Networks of Hexagonal Hierarchy from a Self-Similar Tritopic Molecule Yan-Qiong Sun,†,§ Chen Yang,† Zhengtao Xu,*,† Matthias Zeller,‡ and Allen D. Hunter‡ Department of Biology and Chemistry, City UniVersity of Hong Kong, 83 Tat Chee AVenue, Kowloon, Hong Kong, P. R. China, and Department of Chemistry, Youngstown State UniVersity, One UniVersity Plaza, Youngstown, Ohio 44555
CRYSTAL GROWTH & DESIGN 2009 VOL. 9, NO. 4 1663–1665
ReceiVed February 14, 2009
ABSTRACT: We use the unifying concept of self-similarity to design and construct solid-state networks. The coordination networks reported here feature distinct correlation between the self-similar features of discrete molecules and the hierarchical patterns in infinite networks. We use as the building block a symmetrically backfolded, supertritopic dendrimer, which coordinates with AgSbF6 to form complex layered networks that can be dissected as hexagonal hierarchy patterns inherently derived from the self-similar features of the individual molecules. The concept of self-similarity unifies the complex and the simple in nature, and is widely used in studying the myriad systems including costal lines, trees, neural networks, and even urban development.1 At the molecular level, self-similarity finds itself in the well-known dendrimers2 and the less common nondendritic systems.3 Studies of functionally sophisticated dendrimers are mostly centered on the molecular structures and properties, while efforts to integrate dendrimers into crystalline networks remain quite limited.4 Such cross-cutting efforts are, however, important in many regards. Besides the reasons elegantly outlined by Wuest,4d such efforts may, in general, help uncover fundamental building principles of extended structures, and integrate richer molecular functions into the intensely studied crystalline networks.5 Here we introduce a dendritic molecule (L, Figure 1) with an unconventional backfolded geometry as a tectonic unit that bridges the self-similar features between the individual molecule and the resultant networks, generating within a single crystalline structure infinite nets featuring the self-similar motif of a hexagonal hierarchy (see Figure S1, Supporting Information for the motif).6 As seen in Figure 1a, L is a symmetrically back-folded, selfsimilar molecule with functional groups located at end points associated with distinct levels of the structural hierarchy. Specifically, the termini of the three G1 branches are equipped with the -CN groups, while the MeS- thioether groups are affixed to the six G2 termini. Molecule L thus compares well with the ternary tree that is superimposable on a geometrically equivalent Sierpinski triangle in Figure 1b. The ternary tree consists of three identical main branches set off at 120°; each of the three ends is itself the starting point of three subbranches in the same direction, and so it goes on. On the other hand, the Sierpinski triangle is obtained by cutting at the midpoints of the edges of a triangle to make four smaller triangles, of which the central one is removed; one proceeds likewise with each of the remaining three triangles, and so it goes on. As a building block for coordination networks, molecule L offers two distinct sets of chemical functions (e.g., the G1 sites of -CN groups and the G2 sites of the MeS- groups) for coordination to metal ions. This contrasts well with previously used dendrimer building blocks, in which all the binding sites are geometrically equivalent.4c,d The back-folding geometry7 in L also differs from most other dendrimers, which are usually designed to imitate the shape of a biological tree, with the subbranches taking a starburst, radiant geometry (see molecule L1 in Figure 1c, for example4a). * To whom correspondence should be addressed. E-mail: zhengtao@ cityu.edu.hk. † City University of Hong Kong. ‡ Youngstown State University. § Present address: Department of Chemistry, Fuzhou University, Fuzhou, Fujian 350002, China.
As will be discussed below, such a backfolded molecular structure impacts significantly the structural hierarchy of the chemical connectivity in the resultant nets. Molecule L and AgSbF6 crystallized in a mixed solvents of toluene and THF to form a complex, multilayer compound (henceforth called 1).8 The crystal structure of 1 features an overall composition of 3L · 8AgSbF6 · 6THF, with two types of cationic layers alternating one another along the c axis, and the SbF6- anions and THF guests located in the interstices (see Figure S2, Supporting Information).9 Both layers consist of two-dimensional (2D) networks based on the coordination interactions between the Ag+ ions and molecules of L: one has the composition of 2L · 5Ag+, and features a double sheet structure with two honeycomb networks stacked together; the other (L · 3Ag+) contains only one single sheet. We now elaborate on the two layers while emphasizing the selfsimilar features. In the double sheet layer (2L · 5Ag+), the G1 branches of L bond to one set of Ag+ ions to form an infinite net, while the G2 branches bond to a different set of Ag+ ions and form a second netsand the two nets are hierarchically related. As seen in Figure 2a, the G1 sites of -CN groups coordinate to a first set of Ag+ ions in a trigonal planar fashion (Ag-N distances: 2.273 and 2.275 Å), and result in a 2D hexagonal net based on the G1 branches.10 Two such nets are stacked together to form a double sheet honeycomb structure, with the Ag+ ions from one net overlapping with the amine center of the other net (average distance between the nets: 3.81 Å). The G2 sites of the MeS- groups are positioned inside these G1 hexagons, and coordinate to a second set of Ag+ ions (in a roughly trigonal planar geometry; Ag-S distances: 2.624, 2,642, and 2.664 Å). Overall, 12 S atoms are located within each G1 hexagon of the above double-sheet network, and they pick up three Ag+ ions (confirmed by X-ray diffraction and elemental analysis) that are disordered over six positions. The six half-occupied Ag+ sites are arranged in a boat conformation (like in cyclohexane), and interconnected by the MeS- groups to form a distinct hexagonal shape on a smaller structural scale (i.e., the G2 hexagon), as shown in Figure 2b.11 Thus, while the G1 branches of molecule L and the associated Ag+ ions constitute the first order hexagonal net, the G2 branches and the associated Ag+ ions (the G2 hexagon) track the second order net. Overall, a clean-cut dual mapping exists from the G1 and G2 branches in molecule L to the first order net and the second order net in the 2D net of 2L · 5Ag+, and the selfsimilar pattern formed by the first- and second-order nets here is topologically equivalent to the hierarchical pattern of Figure S1, Supporting Information. A visually more appealing presentation of the second-order hexagonal feature of this network can be obtained when the
10.1021/cg9001863 CCC: $40.75 2009 American Chemical Society Published on Web 03/06/2009
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Figure 1. Three self-similar objects. (a) A supertritopic molecule (L) with rigid, backfolded secondary branches. (b) A ternary tree (red) superimposed on a geometrically equivalent Sierpinski triangle. (c) A molecule (L1) with flexible secondary branches and less distinct backfolded character; it can take a radiant form that differs from the backfolded shapes in (a) and (b).
Figure 2. The two types of networks in 1. (a) A hexagonal sheet based on the coordination between the -CN groups and Ag+ ions in the double sheet network. (b) A full view of the double sheet network together with the SbF6- anions and a secondary net derived from these anions (the green grid). The primary net is also shown in a purple grid. (c) The single sheet network. The upper left inset shows the coordination sphere of the Ag+ ion.
positions of the SbF6- anions are considered. The two types of SbF6- anions are distributed on both sides of the coordination net. In a projection normal to the 2D net (Figure 2b), pairs of type I are seen at the center of each hexagon (associated with the G2 hexagon Ag+ ions at Ag-F distances of 3.552 and 3.724 Å); type II lie beyond the G2 hexagon and form a hexagonal shape within each G1 hexagon, there being six of them within each G1 hexagon. To visualize the second-order hexagonal net, a dot is placed at the midpoint between each pair of nearest SbF6- anions within each G1 hexagon; it is by connecting these dots that one obtains a secondorder net, which is topologically equivalent to the chemical connectivity based on G2 branches and the associated Ag+ ions. A second-order net thus formulated apparently reflects the hexagonal hierarchy into which the cations and anions are arranged so as to optimize the energetically significant electrostatic interaction in this system. In the single sheet layer of 1, the Ag+ ion is coordinated in a trigonal planar fashion to two MeS- groups (from the same L molecule) and one -CN group (from a neighboring L molecule; see also Figure 2c; bond distances: Ag-N 2.154 Å, Ag-S 2.507 and 2.511 Å). The resultant 2D pattern features a hexagonal net consisting of two types of hexagonal tiles: one formed by the six G2 branches within the same L molecule (this one contains the triphenylamine core of molecule L), the other by three G1 branches and three G2 branches in an alternate fashion. Thus, the G1 branches and the G2 branches are now integrated within the same hexagonal net, contrasting sharply with their hierarchical division in the above double sheet structure. In other words, the -CN group and the two associated MeS- groups act jointly as a trigonal planar building unit for the hexagonal net. Notably, this hierarchical convergence of the G1 and G2 branches is effected by the self-similar, backfolded geometry of L, in which each G2 branch is folded 120° back from
the main branch. By contrast, in a starburst geometry, the corresponding angle would be acute, and would not lead to a trigonal orientation between the G1 and G2 branches. Features of hexagonal hierarchy in other forms, however, do exist in this single sheet assembly. The two types of hexagonal tiles here exhibit a 2:1 ratio, and their distribution is isostructural to that of the second-order net in the above double sheet structure. The hexagonal hierarchy becomes prominent when the SbF6- anions located on the two sides of this network are included. Viewed normal to the network (Figure 2c), the anions distinctly trace a hexagonal net on a higher structural order relative to the hexagon tiles. The hierarchical relationship thus uncovered is identical to that of the above-mentioned double sheet, and serves to unify these two networks that differ markedly in both chemical connectivity and composition. Such unification further holds in the network formed by a dendritic building block L1 (composition: L1 · 4AgCF3SO3) reported earlier.4a As seen in Figure S3, Supporting Information, the hierarchical division of the primary (with the -CN termini) and secondary branches (the ethylene oxide chain), as well as the arrangement of the cations and anions, is similar to the double sheet in 1. There is, however, one major difference. Unlike the G2 Ag+ sites that are linked together by the MeS- groups in the double sheet of 1 (Figure 2b), no chemical link exists between the six second-order Ag+ ions to form a secondary hexagon loop here. Each second-order Ag+ ion is instead surrounded by two of the outgoing, radiant ethylene oxide side chains, forming a trefoil-like motif around the first-order Ag+ ion. This comparison suggests another significant role of the backfolded geometry of L: it predisposes the G2 branches to form an infinite chemical connectivity that is geometrically more compatible with the secondorder net in a hexagonal hierarchy. Further studies are, however,
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needed to fully characterize the role of the backfolded geometry in network formation. In summary, the crystal structure of 1 reveals a clear correlation of the self-similar features between the molecule and the resultant networks, and serves to illustrate self-similarity as a rational design element in the making of advanced network systems. On the practical side, the helical shape in backfolded, supertritopic dendrimers helps impose non-centrosymmetric space groups in the resultant networks and might lead to potentially useful properties such as nonlinear optics and piezoelectricity.5b,c,12
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Acknowledgment. This work is supported by the Research Grants Council of Hong Kong [Project No. 9041212 (CityU 103407)]. Y.S. is supported by a postdoc grant from the Research Scholarship Enhancement Scheme of CityU. The diffractometer was funded by NSF grant 0087210, by the Ohio Board of Regents grant CAP-491, and by YSU. Supporting Information Available: Crystallographic data in CIF format for 1. Detailed experimental procedures. Additional figures of crystal structures. This material is available free of charge via the Internet at http://pubs.acs.org.
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