Entropy undeformed chains

The minus sign is natural since entropy is maximal for the undeformed chain. Integration of Equation (27) yields for the entropy change in one direction - kJ2 (x - In three dimensions, we get for the entropy change of the coil. 

The reversible recovery of a deformed elastomer to its original (undeformed) state is due to an entropic driving force. The entropy of polymer chains is minimum in the extended conformation and maximum in the random coil conformation. Cross-linking of an elastomer to form a network structure (IX) is... 

The aim of this section is to find the relation between the elastic force and the deformation for a polymer network. For that purpose the change in entropy associated with deformation of the chains in the network must be evaluated. Figure 3.7 shows the distribution of the chain end-to-end vectors in the deformed (stretched) and undeformed (unstrained) states. The distribution has spherical symmetry in the undeformed state, and when the... 

If the uncrosslinked, undeformed network is taken as the reference state, a second contribution to the entropy (called AS ei) must be included that is the reduction in entropy arising from the restriction of network chain ends to crosslinking points. To form a crosslink, a chain end must be in a small volume element (F). The decrease in entropy caused by such a constraint on the chain end is... 

In an equilibrium undeformed network, subchains prefer to reside in the state of Gaussian coils, which can be realized by a maximum number of conformations, thus providing the highest entropy to the system. When the stress extending the network is applied, the subchains are elongated. The potential extensibility of the coil can be estimated as N/VN, because the length of a fully extended chain is proportional to N, while the most probable end-to-end distance in the coil is proportional to Therefore, the subchain consisting of 100 units... 

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