Ultra-slow self-similar coarsening of physical fibrillar gels formed by semiflexible polymers

Biopolymers tend to form fibrils that self-assemble into open network structures. While permanently crosslinked flexible polymers are relatively well understood, structure-property relationships of open networks and pseudo-gels formed by bundles of biopolymers are still controversial. Here we employ a generic coarse-grained bead-spring chain model incorporating semiflexibility and cohesive nonbonded interactions, that forms physical instead of chemical crosslinks. For flexible chains, the cohesive forces lead to the formation of a droplet phase while, at the same concentration, stiffer chains form bundles that self-assemble into percolated networks. From comprehensive molecular dynamics simulations we find that the reversible crosslinks allow for permanent relaxation processes. However, the associated reorganization of the filamentous network is severely hindered, leading to aging of its topology. Based on morphometric analyses, the ultra-slow coarsening in these systems is proven to be self-similar, which implies a number of scaling relations between structural quantities as the networks age. The percolated structures are characterized by different dynamic regimes of slow, anomalous diffusion with highly non-Gaussian displacements. Relaxation dynamics is found to become extremely slow already on moderate length scales and further slowing down as coarsening proceeds. Using a minimal model supported by observations on filament rupture and rearrangement, our study helps to shed light on various interrelated structural and dynamical aspects of coarsening nonergodic systems relevant for fibrous networks, pseudo-gels, and physical fibrillar gels.