The glass and rubber states

The larger value of the exponent in this case, as compared to the simple random walk, reflects the swelling of the chain due to the condition of self-avoidance. The exponent of N in the self-avoiding random walk is very close to the experimentally measured value of 0.59. In any case, the polymer chain is highly coiled, as illustrated in Fig. 12.12. This description of the polymer applies equally well to the molten state, as was first postulated by Rory (see the Further reading section). The reasons behind this behavior can be attributed to the interactions between polymer chains in the molten state, which are described in the book by de Gennes (see the Further reading section). 

To demonstrate the entropic origin of the elastic response of the rubber state, we consider the thermodynamics of this state, in which changes in the internal energy E are given by 

From the first of these, we can relate the force to thermodynamic derivatives with respect to L as 

The second term on the right-hand side is usually negligible because the change in volume with extension of the solid is very small, (dQ/dL)pj 0. This leaves two important contributions to the force, one being energy-related, the other entropy-related. It turns out that in the rubber state 

This book contains an extensive collection of articles that cover most aspects of the physics of quasicrystals. 

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