Abstract
SummaryFractals are a series of intricate patterns with aesthetic, mathematic, and philosophic significance. The Sierpiński triangles have been known for more than one hundred years, but only recently discrete shape-persistent low-generation (mainly ST-1) fractal supramolecules have been realized. Herein, we report a retro-assembly pathway to the nanometer-scale, supra-macromolecular second-generation Sierpiński triangle and its third-generation saturated counterpart (Pascal's triangle). These gigantic triangular assemblies are unambiguously confirmed by NMR, DOSY, ESI-MS, TWIM-MS, TEM, and AFM analyses. Notably, the dense-packed counterions of these discrete triangular architectures could further form supramolecular hydro-gels in water. This work not only provides a fundamental chemical pathway to explore various giant supramolecular constructs and further overcome the synthetic limitation of complicated molecular fractals, but also presents a new type of supramolecular hydro-gels with potential in controlled release applications.
Highlights
Self-similar fractals were described as ‘‘exactly the same at every scale or nearly the same at different scales’’ by Mandelbrot in 1975 (Mandelbrot, 1982; Peitgen et al, 1992)
We report a retro-assembly pathway to the nanometer-scale, supra-macromolecular secondgeneration Sierpinski triangle and its third-generation saturated counterpart (Pascal’s triangle). These gigantic triangular assemblies are unambiguously confirmed by nuclear magnetic resonance (NMR), diffusion-ordered spectroscopy (DOSY), electrospray ionization mass spectrometry (ESI-MS), traveling wave ion mobility mass spectrometry (TWIM-MS), transmission electron microscopy (TEM), and atomic force microscopy (AFM) analyses
For Pascal’s triangle (PT; Figure 1), it is a triangular array of the binomial coefficients, which is named after the French mathematician Blaise Pascal (Wolfram, 1984)
Summary
Self-similar fractals were described as ‘‘exactly the same at every scale or nearly the same at different scales’’ by Mandelbrot in 1975 (Mandelbrot, 1982; Peitgen et al, 1992).
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