Knots, and entanglements

Also, is there any hope we can still manage with simple energy arguments Or do we need to tackle the problem by means of mechanics, tracing all the molecules It would not be hard for an ideal gas. Its pressure is just an overall result of all the individual hits by the molecules on the piston. This concept immediately leads to the ideal gas equation of state (we encourage the reader to reproduce this derivation, it is very beautiful). However, there is no such simple picture for a polymer. Even in the case of an ideal chain, the motion of segments is extremely complicated, due to knots and entanglements. 

Just as a rope can be stretched, folded back on itself, curled up into a ball, entangled, knotted, and so forth, a polymer molecule can take on many conformations. Consider a molecule as a chain of N links, each link of length Iq and attached to the preceding link by a rotating joint. 

Forgan RS, Sauvage JP, Stoddart JF (2011) Chcanical topology complex molecular knots, links, and entanglements. Chem Rev 111 5434—5464... 

The driving force for recovery is entropic, as in a cross-linked rubber. There are no chemical cross-links in a thermoplastic, but chain entanglements ( knots ) and other physical interactions between molecules have a similar effect in causing the iruterial to behave like a network. 

Figure 11.3 Schematic drawing of an entanglement network of long cylindrical micelles. Note the different length scales kis the mesh size, / the mean distance between two knots, and m the contour length between two knots.

Figure 4.44 Classification of entanglements such as twists, knots, and loops. In this figure, toward the bottom and right sides, entanglements become more complicated. (See color insert.)...

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