Force-Extension Relation and Plateau Modulus for Wormlike Chains

We derive the linear force-extension relation of a wormlike chain of arbitrary stiffness including entropy elasticity, bending, and thermodynamic buckling. From this we infer the plateau modulus G⁰ of an isotropic entangled solution of wormlike chains. The entanglement length Lₑ is expressed in terms of the characteristic network parameters for three different scaling regimes in the entangled phase. The entanglement transition and the concentration dependence of G⁰ are analyzed. Finally we compare our findings with experimental data.