Time is Length in Self-Similar Logarithmic Aging of Physically Cross-Linked Semiflexible Polymer Networks

Physical aging in polymers is a fundamental yet poorly understood phenomenon, as diverse macromolecular systems exhibit remarkably similar slow dynamics. Through molecular dynamics simulations of physically cross-linked networks composed of semiflexible polymers, we identify a previously unexplored class of self-similar aging. The network undergoes ultraslow coarsening characterized by a logarithmically growing mesh size, L(t)∼lnt, which governs the spatial organization, cohesive and bending energies, and the aging dynamics of the system. This single time-dependent length scale defines an internal clock, giving rise to spatiotemporal self-similarity of both structure and dynamics-offering a perspective on aging in soft and disordered materials.