One-component systems subject to a tensile force

Consider a cross-linked fibrous system, composed of highly axially oriented crystalline regions co-existing with amorphous zones the latter being devoid of any vestiges of crystalline order. The fiber is subject to a uniform tensile force,/, acting 

According to the first law of thermodynamics, the change in internal energy E of any system can be written with complete generality as 

For a one-component system the intensive-extensive pairs p, V and /, L are those of interest. Here, p and V are the pressure and volume, respectively, and Lis the length of the fiber. For a process that is conducted reversibly, dQ = T dS, where S is the entropy. Thus 

For present purposes, it is convenient to choose p, T and / as the independent variables. It is advantageous to utilize the equivalent relation 

For the system to be in equilibrium at constant p, T and/, the function G — fL must be a minimum with respect to all permissible displacements. In particular. 

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One-component system subject to a tensile force highly ordered chains, where B is given by Eq. (8.21),... 

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