Shape and fluctuations of frustrated self-assembled nano ribbons

Abstract

Self-assembly is an important process by which nontrivial structures are formed on the sub-micron scales. Such processes are governed by chemical and physical principles that dictate how the molecular interactions affect the supramolecular geometry. Currently there is no general framework that links between molecular properties and the supramolecular morphology with its size parameters. Here we introduce a new paradigm for the description and analysis of supramolecular structures that self-assemble via short-range interactions. Analysis of molecular interactions determines inputs to the theory of incompatible elasticity, which provides analytic expressions for supramolecular shape and fluctuations. We derive quantitative predictions for specific amphiphiles that self-assembled into chiral nanoribbons. These are quantitatively confirmed experimentally, revealing unique shape evolution, unusual mechanics and statistics, proving that the assemblies are geometrically incompatible. The success in predicting equilibrium and statistics suggests the approach as a new framework for quantitative study of a large variety of self-assembled nanostructures.

Geometric Frustration in Molecular Crystals

“…This yields conformations that continuously vary between helical ribbons with a straight center‐line (for relatively narrow ribbons) to cylindrical tapes of helical centre‐line (for wider ribbons), which for very developed ribbons may close into a hollow tubes. Such structures have been observed in manmade bi‐layered structures, [15] naturally occurring seed‐pods [14] and macromolecular assemblies [16,17] . For the case of Benzamide, the width of the formed bilayers is comparable with their thickness and helical ribbons of straight centerlines are observed.…”

“…Such structures have been observed in manmade bi-layered structures, [15] naturally occurring seed-pods [14] and macromolecular assemblies. [16,17] For the case of Benzamide, the width of the formed bilayers is comparable with their thickness and helical ribbons of straight centerlines are observed.…”

Frustrated self-assembly of non-Euclidean crystals of nanoparticles

“…One interesting mechanism that naturally emerges in this theory is the propagation of chirality from the molecular scale (i.e., l - or d -Cys ligands on the NPs) to the assembled helices at the micron scale. As pointed out in the literature, chiral symmetry breaking mechanisms are highly nontrivial, and LH structures at the molecular scale can lead to either LH or RH structures at larger length scales, depending on the binding mechanism and the direction 62 – 64 . Here, the intrinsic chiral symmetry breaking of binding tetrahedra into 1D tetrahelices 65 provides a convenient channel for molecular scale chirality to propagate to the micron scale, as we discussed.…”

Multiscale Structural Elucidation of Peptide Nanotubes by X-Ray Scattering Methods

“…One potential avenue is exploring the complex pathways of self-assembly involving the coexistence of multiple structural motifs. A particular challenge is formulating theoretical models that can predict structural parameters from molecular properties (Nyrkova and Semenov, 2010 ; Zhang et al, 2019 ). The analysis software tools need to be better optimized for complete modeling of the self-assembled structures from the known molecular architecture.…”