Leonardo's rule, self-similarity and wind-induced stresses in trees

Examining botanical trees, Leonardo da Vinci noted that the total cross-section of branches is conserved across branching nodes. In this Letter, it is proposed that this rule is a consequence of the tree skeleton having a self-similar structure and the branch diameters being adjusted to resist wind-induced loads

Supramolecular copolymerization driven by integrative self-sorting of hydrogen-bonded rosettes.

Molecular recognition to preorganize noncovalently polymerizable supramolecular complexes is a characteristic process of natural supramolecular polymers, and such recognition processes allow for dynamic self-alteration, yielding complex polymer systems with extraordinarily high efficiency in their targeted function. We herein show an example of such molecular recognition-controlled kinetic assembly/disassembly processes within artificial supramolecular polymer systems using six-membered hydrogen-bonded supramolecular complexes (rosettes). Electron-rich and poor monomers are prepared that kinetically coassemble through a temperature-controlled protocol into amorphous coaggregates comprising a diverse mixture of rosettes. Over days, the electrostatic interaction between two monomers induces an integrative self-sorting of rosettes. While the electron-rich monomer inherently forms toroidal homopolymers, the additional electrostatic interaction that can also guide rosette association allows helicoidal growth of supramolecular copolymers that are comprised of an alternating array of two monomers. Upon heating, the helicoidal copolymers undergo a catastrophic transition into amorphous coaggregates via entropy-driven randomization of the monomers in the rosette

Self-folding of supramolecular polymers into bioinspired topology.

Folding one-dimensional polymer chains into well-defined topologies represents an important organization process for proteins, but replicating this process for supramolecular polymers remains a challenging task. We report supramolecular polymers that can fold into protein-like topologies. Our approach is based on curvature-forming supramolecular rosettes, which affords kinetic control over the extent of helical folding in the resulting supramolecular fibers by changing the cooling rate for polymerization. When using a slow cooling rate, we obtained misfolded fibers containing a minor amount of helical domains that folded on a time scale of days into unique topologies reminiscent of the protein tertiary structures. Thermodynamic analysis of fibers with varying degrees of folding revealed that the folding is accompanied by a large enthalpic gain. The self-folding proceeds via ordering of misfolded domains in the main chain using helical domains as templates, as fully misfolded fibers prepared by a fast cooling rate do not self-fold

Light-induced unfolding and refolding of supramolecular polymer nanofibres.

Unlike classical covalent polymers, one-dimensionally (1D) elongated supramolecular polymers (SPs) can be encoded with high degrees of internal order by the cooperative aggregation of molecular subunits, which endows these SPs with extraordinary properties and functions. However, this internal order has not yet been exploited to generate and dynamically control well-defined higher-order (secondary) conformations of the SP backbone, which may induce functionality that is comparable to protein folding/unfolding. Herein, we report light-induced conformational changes of SPs based on the 1D exotic stacking of hydrogen-bonded azobenzene hexamers. The stacking causes a unique internal order that leads to spontaneous curvature, which allows accessing conformations that range from randomly folded to helically folded coils. The reversible photoisomerization of the azobenzene moiety destroys or recovers the curvature of the main chain, which demonstrates external control over the SP conformation that may ultimately lead to biological functions

Self-assembled poly-catenanes from supramolecular toroidal building blocks

Mechanical interlocking of molecules (catenation) is a nontrivial challenge in modern synthetic chemistry and materials science1,2. One strategy to achieve catenation is the design of pre-annular molecules that are capable of both efficient cyclization and of pre-organizing another precursor to engage in subsequent interlocking3,4,5,6,7,8,9. This task is particularly difficult when the annular target is composed of a large ensemble of molecules, that is, when it is a supramolecular assembly. However, the construction of such unprecedented assemblies would enable the visualization of nontrivial nanotopologies through microscopy techniques, which would not only satisfy academic curiosity but also pave the way to the development of materials with nanotopology-derived properties. Here we report the synthesis of such a nanotopology using fibrous supramolecular assemblies with intrinsic curvature. Using a solvent-mixing strategy, we kinetically organized a molecule that can elongate into toroids with a radius of about 13 nanometres. Atomic force microscopy on the resulting nanoscale toroids revealed a high percentage of catenation, which is sufficient to yield ‘nanolympiadane’10, a nanoscale catenane composed of five interlocked toroids. Spectroscopic and theoretical studies suggested that this unusually high degree of catenation stems from the secondary nucleation of the precursor molecules around the toroids. By modifying the self-assembly protocol to promote ring closure and secondary nucleation, a maximum catenation number of 22 was confirmed by atomic force microscopy

Simultaneous SAXS and SANS Analysis for the Detection of Toroidal Supramolecular Polymers Composed of Noncovalent Supermacrocycles in Solution.

Molecular self-assembly primarily occurs in solution. To better understand this process, techniques capable of probing the solvated state are consequently required. Small-angle scattering (SAS) has a proven ability to detect and characterize solutions, but it is rarely applied to more complex assembly shapes. Here, small-angle X-ray and neutron scattering are applied to observe toroidal assemblies in solution. Combined analysis confirms that the toroids have a core-shell structure, with a π-conjugated core and an alkyl shell into which solvent penetrates. The dimensions determined by SAS agree well with those obtained by (dried-state) atomic force microscopy. Increasing the number of naphthalene units in the molecular building block yields greater rigidity, as evidenced by a larger toroid and a reduction in solvent penetration into the shell. The detailed structural analysis demonstrates the applicability of SAS to monitor complex solution-based self-assembly

Self-assembled poly-catenanes from supramolecular toroidal building blocks

Mechanical interlocking of molecules (catenation) is a nontrivial challenge in modern synthetic chemistry and materials science1,2. One strategy to achieve catenation is the design of pre-annular molecules that are capable of both efficient cyclization and of pre-organizing another precursor to engage in subsequent interlocking3–9. This task is particularly difficult when the annular target is composed of a large ensemble of molecules, that is, when it is a supramolecular assembly. However, the construction of such unprecedented assemblies would enable the visualization of nontrivial nanotopologies through microscopy techniques, which would not only satisfy academic curiosity but also pave the way to the development of materials with nanotopology-derived properties. Here we report the synthesis of such a nanotopology using fibrous supramolecular assemblies with intrinsic curvature. Using a solvent-mixing strategy, we kinetically organized a molecule that can elongate into toroids with a radius of about 13 nanometres. Atomic force microscopy on the resulting nanoscale toroids revealed a high percentage of catenation, which is sufficient to yield ‘nanolympiadane’10, a nanoscale catenane composed of five interlocked toroids. Spectroscopic and theoretical studies suggested that this unusually high degree of catenation stems from the secondary nucleation of the precursor molecules around the toroids. By modifying the self-assembly protocol to promote ring closure and secondary nucleation, a maximum catenation number of 22 was confirmed by atomic force microscopy