Convolution theory for dynamic systems: a bottom-up approach to the viscoelasticity of polymeric networks

Biological materials such as the cytoskeleton are characterized by remarkable viscoelastic properties and therefore represent the subject of numerous micro- and macrorheological experimental studies. By generalizing the previously introduced dynamic convolution theory (DCT) to two dimensions, we devise a bottom-up approach for the viscoelastic properties of extended, crosslinked semiflexible polymer networks. Brownian dynamics (BD) simulations serve to determine the dynamic linear self- and cross-response properties of isolated semiflexible polymers to externally applied forces and torques; these response functions are used as input to the DCT. For a given network topology, the frequency-dependent response of the network subject to a given external force/torque distribution is calculated via the DCT allowing to resolve both micro- and macrorheological properties of the networks. A mapping on continuum viscoelastic theory yields the corresponding viscoelastic bulk moduli. Special attention is drawn to the flexibility of crosslinkers, which couple angular degrees of freedom at the network nodes and which are found to sensitively affect the resulting rheological properties of the polymeric meshwork.