Structure Formation in 2D Assemblies Comprising Functional Tripod

Article Cite This: J. Phys. Chem. C XXXX, XXX, XXX-XXX

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Structure Formation in 2D Assemblies Comprising Functional Tripod Molecules with Reduced Symmetry Paweł Szabelski,*,† Damian Nieckarz,§ and Wojciech Rzẏ sko‡ †

Department of Theoretical Chemistry and ‡Department for the Modeling of Physico-Chemical Processes, Maria-Curie Skłodowska University, Pl. M.C. Skłodowskiej 3, 20-031 Lublin, Poland § Supramolecular Chemistry Laboratory, Biological and Chemical Research Centre, University of Warsaw, Ul. Ż wirki i Wigury 101, 02-089 Warsaw, Poland ABSTRACT: Surface-confined self-assembly of organic building blocks is a versatile method of creation of low dimensional structures with potential applications in nanotechnology and material engineering. A key factor which often determines morphology of such 2D supramolecular assemblies is the geometry and functionality of a molecular tecton at play. In this contribution, we use theoretical modeling to predict the structure of adsorbed systems in which tripod molecules with reduced symmetry interact via a short-range anisotropic pair potential. To that end the self-assembly of a tripod molecule with one shortened/elongated arm, adsorbed on a triangular lattice, is modeled using the Monte Carlo simulation method. The probe asymmetric molecule consists of a few interconnected segments, and it is equipped with terminal interaction centers (active segments) with differently assigned interaction directions. Our study focuses on the effect of directionality of intermolecular interactions on the morphology of the resulting supramolecular 2D assemblies. It is demonstrated that a suitable encoding of the interaction directions allows for the creation of largely diversified adsorbed structures including aperiodic porous networks, molecular ladders, strings, ribbons and dispersed aggregates. Main differences and similarities between the findings reported for the asymmetric molecules and their C3-symmetric counterparts are also discussed. The obtained results can be helpful in designing new molecular tectons for controlled on-surface self-assembly and coupling reactions, as they provide useful information on the molecule−superstructure relation. This preliminary information can, for example, facilitate screening of molecular libraries to select an optimal molecule able to create low-dimensional structures with predefined properties. bearing pyridyl groups16,17 have been frequently used to construct extended supramolecular structures adsorbed on graphite or metallic substrates in ultra high vacuum or from liquid phase. One advantage of these tripod tectons is the possibility of formation of open networks whose regular pores can serve as void spaces for selective adsorption and immobilization of guest species.3 As it has been shown experimentally, the porous networks can be stabilized by various intermolecular interactions including hydrogen bonding,11,16 metal−ligand coordination17 or even van der Waals interactions.12,13 Despite diversified nature of these interactions, a common element of the 2D porous networks is the geometry of the building block and directionality of molecule− molecule interactions. The latter factor plays a special role in the structure formation as it often determines periodicity, porosity and chirality of the obtained assemblies. For example, even for the same tripod backbone it is possible to introduce functional groups whose different intramolecular distribution results in the formation of assemblies with markedly different

1. INTRODUCTION Molecular properties such as shape, size, and functionality play a deciding role in the formation of self-assembled superstructures sustained by intermolecular interactions of different types. Careful tuning of these properties often enables directing the self-assembly toward architectures with predefined morphology and functions. This approach is particularly effective in the case of assembling processes running in confined environments, as it occurs, for example, in adsorbed systems.1 Because of the reduced rotational and translational freedom of adsorbed molecules the formation of intermolecular bonds leading to ordered superstructures can occur more effectively and selectively compared to bulk phase. The onsurface self-assembly of organic functional molecules has been thus one of the most intensively studied approaches to lowdimensional structures with potential applications in nanotechnology and material engineering.2−4 To date numerous organic molecular building blocks for the 2D self-assembly have been synthesized, with shapes ranging from simple linear5 or bent6 to star-like7−10 equipped with different functional groups. Among them tripod-shaped units such as polyaromatic carboxylic acids,11 dehydrobenzoannulenes (DBAs),12,13 stilbenoid compounds,14,15 and tripods © XXXX American Chemical Society

Received: July 13, 2017 Revised: September 16, 2017 Published: October 23, 2017 A

DOI: 10.1021/acs.jpcc.7b06902 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Monte Carlo (MC) simulations which have been frequently used to predict equilibrium structure formation in adsorbed overlayers comprising diverse building blocks. In this approach, the molecules are usually represented as collections of interconnected segments arranged in diverse flat shapes, (rods, tripods, crosses). These segments represent distinctive fragments of a real molecule (phenyl rings, functional groups, etc.) and their properties are set individually based on the chemical character of the composite fragments (e.g., ability to form bonds, their directionality). If particular molecular geometry and distribution of interaction centers are assumed for the model building block, this probe tecton can describe a broad class of chemically different molecules matching the same set of structural/interaction properties. Such a defined prototype molecular structure is an input for the MC simulations of which scheme is usually identical, regardless of the building block at play, making MC calculations a general and useful method for studying 2D self-assembly. Calculations of this type have been performed for various tripod molecules, including C3-symmetric units16,17,21−25 and molecules with reduced symmetry,13,26 resulting in very good matches with the experiment. For example, the lattice models we proposed for the 2D self-assembly of such molecules as DBAs13,21,22 and TPB16,17 revealed to be able to reproduce correctly the corresponding adsorbed phases as well as their coexistence. Our MC modeling was also recently used in the case of the heterogeneous C3-symmetric tectons to predict the effect of differently assigned interaction directions on the pattern formation.27 As these previous studies were limited to highly symmetric molecules, in the present contribution we extend them for the case of molecules with reduced symmetry which have been recently used in the experiment. To that purpose we consider the on-surface self-assembly of functional Y-shaped molecules with one shorter/longer arm. The main objective of our investigations is to asses the combined effect of directionality of intermolecular interactions and reduced molecular symmetry on the morphology of the resulting superstructures. We also discuss main similarities and differences between the obtained assemblies and the superstructures formed by the C3-symmetric tectons. Our aim in this case is to formulate general hints at how to design geometry of the tripod molecules and how to functionalize them to obtain new superstructures with desired properties. These hints can be useful in the synthesis of organic building blocks for 2D selfassembly as well as for on-surface polymerization reactions.

morphologies. Manipulating the directionality of interactions by specific functionalization of tripod-shaped molecules is thus a convenient route to obtain supramolecular constructs with largely diversified geometry. This refers not only to the selfassembled systems in which relatively weak hydrogen bonding or metal−ligand coordination plays the dominant role but also to covalently bonded structures whose architecture can be steered by using tripod molecules with suitably attached reactive groups or atoms.18 In most of the experimental studies on the surface-confined self-assembly of star-shaped molecules functional tripods with C3 symmetry have been used.3 These molecules are usually built of a flat core and peripheral arms bearing terminal functional groups of one type, providing intermolecular interactions of the same strength and directionality.11,16,17 Alternatively, like for the DBAs, the arms can be pairs of alkyl chains whose interdigitation stabilizes the resulting superstructures.12,13 For these molecules the outcome of the selfassembly are usually chiral and achiral porous networks with regular, typically hexagonal, void spaces. While the selfassembly of molecular tripods with identical arms has been extensively studied, the effect of structural heterogeneity of these building blocks on the adsorbed patterns they form has gained much less attention. Such studies have been recently reported by El Garah et al., who used 1,3,5-tris(pyridine-3ylethynyl)benzene (TPB) with nitrogen atoms in the meta positions in the three outer phenyl rings.19 Because of the rotation of pyridyl groups along the alkynyl spacers different planar regioisomers of TPB have been identified, characterized by different directionality of intermolecular hydrogen bonds. As a consequence, different 2D self-assembled structures including porous and compact patterns have been observed for these regioisomers, highlighting the role of the heterogeneous directionality of molecule−molecule interactions offered by each tecton. Another type of structural heterogeneity of molecular tripods that has been recently studied is the shape anisotropy induced by elongation of one arm. Molecules having this property, including DBAs13 and asymmetric tricarboxylic acids20 have been shown to exhibit much richer phase behavior compared to their C3-symmetric counterparts. For example, for the asymmetric DBA, competing porous networks with different geometries have been observed when the molecule was adsorbed at the graphite/organic liquid phase interface.13 In the studies mentioned above the molecules were equipped with three arms of the same composition (the same terminal functional groups) but differing in length only. Consequently, the directionality of interactions assigned to each arm was the same and systematic studies on the role of different interaction directions have not been performed for such asymmetric units. To asses the effect of anisotropy of intermolecular interactions on the structure formation in adsorbed overlayers a series of test STM experiments is required in which Y-shaped molecular tectons with differently distributed interaction centers are used. As the synthesis of these various tectons can be sometimes tedious, an useful approach in this case is the use of theoretical methods which allow for a quick identification of the main molecular features responsible for the formation of 2D superstructures with predefined morphology. Computer simulations based on simplified representations of interacting molecules are an useful tool which allows for modeling of large molecular assemblies under variable conditions. This refers specially to the coarse grained lattice

2. THE MODEL AND SIMULATIONS To examine the effect of reduced symmetry of functional tripod molecules on the adsorbed patterns they form we used rigid planar tectons of type 1 and 2 shown in Figure 1. Both these tectons were assumed to consist of a few interconnected segments (5 for 1 and 6 for 2) each of which was allowed to occupy one vertex of a triangular lattice. The molecules were equipped with three active terminal arm segments (shown in red) providing directional attractive intermolecular interactions whose range was limited to nearest neighbors on the lattice. Six exemplary combinations of the interaction directions a−f were considered, as shown in the bottom part of Figure 1. The adsorbed molecules were allowed to interact only when their active segments occupied neighboring sites and when the corresponding interaction directions were collinear (→ ← ). In such a case the segment−segment interaction was characterized B


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adsorbed overlayer was slowly cooled down from T = 1.04 to the target temperature T = 0.04 within 1000 steps of equal length. The simulations were performed for L = 200 and ε = −1. The energies and temperatures in our model are expressed in units of ε and |ε|/k, respectively. The results discussed in the following sections are averages over 10 independent system replicas.

3. RESULTS AND DISCUSSION Before we discuss the simulated results let us first outline briefly their experimental context. The tectons sketched in Figure 1 can be viewed as tripod polyaromatic molecules, for example asymmetric homologues of 1,3,5-triphenylbenzene, so that each of the segments represents a phenyl ring. One way to equip these molecules with centers providing the directional shortrange interactions is to functionalize the terminal phenyl rings with groups such as hydroxyl, formyl or carboxylic. Accordingly, a suitable choice of meta and para positions in molecular arms would result in the interaction schemes shown in the figure. For these groups, the intermolecular connections assumed here (→ ← ) are sustained by O..H hydrogen bonds which are formed between two molecules. This assumption is more likely to be fulfilled in real systems where adsorbate density is relatively low and nodes with higher connectivity are not formed (e.g., involving three molecules). Such systems can be realized in ultra high vacuum (UHV) conditions where submonolayer coverage can be precisely controlled and, moreover, solvent molecules do not affect the structure formation. A special type of systems in which the highly directional 2fold connections can be easily formed are the metal−organic adsorbed superstructures in UHV, including also precursors of the surface-assisted Ullmann coupling reactions. When, for example, the terminal segments of 1 and 2 are pyridyl groups with N atoms in meta and para positions and copper atoms are used to create 2-fold coordination nodes, the resulting superstructures would be cemented by the links with directionality imposed by the positions of the heteroatoms.29,30 In the case of the Ullmann coupling, the directional interactions shown in Figure 1 are determined by the positions of halogen atoms attached to the terminal phenyl rings.18,31,32 Dehalogenation of these molecules which occurs on coinage metallic surfaces produces activated monomers which, via metal−organic precursors structures, recombine to form C−C bonds with directionality encoded in the monomers (positions of the halogen atoms). As these metal−organic interaction schemes are usually selective in terms of connectivity (metal− organic links engage two molecules), the model proposed here can be used to predict structure formation in the corresponding experimental systems. 3.1. Asymmetric Molecules. 3.1.1. Enantiopure Overlayers. To examine the effect of molecular shape anisotropy on the morphology of the self-assembled overlayers we first performed the simulations for the units a, b and c. These building blocks are characterized by the lowest symmetry of the interaction directions and they are chiral in 2D. Specifically, the building blocks a, b and c can adopt one of two possible planar mirror-image conformations when adsorbed. These conformations are further called R and S of which the first one, according to the convention accepted here, corresponds to the molecules from Figure 1. To preserve the same, relatively low, surface coverage for 1 and 2 (ρ = 0.15), in the simulations we used 1200 molecules of 1 and 1000 molecules of 2.

Figure 1. Schematic structure of the tripod molecules 1 and 2 adsorbed on a triangular lattice. The red segments represent active centers providing short-range interactions with directionality (red arrows) shown for each case a−f. The red dots next to 1 indicate the possible interaction directions considered in the model. Analogous interaction directions refer to each active segment of 1 and 2. For the chiral tectons a, b, c, and f one surface enantiomer, R was shown for clarity.

by the energy parameter ε; otherwise the energy of interaction was equal to zero. The simulations were performed on a rhombic L × L fragment of the triangular lattice of equivalent adsorption sites with periodic boundary conditions in both planar directions. As the adsorbing surface was treated energetically homogeneous, the energy of molecule−surface interaction was, for convenience, assumed to be equal to zero. The calculations were carried out using the Monte Carlo method in canonical ensemble with the standard Metropolis sampling.16,17,22,28 The simulation protocol described here is very similar to that used previously in the case of the C3-symmetric tectons.27 Accordingly, in the first step N molecules of a given type (1a−1f, 2a−2f) were randomly distributed on the surface. The corresponding surface coverage, ρ was equal to N S /L 2 segments/lattice site where s is number of segments in 1 (5) and 2 (6). Next, the adsorbed overlayer was equilibrated in a series of MC steps, each of which consisted of an attempt to translate and rotate a randomly chosen molecule. To that end the energy of the selected molecule in its actual position, Uold was calculated by summing out the segment−segment interactions with nonzero, ε contribution from the directional (→ ← ) interaction. The selected molecule was next translated to a new randomly chosen position on the surface and simultaneously rotated in plane by a multiple of 60 deg. If the cluster of adsorption sites matching the shape of the molecule was unoccupied the energy of interaction in the new position, Unew was calculated using the same procedure as for Uold; otherwise the trial ended. To accept the new molecular configuration the probability p = min[1,exp(−ΔU/kT)] where ΔU = Unew−Uold, T is the system temperature and k stands for the Boltzmann constant was calculated and compared with a randomly generated number r ∈ (0,1). If r < p, the new configuration was accepted; otherwise the molecule was left in the original position. To equilibrate the adsorbed overlayers we used typically N × 109 MC steps. To eliminate the risk of trapping the simulated systems in metastable states we additionally used the cooling procedure27 during which the C


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Figure 2. Snapshots of the adsorbed overlayers comprising 1200 molecules of 1 and 1000 molecules of 2 (a-c, R) simulated at T = 0.04. The insets next to the snapshots present magnified fragments of typical structures formed by the corresponding molecules.

surface. The void spaces in these chains measure 1 and 4 adsorption sites, respectively. As it seen in the middle insets, the observed chain formation is largely enhanced by the presence of two identical interaction directions (↓↓) assigned to the molecular arms of the same length. However, as we will show later the creation of the single-stranded forms by 1b and 2b is also strongly affected by the third interaction direction (diagonal arrow) which is not collinear with the two remaining ones. On the other hand, the lack of identical interaction directions in the molecules of type c leads to the ladder structures which are similar to those obtained for 1a and 2a. For these c-based constructs the contributing molecular strands are shifted with respect to each other, so that the resulting pores are less regular, as compared to a. The pores in the ladders built of 1c and 2c cover 8 and 14 adsorption sites, respectively. To get deeper insight into the formation of the structures shown in Figure 2 we examined how intermolecular bonding changes with temperature in the corresponding systems comprising a, b, and c (R). Figure 3 presents the effect of temperature on the average number of bonds per molecule, calculated for these tectons. The temperature dependencies of the type shown in Figure 3 carry information on how many bonds on average a given molecule forms with its neighbors, with no distinguishing between particular bimolecular configurations. As it can be seen in the figure, the structural similarity

Figure 2 presents the results of the calculations performed for the enantiopure overlayers comprising molecules a−c (R). The obtained findings demonstrate that the three different assignments of the interaction directions are responsible for the formation of quasi-one-dimensional structures with diverse morphologies including molecular ladders (a, c) and strings (b). In these cases, qualitative features of the self-assembled structures (ladders, strings) are influenced mainly by the directionality of intermolecular interactions, so that the shape of the building block plays only a secondary role. This can be easily noticed while comparing the results simulated for 1 and 2 having the same interaction directions (a, b, and c). The ladders comprising the molecules of type a consist of molecular strands cemented by the interactions between shorter (1) and longer (2) molecular arms (see the insets). As a consequence, the void spaces in these superstructures are different in terms of shape and size. For the molecule 1a the nanopores are hexagonal and they embrace 10 adsorption sites while for 2a the voids are bigger and more elongated, with parallelogram shape and area equal to 15 adsorption sites. In the case of the tectons of type b we can observe qualitative changes in the morphology of the self-assembled structures. These building blocks engage two shorter (1) and longer (2) arms to form chain links comprising two oppositely oriented molecules each. Such links are connected by the third arm (longer for 1 and shorter for 2) to form straight chains propagating on the D


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coordination during the self-assembly. When a sufficiently slow cooling/heating procedure with constant rate, ensuring equilibration in each step, is applied in the experiment, these dependencies can be used to compare the ability of different molecules to form specific connections at a selected temperature (i.e., after certain heating/cooling time). From the calculated results it follows that the main difference between the two types of system (a/c vs b) originates primarily from the different temperature dependencies of the contributions with n = 1 and n = 2 shown in Figure 4. This is particularly visible in the case of the molecules having two bonds. The amount fraction of these molecules is in general higher for the tectons of type b, especially at moderate temperatures (0.2−0.4). The observed effect is a direct consequence of the facilitated formation of bimolecular bclusters (chain links) in which each molecule has two bonds. Such clusters are energetically favored (larger number of bonds) so that they are formed by b even at relatively high temperatures. Note that, in this case only two molecules of b are required and for each of them n = 2. On the other hand, a molecule of a and c needs two partners to reach coordination equal to two and this process is stepwise: first a bimolecular cluster sustained by one bond has to be formed and next third molecule has to be added. As this process is more complex, involving three molecules, and the initial bimolecular clusters are stabilized by one bond characterized by lower thermal stability, the population of molecules a and c with n = 2 is much lower compared to b. In consequence the average number of bonds shown in Figure 3 is initially higher for the tectons 1b and 2b (T > 0.2). When the temperature is further decreased, enhanced elongation of the chains and ladders takes place, as manifested by the rapid increase of the fraction of molecules with n = 3. In this case, the shape of the curves from Figure 3 is almost entirely determined by the corresponding contributions with n = 3. At the final stage (T < 0.1) most of the molecules are fully coordinated with much less abundant ones terminating the chains and ladders and having then n = 2 (about 0.1 at T = 0.04). The self-assembly of the asymmetric tectons 1 and 2 discussed above results in the formation of structures which are very similar to those obtained previously for the molecules with backbone comprising three arms of equal length (one segment

Figure 3. Effect of temperature on the average number of intermolecular bonds calculated for the adsorbed systems comprising 1200 molecules of 1 and 1000 molecules of 2 (a−c, R).

between some of the molecular assemblies presented in Figure 2 is closely related to the shape of the curves plotted in Figure 3. Specifically, an important observation is that the selfassembly of the ladders is described by the temperature dependencies which are identical for 1a/1c (black) and for 2a/ 2c (blue), being additionally very similar to each other (1 vs 2). This demonstrates that the asymmetric assignment of the interaction directions which are all different results in the same assembly mechanism, regardless of molecular shape. A similar conclusion refers to the strings formed by 1b and 2b, for which the corresponding plots nearly overlap. In this case, however, the obtained curves (red and green) are less steep and this effect can be attributed to the presence of the identical interaction directions (↓↓) in 1b and 2b which dictate the formation of the qualitatively different string-like molecular architectures. To explain the qualitative differences in the shape of the curves calculated for a/c and b in Figure 4 we showed how the amount fraction of molecules with n = 0...3 bonds varies with temperature. The curves plotted therein are the contributions to the net effect presented in Figure 3 and they provide detailed information on the changes in molecular

Figure 4. Effect of temperature on the amount fraction of molecules with n = 0...3 bonds (n shown in the circles) calculated for the adsorbed systems comprising 1200 molecules of 1 and 1000 molecules of 2 (a−c, R). E


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Figure 5. Snapshots of the racemic overlayers comprising 1200 molecules of 1 and 1000 molecules of 2 (a−c) simulated at T = 0.04. The surface enantiomers R and S are colored in gray and red, respectively. The insets next to the snapshots (a, b) present magnified fragments of the new mixed ordered structures formed in the racemates.

each).27 This observation proves that the main factor responsible for the formation of the structurally different assemblies (strings, ladders) comprising molecules of type a, b, and c is the particular assignment of the interaction directions. In consequence the use of the molecules 1, 2, and their counterparts with C3-symmetric backbone, all of which exhibit the same interaction pattern (a−c), allows for the creation of strings and ladders whose parameters (pore size and shape) can be finely tuned by choice of a tecton with appropriate aspect ratio. Not surprisingly, because of the same intermolecular interaction patterns, the self-assembly of the structures from Figure 2 and the corresponding ones formed by the molecules with arms of equal length is governed by identical mechanisms. This results in temperature dependencies such as these shown Figures 3 and 4 which are identical or very similar for molecules having the same set of interaction directions, regardless of the backbone shape.27 Very recently metal−organic chain-like structures similar to these shown in Figure 2b have been obtained experimentally via the Ullmann coupling of 1,3,5-tris(3-bromophenyl)benzene (mTBPB) on Ag(111), a molecule with C3-symmetric polyphenyl backbone.33 This prochiral brominated tripod monomer, because of the rotability of m-phenylene units, can adopt an adsorbed conformation (surface enantiomer) in which positions of the halogens are identical with the interaction

directions assumed for the tecton b. As the metal−organic bonding and subsequent covalent linkage of mTBPB is steered by the directional Br−Ag−Br links matching the interactions of b, the resulting experimental porous chain structures have morphologies which are very close to these from Figure 2b and which are identical with our MC results obtained previously for the C3-symmetric tectons.27 On the basis of the deciding role of the b-type interaction directions, which regardless of backbone symmetry (C3, 1, 2), produce model porous chains it can be expected that the use of the corresponding asymmetric units in the experiment should result in the complementary superstructures with pores of different sizes (see Figure 2b). This observation opens up a way to control porosity of the chains, which, as demonstrated experimentally can be further converted into porous nanoribbons,33 so that intrinsic properties of the nanoribbons can be indirectly tuned by a suitable choice of the monomer of b-type. Another experimental example in which directional interactions result in the formation of chains and ladders with connectivities similar to these from Figure 2 is the metal− organic self-assembly of cross-shaped pyridyl-functionalized porphyrin derivatives (PD) on a Au(111).34,35 In those STM studies it has been demonstrated that when three out of four arms of PDs are equipped with pyridyl groups, such molecules coadsorbed with Cu atoms create double strand ladders. This F


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Figure 6. Effect of temperature on the average number of R-S bonds in the racemates comprising 1200 molecules of 1 and 1000 molecules of 2 (a− c, f). The solid and dashed lines correspond to the directional R-S interactions from Figure 1 and to the total number of R-S intermolecular contacts in the overlayer (see text for details), respectively.

adsorption of such tectons is not biased so that the corresponding enantiomers R and S should be equally populated on the surface. Accordingly, we performed the simulations for the racemic mixtures comprising 1200 molecules of 1 (600 R + 600 S) and 1000 molecules of 2 (500 R + 500 S). The main objective of these calculations was to explore how the presence of the other enantiomer affects structure formation in the adsorbed overlayers. Figure 5 presents the snapshots of the racemic systems comprising the units 1 and 2 (a−c). Interestingly, the obtained findings show that even though for the enentiopure overlayers the selfassembly resulted in similar structures for the molecules with the same interaction directions, in the present case the situation is markedly different. This can be seen especially in the case of the tectons of type a and b. Here, for the smaller molecule 1a, we can observe the formation of mixed disordered domains with sparse ladder structures attached at the domain boundaries. These ladders are homochiral (red and gray) and, what is new, they can have also mixed racemic composition which characterizes the structure from the magnified fragment of Figure 5a. The special assignment of the interaction directions in 1a enables zipping of two homochiral strands (red and gray) to create the mixed ladders. This bonding type is also responsible for the diverse intermolecular connections between like and unlike enantiomers of 1a, producing disordered mixed networks dominating in the system. Formation of such disordered structures is, however, completely absent when the shape of the backbone is changed

construction principle is equivalent to the one governing the formation of the ladders comprising molecules of type a and c. Specifically, the PD molecule with three active arms (N atoms) can be viewed effectively as a tripod building block with specific interaction directions, that is two parallel vertical (↑ and ↓) and one horizontal (→). The two oppositely oriented vertical interaction directions are responsible for the growth of the PD strands while the horizontal interactions bridge them. Note that, this interaction scheme is preserved for molecules of type a and c which provide the opposite (parallel) interaction directions and the additional differently oriented bridging interaction direction. In consequence, ladders are also formed by these model tectons, highlighting correspondence between the simulated results and the experiment. Moreover, when the PD molecules bear two pyridyl groups in a pair of collinear arms (i.e ↑ and ↓), the resulting structures are the single chains. Formation of analogous chains in our case (tecton b) occurs due to the two identical interaction directions (↓↓) which make b behave effectively as a ditopic functional unit. Here, the identical interaction directions create one common interaction center enabling the attachment of one, suitably oriented (↑↑) molecule b. The similar ditopic encoding of the interactions in PDs and in the model tectons b results in structural similarity between the corresponding quasi one-dimensional structures observed in the experiment and modeled here. 3.1.2. Racemic Overlayers. As the molecules of type a−c are chiral in 2D, it is worth to consider one additional case which is relevant to the experiment. Normally, in real situations G


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depends on molecular perimeter and it can vary from zero to 22 for 1 and 26 for 2. Higher values of this parameter correspond to the formation of more compact mixed structures and for that reason the parameter provides additional information on the morphology (compact/openwork) of the simulated racemates. Figure 6 presents the temperature dependence of the two parameters introduced above, calculated for the racemates of a−c (1, 2). As can be seen in the figure, at high temperatures (T > ∼0.4) the corresponding dependencies calculated for the three tectons are very similar. At this stage, when the temperature is too high for the molecules to condensate, the number of directional bonds is close to zero and the number of R−S contacts is very low (about 1), being determined by the random distribution of the enantiomers for which, at the low coverage assumed here (ρ = 0.15), the chance for R and S to occupy neighboring lattice sites is consequently small. The same conclusion refers to pairs of like enantiomers. When the temperature is decreased to about 0.2 the adsorbed molecules start to condensate and form the diverse molecular structures from Figure 5. This structural change is accompanied by the increase in the number of directional bonds (solid lines), which is the most intense for the tecton 1b whose enantiomers form the triangular aggregates with racemic composition. In the remaining cases we are dealing with much lower contact values of this parameter (at T = 0.04), meaning more or less effective resolution of the enantiomers. For example, for the units 1a the formation of mixed R−S ladders and disordered domains results in the increased number of directional bonds, equal to about 1.25. A similar effect can be observed for the molecules 2b and 2c, first of which is able to form chains with mixed composition and the second creates mixed disoredered structures along with the homochiral ladders. On the other hand, in accordance with Figure 5, the chiral resolution is the most effective for the units 2a and 1c, for which the number of directional bonds is the smallest and equals to 0.55 and 0.3, respectively. The nonzero values obtained here originate mainly from the presence of mixed structures which connect the ladders of diversified length. Analysis of the temperature dependencies plotted for the average number of R−S contacts shows that at low temperatures these curves coincide with (a) or are close (b, c) to the corresponding curves obtained for the directional bonds. This effect means that at low temperatures intermolecular R−S contacts are almost entirely limited to the directional interactions. The differences observed between these two structural characteristics, especially for 1c, originate mainly from the formation of the disordered mixed structures which connect the ladders and in which the enantiomers are packed in a way that enables side contact of molecular arms. As this relative molecular position gives a big contribution to the average number of R−S contacts, even small number of such configurations makes the corresponding curve (dashed line, 1c) placed above that one calculated for the directional bonds alone. Note that, this effect is not observed for 2a, which also creates homochiral ladders. In this case, however, the connecting disordered structures are much more openwork compared to 1c. Another effect which is manifested in the shape of the dashed curves from Figure 6 is the formation of isolated structures built of enantiomer of one type. This can be seen for 2a and 1c, for which at the low temperature (T < 0.1) the corresponding curves drop below the level reached at high temperatures. Here the number of R−S contacts which at the

to 2. In this case we are dealing with the chiral resolution producing mirror-image ladders comprising 2a (R) and 2a (S) of which the first was shown in Figure 2a. The observed effect originates mainly from the incompatibility of the interaction directions encoded into the enantiomers of 2a which prevents the formation of mixed ladders. Strong effect of molecular shape was also found in the case of molecules of type b, for which small dispersed aggregates (1) and chains with different composition (2) were observed. These new structures are shown in the insets to Figure 5. For the molecule 1b the created triangular aggregates have racemic composition (3R + 3S) while for the unit 2b the chains are either homochiral (red, gray) or more frequently they comprise both enantiomers forming homochiral blocks of different length which occur in a random sequence (see the inset on the right). The selfassembly of the racemates comprising the molecules of type c results in the chiral resolution of the enantiomers, regardless of molecular shape. Both tectons 1 and 2 create homochiral mirror-image ladders built of the corresponding enantiomer R or S and these ladders (R) have identical structure as those occurring in the enantiopure systems from Figure 2c. As it can be seen in Figure 5c, the chiral resolution is somewhat less effective for the molecule 2c, for which within the assumed simulation time the formation of homochiral ladders was usually accompanied by the appearance of disordered mixed domains. The six-membered aggregates simulated for the rac-1b resemble the experimental structures which have been observed when both surface enantiomers of mTBPB take part in the selfassembly.33 The intermolecular connectivity in these mTBPB aggregates is identical with that one corresponding to the modeled nanostructures, and this results from the same set of interaction directions assumed in the theory and experiment. The more triangular shape of the simulated aggregates, as compared to the experimental hexagonal geometry, originates mainly form the elongated shape of the unit 1b. When molecules equipped with arms of equal length are used in the simulations the hexagonal shape of the racemic aggregates is accurately reproduced.27 Creation of such cyclic aggregates is not possible for the unit 2b, as it would result in the overlap of the longer arms inside the aggregate, so that mixed R-S chains are the optimal structure. Regarding the mixed ladders occurring in the rac-1a overalyer, their formation follows the principle discussed previously for the model enantiopure systems (see Figure 2) and also for the experimental data on the achiral PDs.34,35 3.1.3. Extent of Chiral Resolution. To quantify the extent of chiral resolution in the systems discussed above for all of them we calculated two structural parameters. First of these parameters is the average number of directional R-S bonds per molecule. This parameter, for a molecule R(S) means the number of neighboring molecules S(R) forming the directional (→ ← ) interactions and it varies form zero to three. Accordingly, at the target low temperature the chiral resolution is characterized by the parameter values close to zero, while the formation of fully mixed R-S structures corresponds to three. The second, additional, parameter is the average number of R-S contacts between adsorbed unlike enantiomers. It is defined as the sum of lines which can be drawn from all of the segments of R(S) to connect them with neighboring segments belonging to the molecules of type S(R). This parameter measures mixing of unlike enantiomers which do not necessarily interact with each other (→ ← ) but occupy neighboring lattice sites. Its value H


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Figure 7. Snapshots of the adsorbed overlayers comprising 1200 molecules of 1 and 1000 molecules of 2 (d,e; R) simulated at T = 0.04. The insets next to (d) and below (e) the snapshots present magnified fragments of the ordered structures formed by the corresponding molecules. The black line in the bottom-left panel delimits the unit cell of the locally periodic porous pattern created by 1e. The green lines therein show two possible orientations of the large pores. The structure encircled in black in the bottom-right panel is the basic element of the ribbons comprising 2e.

high temperatures is dictated mainly by the random distribution of adsorbed molecules, decreases due to clustering of like enantiomers forming well-separated ladders. For the remaining molecules increases are observed, resulting from the formation of mixed R−S connections occurring at different abundances: very high for 1b and much smaller for 1a and 2c. The ordered structures formed in the racemic assemblies comprising the units a−c are in general qualitatively similar to those simulated for the corresponding molecules with C3symmetric backbone.27 This refers to the tectons of type a and c for which the homochiral ladders were also observed. Moreover, our previous simulations performed for the molecule of type b but having three identical arms revealed the formation of dispersed racemic clusters with hexagonal shapebeing an analogue of the triangular aggregates reported here (1b). On the other hand, the formation of the ladders (1a) and chains (2b) with mixed composition was not observed for the corresponding tripods with arms of equal length. 3.2. Molecules with Higher Symmetry. 3.2.1. Achiral Molecules. The results of this section refer to the molecular units with higher symmetry of the interaction directions. Among them there are the achiral molecules of type d and e which have one symmetry plane and the C3-symmetric molecule f that is chiral in 2D. Figure 7 presents the snapshots obtained for the molecules of the first kind; 1200 molecules of 1d and 1e and 1000 molecules of 2d and 2e.

In the case of the smaller tecton of type d we can observe that the self-assembly produces numerous ladder and chain fragments of different length which are interconnected in diverse manners. The exemplary ladder structures formed by 1d and 2d are shown in the insets to the top part of Figure 7. The elongated pores in these ladders cover 8 and 14 lattice sites, respectively. Apart form these molecular architectures, also sparse isolated straight chains can be found on the surface for both tectons. However, majority of the chains is paired in parallel and bridged in an irregular way to form disordered double strands. The observed formation of disordered structures is particularly interesting from the point of view of the symmetry of the interaction directions. Note that the molecules of type d differ from b(R) only by the interaction direction assigned to the long/short arm (1/2) (see Figure 1). For the first type this direction is collinear with the two remaining ones (i.e., with ↓↓) while for the latter it is rotated by 60 degrees. Even though the molecules of type d have higher symmetry than b they create structures which are strongly disordered as compared to the uniform single chains observed for 1b and 2b. As we mentioned earlier, the rotation of the interaction direction in b (R) is the main source of the regular single-chain growth. This rotation eliminates effectively the possibility of pairing of neighboring chains and prevents ramification of the self-assembled structures. I


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Figure 8. Effect of temperature on the average number of intermolecular bonds per molecule (left) and on the amount fraction of molecules with n = 0...3 bonds (right, n shown in the circles) calculated for the adsorbed systems comprising 1200 molecules of 1 and 1000 molecules of 2 (d, e).

assignment of the interaction directions is described by nearly identical dependencies. This observation is not surprising for the molecules of type d, which form disordered structures with similar morphologies (chains and ladders, see Figure 7d), and the contributing molecules of 1d and 2d create identical connecting motifs. Interestingly, for the molecules of type e whose variants 1 and 2 self-assembly into the superstructures with entirely different architectures the coincidence of the corresponding temperature dependencies is also present. We attribute this effect to the similar formation mechanisms of the trimolecular ring aggregates with triangular (1) and hexagonal (2) shapes being the small pores incorporated in the networks and ribbons from Figure 7e, respectively. Enhanced formation of these initial structures occurs at T ≈ 0.25(results not shown). Further growth of these structures occurs via attachment of three new molecules to the free molecular arms which are not engaged in the pore formation. Because of the different aspect ratios of 1 and 2 the growing assemblies have different morphologies but the propagation scenario is the same. Comparison of this scenario with that one corresponding to the molecule of type d, shown in the right part of Figure 8, reveals that the main differences here originate from the shape of the corresponding contributions with n = 2 (long dashed lines). This effect is similar to what was observed for the molecules a and c vs b (see Figure 4) and its occurrence can be explained using the arguments we put forward previously for these three chiral tectons. The formation of the ribbons comprising molecule 2d originates from the special anchor-like assignment of the interaction directions combined with the appropriate aspect ratio of this building block. Even though our results are yet theoretical predictions an relate to a chemically different system, it is worth mentioning that polyaromatic brominated molecules with anchor shape have been recently used to synthesize graphene nanoribons via the on-surface Ullman polymerization.36 In the case of the remaining structures shown in Figure 7, based on the correct predictions for the prochiral mTBPB molecule, it can be expected that the corresponding experimental structures can be realized using the interaction encoding discussed here, especially with the metal-coordination chemistry and subsequent polymerization. 3.2.2. Enantiopure Networks Comprising Tectons of Type f. The simulations performed for the C3-symmetric tectons of

A set of structures with entirely different morphologies was obtained for the molecules of type e. In this case the outcome of the self-assembly was found to be strongly dependent on the molecular backbone. The bottom part of Figure 7 presents the results of the simulations performed for 1200 molecules of 1e and 1000 molecules of 2e. As it is seen in the figure, the selfassembly of 1e produces an extended porous network with complex architecture, in which three types of pores can be distinguished. These are the large pores with elongated shape (74 sites) and smaller pores of two kinds including triangular (6 sites) and sandglass shaped (15 sites). The obtained structure is composed of rows and/or domains in which the large pores have one of the two possible orientations shown schematically by the green lines in Figure 7. Even though these orientations differ by 45 deg the overall structure is free from defects and it is locally periodic. In this case the parallelogram unit cell shown in the figure has dimensions √97 by √157 and the associated network density equals to 0.33 segment/site. When the molecular backbone is changed to 2 the adsorbed molecules organize into the ribbons shown Figure 7e. This type of structures is especially intriguing as the ribbons are well ordered and have constant width that is determined by the size of the basic structural element shown in the magnified fragment of the figure. This structural unit comprises six molecules forming a stack with three small rhombic pores each of which covers four sites. The stacks are connected by two molecules of 2e and this connection results in additional pores: two hexagonal (seven sites) and one elongated (24 sites) in the propagating ribbon. Moreover, the stack units can be connected in a few ways, depending on the attachment of the two linking molecules. This diversity results in the elongated pores which can be rotated by ±60 deg with respect to the stack. In consequence, the ribbon consist of evenly spaced stacks which are connected by the elongated pores whose orientation (±60 deg) is distributed randomly along the ribbon. The associated offsets between the stack units produce less regular ribbon edges, but the continuity of the ribbon remains preserved. To compare the ways in which the structures from Figure 7 emerge in the simulated overlayers in Figure 8, we plotted the corresponding temperature dependencies of the average number of bonds per molecule (left) and amount fraction of molecules with n bonds (right). As it can be seen in the left part, the self-assembly of the molecules with the same J


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2 both of which also form aperiodic networks when the interaction directions are assigned in a way that is shown in the bottom part of Figure 9 for the achiral molecule g.37 The magnified fragments of the networks shown therein for the molecules 1g and 2g display the level of organization that is identical with that observed for the corresponding units of type f. In particular, the formation of pores with different shapes/ sizes is controlled by the same arm-engagement principles. In this context, the creation of irregular porous networks such as those observed herein is conditioned by the reduced symmetry of the backbone in combination with the C3-symmetric assignment of the interaction directions. To demonstrate how these features, which are common for f and g, influence the growth of the corresponding networks in Figure 10 we presented the associated temperature dependences. For comparative purposes we showed also the results calculated previously for the molecules of type g (1000 molecules 2g).37 As it is seen in the figure, the average number of bonds per molecule changes with temperature in the same fashion for all of the tectons. The corresponding curves plotted for the molecules of the same size overlap, and moreover they are nearly identical for the units with the different interaction directions (f, g). This suggests the same self-assembly scenario for the tripod molecules with the asymmetric backbone and with the C3-symmetric assignment of the interaction directions. Indeed, this can be seen in the right panel of Figure 10 showing that the contributions from the molecules with 0−3 bonds are very similar (red vs black lines). At the low temperatures (T < 0.2), the molecules with three bonds start to dominate in the simulated overlayers, so that the average number of bonds reaches about three meaning full coordination of most of the molecules. Even though, a similar temperature dependence was observed for the tripods with arms of equal length,37 the networks obtained for those highly symmetric units were fully periodic with regular hexagonal pores of uniform size. The spontaneous formation of chiral porous networks by tripod-shaped molecules is a phenomenon which has been observed in numerous experimental systems comprising for example the molecules of DBAs,13,21,22 stilbenoid compounds14,15 and carboxylic acids.38 In that sense, the structures presented in Figure 9f are similar in terms of connectivity (three bonds per molecule) and chirality (unique rotation of

type f(R) revealed the formation of the aperiodic homochiral networks which are shown in Figure 9.

Figure 9. (Top) Snapshots of the adsorbed overlayers comprising 1200 molecules of 1f (R) and 1000 molecules of 2f (R) simulated at T = 0.04. The insets are the magnified fragments of the simulated molecular assemblies. The black and blue circles denote regular hexagonal pores whose rims are formed by molecular arms of the same and different length, respectively. (Bottom) Fragments of analogous aperiodic networks created by the C3-symmetric molecule of type g.30 The meaning of the colored circles used therein is the same as for f.

In this case, for both molecular backbones 1 and 2 we can observe the extended openwork domains in which the nanovoids have rims comprising six molecules (12 molecular arms) with unique rotation direction. As the molecular units 1f and 2f are equipped with arms of unequal length there are several ways in which these arms can be engaged in the pore formation. For example, for 1f the small hexagonal pores are created when all of the contributing arms have the same (shorter) length (black circles). On the other hand, such regular but larger hexagonal pores can be also obtained when all of the six contributing molecules 1f provide two unequally long arms (blue circles). The opposite situation refers to the tecton 2f, for which the bigger and smaller regular hexagonal pores correspond to molecular arms of the same (longer) and different length, respectively. The remaining arrangements of the molecules in the pore rims are responsible for the irregular shape of the pores occurring in both overlayers from Figure 9. The aperiodic networks depicted there are very similar in terms of connectivity and lack of long-distance order. As we demonstrated previously, this effect originates mainly from the reduced symmetry of the backbone of the molecules 1 and

Figure 10. Effect of temperature on the average number of intermolecular bonds per molecule (left) and on the amount fraction of molecules with n = 0...3 bonds (right, n shown in the circles) calculated for the adsorbed systems comprising 1200 molecules of 1 and 1000 molecules of 2 (f, g; R). K


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Figure 11. Snapshots of the racemic overlayers comprising 1200 molecules of 1f and 1000 molecules of 2f simulated at T = 0.04. The enantiomers R and S are shown in gray and red, respectively. The inset in the left panel shows a magnified fragment of the disordered domain formed by the first tecton.

temperature is sufficiently low. The main reason for this effect is the dense mixed packing of R and S in which an enantiomer of one handedness can be fully surrounded by enantiomers of the opposite handedness (see the inset). The chiral resolution demonstrated for 2f is a manifestation of the incompatibility of the enantiomers (red and gray) to create mixed structure in which they reach energetically beneficial configurations, so that the separate homochiral domains are formed instead. For example, a similar effect has been observed for the homochiral domains created by the chiral DBA derivatives self-assembled at the graphite (HOPG)/ organic solvent interface.40 On the other hand, mixing of surface enantiomers of tripod shaped building blocks has been observed for such molecule as the chlorinated C3-symmetric triazatrinaphthylene derivative adsorbed on HOPG from tetradecane liquid phase, producing networks with hexagonal cavities.41 As in our case, the tecton 1f has a reduced symmetry and elongated shape which enables dense packing of the opposite enantiomers (see the inset) the porous network is not formed. Moreover, the diversity of the allowed interarm connections (long−long, short−short, long−short) which are characterized by the same interaction energy results in the disordered racemic assembly shown in Figure 11. In general, an increased number of equivalent interarm interactions is a factor which can introduce substantial disorder to adsorbed molecular assemblies, as it has been observed for example for the mixture of DBA and bis-DBA molecules.42 The results of this section show that molecular shape is an important factor which can strongly affect the level of organization of molecules whose interaction directions display certain symmetry type. This is particularly visible for the achiral tectons of type e which can form either complex porous networks (1) or ribbons (2), depending on the backbone shape. A similarly profound effect refers to the chiral molecules of type f which, when adsorbed as racemates, self-assembly into disordered mixed domains (1) or undergo chiral resolution (2) forming porous enantiopure aperiodic networks. In the case of the remaining adsorbed systems discussed in this part the influence of the backbone was found to be much weaker. Here, the aspect ratio of the tripod backbone was found not to affect the overall morphology of the simulated superstructures: ladders and strings for 1d and 2d and irregular networks for 1f (R) and 2f (R). For these superstructures the decisive role plays the directionality of interactions which is responsible for the occurrence of identical stabilizing molecular motifs in the corresponding assemblies. The backbone shape affects only

pore rims). However, their distinctive feature is the aperiodic structure in which pores of different hexagonal shapes can be found, contrary to the periodic networks formed by the aforementioned real molecules. In the case of the achiral asymmetric DBA molecules whose backbone shape is close to 1f, the ordered porous patterns emerge due to the asymmetry of interactions provided by the molecular arms of different lengths.13 Specifically, the interdigitation of the alkyl chain arms of DBA occurs according to the scheme: short−short and long−long and no mixed short−long connections are formed due to unfavorable energetic effect. In our case, the energy of intermolecular interactions (→ ← ) is not dependent on the arm length, so that diverse interarm connections are possible producing pores with the different shapes. This general observation is important for designing porous networks with controlled morphology, that is aperiodic vs periodic, and it means that interaction centers of the same type should be builtin the tripod units to obtain the glassy structures show in Figure 9. Such interaction centers can be for example halogen atoms of the same kind, which would allow for the construction of the corresponding metal organic/covalent networks. 3.2.3. Racemic Overlayers Comprising Tectons of Type f. Because the tectons of type f are chiral in 2D, like for a−c, we performed also the simulations for the corresponding racemic mixtures comprising 600 R + 600 S molecules of 1 and 500 R + 500 S molecules of 2. Figure 11 presents exemplary snapshots obtained for these two adsorbed systems. The simulated racemic assemblies shown in the figure demonstrate clearly completely different molecular organizations of 1f and 2f.39 For the first molecule we can observe the formation of a disordered mixed domain while for the latter molecule chiral resolution takes place, producing separated homochiral networks. These networks are irregular with morphology that is identical with the one found for the corresponding enantiopure systems (see Figure 9). The different kinds of ordering observed for 1f and 2f are reflected in the shape of the temperature dependencies characterizing the extent of chiral resolution shown in Figure 6f. Specifically, for the latter molecule the average number of directional R-S bonds and the average number of R−S contacts both drop below 0.5 at low temperatures, indicating the effective separation of the enantiomers and the formation of openwork structures. On the other hand, for the first molecule the average number of R−S bonds is then equal to about 2.3 which means the enhanced R−S mixing that can be seen in Figure 11. Moreover, contrary to the remaining chiral molecules, the average number of contacts calculated for 1f reaches exceptionally high value ∼5 per molecule when the L



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secondary features these constructs, for example, the size of nanocavities occurring in them.

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AUTHOR INFORMATION

Corresponding Author

*(P.S.) Telephone: +48 081 537 56 20. Fax: +48 081 537 56 85. E-mail: [email protected].

4. CONCLUSIONS

ORCID

The results of our theoretical studies show that the tripod molecular building blocks with reduced backbone symmetry exhibit rich self-assembly behavior depending on the directionality of intermolecular interactions they can form when adsorbed on solid substrates. The simulations carried out for the molecules which are chiral in 2D and which characterized by the lowest symmetry of the interaction directions (a−c, R) revealed the formation of superstructures with ladder (a,c) and chain architectures (b). For these tectons the shape of the tripod backbone (1,2) was found to influence only secondary geometric features of the assemblies, such as the ladder width or pore size, so that the overall morphology of the corresponding constructs was the same for 1 and 2. A similar conclusion refers to the units of type f (R) which are also chiral in 2D but have higher symmetry compared to a−c. These molecules, both 1 and 2, create aperiodic porous networks comprising analogous structural binding motifs and nanocavities of similar shapes. On the other hand, when the other enantiomer (S) of these chiral units is present in the adsorbed overlayer the effect of molecular shape becomes visible, especially for the molecules of type b and f. Here the racemic self-assembly of the first unit produces mixed structures with entirely different morphologies (triangular aggregates for 1 and chains for 2) while for the latter unit random mixing (1) or chiral resolution takes place (2). In the case of the achiral tectons of type d and e, the simulations demonstrated that the backbone shape has a profound effect on the assemblies created only by molecules of the latter type. The superstructures formed by 1e and 2e were the complex networks with large pores and the ribbons, respectively. Such superstructures are exceptional in terms of hierarchic level of organization and they were not observed for any the remaining tectons studied herein. The achiral molecules of the other type d, even though also symmetric, were instead found to create disordered ladder and chain structures, similar to those observed for the chiral units a−c (R). The theoretical predictions presented in this work provide preliminary information on how to design molecular tripod building blocks such as functional organic (e.g., polyaromatic) molecules to create adsorbed superstructures with predefined morphology. This refers to the backbone shape as well as to the distribution of the interaction centers in the molecule. In particular, the obtained results can facilitate the choice of chemical modification of the parent tripod molecule to produce functional units able to form desired adsorbed motifs. As test synthesis of a family of candidate molecular building blocks differing by the features mentioned above can be tedious or expensive, the proposed approach can help in directing the synthesis and screening molecular libraries to select the optimal tecton. Moreover, the set of general hints we give in this work can be also used for tailoring of covalently bonded adsorbed nanostructures, synthesized for example via the Ullmann coupling. In this case, our model can be used to identify the molecule-superstructure relation which refers to the metal− organic precursors of the Ullman reaction which are stabilized by reversible bonds.

Paweł Szabelski: 0000-0002-3543-9430 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Polish National Science Centre, Research Grant 2015/17/B/ST4/03616. REFERENCES

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Structure Formation in 2D Assemblies Comprising Functional Tripod

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