Nanoassembly of a Fractal Polymer: A Molecular "Sierpinski Hexagonal Gasket"

Newkome, George R.; Wang, Pingshan; Moorefield, Charles N.; Cho, Tae Joon; Mohapatra, Prabhu P.; Li, Sinan; Hwang, Seok Ho; Lukoyanova, Olena; Echegoyen, Luís; Palagallo, Judith; Iancu, Violeta; Hla, Saw‐Wai

doi:10.1126/science.1125894

Cited by 303 publications

(215 citation statements)

References 16 publications

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“…Sierpi ski hexagons could be synthesized in solution from bis-terpyridine building blocks coordinatively bound to 36 Ru and 6 Fe centers and imaged by STM after subsequent deposition onto Au(111). 13 More recently, self-assembly of STs directly on surfaces has emerged as alternative approach. Feasibility was first demonstrated with dibromo-terphenyl and dibromo-quaterphenyl on Ag(111), resulting in STs based on hydrogen and halogen-bonds.…”

Section: Resultsmentioning

confidence: 99%

From Au–Thiolate Chains to Thioether Sierpiński Triangles: The Versatile Surface Chemistry of 1,3,5-Tris(4-mercaptophenyl)benzene on Au(111)

et al. 2016

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Self-assembly of 1,3,5-tris(4-mercaptophenyl)benzene (TMB) -a three-fold symmetric, thiol functionalized aromatic molecule -was studied on Au(111) with the aim to realize extended Authiolate linked molecular architectures. The focus lay on resolving thermally activated structural and chemical changes by a combination of microscopy and spectroscopy. Thereby Scanning Tunneling Microscopy provided submolecularly resolved structural information, while the chemical state of sulfur was assessed by X-ray Photoelectron Spectroscopy. Directly after room temperature deposition only less well ordered structures were observed. Mild annealing promoted the first structural transition into ordered molecular chains, partly organized in homochiral molecular braids. Further annealing led to self-similar Sierpi ski triangles, while annealing at even higher temperatures again resulted in mostly disordered structures. Both the irregular aggregates observed at room temperature and the chains were identified as metalorganic assemblies, whereby two out of the three intermolecular binding motifs are energetically equivalent according to Density Functional Theory simulations. The emergence of Sierpi ski triangles is driven by a chemical transformation, i.e. the conversion of coordinative Au-thiolate to covalent thioether linkages, and can be further understood by Monte Carlo simulations. The great structural variance of TMB on Au(111) can on one hand be explained by the energetic equivalence of two binding motifs. On the other hand, the unexpected chemical transition even enhances the structural variance and results in thiol-derived covalent molecular architectures.3 KEYWORDS surface chemistry, on-surface synthesis, thiolate, thioether, fractals, STM, XPS, DFT, Monte CarloThe notorious affinity of thiols to gold is beneficial for molecular nano-science. 1 Important examples include ligation of gold nanoparticles, 2, 3 two probe conductance measurements of single molecules, [4][5][6][7] and surface functionalization of Au(111) by Self-Assembled Monolayers (SAMs). 8,9 All of these applications rely on anchoring via strong Au-thiolate bonds. Even though thiolate SAMs are widespread, structural details of the anchor bond were discussed controversially for a long time. Yet, a consensus seems to be reached insofar as Au-thiolate complexes formed with gold adatoms play an important role. 10 The promising properties of RSAu-SR linkages, in particular their electric conductance and their ability to form spontaneously on Au(111) motivated the present study with the aim to utilize these linkages for extended molecular nanostructures. To this end 1,3,5-tris(4-mercaptophenyl)benzene (TMB) as a threefold functionalized and suitable model compound for network formation is studied on Au(111).Owing to both the extended triphenylbenzene backbone and the three-point anchoring via thiolate-surface bonds, planar adsorption is anticipated as an important prerequisite for extended networks. In contrast to SAMs, where the prevalent monothiols adopt upri...

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Section: Resultsmentioning

confidence: 99%

From Au–Thiolate Chains to Thioether Sierpiński Triangles: The Versatile Surface Chemistry of 1,3,5-Tris(4-mercaptophenyl)benzene on Au(111)

et al. 2016

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“…(15). For particular values of the number of steps, Rule 90 generates exact shapes of the Sierpinski gasket (SG).…”

Section: Cellular Automatamentioning

confidence: 99%

“…In particular, models based on deterministic or exact self-similar fractals (i.e., fractals that are self-similar at every point, such as the Koch snowflake, Cantor set, or Mandelbrot cube) have been frequently used, since this type of fractals allows an analytical representation of various geometrical parameters (radius of gyration) or of the scattering intensity spectrum. Although for most fractals generated by natural processes, this is only an approximation, in the case of deterministic nano-and micro-materials obtained recently such as 2D Sierpinski gaskets [15] and Cantor sets [16], or 3D Menger sponge [17] and octahedral structures [18], this approximation becomes exact.…”

Section: Introductionmentioning

confidence: 99%

Small-Angle Scattering from Mass and Surface Fractals

Anitas¹

2018

Complexity in Biological and Physical Systems - Bifurcations, Solitons and Fractals

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The concepts of mass and surface fractals are introduced, and the corresponding smallangle scattering (SAS; X-rays, neutrons) intensities are computed. It is shown how to resolve the fractal structure of various complex systems from experimental scattering measurements, and how obtained data are related to specific features of the fractal models. We present and discuss various mass and surface fractal structures, including fractals generated from iterated function systems and cellular automata. In addition to the fractal dimension and the overall fractal size, the suggested analysis allows us to obtain the iteration number, the number of basic units which form the fractal and the scaling factor.

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“…Self-assembly protocols have been developed to achieve regular surface tessellations, including the semiregular Kagomé lattice (11)(12)(13), and even more complex tiling patterns or surface decorations (25)(26)(27)(28)(29)(30). Despite the striking advances, five-vertex structures remain a challenging issue, reflecting the lack of adequate complementary polygonal molecular modules and planar fivefold coordination nodes, respectively.…”

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confidence: 99%

Five-vertex Archimedean surface tessellation by lanthanide-directed molecular self-assembly

Écija

Urgel

Papageorgiou

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

128

109

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The tessellation of the Euclidean plane by regular polygons has been contemplated since ancient times and presents intriguing aspects embracing mathematics, art, and crystallography. Significant efforts were devoted to engineer specific 2D interfacial tessellations at the molecular level, but periodic patterns with distinct five-vertex motifs remained elusive. Here, we report a direct scanning tunneling microscopy investigation on the ceriumdirected assembly of linear polyphenyl molecular linkers with terminal carbonitrile groups on a smooth Ag(111) noble-metal surface. We demonstrate the spontaneous formation of fivefold Celigand coordination motifs, which are planar and flexible, such that vertices connecting simultaneously trigonal and square polygons can be expressed. By tuning the concentration and the stoichiometric ratio of rare-earth metal centers to ligands, a hierarchic assembly with dodecameric units and a surface-confined metalorganic coordination network yielding the semiregular Archimedean snub square tiling could be fabricated.T he tiling of surfaces is relevant for pure art (1), mathematics (2, 3), material physics (4), and molecular science (5). Johannes Kepler's pertaining, rigorous analysis revealed four centuries ago that in the Euclidean plane 11 tessellations based on symmetric polygonal units exist (6): three consist of a specific polygon (so-called regular tilings with squares, triangles, or hexagons, respectively), whereas eight require the combination of two or more different polygons (named semiregular or Archimedean tilings from triangles, squares, hexagons, octagons, and dodecagons).Manifestations of regular tessellations at the atomic and molecular level are ubiquitous, including crystalline planes and surfaces of elemental or molecular crystals, and honeycomb structures encountered, e.g., for graphene sheets, strain relief and supramolecular lattices. In addition, the family of semiregular Archimedean tilings features intriguing characteristics. They may represent geometrically frustrated magnets (7) or provide novel routes for constructing photonic crystals (8). However, with the exception of the frequently realized trihexagonal tiling (also known as the Kagomé lattice) (9-15), the other semiregular Archimedean tiling patterns remain largely unexplored.Three of the semiregular Archimedean tilings correspond to five-vertex configurations (Fig. 1 A-C): the snub hexagonal tiling (four triangles and one hexagon at each vertex, labeled 3.3.3.3.6), the elongated triangular tiling (three triangles and two squares join at each vertex in a 3.3.3.4.4 sequence), and the snub square tiling (three triangles and two squares at each vertex; labeled 3.3.4.3.4). They have been identified in bulk materials, such as layered crystalline structures of complex metallic alloys (4, 16-18), supramolecular dendritic liquids (19), liquid crystals (20), special star-branched polymers (21, 22), and binary nanoparticle superlattices (23). Moreover, recent experiments with colloids at a quasicrystalline substra...

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Nanoassembly of a Fractal Polymer: A Molecular "Sierpinski Hexagonal Gasket"

Cited by 303 publications

References 16 publications

From Au–Thiolate Chains to Thioether Sierpiński Triangles: The Versatile Surface Chemistry of 1,3,5-Tris(4-mercaptophenyl)benzene on Au(111)

From Au–Thiolate Chains to Thioether Sierpiński Triangles: The Versatile Surface Chemistry of 1,3,5-Tris(4-mercaptophenyl)benzene on Au(111)

Small-Angle Scattering from Mass and Surface Fractals

Five-vertex Archimedean surface tessellation by lanthanide-directed molecular self-assembly

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