Nonaffine Deformation and Elasticity of Polymer Networks

We demonstrate that the origin of the nonlinear elasticity of polymer networks rests in their nonaffine deformations. We introduce the affine length Raff, which separates the solid-like elastic deformations on larger scales from liquid-like nonaffine deformations on smaller scales. This affine length grows with elongation λ as Raff ∼ λ3/2 and decreases upon compression as Raff ∼ λ1/2. The behavior of networks on scales up to Raff is that of stretched or compressed individual chains (we call them affine strands). The affine strands are stretched in the elongation direction and confined and folded in the effective tubes in the compression direction. The fluctuations of affine strands determine the diameters of the confining tubes a, which change nonaffinely with the network deformation a ∼ λ1/2. Our model gives a unified picture of deformations of both phantom and entangled networks and leads to a stress−strain relation that is in excellent agreement with experiments.