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Influence of molecular shape and interaction anisotropy on the self-assembly of tripod building blocks on solid surfaces
Accepted Manuscript Title: Influence of molecular shape and interaction anisotropy on the self-assembly of tripod building blocks on solid surfaces Authors: Paweł Szabelski, Damian Nieckarz, Wojciech R˙zysko PII: DOI: Reference:
S0927-7757(17)30331-X http://dx.doi.org/doi:10.1016/j.colsurfa.2017.04.009 COLSUA 21519
To appear in:
Colloids and Surfaces A: Physicochem. Eng. Aspects
Received date: Accepted date:
24-2-2017 6-4-2017
Please cite this article as: Paweł Szabelski, Damian Nieckarz, Wojciech R˙zysko, Influence of molecular shape and interaction anisotropy on the self-assembly of tripod building blocks on solid surfaces, Colloids and Surfaces A: Physicochemical and Engineering Aspectshttp://dx.doi.org/10.1016/j.colsurfa.2017.04.009 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Influence of molecular shape and interaction anisotropy on the self-assembly of tripod building blocks on solid surfaces Paweł Szabelski*1, Damian Nieckarz2 and Wojciech Rżysko3 1
Department of Theoretical Chemistry and 3Department for the Modeling of Physico-Chemical Processes, Maria-Curie Skłodowska University, Pl. M.C. Skłodowskiej 3, 20-031 Lublin, Poland 2
Supramolecular Chemistry Laboratory, University of Warsaw,
Biological and Chemical Research Centre, Ul. Żwirki i Wigury 101, 02-089 Warsaw, Poland
*Corresponding author
Phone: +48 081 537 56 20 Fax:
+48 081 537 56 85
E-mail: [email protected]
Graphical Abstract
Highlights
Monte Carlo simulations of tripod functional molecules were carried out Different interaction modes and molecular shapes were considered Molecular symmetry determines periodicity and porosity of 2D networks Superstructures with different thermal stability can be designed The proposed approach can help select the optimal building block
Abstract Molecular shape and directionality of intermolecular interactions are important factors which affect structure formation in adsorbed overlayers. In this contribution, using theoretical methods we demonstrate the importance of these factors in the surface-confined self-assembly of tripod-shaped organic molecules with reduced symmetry. To that end a lattice Monte Carlo model is proposed in which the molecules are represented in a coarse grained way, as flat rigid structures comprising a few connected segments adsorbed on a triangular lattice. The calculations are performed for the molecules equipped with terminal active centers providing directional intermolecular interactions. These results are compared with analogous data obtained for C3-symmetric units and Y-shaped molecules whose all composite segments are active. The simulated results show that for the directional interactions, the reduction of molecular symmetry leads to the formation of disordered, glassy, porous networks with hexagonal nanovoids of different shapes. Moreover, it is demonstrated that the interaction mode involving all molecular segments of the asymmetric building blocks is responsible for the formation of compact patterns. Relative thermal stability of the simulated assemblies is also compared, highlighting deciding role of the interaction mode in stabilization of the adsorbed superstructures. The findings of our theoretical investigations can be helpful in designing new molecular blocks and programming their interactions to create 2D molecular superstructures with tunable morphology and functions. Keywords: Adsorption; Self-assembly; Functional molecules; Monte Carlo simulations; Pattern formation
Introduction Functional organic molecules have been long recognized as versatile building blocks for the construction of two-dimensional superstructures adsorbed on solid substrates. These planar superstructures are usually obtained via the controlled on-surface self-assembly of molecular tectons equipped with suitably distributed interaction centers, at the liquid/solid interface as well as in ultra high vacuum (UHV) [1,2]. Among different molecular interactions stabilizing 2D molecular assemblies on graphite and metallic surfaces, hydrogen bonding [3,4], metal-ligand coordination [5,6] and van der Waals interactions [7-9] have been most frequently used in laboratory practice. One objective of such experimental studies is to direct the assembly towards molecular patterns with predefined structural and physico-chemical properties. A telling example are the nanoporous networks which have been the
subject of intense experimental studies over the last decade [10]. The nanoporous networks are extended planar architectures comprising nanosized void spaces having different shapes, for example, hexagonal, square, rectangular, rhombic etc. The unique openwork structure of these molecular constructs make them promising material for selective adsorption of guest molecules which are complementary in shape to the nanopores [11,12]. This sieving effect can be used in (enantio)selective separations, heterogneous catalysis and molecular sensing [13]. Moreover, the regular spatial distribution of the void spaces enables periodic (irreversible) immobilization of foreign matter with specific chemical, physical or biological functions [14]. Functional arrays obtained in this way can serve as future active elements in optoelectronics, magnetic systems and biochemical assays. One central question in the construction of 2D molecular systems on solid supports is how to chose an elementary building block with respect to shape, size and functions, to obtain the superstructure with desired morphology. To date numerous examples of linear and nonlinear functional organic molecules have been proposed, able to self-assembly into porous networks with diverse pore shape and size [10]. In this case, the design rules have been deduced from series of experiments requiring synthesis of candidate building blocks differing in geometry and intermolecular distribution of interaction centers. As the synthesis of new functional units can be tedious and time consuming, an alternative strategy in tailoring of 2D molecular assemblies can be the use of theoretical methods, in particular computer simulations. Computer simulations have been an useful tool in the field of molecular self-assembly, providing quickly-obtainable information on the effect of molecular parameters on the resulting superstructures. This theoretical method has been successfully used to predict structure formation in the overlayers comprising such molecules as, for example, dehydrobenzo[12]annulene derivatives (DBAs)
[15],
trimesic
acid
[16]
and
others
[17,18].
A particularly convenient version of this method are the coarse-grained Monte Carlo simulations in which the molecules and the adsorbing surface are represented in a discretized way. In this simplified
approach, the effect of such intrinsic molecular features as the geometry and directionality of interactions can be studied without going into details at the quantum level. Recent reports comparing the experimental 2D molecular porous patterns with their theoretical counterparts confirm that the lattice MC simulations are a reliable method with high predictive power [15,16,19,20]. In particular, this technique revealed to be able anticipate the existence of new exotic adsorbed superstructures which has been later confirmed experimentally [21]. In most of the experimental and theoretical studies on the self-assembly of nanoporous networks build of star-shaped functional units, C3-symmetric organic molecules such as: DBAs [10,15], polyphenyl structures with terminal carboxylic [16,19,20], pyridyl [3] and cyano groups [22] have been used. However, recently also the tripod molecular building blocks with reduced symmetry have attracted considerable attention, as a new promising candidate for the creation of nanoporous networks on surfaces [7,20,23]. Motivated by the interest in these asymmetric units, in this contribution we examine how the 2D self-assembly of such building blocks is affected by the molecular aspect ratio and nature of interaction centers. To that end we consider simple asymmetric tripod molecules which are equipped with terminal arm interaction centers providing directional interactions. To asses the role of the directional interactions, the obtained results are compared with analogous data corresponding to molecules for which the interactions are assumed to be isotropic. Moreover, the comparison is also made with the C3-symmetric parent molecules, aiming at the identification of the effects induced by molecular shape anisotropy. The main objective of our study is to determine what new structures can be obtained with the asymmetric building blocks and to provide hints on designing tripod molecular units with reduced symmetry, able to create porous patterns with desired morphologies. Another objective of our theoretical investigations is to compare thermal stability of the simulated structures and to identify key molecular parameters which affect this property. The model and simulations To model the 2D self-assembly of asymmetric tripod-shaped molecules we used the coarse grained mapping [3,15] in which these building blocks were represented by collections of segments
arranged in the shapes a and b shown in Fig. 1. The units a and b can be treated as modifications of the parent molecule A, whose one and two arms were elongated by one segment, respectively. The molecule B corresponds to the isotropic scaling of A assuming elongation of each arm by one segment. The building blocks form Fig. 1 were treated as rigid planar structures whose composite segments occupied one adsorption site on a triangular lattice each. The molecules were allowed to interact via attractive short-ranged segmentsegment interaction potential whose range was limited to nearest neighbors on the lattice. To account for the directional nature of the interactions, mimicking for example hydrogen bonding, the molecules were able to interact when the terminal arm segments occupied neighboring adsorption sites and the associated interaction directions were collinear ( , see the red arrows in Fig. 1) [24]. In this case the energy of interaction, was equal to -1. For all of the remaining bimolecular configurations this energy was assumed to be equal to zero. Similarly, the energy of molecule-surface was neglected in the calculations, as the adsorbing surface was assumed to be energetically homogeneous. To asses the effect of molecular shape anisotropy on the structure formation in the considered systems we also performed the simulations for the C3-symmetric molecules A and B. Moreover, to examine how the directionality of interactions affects the self-assembly, comparative calculations assuming isotropic intermolecular interactions were also carried out for a, b, A and B. The term isotropic used here refers to all of the six interaction directions which can be assigned to a molecular segment on a triangular lattice. Accordingly, in the isotropic model all of the composite segments of the building blocks from Fig. 1 were able to interact with neighboring foreign segments, with energy
per interaction. The simulations were performed on a 200 by 200 triangular lattice using the conventional canonical Monte Carlo method with Metropolis sampling. Periodic boundary conditions in both planar directions were imposed to minimize edge effects. In the calculations we used the same algorithm which was described in detail in our previous works [3,15,24]. It’s basic elements can be summarized as follows. In the first step N molecules of a given type were distributed randomly on the
surface constituting the initial configuration. In this step the system temperature, T was fixed. Next, an attempt was made to change the adsorbed configuration by moving a randomly selected molecule to a new position on the lattice. To that end the potential energy of the selected molecule in the actual (old) state, U o was calculated by summing the contributions , depending to the rules assumed in the directional ( ) or in the isotropic (six nearest neighbors) model. The selected molecule was then randomly translated and rotated in plane by a multiple of 60 degrees. If in the new position the insertion of the molecule was possible (appropriately shaped set of unoccupied sites) the potential energy in this new configuration, U n was calculated using the same procedure as for U o ; otherwise the molecule was left in its original position. To accept or reject the new configuration the acceptance probability, p min[1,exp(U / kT )] where U Un Uo and k is the Boltzmann constant, was calculated and compared with uniformly distributed random number r(0,1) . If r p then the new configuration was accepted. In the opposite case the no change was made to the system and the procedure started from the beginning. The above sequence, which constitutes on MC step, was repeated a large number of times, typically 1011, until the system has reached the equilibrium state. To facilitate the equilibration and to minimize the risk of trapping the system in metastable states we used the cooling procedure in which the overlayer was slowly cooled down from the starting temperature 3 Ts 5 to the target value 0.1 within 1000 decrements of equal length. To calculate the associated specific heat capacities, Cv (T ) we used the fluctuation theorem, according to which
Cv ( U U 2 ) / NkT 2 where U stands for the total potential energy of the adsorbed phase and 2
denotes averaging over molecular configurations. All of the simulations described herein were performed for N 1000 molecules (a, b, A, B). This value of N was carefully chosen to allow for unrestricted growth of the associated porous and nonporous superstructures. The obtained results are averages over ten independent system replicas. In the calculations we used reduced units, that is the energies and temperatures in our model are expressed in units of and / k , respectively.
Results and discussion Directional interactions To examine the effect of directional interactions on the 2D pattern formation we first performed the simulations for the smaller asymmetric building block a. Figure 2 presents a representative snapshot obtained for this tecton at T 0.1. As it is seen in the figure, the molecules of a self-assembly into an extended disordered porous network comprising hexagonal void space of different shapes. Among them regular smaller (aI, red) and bigger (aII, blue) hexagons can be indicated, as colored in the magnified fragment of the network. These pores measure 6 and 8 lattice spacing units in diameter (corner-to corner distance), respectively. The smaller pores are built of 6 molecules a which engage their shorter arms to create the pore rim. In the case of the larger regular pores the pore rim consist of both shorter and longer arms, which are arranged alternatingly with two possible rotation directions and thus with different chirality (see adjacent pores aII). Apart from these two types of regular pores also the four irregular structures shown in the right part of Fig. 2 can be found in the network. Regarding the larger tecton b, a similar disordered porous network is formed and it is showed in Fig. 3. Like for the molecule a, the simulated superstructure is continuous, without internal undercoordinated molecules. The regular hexagonal pores which are present in the network can be divided into two types: smaller ones (bI, orange) with diameter equal to 8 and bigger ones (bII, green) with diameter equal to 10 lattice units. Note that the pores aII and bI are identical in shape and size but they differ in the local structure (i.e. remaining molecular arms not engaged in the pore formation, short for a and long for b). Four additional types of regular pores can be indicted, whose examples are shown in the right part of Fig. 3. The presence of two longer arms in the backbone of b is, except for aII and bI, responsible for the formation of larger pores, compared to a. This refers to aI vs. bII and to the irregular pores shown in Figs. 2 and 3. In consequence the network created by b is more extended than this one comprising a.
To compare the simulated networks in a quantitative way, in Fig. 4 we plotted the results of the statistical analysis of the regular hexagonal pore content in the networks a and b. The results shown in the left part show clearly that the average number of the small pores (aI) in the network a is about two times smaller than the number of the larger pores (aII). The opposite situation can be encountered in the case of the second molecule b. Taking into account the fact that the pores aII and bI have identical diameters (8) we may conclude that that the self-assembly of both a and b produces networks with the same number of mid-sized regular hexagonal nanovoids. For the tecton a the additional regular pores (aI) are smaller in diameter while for b they are bigger (aII), occurring twice less frequently. To get deeper insight into the mechanism of the formation of the amorphous networks from Figs. 2 and 3, we calculated the effect of temperature on the connectivity of these structures. The results of the calculations are shown in the right part of Fig.4 and they present the average number of molecules with n 0..3 bonds as a function of the temperature. From the plotted curves it follows that the molecular systems comprising a and b exhibit nearly identical temperature dependence of the structure formation (compare solid and dashed lines). In both cases, at T 0.2 we can observe a rapid increase in the number of molecules with n 3 , being an indication of the network formation in which each molecule engages its three arms. The value ~0.8 that is only slightly lower than 1 obtained at the temperatures close to 0.1 is a natural consequence of the effect associated with the unsaturated peripheral molecules with n 2 (blue curve) which occur then at the amount fraction equal to about 0.2. A detailed analysis of the bonds formed by molecules a and b reveals that these bonds can be divided into three types, that is: short arm-short arm (s-s), long arm-long arm (l-l) and short arm-long arm (s-l). Figure 5 presents the effect of temperature on the number of these bonds calculated for a and b. Even though the average connectivity of a and b changes in the same way with temperature (see Fig. 4), the number of s-s, l-l and s-l occurring in the assemblies comprising a and b is markedly different. This can be seen clearly at low temperatures where for a the bonds s-l and s-s dominate over
the bonds l-l and for b the contributions from s-l and l-l are much larger than from s-s. However, for both molecules the most prevalent are the s-l bonds which stabilize the larger (aII for a) and the smaller (bI for b) regular pores which occur most frequently in the corresponding overlayers. The second dominating effect of the remaining connections s-s (a) and l-l (b) is equally well reflected in the relative abundance of the corresponding pores (see Fig 4). In this case, the regular pores aI and bII whose rims comprise molecular arms of the same length, 1 and 2 segments respectively, are represented less frequently than their counterparts aII and bI with mixed arm composition. the same way with temperature (see Fig. 4), the number of s-s, l-l and s-l occurring in the assemblies comprising a and b is markedly different. This can be seen clearly at low temperatures where for a the bonds s-l and s-s dominate over the bonds l-l and for b the contributions from s-l and l-l are much larger than from s-s. However, for both molecules the most prevalent are the s-l bonds which stabilize the larger (aII for a) and the smaller (bI for b) regular pores which occur most frequently in the corresponding overlayers. The second dominating effect of the remaining connections s-s (a) and l-l (b) is equally well reflected in the relative abundance of the corresponding pores (see Fig 4). In this case, the regular pores aI and bII whose rims comprise molecular arms of the same length, 1 and 2 segments respectively, are represented less frequently than their counterparts aII and bI with mixed arm composition. The results discussed so far indicate that the connectivity of the networks build of the asymmetric molecules differing in the aspect ratio can be described by very similar temperature dependencies. To examine the role of molecular symmetry in the 2D self-assembly we compared selected characteristics calculated for a and b with the analogous data obtained for their C3-symmetric counterparts A and B of which the first was studied in detail our previous works [24]. For comparative purposes, let us start with the snapshots of the networks simulated with the molecules A and B which are shown in Fig. 6.
Contrary to a and b, the networks comprising A and B are fully periodic and they are characterized by the rhombic unit cells with side equal to 3 3 and 5 3 , respectively. The corresponding pore diameter measures 8 for A and 10 for B, and the hexagonal pores observed here are identical in size/shape with aI (A) and bII (B) discussed earlier. The left part of Fig. 7 presents the effect of temperature on the average number of bonds per molecule, calculated for the building blocks a, b, A and B. The results shown in the figure demonstrate that for T 0.3 the steep increases of the curves corresponding to a and b are shifted towards lower temperatures
compared
to
A
and
B.
This
effects
means
that
for
the
C3-symmetric molecules A and B the network formation can be achieved somewhat easier, yet at higher temperatures, around T 0.3 . As for all of the molecules the interaction pattern is identical (directional interactions between terminal arm segments), at sufficiently low temperatures the plotted curves reach a common value close to three (close to full coordination: 3 bonds/molecule) and the observed differences come exclusively from the molecular size/shape effects. In general, for the asymmetric units the increased configurational entropy may lead to the formation of a wide range adsorbed structures which are characterized by higher net potential energy (comprising unsaturated molecules). In consequence, reaching the state in which all of the molecules a and b are fully coordinated requires lower temperatures compared to A and B. This tendency manifests itself also in the associated specific heat curves shown in the right panel of Fig. 7. As it can be expected based on the results from the left panel, the peaks corresponding to a and b are nearly identical in shape with the same position of the maximum on the temperature axis (~0.22). These peaks are shifted towards lower values of T as compared to A and B indicating lower thermal stability of the networks built of the asymmetric molecules a and b. The results of this section show that the molecular symmetry is an important factor which can affect the outcome of the self-assembly of tripod-shaped molecules on solid surfaces, producing either periodic or aperiodic (amorphous) networks. The observed amorphic structures are similar to the
experimental results on the 2D random tiling with tetracarboxylic acids [25] and to the results of the MC simulations performed by Šimėnas et al. for the asymmetric building blocks with intermolecular hydrogen bonds [20]. The MC simulations show that both structural units a and b are capable of forming regular medium-sized hexagonal pores, making both molecules equally applicable for that purpose. The formation of additional regular pores which are smaller or bigger can be controlled by the appropriate, yet simple choice of the building block at play. Regarding thermal stability of the obtained assemblies, the calculations revealed that the networks comprising the asymmetric building blocks a and b are generally less stable than their analogs built of the C3-symmetric molecules A and B.
Isotropic interactions To asses the effect of directionality of intermolecular interactions on the 2D self-assembly in this section we present the results simulated for the molecules whose all segments are allowed to interact along the six directions on a triangular lattice. This type of interaction, even though with discrete directionality, is further called isotropic to highlight the unprivileged role of any interaction direction. The situation considered here can refer to, for example, molecular tripods with arms comprising alkyl chains [7,15] or longer functionalized rod-like fragments [25,26]. Figure 8 presents snapshots of the adsorbed overlayers comprising 1000 molecules of a and b at T 0.1. As it is seen there, both molecules form compact domains when the isotropic interactions are switched on. These structures are characterized by parallelogram 2 19 and rectangular 23 3 unit cells, respectively. In the case of the molecule a there are two alternative packings of the short arms in the molecular rows, as shown in the circular zones highlighted in yellow and green in the left part of Fig. 8. This structural diversity is responsible for the coexistence of neighboring closely packed rows and domains whose local ordering can be described by the rectangular unit cell (arrangement in yellow) and by a parallelogram unit cell (arrangement in yellow); results not shown. In the case of the molecule b
bearing two longer arms the entire domain is fully periodic, indicating the decisive effect of the arm length on the range of ordering in the simulated molecular systems. To examine further how the molecular symmetry influences the pattern formation, in the following we present the results simulated for the symmetric molecules A and B with isotropic interactions. Ordering in 2D assemblies comprising these units were studied in detail in our previous works [15,27] and the results shown below are used for comparative purposes. The snapshots shown in Fig. 9 demonstrate that the smaller building block a self-assemblies into a compact domain whose spatial order can be locally described by the rectangular 2 2 3 unit cell shown in the figure. Like for the tecton a, we can also distinguish two alternative packings of the molecules in neighboring rows (see the highlighted zones), responsible for the reduced range of ordering in the entire domain. The other molecular packing can be described by a rhombic unit cell with side equal to 2 (not shown). The obtained structure can be viewed as a collection of densely packed A-rows running in either the same or in the opposite directions, as shown schematically by the black arrows in Fig. 9. The densely packed overalyer shown in the figure have been experimentally observed for such molecules as naphthalene [28] and pyridine [29] derivatives. Elongation of the molecular arms of A, by one segment, produces the unit B which forms the porous chiral network presented in the left part of Fig. 9. This structure is described by a rhombic unit cell with side equal to
21 and it has unique rotation direction (see the black arrow),
thus it is homochiral. As the self-assembly of B was not biased in the simulations, the final structure had either the rotation direction shown in the figure or the opposite one with 50% chance. Chiral porous networks with identical morphology have been experimentally observed, for example, for DBAs [10,15] and other tripod organic molecules adsorbed on solid supports [22,25,26]. To examine the effect of temperature on the structural properties of the adsorbed overlayers comprising the molecules with isotropic interactions in Fig. 10 we plotted the corresponding average numbers of bonds per molecule as functions of T. In this case, conrary
to the directional interaction mode, the obtained dependencies show clearly that the symmetry of the molecules is not the deciding factor which affects the phase transformation. This is evident when comparing the black and red curves (a, b) which are considerably shifted with respect each other. The sharp increase occurs here at T 1.5 for a and at T 1.8 for b. For the symmetric molecules A and B we can observe only a small relative shift of the corresponding curves (blue, green). One important feature of the curves show in Fig. 10 is that, unlike for the directional mode, these curves do not reach a common value at sufficiently low temperatures. This effect is a direct consequence of the different maximum numbers of bonds which a molecule of each type can create in the corresponding structure shown in Figs. 8 and 9. The observed difference, being proportional to molecular size, has also a significant influence on the transition temperature corresponding to a, b, A and B. To understand the relative vertical position of the low-temperature parts of the curves from the left part of Fig. 10 it is useful to calculate the maximum number of bonds mentioned previously. This quantity is equal to 22 (a), 26 (b), 18 (A) and 21 (B); calculated for the infinite defect-free structures. The obtained values agree perfectly with the data plotted in the figure and they explain the observed sequence of curves. Regarding the position of the steep increases on the obtained curves, this feature is also correlated with the maximum number of bonds and generally the transition temperature in this particular case increases with increasing number of segments in the molecules having the same symmetry. The observed regularity is clear for the molecule (b) with the largest maximal number of bonds (red line) but for the group of the three remaining curves it is less evident. The above conclusions are based on purely energetic arguments which are easy to formulate based on the system parameters. However, entropic effect can also influence the relative position of the curves, especially of these corresponding to the molecules with very similar maximum numbers of bonds (compare for example a and B). The associated thermal stability of the 2D patterns formed by the tripod molecules with isotropic interactions can be read out from the specific heat curves plotted in the right part of Fig. 10. In this case, it is clear that the assemblies built of B are most stable, requiring higher temperatures T 1.8 for breaking them. In the three remaining cases (a, b, A), the peaks are centered at about the same
value of T 1.5 indicating similar thermal stability of the corresponding structures. When comparing these transition temperatures with their counterparts estimated for the directional interaction mode ( T 0.2 0.3 ) we can notice that these values are considerably larger. The increased thermal stability of the structures sustained by the isotropic interactions is a direct consequence of the considerably larger number of intermolecular bonds (18-26 per molecule) compared to the molecules with directional interactions (always 3 per molecule). The simulated results reveal that for the tripod shaped molecules with isotropic interactions molecular size and thus the maximum number of bonds are important factors which affect structure formation and thermal stability. As we found for the four exemplary tectons, the symmetry plays less important role when thermal properties of the assemblies are considered. On the other hand, the molecular geometry affects significantly porosity of the obtained structures. As we found, the presence of one short arm (one-segment long) in the tripod molecule is enough to produce compact overlayers. When two (a) or three (A) arms of this type are present in the tripod, structural diversity is introduced to the resulting compact patterns (see Fig. 8a and 9A) and these 2D constructs are characterized by the reduced range of ordering. This situation changes when the molecule bears at least two longer arms. In this case periodic compact patterns (2 longer arms, b) or hexagonal porous patterns (3 longer arms, B) can be created, depending on the selected building block. In summary, the insights of this part provide information on how long should be the molecular arms compared to the core size (central segment) to obtain two-dimensional architectures with desired morphology. Conclusions The results of this study demonstrate that molecular shape anisotropy plays an important role in the surface-confined assembly of tripod-shaped functional building blocks. The obtained findings highlight the molecular geometry and interaction mode as two intrinsic molecular features which are responsible for the formation of 2D assemblies with largely diversified architectures. In particular, the simulations revealed that breaking the symmetry of the C3 -type molecule A with directional
interactions produces extended porous networks which are nonuniform in terms of pore shape and size. This effect was observed for both asymmetric units a and b differing in the aspect ratio. The calculations performed for the molecules with all active segments (a, b, A) showed that this interaction mode is responsible for the formation of compact assemblies. In this case, in order to create a nanoporous network the tripod molecule has to comprise arms having length greater than one segment (molecule B). This means that to self-assembly a porous network using tripod molecules with several interacting side arm groups, the arms should be in practice considerably longer than the size of the core, at it has been confirmed in many experimental systems. Regarding thermal stability of the simulated structures, we observed that the aperiodic porous networks formed by the asymmetric molecules a and b with directional interactions are more stable than those comprising the C3-symmetric units A and B. For the isotropic interaction mode the molecular symmetry effect was, however, found to be less important and the transition temperature revealed to be more affected by the molecular size, thus by the maximum number of interactions available for a molecule of a given type. Moreover, because of the lower allowed number of interactions stabilizing the networks from Fig. 2,3 and 6 these superstructures were characterized by considerably lower transition temperatures, thus lower thermal stability, compared to the isotropic interaction mode. The theoretical findings reported in this work can be helpful in preliminary screening of molecular libraries to select the optimal building block able to form superstructures with predefined properties. In particular, they show that asymmetric tripod-shaped molecules can be used to build disordered (amorphic) porous networks comprising regular and irregular hexagonal void spaces. These porous matrices can, for example, exhibit adsorptive properties towards a wider class of guest molecules, compared to the honeycomb networks. The general approach proposed here can be easily extended on tripod building blocks with different aspect ratios and differently assigned interaction directions. Self-assembly of such molecules on solid substrates is the subject of our ongoing research.
Acknowledgement This work was supported by the Polish National Science Centre research grant 2015/17/B/ST4/03616.
References
[1] A. Kühnle, Self-assembly of organic molecules at metal surfaces, Curr. Opin. Colloid Interface Sci. 14 (2009) 157-168. [2] S. De Feyter, F.C. De Schryver, Two-dimensional supramolecular self-assembly probed by scanning tunneling microscopy, Chem. Soc. Rev. 32 (2003) 139-150. [3] A. Ciesielski, P. Szabelski, W. Rżysko, A. Cadeddu, T.R. Cook, P.J. Stang, P. Samori, Concentration dependent supramolecular engineering of H-bonded nanostructures at surfaces: predicting self-assembly in 2D, J. Am. Chem. Soc. 135 (2013) 6942-6950. [4] J.A. Theobald, N.S. Oxtoby, M.A. Phillips, N.R. Champness, P.H. Beton, Controlling molecular deposition and layer structure with supramolecular surface assemblies, Nature 424 (2003) 1029-1031.
[5] L. Dong, Z. Gao, N. Lin, Self-assembly of metal-organic coordination structures on surfaces, Prog. Surf. Sci. 91 (2016) 101-135. [6] D. Kühne, F. Klappenberger, R. Decker, U. Schlickum, H. Brune, S. Klyatskaya, M. Ruben, J.V. Barth, High-quality 2D metal-organic coordination network providing giant cavities within mesoscale domains, J. Am. Chem. Soc. 131 (2009) 3881-3883.
[7] J. Adisoejoso, K. Tahara, S. Lei, P. Szabelski, W. Rżysko, K. Inukai, M.O. Blunt, Y. Tobe, S. De Feyter, One building block, two different nanoporous self-assembled monolayers: a combined STM and Monte Carlo study, ACS Nano 6 (2012) 897-903. [8] K. Miyake, Y. Hori, T. Ikeda, M. Asakawa, T. Shimizu, S. Sasaki, Alkyl chain length dependence of the self-organized structure of alkyl-substituted phthalocyanines, Langmuir 24 (2008) 4708-4714. [9] D. Bléger, D. Kreher, F. Mathevet, A.J. Attias, G. Schull, A. Huard, L. Douillard, C. Fiorini-Debuischert, F. Charra, Surface noncovalent bonding for rational design of hierarchical molecular self-assemblies, Angew. Chem. Int. Ed. 46 (2007) 7404-7407.
[10] T. Kudernac, S. Lei, J.A.A.W. Elemans, S. De Feyter Two-dimensional supramolecular self-assembly: nanoporous networks on surfaces, Chem. Soc. Rev. 38 (2009) 402-421. [11] E. Ghijsens, H. Cao, A. Noguchi, O. Ivasenko, Y. Fang, K. Tahara, Y. Tobe, S. De Feyter, Towards enantioselective adsorption in surface-confined nanoporous systems, Chem. Commun. 51 (2015) 4766-4769. [12] H. Bertrand, F. Silly, M.P. Teulade-Fichou, L. Tortech, D. Fichou, Locking the free-rotation of a prochiral star-shaped guest molecule inside a two-dimensional nanoporous network by introduction of chlorine atoms, Chem. Commun. 47 (2011) 1009110093.
[13] X. Zhang, Y. Shen, S. Wang, Y. Guo, K. Deng, C. Wang, Q. Zeng, One plus two: supramolecular coordination in a nano-reactor on surface, Sci Rep. 2 (2012) 742. [14] J. Teyssandier, S. De Feyter, K.S. Mali, Host-guest chemistry in two-dimensional supramolecular networks, Chem. Commun. 52 (2016) 11465-11487. [15] P. Szabelski, S. De Feyter, M. Drach, S. Lei, Computer simulation of chiral nanoporous networks on solid surfaces, Langmuir 26 (2010) 9506-9515. [16] T. Misiūnas, E.E. Tornau, Ordered assemblies of triangular-shaped molecules with strongly interacting vertices: phase diagrams for honeycomb and zigzag structures on triangular lattice, J. Phys. Chem. B 116 (2012) 2472-2482. [17] M. El Garah, A. Dianat, A. Cadeddu, R. Gutierrez, M. Cecchini, T.R. Cook, A. Ciesielski, P.J. Stang, G. Cuniberti, P. Samorì, Atomically precise prediction of 2D self-assembly of weakly bonded nanostructures: STM insight into concentrationdependent architectures, Small 12 (2016) 343-350. [18] C.A. Palma, P. Samorì, M. Cecchini, Atomistic simulations of 2D bicomponent selfassembly: from molecular recognition to self-healing, J. Am. Chem. Soc. 132 (2010) 17880-17885. [19] A. Ibenskas, E.E. Tornau, Statistical model for self-assembly of trimesic acid molecules into homologous series of flower phases, Phys. Rev. E 86 (2012) 51118-51130. [20] M. Šimėnas, A. Ibenskas, E.E. Tornau, Coronene molecules in hexagonal pores of tricarboxylic acids: a Monte Carlo study, J. Phys. Chem. C 119 (2015) 20524-20534 [21] D. Nieckarz, P. Szabelski, Simulation of the self-assembly of simple molecular bricks into Sierpiński triangles, Chem. Commun. 50 (2014) 6843-6845.
[22] G. Copie, F. Cleri, Y. Makoudi, C. Krzeminski, M. Berthe, F. Cherioux, F. Palmino, B. Grandidier, Surface-induced optimal packing of two-dimensional molecular networks, Phys. Rev. Lett. 114 (2015) 66101-66106. [23] R.A. Barnard, A. Dutta, J.K. Schnobrich, C.N. Morrison, S. Ahn, A.J. Matzger, Two-dimensional crystals from reduced symmetry analogues of trimesic acid, Chem. Eur. J. 21 (2015) 5954-5961. [24] P. Szabelski, W. Rżysko, D. Nieckarz, Directing the self-assembly of tripod molecules on solid surfaces: a Monte Carlo simulation approach, J. Phys. Chem. C 120 (2016) 13139-13147. [25] Z. Mu, L. Shu, H. Fuchs, M. Mayor, L. Chi, Two-dimensional chiral networks emerging from the aryl-F···H hydrogen-bond-driven self-assembly of partially fluorinated rigid molecular structures, J. Am. Chem. Soc. 130 (2008) 10840-10841. [26] B. Liu, Y.F. Ran, Z. Li, S.X. Liu, C. Jia, S. Decurtins, T. Wandlowski, A Scanning Probe Microscopy study of annulated redox-active molecules at a liquid/solid interface: the overruling of the alkyl
chain
paradigm,
Chem.
Eur.
J.
16
(2010)
5008-5012. [27] P. Szabelski, W. Rżysko, T. Pańczyk, E. Ghijsens, K. Tahara, Y. Tobe, S. De Feyter, Self-assembly of molecular tripods in two dimensions: structure and thermodynamics from computer simulations, RSC Adv. 3 (2013), 25159-25165. [28] S.D. Ha, B.R. Kaafarani, S. Barlow, S.R. Marder, A. Kahn, Multiphase growth and electronic structure of ultrathin hexaazatrinaphtylene on Au(111), J. Phys. Chem. C 111 (2007) 1049310497. [29] D. Trawny, P. Schlexer, K. Steenbergen, J.P. Rabe, B. Paulus, H.U. Reissig, Dense or porous packing? Two-dimensional self-assembly of star-shaped mono-, bi-, and terpyridine derivatives, ChemPhysChem 16 (2015) 949-953.
Figure 1. Model tripod-shaped molecules used in the simulations, adsorbed on a triangular lattice. The structures a, b and B can be viewed as modifications of the parent molecule A, obtained by elongation of one, two and three arms of A by one segment, respectively. The red arrows next to b show the interaction directions assumed in the calculations for all of the molecules from the figure.
Figure 2. Snapshot of the adsorbed overlayer comprising 1000 molecules a with directional interactions; T 0.1 (left). Magnified fragment of the obtained network with small (aI) and big (aII) regular hexagonal pores marked in red and blue, respectively and examples of other six-membered irregular pores found in the network (right).
Figure 3. Snapshot of the adsorbed overlayer comprising 1000 molecules b with directional interactions; T 0.1 (left). Magnified fragment of the obtained network with small (bI) and big (bII) regular hexagonal pores marked in green and orange, respectively and examples of other sixmembered irregular pores found in the network (right).
Figure 4. Average number of the regular hexagonal pores in the networks comprising 1000 molecules a and b with directional interactions; T 0.1 (left). The same color code for the different pore types is used as in Fig. Z. (left) Effect of temperature on the amount fraction of the molecules a (solid lines) and b (dashed lines) with n 0..3 bonds in the corresponding overlayers containing 1000 molecules.
Figure 5. Effect of temperature on the average number of bonds of type: short-short (s-s), long-long (ll) and short-long (s-l), calculated for 1000 molecules a and b with directional interactions. The symbols s and l indicate which molecular arm of a and b (short or long) takes part in the bonding.
Figure 6. Snapshot of the adsorbed overlayer comprising 1000 molecules A and B with directional interactions; T 0.1. Magnified fragments of the obtained networks with the corresponding rhombic unit cells (red lines) are shown in the insets.
Figure 7. Effect of temperature on the average number of bonds per molecule calculated for 1000 molecules a, b, A and B with directional interactions; T 0.1 (left). Specific heat capacity curves calculated for these molecular systems (right).
Figure 8. Snapshot of the adsorbed overlayer comprising 1000 molecules a and b with isotropic interactions; T 0.1. Magnified fragments of the obtained structures with the corresponding rectangular unit cells (red lines) are shown in the insets. The circular zones highlighted in green and yellow present two alternative packings of the short arms of a in the molecular rows.
Figure 9. Snapshot of the adsorbed overlayer comprising 1000 molecules A and B with isotropic interactions; T 0.1. Magnified fragments of the obtained structures with the corresponding unit cells (red lines) are shown in the insets. The circular zones highlighted in green and yellow present two alternative packings of the short arms of A in the molecular rows. The black arrows in the insets indicate the propagation directions of the one-molecule wide rows formed by A and the rotation direction of the homochiral porous network built of B.
Figure 10. Effect of temperature on the average number of bonds per molecule calculated for 1000 molecules a, b, A and B with directional interactions; T 0.1 (left). Specific heat capacity curves calculated for these molecular systems (right).
S0927-7757(17)30331-X http://dx.doi.org/doi:10.1016/j.colsurfa.2017.04.009 COLSUA 21519
To appear in:
Colloids and Surfaces A: Physicochem. Eng. Aspects
Received date: Accepted date:
24-2-2017 6-4-2017
Please cite this article as: Paweł Szabelski, Damian Nieckarz, Wojciech R˙zysko, Influence of molecular shape and interaction anisotropy on the self-assembly of tripod building blocks on solid surfaces, Colloids and Surfaces A: Physicochemical and Engineering Aspectshttp://dx.doi.org/10.1016/j.colsurfa.2017.04.009 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Influence of molecular shape and interaction anisotropy on the self-assembly of tripod building blocks on solid surfaces Paweł Szabelski*1, Damian Nieckarz2 and Wojciech Rżysko3 1
Department of Theoretical Chemistry and 3Department for the Modeling of Physico-Chemical Processes, Maria-Curie Skłodowska University, Pl. M.C. Skłodowskiej 3, 20-031 Lublin, Poland 2
Supramolecular Chemistry Laboratory, University of Warsaw,
Biological and Chemical Research Centre, Ul. Żwirki i Wigury 101, 02-089 Warsaw, Poland
*Corresponding author
Phone: +48 081 537 56 20 Fax:
+48 081 537 56 85
E-mail: [email protected]
Graphical Abstract
Highlights
Monte Carlo simulations of tripod functional molecules were carried out Different interaction modes and molecular shapes were considered Molecular symmetry determines periodicity and porosity of 2D networks Superstructures with different thermal stability can be designed The proposed approach can help select the optimal building block
Abstract Molecular shape and directionality of intermolecular interactions are important factors which affect structure formation in adsorbed overlayers. In this contribution, using theoretical methods we demonstrate the importance of these factors in the surface-confined self-assembly of tripod-shaped organic molecules with reduced symmetry. To that end a lattice Monte Carlo model is proposed in which the molecules are represented in a coarse grained way, as flat rigid structures comprising a few connected segments adsorbed on a triangular lattice. The calculations are performed for the molecules equipped with terminal active centers providing directional intermolecular interactions. These results are compared with analogous data obtained for C3-symmetric units and Y-shaped molecules whose all composite segments are active. The simulated results show that for the directional interactions, the reduction of molecular symmetry leads to the formation of disordered, glassy, porous networks with hexagonal nanovoids of different shapes. Moreover, it is demonstrated that the interaction mode involving all molecular segments of the asymmetric building blocks is responsible for the formation of compact patterns. Relative thermal stability of the simulated assemblies is also compared, highlighting deciding role of the interaction mode in stabilization of the adsorbed superstructures. The findings of our theoretical investigations can be helpful in designing new molecular blocks and programming their interactions to create 2D molecular superstructures with tunable morphology and functions. Keywords: Adsorption; Self-assembly; Functional molecules; Monte Carlo simulations; Pattern formation
Introduction Functional organic molecules have been long recognized as versatile building blocks for the construction of two-dimensional superstructures adsorbed on solid substrates. These planar superstructures are usually obtained via the controlled on-surface self-assembly of molecular tectons equipped with suitably distributed interaction centers, at the liquid/solid interface as well as in ultra high vacuum (UHV) [1,2]. Among different molecular interactions stabilizing 2D molecular assemblies on graphite and metallic surfaces, hydrogen bonding [3,4], metal-ligand coordination [5,6] and van der Waals interactions [7-9] have been most frequently used in laboratory practice. One objective of such experimental studies is to direct the assembly towards molecular patterns with predefined structural and physico-chemical properties. A telling example are the nanoporous networks which have been the
subject of intense experimental studies over the last decade [10]. The nanoporous networks are extended planar architectures comprising nanosized void spaces having different shapes, for example, hexagonal, square, rectangular, rhombic etc. The unique openwork structure of these molecular constructs make them promising material for selective adsorption of guest molecules which are complementary in shape to the nanopores [11,12]. This sieving effect can be used in (enantio)selective separations, heterogneous catalysis and molecular sensing [13]. Moreover, the regular spatial distribution of the void spaces enables periodic (irreversible) immobilization of foreign matter with specific chemical, physical or biological functions [14]. Functional arrays obtained in this way can serve as future active elements in optoelectronics, magnetic systems and biochemical assays. One central question in the construction of 2D molecular systems on solid supports is how to chose an elementary building block with respect to shape, size and functions, to obtain the superstructure with desired morphology. To date numerous examples of linear and nonlinear functional organic molecules have been proposed, able to self-assembly into porous networks with diverse pore shape and size [10]. In this case, the design rules have been deduced from series of experiments requiring synthesis of candidate building blocks differing in geometry and intermolecular distribution of interaction centers. As the synthesis of new functional units can be tedious and time consuming, an alternative strategy in tailoring of 2D molecular assemblies can be the use of theoretical methods, in particular computer simulations. Computer simulations have been an useful tool in the field of molecular self-assembly, providing quickly-obtainable information on the effect of molecular parameters on the resulting superstructures. This theoretical method has been successfully used to predict structure formation in the overlayers comprising such molecules as, for example, dehydrobenzo[12]annulene derivatives (DBAs)
[15],
trimesic
acid
[16]
and
others
[17,18].
A particularly convenient version of this method are the coarse-grained Monte Carlo simulations in which the molecules and the adsorbing surface are represented in a discretized way. In this simplified
approach, the effect of such intrinsic molecular features as the geometry and directionality of interactions can be studied without going into details at the quantum level. Recent reports comparing the experimental 2D molecular porous patterns with their theoretical counterparts confirm that the lattice MC simulations are a reliable method with high predictive power [15,16,19,20]. In particular, this technique revealed to be able anticipate the existence of new exotic adsorbed superstructures which has been later confirmed experimentally [21]. In most of the experimental and theoretical studies on the self-assembly of nanoporous networks build of star-shaped functional units, C3-symmetric organic molecules such as: DBAs [10,15], polyphenyl structures with terminal carboxylic [16,19,20], pyridyl [3] and cyano groups [22] have been used. However, recently also the tripod molecular building blocks with reduced symmetry have attracted considerable attention, as a new promising candidate for the creation of nanoporous networks on surfaces [7,20,23]. Motivated by the interest in these asymmetric units, in this contribution we examine how the 2D self-assembly of such building blocks is affected by the molecular aspect ratio and nature of interaction centers. To that end we consider simple asymmetric tripod molecules which are equipped with terminal arm interaction centers providing directional interactions. To asses the role of the directional interactions, the obtained results are compared with analogous data corresponding to molecules for which the interactions are assumed to be isotropic. Moreover, the comparison is also made with the C3-symmetric parent molecules, aiming at the identification of the effects induced by molecular shape anisotropy. The main objective of our study is to determine what new structures can be obtained with the asymmetric building blocks and to provide hints on designing tripod molecular units with reduced symmetry, able to create porous patterns with desired morphologies. Another objective of our theoretical investigations is to compare thermal stability of the simulated structures and to identify key molecular parameters which affect this property. The model and simulations To model the 2D self-assembly of asymmetric tripod-shaped molecules we used the coarse grained mapping [3,15] in which these building blocks were represented by collections of segments
arranged in the shapes a and b shown in Fig. 1. The units a and b can be treated as modifications of the parent molecule A, whose one and two arms were elongated by one segment, respectively. The molecule B corresponds to the isotropic scaling of A assuming elongation of each arm by one segment. The building blocks form Fig. 1 were treated as rigid planar structures whose composite segments occupied one adsorption site on a triangular lattice each. The molecules were allowed to interact via attractive short-ranged segmentsegment interaction potential whose range was limited to nearest neighbors on the lattice. To account for the directional nature of the interactions, mimicking for example hydrogen bonding, the molecules were able to interact when the terminal arm segments occupied neighboring adsorption sites and the associated interaction directions were collinear ( , see the red arrows in Fig. 1) [24]. In this case the energy of interaction, was equal to -1. For all of the remaining bimolecular configurations this energy was assumed to be equal to zero. Similarly, the energy of molecule-surface was neglected in the calculations, as the adsorbing surface was assumed to be energetically homogeneous. To asses the effect of molecular shape anisotropy on the structure formation in the considered systems we also performed the simulations for the C3-symmetric molecules A and B. Moreover, to examine how the directionality of interactions affects the self-assembly, comparative calculations assuming isotropic intermolecular interactions were also carried out for a, b, A and B. The term isotropic used here refers to all of the six interaction directions which can be assigned to a molecular segment on a triangular lattice. Accordingly, in the isotropic model all of the composite segments of the building blocks from Fig. 1 were able to interact with neighboring foreign segments, with energy
per interaction. The simulations were performed on a 200 by 200 triangular lattice using the conventional canonical Monte Carlo method with Metropolis sampling. Periodic boundary conditions in both planar directions were imposed to minimize edge effects. In the calculations we used the same algorithm which was described in detail in our previous works [3,15,24]. It’s basic elements can be summarized as follows. In the first step N molecules of a given type were distributed randomly on the
surface constituting the initial configuration. In this step the system temperature, T was fixed. Next, an attempt was made to change the adsorbed configuration by moving a randomly selected molecule to a new position on the lattice. To that end the potential energy of the selected molecule in the actual (old) state, U o was calculated by summing the contributions , depending to the rules assumed in the directional ( ) or in the isotropic (six nearest neighbors) model. The selected molecule was then randomly translated and rotated in plane by a multiple of 60 degrees. If in the new position the insertion of the molecule was possible (appropriately shaped set of unoccupied sites) the potential energy in this new configuration, U n was calculated using the same procedure as for U o ; otherwise the molecule was left in its original position. To accept or reject the new configuration the acceptance probability, p min[1,exp(U / kT )] where U Un Uo and k is the Boltzmann constant, was calculated and compared with uniformly distributed random number r(0,1) . If r p then the new configuration was accepted. In the opposite case the no change was made to the system and the procedure started from the beginning. The above sequence, which constitutes on MC step, was repeated a large number of times, typically 1011, until the system has reached the equilibrium state. To facilitate the equilibration and to minimize the risk of trapping the system in metastable states we used the cooling procedure in which the overlayer was slowly cooled down from the starting temperature 3 Ts 5 to the target value 0.1 within 1000 decrements of equal length. To calculate the associated specific heat capacities, Cv (T ) we used the fluctuation theorem, according to which
Cv ( U U 2 ) / NkT 2 where U stands for the total potential energy of the adsorbed phase and 2
denotes averaging over molecular configurations. All of the simulations described herein were performed for N 1000 molecules (a, b, A, B). This value of N was carefully chosen to allow for unrestricted growth of the associated porous and nonporous superstructures. The obtained results are averages over ten independent system replicas. In the calculations we used reduced units, that is the energies and temperatures in our model are expressed in units of and / k , respectively.
Results and discussion Directional interactions To examine the effect of directional interactions on the 2D pattern formation we first performed the simulations for the smaller asymmetric building block a. Figure 2 presents a representative snapshot obtained for this tecton at T 0.1. As it is seen in the figure, the molecules of a self-assembly into an extended disordered porous network comprising hexagonal void space of different shapes. Among them regular smaller (aI, red) and bigger (aII, blue) hexagons can be indicated, as colored in the magnified fragment of the network. These pores measure 6 and 8 lattice spacing units in diameter (corner-to corner distance), respectively. The smaller pores are built of 6 molecules a which engage their shorter arms to create the pore rim. In the case of the larger regular pores the pore rim consist of both shorter and longer arms, which are arranged alternatingly with two possible rotation directions and thus with different chirality (see adjacent pores aII). Apart from these two types of regular pores also the four irregular structures shown in the right part of Fig. 2 can be found in the network. Regarding the larger tecton b, a similar disordered porous network is formed and it is showed in Fig. 3. Like for the molecule a, the simulated superstructure is continuous, without internal undercoordinated molecules. The regular hexagonal pores which are present in the network can be divided into two types: smaller ones (bI, orange) with diameter equal to 8 and bigger ones (bII, green) with diameter equal to 10 lattice units. Note that the pores aII and bI are identical in shape and size but they differ in the local structure (i.e. remaining molecular arms not engaged in the pore formation, short for a and long for b). Four additional types of regular pores can be indicted, whose examples are shown in the right part of Fig. 3. The presence of two longer arms in the backbone of b is, except for aII and bI, responsible for the formation of larger pores, compared to a. This refers to aI vs. bII and to the irregular pores shown in Figs. 2 and 3. In consequence the network created by b is more extended than this one comprising a.
To compare the simulated networks in a quantitative way, in Fig. 4 we plotted the results of the statistical analysis of the regular hexagonal pore content in the networks a and b. The results shown in the left part show clearly that the average number of the small pores (aI) in the network a is about two times smaller than the number of the larger pores (aII). The opposite situation can be encountered in the case of the second molecule b. Taking into account the fact that the pores aII and bI have identical diameters (8) we may conclude that that the self-assembly of both a and b produces networks with the same number of mid-sized regular hexagonal nanovoids. For the tecton a the additional regular pores (aI) are smaller in diameter while for b they are bigger (aII), occurring twice less frequently. To get deeper insight into the mechanism of the formation of the amorphous networks from Figs. 2 and 3, we calculated the effect of temperature on the connectivity of these structures. The results of the calculations are shown in the right part of Fig.4 and they present the average number of molecules with n 0..3 bonds as a function of the temperature. From the plotted curves it follows that the molecular systems comprising a and b exhibit nearly identical temperature dependence of the structure formation (compare solid and dashed lines). In both cases, at T 0.2 we can observe a rapid increase in the number of molecules with n 3 , being an indication of the network formation in which each molecule engages its three arms. The value ~0.8 that is only slightly lower than 1 obtained at the temperatures close to 0.1 is a natural consequence of the effect associated with the unsaturated peripheral molecules with n 2 (blue curve) which occur then at the amount fraction equal to about 0.2. A detailed analysis of the bonds formed by molecules a and b reveals that these bonds can be divided into three types, that is: short arm-short arm (s-s), long arm-long arm (l-l) and short arm-long arm (s-l). Figure 5 presents the effect of temperature on the number of these bonds calculated for a and b. Even though the average connectivity of a and b changes in the same way with temperature (see Fig. 4), the number of s-s, l-l and s-l occurring in the assemblies comprising a and b is markedly different. This can be seen clearly at low temperatures where for a the bonds s-l and s-s dominate over
the bonds l-l and for b the contributions from s-l and l-l are much larger than from s-s. However, for both molecules the most prevalent are the s-l bonds which stabilize the larger (aII for a) and the smaller (bI for b) regular pores which occur most frequently in the corresponding overlayers. The second dominating effect of the remaining connections s-s (a) and l-l (b) is equally well reflected in the relative abundance of the corresponding pores (see Fig 4). In this case, the regular pores aI and bII whose rims comprise molecular arms of the same length, 1 and 2 segments respectively, are represented less frequently than their counterparts aII and bI with mixed arm composition. the same way with temperature (see Fig. 4), the number of s-s, l-l and s-l occurring in the assemblies comprising a and b is markedly different. This can be seen clearly at low temperatures where for a the bonds s-l and s-s dominate over the bonds l-l and for b the contributions from s-l and l-l are much larger than from s-s. However, for both molecules the most prevalent are the s-l bonds which stabilize the larger (aII for a) and the smaller (bI for b) regular pores which occur most frequently in the corresponding overlayers. The second dominating effect of the remaining connections s-s (a) and l-l (b) is equally well reflected in the relative abundance of the corresponding pores (see Fig 4). In this case, the regular pores aI and bII whose rims comprise molecular arms of the same length, 1 and 2 segments respectively, are represented less frequently than their counterparts aII and bI with mixed arm composition. The results discussed so far indicate that the connectivity of the networks build of the asymmetric molecules differing in the aspect ratio can be described by very similar temperature dependencies. To examine the role of molecular symmetry in the 2D self-assembly we compared selected characteristics calculated for a and b with the analogous data obtained for their C3-symmetric counterparts A and B of which the first was studied in detail our previous works [24]. For comparative purposes, let us start with the snapshots of the networks simulated with the molecules A and B which are shown in Fig. 6.
Contrary to a and b, the networks comprising A and B are fully periodic and they are characterized by the rhombic unit cells with side equal to 3 3 and 5 3 , respectively. The corresponding pore diameter measures 8 for A and 10 for B, and the hexagonal pores observed here are identical in size/shape with aI (A) and bII (B) discussed earlier. The left part of Fig. 7 presents the effect of temperature on the average number of bonds per molecule, calculated for the building blocks a, b, A and B. The results shown in the figure demonstrate that for T 0.3 the steep increases of the curves corresponding to a and b are shifted towards lower temperatures
compared
to
A
and
B.
This
effects
means
that
for
the
C3-symmetric molecules A and B the network formation can be achieved somewhat easier, yet at higher temperatures, around T 0.3 . As for all of the molecules the interaction pattern is identical (directional interactions between terminal arm segments), at sufficiently low temperatures the plotted curves reach a common value close to three (close to full coordination: 3 bonds/molecule) and the observed differences come exclusively from the molecular size/shape effects. In general, for the asymmetric units the increased configurational entropy may lead to the formation of a wide range adsorbed structures which are characterized by higher net potential energy (comprising unsaturated molecules). In consequence, reaching the state in which all of the molecules a and b are fully coordinated requires lower temperatures compared to A and B. This tendency manifests itself also in the associated specific heat curves shown in the right panel of Fig. 7. As it can be expected based on the results from the left panel, the peaks corresponding to a and b are nearly identical in shape with the same position of the maximum on the temperature axis (~0.22). These peaks are shifted towards lower values of T as compared to A and B indicating lower thermal stability of the networks built of the asymmetric molecules a and b. The results of this section show that the molecular symmetry is an important factor which can affect the outcome of the self-assembly of tripod-shaped molecules on solid surfaces, producing either periodic or aperiodic (amorphous) networks. The observed amorphic structures are similar to the
experimental results on the 2D random tiling with tetracarboxylic acids [25] and to the results of the MC simulations performed by Šimėnas et al. for the asymmetric building blocks with intermolecular hydrogen bonds [20]. The MC simulations show that both structural units a and b are capable of forming regular medium-sized hexagonal pores, making both molecules equally applicable for that purpose. The formation of additional regular pores which are smaller or bigger can be controlled by the appropriate, yet simple choice of the building block at play. Regarding thermal stability of the obtained assemblies, the calculations revealed that the networks comprising the asymmetric building blocks a and b are generally less stable than their analogs built of the C3-symmetric molecules A and B.
Isotropic interactions To asses the effect of directionality of intermolecular interactions on the 2D self-assembly in this section we present the results simulated for the molecules whose all segments are allowed to interact along the six directions on a triangular lattice. This type of interaction, even though with discrete directionality, is further called isotropic to highlight the unprivileged role of any interaction direction. The situation considered here can refer to, for example, molecular tripods with arms comprising alkyl chains [7,15] or longer functionalized rod-like fragments [25,26]. Figure 8 presents snapshots of the adsorbed overlayers comprising 1000 molecules of a and b at T 0.1. As it is seen there, both molecules form compact domains when the isotropic interactions are switched on. These structures are characterized by parallelogram 2 19 and rectangular 23 3 unit cells, respectively. In the case of the molecule a there are two alternative packings of the short arms in the molecular rows, as shown in the circular zones highlighted in yellow and green in the left part of Fig. 8. This structural diversity is responsible for the coexistence of neighboring closely packed rows and domains whose local ordering can be described by the rectangular unit cell (arrangement in yellow) and by a parallelogram unit cell (arrangement in yellow); results not shown. In the case of the molecule b
bearing two longer arms the entire domain is fully periodic, indicating the decisive effect of the arm length on the range of ordering in the simulated molecular systems. To examine further how the molecular symmetry influences the pattern formation, in the following we present the results simulated for the symmetric molecules A and B with isotropic interactions. Ordering in 2D assemblies comprising these units were studied in detail in our previous works [15,27] and the results shown below are used for comparative purposes. The snapshots shown in Fig. 9 demonstrate that the smaller building block a self-assemblies into a compact domain whose spatial order can be locally described by the rectangular 2 2 3 unit cell shown in the figure. Like for the tecton a, we can also distinguish two alternative packings of the molecules in neighboring rows (see the highlighted zones), responsible for the reduced range of ordering in the entire domain. The other molecular packing can be described by a rhombic unit cell with side equal to 2 (not shown). The obtained structure can be viewed as a collection of densely packed A-rows running in either the same or in the opposite directions, as shown schematically by the black arrows in Fig. 9. The densely packed overalyer shown in the figure have been experimentally observed for such molecules as naphthalene [28] and pyridine [29] derivatives. Elongation of the molecular arms of A, by one segment, produces the unit B which forms the porous chiral network presented in the left part of Fig. 9. This structure is described by a rhombic unit cell with side equal to
21 and it has unique rotation direction (see the black arrow),
thus it is homochiral. As the self-assembly of B was not biased in the simulations, the final structure had either the rotation direction shown in the figure or the opposite one with 50% chance. Chiral porous networks with identical morphology have been experimentally observed, for example, for DBAs [10,15] and other tripod organic molecules adsorbed on solid supports [22,25,26]. To examine the effect of temperature on the structural properties of the adsorbed overlayers comprising the molecules with isotropic interactions in Fig. 10 we plotted the corresponding average numbers of bonds per molecule as functions of T. In this case, conrary
to the directional interaction mode, the obtained dependencies show clearly that the symmetry of the molecules is not the deciding factor which affects the phase transformation. This is evident when comparing the black and red curves (a, b) which are considerably shifted with respect each other. The sharp increase occurs here at T 1.5 for a and at T 1.8 for b. For the symmetric molecules A and B we can observe only a small relative shift of the corresponding curves (blue, green). One important feature of the curves show in Fig. 10 is that, unlike for the directional mode, these curves do not reach a common value at sufficiently low temperatures. This effect is a direct consequence of the different maximum numbers of bonds which a molecule of each type can create in the corresponding structure shown in Figs. 8 and 9. The observed difference, being proportional to molecular size, has also a significant influence on the transition temperature corresponding to a, b, A and B. To understand the relative vertical position of the low-temperature parts of the curves from the left part of Fig. 10 it is useful to calculate the maximum number of bonds mentioned previously. This quantity is equal to 22 (a), 26 (b), 18 (A) and 21 (B); calculated for the infinite defect-free structures. The obtained values agree perfectly with the data plotted in the figure and they explain the observed sequence of curves. Regarding the position of the steep increases on the obtained curves, this feature is also correlated with the maximum number of bonds and generally the transition temperature in this particular case increases with increasing number of segments in the molecules having the same symmetry. The observed regularity is clear for the molecule (b) with the largest maximal number of bonds (red line) but for the group of the three remaining curves it is less evident. The above conclusions are based on purely energetic arguments which are easy to formulate based on the system parameters. However, entropic effect can also influence the relative position of the curves, especially of these corresponding to the molecules with very similar maximum numbers of bonds (compare for example a and B). The associated thermal stability of the 2D patterns formed by the tripod molecules with isotropic interactions can be read out from the specific heat curves plotted in the right part of Fig. 10. In this case, it is clear that the assemblies built of B are most stable, requiring higher temperatures T 1.8 for breaking them. In the three remaining cases (a, b, A), the peaks are centered at about the same
value of T 1.5 indicating similar thermal stability of the corresponding structures. When comparing these transition temperatures with their counterparts estimated for the directional interaction mode ( T 0.2 0.3 ) we can notice that these values are considerably larger. The increased thermal stability of the structures sustained by the isotropic interactions is a direct consequence of the considerably larger number of intermolecular bonds (18-26 per molecule) compared to the molecules with directional interactions (always 3 per molecule). The simulated results reveal that for the tripod shaped molecules with isotropic interactions molecular size and thus the maximum number of bonds are important factors which affect structure formation and thermal stability. As we found for the four exemplary tectons, the symmetry plays less important role when thermal properties of the assemblies are considered. On the other hand, the molecular geometry affects significantly porosity of the obtained structures. As we found, the presence of one short arm (one-segment long) in the tripod molecule is enough to produce compact overlayers. When two (a) or three (A) arms of this type are present in the tripod, structural diversity is introduced to the resulting compact patterns (see Fig. 8a and 9A) and these 2D constructs are characterized by the reduced range of ordering. This situation changes when the molecule bears at least two longer arms. In this case periodic compact patterns (2 longer arms, b) or hexagonal porous patterns (3 longer arms, B) can be created, depending on the selected building block. In summary, the insights of this part provide information on how long should be the molecular arms compared to the core size (central segment) to obtain two-dimensional architectures with desired morphology. Conclusions The results of this study demonstrate that molecular shape anisotropy plays an important role in the surface-confined assembly of tripod-shaped functional building blocks. The obtained findings highlight the molecular geometry and interaction mode as two intrinsic molecular features which are responsible for the formation of 2D assemblies with largely diversified architectures. In particular, the simulations revealed that breaking the symmetry of the C3 -type molecule A with directional
interactions produces extended porous networks which are nonuniform in terms of pore shape and size. This effect was observed for both asymmetric units a and b differing in the aspect ratio. The calculations performed for the molecules with all active segments (a, b, A) showed that this interaction mode is responsible for the formation of compact assemblies. In this case, in order to create a nanoporous network the tripod molecule has to comprise arms having length greater than one segment (molecule B). This means that to self-assembly a porous network using tripod molecules with several interacting side arm groups, the arms should be in practice considerably longer than the size of the core, at it has been confirmed in many experimental systems. Regarding thermal stability of the simulated structures, we observed that the aperiodic porous networks formed by the asymmetric molecules a and b with directional interactions are more stable than those comprising the C3-symmetric units A and B. For the isotropic interaction mode the molecular symmetry effect was, however, found to be less important and the transition temperature revealed to be more affected by the molecular size, thus by the maximum number of interactions available for a molecule of a given type. Moreover, because of the lower allowed number of interactions stabilizing the networks from Fig. 2,3 and 6 these superstructures were characterized by considerably lower transition temperatures, thus lower thermal stability, compared to the isotropic interaction mode. The theoretical findings reported in this work can be helpful in preliminary screening of molecular libraries to select the optimal building block able to form superstructures with predefined properties. In particular, they show that asymmetric tripod-shaped molecules can be used to build disordered (amorphic) porous networks comprising regular and irregular hexagonal void spaces. These porous matrices can, for example, exhibit adsorptive properties towards a wider class of guest molecules, compared to the honeycomb networks. The general approach proposed here can be easily extended on tripod building blocks with different aspect ratios and differently assigned interaction directions. Self-assembly of such molecules on solid substrates is the subject of our ongoing research.
Acknowledgement This work was supported by the Polish National Science Centre research grant 2015/17/B/ST4/03616.
References
[1] A. Kühnle, Self-assembly of organic molecules at metal surfaces, Curr. Opin. Colloid Interface Sci. 14 (2009) 157-168. [2] S. De Feyter, F.C. De Schryver, Two-dimensional supramolecular self-assembly probed by scanning tunneling microscopy, Chem. Soc. Rev. 32 (2003) 139-150. [3] A. Ciesielski, P. Szabelski, W. Rżysko, A. Cadeddu, T.R. Cook, P.J. Stang, P. Samori, Concentration dependent supramolecular engineering of H-bonded nanostructures at surfaces: predicting self-assembly in 2D, J. Am. Chem. Soc. 135 (2013) 6942-6950. [4] J.A. Theobald, N.S. Oxtoby, M.A. Phillips, N.R. Champness, P.H. Beton, Controlling molecular deposition and layer structure with supramolecular surface assemblies, Nature 424 (2003) 1029-1031.
[5] L. Dong, Z. Gao, N. Lin, Self-assembly of metal-organic coordination structures on surfaces, Prog. Surf. Sci. 91 (2016) 101-135. [6] D. Kühne, F. Klappenberger, R. Decker, U. Schlickum, H. Brune, S. Klyatskaya, M. Ruben, J.V. Barth, High-quality 2D metal-organic coordination network providing giant cavities within mesoscale domains, J. Am. Chem. Soc. 131 (2009) 3881-3883.
[7] J. Adisoejoso, K. Tahara, S. Lei, P. Szabelski, W. Rżysko, K. Inukai, M.O. Blunt, Y. Tobe, S. De Feyter, One building block, two different nanoporous self-assembled monolayers: a combined STM and Monte Carlo study, ACS Nano 6 (2012) 897-903. [8] K. Miyake, Y. Hori, T. Ikeda, M. Asakawa, T. Shimizu, S. Sasaki, Alkyl chain length dependence of the self-organized structure of alkyl-substituted phthalocyanines, Langmuir 24 (2008) 4708-4714. [9] D. Bléger, D. Kreher, F. Mathevet, A.J. Attias, G. Schull, A. Huard, L. Douillard, C. Fiorini-Debuischert, F. Charra, Surface noncovalent bonding for rational design of hierarchical molecular self-assemblies, Angew. Chem. Int. Ed. 46 (2007) 7404-7407.
[10] T. Kudernac, S. Lei, J.A.A.W. Elemans, S. De Feyter Two-dimensional supramolecular self-assembly: nanoporous networks on surfaces, Chem. Soc. Rev. 38 (2009) 402-421. [11] E. Ghijsens, H. Cao, A. Noguchi, O. Ivasenko, Y. Fang, K. Tahara, Y. Tobe, S. De Feyter, Towards enantioselective adsorption in surface-confined nanoporous systems, Chem. Commun. 51 (2015) 4766-4769. [12] H. Bertrand, F. Silly, M.P. Teulade-Fichou, L. Tortech, D. Fichou, Locking the free-rotation of a prochiral star-shaped guest molecule inside a two-dimensional nanoporous network by introduction of chlorine atoms, Chem. Commun. 47 (2011) 1009110093.
[13] X. Zhang, Y. Shen, S. Wang, Y. Guo, K. Deng, C. Wang, Q. Zeng, One plus two: supramolecular coordination in a nano-reactor on surface, Sci Rep. 2 (2012) 742. [14] J. Teyssandier, S. De Feyter, K.S. Mali, Host-guest chemistry in two-dimensional supramolecular networks, Chem. Commun. 52 (2016) 11465-11487. [15] P. Szabelski, S. De Feyter, M. Drach, S. Lei, Computer simulation of chiral nanoporous networks on solid surfaces, Langmuir 26 (2010) 9506-9515. [16] T. Misiūnas, E.E. Tornau, Ordered assemblies of triangular-shaped molecules with strongly interacting vertices: phase diagrams for honeycomb and zigzag structures on triangular lattice, J. Phys. Chem. B 116 (2012) 2472-2482. [17] M. El Garah, A. Dianat, A. Cadeddu, R. Gutierrez, M. Cecchini, T.R. Cook, A. Ciesielski, P.J. Stang, G. Cuniberti, P. Samorì, Atomically precise prediction of 2D self-assembly of weakly bonded nanostructures: STM insight into concentrationdependent architectures, Small 12 (2016) 343-350. [18] C.A. Palma, P. Samorì, M. Cecchini, Atomistic simulations of 2D bicomponent selfassembly: from molecular recognition to self-healing, J. Am. Chem. Soc. 132 (2010) 17880-17885. [19] A. Ibenskas, E.E. Tornau, Statistical model for self-assembly of trimesic acid molecules into homologous series of flower phases, Phys. Rev. E 86 (2012) 51118-51130. [20] M. Šimėnas, A. Ibenskas, E.E. Tornau, Coronene molecules in hexagonal pores of tricarboxylic acids: a Monte Carlo study, J. Phys. Chem. C 119 (2015) 20524-20534 [21] D. Nieckarz, P. Szabelski, Simulation of the self-assembly of simple molecular bricks into Sierpiński triangles, Chem. Commun. 50 (2014) 6843-6845.
[22] G. Copie, F. Cleri, Y. Makoudi, C. Krzeminski, M. Berthe, F. Cherioux, F. Palmino, B. Grandidier, Surface-induced optimal packing of two-dimensional molecular networks, Phys. Rev. Lett. 114 (2015) 66101-66106. [23] R.A. Barnard, A. Dutta, J.K. Schnobrich, C.N. Morrison, S. Ahn, A.J. Matzger, Two-dimensional crystals from reduced symmetry analogues of trimesic acid, Chem. Eur. J. 21 (2015) 5954-5961. [24] P. Szabelski, W. Rżysko, D. Nieckarz, Directing the self-assembly of tripod molecules on solid surfaces: a Monte Carlo simulation approach, J. Phys. Chem. C 120 (2016) 13139-13147. [25] Z. Mu, L. Shu, H. Fuchs, M. Mayor, L. Chi, Two-dimensional chiral networks emerging from the aryl-F···H hydrogen-bond-driven self-assembly of partially fluorinated rigid molecular structures, J. Am. Chem. Soc. 130 (2008) 10840-10841. [26] B. Liu, Y.F. Ran, Z. Li, S.X. Liu, C. Jia, S. Decurtins, T. Wandlowski, A Scanning Probe Microscopy study of annulated redox-active molecules at a liquid/solid interface: the overruling of the alkyl
chain
paradigm,
Chem.
Eur.
J.
16
(2010)
5008-5012. [27] P. Szabelski, W. Rżysko, T. Pańczyk, E. Ghijsens, K. Tahara, Y. Tobe, S. De Feyter, Self-assembly of molecular tripods in two dimensions: structure and thermodynamics from computer simulations, RSC Adv. 3 (2013), 25159-25165. [28] S.D. Ha, B.R. Kaafarani, S. Barlow, S.R. Marder, A. Kahn, Multiphase growth and electronic structure of ultrathin hexaazatrinaphtylene on Au(111), J. Phys. Chem. C 111 (2007) 1049310497. [29] D. Trawny, P. Schlexer, K. Steenbergen, J.P. Rabe, B. Paulus, H.U. Reissig, Dense or porous packing? Two-dimensional self-assembly of star-shaped mono-, bi-, and terpyridine derivatives, ChemPhysChem 16 (2015) 949-953.
Figure 1. Model tripod-shaped molecules used in the simulations, adsorbed on a triangular lattice. The structures a, b and B can be viewed as modifications of the parent molecule A, obtained by elongation of one, two and three arms of A by one segment, respectively. The red arrows next to b show the interaction directions assumed in the calculations for all of the molecules from the figure.
Figure 2. Snapshot of the adsorbed overlayer comprising 1000 molecules a with directional interactions; T 0.1 (left). Magnified fragment of the obtained network with small (aI) and big (aII) regular hexagonal pores marked in red and blue, respectively and examples of other six-membered irregular pores found in the network (right).
Figure 3. Snapshot of the adsorbed overlayer comprising 1000 molecules b with directional interactions; T 0.1 (left). Magnified fragment of the obtained network with small (bI) and big (bII) regular hexagonal pores marked in green and orange, respectively and examples of other sixmembered irregular pores found in the network (right).
Figure 4. Average number of the regular hexagonal pores in the networks comprising 1000 molecules a and b with directional interactions; T 0.1 (left). The same color code for the different pore types is used as in Fig. Z. (left) Effect of temperature on the amount fraction of the molecules a (solid lines) and b (dashed lines) with n 0..3 bonds in the corresponding overlayers containing 1000 molecules.
Figure 5. Effect of temperature on the average number of bonds of type: short-short (s-s), long-long (ll) and short-long (s-l), calculated for 1000 molecules a and b with directional interactions. The symbols s and l indicate which molecular arm of a and b (short or long) takes part in the bonding.
Figure 6. Snapshot of the adsorbed overlayer comprising 1000 molecules A and B with directional interactions; T 0.1. Magnified fragments of the obtained networks with the corresponding rhombic unit cells (red lines) are shown in the insets.
Figure 7. Effect of temperature on the average number of bonds per molecule calculated for 1000 molecules a, b, A and B with directional interactions; T 0.1 (left). Specific heat capacity curves calculated for these molecular systems (right).
Figure 8. Snapshot of the adsorbed overlayer comprising 1000 molecules a and b with isotropic interactions; T 0.1. Magnified fragments of the obtained structures with the corresponding rectangular unit cells (red lines) are shown in the insets. The circular zones highlighted in green and yellow present two alternative packings of the short arms of a in the molecular rows.
Figure 9. Snapshot of the adsorbed overlayer comprising 1000 molecules A and B with isotropic interactions; T 0.1. Magnified fragments of the obtained structures with the corresponding unit cells (red lines) are shown in the insets. The circular zones highlighted in green and yellow present two alternative packings of the short arms of A in the molecular rows. The black arrows in the insets indicate the propagation directions of the one-molecule wide rows formed by A and the rotation direction of the homochiral porous network built of B.
Figure 10. Effect of temperature on the average number of bonds per molecule calculated for 1000 molecules a, b, A and B with directional interactions; T 0.1 (left). Specific heat capacity curves calculated for these molecular systems (right).