Twists, and entanglements

Polymer conformation within the solvent system in question also has an impact on both the ink viscosity and the cleanliness of drop break up. Some polymer chains have a tendency to fold in upon themselves, thus not entangling as much with other polymer chains in solution. These tend to break off well and not form satellites, whereas other polymers can form very twisted and entangled networks in solution. These very entangled polymer chains more often lead to what is termed "stringy break-up" and usually form the unwanted satellites. 

R. C. Lacher and D. W. Sumners, in Computer Simulations of Polymers, R. J. Roe, Ed., Prentice-Hall, En ewood Cliffs, NJ, 1991, pp. 365—373. Data Structures and Algorithms for the Computation of Invariants of Entanglements Link, Twist, and Writhe. 

Fig. 19 Sol-gel quick transcription of twisted and helical ribbons from self-assemblies of 16-2-16 tartrate, (a) Chemical formula of 16-2-16 tartrate, organic self-assembled (b) twisted ribbons and (c) helical ribbons. After the polycondensation of prehydrolyzed TEOS, silica (d) twisted and (e) helical nanoribbons are obtained. At a mesoscopic level, (f) they form an entangled 3D network, and macroscopically, (g) gel formation is observed. Reprinted with Permission from Oda eta/. Copyright 2014 American Chemical Society.

Filament. Eully drawn flat yams and partially oriented (POY) continuous filament yams are available in yam sizes ranging from about 3.3—33.0 tex (30—300 den) with individual filament linear densities of about 0.055 to 0.55 tex per filament (0.5—5 dpf). The fully drawn hard yams are used directly in fabric manufacturing operations, whereas POY yams are primarily used as feedstock for draw texturing. In the draw texturing process, fibers are drawn and bulked by heat-setting twisted yam or by entangling filaments with an air jet. Both textured and hard yams are used in apparel, sleepwear, outerwear, sportswear, draperies and curtains, and automotive upholstery. 

The best way to demonstrate the motion was found [94] to be starting with a rotation tt rad about a horizontal axis to produce a configuration shown in figure 5. The ball can be rotated indefinitely about its vertical axis without the wires becoming permanently entangled. The initial arrangement is restored after each rotation of 47r, i.e. two complete revolutions. The total motion differs from normal rotation about an axis the difference arises with the initial half twist about a horizontal axis. As the ball is then rotated about the vertical axis, the axis of the initial half turn also rotates. The composite motion is more like a continuous wobble than a rotation and the three dimensions of space therefore participate more symmetrically in the motion. 

A common type of junction is shown in Figure 17.12a. Many polysaccharides form double helices below a given temperature and at given physicochemical conditions. Apparently, the helices often involve two molecules. This may be difficult to achieve because of geometrical constraints the parts of a molecule not incorporated in the helix then would also become twisted to the same extent (but in the opposite sense), which is largely prevented by the entanglements in the system. However, in many polysaccharides, complete rotation (i.e., by 360°) about the bonds between monomers appears to be possible, at least at some positions along... 

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