Directing the Self-Assembly of Tripod Molecules on Solid Surfaces: A

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Directing the Self-Assembly of Tripod Molecules on Solid Surfaces: A Monte Carlo Simulation Approach Pawel Szabelski, Wojciech R#ysko, and Damian Nieckarz J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b03842 • Publication Date (Web): 01 Jun 2016 Downloaded from http://pubs.acs.org on June 2, 2016

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The Journal of Physical Chemistry

Directing the Self-assembly of Tripod Molecules on Solid surfaces: A Monte Carlo Simulation Approach Paweł Szabelski*1, Wojciech Rżysko2 and Damian Nieckarz3 1

Department of Theoretical Chemistry and 2Department for the Modeling of PhysicoChemical Processes, Maria-Curie Skłodowska University, Pl. M.C. Skłodowskiej 3, 20-031 Lublin, Poland 3 Supramolecular Chemistry Laboratory, University of Warsaw, Biological and Chemical Research Centre, Ul. Żwirki i Wigury 101, 02-089 Warsaw, Poland

Abstract

Directing the self-assembly of organic molecules towards low-dimensional superstructures has been an attractive method of fabrication of functional materials with programmable architecture. In this contribution, using theoretical modeling, we demonstrate how fine tuning of directional intermolecular interactions which are encoded in a simple organic building block allows for the creation of surface-confined assemblies with largely diversified morphology. To that end the self-assembly of a model tripod-shaped molecule adsorbed on a triangular lattice was simulated using the canonical ensemble Monte Carlo method. The simulations were performed for flat, rigid building blocks built of four discrete segments (core plus three arm segments) and equipped with adjustable peripheral interaction centers providing directional intermolecular bonds. The simulated results revealed that changes in the directionality of interactions imposed on the centers are responsible for the emergence of different molecular structures including ordered porous networks, chain and ladder structures and chiral patterns. The obtained assemblies were analyzed and classified with respect to their structural and energetic properties. Our theoretical investigations showed that small changes in the position of the outer interaction centers in a tripod functional molecule can have dramatic effect on the morphology of the resulting 2D structures. On the other hand, these findings can be helpful in predicting the self-assembly of organic tripod molecules with the different interaction patterns discussed in this study. This information, can be relevant, for example, to synthetic chemists seeking for an optimal building block able to self-assembly into a 2D superstructure with predefined properties.

*Corresponding author Phone: +48 081 537 56 20 Fax: +48 081 537 56 85 E-mail: [email protected]

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Introduction

Controlled self-assembly of molecular structures has been recently an intensively studied topic in the field of supramolecular chemistry. The great interest in the fabrication of supramolecular assemblies according to the bottom-up strategy comes mainly from the large possibilities of steering the assembly processes towards desired molecular architectures. For example, morphology of the resulting superstructures can be finely tuned by a suitable choice of an input molecular building block and external conditions1 as well as of additional stimuli such as light, electric or magnetic fields2-4. An important requirement to be fulfilled in order to construct extended defect-free structures has been the selective intermolecular recognition leading to the formation of correct supramolecular connections. This elementary recognition, provided by molecular interaction centers, can be less efficient when the molecules have a large number of degrees of

freedom, like it occurs in bulk phase. On the other hand,

reduction of dimensionality of space available to interacting molecules can substantially facilitate the error-free propagation of molecular constructs. An effective method to achieve this has been the surface-confined molecular self-assembly in which organic building blocks adsorbed on solid supports spontaneously and easily form diversified patterns.5,6 To build 2D ordered supramolecular structures different intermolecular interactions have been used to date, including hydrogen bonding,7-10 metal-organic ligand coordination1013

or even van der Waals interactions.14-16 Among simple organic molecular building blocks

suitable for that purpose both linear and ramified units equipped with appropriately distributed interaction centers have been most prevalent. A special class of such molecules are the

tripod-shaped

units

including

for

example,

polyaromatic

carboxylic

acids,

dehydrobenzoannulenes (DBAs),14,15 stilbenoid compounds,17,18 tripods bearing pyridyl groups7,10 and others19 which can self-assemble into regular 2D porous networks when


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adsorbed on graphite or metallic substrates in ultra high vacuum conditions and from liquid phase. Such regular networks are of special importance to nanotechnology and material science as they can serve as functional matrices in which guest molecules can be immobilized in a spatially ordered arrangement. These novel 2D materials are of application potential in molecular sensing, adsorption, catalysis, light harvesting and they have been the subject of intense experimental and theoretical studies during recent years.10,15,19 An important feature of 2D porous networks is their spatial regularity and this parameter is largely dependent on the way in which the interaction centers are distributed within the building block. So far, the construction of 2D porous networks has involved mainly highly symmetric molecules such as C3 -symmetric tripods which usually self-assemble into open networks with hexagonal void spaces.14,19,20 There have been also attempts to use molecular bricks with reduced symmetry, such as

DBAs14 or asymmetric analogues of

trimesic acid.21 In these cases one arm of the tripod was elongated, however its functionality (e.g. terminal arm groups) was unchanged. Very recently El Garah et. al reported a systematic study on the effect of the meta position of nitrogen atom in the outer phenyl rings of 1,3,5tris(pyridine-3-ylethynyl)benzene (TPB) on the surface confined self-assembly of this molecule.22 As a results of the rotation of pyridyl groups along the alkynyl spacers different regioisomers of TPB have been identified, responsible for the formation of diversified porous and compact adsorbed patterns. These findings have demonstrated that different positions of interaction centers within arms of a tripod building block can lead to largely diversified 2D structures. Understanding of the individual role of each of these conformers in the pattern formation is thus indispensable for custom designing 2D molecular architectures. This task is especially hard when the surface conformers can coexist in the adsorbed phase (for example due to rotability of molecular fragments bearing the functional groups) and create mixed patterns.



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To decipher the individual role of molecular building blocks equipped with differently distributed interaction centers in the self-assembly on solid surfaces it is useful to employ computer simulations.7,10,15,22-26 This approach allows for selective observation of the 2D structures formed by just one type of molecular conformer without interference of the remaining ones. Such information can be especially important when a molecule with fixed position of interaction centers (no ratability is allowed) is to be synthesized to create an adsorbed superstructure with predefined morphology. As we demonstrated in our previous studies on metal-organic adsorbed systems, the proposed theoretical methodology revealed to be highly effective and resulted in the information on the possibility of creation of new molecular structures using tectons with suitably encoded interactions.23 In this contribution we extend our studies and consider a simple tripod molecule that is equipped with arm centers providing different intermolecular interaction directions. To that end we perform Monte Carlo simulations of the 2D self-assembly of a few functional variants of the tripod molecule and identify basic structural differences between the obtained assemblies. The main purpose of this study is to formulate a general set of molecule-superstructure rules which would be applicable to a wide class of molecular tripods having interaction centers with similar properties. These rules can be useful to synthetic chemists, as they can substantially shorten screening of molecular libraries to select the optimal building block able to self-assembly into a superstructure with presumed properties.

The model and computation

To explore the effect of intramolecular distribution of interaction centers on the surface-confined self-assembly of tripod molecules we used the same coarse-grained model as in our previous studies.7,10,15 In the adopted approach the basic molecular building block


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consisted of four interconnected segments arranged in a tripod with a core and three arms of equal length (one segment each). One molecular segment was allowed to occupy one adsorption site on a triangular lattice representing a (111) crystalline surface. Figure 1 shows mapping of the structure of the tripod molecules used in this study on a triangular lattice.

Figure 1. Schematic structure of the model molecules A-F adsorbed on a triangular lattice and used in the simulations. The red arrows indicate different interaction directions assumed for each building block. In the case of the prochiral molecules B, D, E and F only one surface enantiomer (R) is shown for clarity.

The molecules from Fig. 1 were assumed to bear functional arm groups enabling directional intermolecular interactions (e.g. hydrogen bonds) in the adsorbed phase. To that end, the arm segments were assigned unique interaction directions which are represented by the red arrows in the figure. Interaction between a pair of molecules was possible only when their arm segments occupied neighboring adsorption sites and the corresponding interaction directions were collinear. In this case, the energy of interaction between the neighboring segments was equal to ε = −1. All remaining intermolecular interactions, including core-arm interactions and arm-arm interactions in configurations other than those enabling the collinear alignment of the interaction directions were neglected. Similarly, we assumed that the adsorbing surface



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is energetically homogeneous and for simplicity set zero energy for the molecule-substrate interaction. Note that among the molecules from Fig. 1 only the units A and C are achiral. The remaining building blocks can exist in two mirror-image configurations when adsorbed, one of which is shown for each molecule. These molecules are further called prochiral and due to this special property they can form mixtures comprising both surface enantiomers. In the following we consider also such mixtures with particular focus on the racemic assemblies. The prochiral molecules shown in Fig. 1 were arbitrarily called R-enantiomers while their mirror-image counterparts S-enantiomers. To simulate structure formation in the overlayers comprising molecules A-F we used the Monte Carlo simulation method in the canonical ensemble (CMC)7,10,15,29. The calculations were performed on a L × L rhombic fragment of the triangular lattice for which periodic boundary conditions in both planar directions were imposed. According to the CMC approach the number of molecules, N, system size, L and temperature, T were fixed. The simulations started with the surface covered by N randomly distributed molecules A-F. The corresponding adsorbate density was defined as ρ = 4 N / L2 and expressed in segments per lattice site units. In the case of racemic mixtures of the prochiral tectons B, D, E and F from Fig. 1 the adsorbed overlayer contained the R-enantiomer at a fraction 0.5. To equilibrate the system a series of elementary MC steps were performed, each step being an attempt to translate/rotate a randomly selected molecule to a new position on the lattice. To that end we used the conventional Metropolis sampling29 for which the acceptance probability is equal to

p = min[1, exp(−∆U / kT )]

(1)


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where ∆U = U n −U o and U o and U n are the potential energies of the molecule in the actual and new configuration and these energies are calculated as

3

Ui = ε ∑ s j

i = n, o

(2)

j =1

where the summation runs over the three arm segments of A-F. The molecule-dependent variable s j reflects the different interaction directions assumed for these building blocks. It is equal to 1 when a neighboring adsorption site - determined by the assigned interaction direction (see the red arrows in Fig. 1) - is occupied by a foreign arm segment and furthermore the interaction direction of the neighboring molecular segment is collinear with that of the selected segment. In the remaining cases s j is equal to zero. To accept or reject the new configuration the calculated acceptance probability, p was compared with a randomly generated number r ∈(0,1) . If r < p the new configuration was accepted; otherwise the trial ended and the whole procedure was repeated. During the simulation run the above sequence was performed typically N ×108 times. To minimize the risk of trapping the simulated systems in metastable states we used a cooling mode in which the adsorbed overlayer was linearly cooled down from T =1.04 to T = 0.04 within 103 decrements of equal length. The energies in our model are expressed in ε units and temperatures are given in ε / k units. The results discussed in the following sections are averages over five independent system replicas.



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Results and discussion

Structure formation in one-component systems

To highlight differences in the 2D self-assembly of the building blocks from Fig. 1 let us first analyze the corresponding snapshots obtained from the simulations. These data were calculated for L = 200 , for two arbitrarily chosen numbers of the adsorbed molecules, that is for N = 2000 and N = 4000 . The associated density of the adsorbed phase, ρ was equal to 0.2 and 0.4, respectively. Figure 2 presents the results obtained for the simplest C3-symmetric tecton

A

resembling such

molecules as trimesic acid9 or

1,3,5-tris(pyridine-4-

ylethynyl)benzene.7,10

Figure 2. Snapshots of the adsorbed overlayers comprising 2000 (a) and 4000 (b) molecules A. The insets show magnified fragments of the simulated structures. The red lines delimit the unit cells characterizing the obtained ordered patterns.

As it can be easily anticipated, at the lower density (0.2, a) the molecules of A form an extended porous network with hexagonal void spaces. The simulated structure is characterized by a rhombic (3 3 ×3 3) unit cell and it has density equal to 0.342 . The geometry of the network from Fig. 1 agrees very well with that observed in numerous experimental systems comprising such molecules as trimesic acid and its bigger analogues.9,30


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When the density of the adsorbed phase increases a more complex picture of the system emerges. In this case (b) we can observe zones of tightly packed molecules forming the lamellar pattern shown in the bottom inset. This pattern is characterized by a rectangular (2× 3 3) unit cell and it is more than two times denser than the porous pattern, with

ρ = 0.770 . Creation of such a dense pattern has been observed experimentally for 1,3,5-tris(4carboxyphenyl)benzene adsorbed at the organic solvent/graphite interface.9,31 Another local motif which can be frequently encountered in the snapshot from Fig. 2b is a molecule of A entrapped in the hexagonal pore. The structures shown in Fig. 1 were obtained for a particular set of parameters ( ρ ,T ) and they are shown mainly to illustrate the effect of directionality of intermolecular interactions on the structure formation. In fact the emergence of the patterns (porous, dense, entrapped) and their coexistence is strongly dependent on both temperature and density of the adsorbed phase. This has been demonstrated experimentally30,31 and studied theoretically in detail by Tornau and coworkers24-26 who obtained the same type of motifs as these shown in Fig. 1. For the purpose of this study we limit our discussion to the particular set of parameters assumed previously. The molecule B is a modified version of A in which only one interaction direction is not collinear with the associated arm, being rotated clockwise by 60 degrees. This small change, however, exerts a significant effect on the self-assembly, as it prevents the formation of a porous network. As it is seen in Fig. 3, long ladder-type structures are created instead.



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Figure 3. Snapshots of the adsorbed overlayers comprising 2000 (a) and 4000 (b) molecules B. The insets show magnified fragments of the simulated structures. The red line in panel (b) delimits the parallelogram unit cell characterizing the ordered pattern obtained at the higher surface coverage. The ladders consist of two molecular rows zipped with molecular arms having the interaction directions collinear with these arms (see the inset in Fig. 3a). The void spaces in the ladders are parallelogram in shape and they cover six lattice sites being able to, for example, accommodate quite big guest species. At the lower surface coverage (a) the ladders are able to grow in the three directions imposed by the symmetry of the lattice. With increasing density of the adsorbed phase the orientational freedom of the ladders vanishes and they are aligned parallel to each other. This results in the creation of porous stripes comprising tightly attached ladders and characterized by a longer range of ordering. An example of a periodic porous pattern obtained in this way is shown in the inset to Fig. 3b. This pattern is characterized by a rectangular ( 7 × 21) unit cell and density ρ = 0.660 . In the case of molecule C we are dealing with the structure in which two interaction directions were rotated with respect to the corresponding molecular arms (clockwise and anticlockwise). In consequence all of the interaction directions are now aligned parallel. Even though this uniform alignment of interaction directions might seem helpful in the formation of highly ordered structures the results of the simulations demonstrate something different. Conversely, for molecule C we can observe the formation of irregular chain and ladder structures shown in Fig. 4.


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Figure 4. Snapshots of the adsorbed overlayers comprising 2000 (a) and 4000 (b) molecules C. The insets I and II show magnified fragments of the simulated structures.

The ladder fragments (I) consist of molecules which are joined by the arms with rotated (clockwise) interaction directions. These joints are structurally different from the connections observed previously for molecule B for which the interaction directions were collinear with the engaged arms. The ladders formed by C comprise narrow void spaces covering four lattice sites each. These nanocavities are smaller and wiggly compared to the tecton B. The second structural motif (II) in the overlayer from Fig. 4 are the straight chains in which extremely small one-site sized void spaces can be indicated. At low surface coverage both structural motifs I and II are interconnected producing winded strings with irregular (aperiodic) internal geometry. Like for the molecule B, under these conditions the strings grow along the three main directions of the lattice. However, contrary to B we can observe also the formation of patches of a network (see the right upper corner in Fig. 4a). This irregular structure is more visible at higher surface coverages (b) at which the strings are aligned horizontally and often connected. The simulated snapshots demonstrate clearly that the achiral molecule C is able to create more diversified intermolecular connections leading to the formation of distorted structures with short range order. In this view, the use of this tecton to obtain regular and reproducible 2D assemblies seems strongly limited.



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The next molecule D differs from A in the two interaction directions which are both rotated clockwise by 60 degrees. For this tecton, like in the case of B we can observe the formation of ladder structures of one type which are shown in Fig. 5.

Figure 5. Snapshots of the adsorbed overlayers comprising 2000 (a) and 4000 (b) molecules D. The insets show magnified fragments of the simulated structures. The red line in panel (b) delimits the parallelogram unit cell characterizing the ordered pattern obtained at the higher surface coverage. The ladders made of D comprise molecular rows which are zipped in a way observed previously for the motif I formed by molecules of C. However, because of the different arrangement of the interaction directions which do not contribute to the zipping the resulting void spaces are bigger and more round compared to C. In this case the nanopores cover five lattice sites each. At the increased surface coverage (0.4, b) the ladders tend to orient unidirectionally and create stripes of periodic porous network. An example of this network is shown in the magnified fragment in panel (b). The obtained structure is characterized by a parallelogram ( 7 × 19 ) unit cell with density ρ = 0.711 . The molecule E is structurally similar to A in the sense that it is also C3 -symmetric. However, E is a prochiral molecule in which all of the interaction directions were rotated clockwise by 60 degrees with respect to the corresponding arms. Figure 5 shows exemplary snapshots obtained for this tecton.


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Figure 6. Snapshots of the adsorbed overlayers comprising 2000 (a) and 4000 (b) molecules E. The insets show magnified fragments of the simulated structures. The red line in panel (a) delimits the rhombic unit cell characterizing the obtained porous pattern.

As it is seen in Fig. 6a, at the lower surface coverage the molecules of E self-assemble into an extended defect-free porous network with hexagonal void spaces. The simulated network is chiral and it is characterized by a rhombic ( 21× 21 ) unit cell and density 0.440 that is

somewhat higher compared to A (0.342). At the higher surface coverage (0.4) we can observe the formation of domain walls whose magnified fragment is shown in the bottom inset to panel (b). Moreover, numerous molecules entrapped in the hexagonal pores can be also found, as demonstrated in the upper inset. Creation of the network shown in Fig.6 has been observed experimentally for such molecules as 1,3,5-tris[40-carboxy(1,10-biphenyl-4-yl)]benzoic acid (CTBPB) adsorbed on graphite from organic liquid phase.32 The last molecule F from our set is structurally similar to C and it differs from C only in the orientation of the upper interaction direction (compare Fig.5 and Fig.7). The selfassembly of the tecton F results in the formation of numerous linear chains with the smallest one site-sized void spaces, as illustrated in Fig. 7.



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Figure 7. Snapshots of the adsorbed overlayers comprising 2000 (a) and 4000 (b) molecules F. The insets show magnified fragments of the simulated structures. The red lines in panel (b) connect void spaces of the molecular chains.

The chains are randomly distributed on the surface and they grow along the three main directions of the lattice. Unlike for the chain- and ladder-forming molecules B, C and D, at the higher surface coverage (0.4) there is still enough room for the chains of F to grow in the three directions. This occurs due to a very high packing density of the parallel molecular chains which are attached to each other and form compact patches. In these bigger structures however the chains are randomly shifted with respect to each other so that no long range ordering can be indicated. The bottom inset to Fig. 5b illustrates this effect. The red lines therein connect nanopores (one site) of the parallel chains which, however, do not form a periodic superstructure. In this context, the use of molecule F for the self-assembly of molecular constructs with well-defined geometry is limited to relatively low surface coverages at which mostly isolated straight chains are formed. To summarize our structural analysis of the assemblies formed by the tectons A-F let us indicate basic similarities and differences between them. In general, there are three types of self-assembled structures which can be created by the considered molecules. These are the porous networks, ladders and chains. The porous networks can be obtained most easily using molecules A and E at the low surface coverage but also (with lower regularity) at the higher surface coverage. Such networks are also obtainable for molecules B and D at higher


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asdorbate densities but the range of ordering in these networks can be smaller compared to the C3 -symmetric molecules A and F. The main reason for this effect lies in the ladder-based

structure of these networks. In this case, the composite ladders are only attached and not linked by the directional intermolecular interactions, so that they can be shifted with respect to each other. In consequence, long-range periodicity does not have to be preserved in such networks. On the other hand, molecules B and D are those for which the formation of ladders is the most effective at low surface coverages. In this case, regular isolated structures with well defined void spaces can be obtained in a reproducible manner. For the molecules C and

F we can observe quite efficient formation of straight molecular chains. However, for the first molecule this process is additionally accompanied by the creation of ladder structures and leads to distorted patterns (strings and networks) in which the ladders and chains of C are intermixed. For that reason the molecule F seems to be a much better candidate for the construction of molecular chains as compared to C which self-assembles into structures with the largest degree of disorder among the considered tectons. Taking into account the above discussion the molecules and the resulting superstructures can be linked in the following way:

A, E – porous networks, B, D – ladders and C, F – chains. The similarity between the superstructures obtained for the pairs of molecules mentioned above can be also observed in certain quantitative dependencies calculated for the corresponding 2D systems. Figure 8 presents the effect of temperature on the average number of bonds (0-3) which a single molecule of A-F can form with its adsorbed neighbors. The simulated dependencies provide important information on the self-assembly scenario, as they describe changes in connectivity of the molecular constructs with decreasing temperature. One general observation from Fig. 8 is that at sufficiently low temperatures ( T = 0.1 ) molecules of all types are fully coordinated, having all three interactions engaged in the structure formation.



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Figure 8. Average number of bonds per molecule as a function temperature calculated for the adsorbed systems comprising 2000 (left) and 4000 (right) tectons A-F.

This refers to both low and high surface coverage with one exception being molecule A at N = 4000 . In this particular case the excess molecules which are not involved in the formation

of the porous network are either located in the patches of the densely packed lamellar pattern shown in Fig.2b or they are occluded in the hexagonal pores of the network. In the first situation the molecules of A form only two bonds with neighboring molecules while for the latter one they are noninteracting with zero contribution. As a consequence the obtained average number of bonds per molecule is much lower compared to the perfect hexagonal network shown in Fig. 2a. A similar, although less profound effect can be observed for the structurally similar molecule E at N = 4000 . An important effect which is clearly seen in Fig. 8 is that the following pairs of curves: A-E, B-D and C-F coincide (for the last pair some differences are observed only at low temperatures) which confirms the results of our visual inspection of the simulated snapshots. The curves plotted in Fig. 8 are, however, characterized by different slopes among which that one corresponding to A and E is the largest at the lower temperatures ( 0.2 < T < 0.4 ). For the pair B-D the slope is only slightly smaller than for A and

E and for C-F this less increasing trend is much more pronounced. The observed effects are visible manifestation of the structural changes occurring in the adsorbed overlayer and they


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inform how rapid are these changes when the temperature decreases. To get better insight into the temperature-induced transformation of the modeled adsorbed assemblies in Fig. 9 we presented the influence of T on the amount fraction of molecules having from 0 to 3 bonds ( N = 2000 ). To that purpose we selected only molecules A, B and C as their corresponding pair members give very similar dependencies.

Figure 9. Fraction of molecules having from 0 to 3 bonds as a function temperature calculated for the adsorbed systems comprising 2000 tectons A-C.



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As it follows from Fig. 9, the most rapid changes occur for the system comprising A for which the number of molecules with one and two bonds drops sharply at T equal to about 0.32. The sharp transition observed for this tecton originates mainly from the uniform structure of the emerging hexagonal network which can grow freely in any of the six lattice directions on the triangular lattice. In consequence the nucleation and domain growth is very efficient leading to fast consumption of undercoordinated molecules. At high temperatures, apart from being uncoordinated, the molecules of A create mainly bimolecular clusters (red line) in which each of them engages one arm ( n =1 ). As the temperature decreases, the number of the clusters increases but next they are quickly incorporated in to the growing domain due to the Ostwald ripening. For the molecule B the changes in the population of molecules with one bond are similar to what was observed for A, however they are less rapid at sufficiently low temperatures. For this tecton the contribution from the molecules with two bonds (blue line) is much higher compared to A. The main reason for this is the formation of dispersed four-membered aggregates being elementary structural units of the ladders shown in Fig. 3. In such cage-like clusters each molecule of B form two bonds with its neighbors. With decreasing temperature the ladders start to grow so that the molecules in the interior of the ladders can have three neighbors being fully coordinated. A noticeable difference between the results obtained for A and B and for C is that for the last molecule there is a large effect associated with the presence of molecules with two bonds (blue line). This effect comes form the exceptional parallel orientation of the interaction directions assigned to the molecule C. Specifically, this structural unit (and also F) can form bimolecular clusters in which two arms of each contributing molecule are engaged ( n = 2 ). This can be seen in the magnified chain II shown in the inset to Fig. 4. The temperature dependencies shown in Figs. 8 and 9 indicate that the most rapid changes in the structure of the adsorbed overlayer can be encountered in the case of the C3-


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symmetric molecules A and F. Here, the propagation of the growing superstructure is the fastest as the molecules can be easily incorporated at the perimeter of the largest domain adsorbed on the surface. With incising size of the domain its perimeter also grows, so that capture of new molecules becomes more efficient. For the remaining tectons, the development of the ladders and chains is less effective as the adsorbed molecules can be attached to these structures only at the ends, regardless of the structure size (length). In consequence structural changes at sufficiently low temperatures are less intense compared to A and F.

Racemic assemblies

As previously pointed out, four molecules (B-F) out of these shown in Fig. 1 are prochiral and they can adopt mirror-image configurations R and S when adsorbed. This property makes it interesting to examine structure formation in the corresponding assemblies comprising both enantiomers. In the following we consider the most probable situation from the experimental point of view in which the enantiomers are equally populated. Figure 10 presents the results obtained for the racemic mixtures composed of 1000 R (gray) and 1000 S (red) enantiomers of B-F adsorbed on the 200 by 200 triangular lattice. As it follows from the figure there is a clear difference between the morphologies of the assemblies formed by B and D and by the two remaining molecules. In the case of B and

D we can observe demixing leading to the creation of homochiral ladders with diversified length. Note that the ladders formed in the racemates of B and D are identical with their homochiral counterparts. Apart form these ladders, also irregular structures cemented by the trimolecular nodes (II) can be found in the adsorbed phase. In this context, the similarity between the molecules B and D which was observed in one-component systems (compare Fig. 3 and 5) is also visible in the corresponding racemates.



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Figure 10. Snapshots of the adsorbed overlayers comprising 1000 R (gray) and 1000 S (red) enantiomers of B-F adsorbed on the 200 by 200 triangular lattice. The insets I and II show magnified fragments of the simulated structures.

On the contrary, the structures obtained for the racemic mixtures of E and F differ markedly from the corresponding structures simulated for the one-component system. Here, the enantiomers of E form a mixed 2D crystal instead of separating into two porous networks of opposite rotation directions. The main reason for this effect is the substantially lower energy of a single molecule of E belonging to the racemic crystal as compared to the homochiral porous network. Specifically, a molecule of E can establish maximally three bonds when in the porous network while it can have six bonds in the racemic crystal. This new 2D crystal (I) is characterized by the stoichiometric 1:1 (R:S) ratio and by a rhombic ( 2 3 × 2 3 ) unit cell with density equal to 0.77. Regarding the molecule F we are dealing with the most peculiar phase behavior among the considered racemates. In this case, we can observe the creation of numerous isolated clusters comprising six molecules each. The composition of the clusters (3R+3S)


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agrees with the overall racemic ratio of the adsorbed phase. The enhanced tendency to form small clusters of rac-F has again energetic reasons. Formation of homochiral chains such as those shown in Fig. 7 would result in the maximal number of bonds per molecule equal to 3. This number can be increased when the molecules self-assemble into the six-membered aggregates in which they can form 4 bonds each. As the maximal coordination number of a molecule F in these two structures (chains and clusters) differs only by one sparse chains with mixed composition coexist also on the surface. To describe pattern formation in the racemic overlayers in a quantitative way we calculated the effect of temperature on the mean coordination number of a molecule B, D-F.

Figure 11. Average number of bonds per molecule (top) and average number of R-S bonds, h as functions of temperature calculated for the adsorbed systems comprising 2000 tectons B, D, E and F.



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Additionally, to characterize the extent of chiral segregation in these systems we determined the average numbers of heterogeneous R-S bonds per molecule, h and plotted them as functions of T. The parameter h is equal to the number of lines which can be drawn between a selected molecule (R or S) and adjacent foreign segments (S or R). Lower values of h correspond to more efficiently separated enantiomers while higher values of h mean enhanced mixing. Figure 11 presents the dependencies discussed above. As it is seen in the top part of the figure, the curves obtained for the racemates are not much different from their counterparts calculated for the one-component systems (see Fig. 8). In the present case we observe again that at low temperatures ( T

Directing the Self-Assembly of Tripod Molecules on Solid Surfaces: A

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