Can percolation theory explain the gelation behavior of diblock copolymer worms?

It is well known that polymerization-induced self-assembly (PISA) offers an efficient synthetic route for the production of highly anisotropic diblock copolymer worms. When prepared in aqueous media, such worms form thermoresponsive free-standing hydrogels that are (i) readily sterilizable, (ii) can act as a 3D matrix for the culture of normal mammalian cells and (iii) can induce stasis in human stem cell colonies. Herein we critically examine the gelation behavior of two types of diblock copolymer worms in terms of recent advances in percolation theory for rigid rods, which explicitly account for the effect of rod length polydispersity. More specifically, we use small-angle X-ray scattering (SAXS) to determine the weight-average worm contour length, L(w), and the mean worm cross-sectional radius, R. This approach enables a direct comparison to be made between the theoretical critical worm volume fraction, φ(c), required for gelation and the experimental values indicated by rheological measurements and tube inversion experiments. Given that these diblock copolymer worms are relatively flexible rather than truly rod-like, reasonably good agreement between these two parameters is observed, particularly for shorter, relatively stiff worms. For longer, more flexible worms a proportionality constant of approximately two is required to reconcile theory with experimental values for φ(c). These findings are expected to have important implications for the aqueous gelation behavior exhibited by various other anisotropic nanoparticles, such as cellulose nanocrystals and semicrystalline block copolymer rods, and also fibril-forming small molecule (e.g. dipeptide) gelators.