Multiple networks in soft materials: polycontinuity

Bicontinuous network phases contain a pair of interwoven labyrinths. Analogous patterns with 3,4, .., 8, .., 54,... labyrinths are readily constructed via 2d hyperbolic geometry. Some of these have been realised in synthetic materials, from mesoporous silicates and lyotropic liquid crystals to metal-organic frameworks. We stumbled on polycontinuous forms while exploring 2d hyperbolic geometry.\footnote{Eur Phys J B, 16, 613-630 (2000)} The only known tricontinuous phase found to date in mesoscale self-assembled materials was described via 2d non-euclidean geometry\footnote{Curr Opinion Coll Interf Sci, 8, 5-14 (2003)} many years before its discovery.\footnote{Nat Chem 1, 123–127 (2009)} This example demonstrates the relevance of regular patterns in non-euclidean 2d spaces to self-assembled morphologies in actual materials. One route to explicit ground-up design of mesoscale polycontinuous phases is via star-shaped molecules with immiscible arms, such as Y-shaped ``polyphiles.'' Some results of theoretical geometric modelling,\footnote{Acta Cryst, A69, 241-261 (2013)} simulation\footnote{Proc Natl Acad Sci. USA, 111, 1271–1276 (2014)} and experimental formulation of lyotropic LC mesophases with polyphiles\footnote{Chem Mat, in press (2015); in preparation} will be discussed.