Understanding the Role of Trapezoids in Honeycomb Self‐Assembly—Pathways between a Columnar Liquid Quasicrystal and its Liquid‐Crystalline Approximants

Abstract

AbstractQuasiperiodic patterns and crystals—having long range order without translational symmetry—have fascinated researchers since their discovery. In this study, we report on new p‐terphenyl‐based T‐shaped facial polyphiles with two alkyl end chains and a glycerol‐based hydrogen‐bonded side group that self‐assemble into an aperiodic columnar liquid quasicrystal with 12‐fold symmetry and its periodic liquid‐crystalline approximants with complex superstructures. All represent honeycombs formed by the self‐assembly of the p‐terphenyls, dividing space into prismatic cells with polygonal cross‐sections. In the perspective of tiling patterns, the presence of unique trapezoidal tiles, consisting of three rigid sides formed by the p‐terphenyls and one shorter, incommensurate, and adjustable side by the alkyl end chains, plays a crucial role for these phases. A delicate temperature‐dependent balance between conformational, entropic and space‐filling effects determines the role of the alkyl chains, either as network nodes or trapezoid walls, thus resulting in the order‐disorder transitions associated with emergence of quasiperiodicity. In‐depth analysis suggests a change from a quasiperiodic tiling involving trapezoids to a modified one with a contribution of trapezoid pair fusion. This work paves the way for understanding quasiperiodicity emergence and develops fundamental concepts for its generation by chemical design of non‐spherical molecules, aggregates, and frameworks based on dynamic reticular chemistry.