Construction of Sierpiński triangles up to the fifth order - Journal of the

Article pubs.acs.org/JACS

Construction of Sierpiń ski Triangles up to the Fifth Order Chao Li,†,∇ Xue Zhang,†,∇ Na Li,†,∇ Yawei Wang,† Jiajia Yang,† Gaochen Gu,† Yajie Zhang,† Shimin Hou,*,† Lianmao Peng,† Kai Wu,‡ Damian Nieckarz,§ Paweł Szabelski,∥ Hao Tang,⊥ and Yongfeng Wang*,†,# †

Key Laboratory for the Physics and Chemistry of Nanodevices, Department of Electronics, Peking University, Beijing 100871, China BNLMS, SKLSCUSS, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China § Supramolecular Chemistry Laboratory, Biological and Chemical Research Centre, University of Warsaw, Ż wirki i Wigury 101, 02-089 Warsaw, Poland ∥ Department of Theoretical Chemistry, Maria-Curie Skzodowska University, Pl. M.C. Skzodowskiej 3, 20-031 Lublin, Poland ⊥ CEMES-CNRS, Boîte Postale 94347, 31055 Toulouse, France # Peking University Information Technology Institute, Tianjin 300450, China ‡

S Supporting Information *

ABSTRACT: Self-similar fractal structures are of fundamental importance in science, mathematics, and aesthetics. A series of molecular defect-free Sierpiński triangle fractals have been constructed on surfaces recently. However, the highest order of the fractals is only 4 because of the limitation of kinetic growth. Here complete fifth-order Sierpiński triangles with a lateral length of 0.05 μm were successfully prepared in ultrahigh vacuum by a combination of templating and coassembly methods. Fe atoms, 4,4″-dicyano-1,1′:3′,1″terphenyl, and 1,3-bis(4-pyridyl)benzene molecules were used to build fractals on the reconstructed Au(100)-(hex) surface. The new strategy may be applied to construct various Sierpiński triangles of higher orders.

■

INTRODUCTION Self-similar fractals with fractional Hausdorff dimensions are “exactly the same at every scale or nearly the same at different scales”.1 They are of fundamental importance in science, engineering, mathematics, and aesthetics. Various fractals have been prepared either in solutions or on surfaces through sophisticated design.2−8 Recently, defect-free Sierpiński triangles (STs), representatives of various prototypical fractals, have been theoretically predicted and experimentally fabricated on single-crystalline surfaces.9−18 The reported STs are bonded via halogen bonding,10 metal−organic coordination,11−14 hydrogen bonding,15 and covalent bonding interactions.16,17 Preparation of high-order STs is a prerequisite to experimentally test the theoretically predicted magnetic, mechanical, and optical properties.19,20 Meanwhile, controlled fabrication of large STs is beneficial for understanding the formation mechanism of fractal structures. During the process of crystal growth, the Ostwald ripening mechanism makes small crystals disappear and leads to the formation of large crystals.21 However, it is difficult to form large STs, and the order of obtained STs is still limited to 4 in both experiments10−18 and simulations.9,22−24 The phenomenon is mainly due to the random formation of nucleation centers and followed limitation of kinetic growth. STs can grow larger © 2017 American Chemical Society

only by attachment of molecules or atoms at the three accessible vertices because both the atoms and molecules along the three sides of STs are saturated. When STs get larger, their perimeters increase while the number of active sites remains constant. As a result, the growth probability decreases, and STs of small orders form. Here we used a templating method25−28 to guide the formation of nucleation centers and a coassembly method29−34 to control the formation of STs. By the combination of these two methods, complete fifth-order STs with a lateral length of 0.05 μm were constructed on the reconstructed Au(100)-(hex) substrate. Through the templating effect of Au(100), Fe atoms and 4,4″-dicyano-1,1′:3′,1″-terphenyl (C3PC) molecules form one-dimensional (1D) double chains with metal−organic coordinating STs as building blocks. When around 13−26% of the C3PC molecules are replaced by 1,3-bis(4-pyridyl)benzene (BPyB) molecules, the coassembly effect breaks the chain structure and leads to the formation of STs up to the fifth order. Received: June 2, 2017 Published: September 8, 2017 13749

DOI: 10.1021/jacs.7b05720 J. Am. Chem. Soc. 2017, 139, 13749−13753

Article

Journal of the American Chemical Society

■

METHODS

The self-similarity property of the experimentally observed STs and corresponding models is presented in Figure 1b. The iterative procedure for the formation of STs is demonstrated by the brown triangles. Each initial equilateral ST-n is sequentially rescaled by a factor of 0.5, triplicated, and packed to generate an ST-(n+1). Three copies are formed when the side of an ST is doubled, which leads to the Hausdorff dimension of ln(3)/ ln(2) ≈ 1.58. In a C3PC-BPyB-Fe-ST-n, the total numbers of C3PC and BPyB molecules (Mn) and Fe atoms (An) are Mn = 3 /2(3n + 1) and An = 3n. For an ST-5, there are 366 molecules and 243 Fe atoms inside. Differentiation between C3PC and BPyB Molecules. There are two ways to differentiate between C3PC and BPyB molecules in STs. In STM images, C3PC molecules are expected to appear longer than BPyB molecules because of their different geometric sizes. The inset of Figure 2a shows a high-resolution STM image of an ST-1, where one large C3PC and small BPyB are marked by red and black dots, respectively. However, it is difficult to discern molecules in large-scale STM images (Figure 1) by their apparent lateral lengths. The challenge is tackled by mapping molecular states at certain

The experiments were performed using a scanning tunneling microscope (UNISOKU, USM-1500) with a base pressure of 10−10 Torr. The Au(100) and Au(111) surfaces were prepared by repetitive cycles of Ar ion sputtering and annealing. Fe atoms and C3PC and BPyB molecules were thermally deposited onto the substrates at room temperature from different Ta boats. All of the STM images were acquired with a Pt/Ir tip at a temperature of 4.3 K. The dI/dV spectra were acquired with a lock-in amplifier using a sample bias modulation of 30 mV. The STM images were processed with the software WSxM.35

■

RESULTS AND DISCUSSION Sierpiń ski Triangles up to the Fifth Order. Figure 1 shows typical STM topographic images of STs on Au(100)

Figure 1. Sierpiński triangles of high orders on Au(100). (a) The structure formed by Fe atoms and C3PC and BPyB molecules via coordination interaction. Its lower-right part is patched with modeled molecules and marked by white dashed line. The chemical structures of the C3PC and BPyB molecules are displayed at the upper left. The model of a coordination node comprising one Fe atom, one BPyB molecule, and two C3PC molecules is shown at the upper right. The white arrows indicate the surface [011] direction. Imaging parameters: V = 50 mV, I = 0.04 nA. (b) The family of C3PC-BPyB-Fe-ST-n with n equal to 0−5 and their corresponding models of STs.

after sublimation of Fe atoms and C3PC and BPyB molecules onto the substrate and annealing at 100 °C for 5 min. During preparation, the metal-to-linker ratio is larger than 2:3 and the C3PC-to-BPyB ratio is around 3:1. The STs are stabilized by coordination interactions between Fe atoms and the molecules, as shown by the models in the upper-right part of Figure 1a. Here we denote STs of order n as C3PC-BPyB-Fe-ST-n or STn, where n = 0 to 5. The structure shown in Figure 1a consists of two C3PC-BPyB-Fe-STs-5 and one C3PC-BPyB-Fe-ST-2. There are 495 Fe atoms and 745 molecules in the structure, much more than in previously reported STs.10,12 Its lower-right part is patched with modeled molecules and marked by white dashed line to get a larger ST.

Figure 2. Spectra and maps of differential conductance (dI/dV) measured on STs. (a) dI/dV curves acquired on the BPyB (black) and C3PC (red) molecules. The measured sites were marked on molecules by the black (BPyB) and red (C3PC) dots, respectively. (b) Constantheight dI/dV map of an ST-5 at V = 2 V with a modulation voltage of 30 mV. Three BPyB molecules in the upper part of the ST-5 are marked by white dots to guide the eye. The white arrow indicates the [011] direction. 13750

DOI: 10.1021/jacs.7b05720 J. Am. Chem. Soc. 2017, 139, 13749−13753

Article

Journal of the American Chemical Society

models are displayed in Figure 3b. The structure is stabilized through the coordination interaction between Fe atoms and molecular cyano groups. The template effect of the reconstructed Au(100)-(hex) substrate plays a dominant role in the formation of chains. As a resulf of the high corrugation of the surface reconstruction, molecular diffusion along [011] is expected to be easier than along other directions.14 The diffusion anisotropy favors the formation of one-dimensional structures instead of STs of higher orders. As a result, the highest order of STs formed by Fe and C3PC on Au(100) is only 3. The nearly equal distance between chains might be due to the long-range repulsion from the outermost positively charged H atoms of the chains. In the next step, we studied the structures formed by BPyB molecules and Fe atoms on Au(100). As expected, they formed STs via coordination bonds between Fe and N atoms (Figure 3c). A BPyB-Fe-ST-3, the largest observed ST, is marked by white dashed circle, and its corresponding model is shown in Figure 3d. One of its sides is adsorbed along the [011̅] direction, which is perpendicular to the reconstructed rows. There is a 30° orientation difference between BPyB-Fe-STs and C3PC-Fe-STs. The periodic distance between reconstructed rows (depicted by dashed green lines) is 1.44 nm. The calculated distance between two Fe atoms bonded to a C3PC molecule along the [011̅] direction is 1.46 nm (Figure 3b). The perfect match between these two distances is one of reasons for the formation of chains. If BPyB-Fe-STs and C3PC-Fe-STs adsorbed on Au(100) with the same orientation, the distance for BPyB would be only 1.17 nm (Figure 3d), which is much different from 1.44 nm. After rotation by 30° (Figure 3d), the distance is 1.35 nm, and the structure matching between the BPyB-Fe-STs and reconstructed rows gets much better. The experiments indicate that only coassembly of C3PC, BPyB, and Fe can lead to the formation of STs up to the fifth order. Figure 3e shows the structure formed at a BPyB:C3PC ratio of 1:3. From the statistics of this surface coverage ratio, the occupancies of ST-4 and ST-5 are 58% and 14%, respectively (Figure 3f). The ST-n occupancy is defined as the percentage of molecules forming ST-n with respect to the total number of molecules deposited on Au(100). The Templating Effect. In order to address the role of the templating effect on the formation of high-order STs, we repeated the experiments on Au(111) with a BPyB:C3PC ratio of 1:3 and all of the other parameters unchanged. Figure 4a shows a large-scale STM image of the formed coordination structures. The high-resolution STM image (Figure 4b) reveals that the STs consist of both C3PC and BPyB molecules, where the BPyB molecules are marked by white dots. The highest order of STs prepared on Au(111) by the coassembly method is only 3. In contrast, the orders of both C3PC-Fe-STs and BPyB-Fe-STs on Au(111) can reach 4 (Figure S3). The adsorption orientations of C3PC and BPyB molecules on Au(111) (Figure 4c) are derived from their STM images (Figure S3). Both sides of the molecular backbone of C3PC adsorb along the ⟨112̅⟩ directions. However, there is a 30° difference for the preferred adsorption direction of BPyB on Au(111) (Figure 4c). BPyB molecules in STs on Au(111) are forced to adsorb along the ⟨112̅⟩ direction, which is energetically unfavorable (Figure 4b). Because of the lack of a template, the C3PC-BPyB-Fe-STs tend to distort, and only small STs are formed on Au(111). The experiments demonstrate that both the templating effect and coassembly are crucial for the formation of high-order STs.

energies. Spectra of differential conductance (dI/dV) were measured at the centers of the C3PC and BPyB molecules, as shown in Figure 2a. Although the conductance peaks dominated by the lowest unoccupied molecular orbitals (LUMOs) of both molecules are close to 2.0 V, the conductance value of BPyB (black curve) is larger than that of C3PC (red curve). Therefore, the dI/dV map of a C3PCBPyB-Fe-ST-5 was recorded at 2.0 V (Figure 2b), where BPyB molecules appear remarkably brighter than C3PC molecules, and three BPyB molecules in the upper part are marked by white dots to guide the eye. It is easier to visually identify BPyB molecules by vertical contrast in the dI/dV map than by lateral length in the STM image (Figure S1). C3PC and BPyB molecules have different geometric sizes, and their coassembly might lead to wavy edges for the C3PC-BPyB-Fe-STs (Figure S2). Effect of Coassembly on the Formation of STs. The structure formed by Fe atoms and C3PC molecules was investigated first. After they were sublimated onto Au(100) and annealed at 100 °C for 5 min, arrays of one-dimensional double chains of ST-2 (Figure 3a) were observed along the surface [011] direction. The corresponding molecular and atomic

Figure 3. Effect of coassembly on the formation of STs on Au(100). (a, b) Large-scale STM image of double chains of ST-2 formed by Fe atoms and C3PC molecules and corresponding molecular model. (c, d) STM image of STs formed by Fe atoms and BPyB molecules and corresponding molecular model. (e) Large-scale STM image of STs formed by Fe atoms and BPyB and C3PC molecules. (f) Distribution of STs of different orders. The white arrows in the STM images indicate the [011] direction. Imaging parameters: (a) V = 1 V, I = 0.05 nA; (c) V = 0.1 V, I = 0.05 nA; (e) V = 100 mV, I = 0.04 nA. 13751

DOI: 10.1021/jacs.7b05720 J. Am. Chem. Soc. 2017, 139, 13749−13753

Article

Journal of the American Chemical Society

Figure 5. Influence of the C3PC:BPyB ratio on the formation of STs. (a) With a small BPyB:C3PC ratio of 1:10, 1D chains and STs of different orders coexist on the substrate. (b) BPyB molecules in the chain are marked by white dots. (c) When the BPyB:C3PC ratio reaches 1:5, the occupancy of chains decreases dramatically, and STs of high orders dominate the surface. (d) With a large BPyB:C3PC ratio of 2:1, the surface structures are determined by BPyB molecules, and only small STs are obtained. Imaging parameters: (a) V = 1 V, I = 0.05 nA; (b) V = 1 V, I = 0.05 nA; (c) V = 1 V, I = 0.04 nA; (d) V = 1 V, I = 0.05 nA. The white arrows indicate the [011] direction.

Figure 4. STs formed on Au(111) via coassembly. (a) Large-scale STM image of STs formed by Fe atoms and C3PC and BPyB molecules. (b) Enlarged STM image of STs in (a). The BPyB molecules are highlighted by white dots nearby. (c) Possible adsorbed orientations of C3PC and BPyB molecules on Au(111) deduced from STM images. Imaging parameters: (a) V = 1 V, I = 0.05 nA; (b) V = 10 mV, I = 0.05 nA. The white arrows indicate the [011̅ ] direction.

Formation Mechanism of STs of High Orders. To elaborate the formation mechanism of high-order STs, a series of controlled experiments were performed with other BPyB:C3PC ratios on the substrate. With small BPyB:C3PC ratios such as 1:10, 1D chains and STs of different orders coexist on the substrate (Figure 5a). In the chains, a small amount of C3PC molecules are replaced by BPyB, which are marked by neighboring white dots in Figure 5b. It should be be noted that the bridged and four adjacent molecules are all C3PC (Figures 5b and S4). When the BPyB:C3PC ratio reaches to 1:5, the occupancy of chains decreases dramatically, and STs of high orders dominate the surface (Figure 5c). At a ratio of 1:3, 1D crystalline chains totally disappear on the substrate (Figure 3e). When there are more BPyB molecules on Au(100), such as a BPyB:C3PC ratio of 2:1, the surface structures are determined by BPyB molecules, and only small STs are obtained (Figure 5d). In each ST-5, the percentage of BPyB ranges from 13% to 26% (Figure S5). This means that STs of high orders can be formed only with appropriate small BPyB:C3PC ratios. As a result of the templating effect of Au(100), the formation of nucleation centers is guided, and 1D chains with STs as building blocks are formed by Fe atoms and C3PC molecules. In C3PC-Fe-STs, the N−Fe−N bond angle calculated by density functional theory is around 120° (Figure S6). However, the four N−Fe−N angles around the labeled bridged C3PC molecules deviate from 120° remarkably (Figure 6a). They are 150°, 90°, 90°, and 150°, which makes the central bridged molecule energetically unfavorable. If the bridged C3PC molecule were replaced by a BPyB molecule, it would bind to only one Fe atom because of its short length (Figure 6b). If a

Figure 6. (a) Molecular and atomic model of the central structure of double chains. (b, c) Model in (a) with the bridged C3PC (b) or its neighboring molecule (c) replaced with a BPyB molecule.

BPyB molecule is substituted for one of the four adjacent C3PC molecules around the bridged C3PC molecule (Figure 6c), it would pull the bonded Fe atom away from the original position (Figure 6c), leading to the dissociation of the corresponding coordination bond to the bridged C3PC molecule. In either case, the chain structure gets more unstable and might collapse to form STs of high orders, where all of the molecules are saturated except those at three vertices. In C3PCBPyB-Fe-STs, the calculated Fe−C3PC and Fe−BPyB energies are −1.4 and −1.3 eV, respectively. Monte Carlo simulations indicate that this slight energy difference does not influence the growth of STs clearly (Figure S7). 13752

DOI: 10.1021/jacs.7b05720 J. Am. Chem. Soc. 2017, 139, 13749−13753

Article

Journal of the American Chemical Society

■

(11) Sun, Q.; Cai, L.; Ma, H.; Yuan, C.; Xu, W. Chem. Commun. 2015, 51, 14164−14166. (12) Li, N.; Zhang, X.; Gu, G.-C.; Wang, H.; Nieckarz, D.; Szabelski, P.; He, Y.; Wang, Y.; Lü, J.-T.; Tang, H.; Peng, L.−M.; Hou, S.-M.; Wu, K.; Wang, Y.-F. Chin. Chem. Lett. 2015, 26, 1198−1202. (13) Zhang, X.; Li, N.; Liu, L.; Gu, G.; Li, C.; Tang, H.; Peng, L.; Hou, S.; Wang, Y. Chem. Commun. 2016, 52, 10578−10581. (14) Li, N.; Gu, G.; Zhang, X.; Song, D.; Zhang, Y.; Teo, B. K.; Peng, L.-M.; Hou, S.; Wang, Y. Chem. Commun. 2017, 53, 3469−3472. (15) Zhang, X.; Li, N.; Gu, G.-C; Wang, H.; Nieckarz, D.; Szabelski, P.; He, Y.; Wang, Y.; Xie, C.; Shen, Z.-Y; Lü, J.-T.; Tang, H.; Peng, L.M.; Hou, S.-M.; Wu, K.; Wang, Y.-F. ACS Nano 2015, 9, 11909− 11915. (16) Gu, G.; Li, N.; Liu, L.; Zhang, X.; Wu, Q.; Nieckarz, D.; Szabelski, P.; Peng, L.; Teo, B. K.; Hou, S.; Wang, Y. RSC Adv. 2016, 6, 66548−66552. (17) Rastgoo-Lahrood, A.; Martsinovich, N.; Lischka, M.; Eichhorn, J.; Szabelski, P.; Nieckarz, D.; Strunskus, T.; Das, K.; Schmittel, M.; Heckl, W. M.; Lackinger, M. ACS Nano 2016, 10, 10901−10911. (18) Gu, G.-C; Li, N.; Zhang, X.; Hou, S.-M; Wang, Y.-F; Wu, K. Acta Phys.-Chim. Sin. 2016, 32, 195−200. (19) Wang, A.; Zhao, M. Phys. Chem. Chem. Phys. 2015, 17, 21837− 21844. (20) van Veen, E.; Yuan, S.; Katsnelson, M. I.; Polini, M.; Tomadin, A. Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 93, 115428. (21) Voorhees, P. W. J. Stat. Phys. 1985, 38, 231−252. (22) Nieckarz, D.; Szabelski, P. J. Phys. Chem. C 2013, 117, 11229− 11241. (23) Nieckarz, D.; Szabelski, P. Chem. Commun. 2016, 52, 11642− 11645. (24) Zhang, Z.; Xie, W.-J; Yang, Y.; Sun, G.; Gao, Y.-Q Acta Phys.Chim. Sin. 2017, 33, 539−547. (25) Smerdon, J.; Young, K.; Lowe, M.; Hars, S.; Yadav, T.; Hesp, D.; Dhanak, V.; Tsai, A.; Sharma, H.; McGrath, R. Nano Lett. 2014, 14, 1184−1189. (26) Liu, M.; Liu, M.; She, L.; Zha, Z.; Pan, J.; Li, S.; Li, T.; He, Y.; Cai, Z.; Wang, J.; Zheng, Y.; Qiu, X.; Zhong, D. Nat. Commun. 2017, 8, 14924. (27) O’Sullivan, M. C.; Sprafke, J. K.; Kondratuk, D. V.; Rinfray, C.; Claridge, T. D.; Saywell, A.; Blunt, M. O.; O’Shea, J. N.; Beton, P. H.; Malfois, M.; Anderson, H. L. Nature 2011, 469, 72−75. (28) Vang, R. T.; Honkala, K.; Dahl, S.; Vestergaard, E. K.; Schnadt, J.; Lægsgaard, E.; Clausen, B. S.; Nørskov, J. K.; Besenbacher, F. Nat. Mater. 2005, 4, 160−162. (29) Chen, T.; Yang, W.; Wang, D.; Wan, L. Nat. Commun. 2013, 4, 1389. (30) Kudernac, T.; Lei, S.; Elemans, J. A.; De Feyter, S. Chem. Soc. Rev. 2009, 38, 402−421. (31) Mura, M.; Silly, F.; Burlakov, V.; Castell, M. R.; Briggs, G. A. D.; Kantorovich, L. N. Phys. Rev. Lett. 2012, 108, 176103. (32) Shi, Z.; Lin, N. J. Am. Chem. Soc. 2010, 132, 10756−10761. (33) Langner, A.; Tait, S. L.; Lin, N.; Rajadurai, C.; Ruben, M.; Kern, K. Proc. Natl. Acad. Sci. U. S. A. 2007, 104, 17927−17930. (34) De Feyter, S.; Miura, A.; Yao, S.; Chen, Z.; Würthner, F.; Jonkheijm, P.; Schenning, A. P.; Meijer, E.; De Schryver, F. C. Nano Lett. 2005, 5, 77−81. (35) Horcas, I.; Fernández, R.; Gomez-Rodriguez, J.; Colchero, J.; Gómez-Herrero, J.; Baro, A. Rev. Sci. Instrum. 2007, 78, 013705.

CONCLUSIONS Complete fifth-order STs with a lateral length of 0.05 μm were successfully prepared on the reconstructed Au(100)-(hex) substrate by a combination of templating and coassembly methods. The growth mechanism of STs was investigated by low-temperature scanning tunneling microscopy. The new strategy may be applied to construct various Sierpiński triangles of higher orders.

■

ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.7b05720. Representative extended analysis of additional STM and DFT results (PDF)

■

AUTHOR INFORMATION

Corresponding Authors

*[email protected] *[email protected] ORCID

Na Li: 0000-0001-6924-8387 Shimin Hou: 0000-0002-5042-4405 Kai Wu: 0000-0002-5016-0251 Paweł Szabelski: 0000-0002-3543-9430 Yongfeng Wang: 0000-0002-8171-3189 Author Contributions ∇

C.L., X.Z., and N.L. contributed equally.

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (21522301, 21373020, 21403008, 61621061, 21433011, 91527303, and 21333001) and the Ministry of Science and Technology (2014CB239302, 2013CB933404, and 2017YFA0205003).

■

REFERENCES

(1) Mandelbrot, B. B. The Fractal Grometry of Nature; Freeman: San Francisco, CA, 1982. (2) Brune, H.; Romainczyk, C.; Roder, H.; Kern, K. Nature 1994, 369, 469−471. (3) Wang, M.; Van Enckevort, W. J.; Ming, N.-b.; Bennema, P. Nature 1994, 367, 438−441. (4) Newkome, G. R.; Wang, P.; Moorefield, C. N.; Cho, T. J.; Mohapatra, P. P.; Li, S.; Hwang, S.-H.; Lukoyanova, O.; Echegoyen, L.; Palagallo, J. A.; Iancu, V.; Hla, S.-W. Science 2006, 312, 1782−1785. (5) Fujibayashi, K.; Hariadi, R.; Park, S. H.; Winfree, E.; Murata, S. Nano Lett. 2008, 8, 1791−1797. (6) Otero, R.; Lukas, M.; Kelly, R. E.; Xu, W.; Lægsgaard, E.; Stensgaard, I.; Kantorovich, L. N.; Besenbacher, F. Science 2008, 319, 312−315. (7) Fractals in Science; Bunde, A., Havlin, S., Eds.; Springer: Berlin, 1994. (8) Sarkar, R.; Guo, K.; Moorefield, C. N.; Saunders, M. J.; Wesdemiotis, C.; Newkome, G. R. Angew. Chem., Int. Ed. 2014, 53, 12182−12185. (9) Nieckarz, D.; Szabelski, P. Chem. Commun. 2014, 50, 6843−6845. (10) Shang, J.; Wang, Y.; Chen, M.; Dai, J.; Zhou, X.; Kuttner, J.; Hilt, G.; Shao, X.; Gottfried, J. M.; Wu, K. Nat. Chem. 2015, 7, 389− 393. 13753

DOI: 10.1021/jacs.7b05720 J. Am. Chem. Soc. 2017, 139, 13749−13753