Thermal Hysteresis and Seeding of Twisted Fibers Formed by Achiral Discotic Particles

Using transient equilibria (TREQ) to measure the thermodynamics of slowly assembling supramolecular systems

Supramolecular chemistry involves the noncovalent assembly of monomers into materials with unique properties and wide-ranging applications. Thermal analysis is a key analytical tool in this field, as it provides quantitative thermodynamic information on both the structural stability and nature of the underlying molecular interactions. However, there exist many supramolecular systems whose kinetics are so slow that the thermodynamic methods currently applied are unreliable or fail completely. We have developed a simple and rapid spectroscopic method for extracting accurate thermodynamic parameters from these systems. It is based on repeatedly raising and lowering the temperature during assembly and identifying the points of transient equilibrium as they are passed on the up- and down-scans. In a proof-of-principle application to the coassembly of polydeoxyadenosine (polyA) containing 15 adenosines and cyanuric acid (CA), we found that roughly 30% of the CA binding sites on the polyA chains were unoccupied, with implications for high-valence systems.

Chiral and achiral mechanisms of self-limiting assembly of twisted bundles

A generalized theory of the self-limiting assembly of twisted bundles of filaments and columns is presented. Bundles and fibers form in a broad variety of supramolecular systems, from biological to synthetic materials. A widely-invoked mechanism to explain their finite diameter relies on chirality transfer from the molecular constituents to collective twist of the assembly, the effect of which frustrates the lateral assembly and can select equilibrium, finite diameters of bundles. In this article, the thermodynamics of twisted-bundle assembly is analyzed to understand if chirality transfer is necessary for self-limitation, or instead, if spontaneously-twisting, achiral bundles also exhibit self-limited assembly. A generalized description is invoked for the elastic costs imposed by twist for bundles of various states of intra-bundle order from nematic to crystalline, as well as a generic mechanism for generating twist, classified both by chirality but also the twist susceptibility of inter-filament alignment. The theory provides a comprehensive set of predictions for the equilibrium twist and size of bundles as a function of surface energy as well as chirality, twist susceptibility, and elasticity of bundles. Moreover, it shows that while spontaneous twist can lead to self-limitation, assembly of twisted achiral bundles can be distinguished qualitatively in terms of their range of equilibrium sizes and thermodynamic stability relative to bulk (untwisted) states.

Curved boundaries and chiral instabilities - two sources of twist in homeotropic nematic tori

Many liquid crystalline systems display spontaneous breaking of achiral symmetry, as achiral molecules aggregate into large chiral domains. In confined cylinders with homeotropic boundary conditions, chromonic liquid crystals - which have a twist elastic modulus which is at least an order of magnitude less than their splay and bend counter parts - adopt a twisted escaped radial texture (TER) to minimize their free energy, whilst 5CB - which has all three elastic constants roughly comparable - does not. In a recent series of experiments, we have shown that 5CB confined to tori and bent cylindrical capillaries with homeotropic boundary conditions also adopts a TER structure resulting from the curved nature of the confining boundaries [P. W. Ellis et al., Phys. Rev. Lett., 2018, 247803]. We shall call this microscopic twist, as the twisted director organization not only depends on the confinement geometry but also on the values of elastic moduli. Additionally, we demonstrate theoretically that the curved geometry of the boundary induces a twist in the escaped radial (ER) texture. Moving the escaped core of the structure towards the center of the torus not only lowers the splay and bend energies, but lowers the energetic cost of this distinct source for twist that we shall call geometric twist. As the torus becomes more curved, the ideal location for the escaped core approaches the inner radius of the torus.