Polymer chain folding

One of the most remarkable features of polymer crystallization is that such chain molecules can form lamellar crystals that contain heavily folded polymer chains. In experiments, the structural analysis of these lamellar crystals became possible when polyethylene single crystals were first prepared from a solution [100-102]. It was found that the orientation of the polymer chains... 

The most direct evidence of the crystallinity in polymers is provided by x-ray diffraction studies. The x-ray patterns of many crystalline polymers show both sharp features associated with regions of three-dimensional order, and more diffuse features characteristic of molecularly disordered substances like liquids. The occurrence of both types of feature is evidence that ordered regions (called crystallites) and disordered regions coexist in most crystalline polymers. X-ray scattering and electron microscopy have shown that the crystallites are made up of lamellae which are built-up of folded polymer chains as explained below. 

Fig. 14.—Polymer Single Crystal from Esparto-grass Xylan. (Screw dislocations and lamellar texture are typical of these crystals, which contain folded polymer-chains. The insert shows the schematic diagram of the electron diffractogram that corresponds to the dry crystal form (see Section V,l, p. 460), and confirms that the molecular axis is normal to the lamellar plane).

Fig. 15.—Schematic Diagram of Folded Polymer-Chains in a Single Crystalline Layer of a Macromolecular Crystal as shown in Fig. 14.

X-ray scattering and electron microscopy have shown that the crystallites are made up of lamellae which, in turn, are built-up of folded polymer chains as explained below. 

Fig. 2.4. Sketch of the basic stractural components in HDPE geomembrane morphology - based on our understanding as of today. Folded polymer chains form extended lamellae (top left). Twisted stacks of lamellae create longitudinal fibrils (bottom). The sphere-shaped spheralite (top right) is composed of radial fibrils pointing outwards with amorphous areas in between. This stmctural model enables the interpretation of basic processes, such as stress crack formation, see Sect. 5.3.4...

In dilute polymer solutions, hydrodynamic interactions lead to a concerted motion of tire whole polymer chain and tire surrounding solvent. The folded chains can essentially be considered as impenneable objects whose hydrodynamic radius is / / is tire gyration radius defined as... 

Polymer chain ends disrupt the orderly fold pattern of the crystal and tend to be excluded from the crystal and relegated to the amorphous portion of the sample. 

Figure 4.4 Idealized representation of a polymer crystal as a cylinder of radius r and thickness 1. Note the folded nature of polymer chains in crystal.

Both hollow pyramids and corrugated pyramids are thoroughly documented and fairly well understood. Such structures are consistent with the notion that successive layers of folded chains do not fold at the same place, but offset this fold stepwise to generate the pyramid face. The polymer chains are perpendicular to the planar faces of the pyramid and are therefore tilted at an angle relative to the base of the pyramid. 

Fig. 22.5. A chain-folded polymer crystal. The structure is like that of a badly woven carpet. The unit cell shown below, is relatively simple and is much smaller than the polymer chain.

Andrew Keller (1925-1999) who in 1957 found that the polymer polyethylene, in unbranched form, could be crystallised from solution, and at once recognised that the length of the average polymer molecule was much greater than the observed crystal thickness. He concluded that the polymer chains must fold back upon themselves, and because others refused to accept this plain necessity, Keller unwittingly launched one of the most bitter battles in the history of materials science. This is further treated in Chapter 8, Section 8.4.2. 

With the first successful growth of a polymer single crystal in the 1950s it was found that the polymer chains are folded back and forth many times inside the crystal [161]. 

The single crystal of a polymer is a lamellar structure with a thin plateletlike form, and the chain runs perpendicular to the lamella. The crystal is thinner than the polymer chain length. The chain folds back and forth on the top and bottom surfaces. Since the fold costs extra energy, this folded chain crystal (FCC) should be metastable with respect to the thermodynamically more stable extended chain crystal (ECC) without folds. 

Whenever the polymer crystal assumes a loosely packed hexagonal structure at high pressure, the ECC structure is found to be realized. Hikosaka [165] then proposed the sliding diffusion of a polymer chain as dominant transport process. Molecular dynamics simulations will be helpful for the understanding of this shding diffusion. Folding phenomena of chains are also studied intensively by Monte Carlo methods and generalizations [166,167]. 

Larger polymers are known as proteins. Aside from the amide linkages, the polymer chain is very flexible, giving rise to the possibility of an enormous number of different conformers. It is nothing short of remarkable, therefore, that proteins rapidly fold into a single conformation. Very strong forces must be at work. 

The formation of the microstructure involves the folding of linear segments of polymer chains in an orderly manner to form a crystalline lamellae, which tends to organize into a spherulite structure. The SCB hinder the formation of spherulite. However, the volume of spherulite/axialites increases if the branched segments participate in their formation [59]. Heterogeneity due to MW and SCB leads to segregation of PE molecules on solidification [59-65], The low MW species are accumulated in the peripheral parts of the spherulite/axialites [63]. The low-MW segregated material is brittle due to a low concentration of interlamellar tie chains [65] and... 

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