Relaxation of ideal polymer networks

Abstract

The response of swollen polymer networks to an applied weak force is studied. Polymer chain fluids and pre-gels are modelled as Rouse networks of different geometries. Mode analysis in the continuous limit gives the anomalous self diffusion of these networks. Linear response theory is then used to obtain their relaxation close to equilibrium. In all cases, velocities decay with power laws in time, with a power proportional to the given topological (graph) dimension. This behaviour allows for the classification of three dynamic regimes: subcritical topologies accommodate power-law relaxation; logarithmic relaxation occurs within the critical two dimensions for surface arrays; upper-critical topologies, such as those prevailing in dense gels, allow bounded relaxation. Computer simulations are also shown to agree with the calculations.