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Controlling Molecular Growth between Fractals and Crystals on Surfaces Xue Zhang, Na Li, Gao-Chen Gu, Hao Wang, Damian Nieckarz, Pawel Szabelski, Yang He, Yu Wang, Chao Xie, Ziyong Shen, Jing-Tao Lu, Hao Tang, Lian-Mao Peng, Shi-Min Hou, Kai Wu, and Yongfeng Wang ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.5b04427 • Publication Date (Web): 27 Oct 2015 Downloaded from http://pubs.acs.org on November 1, 2015
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Controlling Molecular Growth between Fractals and Crystals on Surfaces Xue Zhang,†,# Na Li,†,# Gao-Chen Gu,† Hao Wang,† Damian Nieckarz,‡ Pawel Szabelski,‡ Yang He,† Yu Wang,† Chao Xie,† Zi-Yong Shen,† Jing-Tao L¨u,¶,§ Hao Tang,k Lian-Mao Peng,† Shi-Min Hou,∗,†,§ Kai Wu,∗,⊥ and Yong-Feng Wang∗,†,§ Key Laboratory for the Physics and Chemistry of Nanodevices, Department of Electronics, Peking University, Beijing 100871, China, Department of Theoretical Chemistry, Maria-Curie Sklodowska University, Pl. M.C. Sklodowskiej 3, 20-031 Lublin, Poland, 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, Boˆıte Postale 94347, 31055 Toulouse, France, and BNLMS, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China E-mail:
[email protected];
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[email protected] Abstract Recent studies demonstrate that simple functional molecules, which usually form two-dimensional (2D) crystal structures when adsorbed on solid substrates, are also ∗
To whom correspondence should be addressed Department of Electronics, Peking University ‡ Maria-Curie Sklodowska University ¶ School of Physics, Huazhong University of Science and Technology § BIR k CEMES-CNRS ⊥ College of Chemistry and Molecular Engineering, Peking University # These authors contributed equally to this paper †
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able to self-assemble into ordered openwork fractal aggregates. To direct and control 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 Sierpi´ nski triangle (ST) fractals and 2D molecular crystals which were formed by 4,4”-dihydroxy-1,1’:3’,1”-terphenyl molecules on Au(111) in ultra-high vacuum. Growth competition between the STs and 2D crystals was realized by tuning substrate, 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 non-fractal structures made up of the same molecular building block.
KEYWORD: fractal · Sierpi´ nski triangle · molecular crystal · hydrogen bond · selfassebly · scanning tunneling microscopy Self-similar fractal structures occur in nature in the form of clouds, trees, snowflakes, lightenings, the human circulatory system and many other objects. To understand in depth basic mechanism governing for 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 which is particularly suitable for that purpose is the molecular or atomic assembly prepared by chemical or physical method. Due to the importance of molecular/atomic fractals in both fundamental science and technology, it is crucial to construct them in a step-wise 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 self-similar mathematical sets, for example the Sierpi´ nski triangle (ST) or hexagon, have 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 2
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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 three-fold nodal motifs which are the basic structural elements of the STs. 9 In 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 have been observed in most of adsorbed systems where 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 self-assemble into the STs, it is important to identify 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 the three-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 to form multiple cyclic motifs. 16 To explore the above possibility, a V-shaped 4,4”-dihydroxy-1,1’:3’,1”-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 towards each of these outcomes. Our experimental investigations were further complemented
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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.
Results and discussion a
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Figure 1: (a) DFT-optimized structure of the H3PH trimer sustained by the cyclic O· · ·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 consequtive 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 H3PH-ST-3 imaged at 10 mV. The white arrows in the STM images indicate the < 11¯2 > direction, and their length corresponds to 0.5nm (e), 0.8nm (f), 1.2nm (g), and 2.5nm (h), respectively.
Figure 1a-d presents the DFT-optimized (a) and anticipated (b-d) molecular configurations, in which the H3PH molecules form three-fold nodes sustained by the cyclic O· · ·H4
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O bonds. These configurations correspond to the successive generations of the canonical Sierpi´ nski triangle, and they are denoted here by 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 which starts with an equilateral triangle (Figure 1a, up-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, up-right corner) and the above steps are repeated to obtain subsequent generations of the ST. When the side of the ST triangle is doubled, its 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 which are structurally 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-bonds STs, we developed a simplified coarse-grained model based on our previous results related to the fractal structure formation in surfaceconfined 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 the H3PH. To model the fractal self-assembly, we performed lattice Monte Carlo simulations in which H3PH molecules were treated as flat, rigid and bent-shaped structures comprising three connected segments shown 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 (→←) of the interaction directions. Moreover, additional restrictions on the formation of molecular
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nodes were imposed to accelerate the self-assembly of extended 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 self-assembly 10,17 and to the recent experimental findings on the 2D halogen-bonded systems, 9 the three-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
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 three-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 inter-actions 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 grey circles indicate the temperatures at which the snap-shots shown in Figure S3 were taken. (c) Snapshot of the over-layer comprising 1333 molecules of H3PH adsorbed on a triangular lattice; T = 0.1. 6
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An important consequence of the general topological requirement stated above is that the nature of the interactions cementing the three-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 down (T
