Stage-wise Pre-assembly in Melt Prior to Transitions to Bicontinuous Cubic Phases

We investigate two unusual phenomena in self-assembly of anisotropic molecules from isotropic (Iso) melt: a heat-capacity (C_p) maximum, and spontaneous formation of the recently discovered chiral liquid phase in achiral compounds (Iso*). Based on experiments on newly synthesised non-chiral monomers, dimers and polymers, we construct a thermodynamic theory that shows why many liquid crystals (LC) and some crystals form melt in two stages, i.e. (i) continuous equilibrium growth of nano-clusters in the melt through strong intermolecular core-core interactions, causing the C_p-maximum, followed by (ii) establishment of chiral long-range order (LRO) through a second-order Iso-Iso* transition and/or a first-order phase transition to a phase with positional LRO (Iso-LC, Iso*-LC, Iso*-crystal or Iso-crystal) such as bicontinuous cubic phases, including gyroid structures. The first process is found to be equivalent to cluster formation in solutions, known as “supramolecular polymerization”, where the lack of inter-cluster interaction rule out the establishment of LRO. Furthermore, we argue that separation into a broad and a sharp transition is universal in condensed matter where strong interactions by themselves cannot lead to LRO, either because the clusters are 1D or due to strong frustration. A situation similar to that in LCs is seen in spin ordering in magnetic crystals, but only near 0 K.