Article pubs.acs.org/JPCC
Understanding Pattern Formation in 2D Metal−Organic Coordination Systems on Solid Surfaces Damian Nieckarz and Paweł Szabelski* Department of Theoretical Chemistry, Maria-Curie Skłodowska University, Pl. M. Curie-Skłodowskiej 3, 20-031 Lublin, Poland S Supporting Information *
ABSTRACT: Creation of two-dimensional superstructures using coordination chemistry principles is a promising method to fabricate new nanomaterials with predefined architecture and functionality. In this work we use a simple lattice Monte Carlo (MC) model to study the mixed selfassembly of a family of ditopic linkers and metal atoms adsorbed on a triangular lattice. In particular, we focus on the role of directional short-range metal−linker interactions in the formation of local coordination motifs responsible for the development of periodic and random molecular patterns. To that end canonical ensemble MC simulations were performed in which both components of the adsorbed mixture were assumed to consist of discrete segments, each of which occupies one lattice site. Accordingly, the metal atoms were modeled as single segments while the linker was represented by a rigid linear chain whose terminal segments are able to form directional bonds with a neighboring metal atom. The simulated results demonstrated that depending on the assumed directionality of the metal−linker interaction and composition of the adsorbed phase, the self-assembly can lead to the formation of largely diversified planar structures including random strings, nanorings, chiral and achiral porous networks, and fractal-like aggregates. The insights from our theoretical investigations can be helpful in designing 2D metal−organic molecular architectures comprising simple functional building blocks.
1. INTRODUCTION Engineering matter at the atomic and molecular scale to create two-dimensional ordered superstructures is a fascinating topic that has recently drawn close attention. One of the most promising approaches in this area is the bottom-up strategy, in which controlled self-assembly of functional molecular building blocks on solid substrates plays a central role.1−3 The great advantage of that method is the possibility of creation of assemblies whose architecture can be finely tuned by suitable modification of the building material, including its size, shape, and functionality. The 2D patterns emerging spontaneously in adsorbed overlayers can be sustained by different intermolecular interactions, such as van der Waals interactions,4−10 hydrogen bonding,11−19 metal−ligand coordination,20−24 or even covalent interactions.25,26 The number of potential structures obtainable by the surface-confined self-assembly technique is virtually unlimited, being largely dependent on the individual properties of the components and the ways in which they can connect to each other. This perspective opens up a way for custom designing of new hybrid surfaces with programmed structural and physicochemical properties. The bottom-up principles of self-assembly have been recently recognized as a practical and powerful approach to create lowdimensional structures comprising linear and branched functional organic molecules and their mixtures.1−3,27,28 This refers mainly to the self-assembled overlayers adsorbed on solid substrates such as graphite3 and metallic crystals1,2 which have © XXXX American Chemical Society
been predominantly used in scanning tunneling microcopy (STM) imaging. To date numerous examples of two-dimensional molecular architectures formed spontaneously either in ultra high vacuum (UHV) or from liquid phase have been reported in the literature. A large variety of molecular structures, including compact periodic patterns,3 open molecular networks,1,2,29 chiral assemblies,3,8,9,27,30,31 and glassy overlayers32−34 have been observed. Among the numerous examples of ordered molecular arrays, those with void spaces, so-called 2D porous networks,29 are of special importance. The periodic arrangement of 2D nanocavities that is provided by porous networks makes those structures especially attractive from the perspective of future nanotechnological applications related to adsorption, sensing, and catalytic processes. A convenient route to highly ordered 2D porous networks with predefined morphology is the selfassembly of organic linker molecules and transition metal atoms which are able to form directional coordination bonds. Those structures are readily obtainable under UHV conditions where solvent molecules do not interfere with the self-assembly, so that the final outcome can be precisely tailored by changing composition, density, and temperature of the adsorbed overalyer. In this case organic building blocks with different Received: March 5, 2013 Revised: May 1, 2013
A
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liquid/graphite interface.27,56−58 In the adopted approach the number of interaction parameters was substantially reduced, so that interpretation of the influence of such factors as directionality and strength of interactions, molecular size, and shape of the building block was largely facilitated. Following this idea, in this contribution we use the lattice MC model to explore the surface-confined self-assembly of metal atoms and linear linker molecules able to form directional coordination bonds in cis and trans positions. The main objective of the present study is to decipher the role of the cis and trans conformers in the formation of ordered and disordered assemblies and to identify new possible structures comprising these building blocks. Although our theoretical investigations were originally motivated by the self-assembly experiments with polyphenyl dicarbonitriles, the results reported herein shall be applicable to a wide range of metal−organic systems comprising structurally similar rod-like linkers with peripheral electron donor centers.46
number and intramolecular distribution of well-defined coordination centers (e.g., N, O, or S atoms) are usually codeposited with atomic Cu, Fe, Co, and Ni on metallic surfaces such as, e.g., Au(111) and Ag(111) and others.1,2 By a suitable choice of the adsorbed metal whose atoms play the role of connecting points for the linker molecules it is often possible to direct the formation of local coordination motifs with predefined connectivity.21,35−37 This possibility, in combination with the large diversity of linkers which can be designed and synthesized, frames the simple and elegant concept of metal− organic nanoporous grids. The practical usefulness of that concept has been proven in numerous experimental systems in which the formation of ordered networks with square,22,23 rectangular,38 and hexagonal nanocavities21,35,36 has been induced. An important property of organic linkers that facilitates designing of the corresponding 2D metal−organic structures is the strict adsorption mode of the molecular building block. This feature is often provided by molecules such as compact substituted porphyrins39,40 and peropyrenes,41 for which a variety of one- and two-dimensional nanostructures can be engineered, depending on the distribution of electron donor centers within the molecule.40 A much more complex situation can be encountered, however, when the building block exhibits some internal flexibility,42 especially when it deconvolutes into distinct conformers upon adsorption.43,44 A clear manifestation of this effect has been recently observed for molecules such as polyphenyl dicarbonitriles45,46 and dicyanoazobenzene47 having carbonitrile terimnations in the meta position coadsorbed with cobalt atoms on Ag(111) and Au(111), respectively. In those instances, the rotatability of CN-terminated phenyl rings around the long molecular axis allowed the molecules to be adsorbed either in the cis conformation or in any of the two mirror-image trans conformations. In consequence, instead of the regular open network formed by, for example, p-polyphenyl dicarbonitriles coassembled with elementary Co,21,35,36 complex random metal−organic structures comprising strings with a large variety of coordination motifs have been observed in STM experiments.48 Understanding the individual role of the cis and trans conformers of a linker molecule in the formation of 2D metalcoordination structures is a difficult task, as those entities cannot be isolated, so that their self-assembly cannot be studied separately. A possible solution to this problem is the use of theoretical methods, especially computer simulations in which development of patterns comprising selected conformers can be traced. To date different simulation techniques, including Molecular Dynamics49−51 and Monte Carlo32,33,39,52−55 calculations, have been used to model the self-assembly of functional molecular building blocks adsorbed on solid substrates. In the case of a metal−organic system, the MC studies, which are scarce in the literature,55 focused mainly on those molecules which are not able to exist in more than one adsorbed conformation (e.g., cis and trans etc.). Despite this assumption, those simulations required a large set of molecule−molecule and metal−molecule interaction parameters obtained, for example, from ab initio calculations, characterizing the potential energy of different coordination motifs. Recently we proposed a simple and effective coarse-grained MC model of the 2D self-assembly of star-shaped molecules which were revealed to be able to reproduce both porous and compact patterns observed experimentally for dehydrobenzo[12]annulenes derivatives adsorbed at the
2. THE MODEL AND SIMULATIONS A useful theoretical tool 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. 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. In this case, the geometry of the building block as well as adsorbate−adsorbate and adsorbate−substrate interactions can be described by a minimal number of adjustable parameters. While this approach has been widely used to model self-assembly of various functional organic molecules27,52,56−58 on solid substrates its application to 2D metal−organic systems is quite uncommon and so far the lattice MC method has been tested only for the bis(terpyridine) derivative55 and for small porphyrins.39,40 Theoretical foundations of the MC lattice models lie on mapping of the structure of adsorbed species on a lattice (usually square, triangular, or hexagonal) and on defining directional metal−ligand interactions which in many cases can be easily deduced based on the distribution of coordination centers within the linker molecule and coordination number of a metal atom. Additionally, when the predicted symmetry of the metal−organic nodes matches the symmetry of the substrate it is possible to consider only a limited number of relevant orientations of the nodal motif with respect to the surface. In this case, modeling of the selfassembly becomes much simpler, as a smaller number of interaction energy parameters (adsorption energy and intermolecular interactions) are needed, obtainable, for example, from DFT calculations. To predict the outcome of surfaceassisted self-assembly in metal−organic overlayes the discrete picture of a modeled system has to be combined with a simulation method that enables fast equilibration of the (usually) large set of molecules. As mentioned previously, a perfect candidate for our purposes is the canonical MC method whose main principles are briefly outlined below. In the MC method for the canonical ensemble a thermodynamic state of a system is described by the volume (substrate area), the number of molecules, and the temperature, whose fixed character correlates well with the conditions under which most of experiments on molecular self-assembly are B
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Figure 1. Schematic structure of the planar conformers of the dicarbonitrile linkers: (A) pNC-pPh3-pCN, (B) mNC-pPh3-mCN, and (C) pNC-pPh3mCN and their model counterparts used in the simulations on a triangular lattice. The red arrows in the bottom part indicate the directional metal− linker interactions assumed for each structure. Mirror-image adsorbed conformations of the prochiral molecules B and C are marked by L and R. The metal atom shown in red occupies one lattice site.
the rotatability of the terminal phenyl rings around the backbone axis. Upon adsorption the prochiral molecule B can adopt either the cis conformation or one of the two mirrorimage trans conformations BL and BR. For molecule C the two enantiomeric structures CL and CR can be found on the surface. To account for the possible adsorbed conformations of linkers A−C, we assumed that the model molecules consist of a common rigid linear part but differ in directionality of the metal−NC interactions, as illustrated by the red arrows in the bottom part of Figure 1. Specifically, the linker was assumed to comprise three collinear segments, each of which represents a phenyl ring and occupies one site on the triangular lattice shown in Figure 1. A metal atom was represented by a single segment allowed to occupy one site. The adsorbed species were assumed to interact via short-ranged segment−segment interaction potential limited to nearest neighbors on a triangular lattice. To include the anisotropic nature of the metal−NC interaction the terminal segments of the linker molecule were allowed to interact only with those metal atoms which are adsorbed on the preferred neighboring lattice sites. For each molecular structure shown in the bottom part of Figure 1 the preferred neighboring lattice sites are marked by the red arrows pointing to them. In the simplified approach adopted herein we assumed that the maximum coordination number of the metal atom is equal to three21,35,36 although metal−organic nodes with higher lateral coordination, from 4 to 6, have also been observed experimentally.61,62 Moreover, the terminal linker segments attached to the metal atom (forming together a coordination node) were not allowed to occupy neighboring lattice sites at its perimeter. This assumption is illustrated for linker A in Figure 2 in which we showed the corresponding nodal motifs meeting the above criterion. To reflect the dominant role of the metal−NC bonding in the self-assembly process the energy of interaction between a terminal segment of the linker and a metal atom in the preferred configuration (enabling the directional interactions from Figure 1), ε, was set to −10
performed. To predict the equilibrium molecular configuration a sequence of trial moves, including, for example, random translations and/or rotations of adsorbed molecules, are performed on the lattice, aiming at minimization of the free energy of the system. This procedure involves calculation of the potential energy of the system, that is summing out adsorbate− adsorbate and adsorbate−substrate interactions before (old state) and after the trial move (new state). In the simple Metropolis version of the MC method the new configuration is accepted with the probability that is proportional to the ratio of the Boltzmann factors associated with the new and old state.59 The above sequence is repeated until the system reaches equilibrium for the assumed set of variables, so that equilibrium properties of the emerging molecular structures can be analyzed. Herein we took advantage of the combination of the discrete mapping with the MC simulation technique and built a theoretical model of the 2D self-assembly of metal atoms mixed with linear linkers. The model described below was inspired by the recent experimental findings which have been reported for the mixed self-assembly of dicarbonitrile linkers and transition metal atoms codeposited on closely packed metallic surfaces, such as Ag(111), Au(111), and Cu(111).21,35,36,48,60 In those STM studies the rod-like molecules NC-pPh3-CN comprising three collinear phenyl rings with a carbonitrile group attached at each outer phenyl ring have been predominantly used as a bridging ligand. Depending on the position of the CN groups in the outer phenyl rings (para or meta) different conformers have been observed on the surface, able to form directional coordination bonds with the coadsorbed metal atoms. The possible conformers of the NC-pPh3-CN molecules differing by the position of the CN bond sites are shown schematically in the top part of Figure 1. Among the molecules presented in the figure only molecule A, having both CN groups in the para position, adopts a unique conformation when adsorbed. In the case of molecules B and C we are dealing with three and two surface conformers, respectively, and this results directly from C
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energetic and geometric heterogeneity and assume that intramolecular hydrogen bonding does not compete or interfere with the metal−ligand coordination. The main purpose of this simplification is to study in depth the original role of the metal−linker coordination in the formation of metaloorganic structures under 2D confinement. The model and the simulation scheme outlined below can be easily modified to account for these additional factors. The simulations were performed on a 200 × 200 rhombic fragment of a triangular lattice with equivalent adsorption sites with use of the conventional canonical ensemble MC simulation method with Metropolis sampling.56,59 To eliminate edge effects, periodic boundary conditions in both planar directions were used. Briefly, the simulations were organized as follows. At the initial step a mixture of Nm metal atoms and Nl randomly oriented linker molecules (Nm + Nl = N in total) were distributed on the lattice. Next, one of the adsorbed species, m or l, was chosen at random and its potential energy in the old configuration, Eold, was calculated. To that end, for each segment of the selected component (one for a metal atom) six neighboring sites were checked. If the neighboring site of the segment was occupied by the other component the potential energy was increased by ε, provided that the interaction occurred between the metal atom and the terminal
Figure 2. Coordination nodal motifs comprising 1, 2, and 3 molecules of linker A (gray) allowed in the simulations (see text for details). The metal atom is shown in red.
expressed in kT units of energy. All of the remaining segment− segment interactions in the system were assumed to be equal to 0. This refers to the linker−linker and metal−metal interactions as well as to the metal−linker interaction in configurations other than those allowing for the formation of the assumed directional bonds for a given molecular structure. One important note which has to be made here is that the proposed model does not include two effects, which can have potential impact on the self-assembly. Namely, we disregard the influence of the adsorbing surface, including its corrugation and
Figure 3. Snapshots of the simulated hexagonal networks comprising (a) 1800 molecules of A and 1200 metal atoms and (b) 900 molecules of the longer four-membered homologue of A mixed with 600 metal atoms. The black solid lines in the magnified fragments of the networks delimit the corresponding rhombic unit cells. STM images of the honeycomb metal−organic nanomeshes formed by the molecules of (c) pNC-pPh3-pCN and (d) pNC-pPh4-pCN codeposited with cobalt atoms on Ag(111). Reproduced and adapted with permission from ref 36. Copyright 2007 American Chemical Society. For each STM image the model of the corresponding 3-fold Co-linker coordination motif is shown beside. D
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Figure 4. Snapshots of the simulated overlayers comprising (a) 1800 molecules of cis-B and 1200 metal atoms and (b) 3600 molecules of cis-B mixed with 2400 metal atoms. (c) The ring-shaped structural unit dominating in the system and (d) larger parent structures built of three connected ringshaped subunits. The orange lines in part d show connectivity of the subunits with the central void space. The number of the connections (0−3) is given above each scheme.
the theoretical results can be directly compared with the experimental counterparts.21,35 Figure 3 shows snapshots of the simulated overlayers consisting of 1800 molecules of A (a) and 900 molecules of its longer homologue built of four segments (b), mixed with 1200 and 600 metal atoms, respectively. The main reason for choosing these numbers of adsorbed species was to model the self-assembly at submonolayer coverage and to induce the formation of extended superstructures which, as we examined, occurs in both cases at the stoichiometric linker-to-metal ratio 3:2 used here. As is seen in parts a and b of Figure 3, the adsorbed components selforganize into highly ordered porous networks with hexagonal cavities. These isomorphic structures are characterized by a rhombic unit cell with side a and pore diameter d (corner-tocorner) both of which scale linearly with the number of segments in the linker, n, that is: a = √3(n + 1) and d = 2(n + 1), expressed in lattice spacing units. The obtained scaling relations are true also for longer homologues of A (n > 4, results not shown). The dominating coordination motif of the assemblies form Figures 3a and 3b is the metal atom with three attached linker molecules forming a C3-symmetric node. The occurrence of this preferred motif leads to the creation of extended achiral hexagonal networks whose unit cells comprise three linker molecules and two metal atoms, reflecting the assumed stoichiometric composition of the mixture. An important feature of the results simulated for the linker A and for its longer homologue is that they agree perfectly with the experimental results shown in parts c and d, respectively, proving the validity of the simple coarse-grained model proposed herein. To explore further the self-assembly in one-component systems we carried out separate simulations for the conformers of molecule B from Figure 1, that is for cis-B and for trans-BL. In the case of trans-B only one surface enantiomer was considered, as the obtained results are qualitatively the same as for its mirror-image structure, trans-BR. The calculations were performed for the 3:2 linker-to-metal ratio assumed previously for molecule A. Let us start with the cis isomer, for which the simulated results are presented in Figure 4.
segment of the linker oriented in such a way that the directional bond can be formed. In the remaining situations the contribution from the segment−segment interaction to Eold was equal to 0. Similarly, the energy of interaction between a molecular segment and an adsorption site was chosen to be 0.56 Once the net potential energy Eold was summed out, an attempt was made to move the selected atom/linker molecule to a new randomly chosen position on the lattice. In the case of the linker molecule the displacement move was additionally accompanied by a random in-plane rotation of the backbone, by a multiple of 60°. The selected atom/molecule was inserted in the new position only when the following conditions were fulfilled: (1) the corresponding lattice sites in the new position were unoccupied and (2) the move did not involve the formation of a node in which the terminal linker segments occupy neighboring lattice sites at the perimeter of the metal atom (see Figure 2). If this was the case, the energy of the metal atom/linker molecule in the new configuration, Enew, was calculated by using the same procedure as described above for Eold. To decide whether the new configuration should be accepted or not, the acceptance probability p = min{1,exp[−(Enew − Eold)/kT]} was calculated and compared with a randomly generated number r ∈ (0,1). If r < p the new configuration was accepted; otherwise the move was rejected and the atom/molecule was left in the original position. During one MC step the above sequence was repeated N times, that is once per adsorbed entity on average. To equilibrate the system we used from 107 to 1011 MC steps, depending on the density and composition of the mixture. The explored range of density, defined as fraction of occupied lattice sites (metal + linker), varied from 0.1 to 0.33. All of the calculations were carried out at 1 kT, where the temperature can be chosen arbitrarily, as the energy parameters in the model are expressed in kT units. No annealing of the simulated assemblies was performed.
3. RESULTS AND DISCUSSION One-Conformer Systems. To test the predictive potential of the proposed model we first performed the MC simulations for one-component systems comprising molecules A, for which E
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Figure 5. Snapshots of the simulated homochiral porous networks comprising (a) 1800 molecules of trans-BL and 1200 metal atoms and (b) 900 molecules of the longer homologue of trans-BL comprising four segments mixed with 600 metal atoms. The black solid lines delimit the associated unit cells.
elimination of the interfering trans conformer, which can be very challenging from the experimental point of view. An important property of the conformer cis-B is that, contrary to linker A, it is not able to self-assembly into extended networks. Instead, creation of closed isolated subunits is the dominating process for this molecule when coadsorbed with three-coordinate metal. Even though in Figure 4b random chains of different length can be easily found, the main structural motif remains the nanoring from Figure 4c. The primary reason for that is the increased probability of formation of the 3-fold coordination nodes ccc2 and ccc2* shown in Figure S1, comprising two parallel molecules of B (see also the hexagon walls in Figure 4c). Specifically, there are 4 possible arrangements of three cis-B molecules in the 3-fold node, 2 of which comprise a pair of parallel linker molecules (see Figure S1). The two remaining configurations are mirror-image windmill motifs resembling that one from Figure 2 (case 3). Taking into account rotational degeneracy of these nodes, that is 2 for each windmill motif and 6 for ccc2 and ccc2*, it becomes clear that the formation of the windmill motifs is largely suppressed. An additional factor that promotes the creation of the 3-fold nodes with parallel arms is the effective stabilization of these structures by a metal atom attached to the second end of the pair of parallel linkers. In this case, the second metal atom is in 2-fold coordination once it attaches to the node, resulting in lower potential energy compared to the windmill motif for which the second metal atom can be coordinated by only one linker molecule. The special properties of molecule cis-B discussed above make it act as a kind of dispersive agent, which prevents formation of extended superstructures in the adsorbed overlayer. This situation changes completely when linker B adopts the trans conformation, so that the directional ligand−metal interactions point to opposite sides of its linear backbone. Figure 5 presents the results of the simulations performed for 1800 molecules of trans-BL (a) and for 900 molecules of its
As is seen in parts a and c of Figure 4, the molecules of cis-B self-assemble forming locally ordered nanostructures of a hexagonal shape, each of which contains 9 linker molecules and 6 metal atoms (3:2 ratio). These isolated nanorings are randomly distributed over the surface, and at moderate surface densities (1800 molecules) they rarely form more complex locally ordered structures such as, for example, the one encircled in black in Figure 4a. However, at the higher, two times larger surface coverage (3600 molecules) the creation of these complex units is promoted. This can be seen in Figure 4b, in which four such units, encircled in black, can be identified. A closer inspection reveals that their internal structure is largely dependent on the way in which the three hexagonal subunits form Figure 4c are connected. As is demonstrated in Figure 4d, there are four possible arrangements of the hexagonal subunits, resulting in the metal−linker assemblies with the same overall shape and the same composition (27 linker molecules and 18 metal atoms, 3:2 ratio) but differing in internal architecture. In particular, each of the structures presented in Figure 4d comprises four void spaces (orange circles) of which the central one is connected with a different number (0−3) of neighboring cavities, as indicated by the orange lines. The structural diversity of the complex units originates from the possibility of connection of the nanorings (Figure 4c) through opening of the hexagon wall built of one linker molecule or partial opening of the wall comprising two parallel linker molecules. In the first situation the opened peripheral ring is internally connected with the central void space, while in the latter case the connection is blocked. Depending on how many hexagonal subunits (0−3) are opened in each way, the resulting structure can contain from 0 to 3 intercavity channels. Similar cyclic structures have been recently obtained with nonlinear porphyrin modules adsorbed on copper surface,63 suggesting that the supramolecules form Figure 11 can indeed be realized experimentally. However, this task requires a complete F
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Figure 6. Snapshots of the simulated overlayers comprising (a) 1800 molecules of CL and 1200 metal atoms and (b) 2700 molecules of CL mixed with 1800 metal atoms. Part c shows a frequent structural motif resembling the Sierpiński triangle.
Figure 7. Snapshots of the simulated overlayers comprising (a) 1800 molecules of trans-BL and trans-BR (1:1) and 1200 metal atoms and (b) 3600 molecules of trans-BL and trans-BR (1:1) mixed with 2400 metal atoms. The black arrows in the magnified fragments 1 and 2 show the rotation direction of the local structural motifs. The letters L and R in the magnified fragment 3 denote the corresponding enantiomers of trans-B forming the ordered lamellar structure.
6 shows snapshots of the adsorbed overlayer comprising 1800 (a) and 2700 (b) molecules of CL. The results presented in the figure demonstrate the spontaneous self-assembly of the molecules of CL into triangular-shaped hierarchical structures resembling the deterministic fractal called the Sierpiński triangle. Figure 6a shows a magnified image of the ordered structural motif which appears frequently in the overlayer. This motif can be treated as a realization of the second iteration of the Sierpiński triangle, in which the three smaller triangles, each comprising 9 metal atoms, are connected by the three linker molecules. There are two types of coordination nodes which can be found in the pattern form in Figure 6c. They consist of the metal atom with (1) two linkers attached through an A-type bond and one linker attached through a B-type bond and (2) two linkers attached through a B-type bond and one linker attached through an Atype bond (see nodes 3 and 4 in Figure S1). Sequential combination of these two nodes is responsible for the creation of the perfect structural unit from Figure 6c but also for the formation of a series of erroneous structures which can be seen in Figure 6a,b. In the latter case we can observe that at the low surface coverage (see Figure 6a) the molecules of CL can form even larger triangular aggregates with diversified internal morphology. The structural diversity of these aggregates is additionally promoted by the occurrence of the windmill coordination nodes 1 and 2 sketched in Figure S1. The results obtained for the linker C demonstrate that complex self-similar molecular structures can be formed in metal−organic overlayers comprising simple rod-like molecules
longer homologue comprising four segments (b). In both cases we can observe the formation of perfectly ordered networks with hexagonal void spaces. These structures are chiral and they have the same rotation direction, which is a direct consequence of the assumed chirality (L) of the building linkers. The main structural unit repeating periodically in the obtained assemblies is the windmill coordination node, which is the only type of a 3fold node that can be formed by the molecules of trans-BL (see Figure S1). This configurational limitation is responsible for the fast self-assembly of the linker molecules into scalable chiral porous networks whose unit cell side and pore diameter (corner-to-corner) change with the linker length according to the following: a = √3(n2 + 3) and d = 2n, respectively. The results obtained for linkers trans-B and A indicate clearly that the presence of oppositely directed coordination centers in these linkers promotes development of extended ordered patterns in the simulated systems. The third type of linker we consider in this section is molecule CL, which combines bonding properties of molecules A and B.59 Namely, a molecule of C can form one bond that is collinear with the backbone (A-type) and one bond that is rotated by 60° with respect to the backbone (B-type) (see Figure 1). These bonds are neither collinear/parallel, as for A/ trans-B, nor pointing to the same side of the molecule, as for cis-B. As one may expect, these mixed properties should result in the formation of self-assembled architectures whose range of ordering is between that of A and trans-B (long-range) and cisB (short-range). Indeed, the results of our simulations confirm this hypothesis and, moreover, they are quite surprising. Figure G
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Figure 8. Relative content of the 3-fold coordination nodes calculated for the mixture trans-BL + trans-BR (1:1) comprising 1200 metal atoms and 1800 linker molecules (a). Mirror image nodes whose letter codes are displayed under each bar were counted together. For clarity one surface enantiomer of each node was presented; error bars are plotted as black vertical lines. Changes in the relative contents of (RRR + LLL) and (LRR + LLR) during the simulation performed for one system replica (b). The results shown in part a were obtained by averaging the last 10% of the corresponding MC data points from 10 independent sets of curves as those shown in part b.
distributed hexagonal void spaces. These nanocavities are rarely grouped into structures which are small fragments of the corresponding homochiral networks comprising one enatiomer of trans-B (see Figure 5a). An example of such a small fragment built of three hexagonal pores with the same rotation direction is shown in inset 1 to Figure 7. An interesting feature of the simulated assemblies is that they allow also for the coexistence of pores having opposite rotation directions in one domain. In this case the pores are separated by a few linker molecules forming different 3-fold coordination nodes allowing for smooth change of the rotation direction when going from pore to pore. Inset 2 to Figure 7 illustrates this situation. In fact the pores shown in the inset are glued by short ladder structures comprising a few parallel molecules of trans-B with alternating chirality (L and R). These structures are fragments of the dense ordered lamellar patterns of which one example is shown in inset 3 to Figure 7. The common structural element of all patterns of this type is the L-R ladder. Connection of a few parallel ladders through, for example, molecules of trans-BR results in the densely packed structure shown in inset 3. Obviously, neighboring molecular ladders can be independently connected by either molecules of trans-BL or trans-BR, which allows for the creation of different periodic and aperiodic lamellar patterns. The results obtained for linker B indicate clearly that the presence of both enantiomers in the adsorbed overlayer introduces disorder to the self-assembled structure. The main reason for that is the increased number of possible 3-fold coordination nodes which can be formed when the enantiomers trans-BL and trans-BR are at play (see Figures S1 and S2). Recall that for the corresponding enantiopure assemblies (see Figure 5a) the perfect hexagonal ordering is a direct consequence of the only type of 3-fold coordination node that can be created by molecules of trans-BL(R). In consequence, as one can expect, the appearance of the second enantiomer should strongly disturb the hexagonal pattern, as it provides two additional competing nodal motifs LLR and RRL having 6-fold rotational degeneracy. Some of the nodal motifs from Figure 7 are, of course, the enantiopure windmill motifs which are the basic structural units of the corresponding homochiral networks. In consequence, the hexagonal pores of these networks are present
with directional interactions. This theoretical prediction is in accordance with the recent experiments on the fractal selfassembly on solid surfaces which have proved that a suitable design of molecular building blocks and interactions between them enables construction of 2D patterns resembling deterministic fractal sets. To the best of our knowledge, there have been reported two such systems in which spontaneous creation of ordered fractal patterns was observed. First of them is the self-assembly of DNA tiles on mica64 and the second is the self-organization of bis-terpyridine building blocks coadsorbed with Ru and Fe on the Au(111) surface.65 In those instances, the creation of aggregates resembling the Sierpiński triangle and the Sierpiński hexagon has been observed, respectively. The above experimental results suggest that the theoretically predicted formation of the triangular fractal pattern from Figure 6 can occur also in real 2D systems comprising the linker C. However, an important condition that has to be satisfied to achieve this is the enantiopurity of the adsorbed linker (CL or CR). This would require, for example, chemical modification of the original molecule to ensure its correct handedness when adsorbed and to prevent chirality switching. Mixed Systems. A normal situation encountered when dealing with the adsorption of prochiral molecules on achiral solid surfaces is the formation of a racemic overlayer comprising equal amounts of both surface enantiomers. This observation is relevant to the prochiral linkers trans-B and C, as they can deconvolute into the mirror-image structures L and R upon adsorption. To examine the self-assembly in the overlayers containing both enantiomers of trans-B and C we performed MC simulations for the corresponding racemic mixtures. The main purpose of the calculations was to determine how the presence of the second enantiomer (R) affects the structure formation in these systems. Figure 7 presents the results obtained for 1800 molecules of trans-B (900 L + 900 R) coadsorbed with 1200 metal atoms (a) and for 3600 molecules of trans-B (1800 L + 1800 R) mixed with 2400 metal atoms. In both cases the linker-to-metal ratio was equal to 3:2, as used previously. As follows from Figure 7, the racemic self-assembly leads to the formation of extended disordered patterns with randomly H
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Figure 9. Snapshots of the simulated overlayers comprising (a) 1800 molecules of CL and CR (1:1) and 1200 metal atoms and (b) 2700 molecules of CL and CR (1:1) mixed with 1800 metal atoms. Part c presents a magnified version of the structural motif encircled in black in panel a.
Figure 10. Snapshots of the overlayers obtained for the mixture cis-B + trans-BL + trans-BR (2:1:1) comprising (a) 1800 linker molecules and 1200 metal atoms and (b) 2700 linker molecules and 1800 metal atoms. The magnified fragments in parts a and b show the structure of syndiotactic and isotactic molecular chains, respectively.
both enantiomers of C can be identified. An important feature which differs the racemic assembly from its enantioputre counterpart is the increased connectivity of the mixed L + R structure. In this case the deformed triangular subunits are bridged to form extended networks at both low and high surface density, as shown in Figure 9. Note, however, that this structural difference has no significant effect on the overall porosity of the reticulated assemblies obtained for CL and for CL + CR. Contrary to linker B, the coexistence of the surface enantiomers of C does not lead to the creation of a dense mixed molecular pattern that would alter considerably the morphology of the overlayer. The reason for that is the topology of the possible 3-fold coordination nodes that can be formed by the enantiomers of C when mixed (see Figure S2). For example, the presence of the A-type bond in a molecule of C excludes the possibility of formation of the dense ladder-type structures observed for the linker B (see Figure S2). The last example we consider here is the overlayer comprising the three possible conformers of linker B from Figure 1, including cis-B, trans-BL, and trans-BR. This case corresponds to the experimental systems in which the molecules of mNC-pPh3-mCN48 and dicyanoazobenzene47 were codeposited with Co atoms on (111) metallic supports. Following the observation that the deconvolution of those structures upon adsorption into the distinct conformers is not biased, that is the surface conformers are populated approximately with natural statistical ratio,48 we assumed that the cis-B, trans-BL, and trans-BR forms occur in 2:1:1 proportion. Accordingly, the simulations were performed for the mixtures consisting of 1800 linker molecules and 1200
also in the racemic assembly. However, a new pattern that is not inherited from the enantiopure networks is the lamellar pattern comprising parallel ladders of alternating trans-BL and trans-BR molecules. To quantify structural properties of the racemic assembly trans-BL + trans-BR we calculated the relative content of the 3-fold nodes in the mixture shown in Figure 7a. These results were normalized with respect to the total number of 3-fold coordination nodes and they are plotted in Figure 8 (for detailed statistics see Tables S1 and S2). As is seen in Figure 8a, the relative content of the windmill LLL and RRR nodes is about five times smaller than that of the nodes LRR and LLR. This tendency, despite the fluctuating structure of the assembly, remains constant during the simulation, as demonstrated in panel b. The strong difference between morphologies of enantiopure and racemic assemblies that was observed for linker B was revealed to be less profound in the case of linker C. This can be seen in Figure 9, which presents the results of the simulations performed for racemic mixtures comprising 1800 molecules of C (900 L + 900 R) coadsorbed with 1200 metal atoms (a) and for 2700 molecules of C (1350 L + 1350 R) mixed with 1800 metal atoms. In this case, the outcome of the self-assembly resembles the fractal-like structure obtained for pure CL but it is much less regular, as it contains a larger number of nodal motifs. Specifically, the molecules in the racemic overlayer self-organize into different deformed triangular-shaped structures which can be treated as disturbed versions of the perfect unit from Figure 6c or of its subunits. One of such disturbed structures is shown in Figure 9c in which 3-fold coordination nodes comprising I
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Figure 11. Relative content of the different 3-fold coordination nodes calculated for the mixture cis-B + trans-BL + trans-BR (2:1:1) comprising 1200 metal atoms and 1800 linker molecules. Mirror image nodes whose letter codes are displayed under each gray bar were counted together. The results are averges over ten independent systems; error bars are plotted as black vertical lines. For clarity one surface enantiomer of each node was presented.
Figure 10a. Interestingly, these motifs are responsible for the formation of the local ordered structures observed previously in the pure and mixed overlayers comprising linker B and/or C (see Figures 4, 5, and 7), that is, chiral hexagonal pores (RRR), ladder structures (LRR), nanorings (ccc2), and chains (Lcc1). Among the four types of nodes mentioned above, the largest contribution comes from Lcc4 (∼45%), which is responsible for the growth of random chains. A special property of this nodal motif that makes it most abundant is (1) the possibility of bonding a second metal atom via two interactions at once (low potential energy) and (2) the stoichiometry (2 cis + 1 trans) which reflects the assumed composition of the adsorbed phase. As for the mixture comprising only the enantiomers trans of linker B, in the present case we observed that the relative content from Figure 11 does not change much during the simulation. For detailed statistics of the coordination nodes and changes in their absolute number during the simulation see Tables S3 and S4 and Figure S3. The theoretical distribution presented in Figure 11 agrees qualitatively with its experimental counterpart obtained for a similar metal−organic system.48 Even though in the experiment enhanced formation of 4-fold coordination nodes was observed, the dominating contribution to 3-fold node statistics came from cc4 motifs (70%) and, as in the simulations, cc1 and LRc1 nodes were extremely rare (
