Numerical Engineering of Molecular Self-Assemblies in a Binary

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Numerical Engineering of Molecular Self-Assemblies in a Binary System of Trimesic and Benzenetribenzoic Acids Andrius Ibenskas, Mantas Šim#nas, and Evaldas E. Tornau J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b00558 • Publication Date (Web): 01 Mar 2016 Downloaded from http://pubs.acs.org on March 2, 2016

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The Journal of Physical Chemistry

Numerical Engineering of Molecular Self-Assemblies in a Binary System of Trimesic and Benzenetribenzoic Acids ˇ enas,‡ and E. E. Tornau† A. Ibenskas,∗,† M. Sim˙ †Semiconductor Physics Institute, Center for Physical Sciences and Technology, A. Goˇstauto 11, LT-01108 Vilnius, Lithuania ‡Faculty of Physics, Vilnius University, Saul˙etekio 9, LT-10222 Vilnius, Lithuania E-mail: [email protected]

Abstract Self-assembly of two-component mixture of trimesic acid (TMA) and 1,3,5-benzenetribenzoic acid (BTB) was studied by a Monte Carlo calculation. To describe the ordering, the three-state lattice model with homo- and heteromolecular dimeric and trimeric interactions was proposed. We also took advantage of the same symmetry and size effect of TMA and BTB molecules. The molecular interactions between TMA and BTB molecules were calculated by the density functional theory. Our simulations reproduced the self-assembly of all pure and bicomponent phases of TMA and BTB previously found in the experiments. Several new mixed structures were predicted at TMA:BTB ratios of 2:1, 1:1 and 1:2. The conditions of TMA and BTB phase intermixing and coexistence were also clarified by the ground state analysis. The simplest hypothetical structures which might occur due to the mixed trimeric interactions were studied, and their formation conditions were determined.

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Introduction The properties of nanoporous supramolecular networks have been investigated extensively over the past decade. A crucial role in the self-assembly of such structural aggregates is played by the non-covalent and reversible interactions, in particular hydrogen bonding, owing to its anisotropic character and strength. Aromatic carboxylic acids are quite popular as organic building blocks, since they are capable of spontaneous ordering via H-bonds. At the same time, their properties might be modified by attaching relevant functional groups to the core of the molecule. Supramolecular networks might also acquire important magnetic and optical properties that cannot arise from a single molecule. The recent applications of supramolecular networks include gas sensors, 1 drug and gene delivery, 2 anion sensors and organic catalysts, 3 self-healing materials, 4 green chemistry, 5 lubricants and coating materials. 6 The geometry of self-assembled supramolecular structures is inherently related to the underlying symmetry of molecules. Trimesic acid (TMA, see Fig. 1a) and its derivatives possessing the three-fold symmetry are known to arrange into regular and irregular hexagonal patterns on graphite and metallic surfaces. TMA molecules were shown to assemble into the honeycomb structure and flower polymorphs, 7–10 oblique, 11 zigzag (under sonication 12 ) and different other planar phases (ribbon, herringbone, etc) at potential-induced adsorption 13 conditions. Very similar flower pattern is also adopted by structurally related molecules with pyridine central ring. 14 Coadsorption of TMA with solvents of different polarity 15 and aliphatic alcohols 16 was found to promote formation of TMA dimer stripes. The 1,3,5-benzene-tribenzoic acid (BTB, see Fig. 1b), the enlarged derivative of TMA, is known to aggregate into several non-densely-packed polymorphic architectures: honeycomb and oblique (or ribbon). These phases differ in packing density and H-bonding pattern. 17–20 The prevalence of one or the other BTB polymorph depends on temperature and molecular concentration. 20 Less polar solvents lead 21 to formation of several new (rectangular and close-packed) structures, the former being the most stable one. There was observed the 2 ACS Paragon Plus Environment

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structural transition between the honeycomb and compact phase of BTB induced by the sample bias. 22,23 The next higher order derivative of TMA with two phenyl spacers in each arm (TCBPB) showed preference for displaced honeycomb and oblique structures. 24 In contrast to BTB, other structurally similar molecules possessing either phenyl or triazine core with methyl, hydroxyl, phenyl, nitrile or halogen end-groups arrange side by side and assemble into close-packed 25,26 or interdigitated nanoporous single- 27–29 and multicomponent 30 networks, stabilized by van der Waals, hydrogen, halogen or halogen-hydrogen bonds.

Figure 1: Schematic representation of (a) TMA, and (b) BTB molecules. Large (small) gray circles denote carbon (hydrogen) atoms and red circles denote oxygen atoms. Compared to a mono-molecular ensemble, a bicomponent supramolecular network offers a greater flexibility in the choice of molecular building blocks and their bonding motifs. Triangular-shaped TMA and melamine molecules are widely exploited as building blocks in assemblies with other molecules. Experiments have shown that TMA can assemble into planar hexagonal structures with other triangular (BTB, 31 1,3,5-tris(4-pyridyl)-2,4,6-triazine (TPT) 32,33 ) and linear (4,4’-bipyridine (Bpy) 33 ) molecules, the latter TMA-Bpy mixture leading to a pattern of elongated hexagons. Both BTB and TPT species, like TMA, have three bonding vertices and might link with three nearest foreign molecules building regular hexagons. Such an arrangement was observed also for other bicomponent molecular mixtures where either both molecules are triangular (melamine and melem, 34 melamine and cyanuric acid 35–37 ), or triangular and linear. 38,39 It should be noted that both TPT and Bpy molecules do not favor monocomponent adsorption and act as simple linkers in a bicomponent network with TMA molecules. 3 ACS Paragon Plus Environment


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In contrast, the bicomponent adsorption of TMA-BTB system demonstrates very diverse phase diagram: 31 six different phases were obtained by changing the concentrations of TMA and BTB in solutions of fatty acids. In addition to the three pure phases, which might be formed by pure TMA-TMA and BTB-BTB dimeric and TMA-TMA-TMA trimeric H-bond interactions, three hybrid TMA-BTB hexagonal structures, bonded by dimeric TMA-BTB interactions, were identified. Along with the main experimental tool - the scanning tunneling microscopy, the theoretical modeling can provide necessary extra insight to interpret experimental structures at submolecular resolution and identify the key interactions driving the self-assembly of the studied system. Interaction values can be estimated by the density functional theory (DFT) 40–42 and molecular mechanics 43 calculations. The lattice Monte Carlo (MC) method, known for its efficiency and robustness, might be employed to predict the morphology of possible supramolecular networks. 44–50 Ordering of symmetric triangular molecules into the honeycomb phase and its flower homologues was previously reproduced by MC calculations using the three-state phase transition model 51–53 based on the Bell-Lavis model, 54,55 with attractive dimeric (tip-to-tip) and trio interactions mimicking the H-bonding. In order to describe the self-assembly of the reduced-symmetry triangular molecules with additional (compared to TMA) phenyl ring along one of the molecular axes, a more complex sevenstate model was proposed 56 and extended to account for inclusion of the guest (coronene) molecules which stabilize the formation of some structures via the host-guest interactions. In bicomponent systems the intermolecular interactions are usually more complex. Besides homomolecular, there exist heteromolecular interactions which depend on the functionality, symmetry and size of molecules. These interactions determine, whether a binary mixture segregates or assembles into a hybrid structure. Due to mismatch in molecular size, more complex exclusion rules are required in such models. In a rather generalized bicomponent model 50 for the assembly of rigid triangular molecules, interactions were allowed between segments of arms of two molecules, and honeycomb network was formed with


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interdigitation of molecular arms. Molecules of different tricarboxylic acids were shown to interact via vertices, as observed for the TMA-BTB system. 31 In this research an extended version of the three-state model on a triangular lattice is proposed for the ordering of the TMA-BTB bimolecular mixture. Since TMA and BTB have the same symmetry and functionality, it is possible to investigate such a mixture by taking into account only size-related effects making it an attractive model system. A mixing condition for a binary system can be established from the ground state analysis. It is known that intermixing of two components should be preferred over segregation when heteromolecular interaction is larger than the average value of homomolecular interactions. The homomolecular and some heteromolecular interactions between TMA and BTB molecules are calculated here using DFT method and compared to other similar calculations. Further, the Metropolis MC simulations with non-local Kawasaki dynamics were performed in order to study the assembly of pure and mixed (bicomponent) phases at constant molecular coverage. Our MC simulations demonstrate the occurrence of phases found in the experiment. 31 In addition, we predict several new hybrid structures. In general, our numerical simulation reveals that slight tuning of intermolecular interactions might stimulate the formation of new ordered structures previously not observed in experiments.

Model, interactions and computational setup We use a version of the three-state Bell-Lavis model 54,55 proposed to model the formation of a two-dimensional bonded fluid on the triangular lattice. This model is perfectly suited to describe the ordering of symmetric triangular molecules and was successfully used for modeling of the self-assembly of TMA and similar molecules. 51–53 Here we use the extended version of this model to describe the formation of the ordered TMA-BTB binary networks at various molecular concentrations. TMA molecule has a central phenyl ring and three carboxyl groups along each of three



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Figure 2: Schematic dimeric H-bonding between TMA-TMA, BTB-BTB and TMA-BTB molecules and real (three TMA molecules) and hypothetical (two TMA + one BTB and two BTB + one TMA) trio interactions. In further figures the molecules are shown as redpink (for TMA) and black-grey (for BTB) triangles, where different shades denote different molecular orientations. axes of the molecule. BTB molecule has extra phenyl ring between the central ring and each carboxyl group (Fig. 1). Therefore, though the symmetry of both molecules is the same (C3 ), the radius of the BTB molecule is roughly twice larger than that of the TMA. The molecular size dictates mutual distance between the two molecules when their double dimeric H-bond is established. In this paper the distances are given in units of lattice constant (a) or, alternatively, in terms of the nth nearest neighbor (nNN, where n=1,2, ...) distances of the underlying √ triangular lattice. Thus 1NN distance is a, 2NN distance is a 3, etc. Assuming that the radius of TMA molecule is a, the distance between the centers of two H-bonded TMA molecules is 2a (3NN distance of the underlying lattice), while the distance between two H-bonded BTB molecules is 4a (8NN). Consequently, the distance between H-bonded TMA and BTB molecular pair is 3a (5NN) (Fig. 2). In accordance with the suggested 3-state model, both TMA and BTB molecules have two orientational states differing by 60◦ rotation around the 3-fold symmetry axis, while 6 ACS Paragon Plus Environment

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the third state is a vacancy state. The energy of a binary TMA-BTB system given by the dimeric interactions might be written in a form

Hd = −

1 ∑∑ α β β α ni nj eαβ τi→j τj→i . 2 i,j α,β

(1)

The occupation variable nαi =1, if the lattice site i is occupied by the geometrical center of α the α molecule, and equal to 0 if otherwise. The orientation variable τi→j indicates whether α a carboxyl group of the α molecule on site i is pointing towards the site j (τi→j =1) or not α (τi→j =0). Here the first sum goes over the sites of the lattice and the second sum - over

different types of molecules. It has 4 summands (α, β) = (t, t), (t, b), (b, t) and (b, b), where b denotes BTB molecule and t denotes TMA molecule. β α The H-bond is formed if τi→j τj→i = 1 for two molecules α and β centered on lattice sites

i and j. The H-bond interaction parameter eαβ acts between two TMA molecules if mutual distance between their centers is 2a (ett ), between two BTB molecules if the mutual distance is 4a (ebb ) and between TMA and BTB molecules if the mutual distance is 3a (etb ). The arrangements of molecules also have to obey some exclusion rules which are introduced to account for the size and form of the molecules. This means that for simplicity we exclude (eαβ = ∞) a possibility of physical contact (overlap) between the molecules. The exclusion of all possible neighboring sites up to the H-bonding distance would reduce the flexibility of the model and eliminate some mutual configurations of two molecules in different molecular states which are close to each other and can exist at high molecular densities. Therefore, we used the following exclusion rule: if one of mutual arrangements of molecular pair is allowed at a certain distance, the exclusion does not work at this distance, despite the fact that other mutual arrangement at this distance would lead to slight overlap of molecules. Thus, in our model the center of the TMA molecule cannot be at the 1NN distance from the center of other TMA molecule and at 1NN and 2NN distances from the center of the BTB molecule. Consequently, the BTB molecule cannot be at the 1NN, 2NN and 3NN distances from the center of other BTB molecule. 7 ACS Paragon Plus Environment


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In this model we also account for a possibility of a trio bonding which is known 7–10 to occur in homologic series of TMA flower phases. In a modeling of flower phases 52 the trio bonding was shown to be possible when three molecules of the same state have their centers √ on equilateral triangle of size a 3 (2NN distance of the triangular lattice), while the dimeric bonding becomes possible when the distance between centers of two molecules is 2a (3NN). Due to low conformational stability of BTB phases, the occurrence of such an arrangement for BTB molecules is not supported by the experiments. 17–21 Therefore, we do not consider the phases occurring due to this bonding in our model, but analyze the phases obtained by trio bonding for three TMA molecules, two TMA molecules and a BTB molecule and even two BTB molecules and a TMA molecule. The Hamiltonian of the trio interactions has the form

Ht = −

1∑∑ α β γ β γ α n n n eαβγ τi→j,k τj→k,i τk→j,i , 3 i,j,k α,β,γ i j k

(2)

α where the variable τi→j,k in this case marks either the presence (=1) or absence (=0) of

the carboxyl group of the molecule α on site i in the direction towards the mutual center, where the carboxyl groups of two other molecules centered at j and k might be present or not. The second sum gives three summands (α, β, γ) = (t, t, t), (t, t, b) and (t, b, b) with trio interactions ettt , ettb and etbb , respectively (see Fig. 2). The first interaction is possible when √ three TMA molecules are positioned on equilateral triangle of size a 3 (2NN), the second interaction might occur when two TMA molecules and one BTB molecule are positioned on √ √ isosceles triangle with TMA-TMA distance a 3 and TMA-BTB-distance a 7 (4NN), and the third one is possible when two BTB molecules and one TMA molecule are positioned √ √ on isosceles triangle with BTB-BTB distance a 12 (6NN) and TMA-BTB-distance a 7 (4NN). Thus, the total Hamiltonian is the sum of the interaction energies (1) and (2). The values of the dimeric interactions ett , etb and ebb and trimeric interaction ettt were calculated here for gas phase by the DFT using ORCA 3.0.2 program package and B3LYP 8 ACS Paragon Plus Environment

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functional with 6-31G(2d,2p) basis set. To obtain a reliable H-bond energy, it is necessary to properly account for the van der Waals (vdW) interaction. Therefore, in our calculations we included a non-local electron correlation using Grimme D3 correction. 57,58 We noticed that accounting for the vdW correction increases the absolute values of dimeric interactions per bond by 10-15% (cf. with DFT calculations 59 with and without D3 correction for CDTPA, where the effect was 12%). Finally, we also evaluated the basis set superposition error (BSSE) used to correct for the fact that in calculating the dimer energy the monomers partly share basis functions. The results are rather sensitive to inclusion of the BSSE correction: accounting for it considerably decreases the absolute value of the TMA-TMA dimeric interaction (from 11.57 (no BSSE correction) to 9.39 kcal/mol (with BSSE correction) given per carboxyl group in a bond). The equations used for BSSE correction for dimer and trimer interactions were taken from Refs. 60 and, 61 respectively. Our DFT calculations with both the vdW and the BSSE corrections yielded very similar values for TMA-TMA, TMA-BTB and BTB-BTB dimeric interactions (differing by less than 1%), although they tend to increase slightly with molecular size: ett =9.39, etb =9.47 and ebb =9.49 kcal/mol. The earlier DFT calculations of ett , in which the BSSE correction was neglected, mostly demonstrate that the TMA-TMA dimeric interaction is around 10 kcal/mol (see Table 1). The fact that ett values are quite similar, despite different calculation procedures (account for or neglect of the effects of substrate, vdW and BSSE corrections) might indicate that vdW and BSSE effects roughly compensate for each other and the effect of substrate is either weak or requires some further studies. The only value which falls out of the the main trend is 7.9 kcal/mol 42 obtained for dimeric interaction on the HOPG using vdW correction. Such a low value is explained by the effect of vdW interactions, rather than the effect of substrate inclusion. In our calculations accounting for the vdW interactions always increased the absolute value of dimeric interaction. On the other hand, the HOPG is known for strong vdW interaction and accounting for this surface could lead to some



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Table 1: The H-bond energies (kcal/mol per carboxyl group) calculated by DFT for TMA, BTB and similar carboxylic acids Dimer (BA)2 (CDTPA)2

Trimer 10.21

(BA)3

Substrate 8.74 Gas phase Gas phase

Level of theory

vdW

Reference

B3LYP/6-31G(d,p) PBE

No

Nath et al. 9 Steiner et al. 59

9.34 10.49 (BA)2 (TMA)2 (TTBTA)2 (TMA)2

(TMA)2 (TMA)2 (BHTC)2 ss1 ss2 ll (BHTC)2

10.19 (BA)3 10.01 (TMA)3 10.20 (TTBTA)3 7.90 9.60 10.26

Gas phase

B3LYP/6-31G(d,p)

HOPG

PBE-GGA

MacLeod et al. 62

8.74 8.78 8.92

(TMA)3

6.53

(BHTC)3

Au(111) 8.74 Gas phase

(BHTC)3

8.3

(TMA)3

8.08

9.98

No D3 No

SLG

MacLeod et al. 42

LDA

DF No No

PBE B3LYP/6-31G(d,p)

DF No

Shayeganfar and Rochefort 41 Iancu et al. 40 MacLeod et al. 63

D3

ˇ enas et al. 56 Sim˙

9.90 10.01 10.17

ss1 ss2 ll sl

9.62 9.485 9.49 9.58

(TMA)2 (TMA)2 (BTB)2 TMA-BTB

9.39 11.57 9.485 9.47

Gas phase B3LYP/6-31G(2d,2p) BSSE corrected

Gas phase

B3LYP/6-31G(2d,2p) BSSE corrected no BSSE correction BSSE corrected BSSE corrected

This work D3 D3 D3 D3

Denotations: BA-benzoic acid, BHTC - 3,4’,5-biphenyl tricarboxylic acid, TTBTA terthienobenzenetricarboxylic acid and CDTPA - carboxyl-substituted dimethyl-methylene-bridged triphenylamine, HOPG - highly oriented pyrolytic graphite, SLG - single layer graphene, ss1 and ss2 denote two types of H-bonding by shorter arms of BHTC molecules, ll - bonding by longer arms of molecules, sl denotes bonding by short and long arm. 56


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concerted and unexpected results. In our DFT calculations we neglected the influence of the substrate to intermolecular Hbond energy. Such a problem is complicated and computer time consuming task, especially for as large a molecule as BTB. We just guess that this calculation might change the ett , etb and ebb values obtained for gas phase calculations considerably more than 1%. Thus, for further MC calculations we fixed ett = ebb as a constant reference value and varied etb /ett ratio in between 0.96 and 1.04. The ratio of trimeric to dimeric interactions for various tricarboxylic acids is approximately 0.8-0.9 according to DFT studies (see Table 1). In our DFT calculation for TMA molecules we obtained the ratio of ettt /ett = 0.86. We performed a single-flip Metropolis MC simulation of molecular ordering in the TMA and BTB binary mixture at constant molecular coverages, ct and cb , respectively. Here molecular coverage, or concentration, is the ratio of the number of molecules on the lattice to the total number of lattice sites (L2 ), i.e. in definition of the coverage we assume that a molecule occupies one lattice site. E.g. the molecular density of TMA molecules in our √ model is ρt = 2ct /a2 3. We used the triangular lattice of sizes L = 60, 72 and 90 (in units of lattice constant a) and both periodic (PBC) and open (OBC) boundary conditions. For some calculations we increased the lattice size up to 120 and 150. The Kawasaki dynamics was chosen here as the most appropriate algorithm for reproducing the experiment, 31 where the molecular concentration was assumed to be constant. To increase the speed of calculations and faster equilibration of the system, we used a non-local Kawasaki dynamics 64 which allows particle jumps to distant lattice sites. All simulations are started from the disordered phase at high temperature. Then the temperature is reduced until traces of long-range ordered phases are formed below the phase transition point. From here the simulations were continued for sufficiently long time (∼ 106 ÷ 108 MC steps per site) to ensure the thermodynamic equilibrium of the system for chosen ct and cb combination.



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Results Ground state energies We performed MC calculations in a wide range of TMA and BTB coverages. As a result, we were able to reproduce six TMA-BTB phases (A, B, C, D, E and F) which were previously found in the experiment by Kampschulte et al. 31 In addition to verification of the experiment, our model is also capable to predict several new phases. The obtained phases might be divided into two groups: homogeneous phases A, B and F (Fig. 3) and mixed phases C, D1, D2, E (Fig. 4). The first group comprises the phase of the highest density (TMA flower phase A) and honeycomb TMA and BTB phases (B and F, respectively) which are topologically similar, but differ in pore size. The ground state (GS) energies of A, B and F phases are

1 EA = −cA t (ett + 3 ettt ),

(3)

3 EB = −cB t · 2 ett ,

EF = −cFb · 23 ebb , B F where cA t = 2/9 ≈ 0.22, ct = 1/6 ≈ 0.17 and cb = 1/24 ≈ 0.04 are molecular concentra-

tions in stoichiometric A, B and F phases. Note, that the trimeric interactions are necessary to obtain the A phase. The group of the mixed phases (Fig. 4) might be divided into the C and E phases, which contain unequal number of TMA and BTB molecules, and two phases D1 and D2 assembled of equal number TMA and BTB molecules. It should be noted that only one of the D phases (D1) was found in the experiment. 31 The analogue of the D2 phase was found in bicomponent mixture of TMA and TPT, 32,33 where the latter molecule is very similar to BTB, but with nitrogen atom instead of carboxyl group at the vertice. The ratio of TMA to BTB molecules is 3:1 for the C and 1:3 for the E phase. In the C 12 ACS Paragon Plus Environment

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Figure 3: Pure phases A, B and F and their schematic representation by small red-pink (TMA) and large black-grey (BTB) triangles. Different shades denote different orientations of TMA (red-pink) and BTB (black-grey) molecules.

Figure 4: Mixed phases C, E, D1 and D2 at their stoichiometries and schematic representation of these phases by small red-pink (TMA) and large black-grey (BTB) triangles. Different shades denote different orientations of TMA (red-pink) and BTB (black-grey) molecules. In parentheses: TMA:BTB ratio. 13 ACS Paragon Plus Environment


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phase, every regular six-TMA-molecule honeycomb pore is surrounded by pores consisting of four TMA and two BTB molecules in a shape of irregular hexagon. In the E phase it is the opposite: BTB molecules form regular hexagons which are bridged by TMA molecules. Pure BTB hexagons make only 1/4 of the pores in the E phase, and the rest are irregular hexagons, each comprised of four BTB and two TMA molecules. Since BTB molecules are larger than TMA, the total molecular and bond density is lower for the E phase compared to C. The GS energies of C and E are the following

EC = −cC t (ett + etb ),

(4)

EE = −cEb (ebb + etb ), C E where cC t = 3cb = 2/25 = 0.08 denotes TMA concentration in the C phase, and cb = E 3cEt = 2/49 ≈ 0.041 - BTB concentration in the E phase. Here cC t in C and cb in E represent

3/4 of total coverage of these phases. The D1 and D2 structures are assembled of TMA and BTB molecules in 1:1 proportion: D cD t = cb = 1/27 ≈ 0.037, where D means either D1 or D2. The D1 phase demonstrates

two types of irregular heteromolecular hexagons arranged in alternating rows. The first one is the same as irregular hexagon in the C phase (four TMA + two BTB molecules), and the second one is the same as in the E phase (two TMA + four BTB molecules). In our MC simulations the D1 phase is often accompanied (or replaced) by another structure, D2, which demonstrates one type of hexagonal pores assembled of three TMA and three BTB molecules and unique intermolecular interaction, etb . The GS energies of D1 and D2 phases are

ED1 = −cD t (ett /2 + ebb /2 + 2etb ), ED2 = −cD t ·3etb .


(5)

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Here cD t represents half of the total coverage. Despite topological difference, the D1 and D2 phases have the same lattice periodicity, can easily attach to each other and coexist at any ratios. It is well-known that the equality

ebb + ett = 2etb

(6)

describes a general rule for segregation of two components in a binary system defining the phase boundary between pure and mixed phases: pure phases occur, when the left-hand side is larger, and vice versa. Thus, the energy of the mixed C, E, D1 and D2 phases might compete with the energy of F+B phase coexistence. The competition of phases D1 and D2 is also determined by the formula (6). This equation perfectly holds for the GS energies. The situation at finite temperatures might be slightly more complicated due to the entropic effects. Besides, the commensurability of emerging molecular structures and the substrate lattice, the domain walls between structures and, finally, the ratio of TMA to BTB molecules might have their effects and slightly change the region of validity of this equation. The fact that the mixed phases are found in the experiment 31 implies that the sum of interactions ebb + ett might be slightly smaller than 2etb . Our DFT calculations corroborate this result, though the difference in magnitude of interaction constants is very small and possibly on a verge of calculation accuracy. In contrast, the experimental finding of the D1, rather than the D2 phase, would indicate either the preference of inequality ebb + ett & 2etb or the higher configurational entropy of the D1 phase. Thus, below we explored what phases are obtained in the MC calculations using our model with ebb = ett = etb and how the results change by slight variation of interaction energies.



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TMA:BTB ratios of 3:1, 1:1 and 1:3 We fixed the values of interaction energies ebb = ett and varied the ratio of etb /ett in between 0.96 and 1.04 for TMA:BTB ratios corresponding to mixed phases C, D1, D2 and E. To avoid the effects of size and boundary conditions and facilitate the molecular ordering, some part of our lattice was left unoccupied by molecules. In accordance with equation (6), the coexistence (F+B) of two pure phases B and F is obtained at etb /ett < 1 and all ratios of TMA to BTB molecules (3:1, 1:1 and 1:3) (see Fig. 5a at 3:1, but similar snapshots are obtained at other ratios).

Figure 5: Snapshots at TMA:BTB ratio of 3:1: (a) F+B coexistence (etb /ett = 0.98, PBC) (b) B and C+D2 coexistence (etb /ett = 1, OBC) and (c) C phase (etb /ett = 1.04, PBC) at L = 60. Different shades denote different orientations of TMA (red-pink) and BTB (black-grey) molecules. At etb /ett = 1 both pure and mixed phases are obtained. For the 3:1 ratio, where the occurrence of the C phase is anticipated, we obtain the C phase as well as the coexistence of pure B phase and mixed D2 (1:1) phase (Fig. 5b). Note, that the C phase and the B+D2 mixture have the same GS energy. The domains of the C phase and B+D2 coexistence is maintained also at slightly higher values of etb . At higher values of etb /ett (> 1.02) the C phase is prevailing (Fig. 5c). For 1:1 ratio and etb /ett = 1 we obtain the D2 phase with small insertions of the D1 phase (Fig. 6a) which often play the role of domain boundaries connecting two D2 domains of different orientations. At etb /ett > 1 the D2 is the dominating structure. At 1:3 ratio the E phase is expected at etb /ett > 1 and the F+B coexistence at etb /ett < 1. 16 ACS Paragon Plus Environment

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We obtain the coexistence at etb /ett < 1: the F phase shares the lattice with a small insertion of the B phase similarly to that in Fig. 5a just with notably smaller B-domain. At etb /ett = 11.02 the F phase is still strong, but part of the lattice demonstrates the D2 phase ordering (Fig. 6b). The E phase is obtained at still stronger mixing interaction (Fig. 6c). The GS energy of the E phase and F+D2 mixture is the same. It should be noted that mixed stoichiometric phases C and E are more stable when PBC are used and less stable for calculations using OBC.

Figure 6: Snapshots of (a) D2+D1 coexistence at TMA:BTB ratio of 1:1 (etb /ett = 1, OBC), (b) F and D2 coexistence at TMA:BTB ratio of 1:3 (etb /ett = 1, OBC) and (c) E phase at TMA:BTB ratio of 1:3 (etb /ett = 1.04, OBC) at L = 60. Different shades denote different orientations of molecules.

Intermediate TMA:BTB ratios: new phases Further we explored the structures which might be obtained at intermediate TMA:BTB ratios in between 3:1, 1:1 and 1:3. In between 3:1 and 1:1 the domains of mixed phases D1/D2 and C were expected at etb ≥ ett = ebb . Due to a specific geometry of these phases, they can mix very easily without creating domain walls which would cost some energy. For the ratio of

5 2

: 1, for example, the domains of D2/D1 and B phases were found for

etb /ett closer to 1, and the domains of the D2/D1 and C phases - for etb /ett > 1 (1.02, 1.04). At the ratio of 2:1 we obtained a new stable phase which was not observed in experiment. 31 √ We called it the C1 phase. The unit cell of this phase (length 8a 3, Fig. 7a) consists of building blocks characteristic to phases C (TMA hexagon), D1 (butterfly-like two TMA 17 ACS Paragon Plus Environment


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molecules connected to four BTB molecules) and D2 (mixed TMA and BTB hexagon). The GS energy of the C1 phase is 3 EC1 = − cC1 (ett /2 + etb ), 2 t

(7)

where cC1 = 2cC1 = 1/16 = 0.0625. This phase is obtained with gradual decrease of t b temperature - from disordered phase first entering into the coexistence of D2 and C phases with some C1 phase nucleus and then - into a dominating C1 phase domain. In Fig. 7b we demonstrate a unique situation at the 2:1 ratio when the domain of a pure B phase is frozen in the center of the lattice, and the system becomes multidomain - the domains of three mixed phases (D2, C and C1) are formed around the B phase domain. For the ratio of

3 2

: 1 the D2 phase hexagons (with motifs of the D1 phase which are

needed to switch from one D2 orientation to another) with some TMA hexagons are found.

Figure 7: Snapshots of (a) C1 phase at TMA:BTB ratio of 2:1 (etb /ett = 1.04, PBC, L = 90), (b) C (top left), C1 (top right) and D2 (below and right) coexistence at TMA:BTB ratio of 2:1 with frozen B phase domain in the center (etb /ett = 1.04, OBC, fragment of L = 120) and (c) E1 phase at TMA:BTB ratio of 1:2 (etb /ett = 1, PBC, L = 90. The unit cells of the C1 (a) and the E1 (c) phases are shown. Different shades denote different orientations of molecules. At the reciprocal ratio of 1:2 we found another new phase, the E1 phase (Fig. 7c), which we anticipated in relation to occurrence of the C1 phase at the 2:1 ratio. The E1 phase has √ the largest unit cell (rhombus with a side length 10a 3) of all studied phases. Its GS energy is


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3 EE1 = − cE1 (ebb /2 + etb ), 2 b

(8)

where cE1 = 2cE1 = 1/25 = 0.04. The unit cell of the E1 phase is built of one F t b phase hexagon, four D1-type (consisting of 4 BTB and 2 TMA molecules) and four D2-type hexagons. By analogy we also tried to obtain further homologous series of phases C2 (TMA:BTB √ √ ratio of 52 : 1 and unit cell length 11a 3) and E2 (1 : 25 and 13a 3), but we managed to obtain only small fragments of these phases at their stoichiometries.

Filled hexagons The exclusion rules of our model do not eliminate a possibility for TMA and BTB molecules to approach each other at 2a (3NN) distance. At this distance and identical mutual orientations the molecules have no physical contact with each other. Therefore, it might occur a situation when TMA molecules start to form hexagons inside the hexagonal pores of the BTB honeycombs as in Fig. 8a. Such a structure as a whole cannot exist as a thermodynamically stable phase due to one unsaturated H-bond of the TMA molecule. At etb ≤ ett = ebb , it would always lose the competition to the coexistence of the pure phases F+B, while at etb ≥ ett = ebb it cannot compete with the mixed bimolecular structures at their corresponding stoichiometries. Although the latter situation is closer to reality (mixed phases are experimentally observed), here we consider the case etb = ett = ebb and even etb ≤ ett = ebb when the F+B coexistence still can take place. We assume that this coexistence can occur in some special conditions due to irregularities of substrate, specifics of solvent molecules, etc. Partly filled F phase hexagons are found in our simulations at etb ≤ ett = ebb when the excess of TMA molecules forces them to look for a refuge in the BTB hexagons. The share of TMA and BTB molecules in a perfect F+B coexistence can be expressed by the equation



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F ct /cB t + cb /cb = 1, ′

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(9)

′

where ct = ct and ct is the TMA concentration in a perfect F+B coexistence. In (9) we ′

F take into account that cb = 0 if ct = cB t and ct = 0 if cb = cb . In excess of TMA molecules,

which cannot be fully accommodated by a perfect F+B coexistence, these extra molecules ′

(∆ct = ct − ct ) start to fill the hexagons in the F domain or accumulate at the domain wall of the F+B coexistence. The number of filled hexagons depends on ∆ct , size of B domain and boundary conditions.

Figure 8: Snapshots of (a) F phase and (b, c) F+B coexistence under surplus of TMA ′ ′ molecules: (a) ct = 0, ∆ct = cb = 150/L2 at etb /ett = 1, L = 60 with PBC, (b) ct = ∆ct = ′ 60/L2 , cb = 135/L2 at etb /ett = 0.98, L = 60 with PBC, (c) ct = ∆c = 240/L2 , cb = 540/L2 at etb /ett = 0.98, L = 120 with OBC. Different shades denote different orientations of molecules. ′

For cb = cFb , ct = 0, and all lattice is occupied by the F phase (no B domain). Therefore, all new arriving TMA molecules (∆ct = ct ) fill the centers of F hexagons when the PBC are used (Fig. 8a). We can rationalize this case by introducing the ratio of filled hexagons to all BTB hexagons, Nf /(Nf + N0 ) = 13 ∆ct /cb , where we have taken into account that there are two BTB molecules per hexagon in the F phase, but six TMA molecules are needed to form a single hexagon in the F phase pore. At etb = ett = ebb , the F phase with partly


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filled hexagons survive up to ∆ct ≤ cb (Nf = N0 /2) and disintegrate at higher values of ∆ct . At etb < ett = ebb the F phase with partly filled hexagons persists for even higher values of ∆ct > cb (e. g. Nf = 2N0 at etb /ett = 0.98). ′

When there initially is the B phase domain in the F+B coexistence (ct > 0 in (9)), we obtain Nf /(Nf + N0 ) = ( 15 ÷ 41 )∆ct /cb , because some part of excess TMA molecules (∼ 20 ÷ 30%) is diverted to densification of the domain wall between B and F phase domains (Fig. 8b). When we use the OBC, the number of filled hexagons Nf is even smaller, since some part of excess TMA molecules condenses also on lattice boundaries (Fig. 8c). We ′

′

estimate it as being three-four times smaller than the PBC value for both ct = 0 and ct > 0. The experimental finding of filled hexagons might be a complicated task. The conditions for their realization should comprise highly constrained substrate terrace with the F phase domain subjected to surplus of TMA molecules. Note, that here we neglect the role of solvent molecules which participate in formation of F structure on solid-liquid interface and possibly might prevent the filling of the BTB hexagons.

Structures with both dimeric and trimeric interactions It is known that TMA molecules at high densities can form trimeric configurations. 7–10 The B and A structures are first members of the homologous series of flower phases with none and one trimeric interaction, respectively (3). Thus, the accounting for the trio interaction between three TMA molecules, ettt , in Hamiltonian (2) can lead to formation of the A phase B at molecular densities cA t > ct (cb = 0) or further members of the homologic series of flower ′

A phases, e.g. the A’ phase at even higher molecular densities, cA t > ct . The formation of

this series in numeric calculations is demonstrated in Ref. 52 Here in Fig. 9a we show the B snapshot of A+B coexistence obtained in between cA t and ct when the value of ettt is close to

ett . Note, that the DFT ratio of trimeric to dimeric interaction (0.86 per molecule) is equal to ettt /ett = 1.3 in our MC calculations. At slightly higher molecular densities, the A’+B coexistence is obtained (Fig. 9b). 21 ACS Paragon Plus Environment


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Figure 9: Snapshots of homomolecular phases with trio bonding at ebb = ett = etb , ettt /ett = 1.3 (PBC, fragments of L = 90 lattice): (a) A+B phase coexistence at ct = 0.21, (b) A’+B coexistence at ct = 0.22. The most stable hypothetical structures with mixed trio interactions at ebb = ett = etb , ettt /ett = 1.2 (PBC, L = 72): (c) T1 (ettt /ett = 1.8) and (d) T2 (etbb /ett = 1.5). Different shades denote different orientations of molecules. Contrary to TMA molecules, the trimer configuration in very similar, but larger BTB molecules was not experimentally found due to their low conformational flexibility. 31 But since both TMA and BTB molecules possess the same carboxyl groups at the tips, and TMA molecules at higher densities easily arrange in trimers, we decided to explore the possibility of formation of mixed phases with trimeric interactions. We studied the conditions at which the tips of two TMA molecules are in so close proximity from the tip of BTB molecule that the trimeric TMA-TMA-BTB bonding is possible. Similarly, we were looking for the hypothetic phases with TMA-BTB-BTB trio interactions. In total we studied seven such phases with TMA-TMA-BTB and TMA-BTB-BTB trio interactions with different TMA:BTB ratios and reasonable unit cell length. At not too large magnitudes of ettb and etbb we observed the occurrence of two phases, T1 and T2, which are shown in snapshots of Fig. 9c and d. The = 4cT1 hypothetical T1 phase is obtained at TMA:BTB ratio of 4:1 (cT1 t b = 0.13). In Fig. 9c it was observed at ettb /ett = 1.8, but actually the domains of this phase start to emerge 22 ACS Paragon Plus Environment

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at smaller values of this ratio (> 1.45). The phase T2 is obtained at cT2 = cT2 = 0.054 t b and etbb /ett = 1.5. Here the existence of the T2 phase requires at least the same strength of trimeric and dimeric interaction (per molecule).

Conclusions To study the ordering of a binary mixture of TMA and BTB molecules, we proposed a version of Bell-Lavis model with both dimeric and trimeric bonds taken into account. Exclusion rules defining minimum distances between molecules were introduced to prevent their overlap. The homomolecular and heteromolecular dimeric interactions between TMA and BTB molecules were estimated by the DFT calculations taking into account the van der Waals and BSSE corrections. Interaction energies of the TMA-TMA, BTB-BTB and TMA-BTB dimers were found to be very similar, although there is a mild increase with molecular size. The value of the heterogeneous TMA-BTB interaction seems to be intermediate between the two homomolecular interactions, but the difference is probably within the calculation accuracy. However, since bimolecular TMA-BTB phases are known to be formed in the experiments, 31 it might be assumed that the balance of homomolecular and heteromolecular interactions is slightly in favor of mixing behavior, rather than segregation. In our MC simulations we slightly tuned the values of interactions. When TMA-BTB dimeric interaction was smaller than either of homomolecular interactions, the separation into the pure TMA honeycomb B phase and pure BTB honeycomb F phase occurred for all studied TMA:BTB concentration ratios. On the other hand, when TMA-BTB interaction was stronger compared to the other two interactions, we noticed that bimolecular phases were more prevalent while biphase mixtures occurred less frequently. By tuning the TMA:BTB ratio we were able to reproduce all experimentally known phases. Apart of homomolecular honeycomb (A and F) and flower (B) structures, we obtained three more complex heteromolecular networks (C, D1 and E) with stoichiometric



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TMA:BTB ratios of 3:1, 1:1 and 1:3. At 1:1 ratio, in addition to the experimental structure D1 featuring all three types of dimers, another porous honeycomb phase (D2) was obtained. This phase is formed of only heteromolecular TMA-BTB dimers, and every molecule in this phase forms bonds with three foreign molecules. A similar structure is formed 32,33 in mixtures of other triangular molecules (TMA-TPT). The fact that this structure was omitted in the main experiment 31 might imply lower configurational entropy of the D2 phase in comparison to the D1. It should be noted that the D2 structure favors coexistence with the honeycomb TMA phase B (when TMA:BTB ratio is close to 3:1) and the honeycomb BTB phase F (close to 1:3). Note, that the D2+B phase coexistence has the same ground state energy as the C phase at the ratio of 3:1, while the D2+F coexistence has the same ground state energy as the E phase at the ratio of 1:3. Our MC simulations at TMA:BTB ratios of 2:1 and 1:2 revealed the possibility of formation of new mixed structures, C1 and E1, which were not previously observed in experiments. These phases possess combined motifs of the known experimental phases C and D1/D2 (C1) and E and D1/D2 (E2). Such intermixing is promoted because no energy is lost on domain wall building. The phases C1 and E1 are in fact the higher homologues of the C (3:1) and E (1:3) phases with correspondingly larger unit cell sizes. All heteromolecular phases have higher packing density compared to coexistence of pure honeycomb phases F+B. It is known 8,18 that the experimental realization of TMA-BTB phases at the solid-liquid interface depends on a type of solvent molecules used in experiment and their arrangement in the honeycomb pores. In our calculations we neglect this effect, because there are no experimental data which reliably show how these molecules are formed inside the pores. But it cannot be excluded that some of the new phases found here (D2, C1 and E1) were not experimentally found due to interference of solvent molecules. E. g. if for some solventrelated reason the D2 phase does not form, the phases C1 and E1 does not form as well, since both these phases have certain motifs of the D2 phase. On the other hand, the D2 ordering is more regular ordering with one type of hexagonal pores to compare with the D1


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(see Fig. 4), and the D2 structure is known 32,33 to exist in the TMA-TPT mixture, where the same type of solvent (heptanoic acid) was used as in the main TMA-BTB experiment. 31 As a side effect of our simulations, we observed an interesting phenomenon when BTB hexagons in the F phase are filled by TMA hexagons in a form of a six-molecule ring of the B phase. Such hexagons are not obtained as a single structure, because of one unsaturated H-bond of each TMA molecule. Filled hexagons are observed only for the F+B coexistence in excess of TMA molecules. In our simulation we also studied the possibility of realization of several ordered structures with homomolecular (TMA) and heteromolecular (TMA-TMA-BTB and BTB-BTB-TMA) trio interactions. If the former structures are rather well-known as experimentally found TMA flower phases, the latter ones are rather hypothetical formations which might be formed for higher values of mixed trio interactions.

Acknowledgement A.I. and E.E.T. acknowledge the financial support of the Research Council of Lithuania (long-term program “Nanostructured materials and electronics”). We thank A. Alkauskas and K. Aidas for valuable advices on DFT calculations.

References (1) Bohrer, F. I.; Colesniuc, C. N.; Park, J.; Ruidiaz, M. E.; Schuller, I. K.; Kummel, A. C.; Trogler, W. C. Comparative Gas Sensing in Cobalt, Nickel, Copper, Zinc, and Metal-Free Phthalocyanine Chemiresistors. J. Am. Chem. Soc. 2009, 131, 478-485. (2) Ma, X.; Zhao, Y. Biomedical Applications of Supramolecular Systems Based on HostGuest Interactions. Chem. Rev. 2015, 115, 7794-7839.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(3) Busschaert, N.; Caltagirone, C.; Van Rossom, W.; Gale, P. A. Applications of Supramolecular Anion Recognition. Chem. Rev. 2015, 115, 8038-8155. (4) Blaiszik, B. J.; Kramer, S. L. B.; Olugebefola, S. C.; Moore, J. S.; Sottos, N. R.; White, S. R. Self-Healing Polymers and Composites. Annu. Rev. Mater. Res. 2010, 40, 179-211. (5) Korolkov, V. V.; Allen, S.; Roberts, C. J.; Tendler, S. J. B. Green Chemistry Approach to Surface Decoration: Trimesic Acid Self-Assembly on HOPG. J. Phys. Chem. C 2012, 116, 11519-11525. (6) Bhushan, B. Nanotribology and Nanomechanics in Nano/Biotechnology. Phil. Trans. R. Soc. A 2008, 366, 1499-1537. (7) Griessl, S.; Lackinger, M.; Edelwirth, M.; Hietschold, M.; Heckl, W. M. Self-Assembled Two-Dimensional Molecular Host-Guest Architectures From Trimesic Acid. Single Mol. 2002, 3, 25-31. (8) Lackinger, M.; Griessl, S.; Heckl, W. M.; Hietschold, M.; Flynn, G. W. Self-Assembly of Trimesic Acid at the Liquid-Solid Interface - a Study of Solvent-Induced Polymorphism. Langmuir 2005, 31, 4984-4988. (9) Nath, K. G.; Ivasenko, O.; MacLeod, J. M.; Miwa, J. A.; Wuest, J. D.; Nanci, A.; Perepichka, D. F.; Rosei, F. Crystal Engineering in Two Dimensions: An Approach to Molecular Nanopatterning. J. Phys. Chem. C 2007, 111, 16996-17007. (10) Ye, Y. C.; Sun, W.; Wang, Y. F.; Shao, X.; Xu, X. G.; Cheng, F.; Li, J. L.; Wu, K. A Unified Model: Self-Assembly of Trimesic Acid on Gold. J. Phys. Chem. C 2007, 111, 10138-10141. (11) Payer, D.; Comisso, A.; Dmitriev, A.; Strunskus, T.; Lin, N.; W¯oll, C.; DeVita,


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A.; Barth, J. V.; Kern, K. Ionic Hydrogen Bonds Controlling Two-Dimensional Supramolecular Systems at a Metal Surface. Chem. Eur. J. 2007, 13, 3900-3906. (12) Ha, N. T. N.; Gopakumar, T. G.; Gutzler, R.; Lackinger, M.; Tang, H.; Hietschold, M. Influence of Solvophobic Effects on Self-Assembly of Trimesic Acid at the Liquid-Solid Interface. J. Phys. Chem. C 2010, 114, 3531-3536. (13) Li, Z.; Han, B.; Wan, L. J.; Wandlowski, Th. Supramolecular Nanostructures of 1,3,5Benzene-tricarboxylic Acid at Electrified Au(111)/0.05 M H2 SO4 Interfaces: An in Situ Scanning Tunneling Microscopy Study. Langmuir 2005, 21, 6915-6928. (14) Duong, A.; Dubois, M. A.; Wuest, J. D. Two-Dimensional Molecular Organization of Pyridinecarboxylic Acids Adsorbed on Graphite. Langmuir 2010, 26, 18089-18096. (15) Ha, N. T. N.; Gopakumar, T. G.; Hietschold, M. Polymorphs of Trimesic Acid Controlled by Solvent Polarity and Concentration of Solute at Solid-Liquid Interface. Surface Science 2013, 607, 68-73. (16) MacLeod, J. M.; Ivasenko, O.; Perepichka, D. F.; Rosei, F. Stabilization of Exotic Minority Phases in a Multicomponent Self-Assembled Molecular Network. Nanotechnology 2007, 18, 424031. (17) Ruben, M.; Payer, D.; Landa, A.; Comisso, A.; Gattinoni, C.; Lin, N.; Collin, J. P.; Sauvage, J. P.; De Vita, A.; Kern, K. 2D Supramolecular Assemblies of Benzene-1,3,5triyl-tribenzoic Acid: Temperature-Induced Phase Transformations and Hierarchical Organization with Macrocyclic Molecules. J. Am. Chem. Soc. 2006, 128, 15644-15651. (18) Kampschulte, L.; Lackinger, M.; Maier, A. K.; Kishore, R. S. K.; Griessl, S.; Schmittel, M.; Heckl, W. M. Solvent Induced Polymorphism in Supramolecular 1,3,5Benzenetribenzoic Acid Monolayers. J. Phys. Chem. B 2006, 110, 10829-10836.



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(19) Lee, S. L.; Adisoejoso, J.; Fang, Y.; Tahara, K.; Tobe, Y.; Mali, K. S.; De Feyter, S. Efficient Screening of 2D Molecular Polymorphs at the Solution-Solid Interface. Nanoscale 2015, 7, 5344-5349. (20) Gutzler, R.; Sirtl, T.; Dienstmaier, J. F.; Mahata, K.; Heckl, W. M.; Schmittel M.; Lackinger, M. Reversible Phase Transitions in Self-Assembled Monolayers at the Liquid-Solid Interface: Temperature-Controlled Opening and Closing of Nanopores. J. Am. Chem. Soc. 2010, 132, 5084-5090. (21) Silly, F. Two-Dimensional 1,3,5-Tris(4-carboxyphenyl)benzene Self-Assembly at the 1-Phenyloctane/Graphite Interface Revisited. J. Phys. Chem. C 2012, 116, 1002910032. (22) Cometto, F. P.; Kern, K.; Lingenfelder, M. Local Conformational Switching of Supramolecular Networks at the Solid/Liquid Interface. ACS Nano 2015, 9, 55445550. (23) Lee, S. L.; Fang, Y.; Velpula, G.; Cometto, F. P.; Lingenfelder, M.; Mullen, K.; Mali, K. S.; De Feyter, S. Reversible Local and Global Switching in Multicomponent Supramolecular Networks: Controlled Guest Release and Capture at the Solution/Solid Interface. ACS Nano 2015, 9, 1160811617. (24) Dienstmaier, J. F.; Mahata, K.; Walch, H.; Heckl, W. M.; Schmittel, M.; Lackinger, M. On the Scalability of Supramolecular Networks - High Packing Density vs Optimized Hydrogen Bonds in Tricarboxylic Acid Monolayers. Langmuir 2010, 26, 10708-10716. (25) Sirtl, T.; Schlögl, S.; Rastgoo-Lahrood, A.; Jelic, J.; Neogi, S.; Schmittel, M.; Heckl, W. M.; Reuter, K.; Lackinger, M. Control of Intermolecular Bonds by Deposition Rates at Room Temperature: Hydrogen Bonds versus Metal Coordination in Trinitrile Monolayers. J. Am. Chem. Soc. 2013, 135, 691-695. (26) Silly, F. Two-Dimensional Self-Assembly of 2,4,6-Tris(4’,4”,4”’-trimethylphenyl)-


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1,3,5-triazine Star-Shaped Molecules: Nanoarchitecture Structure and Domain Boundaries. J. Phys. Chem. C 2014, 118, 11975-11979. (27) Baris, B.; Luzet, V.; Duverger, E.; Sonnet, P.; Palmino, F.; Cherioux, F. Robust and Open Tailored Supramolecular Networks Controlled by the Template Effect of a Silicon Surface. Angew. Chem. Int. Ed. 2011, 50, 4094-4098. (28) Silly, F. Selecting Two-Dimensional HalogenHalogen Bonded Self-Assembled 1,3,5Tris(4-iodophenyl)benzene Porous Nanoarchitectures at the SolidLiquid Interface. J. Phys. Chem. C 2013, 117, 20244-20249. (29) Marele, A. C.; Corral, I.; Sanz, P.; Mas-Ballesté, R.; Zamora, F.; Yán ˜ez, M.; GómezRodr´ıguez, J. M. Some Pictures of Alcoholic Dancing: From Simple to Complex Hydrogen-Bonded Networks Based on Polyalcohols. J. Phys. Chem. C 2013, 117, 4680-4690. (30) Baris, B.; Jeannoutot, J.; Luzet, V.; Palmino, F.; Rochefort, A.; Cherioux, F. Noncovalent Bicomponent Self-Assemblies on a Silicon Surface. ACS Nano 2012, 6, 69056911. (31) Kampschulte, L.; Werblowsky, T. L.; Kishore, R. S. K.; Schmittel, M.; Heckl, W. M.; Lackinger, M. Thermodynamical Equilibrium of Binary Supramolecular Networks at the LiquidSolid Interface. J. Am. Chem. Soc. 2008, 130, 8502-8507. (32) Kampschulte, L.; Griessl, S.; Heckl, W. M.; Lackinger, M. Mediated Coadsorption at the Liquid-Solid Interface: Stabilization through Hydrogen Bonds. J. Phys. Chem. B 2005, 109, 14074-14078. (33) Li, M.; Xie, P.; Deng, K.; Yang, Y. L.; Lei, S. B.; Wei, Z. Q.; Zeng, Q. D.; Wang, C. A Dynamic Study of the Structural Change in the Binary Network in Response to Guest Inclusion. Phys. Chem. Chem. Phys. 2014, 16, 8778-8782.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(34) Uemura, S.; Aono, M.; Sakata, K.; Komatsu, T.; Kunitake, M. Thermodynamic Control of 2D Bicomponent Porous Networks of Melamine and Melem: Diverse HydrogenBonded Networks. J. Phys. Chem. C 2013, 117, 24815-24821. (35) Staniec, P. A.; Perdigão, L. M. A.; Rogers, B. L.; Champness, N. R.; Beton, P. H. Honeycomb Networks and Chiral Superstructures Formed by Cyanuric Acid and Melamine on Au(111). J. Phys. Chem. C 2007, 111, 886-893. (36) Xu, W.; Dong, M.; Gersen, H.; Rauls, E.; Vázquez-Campos, S.; Crego-Calama, M.; Reinhoudt, D. N.; Stensgaard, I.; Laegsgaard, E.; Linderoth, T. R. et al. Cyanuric Acid and Melamine on Au(111): Structure and Energetics of Hydrogen-Bonded Networks. Small 2007, 3, 854-858. (37) Zhang, H. M.; Xie, Z. X.; Long, L. S.; Zhong, H. P.; Zhao, W.; Mao, B. W.; Xu, X.; Zheng, L. S. One-Step Preparation of Large-Scale Self-Assembled Monolayers of Cyanuric Acid and Melamine Supramolecular Species on Au(111) Surfaces. J. Phys. Chem. C 2008, 112, 4209-4218. (38) Weber, U. K.; Burlakov, V. M.; Perdigão, L. M. A.; Fawcett, R. H. J.; Beton, P. H.; Champness, N. R.; Jefferson, J. H.; Briggs, G. A. D.; Pettifor, D. G. Role of Interaction Anisotropy in the Formation and Stability of Molecular Templates. Phys. Rev. Lett. 2008, 100, 156101. (39) Silly, F.; Shaw, A. Q.; Porfyrakis, K.; Briggs, G. A. D.; Castell, M. R. Pairs and Heptamers of C70 Molecules Ordered via PTCDI-Melamine Supramolecular Networks. Appl. Phys. Lett. 2007, 91, 253109. (40) Iancu, V.; Braun, K. F.; Schouteden, K.; Van Haesendonck, C. Probing the Electronic Properties of Trimesic Acid Nanoporous Networks on Au(111). Langmuir 2013, 29, 11593-11599.


Page 30 of 34

Page 31 of 34

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(41) Shayeganfar, F.; Rochefort, A. Electronic Properties of Self-Assembled Trimesic Acid Monolayer on Graphene. Langmuir 2014, 30, 9707-9716. (42) MacLeod, J. M.; Lipton-Duffin, J. A.; Cui, D.; De Feyter, S.; Rosei, F. Substrate Effects in the Supramolecular Assembly of 1,3,5-Benzene Tricarboxylic Acid on Graphite and Graphene. Langmuir 2015, 31, 7016-7024. (43) Martsinovich, N.; Troisi A. Modeling the Self-Assembly of Benzenedicarboxylic Acids Using Monte Carlo and Molecular Dynamics Simulations. J. Phys. Chem. C 2010, 114, 4376-4388. (44) Balbás, G. M.; Rohr, C.; Gruber, K.; Hermann, B. A.; Franosch, T. Simulating SelfOrganized Molecular Patterns Using Interaction-Site Models. Eur. Phys. J. E 2012, 35, 25. (45) Petrauskas, V.; Lapinskas, S.; Tornau, E. E. Phase Diagram of Subphtalocyanine Ordering on Ag(111). J. Chem. Phys. 2004, 120, 11815-11821. ˇ enas, M.; Tornau, E. E. Pin-Wheel Hexagons: A Model for Anthraquinone Order(46) Sim˙ ing on Cu(111). J. Chem. Phys. 2013, 139, 154711. ˇ enas, M.; Tornau, E. E. A Model of Melamine Molecules Ordering on Metal Sur(47) Sim˙ faces. J. Chem. Phys. 2014, 141, 054701. (48) Fortuna, S.; Cheung, D. L.; Troisi, A. Hexagonal Lattice Model of the Patterns Formed by Hydrogen-Bonded Molecules on the Surface. J. Phys. Chem. B 2010, 114, 18491858. (49) Szabelski, P.; De Feyter S. Chiral Occlusion in Two-Dimensional Binary Supramolecular Networks Studied by the Monte Carlo Method. CrystEngComm 2011, 13, 55425550.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(50) Lei, S.; Tahara, K.; M¨ ullen, K.; Szabelski, P.; Tobe, Y.; De Feyter, S. Mixing Behavior of Alkoxylated Dehydrobenzo[12]annulenes at the Solid-Liquid Interface: Scanning Tunneling Microscopy and Monte Carlo Simulations. ACS Nano 2011, 5, 4145-4157. (51) Misi¯ unas, T.; Tornau, E. E. Ordered Assemblies of Triangular-Shaped Molecules with Strongly Interacting Vertices: Phase Diagrams for Honeycomb and Zigzag Structures on Triangular Lattice. J. Phys. Chem. B 2012, 116, 2472-2482. (52) Ibenskas, A.; Tornau, E. E. Statistical Model for Self-Assembly of Trimesic Acid Molecules into Homologous Series of Flower Phases. Phys. Rev. E 2012, 86, 051118. ˇ enas, M.; Ibenskas, A.; Tornau, E. E. Ordering of Triangular Molecules into the (53) Sim˙ Honeycomb Phase: Estimation of Critical Temperature for Different Lattice Models of Self-Assembly. Phase Transitions 2013, 86, 866-877. (54) Bell, G. M.; Lavis, D. A. Two-Dimensional Bonded Lattice Fluids. II. Orientable Molecule Model. J. Phys. A: Gen. Phys. 1970, 3, 568-581. ˇ enas, M.; Ibenskas, A.; Tornau, E. E. Phase Transition Properties of the Bell-Lavis (55) Sim˙ Model. Phys. Rev. E 2014, 90, 042124. ˇ enas, M.; Ibenskas, A.; Tornau, E. E. Coronene Molecules in Hexagonal Pores of (56) Sim˙ Tricarboxylic Acids: A Monte Carlo Study. J. Phys. Chem. C 2015, 119, 20524-20534. (57) Grimme, S.; Ehrlich, S.; Goerigk, L. Effect of the Damping Function in Dispersion Corrected Density Functional Theory. J. Comput. Chem. 2011, 32, 1456-1465. (58) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys. 2010, 132, 154104. (59) Steiner, C.; Gliemann, B. D.; Meinhardt, U.; Gurrath, M.; Meyer, B.; Kivala, M.;


Page 32 of 34

Page 33 of 34

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Maier, S. Self-Assembly and Stability of Hydrogen-Bonded Networks of Bridged Triphenylamines on Au(111) and Cu(111). J. Phys. Chem. C 2015, 119, 25945-25955. (60) Boys, S. F.; Bernardi, F. The Calculation of Small Molecular Interactions by the Differences of Separate Total Energies. Some Procedures with Reduced Errors. Mol. Phys. 1970, 19, 553-566. (61) Lendvay, G.; Mayer, I. Some Difficulties in Computing BSSE-Corrected Potential Surfaces of Chemical Reactions. Chem. Phys. Lett. 1998, 297, 365-373. (62) MacLeod, J. M.; Ivasenko, O.; Fu, C.; Taerum, T.; Rosei, F.; Perepichka, D. F. Supramolecular Ordering in Oligothiophene-Fullerene Monolayers. J. Am. Chem. Soc. 2009, 131, 16844-16850. (63) MacLeod, J. M.; Chaouch, Z. B.; Perepichka, D. F.; Rosei, F. Two-Dimensional SelfAssembly of a Symmetry-Reduced Tricarboxylic Acid. Langmuir 2013, 29, 7318-7324. (64) Landau, D. P.; Binder, K. A Guide to Monte Carlo Simulations in Statistical Physics, 3rd. Edition; Cambridge Uni. Press: Cambridge, U.K., 2009.



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Table of Contents/Abstract Graphic


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Numerical Engineering of Molecular Self-Assemblies in a Binary

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