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2009, 113, 21265–21268 Published on Web 11/25/2009
Short-Range Order in a Metal-Organic Network Achim Breitruck, Harry E. Hoster,* and R. Ju¨rgen Behm Institute of Surface Chemistry and Catalysis, Ulm UniVersity, D-89069 Ulm, Germany ReceiVed: September 10, 2009; ReVised Manuscript ReceiVed: NoVember 2, 2009
Supramolecular assemblies on surfaces usually possess a long-range order controlled by the shape of the building blocks and the interactions between them. In this paper, we demonstrate that such a building block concept is applicable also for short-range ordered systems when used in combination with Monte Carlo (MC) techniques. Specifically, we focus on a structure that consists of a mixture of metal-organic complexes and organic trimers distributed on a hexagonal lattice. This distribution obeys a short-range order (SRO) governed by hydrogen bonds between the different types of lattice occupants. We show that this SRO, which is directly observed by scanning tunneling microscopy, can be predicted with high accuracy by MC simulations using pairwise interaction energy parameters which were determined by ab initio calculations. Two-dimensional (2D) nanostructures involving large organic molecules adsorbed on solid surfaces have rapidly become an important field of research in recent years.1-3 These structures are stabilized by very different types of interactions such as hydrogen bonds,3-5 coordinative metal-ligand interactions,6-9 or even covalent bonds.10-15 On energetically smooth surfaces, i.e., in the absence of distinct lateral variations in the substrate-adsorbate interaction, the resulting adlayer structure is unambiguously determined by the shape of the molecules and the positions of the functional groups that allow for defined molecule-molecule interactions (“linker groups”).16 It is commonly perceived that these interactions result in well-ordered structures with a distinct long-range order.17 This assumption, however, is not necessarily correct. Depending on the shape of the organic molecules or molecular building blocks, the intramolecular positions of the linker groups, and the nature of interaction forces, one may also encounter systems that exhibit only short-range order (SRO).18 Under equilibrium conditions, short-range ordered adlayers can be expected when their constituents can form different local bonding configurations of comparable stability, which facilitates thermally excited disorder. In that case, contributions from configurational entropy to the overall free energy of the adlayer have to be considered as well, and may even become decisive for its structural appearance. The short-range ordering phenomena that result from thermal excitation can be studied by Monte Carlo (MC) simulations, where the local interactions and their energies are used as input parameters. These simulations include entropic effects, and for simple systems such as disordered binary surface alloys, they yield SRO characteristics that quantitatively fit to corresponding experimental results.19 In the present paper, we will demonstrate the potential of a related approach by simulating short-range ordered structures in a supramolecular 2D structure. Different from the lattice gas model used for bimetallic nanostructures,19 however, each site is occupied by one of five different objects. The structure * To whom correspondence should be addressed. E-mail: harry.hoster@ uni-ulm.de.
10.1021/jp908748w
Figure 1. (a) Schematic model of the bis(terpyridine) derivative (2,4′BTP) studied in this work with its chemical structure superimposed. (b) Calculated interaction energy between two pyridine molecules for a single hydrogen bond (SHB) and (c) for a twinned hydrogen bond (THB).20
relevant interaction energies used as input for the simulations are based on simple “bond counting”, with bond energies derived from first principles calculations. This approach allows understanding the structures even without knowledge of subtle details of the bonds themselves. Instead, the anisotropy of the molecule-molecule interactions, which is known from the structure of the molecular building blocks, plays a dominating role. To assess the predictive capability of this approach, we will quantitatively compare the simulated short-range order characteristics with those obtained experimentally by scanning tunneling microscopy (STM). As a model system, we chose a metal-organic network based on Cu atoms and the bis(terpyridine) derivative 2-phenyl-4,6-bis(6-(pyridine-2-yl)-4-(pyridine4-yl)pyridine-2-yl)pyrimidine (2,4′-BTP, see Figure 1a). As illustrated in Figure 1b, these molecules form C-H · · · N type hydrogen bonds (HBs), whose strength was calculated by ab initio methods previously.20 At a coverage of 0.39 molecules nm-2, they form an ordered network where all peripheral N atoms are involved in HBs. This structure, which we will refer to as the R-phase, has been thoroughly discussed in previous studies.20-25 Its long-range order and nm-scale structure, as resolved by STM, are shown in Figure 2a and in the inset in this figure, respectively. The metal-organic β-phase, which is the subject of this paper, is formed by vapor deposition of 0.07 Cu atoms nm-2 onto a
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Figure 2. (a) STM image of the metal-free organic precursor layer (R-phase) (115 × 115 nm2; UT ) -2.3 V, IT ) 3.55 pA). The molecular arrangement is resolved in the higher resolution image in the inset in the lower left corner (10 × 10 nm2; UT ) -1.6 V, IT ) 5.6 pA). (b) Metal-organic network evolving after Cu deposition onto the precursor layer shown in part a (β-phase) (115 × 115 nm2; UT ) 1.7 V, IT ) 5.6 pA).
Figure 4. (a) Possible lattice occupations: four different Cu free trimers (A) and a Cu(BTP)3 complex (B). (b) Examples of strongly (1-1; 5-1), medium (5-5), and weakly (2-1) interacting nearest-neighbor trimers. (c) Warren-Cowley short-range order coefficients for the first (NN), second (3 NN), third (2 NN), fourth (7 NN), and fifth (3 NN) neighborhood. Error bars reflect standard deviations.
Figure 3. (a) High-resolution image of the metal-organic network shown in Figure 2b (25 × 25 nm2; UT ) 2.2 V, IT ) 17.8 pA). (b) Schematic representation of the molecular/atomic arrangement within the marked square of part a, comprising Cu(BTP)3 and (BTP)3 units.
surface covered by the R-phase. The sample is kept at room temperature during and after deposition. In STM images, this phase appears as a disperse distribution of triangular bright spots (see Figure 2b). According to images with higher resolution (Figure 3a), the triangular protrusions exhibit C3 symmetry and are surrounded by oval protrusions of lower apparent height. As illustrated in Figure 3b, we assign the triangular and oval features to planar Cu(BTP)3 complexes and single 2,4′-BTP molecules, respectively. The transition to the β-phase instead of incorporating the Cu into the holes of the R-phase must be driven by the formation of the Cu(BTP)3 units. They are stabilized by Cu · · · N-pyridine interactions, which are known to be considerably stronger than C-H · · · N type HBs.26 The limitation to 3-fold coordination results from the repulsion between the flat-adsorbed BTP ligands. BTP molecules without direct contact with Cu adatoms arrange in local configurations determined by HBs. Apart from the domain boundaries, the latter BTP molecules form trimers (dotted circle in Figure 3b) that comprise a 2,4′-BTP dimer stabilized by twinned hydrogen bonds (see Figure 1c),23 and a third molecule oriented in an angle of 60° relative to the dimer axis (see dashed lines, Figure 3b). This structural unit appears in three rotational orientations, differing by 120°. In some occasions, they also form a C3 arrangement. The four observed arrangements of BTP trimers and of the Cu(BTP)3 complex are summarized in Figure 4a. In the following, we will refer to the Cu-free (darker) and Cucontaining (brighter) units as A and B units, respectively. According to our STM data, the A and B units are distributed on a hexagonal lattice, with B units occupying 55% of the sites. It should be noted that lower or higher Cu surface coverages
do not change this fraction but rather lead to the formation of coexisting phases with locally lower or higher Cu contents, respectively.27 The rotational direction of these structural units was found to be uniform over large areas. Domains with opposite chirality could only be reached by macroscopically moving the STM tip over distances >2 µm. Hence, only on such large scales the surface structure is racemic.28 Despite its locally uniform chirality, the β-phase splits into two different rotational domains, where the orientations of A and B units with respect to the substrate differ by 180°. In STM images such as in Figures 2b or 3a, this is apparent from the two opposite directions adopted by the bright triangles. The hierarchy of rotational and homochiral domains is analyzed in more detail elsewhere.27 Time resolved STM images revealed structural fluctuations within the β-phase.29 Specifically, the B units turned out to be mobile: the Cu atoms could leave a Cu(BTP)3 complex and move to a neighboring (BTP)3 unit, equivalent to an exchange of A and B units on two neighboring sites (this involves also a local rearrangement of BTP molecules). This observation leads to two important consequences. First, if the rates of Cu atoms leaving the ligand shells follow an Arrhenius type behavior with k ) k0 exp(-Εa/kBT), the observation of k ≈ 3 mHz leads to an effective hopping barrier of 0.85 eV < Ea < 1.1 eV for k0 in the normal range 1012 s-1 < k0 < 1016 s-1. If we assume that the Cu atom leaves the Cu(BTP)3 complex much faster than the new HBs between the remaining BTP molecules are formed, this yields an upper limit of 1.1 eV for the energy gained by forming a B-unit out of three virtually noninteracting BTP molecules and an uncoordinated Cu atom. Second, the observation of significant mobility at room temperature indicates that the distribution of A and B reflects a local equilibrium situation, i.e., a local minimum of the free energy. In that case, we can simulate this distribution via a Metropolis Monte Carlo30 approach. We will only consider a single rotational domain with periodic boundary conditions. The adlayer is described as a
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Figure 5. (a) Large scale and (b) smaller scale view of a β-domain generated by Monte Carlo simulations; dotted line, typical chain of (BTP)3 units connected by the most stable hydrogen bond combinations.
lattice, where each point is occupied by one of the five units in Figure 4a. Then, the overall energy of the adlayer can be written as31
E ) J0 +
∑ i
∑
1 Ji + J 2 〈j,k〉 jk
J0 represents the contributions from adsorbate-substrate interactions, which in a first order approximation do not depend on the distribution within the adlayer, i.e., if the corrugation of the potential energy of the substrate is assumed to be negligible. The second term comprises the internal bonds in B and in the different types of A units (see Figure 4a), the index i runs over all sites, and Ji reflects the internal bond energies. Note that all Ji of type 1-4 hold for relaxed trimers and were calculated using N · · · H and H · · · H interaction potentials.22 The number of Cu atoms and thus also the number of B units are kept fixed, so that the metal-ligand interaction energy has no influence on the structure. The third term includes the contributions from HBs between the different units. The indices j and k run over all nearest neighbors (the factor 1/2 prevents double counting of neighborhoods). The interaction Jjk between two BTP trimers, between two Cu(BTP)3 complexes, or between a BTP trimer and a Cu(BTP)3 complex are determined from the number of single and twinned hydrogen bonds (SHB, THB) between these units (see the Supporting Information). In a simple approximation, we assume these as distance independent, with energies of ESHB ) 0.101 eV and ETHB ) 0.139 eV, respectively, that were calculated by ab initio methods previously20 (see Figure 1b,c). A similar approach using pairwise interactions was recently shown to yield reasonable interaction energies within a similar system.32 In Figure 4b, we present examples for a strongly, a moderately, and a weakly bound nearest-neighbor couple of site occupants (an overview of all possible neighborhoods is given in the Supporting Information). To reduce the computational effort for the simulation of larger areas, we neglect possible changes of these pairwise interaction energies due to local relaxations and variations of the interactions within the units. The elementary processes involve (i) the exchange of randomly selected A and B units and (ii) the internal restructuring of randomly selected A units. Internal restructuring means a transformation from an initial configuration S0 ) 1...4 into a final configuration S1 * S0. In both cases, the structural modification is accepted if the change of the overall adlayer energy, ∆E, is negative. Otherwise, it is accepted with a probability of exp(-∆E/kBT).30 Typical distributions attained after more than 1000 of such attempts per site are shown in Figure 5. For better comparison with the experiment, we marked
the B units by white triangles. Figure 5b also resolves individual molecules. The simulations fully reproduce the experimentally observed tendency toward formation of longer chains. Interestingly, the formation of these chains is not predominantly driven by attractions or repulsions between the well visible B units but rather by the strong anisotropy in the ability of the A units of types 1-3 to form HBs (see Figure 4a and b). Specifically, the formation of chains similar to those highlighted by the dotted line in Figure 5b increases the number of neighborhoods of type 1-1 in Figure 4b. These chains in turn provide favorable neighborhoods for B units, thus promoting chain formation also for those. For quantitative comparison of simulation and experiment, we calculated the Warren-Cowley short-range order (SRO) parameters33,34
RAB(d) ) 1 -
pAB(d) xB
pAB(d) describes the probability to find an object B in a distance d of a given object A, where d is given as a multiple of nearestneighbor (NN) lattice distances. In this analysis, we do not distinguish between the different types of A because the number of STM images with a resolution as in Figure 3a, where they could in principle be counted separately, is limited. In contrast, the distributions of dark (A) and bright (B) sites on the lattice are resolved in large data sets. In Figure 4c, we compare the SROs of the simulated and experimentally determined distributions of A and B units. Both show a significant deviation from a purely random distribution, which would correspond to R(d) ) 0 for all d. For d ) 1 NN, there is a clear preference for unlike neighbors or, in this case, unlike structural units (A and B), which are of similar size for experiment and simulation. The preference for like neighbors at a distance of d ) 3 NN reflects the frequent occurrence of B-chains separated by a chain of A (see Figure 3a). In total, the simulated distribution of A and B units within the metal-organic network agrees very well with the experimental observations. Within the R-phase, the number of HBs per 2,4′-BTP molecule is maximized,22 so that the formation of the β-phase must be driven by the energy contributions from the metal-ligand interactions. Comparing both phases, we will now estimate a lower limit for this contribution. It should be noted that this only affects the internal stability of the B-units but not the SRO of their lateral distribution. Our simulations yield an average HB energy of ∼0.256 eV molecule-1 in the β-phase. In addition, the lower order of β compared to R implies a gain in configurational entropy, which at 300 K accounts for 0.011 eV molecule-1 at most (see the Supporting Information). Comparing this with the corresponding value of ER ) 0.462 eV molecule-1 for a fully relaxed R-phase,22 the formation of the Cu(BTP)3 complexes must contribute an additional stabilization of more than (0.462 - 0.256 - 0.011) eV molecule-1 ) 0.195 eV molecule-1. 55% of the lattice sites are filled with B units, where each contains one Cu atom and three BTP molecules. We thus have 0.55/3 ) 0.183 Cu atoms molecule-1, and each atom is part of a Cu(BTP)3 complex. Therefore, the formation of this complex must lower the system energy by (at least) ECu-BTP_shell ) 0.195 eV/0.183 ) 1.06 eV per complex. This magnitude agrees well with the activation energy for the hopping of Cu atoms out of Cu(BTP)3 units, which we estimated above to be in the range 0.85 eV < Ea < 1.1 eV. (Note that this comparison relies on a simplified hopping mechanism where the Cu atoms pass through a state with vanishing metal-ligand interaction energies; i.e., the activation energy for migration and bond
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energy are assumed to be similar in value.) Both results also fit to the findings of recent calculations for a metal-organic system based on Cu · · · NC bonds, where the formation of a single Cu(DCA)3 complex on Cu(111) was found to cause an energy gain of 0.99 eV.35 In summary, our quantitative structure analyses in combination with dynamic observations allowed us to estimate the strength of the metal-ligand interactions that drive the transition from the hydrogen-bonded organic adlayer to a metal-organic adlayer. We demonstrated that the lattice gas approach usually used for description and MC simulation of short-range order in 2D assemblies of point-like, isotropically interacting objects can be transferred to structures formed from extended objects with anisotropic interaction characteristics, as present in organic and metal-organic networks. Quantitative comparison between simulation and experiment is possible by statistical evaluation of STM data. In a more general sense, this work represents an example for transferring the concept of assembling structures from multimolecular building blocks from periodically ordered to short-range ordered systems. Acknowledgment. We thank the Deutsche Forschungsgemeinschaft for financial support via the Collaborative Research center 569 (SFB 569) and C. Meier and U. Ziener for providing the BTP molecules. Supporting Information Available: Tabulation of all (BTP)3 and Cu(BTP)3 neighborhoods and calculation of the configurational entropy. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Barth, J. V. Annu. ReV. Phys. Chem. 2007, 58, 375. (2) Gomar-Nadal, E.; Puigmarti-Luis, J.; Amabilino, D. B. Chem. Soc. ReV. 2008, 37, 490. (3) Rosei, F.; Schunack, M.; Yoshitaka, N.; Jiang, P.; Gourdon, A.; Laegsgaard, E.; Stensgaard, I.; Joachim, C.; Besenbacher, F. Proc. Surf. Sci. 2003, 71, 95. (4) de Feyter, S.; de Schryver, F. Chem. Soc. ReV. 2003, 32, 139. (5) Forrest, S. R. Chem. ReV. 1997, 97, 1793. (6) Stepanow, S.; Lin, N.; Barth, J. V. J. Phys.: Condens. Matter 2008, 20, 1. (7) Ruben, M.; Rojo, J.; Romero-Salguero, F. J.; Rojo, J.; Uppadine, L. H. Angew. Chem., Int. Ed. 2004, 43, 3644.
Letters (8) Lin, N.; Stepanow, S.; Ruben, M.; Barth, J. V. Top. Curr. Chem. 2009, 287, 1–44. (9) Barth, J. V. Surf. Sci. 2009, 603, 1533. (10) Grill, L.; Dyer, M.; Lafferentz, L.; Persson, M.; Peters, M. V.; Hecht, S. Nat. Nanotechnol. 2007, 2, 687. (11) Matena, M.; Riehm, T.; Sto¨hr, M.; Jung, T. A.; Gade, L. H. Angew. Chem., Int. Ed. 2008, 47, 2414. (12) Treier, M.; Richardson, N. V.; Fasel, R. J. Am. Chem. Soc. 2008, 130, 14054. (13) Weigelt, S.; Busse, C.; Bombis, C.; Knudsen, M. M.; Gothelf, K. V.; Laegsaard, E.; Besenbacher, F.; Linderoth, T. R. Angew. Chem., Int. Ed. 2008, 47, 4406. (14) Zwaneveld, N. A. A.; Pawlak, R.; Abel, M.; Catalin, D.; Gigmes, D.; Bertin, D.; Porte, L. J. Am. Chem. Soc. 2008, 130, 6678. (15) Boz, S.; Sto¨hr, M.; Soydaner, U.; Mayor, M. Angew. Chem., Int. Ed. 2009, 48, 3179. (16) Fasel, R.; Parschau, M.; Ernst, K.-H. Angew. Chem., Int. Ed. 2003, 42, 5178. (17) Gross, L.; Moresco, F.; Ruffieux, P.; Gourdon, A.; Joachim, C.; Rieder, K.-H. Phys. ReV. B 2005, 71, 165428–1. (18) Xu, W.; Dong, M.; Gersen, H.; Rauls, E.; Vazquez-Campos, S.; Crego-Calama, M.; Reinhoudt, D. N.; Laegsaard, E.; Stensgaard, I.; Linderoth, T. R.; Besenbacher, F. Small 2008, 4, 1620. (19) Bergbreiter, A.; Hoster, H. E.; Sakong, S.; Gross, A.; Behm, R. J. Phys. Chem. Chem. Phys. 2007, 9, 5127. (20) Meier, C.; Ziener, U.; Landfester, K.; Weihrich, P. J. Phys. Chem. B 2005, 109, 21015. (21) Breitruck, A.; Hoster, H.; Meier, C.; Ziener, U.; Behm, R. J. Surf. Sci. 2007, 601, 4200. (22) Hoster, H. E.; Roos, M.; Breitruck, A.; Meier, C.; Tonigold, K.; Waldmann, T.; Ziener, U.; Behm, R. J. Langmuir 2007, 23, 11570. (23) Roos, M.; Hoster, H. E.; Breitruck, A.; Behm, R. J. Phys. Chem. Chem. Phys. 2007, 9, 5672. (24) Ziener, U. J. Phys. Chem. B 2008, 112, 14698. (25) Ziener, U.; Lehn, J. M.; Mourran, A.; Mo¨ller, M. Chem.sEur. J. 2002, 8, 951. (26) Wu, D. Y.; Ren, B.; Jiang, Y.-X.; Xu, X.; Tian, Z. Q. J. Phys. Chem. A 2002, 106, 9042. (27) Breitruck, A.; Hoster, H. E.; Behm, R. J. To be published. (28) Barlow, S. M.; Raval, R. Surf. Sci. Rep. 2003, 50, 201. (29) Breitruck, A.; Hoster, H. E.; Behm, R. J. To be published. (30) Metropolis, N.; Rosenbluth, A. W.; Rosenbluth, M. N.; Teller, A. H. J. Chem. Phys. 1953, 21, 1087. (31) Mu¨ller, S. J. Phys.: Condens. Matter 2003, 15, R1429. (32) Xu, W.; Dong, M.; Gersen, H.; Rauls, E.; Vazquez-Campos, S.; Crego-Calama, M.; Reinhoudt, D. N.; Stensgaard, I.; Laegsaard, E.; Besenbacher, F. Small 2007, 3, 854. (33) Cowley, J. M. J. Appl. Phys. 1950, 21, 24. (34) Warren, B. E. X-Ray diffaction; Dover Publications Inc.: New York, 1990. (35) Pawin, G.; Wong, K. L.; Kim, D.; Sun, D.; Bartels, L.; Hong, S.; Rahman, T. S.; Carp, R.; Marsella, M. Angew. Chem., Int. Ed. 2008, 47, 8442.
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