Langevin dependence of elongation on force

Consider a freely jointed chain of N bonds subject to a constant elonga-tional force / applied to its ends along the z axis. An example could be a chain with two opposite charges and —q at its ends in a constant electric field E applied along the z axis as sketched in Fig. 2.14. If the direct 

The partition function is useful because we will calculate the free energy from it in Eq. (2.111). States with higher energy make a smaller con- 

Different conformations in the freely jointed chain model correspond to different sets of orientations of bond vectors Tj in space [see Fig. 2.14(a)]. The orientation of each bond vector F] can be defined by the two angles of the spherical coordinate system 9 and [Fig. 2.14(b)]. Therefore, the sum 

Therefore, the partition function [Eq. (2.107)] becomes a product of N identical integrals  

The Gibbs free energy G can be directly calculated from the partition function  

---