Chain flexibility and the persistence length

Examples of polymers with very flexible backbones are given in section 6.4, where it is shown that such flexibility can lead to the very low elastic moduli of rubbers. Examples of molecules with very low degrees of flexibility are discussed in section 12.4, where it is seen that the low flexibility can lead to liquid-crystalline behaviour, which in turn can lead to the production of materials with high elastic moduli. Because of the importance of flexibility in determining properties, it is important to have some way of defining it more precisely. 

The chain-length dependence of the characteristic ratio, when the degree of polymerization is below the asymptotic limit, can also be modeled with fewer parameters than are needed to implement the rotational isomeric state scheme. The local details of tire chain structure can be characterized by a unique parameter. The persistence length a can be calculated from the backbone bond vectors as  

Eventually, there is no correlation in direction between the first bond vector and the y tii bond vector, and the sum reaches its asymptotic value. 

The other dimensional measure of the chain molecule is its contour length L. For a chain of intermediate contour length, a L 50a, it can be shown that the mean-squared end-to-end distance is given by  

Polymer molecules in this regime are called semiflexible or wormlike chains. 

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