Controlling Molecular Growth between Fractals and Crystals on

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Xue Zhang,†,# Na Li,†,# Gao-Chen Gu,† Hao Wang,† Damian Nieckarz,‡ Pawez Szabelski,‡ Yang He,† Yu Wang,† Chao Xie,† Zi-Yong Shen,† Jing-Tao Lu¨,z,§ Hao Tang, Lian-Mao Peng,† Shi-Min Hou,*,†,§ Kai Wu,*,^,9 and Yong-Feng Wang*,†,§

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Controlling Molecular Growth between Fractals and Crystals on Surfaces †

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Key Laboratory for the Physics and Chemistry of Nanodevices, Department of Electronics, and ^BNLMS, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China, ‡Department of Theoretical Chemistry, Maria-Curie Skzodowska University, Pl. M.C. Skzodowskiej 3, 20-031 Lublin, Poland, z School of Physics, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan 430074, China, §Beida Information Research (BIR), Tianjin 300457, China, Groupe Matriaux Crystallins sous Contrainte, CEMES-CNRS, Boîte Postale 94347, 31055 Toulouse, France, and 9SPURc, 1 CREATE Way, #15-01, CREATE Tower, Singapore 138602. #X. Zhang and N. Li contributed equally to this paper.

ABSTRACT Recent studies demonstrate that simple functional molecules, which

usually form two-dimensional (2D) crystal structures when adsorbed on solid substrates, are also able to self-assemble into ordered openwork fractal aggregates. To direct and control the growth of such fractal supramolecules, it is necessary to explore the conditions under which both fractal and crystalline patterns develop and coexist. In this contribution, we study the coexistence of Sierpinski triangle (ST) fractals and 2D molecular crystals that were formed by 4,400 -dihydroxy-1,10 :30 ,100 terphenyl molecules on Au(111) in ultrahigh vacuum. Growth competition between the STs and 2D crystals was realized by tuning substrate and molecular surface coverage and changing the functional groups of the molecular building block. Density functional theory calculations and Monte Carlo simulations are used to characterize the process. Both experimental and theoretical results demonstrate the possibility of steering the surface self-assembly to generate fractal and nonfractal structures made up of the same molecular building block. ski triangle . molecular crystal . hydrogen bond . self-assebly . scanning tunneling microscopy KEYWORDS: fractal . Sierpin

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elf-similar fractal structures occur in nature in the form of clouds, trees, snowflakes, lightening, the human circulatory system, and many other objects. To understand in depth the basic mechanism governing the formation of these complex patterns, it is vital to study their growth at a laboratory scale, in a fully controllable environment. A prototypical system that is particularly suitable for that purpose is the molecular or atomic assembly prepared by chemical or physical methods. Due to the importance of molecular/atomic fractals in both fundamental science and technology, it is crucial to construct them in a stepwise manner and study their structural evolution, in particular to determine the conditions under which the fractal structure develops. While molecular and atomic dendritic fractals with irregular shapes, formed through the diffusion limited aggregation (DLA) process, have been realized and studied in detail by scanning tunneling microscopy (STM) with atomic resolution,1,2 molecular structures resembling ordered ZHANG ET AL.

self-similar mathematical sets, for example, ski triangle (ST) or hexagon, have the Sierpin been synthesized in solutions.3
8 Very recently, we reported the self-assembly of extended, defect-free, and surface-supported STs built of halogenated ditopic terphenyl molecules adsorbed on the Ag(111) surface under ultrahigh-vacuum conditions.9 According to these experimental results and to our earlier theoretical predictions,10 a 120 V-shaped molecule equipped with terminal interaction centers is a general prerequisite to grow the ST fractals. The Br
Br halogen bonding provided by the V-shaped molecules used in our previous study favored the formation of planar 3-fold nodal motifs, which are the basic structural elements of the STs.9 As a consequence, open triangular aggregates with unprecedented regularity were created, even after annealing of the adsorbed phase. No molecular crystals were observed with the bromine-terminated molecules at low coverage. This situation is remarkably different from what has been observed in most adsorbed systems, where VOL. 9

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* Address correspondence to [email protected], [email protected], [email protected]. Received for review July 17, 2015 and accepted October 26, 2015. Published online October 27, 2015 10.1021/acsnano.5b04427 C 2015 American Chemical Society

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RESULTS AND DISCUSSION Figure 1a
d presents the DFT-optimized (a) and anticipated (b
d) molecular configurations, in which the H3PH molecules form 3-fold nodes sustained by the cyclic O 3 3 3 H
O bonds. These configurations correspond to the successive generations of the canonical ski triangle, and they are denoted here by Sierpin H3PH-ST-n with n equal to 0 (a), 1 (b), 2 (c), and 3 (d). As demonstrated in the figure by the blue triangles, the creation of the ST-n is an iterative procedure that starts with an equilateral triangle (Figure 1a, top-right corner) on a plane. This initial triangle is rescaled by a factor of 0.5 and triplicated. The three resulting copies are next glued with each other at vertices (Figure 1b, top-right corner), and the above steps are repeated to obtain subsequent generations of the ST. When the side of the ST is doubled, three copies are generated, which results in the Hausdorff dimension of ln(3)/ln(2) ≈ 1.58. As shown in Figure 1e
h, the molecules of H3PH could form triangular fractal aggregates that are structurally ZHANG ET AL.

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molecules usually form periodic two-dimensional (2D) crystals.11
15 As the 2D crystallization can be encountered in the case where molecules are potentially able to selfassemble into STs, it is important to identify the main intrinsic factors affecting the preference of the adsorbed synthons to create STs and 2D crystals. One of such factors is the nature of interactions cementing these assemblies. Depending on directionality, specificity, and strength of the intermolecular interactions, the self-assembly can, for example, result in the formation of either of the two possible structures (ST or 2D crystal) or a mixture of them. In our case, in order to observe the coexistence of the ST fractals and competing crystalline patterns, the terminal groups of the V-shaped molecules should exhibit a similar tendency to form 3-fold nodes (trimers) and nodal motifs with different connectivity. This can be realized, for instance, with the help of hydrogen bonds (H-bonds), which are known to be moderately strong and capable of forming multiple cyclic motifs.16 To explore the above possibility, a V-shaped 4,400 -dihydroxy-1,10 :30 ,100 terphenyl (H3PH) molecule bearing two hydroxyl groups in the outer phenyl rings was studied here. Its self-assemblies on noble metallic substrates were investigated under variable conditions. The main purposes of our study are to uncover the coexistence of the open ST structures and 2D crystal packings in H-bonded systems and to unravel the ways in which the self-assembly can be directed toward each of these outcomes. Our experimental investigations were further complemented by theoretical modeling based on the Monte Carlo (MC) simulations and density functional theory (DFT) calculations, aiming at a better understanding of the interaction patterns in the surface assemblies.

Figure 1. (a) DFT-optimized structure of the H3PH trimer sustained by the cyclic O 3 3 3 H
O hydrogen bonds. (e) Constant height STM image of the adsorbed molecular configuration corresponding to (a) on Au(111) obtained at 100 mV. (b
d) Iterative procedure in which H3PH trimers are sequentially triplicated, rescaled, and glued to form Sierpi nski triangles of the consecutive generations. The blue triangles overlaid on the molecular models illustrate the correspondence between the basic structural units of the molecular self-assembly and geometric construction. (f
h) Constant height topographies of H3PH-ST-1 to H3PHST-3 imaged at 10 mV. The white arrows in the STM images indicate the Æ112æ direction, and their length corresponds to 0.5 nm (e), 0.8 nm (f), 1.2 nm (g), and 2.5 nm (h), respectively.

identical to the molecular ST-n models in Figure 1a
d. The Hausdorff dimension of these aggregates calculated using the box counting method is equal to about 1.53, being close to the theoretical value, 1.58 (see Figure S1). To understand the formation of H-bonded STs, we developed a simplified coarse-grained model based on our previous results related to the fractal structure formation in surface-confined metal
organic assemblies.10,17 The main objective of the investigations described herein is to identify main structural factors (i.e., molecular geometry and directionality of the interactions) responsible for the development of H-bonded ST aggregates comprising molecules such as H3PH. To model the fractal self-assembly, we performed lattice Monte Carlo simulations in which H3PH molecules were treated as flat, rigid, and bent structures comprising three connected segments, as shown VOL. 9

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ARTICLE Figure 2. (a) Coarse-grained representation of the H3PH molecule adsorbed on a triangular lattice representing the Au(111) surface. The red arrows indicate the interaction directions assumed in the simplified pattern of intermolecular hydrogen bonding. A 3-fold heterotactic node (one mirror-image form) responsible for the stabilization of the STs is shown on the right. The red dashed lines illustrate the interactions between molecules forming the node. (b) Number of nodes with different connectivity plotted as a function temperature; these results are averages over 15 replicas of (c). The gray circles indicate the temperatures at which the snapshots shown in Figure S3 were taken. (c) Snapshot of the overlayer comprising 1333 molecules of H3PH adsorbed on a triangular lattice; T = 0.1.

in Figure 2a. These segments correspond to the phenyl rings in H3PH, and each of them was allowed to occupy one site on a triangular lattice representative of the Au(111) or Ag(111) surface. The red arrows pointing from the terminal segments shown in Figure 2a are the interaction directions that enable the formation of H-bonds between neighboring molecules whose hydroxyl groups are in direct contact (Figure 1a and Figure S2a). Accordingly, the interaction between a pair of molecules became possible only when their relative orientation was in a collinear alignment (fr) of the interaction directions. Moreover, additional restrictions on the formation of molecular nodes were imposed to accelerate the self-assembly of extended ZHANG ET AL.

aggregates (see Supporting Information). As demonstrated in Figure 2c, the simplified MC model proposed here predicts the formation of H-bonded fractal triangular aggregates with n varying from 0 to 4. Similar to our previous theoretical results on metal
organic selfassembly10,17 and to the recent experimental findings on the 2D halogen-bonded systems,9 the 3-fold heterotactic nodes in Figure 2a play a key role in stabilizing the STs. In these nodes three H3PH tectons meet to form a unique planar motif involving such alignment of the three contributing molecules where two have parallel peripheral arms (Figure 1a and Figure 2a). The resulting nodal motif is the basic structural unit of the STs observed in the simulations as well as in the experiment.9 VOL. 9

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An important consequence of the general topological requirement stated above is that the nature of the interactions cementing the 3-fold nodes plays only a secondary role so that the STs can be realized using tectons with diverse chemical functional groups. Formation of these nodes directs the fractal growth, and, as shown in Figure 2b, it occurs rapidly when the overlayer is sufficiently cooled (T < ∼0.3; see Supporting Information). This structural transition involves an enhanced self-assembly of the STs that is illustrated in the snapshots (see Figure S3) taken at the temperatures marked by gray circles in Figure 2c. A similar temperature dependence was previously observed for the metal
organic self-assembly of the STs.10 Apart from the STs, quasi-one-dimensional (1D) chains and a 2D crystal coexist on Au(111) (Figure 3a and Figure S5). These periodic chains (Figure 3b) are built of heterotactic tetramers whose schematic structure is shown in Figure 3d. The limited width of facecentered-cubic (fcc) regions of the Au(111) surface prevents widening of the growing wires so that all hydroxyl groups in H3PH are buried inside them to form 4-fold heterotactic nodes. Two-dimensional molecular crystals (Figure 3c) are formed by tightly packed homotactic tetramers (Figure 3e), which constitute an extended 2D crystal. To characterize the competition between the ST fractals and the crystalline phase, we estimated changes in their relative content with varying surface coverage. These results are summarized in Figure 3e. At low coverages, the H3PH molecules selfassemble mainly into the STs and sparse chain structures (Figure S5a). With increasing coverage, the ordered 2D crystals emerge and finally dominate the substrate (Figure S5b). To gain deeper insight into the energetics of the intermolecular interactions stabilizing the H3PH supramolecules, we also performed DFT calculations in which the substrate was neglected. Dimer, trimer, tetramer, pentamer, and hexamer configurations of H3PH were optimized, and the most stable structures along with the corresponding binding energies are listed in Table 1. As can be seen in the table, both total binding energy and binding energy per H-bond increase when the number of H3PH molecules in the cluster grows from 2 to 3 and finally to 4. However, as the number of H3PH molecules further increases, the total binding energy and the binding energy per H-bond decrease rapidly due to the steric hindrance (calculations including substrates gave similar results; see Supporting Information). This is consistent with our experimental observation that the surface remains covered mainly by trimers and tetramers, and only by a small amount of pentamers (0.2%) at a coverage of 0.1 ML. From the substrate-free DFT calculations, we can deduce that the H3PH tetramer is the most energetically favorable structural motif that is responsible for

Figure 3. STs and crystalline structures coexist on Au(111) where quasi-1D and 2D crystals are marked (a). Molecular H3PH wires (b) with periodic structure and 2D crystalline patterns (c) are composed of heterotactic and homotactic tetrameric units shown schematically in (d) and (e). These DFT-optimized structural units are overlaid on the corresponding STM images, which were obtained at constant height mode with a bias voltage of 20 mV (b) and 10 mV (c). The length of the white arrows in (b) and (c) corresponds to 2.5 nm. In (c) the square unit cell with a side of 3.1 nm is delimited by the yellow dashed line. The effect of surface coverage on the relative abundance of the ST and crystalline phase is summarized in (f).

the formation of 2D crystals. However, the structure of molecular trimers (or 3-fold nodes) matches best the symmetry of the (111) metallic substrates studied here, so that the surface-guided ST fractal growth is largely facilitated at low coverage. The binding energies of the 3-fold nodes listed in the table differ by 0.07 eV, which may suggest that the windmill nodes should occur more frequently compared to the heterotactic ones. According to the experimental results, the “incorrect” windmill nodes are practically absent in the adsorbed overlayer. The reason for this discrepancy lies probably in the molecule
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TABLE 1. DFT-Optimized Geometries and Energies (in eV) of the Molecular Clusters Comprising Different Numbers of H3PH Molecules

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motif. Another factor that can be responsible for the observed exclusive tendency of H3PH to form 3-fold heterotactic nodes has an entropic origin, related to intrinsic structural properties of this molecule. To explain this, we use the model bimolecular clusters (2-fold nodes) shown in Figure S2b. Specifically, the formation of a 3-fold node occurs through attachment of a third molecule to one of these clusters. Importantly, the unbound arm of the new molecule can have one of two possible orientations that determine the type of resulting 3-fold node (windmill vs homotactic). Simple statistical considerations based on counting the possible outcomes show that the chance of formation of the heterotactic node is 3 times larger than that of the windmill one. Obviously, this conclusion neglects long-range correlations in the growing structure and assumes that the energies of both 3-fold nodal motifs are identical or very similar. In real situations, when the preference for the formation of the heterotactic nodes can be additionally amplified by the underlying surface, this combined entropic
energetic mechanism could effectively enhance the fractal growth. However, to explore this effect, further DFT calculations are required, in which the surface is taken into account and energies of the possible adsorbed nodal motifs are calculated. To assess the influence of the molecule
substrate interactions on the formation of the STs, additional STM experiments with a more reactive Ag(111) surface were performed, in which all of the remaining parameters and procedures were unchanged. Similar to the previous results obtained with Au(111), STs (Figure 4a) and 2D crystals (Figure 4b) coexist on Ag(111). In this case, the Hausdorff dimension is equal to about 1.53 (see Figure S1), and it equals that obtained previously for the Au(111) surface. However, the structure of the Ag-supported 2D crystals differs remarkably from that shown in Figure 3c for the Au(111) surface. According to the substrate-free DFT calculations, the intermolecular O 3 3 3 H
O hydrogen bonding favors the formation of the tetramer homotactic (windmill) nodes (see Figure 3e). In the case of the closely packed H3PH islands on Au(111) the rather weak molecule
substrate interaction does not change this preference. On Ag(111), however, the stronger corrugation of the molecule
substrate interaction potential promotes the formation of 3-fold heterotactic nodes, which match the symmetry of the surface. This subtle balance between the molecule
molecule and molecule
Ag surface interactions leads to the coexistence of heterotactic trimers and homotactic tetramers in the molecular islands created on Ag(111) (Figure 4b). The magnified image of these coexistent units (Figure 4c) and their simplified model (Figure 4d) show that each H3PH molecule of the tetramer forms a heterotactic trimer with two neighboring molecules, resulting in the ratio 1:4 between the tetrameric and trimeric cyclic

Figure 4. (a) STM image of the H3PH-ST-3 fractal on Ag(111). (b) 2D molecular crystals formed by mixed H3PH trimers and tetramers on Ag(111) where the unit cell is marked with the yellow dashed line. (c, d) Magnified STM image and molecular packing model of (b). The STM images were recorded at the constant height (a, 1.0 V) and constant current (b, c, 1.0 V 10 pA) mode. The length of the white arrow in panels (a)
(c) is equal to 2.5, 3.5, and 1.0 nm, respectively.

H-bonds in these molecular arrays. Due to the lack of long-range reconstruction, which occurs for Au(111), the H3PH molecules adsorbed on the Ag substrate tend to aggregate into large, tightly packed islands, and only around 10% of them form the ST supramolecules (Figure 4a). To determine the role of the strength of hydrogen bonding in the formation of STs, 4,400 -diformyl1,10 :30 ,100 -terphenyl (F3PF, Figure 5a) molecules were synthesized, bearing two terminal formyl groups, which replaced the hydroxyl groups of H3PH. These molecules were deposited on both Au(111) and Ag(111) according to the same experimental protocol described previously. It has been generally accepted that the intermolecular hydrogen bonds provided by VOL. 9

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formyl groups are rather weak. From the charge distribution calculations we performed, it follows that the H atoms of
OH and
CHO carry 0.47 and 0.11 positive charge (Figure 5a and Figure S7), respectively. For comparison, H atoms of the phenyl groups of F3PH possess 0.22 positive charge. On the basis of these results it can be expected that H3PH and F3PF prefer to form H-bonds through exclusive O 3 3 3 H
O and O 3 3 3 H
C connections, respectively. For F3PF this tendency is illustrated in the STM image (Figure 5b) and in the schematic structure (Figure 5c), in which most of the F3PF molecules form 10 O 3 3 3 H
C hydrogen bonds (see the purple lines) with neighboring molecules. This type of binding leads to a “braid” structure instead of ST fractal aggregates. CONCLUSIONS In summary, we have demonstrated the possibility of directing the surface-confined self-assembly of

METHOD Experiments were carried out with a Unisoku scanning tunneling microscope at a temperature of 4.3 K with a base pressure of 10
10 Torr. Single-crystalline Au(111) and Ag(111) surfaces were cleaned by repetitive cycles of Ar ion sputtering and annealing. To achieve high-quality imaging, Pt/Ir tips were annealed first in the vacuum chamber and treated by dipping into substrates in a controlled way. H3PH molecules were

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Figure 5. (a) Schematic molecular structure of F3PF. NPA charges of O and H atoms, which are crucial in the formation of hydrogen bonds, are shown next to these atoms. (b) Braid structure formed by F3PF on Ag(111) at 0.2 ML. The length of the white arrow corresponds to 2.0 nm. (c) Schematic model of the braid structure in which one F3PF molecule interacts with four other molecules, forming 10 weak C
H 3 3 3 O hydrogen bonds.

simple V-shaped molecular bricks toward ordered fractal aggregates and periodic crystalline structures sustained by H-bonds. It was shown for the first time that the ST molecular fractals could coexist with 2D crystals and that the growth competition between these phases could be controlled by tuning the adsorbate density, chemistry of the substrate, and the intermolecular interactions. Using the simplified Monte Carlo modeling and DFT calculations, we found that the key factors that promoted the fractal structure formation were the suitably encoded directional interactions (H-bonding), strong corrugation of the adsorbing (111) surface, and a relatively low adsorbate density. The UHV experiments performed with the ditopic H3PH and F3PF organic tectons on Au(111) and Ag(111) confirmed these predictions. We observed that on Au(111) and at low surface coverage, the H3PH molecules mainly selfassembled into the STs and sparse chain structures whose width was limited by the size of the fcc zones of the reconstructed gold surface. With increasing coverage, the ordered 2D crystal comprising the homotactic tetrameric units emerged, and it coexisted with STs. Further increase in the adsorbate density resulted in the exclusive formation of this crystalline phase. Swapping the substrate to Ag(111) did not lead to qualitatively different results at low coverage, at which the STs also grew, but caused the molecules to form the new compact pattern that is a mixture of 3- and 4-fold nodal motifs. In this case, the main source of the observed molecular arrangement was the subtle interplay between molecule
molecule and molecule
substrate interactions. Finally, the strength of the H-bonding between the terminal interactions became weaker after replacing the
OH groups with
CHO groups. This led to the formation of braid-type crystalline structures rather than STs on both Au(111) and Ag(111). The insights from our combined experimental and theoretical studies can be helpful in steering the 2D self-assembly of different molecular synthons to create fractal supramolecular architectures. These findings hint at how to select the optimal molecular building block, the substrate, and external conditions to obtain the ST molecular fractals and how to stabilize them. Our results can be especially important in the synthesis of covalently bonded fractal supramolecules, which have not been realized up to now and could exhibit unusual physicochemical properties.

thermally deposited on the substrates held at room temperature and imaged at liquid helium temperature. DFT calculations were carried out using the SIESTA code, in which the van der Waals (vdW) density functional, known as the KBM or the OptB88-vdW functional, was employed.18,19 The atomic cores were described by improved Troullier
Martins pseudopotentials,20 and the wave functions of the valence electrons were expanded in terms of a double-ζ plus polarization

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Acknowledgment. This work was jointly supported by National Natural Science Foundation of China (21522301, 21373020, 21403008, 61321001, 21433011, 21133001, 913000002), Ministry of Science and Technology (2014CB239302, 2013CB933404), and the Research Fund for the Doctoral Program of Higher Education (20130001110029). Partial support from the Singapore NRF CREATE-SPURc project is also acknowledged. Supporting Information Available: The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.5b04427. Details of model and calculation, the Hausdorff dimension, large-scale STM images, and a pentamer image (PDF)

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(DZP) finite-range numerical orbital basis set. The appropriateness of the selected vdW functional, the constructed pseudopotentials, and basis functions were tested on a phenol dimer in the gas phase. After optimization, only one hydrogen bond was formed between the two hydroxyl groups in the most stable phenol dimer configuration, and the O
H 3 3 3 O bond length of 2.897 Å was found to be slightly overestimated compared with the experimental value (2.833 Å).21 The associated binding energy was equal to 0.313 eV, in good agreement with the benchmark value (0.306 eV) obtained at the CCSD(T)/cc-pVTZ level.22 Conflict of Interest: The authors declare no competing financial interest.

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