Acta Physico-Chimica Sinica  2017, Vol. 33 Issue (3): 539-547   (5256 KB)
 Article Options PDF (5256 KB) Full Text HTML Abstract Figures References History Received: September 7, 2016 Revised: November 25, 2016 Published on Web: November 25, 2016 Service Email this article to a colleague Add to my bookshell Add to citation manager Email Alert Feedback View Feedback Author ZHANG Zhen XIE Wen-Jun YANG Yi Isaac SUN Geng GAO Yi-Qin
Simulation Studies of the Self-Assembly of Halogen-Bonded Sierpiński Triangle Fractals
ZHANG Zhen1, XIE Wen-Jun1,2, YANG Yi Isaac1, SUN Geng1, GAO Yi-Qin1,2,*
1 Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Beijing National Laboratory of Molecular Sciences, Peking University, Beijing 100871, P. R. China;
2 Biodynamic Optical Center, Peking University, Beijing 100871, P. R. China
Abstract: In this study, a coarse-grained lattice Monte Carlo model was used to investigate the formation of Sierpiński triangle (ST) fractals through self-assembly on a triangular lattice surface. In the simulations, both symmetric and asymmetric molecular building blocks can spontaneously form ST fractal patterns, although the mixture of enantiomers of asymmetric molecule is more difficult to self-organize into ST of a high order owing to the presence of a large variety of competing three-membered nodes. The formation of ST fractals is favored at low surface coverage and is sensitive to temperature. Furthermore, to test whether the assembly pathway and outcome could be controlled by molecular design, we guided the self-assembly process forming ST fractal into the otherwise disfavored self-assembled structures using templates different from the assembling molecules. The templates are designed to act as"catassemblers"that initiate the self-assembling but are excluded from the final assembled structure.
Key words: Self-assembly     Monte carlo simulation     Fractal     Sierpiń     ski triangle     Catassembly

1 Introduction

Molecular self-assembly on 2D surfaces has gained extensive attention for its practical applications in material science and nanotechnology1-4. Myriad functional molecular architectures, including porous networks2, 5, 6, compact periodic patterns7, chiral assemblies7-9 and glassy overlayers10, 11, have been reported to form spontaneously on various surfaces. Within these architectures, fractals like Sierpiński triangle (ST) which exhibit a self-similar pattern at different scales are of special importance in mathematics, engineering and science12. Synthesis of molecular fractals relies mainly on the coordination between metal atoms and organic ligands. Such studies include bis-terpyridine building blocks which can be co-adsorbed with Ru and Fe atoms to form a nanometer-scale Sierpiński hexagon gasket13. Multitopic terpyridine ligands can form hexagon wreath structures of fractal features with Zn (Ⅱ) ions14. Certain organic molecules containing two carbonitrile groups were also found to be coordinated with Ni atoms to form ST fractals of high thermal stability15. Apart from the above coordination mediated molecular fractal formation, Wu et al.16 reported recently the self-assembly of molecular building blocks into defect-free molecular ST fractals through halogen bonds.

Complementary to experiments, computational studies have made important contributions to our understanding of the formation mechanism of molecular fractals. For example, the Monte Carlo (MC) method was successfully used to predict plausible selfassembling STs using simple model systems. Using MC simulation, Niecharz and Szabelski17 proposed that molecular fractals can be formed by coordination bonds. They also found that bent molecular building blocks, equipped with two identical electron donor centers as linkers, can form ST fractal patterns with metal centers18. Recently, the self-assembly of hydrogen-bonded STs was reported19. In their study, symmetric linker molecules were used to create STs.

In this paper, we simulate the formation of ST fractals using both symmetric and asymmetric molecules. The coarse-grained molecular model used in canonical lattice MC is inspired by the molecular design of Wu et al.16. We compare the difference between symmetric and asymmetric molecular building blocks in this spontaneous process, which has not been analyzed from a computational aspect before. We find that the simple coarsegrained model can effectively reproduce the ST fractals observed experimentally for both symmetrical and asymmetrical molecules. The simulations suggest that it is more difficult to form large fractals for the mixture of enantiomers of asymmetric molecules than for symmetric molecules, of which the underlying molecular mechanism is revealed and possible roles of the metal lattice is discussed. The mixed system can form a large variety of nodal motifs. Specifically, the mixture of enantiomers can self-organize into different forms of distorted triangular-shaped structures. The existence of the various nodal motifs reduces the formation probability of the fractal self-assembly with a uniform chirality. In addition, we devised a template to induce the molecular organization of asymmetric building blocks into a pre-designed pattern instead of the spontaneously formed ST fractal pattern. We used such a controlled pattern formation to show the feasibility of catassembly in which the devised template acts as catassembler20, 21.

2 Models and methods

To simulate the self-assembly of molecules into ST fractals, we used a coarse-grained molecular model shown schematically in Fig. 1. The model was inspired by the recent experiments which demonstrated the self-assembly of aromatic bromo compounds including 4, 4″-dibromo-1, 1′:3′, 1″-terphenyl (B3BP) and 4, ${4^{\prime \prime \prime }}$-dibromo-1, 1′:3′, 1″:4″, ${1^{\prime \prime \prime }}$-quaterphenyl (B4BP) into Sierpiński triangles on Ag (111) surface16. The three-fold halogen bonding plays an important role in the formation of the defect-free hierarchical fractal structure. For simplicity, we model the molecular building blocks with rigid planes. A and B shown in Fig. 1 are the models used for molecules B3BP and B4BP, respectively. Due to the asymmetry of B4BP, molecule B forms two enantiomeric surface-bound structures, BL and BR. In the simulated systems, the molecules are confined to a 2D rhombic fragment of a triangular lattice which represents the Ag (111) surface with each vertex serving as an adsorption site, and each phenyl ring of B3BP or B4BP is coarse-grained as one segment occupying one adsorption site.

 Fig. 1 Chemical structures of the B3BP and B4BP molecules Their schematic counterparts are used in the simulation on a triangular grid. The red arrows on the terminal of molecules indicate the direction of C-Br covalent bond. Two mirror-images of molecule B are marked by L and R when adsorbed on the grid. C represents an example of a windmill-like molecule with threemembered arms adsorbed on a triangular lattice. color online

In this simplified approach, the molecules are allowed to interact through triangular halogen bonds. Once the triangular halogen bond is formed, the nucleophile positive region of one Br atom points to the equatorial electrophile region of an adjacent Br atom, with each Br atom acting as both a donor and an acceptor22, 23. It has been reported that this triangular halogen bond plays a key role in many self-assembled molecular networks that involve halogen atoms24, 25. We should note here that different types of angular preferences for halogen-halogen interactions have also been observed26, 27.

Fig. 2 shows the coordination nodal motifs that are allowed in the simulations. The possible nodal motifs of molecules A and B which can be formed in the overlayer have been listed in Figs.S1-S5 (Supporting Information (SI)). The halogen bond interaction between a terminal segment of one molecule with another is characterized by the parameter εa=-1. Moreover, it is important to note that steric hindering effects can strongly impact the formation of fractal patterns. To take into account such an effect, the nearest adsorption sites around one molecule exclude the occupation of any other molecules. When a segment of one molecule lies in the next nearest adsorption site of another molecule, a repulsive interaction εr arises (e.g., εr=0.5 is used in the current model). For simplicity, the interactions between molecules and the lattice substrate are not treated explicitly in this current model.

 Fig. 2 Halogen-bonding motifs comprising 2 or 3 molecules during the simulation (only one terminal segment of a molecule is shown) The dashed blue line was used to separate two types of halogen-bonding motifs. The triangles and pentagons correspond to the nearest and the next nearest adsorption sites, respectively. color online

The MC simulations were performed using the conventional canonical ensemble28, which is characterized by the number of molecules, the volume (substrate area), and the temperature. The substrate is mimicked as a rhombic fragment of a triangular grid of equivalent adsorption sites. We adopted periodic boundary conditions in the plane to eliminate the boundary effect.

The simulation procedure is as follows. In the first step, N molecules are randomly distributed on the grid surface. Next, one of the molecules is randomly selected and its potential interaction energy in an initial configuration (Uold) is calculated. The associated interaction energy includes the attractive halogen bond interaction and the repulsive steric repulsion. OnceUold is calculated, an attempt to move a selected molecule to a randomly chosen new position a cluster of adsorption sites matching the shape of the molecule was chosen randomly. If the selected adsorption sites are unoccupied, the potential energy of this new configuration (Unew) is then calculated. Since the sampling of molecular orientations using standard MC is very inefficient, we make use of the orientational bias sampling28. For the planar molecules considered here, six possible orientations can exist when they adsorb on the surface: when the core of a molecule is pinned to the lattice, there are six different configurations rotating in the plane with a rotation angle of 60 degrees. In the updating scheme, all these six configurations are included in the calculation. To evaluate the acceptance probability, we calculate the Rosenbluth factor w(n) for the new configuration using

 $w(n) = \sum\limits_{j = 1}^6 {{\rm{exp}}} [-{u_{\rm{j}}}/{k_{\rm{B}}}T]$ (1)

where kB is the Boltzmann constant, T is the temperature of the system, and uj denotes the energy of jth trial configurations. Next, we choose one of the six trial configurations, say, x with a probability

 $p(x) = \frac{{{\rm{exp}}[-{u_x}/{k_{\rm{B}}}T]}}{{w(n)}}$ (2)

and for the old configuration, the Rosenbluth factor w (o) is also calculated using Eq.(1). To decide whether the move is successful, the acceptance probability pacc is compared with a random number r ∈ (0, 1)

 ${p_{{\rm{acc}}}} = {\rm{min}}[1, \frac{{w(n)}}{{w\left( {\rm{o}} \right)}}]$ (3)

If r < pacc, the molecule is moved to the new position. Otherwise it remains at its original position. During one MC step the above procedure is repeated N times.

To explore catassembly, we additionally used conventional grand canonical MC (GCMC)28 simulation method on a L × L triangular lattice at a temperature of T. More specifically, the simulation procedure is described as follows. At the first stage of simulation, the substrate is solely occupied by windmill-shaped molecules (Fig. 1C) which comprise a 2D molecular network. The system is then equilibrated by successive of three types of trials including movement, deletion, and creation of molecules on the surface. Once a molecule is randomly selected, an attempt is made to move or to delete. We calculate the energy for a configuration x by

 ${u_x} = \sum\limits_{i = 1}^{4n} {\sum\limits_{j = 1}^6 {{\varepsilon _{\rm{r}}}} } + \sum\limits_{k = 1}^m {\sum\limits_{l = 1}^2 {{\varepsilon _{kl}}} } + {\varepsilon _{{\rm{sub}}}}$ (4)

where n takes a value of 1 or 3, depending the type of molecule, m is 2 or 3, depending on interaction sites of molecule, εr is the repulsive interaction, arises when the next nearest adsorption site of one molecule is occupied by another molecule. εkl is εa, εaw, or εww depending on whether the halogen bond is formed by two BL, a BL and a windmill-like molecule, or two windmill-like molecules, respectively. εsub is the interaction between the molecule and the substrate. To move a molecule, we adopt the same procedure as in the biased MC. To create a molecule, 4n adsorption sites matching the shape of the molecule are randomly chosen. If none of the selected sites are occupied the adsorption of a molecule is attempted with a probability min $[1, \frac{{V\beta {P_i}}}{{({N_i} + 1)}}{\rm{exp}}\{- \beta [u({N_i} + 1)-u({N_i})\left] \} \right]$, where Pi is the partial pressure of the two components and Ni is the number (density) of them. When the selected molecule attempts to desorb, it is attempted with a probability min $[1, \frac{{{N_i}}}{{V\beta {P_i}}}{\rm{exp}}\{- \beta [u({N_i})-u({N_i}-1)\left] \} \right]$28. Since the system is a multi-component one, adsorption and desorption attempts are performed for each kind of molecule under a specified partial pressure. With the increase of the pressure, the coverage of adsorbed molecules on the surface increases. So the pressures of BL and windmill-like molecules used here are P1=10-10 and P2=10-8, respectively. The interaction strengths are εa=-1.6 and εww=-1.0, supplemented by the Lorentz-Berthelot mixing rules as geometric average for the interaction between BL and windmill-like molecules, and εr=0.5. Since the overall interaction of windmill-like molecules with the substrate is stronger than the BL molecules, the interacting strengths of BL and windmilllike molecules with the substrate are taken as 0 and -1.4, respectively.

In the simulations, typically up to 108 MC steps were taken. The simulations were performed on a L× L (L=300) triangular grid and the total number of molecules is N=800. For simplicity, kB and T are assumed to be dimensionless parameters, kB=1 and T=0.2 if not otherwise stated.

In addition, density functional theory (DFT) calculations were used to provide an estimate of the interaction energies in the coarse-grained MC modeling. The effect of substrate was not considered here. All the DFT calculations were carried out by CP2K program29, 30 with a hybrid Gaussian and plane waves approaches. During all the calculations, the energy cutoff for the plane waves is set as 320 Ry and the convergence criteria of selfconsistent field (SCF) method during the wavefunction optimization is set as 5.0 × 10-7. The exchange-correlation energy of electrons is calculated by generalized gradient approximation (GGA) function of Perdew-Burke-Ernzerh31. The molecularly optimized double zeta-polarization (DZP) basis functions are used for all atoms32. During the structure optimizations, the molecules are centered in a very large box with dimensions of 50 nm × 50 nm × 20 nm and no constraints are applied. The optimizations are eV∙nm-1.

3 Results and discussion
3.1 Simulations using molecules A or BL

We first performedMC simulations for a one-component system composed of 800 molecule A, of which the simulated results can be directly compared with the experimental observations in Ref.16. Fig. 3 depicts a typical snapshot of the self-assembled system. ST fractal structures of different orders can be clearly seen from this figure. The self-assembled fractal structure shown in Fig. 3b agrees with that observed in experiment for B3BP on Ag (111)16 showing that our simple coarse-grained model can serve as a reasonable representation of the experimental system. In this structure, each node comprises of three molecular building blocks that form either a clockwise (CW) or counterclockwise (CCW) pattern as shown in the magnified fragment (Fig. 3b, Fig. 3b′). The nodes in one fractal have a unique rotational mode and they are motifs of a uniform chirality. The two fractal patterns which are mirror-images to each other are formed with an equal probability.

 Fig. 3 A typical pattern of the system consisting 800 molecule A The blue arrows denote the two types of rotation of the three-fold bonding: CCW (left) and CW (right). Magnified fragments (a-c) respectively represent the first, the second and the third order of the ST. The magnified fragment (b′) is the enantiomer of (b). color online

The ST fractals formed by molecule A can be of different orders. Such a high dispersity in formation order does not decrease with the further increase of the simulation time, showing that it is difficult for molecule A to form big ST fractals. This phenomenon can be readily explained as follows. The fractals grow through the attachment of molecule A to one of the three accessible vertices of the ST fractals, the number of which remains constant as the perimeter of the assembled structure increases. Such an effect was also seen in the ST fractals formed by simulated annealing of the symmetric linker and metal atoms18. These results highlight the interesting difference between fractal formation and crystal growth. In the latter, the Ostwald ripening mechanism leads to the formation of a large crystal and the disappearance of smaller ones. One can thus conclude that the shape of the building block and the triangular arrangement of molecular bonding are essential for the ST fractal formation.

Next, we investigated the self-assembly of asymmetric building blocks BL (Fig. 1). A typical snapshot of the adsorbed overlayer comprising 800 molecules of BL and containing two types of nonenantiomorphous STs is shown in Fig. 4. This simulation outcome is different from molecule A. The primary reason for their difference lies in the asymmetric feature of the building block BL. For convenience, the pore of the ST formed through three molecules in Fig. 4e and Fig. 4e′ are named type α and β, respectively. Type β but not type α appears to be a regular hexagon. The formation of the ordered fractal patterns is mainly a result of the entropic stabilization of nodes of type a (heterotactic nodes) which have a formation probability three times higher than nodes of type b (windmill nodes). On the other hand, the growth of imperfect fractal patterns is mainly resulted from the formation of the windmill node.

 Fig. 4 A typical pattern of the system consisting 800 molecules BL The blue arrows indicate the rotation of the three-fold bonding arrays. The enlarged fragments (c-e) correspond to the three consecutive generation of the Sierpiński triangle. The enlarged fragment e′ corresponds to the pattern with the chirality of CW. The type α pore is highlighted by a black square. The type β pore is highlighted by a green square. Heterotactic (a) and windmill-like (b) nodes are three-membered nodes. color online

We next explored the effect of surface coverage and temperature on the morphology of the adsorption layer. In Fig.S6 (Supporting Information), we show that at a high surface coverage the molecules of BL tend to form large triangular aggregates with a diversified morphology. At high temperatures, clusters only form transiently and remain small in size (Fig.S7, Supporting Information). In contrast, at low temperatures the system is easily trapped to configurations consisting of a large variety of irregular structures. Only at proper temperatures can the molecules BL aggregate to form stable fractal patterns. We further analyzed the effect of temperature on the nodes of different patterns, including two-fold, heterotactic, and windmill-like halogen-bonding nodes. The number of these nodes at different temperatures were shown in Fig.S8. It was found that the number of heterotactic node increases with the decreasing of temperature. When the overlayer is sufficiently cooled, say, T < ~0.25, the system prefers heterotactic nodes and the number of windmill-like nodes is much smaller. A similar temperature dependence was previously observed for the self-assembly of STs in metal-organic and hydrogenbonded systems18, 19. Configurations with type α and β pores are both observed in the simulation. To further illustrate their differences, we used DFT to calculate the energy of the molecular configurations consisting of the two types of pores (Fig.S9(a) and Fig.S9(b), Supporting Information). The molecular configuration containing type α pore is lower in energy than that of a type β pore by~2.5 kJ∙mol-1 (see Fig.S9). This difference between these molecular configurations is taken into account in terms of an additional energy penalty (an energy of 1.5 energy unit) for the type β pore. As shown in Fig. 5, when such an effect is considered, only one type of stable fractal pattern is formed in the simulation.

 Fig. 5 A typical pattern of the system composing 800 molecules BL in which the interaction of bond with CW chirality is weaker

3.2 Simulations using the mixture of molecules BL and BR

In experiments, when prochiral molecules adsorb on a solid surface, a racemic overlayer composed of equal amounts of both surface enantiomers is expected. Fig. 6 demonstrates the results obtained for the simulation with 800 molecules of BL and BR (with a ratio of 3 : 1) at the temperature T=0.125. The reason for choosing this ratio of BL and BR is that the smallest cycle observed in experiments is consisted of the same type of 3 molecules BL or BR: if BL forms the cycle, the linker is then BR and vice versa. As observed in the experiment16, the first generation of ST is composed of 9 molecules of BL and 3 molecules of BR. We should note that the real system should contain racemic mixtures, namely, with equal populations of BL and BR on the solid surface. The observation of the 3 : 1 structure in the presence of racemic mixtures indicates the possible role of the matching between the lattice and adsorbates in determining the fractal structures. Such an effect should be considered by including explicitly the solid lattice but is not included in the simple models used in this study.

 Fig. 6 typical pattern of the system composing of 800 molecules of BL and BR (3 : 1) The magnified fragment shows the structure with different molecular types between bridge and ring.

To further distinguish between the different structural units observed in the simulations, we again used DFT to calculate the energy of the configuration in Fig.S9c, which includes one molecule BL and two molecules BR. It was found that this configuration has a higher energy than the configuration of type α by~1.3 kJ∙mol-1 (see Fig.S9). This configuration was in fact only observed for the simulation, but not in the experiment. To incorporate such information, in the following simulation we added an energy penalty (again, a value of 1.5 was used) for configurations composed of both BL and BR.

Fig. 6a shows a fractal structure in which every node consists of mixed enantiomers of B. The overall fractal pattern is formed of nodes with a unique chirality (the enantiomorph is not shown here, a structure representing the one observed in the experiment using B4BP16. Such an agreement shows that the simple model used in this study is capable of reproducing fractal structures observed experimentally for both symmetric and asymmetric building blocks. The formation of a variety of triangular-shaped structures are also shown in Fig. 6. The structural diversity of these aggregates is a result of the variance in the coordination nodes. In addition, we also examined the self-assembly of overlayers containing both conformers of molecule B with racemic composition. The first-order of the ST is observed as can be seen in Fig.S10 (Supporting Information). The magnified fragment shows the fractal structure with one type of handedness with the ratio of BL and BR as 1 : 3. We failed to observe large and regular fractal structures in racemic mixture.

3.3 Designing self-assembly patterns

The simulations discussed above showed that the building blocks BL designed here can spontaneously form ST through selfassembly, but not the porous network shown in Fig.S11 (Supporting Information). This preference of structure formation is expected from a thermodynamic point of view. Let′ s take the porous network (Fig. 7a) and the second generation of ST fractal (Fig. 7b) formed by 12 molecules as examples, which are denoted by state A and state B, respectively. The free energy difference of the two states can be estimated through ΔF=EA-kBTln (m) -(EB-kBTln (n)), where EA is the interaction energy of state A, EB is the interaction energy of state B, T is the temperature, m and n are the total number of configurations that is accessible to the system at energies EA and EB, respectively. The free energy of the porous network (Fig. 7a) is about -18.62, while this value for the fractal structure (Fig. 7b) is -21.14, showing that the building blocks of the fractal structure are indeed thermodynamically more stable. We gave detailed information on the calculation in SI. On the other hand, one should note that heterotatic and windmill-like nodes are energetically equivalent. This preference of structure formation originates mainly from the entropic stabilization of the heterotactic nodes with the ratio of heterotactic and windmill-like nodes as 3 : 1. As mentioned above, the number of the windmilllike nodes increases with T, is much smaller compared to heterotactic nodes. While the windmill-like nodes are responsible for the formation of the porous network as shown in Fig.S11. The porous network is impossible to be observed in this system although the temperature is low.

 Fig. 7 Schematic diagrams of two types of self-assembly structures composed of 12 molecules BL

Therefore, the preference of fractal structures over the porous ones leads to an interesting question: is it possible to guide the selfassembly into the porous network structure by making use the idea of catassembly20, 21? In catassembly, catassembler are added into the system to alter the kinetics of an assembly process. Catasemblers do not appear in the final structure and thus do not change the overall thermodynamics but can either change the rate of selfassembling or lead to varied kinetically controlled products. Following this concept, we propose the following strategy. Firstly, catassemblers that can form the desired target structure are introduced into the system. The adsorption of catassembler initiates biased self-assembly. Next, the assemblers displace the catassembler through adsorption to the surface, e.g., as a result of the favored interaction among themselves. The success of such a design requires the critical nuclear size to be small for the catassembler and at the same time the assemblers form a thermodynamically more stable structure which excludes the catassembler. To achieve such a goal, we designed catassemblers that have a larger molecular size but a weaker interacting strength than the assemblers. Once the assemblers adsorb, catassemblers are to be gradually excluded from the surface. As a result, assemblers aggregate and self-organize into a structure guided by the catassemblers instead of the spontaneously formed one. It should be pointed out that the template used here is different from those used in template-assisted self-assembly. In template-assisted self-assembly, templates remain in the final structure as building blocks. In contrast, the catassemblers do not appear in the final self-assembled structure.

On the basis of the above idea, we proposed a MC model using windmill-shaped catassemblers (Fig. 1C) and BL (Fig. 1B). These catassemblers have the same adsorption sites as the windmill node formed by three BL molecules which can further self-organize into highly ordered porous networks (Fig. 8).

 Fig. 8 Four typical snapshots of the structure of the adsorbed phase corresponding to different MC steps during one MC simulation The molecules represented in red and blue corresponding to BL molecule, windmill-like molecule, respectively. color online

We performed calculations using the GCMC simulation method. Fig. 8 shows four snapshots within one MC simulation. As seen from Fig. 8 (t=0), the ordered porous network is initially a template composed of windmill-like catassembler molecules. Compared to catassemblers, BL molecules interact with each other more strongly on the surface and thus once a nucleus is formed by the catassemblers, it is easy for BL to adsorb to and remain in the structure. Fig. 8 (t=9.5 × 105 MC steps and t=2.05 × 107 MC steps) shows that a process in which the self-assembled structure propagates through adsorption, desorption and movement of BL, dictated by the initial structure formed by the catassemblers. In this process, the windmill nodes formed by three molecules BL insert into the gap formed by self-assembled catassemblers, followed by the detachment of a catassembler nearest to the windmill nodes from the surface. The adsorption of a BL to the vacated sites deprives the catassembler from re-adsorbing. The insertion of two other molecules BL into the unoccupied space leads to the formation of a new windmill node. In this manner, the porous network composed of molecules BL continuously grows. Furthermore, due to the steric hindrance of windmill-like molecules, molecules BL are prevented from the spontaneous formation into ST structures and the assemblers assemble into a large ordered porous network. In the simulations, we also observed that faulted connections between BL molecules exist in the porous network which are subsequently amended.

4 Conclusions

In summary, we have demonstrated the formation of highly ordered fractal structures with a specific chirality when simple lattice models are used in simulations. Density functional theory calculations were used to evaluate the relative stability of various unit structures formed in the self-assembly of asymmetric molecule. We observed that both symmetric and asymmetric building blocks can self-assemble into ST. It was found that the ST tends to form at low surface coverage, and only in a limited temperature range. The simulations on the mixtures of the enantiomers of asymmetric molecules showed that the increased number of possible coordination nodes can lead to the formation of the perturbed triangular-shaped structure. It is more difficult for asymmetric molecules to self-organize into ST with a uniform chirality than the symmetric ones. In addition, we reported a conceptual strategy for changing the self-assembly process of BL from ST fractal structure to a disfavored structure. Important factors such as specific surface structures, lattice matching, and interactions potentially support the formation of the higher order of ST fractal structure. However, the current simulation uses highly simplified models which do not take into account the detailed interactions between the solid lattice and the adsorbates. Atomic detailed models are needed to include such effects.

Supporting Information: Possible nodal motifs of molecule Aand molecule B which can be formed in the overlayer have been listed. The snapshots of the adsorbed overlayer under different temperature and high surface coverage were shown. The number of two-fold, heterotatic, and windmill-like halogen-bonding nodes at different temperature were descripted. The energy of the molecular configuration consisting of the three types of pores was calculated by density functional theory. Estimation of the free energies of the porous network and the fractal structure were given. This information is available free of charge via the internet at http://www.whxb.pku.edu.cn.

Acknowledgments: We thank Peking University for providing the computational resources.
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