pubs.acs.org/Langmuir © 2010 American Chemical Society
Computer Simulation of Chiral Nanoporous Networks on Solid Surfaces Pawez Szabelski,*,† Steven De Feyter,‡ Mateusz Drach,† and Shengbin Lei§ Department of Theoretical Chemistry, Maria-Curie Skz odowska University Pl. M. C. Skz odowskiej 3, 20-031 Lublin, Poland, ‡Department of Chemistry, Division of Molecular and Nanomaterials, Laboratory of Photochemistry and Spectroscopy, and Institute of Nanoscale Physics and Chemistry, Katholieke Universiteit Leuven, Celestijnenlaan 200 F, B-3001 Leuven, Belgium, and §The Academy of Fundamental and Interdisciplinary Science, Harbin Institute of Technology, Harbin, 150080, P. R. China
†
Received January 5, 2010. Revised Manuscript Received February 22, 2010 A lattice Monte Carlo (MC) model was proposed with the aim of understanding the factors affecting the chiral selfassembly of tripod-shaped molecules in two dimensions. To that end a system of flat symmetric molecules adsorbed on a triangular lattice was simulated by using the canonical ensemble method. Special attention was paid to the influence of size and composition of the building block on the morphology of the adsorbed overlayer. The obtained results demonstrated a spontaneous self-assembly into extended chiral networks with hexagonal cavities, highlighting the ability of the model to reproduce basic structural features of the corresponding experimental systems. The simulated assemblies were analyzed with respect to their structural and energetic properties resulting in quantitative estimates of the unit cell parameters and mean potential energy of the adsorbed layer. The predictive potential of the model was additionally illustrated by comparison of the obtained superstructures with the recent STM images that have been recorded for different organic tripod-shaped molecules adsorbed at the liquid/pyrolytic graphite interface.
Introduction Controlled creation of nanosized supramolecular structures on solid surfaces has been one of the most intensively studied topics in surface science during recent years. The main reason for the continuously growing interest in the fabrication of two-dimensional periodic architectures on such substrates as metals1,2 or graphite3,4 is the great application potential of these new materials in nanoengineering and nanotechnology.5 A convenient route to highly ordered supramolecular systems at surfaces and interfaces is the self-assembly of modular molecular building blocks, usually organic molecules, with various sizes, shapes, and functionalities. The spontaneous organization of molecular bricks into planar periodic superstructures is directed primarily by intermolecular *Corresponding author E-mail:
[email protected]. Telephone: þ48 081 537 56 20. Fax: þ48 081 537 56 85.
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forces and adsorbate-surface interactions. The resulting networks are typically stabilized by hydrogen bonds,6-14 metal-ligand15-19 coordination, or even van der Waals interactions,20-26 and in many cases, they are readily observable at room temperatures by means of scanning tunneling microscopy (STM). Among the numerous examples of ordered molecular arrays on solid surfaces which have been reported to date, those with void spaces, so-called 2D porous networks,3 are of special importance. The distinct advantage of the porous networks is the regular spatial arrangement of nanometer-sized cavities with uniform well-defined shape. Guest molecules, such as thiols,12,27 coronenes,28-30 fullerenes,31-35 and others, can often be (18) Messina, P.; Dmitriev, A.; Lin, N.; Spillmann, H.; Abel, M.; Barth, J. V.; Kern, K. J. Am. Chem. Soc. 2002, 124, 14000. (19) Spillmann, H.; Dmitriev, A.; Lin, N.; Messina, P.; Barth, J. V.; Kern, K. J. Am. Chem. Soc. 2003, 125, 10725. (20) Charra, F.; Cousty, J. Opt. Mat. 1998, 9, 386. (21) Wu, P.; Zeng, Q.; Xu, S.; Wang, C.; Yin, S.; Bai, C. ChemPhysChem. 2001, 12, 750. (22) Ma., X.-J.; Yang, Y.-L.; Deng, K.; Zeng, Q.-D.; Wang, C.; Zhao, K.-Q.; Hu, P.; Wang, B.-Q. ChemPhysChem. 2007, 8, 2615. (23) Bleger, D.; Kreher, D.; Mathevet, F.; Attias, A.-J.; Schull, G.; Huard, A.; Douillard, L.; Fiorini-Debuischert, C.; Charra, F. Angew. Chem., Int. Ed. 2007, 46, 7404. (24) Furukawa, S.; Uji-i, H.; Tahara, K.; Ichikawa, T.; Sonoda, M.; De Schryver, F. C.; Tobe, Y.; De Feyter, S. J. Am. Chem. Soc. 2006, 128, 3502. (25) Tahara, K.; Furukawa, S.; Uji-i, H.; Uchino, T.; Ichikawa, T.; Zhang, J.; Mamdouh, W.; Sonoda, M.; De Schryver, F. C.; De Feyter, S.; Tobe, Y. J. Am. Chem. Soc. 2006, 128, 16613. (26) Charra, F.; Cousty, J. Phys. Rev. Lett. 1998, 80, 1682. (27) Perdig~ao, L. M. A.; Staniec, P. A.; Champness, N. R.; Beton, P. H. Langmuir 2009, 25, 2278. (28) Schull, G.; Douillard, L.; Fiorini-Debuisschert, C.; Charra, F. Nano Lett. 2006, 6, 1360. (29) Furukawa, S.; Tahara, K.; De Schryver, F. C.; Van der Auweraer, M.; Tobe, Y.; De Feyter, S. Angew. Chem., Int. Ed. 2007, 46, 2831. (30) Lei, S.; Tahara, K.; Feng, X.; Furukawa, S.; De Schryver, F. C.; M€ullen, K.; Tobe, Y.; De Feyter, S. J. Am. Chem. Soc. 2008, 130, 7119. (31) Piot, L.; Silly, F.; Tortech, L.; Nicolas, Y.; Blanchard, P.; Roncali, J.; Fichou, D. J. Am. Chem. Soc. 2009, 131, 12864. (32) Saywell, A.; Magnano, G.; Satterley, C. J.; Perdig~ao, L. M. A.; Champness, N. R.; Beton, P. H.; O’Shea, J. N. J. Phys. Chem. C 2008, 112, 7706. (33) Di Marino, M.; Sedona, F.; Sambi, M.; Carofiglio, T.; Lubian, E.; Casarin, M.; Tondello, E. Langmuir, in press, DOI: 10.1021/la9026927.
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selectively adsorbed in a reversible way,28,30 rendering these networks of interest for adsorption and separation processes in future nanotechnological applications. Moreover, they can be also used as templates for crystal growth in three dimensions or to spatially confine molecular motion.36 A variety of structural and functional modifications of these networks are possible.22,23,37-40 These empirical rules allow one to construct networks with pores of different size and shape,41,42 e.g., square,43 rhombic,27,44 hexagonal,24,25,27,43,45 and so on.31,42 An intriguing structural feature of the porous networks which has been observed in certain cases is the chiral cooperative order resulting from a particular local arrangement of adsorbed molecules.3,4,43,46,47 Namely, the molecules often assemble locally into closed, for example, hexagonal loops with a unique rotation direction. This effect is further transmitted to the growing domain, which contains pores of the same chirality, and it is rotated with respect to the substrate. Spontaneous formation of extended chiral domains with large chiral pores at a liquid-solid interface3,4,31 has been demonstrated recently. In those experiments, highly symmetric star-shaped molecules usually consisting of a flat and rigid aromatic core substituted with alkyl chains have been used as building blocks. Among them the most prevalent ones are dehydrobenzo[12]annulenes (DBAs) derivatives24,25,41 and stilbenoid compounds,23,28 which assemble into a honeycomb patterns with 2D chiral cavities. Interdigitation of the long alkyl chains (molecular arms) leads to a highly ordered chiral superstructure. The chiral honeycomb pattern mentioned above is one out of many ordered patterns which have been observed for tripod-type molecules at the liquid/HOPG interface. This refers especially to DBAs whose assembly is largely influenced by the size and functionality of this structural unit. For example, it has been demonstrated that manipulating the size and shape of the DBA core as well as changing the length of the alkyl chain arms can lead to the formation of ordered porous or nonporous networks of entirely different symmetry.41 Thus, by tuning individual properties of the DBA-based building blocks it has become possible to direct the assembly process toward the desired 2D supramolecular architecture with pores of controlled shape and size. Computer simulations offer an alternative and complementary way to study the self-assembly of functional molecules into 2D ordered superstructures on solid surfaces. On the one hand, this theoretical approach enables an understanding of the key factors (34) Griessl, S. J. H.; Lackinger, M.; Jamitzky, F.; Markert, T.; Hietschold, M.; Heckl, W. M. J. Phys. Chem. B 2004, 108, 11556. (35) Griessl, S. J. H.; Lackinger, M.; Jamitzky, F.; Markert, T.; Hietschold, M.; Heckl, W. M. Langmuir 2004, 20, 9403. (36) Schlickum, U.; Decker, R.; Klappenberger, F.; Zoppellaro, G.; Klyatskaya, S.; Ruben, M.; Silanes, I.; Arnau, K.; Kern, K.; Brune, H.; Barth, J. V. Nano Lett. 2007, 7, 3813. (37) Miyashita, N.; Kurth, D. G. J. Mater. Chem. 2008, 18, 2636. (38) Chang, Y.-L.; West, M.-A.; Fowler, F. W.; Lauher, J. W. J. Am. Chem. Soc. 1993, 115, 5991. (39) Lackinger, M.; Heckl, W. M. Langmuir 2009, 25, 11307. (40) Palma, C.-A.; Bonini, M.; Llanes-Pallas, A.; Breiner, T.; Prato, M.; Bonifazi, D.; Samorı´ , P. Chem. Commun. 2008, 42, 5245. (41) Tahara, K.; Okuhata, S.; Adisoejoso, J.; Lei, S.; Fujita, T.; De Feyter, S.; Tobe, Y. J. Am. Chem. Soc. 2009, 131, 17583-17590. (42) Gutzler, R.; Walch, H.; Eder, G.; Kloft, S.; Hecklab, W. M.; Lackinger, M. Chem. Commun. 2009, 29, 4456. (43) K€uhne, D.; Klappenberger, F.; Decker, R.; Schlickum, U.; Brune, H.; Klyatskaya, S.; Ruben, M.; Barth, J. V. J. Phys. Chem. C 2009, 113, 17851. (44) Ahn, S.; Morrison, C. N.; Matzger, A. J. J. Am. Chem. Soc. 2009, 131, 7946. (45) Staniec, P. A.; Perdig~ao, L. M. A.; Rogers, B. L.; Champness, N. R.; Beton, P. H. J. Phys. Chem. C 2007, 111, 886. (46) Mu, Z.; Shu, L.; Fuchs, H.; Mayor, M.; Chi, L. J. Am. Chem. Soc. 2008, 130, 10840. (47) Schlickum, U.; Decker, R.; Klappenberger, F.; Zoppellaro, G.; Klyatskaya, S.; Auw€arter, W.; Neppl, S.; Kern, K.; Brune, H.; Ruben, M.; Barth, J. V. J. Am. Chem. Soc. 2008, 130, 11778.
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affecting the assembly at the microscopic scale. On the other hand, it allows for the prediction of the morphology of thermodynamically stable phases, based on the properties of the building block. The latter advantage is particularly useful by substantially reducing the number of experiments needed to select the proper molecular building blocks. The most popular methods to study 2D molecular networks from a theoretical point of view have been molecular dynamics (MD)48 and density functional theory (DFT).6,22,48,49 They are useful to test the stability of relatively small assemblies with predefined architecture (typically up to a few dozens of molecules in the case of MD). Another, somewhat underestimated simulation technique in the field of 2D self-assembly is the Monte Carlo method, which offers the possibility of investigating large molecular systems under variable conditions. An important merit of this technique is that it can mimic spontaneous self-organization of functional molecules into naturally emerging 2D patterns without imposing any constraints on the symmetry of the final superstructure. Furthermore, the MC method is able to reproduce the coexistence of different phases and to predict conditions under which these phases are stable. The robustness of the MC method is particularly visible in lattice models in which the substrate and adsorbed molecules are represented in a simplified way.50-52 In this case, the geometry of the building block as well as adsorbateadsorbate and adsorbate-substrate interactions can be described by a minimal number of adjustable parameters. Even though the MC method seems ideally suited for modeling 2D supramolecular architectures, its practical use has been reported for a very limited number of experimental systems.53-56 Osipov and co-workers57 have demonstrated a chiral compact phase in a system of symmetric tripod molecules on a hexagonal lattice, matching the chiral pattern formed by alkoxytriphenylenes at the tetradecane/HOPG interface.20,26 Recently Beton et al. have used the kinetic lattice MC (KLMC) method to model the mixed self-assembly of melamine and PTCDI (perylene tetracarboxylic diimide) on Ag/Si(111).53 They were able to reproduce the morphology of the experimental assemblies and to construct a stability diagram for that system. Moreover, KLMC simulations of melamine adsorbed on Au(111)54 have shown the formation of chiral hexagonal domains with small hexagonal void spaces.9,45,54 A combined technique linking DFT calculations and MC simulations has been used by Hermse and co-workers to study the formation of chiral domains of tartaric acid on Cu(110).58 A similar method has been used very recently to model the chiral ordering of organic trimers distributed on a hexagonal lattice.59 The examples cited above are, to the best our knowledge, the only ones in which the chiral cooperative order in self-assembled organic monolayers has been modeled using the MC method. (48) Linares, M.; Minoia, A.; Brocorens, P.; Beljonne, D.; Lazzaroni, R. Chem. Soc. Rev. 2009, 38, 806. (49) Lin, N.; Stepanow, S.; Ruben, M.; Barth., J. V. Top. Curr. Chem. 2009, 287, 1. (50) Szabelski, P. J. Comput. Chem. 2008, 29, 1615. (51) Szabelski, P.; Sholl, D. S. J. Chem. Phys. 2007, 126, 144709. (52) Szabelski, P. Chem.;Eur. J. 2008, 14, 8312. (53) Weber, U. K.; Burlakov, V. M.; Perdig~ao, L. M. A.; Fawcett, R. H. J.; Beton, P. H.; Champness, N. R.; Jefferson, J. H.; Briggs, G. A. D.; Pettifor, D. G. Phys. Rev. Lett. 2008, 100, 156101. (54) Silly, F.; Weber, U. K.; Shaw, A. Q.; Burlakov, V. M.; Castell, M. R.; Briggs, G. A. D.; Pettifor, D. G. Phys. Rev. B 2008, 77, 201408(R). (55) Garrahan, J. P.; Stannard, A.; Blunt, M. O.; Beton, P. H. Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 15209. (56) Blunt, M. O.; Russell, J. C.; Gimenez-Lopez, M.; Garrahan, J. P.; Lin, X.; Schr€oder; Champness, N. R.; Beton, P. H. Science 2009, 322, 1077. (57) Osipov, M. A.; Stelzer, J. Phys. Rev. E 2003, 67, 061707. (58) Hermse, C. G. M.; van Bavel, A. P.; Jansen, A. P. J.; Barbosa, L. A. M. M.; Sautet, P.; van Santen, R. A. J. Phys. Chem. B 2004, 108, 11035. (59) Breitruck, A.; Hoster, H. E.; Behm, R. J. J. Phys. Chem. C 2009, 113, 21265.
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In this work, we demonstrate how a simple MC simulation method can effectively model the spontaneous 2D chiral organization of achiral molecules adsorbed on a solid surface. Specifically, we present the first theoretical model of the self-assembly of symmetric tripod-shaped molecules into an open chiral network. The major purpose of this study is to understand the origins of self-organization using theoretical tools which we developed here and which could be applicable to a range of similar models.
The Model and Simulation The model described in this section was originally inspired by the recent experimental results on the spontaneous self-assembly of alkoxylated dehydrobenzo[12]annulenes (DBAs) into a chiral porous network at the liquid/HOPG interface.3,24,25 Figure 1 shows the chemical structure of DBA (part a) and an STM image of the open porous honeycomb pattern formed by DBA on HOPG (part c). As seen in Figure 1, DBA has C3-symmetry. The symmetry axis runs perpendicular to the flat aromatic core. The three flexible alkoxy chain pairs are key to the formation of the chiral patterns. Self-assembly leads to the formation of nanowells, as indicated schematically in Figure 1c. Note that DBA is only one example out of the many tripod-shaped symmetrical molecules which have been found to self-assembly into chiral honeycomb patterns on solid surfaces.23,28,46 For that reason, our main effort was to built a simple and general model which would be able to reproduce the common honeycomb structure of ordered monolayers formed by chemically different tripod-shaped organic molecules and to identify the key factors affecting the geometry of these layers. Thus, in our model, as a first approximation, we exclude system-dependent factors such as the flexibility of the building molecular block, the influence of solvent and the possibility of desorption of the molecules from the surface. We consider a system of N tripod-shaped symmetric molecules adsorbed on a 2D triangular lattice with lattice spacing equal to l. The molecules were assumed to be flat rigid structures composed of a central segment called core with three n-membered arms attached to it, as shown schematically in Figure 1d. Each molecular segment was allowed to occupy one adsorption site, i.e. one vertex of the lattice. In the approach adopted here we do not assume any direct correspondence between a segment and a chemical building block of a real molecule. A segment can be a single atom, an isolated CHn group or a longer fragment of either a single alkyl chain or a pair of parallel alkyl chains, or an aromatic ring or any other functional group which can be incorporated in the symmetric tripod molecule. The main function of a segment in the proposed model is to represent a structural unit which characterizes the size of the building block. The molecules were assumed to interact via a short-ranged segment-segment interaction potential limited to nearest-neighbors on a triangular grid. The energy of interaction between a molecular core of one molecule and an arm segment of a neighboring molecule was characterized by εc while that between a pair of arm segments by εa. These energies are expressed in kT units. According to the convention adopted here positive values correspond to intermolecular attraction. To simulate the self-assembly of the tripod-shaped molecules we used the conventional equilibrium lattice Monte Carlo (MC) method for the canonical ensemble. The simulations were performed on a L L rhombic fragment of a triangular lattice using periodic boundary conditions in both directions. The simulation algorithm was organized as follows. In the first step N molecules of a fixed size (arm length) were distributed randomly on the 9508 DOI: 10.1021/la100043w
Figure 1. (a) Chemical structure of DBAs. (b) Schematic model of DBAs with alkyl chains shown in red. (c) High resolution (47 50 nm2) STM image of DBA-OCH18 at the interface between 1,2,4-trichlorobenzene (TCB) and HOPG. Hexagonal pores are formed via the interdigitation of alkyl chains of adjacent molecules, illustrated by six model molecules (from part b) which are overlaid on the STM image. (d) Examples of the model tripod-shaped molecules on a 2D triangular lattice as used in the simulations. The molecules are represented by a central segment (core) and three chain arms. The black arrows indicate the reference lattice axes.
lattice. Next, the adsorbed layer was equilibrated by a series of attempts to move each molecule to a new position. Specifically, for a selected molecule, we calculated the associated interaction energy in the actual configuration X UX ¼
3n þ1 X 6 X
εij
ð1Þ
i ¼1 j ¼1
where εij is equal to εc or εa depending on whether the segmentsegment interaction occurs between a core and an arm or between two arms, respectively or it is equal to 0 when a neighboring adsorption site is empty or it is occupied by a segment belonging to the selected molecule. To move the molecule over the surface a cluster of 3nþ1 adsorption sites matching the shape of the molecule was chosen randomly. If none of the selected cluster sites was occupied the interaction energy UX0 in the new configuration X0 was calculated using eq 1. To decide if the move was successful the transition probability p = min[1,exp(UX0 -UX)] was calculated and compared with a randomly generated number r ∈ (0,1). If r < p the molecule was moved to the next position, otherwise it was left in the original one. The above sequence was repeated for each adsorbed molecule constituting one MC step. To equilibrate the system we used up to 1010 MC steps. The simulations were performed for L = 200, 300, 400 and N varying from 100 to 10000 depending on the size of the building block.
Results and Discussion 1. Influence of Molecular Size and Composition. The results described in this section correspond to two qualitatively Langmuir 2010, 26(12), 9506–9515
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Figure 2. (a) Structure of the compact layer formed by homogeneous molecules (εc = εa = 1) with the shortest possible arm length, n = 1. The shades of gray show molecular domains of opposite orientations which are marked by the red arrows. The red circle shows a typical defect site. (b) 10 10 nm2 UHV STM image of one of the stable ordered phases of hexaazatrinaphthylene on Au(111). The unit cell is shown in black (adapted from ref 60).
different situations in which: (1) the tripod-shaped molecule is composed of identical segments, that is εc = εa = 1, and (2) the molecular core is markedly different from the rest of the molecule, that is εc 6¼ εa = 1. Molecules meeting the first criterion are further called homogeneous while those belonging to the second group are called heterogeneous. One reason for considering these two core-dependent cases is the fact that planar or discotic tripodshaped molecules with 3-fold symmetry and peripheral alkyl substituents are popular building blocks in surface-supported self-assembly. The diverse phase behavior of molecules with peripheral alkyl chains of the same length can be attributed to differences in size, shape and flexibility of the core.24 For those tripod-shaped molecules whose assemblies are stabilized by hydrogen bonding, the situations 1 and 2 can be associated with the ability of the core to form hydrogen bonds with the arms. In the present study, we neglect the effects associated with the size of the core and focus mainly on its energetic properties to show how these properties (εc) influence the symmetry of the simulated assemblies. Let us start the discussion with the influence of the arm length on the morphology of the assembled overlayers comprising homogeneous molecules. Figure 2 shows a fragment of the compact monolayer obtained for the molecules with n = 1, that is for the shortest possible arm length. In this case, equilibration of the system does not lead to the creation of any ordered network with nanowells in the layer. The molecules are closely packed within striped domains of different width, or in single rows, in which they are oriented in the two opposite directions indicated by the red arrows in Figure 2a. As a consequence, the layer is a random sequence of parallel stripes and rows with a very small number of defects (vacancies) resulting mainly from oppositely oriented molecules meeting in one row (see the red circle in Figure 2a). Within large unidirectional domains the adsorbate forms a simple (2 2) structure which resembles, for example that of hexaazatrinaphthylene, a compact tripod-shaped molecule, on Au(111) shown in part b).60 The dense packing of the molecules from part a) originates primarily from the presence of the short 1-membered arm which allows interaction of each arm segment with its five neighboring segments. As we will show later that this exceptionally high coordination number of an arm segment, resulting in an average potential energy per molecule equal to 18εa, is not possible for n larger than 1. The symmetry of the overlayer changes drastically when the arm length increases. Let us now present a qualitative analysis of (60) Ha, S. D.; Kaafarani, B. R.; Barlow, S.; Marder, S. R.; Kahn, A. J. Phys. Chem. C 2007, 111, 10493.
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Figure 3. Examples of small homochiral porous networks containing about 100 homogeneous molecules (εc = εa = 1) simulated using the tripod-shaped molecules with arms of a different length shown in each panel. The thick red lines represent the corresponding unit cells, and the white arrow indicates the rotational direction of the pore.
the obtained superstructures referencing them to the available experimental data. As shown in Figure 3, increasing n beyond 1 has a dramatic impact on the periodicity of the assembly. In this case we can observe the formation of an ordered honeycomb pattern with hexagonal cavities, regardless of the size of the building block. The simulated networks shown in Figure 3 are all chiral with apparent rotation direction of the molecular arms surrounding the hexagonal pores. As we observed, the handedness of the obtained assemblies is not biased which results in equal occurrence of opposite enantiomorphs. The unichiral structures obtained for n > 1 are isomorphic with each other, having the same hexagonal symmetry and the same mean core coordination number, nc equal to 3. The rotation direction of a single chiral pore is transmitted to the entire network causing the corresponding rotation of the adsorbate unit cell with respect to the reference axes from Figure 1d. As shown in Figure 3 by the red lines, the unit cell for n = 2, and thus the whole domain, is rotated anticlockwise while for n = 3 and n = 4 clockwise rotation can be observed. We emphasize that the rotation direction of the domains shown in Figure 3 is entirely random and it is not influenced by the arm length. Note that the overall architecture of the simulated networks shown in Figure 3 agrees very well with that of the self-assembled layers obtained for DBAs on HOPG24,25 (see Figure 1c) or other trifunctional derivatives, 2,4,6-tristyrylpyridine, on HOPG.23,28 Apparently, those experimental assemblies are stabilized by the interdigitation of long alkyl chains attached to the flat aromatic core. On the basis of the result of our simulation, the coarsegrained representation in which a pair of parallel alkyl chains (see Figure 1b) is replaced by the single n-membered linear arm is enough to reproduce the main structural features of the corresponding experimental systems. However, we stress that according to our model the honeycomb porous network from Figure 3 is structurally stable even for large values of n which is in contradiction with the experiment. For example, as has been shown for DBA systems, when the arm length increases the honeycomb porous network is no longer observable because the molecules favorably form a dense linear pattern by desorption of one arm from the surface.29 This effect is probably a consequence of both DOI: 10.1021/la100043w
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Figure 5. Examples of the porous networks with rhombic void spaces obtained for the modified core-arm interaction energy, for the heterogeneous molecules with arm length indicated in each panel. The corresponding unit cells are indicated by the thick red line. The patterns shown in the left and right part were obtained for εa = 1 and εc = 0 and for εa = 1 and εc = -0.25, respectively.
Figure 4. (a) Schematic structure of the partially fluorinated tripod-shaped molecule (PFTM) used by Mu and co-workers.46 (b) Large-scale STM image of PFTM at the phenyloctane/HOPG interface (50 50 nm2). (c, d) High-resolution STM images of homochiral domains formed by PFTM and the corresponding packing models (18 18 nm2). Reproduced with permission from ref 46. Copyright 2008 American Chemical Society. The bottom part shows a fragment of the simulated analogue of (d) comprising homogeneous molecules (εc = εa = 1) with arms of length equal to 2. The rhombic unit cell and the reference lattice axes are indicated in white and black, respectively.
molecular flexibility and stabilization of the desorbed arm by solvent molecules which are not included in our model. To demonstrate the predictive power of the model let us present one more example in which the honeycomb network assembles via hydrogen bonding. Recently Mu and co-workers46 reported the formation of homochiral porous networks (Figure 4) using a partially fluorinated tripod-shaped molecule sketched in part (a). The bottom part of the figure shows a fragment of the simulated analogue of the homochiral domain from part (d). The simulated results agree perfectly with the experimental results in terms of both network periodicity and local order of the molecules surrounding the hexagonal cavities. In this case, the agreement is particularly visible because of a straightforward correspondence between the molecular shape and a segment of the model molecule with n = 2. 9510 DOI: 10.1021/la100043w
Note that the agreement between the simulated assemblies and the experimental patterns shown in Figures 1, 2, and 4 was reached assuming energetic homogeneity of the model surface. Namely, in the proposed approach the energy of interaction between a molecular segment and an adsorption site is uniform over the surface. As a consequence, moving a molecule from one position to another does not change its total energy of interaction with the surface. For that reason the segment-surface interaction energy can be chosen arbitrary, for example zero, as it cancels out when calculating the energy difference between these two molecular states (see eq 1). However, in reality the influence of the molecule-substrate interaction can be significant because of more complex interaction pattern of a tripod molecule with the surface than that assumed in our model. This can originate from both energetic heterogeneity of the surface and multiple adsorbed configurations of the molecule depending, for example, on its local surrounding. The same tripod molecule can form superstructures of a different architecture when adsorbed on various substrates. To describe these superstructures using our model, it is necessary to provide a more detailed description of the moleculesubstrate interaction. Another modification of the model tripod-shaped molecule can be changing the energetic properties of the core. To study this effect, we first assumed that the core is totally inert; that is, we set εc = 0. The left part of Figure 5 presents an example of the ordered superstructure simulated for n = 2. As it follows from Figure 5, the changed core properties lead to the formation of an ordered phase of a completely different symmetry compared to the previous assemblies. Specifically, the molecules are now aligned in parallel rows in which they point to opposite directions. The resulting arrangement of the molecular arms is responsible for the creation of rhombus-shaped void spaces. One striking property of the obtained network is that it is not chiral, and contrary to the honeycomb pattern, it is characterized by a rectangular unit cell. Another distinctive feature of the obtained superstructure is the mean core coordination number which is equal to 1, being smaller than for the hexagonal networks. In the case of larger molecules with n > 2 the presence of the inert core was, however, not enough to induce formation of a pattern resembling that of the left part of Figure 5. Instead, we observed a partially ordered network (see Figure 3) with numerous irregular hexagonal (achiral) pores. To force the molecules equipped with 3-membered arms to assemble into an ordered overlayer with rhombic pores we had to make the core-arm interaction repulsive, that is we lowered εc slightly below zero. The right part of Figure 5 shows a fragment of the resulting assembly obtained for εc = -0.25 in a system of 1000 molecules adsorbed on a 200 200 lattice. The major structural factors of the assembly including the unit cell and pore shape and the mean Langmuir 2010, 26(12), 9506–9515
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Figure 6. Ordered chiral pattern with rhombic void spaces with different sizes obtained using tripod molecules composed of 3-membered arms and a highly repulsive core, εc = -4. The unit cell of the adsorbate is marked by the thick red line. The black arrow indicates the horizontal reference axis.
core coordination number are identical with those observed for n = 2. Moreover, the patterns from Figure 5, are similar to those formed by molecules of 1,3,5-tris(3-carboxypropoxy)benzene (TCPB) on Au(111)10 (see Figure 3 in ref 10). The case of TCPB whose assembly is stabilized mainly by hydrogen bonds between functionalized arms, with marginal role of the core, is in accordance with the assumption we made for the system with n = 2 (εc = 0). Interestingly, further decreasing of εc resulted in totally different adsorbate structures for n = 2 and n = 3. Specifically, for the smaller molecule a fully disordered assembly was observed while for the bigger one a new ordered phase appeared, as shown in Figure 6. The simulated pattern is chiral and it is characterized by a parallellogram unit cell rotated markedly from the horizontal reference axis. The large core-arm repulsion assumed for this system causes the mean core coordination number to drop to zero. Moreover, a new feature observed here is the presence of two sets of rhombic pores with different size. One important remark which has to be made here is that the ordered patterns from Figures 5 and 6 are not possible for tripod molecules of all sizes. Namely, the structures from Figure 5 are obtainable exclusively for the molecules with n = 2 and 3 while the network shown in Figure 6 is inherent to the system with n = 3 only. In the remaining cases, that is for n > 2, a network with rhombic void spaces was never observed, even when the corearm interaction energy was substantially smaller than zero, for example when εc = -10. For these bigger molecules, making the core inert or strongly repulsive always resulted in partially ordered (locally chiral) aperiodic networks with irregular hexagon-shaped void spaces, as shown in Figure 7. Explanation of this effect requires the determination of the mean potential energy of the networks shown in Figures 5-7, which we describe in detail in the next section. Let us also note that although the patterns from Figures 5-7 (εc e 0) have not been observed experimentally at the liquid/HOPG interface it can be expected that their formation can take place in real systems when the molecular core becomes repulsive, for example, due to strong polarization effects. 2. Structural and Energetic Parameters of the Assemblies. To understand better the phase behavior of the tripod molecules, we performed a quantitative analysis of the ordered networks with hexagonal and rhombic pores. To that purpose, we used the structural parameters whose meaning is explained in Figures 4-6. The dependence of these parameters on the arm length is presented in Table 1 for the three distinct types of assemblies. As it follows from the table, the size of the rhombic Langmuir 2010, 26(12), 9506–9515
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Figure 7. Example of a partially ordered hexagonal network simulated for tripod molecules composed of 5-membered arms attached to a highly repulsive core, εc = -10. The red circle indicates a perfectly ordered chiral pore. Table 1. Structural and Energetic Parameters of the Ordered Phases Obtained in the Simulationsa
a The network density is defined as a ratio of the number of molecular segments within the unit cell to the area of the unit cell. The average energy per molecule corresponds to an infinite defect-free layer.
unit cell of the hexagonal network, x varies in a nontrivial way with the arm length of the building block. Similarly, the rotation angle, γ is a rather complex function of n. Conversely, for the network with rhombic void spaces of a uniform size we can observe that the parameters of the rectangular unit cell (a and b) scale linearly with n and that the unit cell is not rotated at any value of n. To present the dependencies obtained for the hexagonal network in a more clear way we plotted the rotation angle and the scale of the unit cell as functions of the arm length in Figure 8. Figure 8 shows that the rotation angle initially increases rapidly with increasing arm length and it tends smoothly to 30 as the arm length further grows. The limiting pffiffiffi value pffiffiffi of the rotation angle (nf¥) corresponds to a perfect ð 3 3ÞR30 phase on a (111) lattice. Note also that the unit cell size, even though given by the nonlinear function of n from Table 1, changes in a linear fashion within the considered arm length interval. In this case, the observed dependency can be approximated by the function x ¼ pffiffiffi l 3ðn þ 0:6Þ which is plotted with the red solid line in Figure 8. To compare the structural properties of the three networks whose unit cells differ in shape, in Figure 9 we show the influence of the arm length on the unit cell area and network density. From Figure 9, it follows that the area of the unit cell of the hexagonal DOI: 10.1021/la100043w
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Figure 8. Dependence of the rotation angle (γ, black) and the size (x/l, red) of the rhombic unit cell of the porous hexagonal network on the arm length of the building block.
Figure 9. Network density (F, black) and area of the unit cell (A/l2, red) as a function of the arm length calculated for the overlayers with hexagonal (arbitrary n, open circles) and rhombic (n = 2, 3, filled circles) pores. The crosses show analogous results obtained for the tripod molecules with n = 3 and a strongly repulsive core (εc = -4).
network increases markedly with elongation of the arm length and that for n = 2,3 it is very close to the corresponding values obtained for the two remaining patterns. A direct calculation shows, however, that the unit cell area of the hexagonal network, in l2 units, is equal to 18.19 for n = 2 and 33.77 for n = 3 being in fact larger than for the networks formed by molecules with inert or weakly repulsive core for which the area of the rectangular unit cell is equal to 15.59 and 27.71, respectively. On the other hand, for molecules with 3-membered arms attached to a strongly repulsive core, the area of the parallelogram unit cell measures 34.64 which is indeed very close to the value obtained for the hexagonal network built of molecules of the same size. Similar relationships can be found by analyzing the influence of the arm length on the network density. The density of the hexagonal network (the largest unit cell area) is considerably lower than for the network consisting of tripod molecules with weakly repulsive core (n = 2, 3). Moreover, for the strongly repulsive core the density of the corresponding network is very close to that calculated for the hexagonal network with n = 3 which equals to 0.59. The network density decreases significantly with elongation of the arm for the patterns with hexagonal and rhombic pores. 9512 DOI: 10.1021/la100043w
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Let us now compare the energetic properties of the simulated ordered networks. To that purpose, for each type of network, in the last column of Table 1 we listed the mean potential energy per molecule calculated by means of eq 1 assuming an infinite defectfree molecular layer. Note that the energy obtained for the first two networks in Table 1 is a sum of two components, the first of which is independent of n and describes the influence of the molecular core while the second is a contribution from the arm-arm interaction. The effect of the core is the strongest in the case of the hexagonal networks (6εc) and it diminishes as the geometry of the assembly changes from hexagonal to linear (2εc). For the phase formed by molecules with 3-membered arms and a highly repulsive core the average energy per molecule is totally independent of εc, as the core-arm interaction is impossible for this structure. A remarkable feature of the dependencies from Table 1 is the constancy of the term related to the core-arm interaction. This special property determines the phase behavior of the tripod molecules when n grows, bearing serious consequences on the morphology of the assemblies at the macroscopic scale. Specifically, when looking at the expression obtained for hexagonal networks we can expect that the influence of the core will decrease gradually with the elongation of the molecular arm. Indeed, for sufficiently big values of n the average energy per molecule is dominated by the interaction of parallel molecular arms whose energy is proportional to 2n þ 1. When n increases, the role of the core becomes marginal and the molecules assemble mainly via arm-arm interactions. For example, as we mentioned before, the molecules with n > 3 are able to selforganize into a network with hexagonal pores even when they contain a strongly repulsive core. However, one should remember that these hexagonal pores do not have to be chiral or even symmetric. The main origin of this structural imperfectness is the possibility for molecular arms to be shifted parallel with respect to each other when forming 2D pore walls (see Figure 7). Because the core is repulsive, the molecules tend to keep their arms away from it in order to reach the equilibrium configuration with the lowest potential energy. As a consequence, the pore consists of six tripod molecules whose terminal arm segments do not contact the molecular cores as already shown in Figure 7. The mean potential energy per molecule, E calculated for a pattern of this type equals to 3(2n - 1)εa while for a network having symmetry as that shown in Figure 6 E is equal to 4(n þ 1)εa. Comparison of these energies gives the structural stability condition for the distorted hexagonal pattern observed for the larger molecules, which is n > 3.5. The obtained result clearly indicates why the ordered pattern from Figure 6 is not possible for tripod molecules with more than three segments in the arm. Interestingly, for molecules with n=2, the stability analysis shows that these molecules are theoretically able to form distorted hexagonal pores when εc is lower than -5.5. However, this effect is not observed in practice because a denser disordered molecular packing with higher potential energy is possible in this case (results not shown). In summary, the core properties have a great effect on the extent of ordering of the hexagonal pores formed by molecules with n > 3, being primarily responsible for the occurrence of the cooperative chiral order in the adsorbed phase. Briefly, for εc > εa one observes perfectly ordered chiral cavities, for example like those shown in Figure 3 for n = 4, while for εc , εa distorted hexagonal pores prevail in the assembled layer (see Figure 7). Regarding tripod molecules with shorter arms, n < 4, lowering the core-arm interaction parameter does not lead to the formation of disordered hexagonal networks observed previously for Langmuir 2010, 26(12), 9506–9515
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bigger molecules. As already mentioned, this is because a more energetically favorable configuration for a single molecule with n = 2 and 3 is achieved when it adopts the network shown in the second row of Table 1. In this case, at moderate values of εc, the molecules tend to minimize the number of the core-arm contacts such that the mean core coordination number is equal to 1. This situation is possible because the energy loss caused by the core-arm interaction can be easily compensated by the energy gain resulting from multiple arm-arm interactions. In other words the network is stabilized effectively by attractive interaction between closely packed molecular arms. When εc further decreases, the core becomes strongly repulsive, forcing the arms (their terminal segments) to stay away from the core. For molecules with n = 2, this effect leads to a complete disordering of the adsorbed layer while for molecules with n = 3 it induces spatial reorganization leading to the creation of the new ordered phase shown in the third row of Table 1. Note that the existence of this phase is possible because of the periodic arm arrangement which allows the molecules to maximize the number of “bonds” between arm segments with simultaneous elimination of the core-arm contacts. In consequence, the resulting network is characterized by the mean potential energy per molecule which is independent of εc, being proportional to the number of contacts between arm segments. The expressions for E shown in Table 1 allow estimating the structural stability of the simulated ordered networks. For example, comparison of the mean energies of the first and second row of Table 1 results in the following general condition for the existence of the honeycomb pattern: εc > 0.25(7 - 2n)εa. As our simulations show, practical application of this relationship is limited only to the small tripod molecules with n = 2 and 3. When εa is positive, as assumed in our model (εa = 1), these two arm lengths are the only ones for which the right side of the obtained inequality is positive. Specifically, we have εc > 0.75 for n = 2 and εc > 0.25 for n = 3. Thus, one can expect that, for example in the case of the smaller molecule, the ordered hexagonal phase dominates for εc larger than 0.75 and it will convert into the linear pattern with rhombic pores as εc decreases. To examine this transition more closely we performed separate simulations whose results are shown in Figure 10. The bottom part of Figure 10 presents the influence of εc on the mean core coordination number obtained from the simulations performed for n = 2. Additionally, in the top part we plotted the theoretically predicted mean potential energy per molecule as a function of εc for both patterns considered above (top part). The crossing point of the corresponding linear plots determines the critical value of εc = 0.75 indicted by the dashed vertical line. As it follows from Figure 10, the symmetry of the molecular network changes abruptly in the vicinity of the transition point, as the mean core coordination number jumps from 1 to ∼2.8 when εc exceeds 0.6. The theoretical prediction of the critical value of εc marked by the dashed line agrees quite well with the results simulated for the finite system but, as clearly seen in Figure 10, the onset of the transition obtained from simulations is shifted toward lower energies compared to the theory. A similar analysis can be performed for the network described in the third row of Table 1. This molecular pattern appears only for n = 3 and it emerges gradually from the previous linear pattern (second row of Table 1) as the core-arm interaction energy is further decreased. The corresponding stability condition for the linear pattern can be obtained by comparison of the average energies given in the second and third row of Table 1. This procedure results in εc > (3 - 2n)εa, which in our case (n = 3, εc = 1) reduces to εc > -3. Indeed, as shown in Figure 6, when the core-arm interaction energy is lower Langmuir 2010, 26(12), 9506–9515
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Figure 10. Theoretical dependence of the average energy per molecule on the core-arm interaction energy calculated for the tripod molecule with n = 2 and εa = 1 (top part). The mean core coordination number as a function of the core-arm interaction energy simulated for a system of 2500 molecules with n = 2 adsorbed on a 200 200 lattice (red circles). The dashed vertical line determines domains of stability of phases L and H predicted by the theory.
than -3, here equal to -4, the new ordered phase with bimodal pore distribution is formed. 3. Origins of Homochirality. In this brief section we address some issues related to the spontaneous chiral symmetry breaking observed in dense overlayers with hexagonal symmetry. As shown in Figure 7 the hexagonal pattern formed by tripod molecules with n > 3 can be largely disordered when the core-arm interaction is sufficiently repulsive. In order to induce perfect chiral ordering of the hexagonal pores it is necessary to increase εc above a critical value which depends on n. A precise determination of the critical value of εc for each n requires running numerous simulations aiming at locating the chiral order-disorder phase transition of the overlayer. However, as we examined, the value of εc = 1 = εa (homogeneous molecules) is enough to obtain perfectly ordered chiral hexagonal networks also for n > 3. For these ordered networks the spontaneous symmetry breaking is possible when the surface coverage is sufficiently high. The mechanism of this phenomenon is explained below. As seen in Figure 3, at low adsorbate densities the homogeneous tripod molecules assemble locally into homochiral domains, regardless of the size of the building block (n > 1). Obviously, the overall adsorbed phase is then a mixture of the two mirrorimage domains whose composition is equimolar on average. During the self-assembly process the tripod molecules organize in larger structures primarily to minimize interfacial energy of the overlayer. In other words, instead of many small clusters with numerous undercoordinated molecules at the perimeter, one unichiral extended superstructure is formed locally at equilibrium. The mechanism of this process relies on a 2D peripheral melting of DOI: 10.1021/la100043w
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Figure 11. Average potential energy per molecule during a Monte Carlo run in a system of about 3500 molecules with n = 2 adsorbed on a 200 200 triangular lattice. Two intervals corresponding to the formation of heterochiral and homochiral networks are indicated by A and B, respectively.
small clusters containing a few molecules and subsequent incorporation of the released molecules at the perimeter of large domains. Note that it is in general very hard to remove a molecule from the interior of an extended homochiral domain without considering desorption. Thus, such a domain becomes more and more stable as it grows with increasing number of fully coordinated molecules (nc = 3). This process is usually followed by a smooth increase in the potential energy of the adsorbate and it ends up with an equilibrium state in which a few large domains exchange peripheral molecules. At low surface coverages the average distance between the domains is relatively large and most of the domains are isolated. This situation changes drastically when the density of the adsorbed phase increases. The chance to move a molecule to the next position is largely reduced such that equilibration of the system takes much longer time and in some instances it is characterized by sharp changes in the system energy. One example of this behavior is presented in Figure 11, which shows changes in the average energy per molecule during a long MC run performed for ∼3500 homogeneous molecules with 2-membered arms on a 200 200 lattice. As seen in Figure 11, the energy initially reaches a plateau which extends up to 4 109 MC steps, suggesting that the adsorbed phase has reached the equilibrium state. However, this conclusion is misleading since further temporal evolution of the system brings an abrupt change in E. Specifically, the average energy per molecule increases then from 20.43 to 20.67. Both values are very close to the theoretical value of 21, as calculated for the perfect honeycomb network using the equation from the first row of Table 1. The above observations indicate that the adsorbed phase undergoes a structural transition and that the structures A and B are highly ordered both with hexagonal symmetry. To show this effect more clearly, in Figure 12 we present example snapshots of phases A and B. The low energy phase A consists of closely packed mirror-image domains which form irregular boundaries. Note also that, within each of the big domains there are subdomains connected by highly ordered molecular zippers of the three types denoted by I, II, and III. These three linear structures allow the domains of the same chirality, which are shifted parallel with respect to each other, to assemble into one extended network. Interestingly, formation of such ordered walls between domains of opposite handedness is not possible, and it is the main source of the structural transition 9514 DOI: 10.1021/la100043w
Figure 12. A large honeycomb network consisting of about 3500
molecules with n = 2 adsorbed on a 200 200 triangular lattice. Parts A and B present the adsorbed layer at the two corresponding stages of the simulation shown in Figure 11. The shades of gray indicate mirror-image domains with hexagonal pores. The magnified fragments in red frames show different types of walls formed between domains of the same chirality. The red solid and dashed lines in part B indicate domain walls of type I and II, respectively.
leading to the formation of the homochiral phase B shown in the bottom part of Figure 12. This is because the energy gain associated with the irregular phase boundary in the heterochiral overlayer A is highly unfavorable from the energetic point of view. Thus, in order to minimize the potential energy the system tends to a complete elimination of one of the two enantiomorphs. The elimination process has a random nature, that is there is equal probability for each enantiomorph to disappear. As we observed, this effect occurs also for saturated overlayers. For example, separate simulations carried out for about 8000 molecules on a 300 300 lattice demonstrated the gradual disappearance of the domain of one handedness and the simultaneous growth of its mirror-image counterpart. Obviously, the MC time required to reach the homochiral state increases with the density of the adsorbed layer. For that reason the system can remain trapped in the heterochiral state for considerable MC time. In conclusion, we emphasize that the main origin of the spontaneous chiral symmetry breaking in the dense overlayers is the assumed rigidity of the tripod molecules. In real systems, because of the flexibility of intramolecular bonds, the molecules are able to adopt optimal configurations at the boundary between hexagonal domains of the opposite chirality. This can be achieved, for example, by coplanar bending of adsorbed molecular arms or by detaching fully or partially the arms from the surface. Thus, in saturated monolayers observed experimentally there can exist a mixture of both enantiomorphs because of the decreased energy penalty associated with the formation of domain walls.
Summary The results of this work demonstrate that complex 2D molecular architectures on solid surfaces can be effectively modeled using simple theoretical tools such as lattice gas Monte Carlo method. Indeed, as we shown for the self-assembly of the rigid tripod-shaped molecules on a triangular lattice, the geometry of the chiral honeycomb pattern obtained from the simulations Langmuir 2010, 26(12), 9506–9515
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assuming only next-neighbor intermolecular interactions, agrees perfectly with the corresponding experimental data. Moreover, our simple model allowed prediction of the structural transformations in the self-assembled hexagonal layer which are induced by changing both size and composition of the building block. For example, it was shown that the molecular core affects largely symmetry of networks comprising relatively small tripod molecules (n < 3) while for bigger molecules (n g 3), we observed that the core influences only the extent of ordering, thus chirality, of hexagonal pores. To fully characterize the obtained assemblies we provided a quantitative description of the stable ordered phases including unit cell parameters and average potential energies of the adsorbate. This allowed us to establish useful links between the size and functionality of the tripod-shaped molecular brick and the structural stability of the resulting extended networks. The insights from this work are of particular interest for the custom design of 2D supramolecular architectures with potential application in chemistry, physics and material science.
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The general theoretical approach proposed in this paper can be used for the prediction of structural properties of various molecular assemblies which are created via intermolecular interactions between building blocks adsorbed on solid surfaces. This conclusion refers mainly to chiral and achiral nanoporous networks formed by highly symmetric star-shaped molecules but it can be easily extended to more complex systems. For example, the MC model we developed can help predict possible ordered phases formed by asymmetric molecules with arms of unequal length or by multicomponent mixtures of either symmetric or asymmetric molecules. These issues are subject of ongoing research. Acknowledgment. This work is supported by K.U.Leuven through GOA 2006/2, the Institute of Promotion of Innovation by Science and Technology in Flanders (I.W.T.), the Fund of Scientific Research Flanders (FWO), the Belgian Federal Science Policy Office through IAP-6/27, the startup funding of HIT. We wish to thank Prof. Y. Tobe and Dr. K. Tahara for fruitful discussions.
DOI: 10.1021/la100043w
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