Tube-like region

Figure 5 The basic concept of P.G. De Gennes reptation of a chain trapped in a tube-like region by migration of "defects" along the nhain.

Figure 3.28 Each of the two images contains superimposed configurations of a chain at many different instants in time in a molecular-dynamics simulation of a melt of such chains in a box. Over the time scale simulated, each chain appears to be confined to a tube-like region of space, except at the chain ends. (From Kremer and Grest, reprinted with permission from J. Chem. Phys. 92 5057, Copyright 1990 American Institute of Physics.)...

A chain or network strand (thick curve) is topologically constrained to a tube-like region by surrounding chains. The primitive path is shown as the dashed curve. The roughly quadratic potential defining the tube is also sketched. 

The Edwards tube model of polymer entanglements was already discussed in Section 7.3.1. The topological constraints imposed by neighbouring chains on a given chain restrict its motion to a tube-like region (see Fig. 7.10) called the confining tube. The motion of the chain along the contour of-... 

A good example of results from a molecular dynamics simulation of entangled polymers is shown in Fig. 9.29. The 40 configurations of the chain shown are equally spaced in time up to the Rouse time of the chain. The chain is clearly confined to a tube-like region, with only the ends of the chain beginning to explore the rest of the volume. 

In the previous chapter, we discussed the dynamics of a polymer in a fixed network. We shall now discuss the polymer dynamics in concentrated solutions and melts. In these systems, though aU polymers are moving simultaneously it can be argu that the reptation picture will also hold. Consider the motion of a certain test polymer arbitrarily chosen in melts. If the test polymer moves perpendicularly to its own contour, it drags many other chains surrounother hand the movement of the test polymer along its contour will be much easier. It will be thus plausible to assume that the polymer is confined in a tube-like region, and the major mode of the dynamics is reptation. 

According to the reptation theory [74,75], the polymer chains are confined laterally to a tube-like region. The chains can only relax by sliding back and forth along the tube like a snake, and cannot cross the wall of the tube. Based on this physical picture of a polymer chain in liquid state, the volume of the reptation tube is presumably considered to be the free volume of a individual chain that can occupy. As illustrated in Figure 19, the volume of the tube, V l,b ,... 

Figure 7.21 Chain segment AB in dense rubber. The points A and B denote the cross-linked points and the dots represent other chains that, in this drawing, are assumed to be perpendicular to the paper. Due to entanglements the chain is confined to the tube-like region denoted by the broken line. The bold line shows the primitive path. (Reproduced from Doi, M. and Edwards, S.E. (1978) J. Chem. Soc. Faraday Trans., 74, 1802. Copyright (1978) Royal Society of Chemistry.)...

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