The term gel is central to many scientific fields, including polymer science, biophysics, and supramolecular chemistry. In polymer science, a gel is said to be formed when polymer chains are linked into a permanent three-dimensional (3-D) network by cross-links that are either chemical bonds or strong physical associations. Linear chains in the absence of such cross-links are expected to form a network that is only defined by topological (entanglement) interactions between the chains; accordingly, such a network is expected to show viscoelastic rather than gel-like, rheology. On the other hand, many systems consisting of extended nanoscale fibers/chains (e.g., supramolecular organo- and hydro-gels, wormlike micelles, and protein filaments like F-actin) do exhibit the rheology of permanent gel networks, even in the absence of putative cross-links. We argue here that linear fibers can indeed form gels through their topological interactions alone, i.e., without cross-links, provided the fibers are sufficiently long (contour length much larger than cross-sectional size), sufficiently stiff (worm-like or rod-like) and temporally persistent, i.e., “unbreakable”. This hypothesis is supported by recent experimental and theoretical studies. In particular, we review recent experiments on wormlike micelles that show a smooth rheological transition from viscoelastic (relaxing) to gel (non-relaxing) behavior upon varying temperature.
