Polymer chain cross-sectional area

Table 1. Comparison of hydrophilic polymers with various chain cross-sectional areas in formation of crystalline complexes with cyclodextrins...

Table 2 Comparison of Hydrophilic Polymers with Various Chain Cross-Sectional Areas for Formation of Crystalline Complexes with Cyclodextrins...

Next we recognize that 6 and X always appear as a ratio in our theory. If we argue that the hole and the polymer chain have comparable cross-sectional areas, we can multiply both the numerator and denominator of the X/6 ratio by this cross section and convert it into the ratio V /V, where is the volume of the flow segment of length X. While we know neither of these volumes directly, there are indications that V /V may be on the order of 10-20 for many linear... 

The rate of solvent diffusion through the film depends not only on the temperature and the T of the film but also on the solvent stmcture and solvent-polymer iuteractions. The solvent molecules move through free-volume holes iu the films and the rate of movement is more rapid for small molecules than for large ones. Additionally, linear molecules may diffuse more rapidly because their cross-sectional area is smaller than that of branched-chain isomers. Eor example, although isobutyl acetate (IBAc) [105-46-4] has a higher relative evaporation rate than -butyl acetate... 

Vincent analyzed the tensile fracture stress o, of a broad range of polymers as a function of the number of backbone bonds per cross sectional area ( 2) and found a nearly linear relation, o 2, as shown in Fig. 12. 2 is related to via the theory of entanglements for random walk chains as [74]... 

In spite of the similarity of the structure of the monomer units the two corresponding isotactic polymers crystallize in two different chain conformations tiie helix of poly-3-methyl-l-butene contains four monomer units per turn (4/1) with a chain repeat of 6.85 A the helix of poly-4-methyl-l-pentene contains 3.5 units per turn (7/2) and has a repeat of 13.85 A. The copolymers tend to crystallize. Their chain conformation and cross sectional area in the crystal lattice are analogous to those of the homopolymer corresponding to the predominant comonomer. For 4-methyl-l-pentene contents higher than 50% some evidence exists that the system simultaneously contains both chain conformations. 

The simplest model of this type is called the freely jointed chain, and is illustrated in Figure 2.21. In it, the skeletal bonds are joined end to end, but are completely unrestricted in direction. This is clearly a situation not found in a real polymer (bond angles in real polymers are relatively fixed). It is also assumed that the chains have zero cross-sectional area, that is that the chains are unperturbed by excluded-volume effects. These effects arise because atoms of a chain exclude from the space they take up all other atoms from all other chains. They are related to excluded-volume effects occurring even in systems as simple as real gases. The expression for the mean-square end-to-end distance of such an idealized chain is particularly simple ... 

The polymer is about 0.8 nm in its maximum width and 0.33 nm2 in cross-sectional area, and can contain about 10,000 glucose residues with their rings in the same plane. In the cell wall these polymers are organized into micro-fibrils that can be 5 nm by 9 nm in cross section. These microfibrils apparently consist of an inner core of about 50 parallel chains of cellulose arranged in a crystalline array surrounded by a similar number of cellulose and other polymers in a paracrystalline array. Microfibrils are the basic unit of the cell wall and are readily observed in electron micrographs. Although great variation exists, they tend to be interwoven in the primary cell wall and parallel to each other in the secondary cell wall (Fig. 1-13). 

Figure 2). Silk fibers swell 192 in cross-sectional area, whereas linen swells 472 (6). Fiber swelling is limited by the interchain forces holding the polymers together in the crystalline areas only when these forces are broken in degradation processes can the fiber swell more. Water is attracted by the peptide bonds of silk and by the cellulosic hydroxyls of linen. The first monolayer of water adsorbed by each polymer molecule is directly adsorbed and thus is tightly held in association with the polymer chain. Subsequent layers of water molecules are indirectly attached and thus are loosely held in association with other water molecules. 

A (a) Molecular cross-sectional area of a polymer chain. 

FIGURE 17.11 The effect of ri (the number of statistical chain elements in a cord between cross-links) on the relation between stress and strain of a polymer gel in elongation. a0 is the force divided by the original cross-sectional area of a cylindrical test piece, v is twice the cross-link density, L is the length, and L0 the original length of the test piece. (After calculations by L. R. G. Treloar. The Physics of Rubber Elasticity. Clarendon, Oxford, 1975.)... 

Fig. 12.18 Correlation of the brittle-fracture stress of a selection of 13 polymers with the molecular cross-sectional area, or number of backbone bonds per unit area, which suggests that in such fractures chain scission plays a very minor role (from Vincent (1972) courtesy of Elsevier).

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