On the Mechanism of Soft Self-Assembly from Melt: The Ubiquitous Heat Capacity Hump and Spontaneous Melt Chirality

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 (Iso*). Based on experiments on new nonchiral monomers, dimers, and polymers, we construct a statistical theory that shows why many complex meso-structures form in two stages: continuous equilibrium growth of nano-clusters in melt through strong interactions, causing the C_p-maximum, followed by establishment of positional long-range order (LRO) through a weak first-order transition. We also show why many achiral compounds additionally form an intermediate chiral Iso* liquid through what we find is a second-order transition. We propose that the first process is equivalent to "supramolecular polymerization" in solutions, where the lack of intercluster interaction rules out 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. Clusters must first grow to critical size when, at T_c, the combined weak interactions reach ∼k_BT_c, prompting LRO formation. A situation similar to that in soft self-assembly is seen in spin ordering in magnetic crystals, but only near 0 K.