From 1 → 3 dendritic designs to fractal supramacromolecular constructs: understanding the pathway to the Sierpiński gasket

Abstract

The iterative synthetic protocols used for dendrimer construction were developed based on the desire to easily craft highly branched macromolecules with ideally an exact mass and tailored functionality. Inspired by arboreal design and precursors of the utilitarian macromolecules known as dendrimers today, our first examples employed predesigned, 1 → 3 or 1 → (1 + 2) C-branched, building blocks. Physical characteristics of the dendrimers, including their globular shapes, excellent solubility, and demonstrated aggregation, revealed the inherent supramolecular potential. The architecture that is characteristic of dendritic materials also exhibits obvious fractal qualities based on self-similar, repetitive, branched frameworks. Thus, both the fractal design and supramolecular aspects of these constructs are suggestive of a larger field of fractal materials that incorporate repeating geometries and are derived by complementary building block recognition and assembly. Use of 〈terpyridine-M(2+)-terpyridine〉 connectivity for the sides and tuned directed organic vertices has opened the door to other types of novel materials. This approach also circumvents the nonideality of dendrimers, since the heteroleptic, one-step, spontaneous self-assembly process facilitates quantitative outcomes.

Laplacian spectra of a class of small-world networks and their applications

“…We believe that recent advances in the synthesis of fractal supramacromolecular polymers21 will open new perspectives for the compounds constructed based on the symmetric small-world networks presented in the report. Finally, we remark that we expect to find more applications of the networks considered here; in particular, the analytic expressions for the Laplacian eigenvalues determined here will be of much help.…”

“…Although the structural disorder leads in case of many real networks like hyperbranched polymers to smoothing-out and averaging, the topological features are still reflected in the typical scaling behaviors20. Furthermore, recently a striking development of chemistry made possible the synthesis of the hierarchical, fractal Sierpinski-type compounds21. Undoubtedly, this new achievement will keep the interest of the theorists on the regular structures, especially on those with loops.…”

Fluorescent metallacycle-cored polymers via covalent linkage and their use as contrast agents for cell imaging

“…Coordination-driven self-assembly is an efficient approach to construct supramolecular coordination complexes (SCCs) (12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24). Due to the directionality of metal−ligand bonds and their moderate bond energies, the structures of SCCs can be finely tuned.…”

Self-assembly of a supramolecular hexagram and a supramolecular pentagram

“…59), the structure is stable even in a mixed counterion systems. It may due to the bigger molecular central holes (>3.5 nm) and larger molecular weight (close to 20,000 Da)36.…”

“…In the field of terpyridine (tpy)-based supramolecular chemistry3536, precise control over the shape and size of the architectures is regarded as a tremendous challenge. Recent noteworthy accomplishments with tpy-based architectures include Sierpinski hexagonal gasket, spoked wheel, ring-in-ring and cage-like macromolecules1617181937383940414243.…”