead to very different 2D DQ powder spectra, and it was thus possible to quantitatively determine the conformation statistics for a sample of amorphous polyethylene terephtha-late) (PET). 

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