Formation of topological bigels in mixtures of colloidal rings and polymers

We study a spherically confined mixture of polymers and colloidal rings. Unlike in standard colloid-polymer mixtures, the polymers interact topologically with the rings by threading them. We find that, above a critical value of the ring radius, threading yields a topological transition from a fluid to a gel-like phase characterised by a space-spanning network of interlocked polymers and rings, which we refer to as a bicomponent gel, or bigel. By exploiting the mixture dual character (rings/polymers), we predict analytically the value of the critical radius. We also show that the mobility of entanglements in the mixture slows down upon entering the gel phase, due to topological hindrance arising from threadings, whilst the transition rates between topological states of the colloidal probes provide another strong dynamical signature of the gel phase.