A 2D Substitutional Solid Solution Through Hydrogen-Bonding of

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A 2D Substitutional Solid Solution Through Hydrogen-Bonding of Molecular Building Blocks Jennifer M Macleod, Josh Lipton-Duffin, Chaoying Fu, Tyler Taerum, Dmitrii F Perepichka, and Federico Rosei ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.7b03172 • Publication Date (Web): 14 Aug 2017 Downloaded from http://pubs.acs.org on August 14, 2017

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A 2D Substitutional Solid Solution Through Hydrogen-Bonding of Molecular Building Blocks Jennifer M. MacLeod,a,b,c* Josh Lipton-Duffin, a,b,c* Chaoying Fu,d Tyler Taerum,d Dmitrii F. Perepichka d* and Federico Rosei b,e* a

School of Chemistry, Physics, and Mechanical Engineering, Queensland University of Technology (QUT), 2 George Street, Brisbane, 4000 QLD, Australia

b

Institut National de la Recherche Scientifique, Centre Énergie, Matériaux, Télécommunications, 1650 Lionel Boulet boulevard, Varennes, QC, Canada, J3X 1S2

c

Institute for Future Environments, Queensland University of Technology (QUT), Brisbane, 2 George Street, 4000 QLD, Australia

d

Department of Chemistry, McGill University, 801 Sherbrooke St. W., Montreal, QC, Canada, H3A 0B8

e

Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu 610054 PR China *Corresponding authors: [email protected]; [email protected]; [email protected]; [email protected]


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ABSTRACT Two-dimensional (2D) molecular self-assembly allows for the formation of well-defined supramolecular layers with tailored geometrical, compositional and chemical properties. To date, random intermixing and entropic effects in these systems have largely been associated with crystalline disorder and glassy phases. Here we describe a 2D crystalline self-assembled molecular system that exhibits random incorporation of substitutional molecules. The lattice is formed from a mixture of trimesic acid (TMA) and terthienobenzenetricarboxylic acid (TTBTA), C3-symmetric hydrogen-bonding units of very different sizes (0.79 and 1.16 nm, respectively), at the solution – highly oriented pyrolitic graphite (HOPG) interface. Remarkably, the TTBTA substitutes into the TMA lattice at a fixed stoichiometry near 12%. The resulting lattice constant is consistent with Vegard’s Law prediction for an alloy with a composition TMA0.88TTBTA0.12, and the substrate orientation of the lattice is defined by an epitaxial relation with the HOPG substrate. The Gibbs free energy for the TMA/TTBTA lattice was elucidated by considering the entropy of intermixing, via Monte Carlo simulations of multiplicity of the substitutional lattices, and the enthalpy of intermixing, via density functional theory calculations. The latter show that both the bond enthalpy of the H-bonded lattice and the adsorption enthalpy of the molecule/substrate interactions play important roles. This work provides insight into the manifestation of entropy in a molecular crystal constrained by both epitaxy and intermolecular interactions, and demonstrates that randomly intermixed yet crystalline 2D solid can be formed through hydrogen bonding of molecular building blocks of very different size. KEYWORDS: self-assembly, hydrogen bonding, scanning tunnelling microscopy, entropy, solid solution


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Molecular self-assembly of two-dimensional (2D) architectures at the solution/solid interface has demonstrated a wealth of geometric and chemical motifs.1,2 Depending on the structure of the molecular building blocks, the non-covalent interactions driving the assembly and on parameters such as concentration and solvent effects, a range of different morphologies, from denselypacked monolayers to porous networks, can be readily obtained on a surface.3-5 Although most 2D self-assembly studies have focused on single-component networks, welldefined films formed from two or more molecules are of considerable interest, both for a fundamental understanding of supramolecular interactions and towards the formation of controlled nanoscale patterns with tailored properties.6-8 For example, the inclusion of guest molecules in porous networks allows for the controlled positioning of a second species into a well-defined 2D molecular crystal.9 This approach has been applied to a number of π-functional guest molecules such as fullerenes,10,11 circulenes12-14,15-16 and other large macrocycles.17,18 Heteromolecular 2D architectures can also be designed by using complementary molecular building blocks.19,20 The most widely explored approach to engineering bicomponent crystals has relied on hydrogen bonding, with recognition programmed into the building blocks through the incorporation of matched donor-acceptor hydrogen bonding sites.21-23 At the solution/solid interface, these interactions are often complemented with stabilization through interdigitation of alkyl chains, leading to a dense molecular layer on the surface.24-31 Porous chicken wire-like bicomponent cocrystals have been formed at the solution/solid interface in systems that exploit the directionality of hydrogen bonding and capitalize on the C3-symmetry of one or both of the bonding units: melamine paired with imidic linkers3, 32 or melem33 or trimesic acid (TMA) paired with 1,3,5-tris(4-pyridyl)-2,4,6-triazine (TPT)34 or 1,3,5-benzenetribenzoic acid (BTB).23, 35 With the exception of glassy phases formed when melamine is coupled with a flexible linker,36 these


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cocrystals form domains that are structurally and stoichiometrically well-defined due to the enthalpic stabilization of the complementary hydrogen bonding. Here, we demonstrate another possibility for hydrogen-bonded binary molecular crystals: a randomly-intermixed substitutional solid solution. In the 1980s, Kitaigorodsky provided comprehensive insight into the formation and stability of bulk (3D) organic solid solutions,37 and since then the field has matured to the point where targeted solid solutions are being used to tailor the functional properties of engineered molecular crystals, such as to modify hardness in pharmaceuticals38 or to improve power conversion efficiency in organic photovoltaics.39 At the same time, fundamental work is still advancing, exploring the limits of Kitaigorodsky’s predictions,40 and extending the approach to tertiary solutions.41 Fewer studies have explored two-dimensional solid solutions. Disordered intermixing has been observed in a number of systems where the two molecular species are size-matched and stabilized through relatively weak intermolecular interactions, for example in binary films of isostructural phthalocyanines that differ only in their metal centers,42,43 aliphatic primary amides,44 and in targeted scanning tunneling microscopy (STM) experiments where similar aliphatics with and without highcontrast “tags” are used to investigate miscibility and dynamics.45-48 The entropic effects leading to a random tiling phase of a homomolecular hydrogen-bonded self-assembled system have been investigated by Beton and coworkers, who showed that the random phase results from a delicate balance between entropy and enthalpy.49 The present study reveals a similar enthalpic/entropic balance underpinning a hydrogen-bonded random phase, this time in a heteromolecular system. Our STM data show that terthienobenzenetricarboxylic acid (TTBTA, Figure 1), a C3-symmetric tricarboxylic acid 47% larger than TMA, can intermix randomly with the latter, forming a crystalline chicken wire phase with a stable stoichiometry near 10:1 TMA:TTBTA. The


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miscibility of these dissimilarly-sized molecules requires flexibility of bond lengths within the hydrogen-bonded lattice, as well as stabilization provided through adsorption interactions. Together, the intermolecular and molecule-substrate interactions and the entropic contribution associated with the randomness of the intermixing define a thermodynamically favorable intermixed phase of a fixed stoichiometry, and demonstrate the possibility for hydrogen-bonded 2D substitutional solid solutions.

Figure 1: (a) Molecular structures of TMA and TTBTA, with carbon atoms shown in gray, oxygen in red, hydrogen in white and sulfur in yellow. (b) Hexagonal “chicken wire” network formed by hydrogen bonding (shown at inset) between tricarboxylic acids. The arrows show the unit cell, a = b = 1.61 nm (for pure TMA) or 2.37 nm (for pure TTBTA), α = 120°.

RESULTS A saturated solution of either TMA or TTBTA in heptanoic acid can spontaneously form a porous network at the solution/HOPG interface (shown schematically in Figure 1b, and in STM images in Figure 2). These chicken wire structures are stabilized by strong 8 cyclic H-bonds between the carboxylic groups, and have been observed for a number of different C3-symmetric


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tricarboxylic acids, including TMA,50 TTBTA,10 and BTB51. On HOPG, the respective dimensions of the chicken wire structures of TMA and TTBTA reflect the difference in their molecular size as well as the epitaxial match with the underlying HOPG. High-resolution images containing both the molecular overlayer and HOPG substrate lattice can be used to determine the epitaxy matrix through an autocorrelation analysis (see Supporting Information). TMA forms a chicken wire network with an epitaxy matrix of

6 1

−1 , corresponding to a hexagonal unit cell 7

with a dimension of 1.61 nm (√43 times the HOPG in-plane lattice constant),52 whereas the TTBTA chicken wire network has an epitaxy matrix of

11 4

4 , with a lattice parameter of −7

2.37 nm (√93 times the HOPG in-plane lattice constant). The epitaxial assertion of the substrate produces a minimal strain in the TTBTA network, as the observed coincidence lattice places the molecules very close to their optimal gas-phase lattice constant (2.39 nm)10. For TMA, a 3% compression from the optimized gas-phase spacing (1.66 nm)52 is needed to achieve the epitaxial match. Mixing TMA and TTBTA on the HOPG surface produces a new (modified) chicken wire network, as observed in the micrograph displayed in Figure 2b. Based on the contrast of individual nodes in STM images, we interpret this to be a mixed phase of TMA and TTBTA. Through a counting analysis over the observed domains of intermixed molecules, we find that TTBTA substitutes for TMA in 12% (±1%) of the lattice sites. The pore spacing (indicated by the lattice vectors in Figure 1) in the intermixed lattice measures 1.70±0.08 nm. This lattice constant is consistent with Vegard’s law, an empirical rule that predicts a linear relationship between the lattice constant (a) and the relative concentration of the constituents in an alloy system.53 For a “molecular alloy” TMA0.88TTBTA0.12, Vegard’s law is applied as follows:


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0.88 0.12 1.70 .

Figure 2. 10 × 10 nm2 STM images (top) and molecular models (bottom) of (a) TMA, (b) TMA with substituted TTBTA, and (c) TTBTA. TMA has been colour-mapped as blue, and TTBTA has been colour-mapped as yellow; the corresponding grayscale images are available in the Supporting Information. STM parameters: -1.2 V, 0.10 nA (a), and -1.0 V, 0.08 nA (b), -0.8 V, 0.10 nA (c). Molecular models showing the orientation of the 2D networks with respect to the HOPG for pure TMA, intermixed TTBTA-TMA phase, and pure TTBTA.

The images reported in Figure 3 show domains of intermixed TMA/TTBTA that coexist next to domains of pure-phase TMA (a) and TTBTA (b). The intermixed domains comprise an average of ≈200 individual molecules, smaller than the neighboring domains of pure TMA, but similar to neighboring domains of TTBTA. The intermixed domains have two symmetrically-equivalent orientations (Figure 3) and are rotated by ca. 20° (-9°) with respect to the TMA (TTBTA) lattices (Figure S3). For epitaxial systems, the rotation of the lattice relates to the commensurability of


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the overlayer with the underlying substrate, and varies with the periodicity of the lattice. The fixed orientation of the intermixed TMA/TTBTA lattice therefore suggests that it is epitaxially matched to the HOPG surface. The observed intermixed lattice dimensions and orientation correspond to an epitaxy matrix of

4 4

−4 , with a lattice constant √48 times larger than 8

HOPG (see Figure 2e, and the included code in the SI for validating the orientation). This epitaxy matrix reproduces the observed rotation of the intermixed lattice with respect to pure TMA (22° as calculated) and pure TTBTA (-9° as calculated) lattices.

Figure 3: (a) STM image of intermixed TTBTA/TMA domains neighboring a pure-TMA domain (at left, with the TMA molecules colour-mapped as blue). (b) STM image of intermixed TTBTA/TMA domains near a pure TTBTA domain (at right, with the TTBTA molecules colourmapped as yellow). Each image is 30 × 30 nm2. STM parameters: -1.0 V, 0.08 nA (a), -1.0 V, 0.08 nA (b). (c) Pair correlation analysis of the local ordering of two TTBTA molecules within the TMA lattice. The pair correlation function, g(k), shows the preference for the 1,4configuration.

The positioning of the TTBTA molecules in the TMA network does not exhibit any long-range order, but indicates a preference for particular spacings between pairs of TTBTA molecules. Figure 3c shows the pair correlation function g(k) for the probability of finding a second TTBTA molecule in a particular position with respect to an existing TTBTA substitution. It equals zero


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for the nearest-neighbor sites, 0.01 for second nearest-neighbor sites, and 0.36 for third nearest neighbor sites. The measured periodicity and relative rotation of each of the three observed types of lattices, along with the assumption of substrate commensurability, leads us to the models shown in Figure 2d-f. The molecular models for the TMA and TTBTA lattices were first optimized using periodic boundary conditions (ωB97X-D/6-31G(d,p)), without considering interactions with the substrate. Then, the pure TMA structure was placed on top of a graphene sheet such that one of the two molecules is centered over a graphene atom and the other over a hole, consistent with their known orientations on HOPG.52 For TTBTA, each molecule is able to adsorb over an identical substrate lattice point.

DISCUSSION The full thermodynamics of molecular self-assembly at the solution/solid interface are defined by a range of parameters, including temperature, concentration, solvent, etc.54,55 Quantifying the enthalpic driving force for the formation of a particular phase from solution requires knowing energetic parameters of a number of different processes (sublimation, desorption, dewetting, dissolution).56 These parameters are not always available, and often require additional dedicated experimentation. Here we focus instead on the relative stability of the intermixed phase. The Gibbs free energy of formation of the mixed phase, ∆Gmix, can be expressed as

∆Gmix=∆Hmix-T∆Smix,


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where ∆Hmix and ∆Smix are the enthalpy and entropy, respectively, associated with the formation of the mixed phase with respect to the pure phase (chosen for this discussion as pure TMA), and T is the temperature.

In a bulk substitutional solid solution, the ∆Hmix term is defined by the interactions between the two species that constitute the mixed phase. In the case of an ideal substitutional solid solution where homo- and hetero-species interactions are energetically equivalent, ∆Hmix = 0, and the entropy of intermixing defines the thermodynamically stable composition. In non-ideal solutions, which have ∆Hmix ≠ 0, both entropy and enthalpy play a role in determining which stoichiometries are stable.

In on-surface assembly, this enthalpic component ∆Hmix comprises both intermolecular interactions and adsorption enthalpies. We have used DFT to elucidate the intermolecular and molecule-substrate interactions, as well as to examine the bond lability necessary to accommodate the larger TTBTA molecule into the TMA lattice. We employed the ωB97X-D functional,57 which adequately describes both the dispersive forces that stabilize adsorption and the hydrogen bonding of the intermolecular interactions. In past work,10,

52, 58

we used the

B3LYP functional in related hydrogen-bonding calculations, so in Table 1 we provide results for hydrogen-bonded dimers optimized using both functionals. Counterpoise corrections for the basis set superposition error have not been applied to the values in Table 1, but are discussed in the SI. Consistent with our previous findings,10 the TTBTA-TTBTA dimer bond is very similar to but slightly stronger than the TMA-TMA bond; the TMA-TTBTA bond energy is intermediate between those of the two homomolecular dimers. A similar trend was previously reported for


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TMA/BTB bond energies.59 In the present case, we speculate that the energies vary due to differences in polarization for the –COOH groups on benzene and thiophene rings.

Table 1: Calculated gas phase bond enthalpies and O-H…O distances for hydrogen bonds.

B3LYP/6-31G(d,p)

ωB97X-D /6-31G(d,p)

Bond energy (kcal/mol per molecule)

Average OH…O distance (Å)

Bond energy (kcal/mol per molecule)

Average OH…O distance (Å)

TMA-TMA

-10.01

1.618

-10.70

1.627

TMA-TTBTA

-10.12

1.613

-10.77

1.627

TTBTA-TTBTA

-10.22

1.612

-10.85

1.626

Dimer

Figure 4 displays the relevant adsorption sites and adsorption energies for TMA/TTBTA adsorption on HOPG. For both molecules, adsorption with the benzene ring placed over a substrate atom is more favorable than adsorption over a hole site by ~2 kcal/mol, while the rotation of the molecules (to reflect the alignment in an epitaxial film) introduces a smaller (~0.3 kcal/mol) perturbation to the energy.


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Figure 4: Representative adsorption geometries and energies for pure TMA and pure TTBTA chicken wire lattices on (a, b) hole site (HS), (c, d) atom site 1 (AS1), (e, f) atom site 2 (AS2) and f(d, h) for the intermixed lattice on AS1. All geometries were calculated at ωB97X-D/631G(d,p).


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The epitaxial nature of the intermixed lattice (see above) implies that the majority of molecules in the intermixed lattice sit on well-defined adsorption sites defined by the geometry and periodicity of the lattice, and that the substitution of the larger TTBTA molecules presents only a local perturbation to epitaxy. This displacement results in an epitaxial penalty as well as a penalty associated with bond distortions.

The epitaxy of the intermixed lattice has important implications for the geometry of the TMATMA bonds that constitute the majority of the domain, since they must be expanded from their equilibrium bond length. To capture this effect we assume in our models that second nearest neighbor (and higher) TMA molecules are fixed on high-symmetry AS1 sites defined by the epitaxy matrix. Calculations (Figures S35 and S36) of the cluster of molecules surrounding a single TTBTA substitution suggest that both the TTBTA-TMA bonds and the TMA-TMA bonds to the next-nearest neighbor TMA molecules are compressed from their preferred distance of d(HOOC...COOH)=3.62 Å (in pure epitaxial TMA domains) to a distance of d(HOOC...COOH )=3.51 Å for TTBTA-TMA and d(HOOC...COOH)=3.53 Å for TMA-TMA. Similarly, we calculated the lattice for two TTBTA substitutions at the 1,4 positions of a pore (Figure S36). In this case, we find a slightly higher compression of bonds between nearest-neighbours and second-nearest neighbours.

Figure 5a shows the results of energy calculations for the extension and compression of TMATMA and TMA-TTBTA bonds from their equilibrium lengths. The energetics of both TMATMA and TMA-TTBTA interactions are nearly identical, with a steeper enthalpic penalty for compressive strain than for tensile strain. Figure 5b shows the energy landscape as a TMA molecule, starting from an optimized adsorption geometry over an AS1 type site, is displaced


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towards a hole site en route to an AS2 site. In these calculations, the benzene core of the molecule is held fixed, and the carboxylic groups are allowed to relax. The energetic landscape of this trajectory illustrates the depth and localization of adsorption in the AS2 site, in contrast to the relatively shallow and wide adsorption minima associated with the AS1 and hole sites, and suggests that the displacement of TMA from its ideal adsorption site can incur a relatively small penalty.

Figure 5: (a) Change in bond enthalpy (ωB97X-D/6-31G(d,p)) as a function of compression or expansion from equilibrium bond distance for TMA-TMA and TMA-TTBTA dimers. The Hbonded –COOH groups were held fixed and all other parts of the molecules allowed to relax. Compression/expansion lengths salient to the observed intermixed phase have been indicated with arrows. (b) Change in adsorption enthalpy (ωB97X-D/6-31G(d,p)) for a TMA molecule optimized on the AS1 site and moved towards AS2 via a hole site (HS). For all sites but AS1, the benzene core was held fixed and only the –COOH groups were allowed to relax.


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To calculate the entropy of an intermixed domain we applied a Monte Carlo model to populate a set of molecular lattices where solute (TTBTA) molecules cannot approach one another nearer than in 1,4 positions (due to strain and in agreement with experimental observation). The number of unique lattices identified at a given stoichiometry was taken to be equal to the multiplicity, Ω(x). The multiplicity for a lattice of 50 molecules is shown in Figure 6 (further discussion of the lattice size effect is provided in the SI). The entropy, S, can be found from the multiplicity according to Boltzmann’s relation, S = kBlnΩ, where kB is Boltzmann’s constant. In the expression for Gibbs free energy, the entropy of intermixing, ∆Smix, represents the difference between the intermixed phase and the pure-TMA phase. Since the multiplicity of the pure TMA phase is 1, the entropy of intermixing is uniquely defined by the multiplicity of the intermixed lattice.

Figure 6: Monte Carlo multiplicities for a lattice of 50 molecules, where solute substitutions are restricted to 1,4 lattice sites (see text). To find ∆Hmix, we applied the DFT-calculated energies of intermolecular and molecule-substrate interactions to a set of lattices generated through the Monte Carlo algorithm. These calculations


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take into account the geometry of the TMA lattice in the vicinity of TTBTA substitutions, which require estimating the energy penalties for compressing and expanding the hydrogen bonds and displacing adsorbed molecules from epitaxial sites. Total domain enthalpies were calculated for 100,000 matrices (200 molecules per lattice with 12% TTBTA) according to the energetic considerations listed in Table S3. Figure 7a shows that the energies are normally distributed with an average enthalpic penalty of 0.62 kcal/mol per TTBTA substitution and a standard deviation of 0.62 kcal/mol. As expected, we find that the mixing of TTBTA into the TMA chicken wire lattice is accompanied by an enthalpic penalty. This relatively small penalty results from an interplay of competing effects: the substitution-related bond strain is compensated by the epitaxy of the intermixed lattice, which imposes favorable TMA-TMA bond distances when compared to the epitaxial TMA homophase, and includes the large adsorption enthalpy associated with the TTBTA molecules. As shown in the SI (Figure S7), the Gibbs free energy for an intermixed lattice restricted to 1,4 substitutions has a minimum at a TTBTA stoichiometry of 0.12 for a per-substitution enthalpic penalty near 0.6 kcal/mol. Figure 7b shows the Gibbs free energy curve that results from extrapolating our calculated per-molecule penalty (0.62 kcal/mol) to other stoichometries: the curve has a well-defined minimum located at a TTBTA stoichiometry of 0.10-0.12, consistent with the stoichiometry observed experimentally. This suggests that the observed intermixed lattice is thermodynamically stable with respect to the TMA homophase. A further discussion of this approach is provided in the SI.


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Figure 7: (a) Calculated ∆Hmix for intermixed TMA/TTBTA domains comprising 200 molecules (10×10 unit cells). (b) The Gibbs free energy for an intermixed lattice of 50 molecules restricted to 1,4 TTBTA substitutions with an average energy penalty per substitution of 0.62 kcal/mol. The entropic contribution is determined from the multiplicities shown in Figure 6 as described in the text. The average domain size plays an important role in the calculation of ∆Hmix. Enthalpic calculations for intermixed domains with 12% TTBTA as a function of domain size are shown in the Figure S8. As the domain size increases towards 300 molecules, the enthalpic penalty of substitution also increases. We associate this increase with an amelioration of strain on the perimeter of the intermixed domains, an effect that becomes less significant as the perimeter:area ratio is reduced in larger domains. These calculations suggest that stable intermixed domains are


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size-limited, and that the formation of an extended 2D lattice may be thermodynamically unfavorable. Finally, these calculations also suggest that the complementary substitutional solid solution of TMA in TTBTA (i.e., the inverse of the observed) is not likely to be thermodynamically stable for several reasons: (1) TTBTA-TMA hydrogen bonds are weaker than TTBTA-TTBTA hydrogen bonds, (2) the adsorption enthalpy of TMA is smaller than that of TTBTA, making substitution unfavorable, and (3) the average lattice constant of an intermixed domain should be compressed from the equilibrium lattice constant, which carries a higher penalty per unit change (n.b. the asymmetry of strain in Figure 5a) than the expanded lattice observed in the present work. This suggests that the surface-confined TMA/TTBTA system falls outside of established design heuristics for mixed crystals, which hold that solid solutions generally form from constituents whose sizes are within 20% of one another, and that particularly for such a large size mismatch the mixing of a small solute into a lattice of a large solvent should be favored over the converse case, which causes significant bond distortion.37 These departures from bulk expectations highlight the importance of molecule-substrate interactions in monolayer solid solutions,60 and suggest that confinement to a surface may yield opportunities for engineering mixed crystals. CONCLUSIONS AND PERSPECTIVES Two C3 symmetric molecules, TMA and TTBTA, with the same carboxylic functional groups but with different sizes, can spontaneously form a randomly intermixed but structurally and stoichiometrically well-defined porous network at the solution/solid interface. The intermixed phase occurs in domains that have the larger TTBTA molecule mixed into the TMA chicken


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wire lattice. The intermixed lattice constant is predicted by Vegard’s law, and the orientation of the lattice allows for coincidence of the average molecular position with substrate lattice sites (i.e., epitaxy). An analysis of the Gibbs free energy of intermixing, considering both the enthalpic and entropic contributions to the intermixed system, suggests that the observed intermixed domains are thermodynamically stable with respect to the TMA homophase. Calculations of total energies for a range of domain sizes indicate that the growth of intermixed lattices is self-limited, consistent with the small size (5-20 nm) of domains observed in our experiments. These energetic considerations provide a detailed view of the delicate enthalpy/entropy balance that underwrites this system, where epitaxy, hydrogen bond elasticity and domain size all play important roles. Epitaxy is intrinsic to surface-confined systems, and its stabilization of this 2D substitutional solid solution suggests that this approach may allow for the engineering of alloy systems not accessible in bulk materials. Further exploration of binary molecular systems, both through experimental and computational studies, will help to elucidate the possibilities for 2D solid solutions based on other intermolecular interactions and exhibiting other symmetries, as well as to determine how these phases fit into the broader phase diagram for multi-component molecular self-assembly at the solution/solid interface. In particular, variabletemperature experiments will provide a useful tool for amplifying or reducing the relative importance of the entropic term, with the possibility of providing control over phase selection.

METHODS Saturated solutions of TTBTA and TMA/hexadecanol in heptanoic acid were prepared separately. We measured the saturation concentration of TTBTA in heptanoic acid as 3.3 × 10–5 M using optical absorption spectroscopy. The saturation concentration of TMA in heptanoic acid


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has previously been reported as ~7.5 × 10–4 M.61 TMA/1-hexadecanol was dropped onto freshly cleaved highly oriented pyrolytic graphite (HOPG).62 Different amounts of TTBTA were mixed into the saturated TMA solution on the surface, in general by adding a droplet of TTBTA solution and then desorbing the existing molecular layer through the application of a voltage ramp (typical parameters -3V to 3V over ~50 ms, applied while the tip is in tunneling range of the surface). Repeated experiments, performed on different days, produced essentially identical results. In experiments to test the guest/host capability, a solution of C60 in heptanoic acid was added dropwise to the surfaces once the molecular structures had stabilized; C60 guests were found to adsorb only in the pores of the homophases of TMA and TTBTA, and not in the intermixed lattice. Heptanoic acid (99%), TMA (97%), 1-hexadecanol (95%) and C60 fullerenes (98%) were obtained from Sigma-Aldrich and used without further purification. The synthesis of TTBTA is described in detail elsewhere.63 HOPG (grade SPI-2) was obtained from SPI Supplies and was cleaved prior to each experiment using adhesive tape. STM images were acquired at room temperature using a Digital Instruments Nanoscope III microscope. STM tips were mechanically cut from 80/20 Pt/Ir wire. Bias voltages are quoted with respect to the sample. STM images were processed using the free WSxM software.64 When possible, the images were calibrated and drift corrected to the underlying HOPG structure; in other cases, the images were corrected to the known structure of the TMA network. The lattice constant for the intermixed domains was measured using full-domain autocorrelations from corrected/calibrated images that also included the TMA or TTBTA homophase. Gas-phase ab initio calculations were performed at the B3LYP/6-31G(d,p) and/or ωB97X-D/631G(d,p) levels using Gaussian 09;65 the former was selected for consistency with previously-


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published calculations of 2D hydrogen bonding assemblies, whereas the latter was employed to capture the dispersive molecule-HOPG interactions.57 All starting geometries were constrained to Cs or higher symmetry to simulate on-surface adsorption. In our previous work, we found that the adsorption energies for TMA on graphene and graphite were quite similar;52 hence, here we consider the adsorption energetics of single molecules of TMA and TTBTA on a graphene flake. Adsorption enthalpies were calculated using ωB97X-D/6-31G(d,p), and represent the interaction energy of a molecule adsorbed in an optimized geometry on a D6h constrained, pre-optimized planar C150H30 graphene flake. The stoichiometry of the intermixed domain was determined from STM images using two different analyses: a domain-by-domain analysis over 14 domains, where the uncertainty is given as a standard deviation, and by considering the total number of TMA and TTBTA molecules in the intermixed domains (nmol~2700), with an uncertainty determined by Poisson statistics. Both analyses produced the same result and uncertainty. Monte Carlo simulations to determine multiplicity and to estimate the enthalpy of molecular domains were performed using a custom code developed in MATLAB. Further description of the MATLAB code is provided in the SI.

ASSOCIATED CONTENT Supporting Information. Epitaxy of pure-TTB lattice, STM images presented without false-color, Relative orientation of intermixed lattice with respect to pure lattice, Gibbs free energy for a freely-intermixed lattice


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with different enthalpic penalties per substitution, Multiplicities for restricted lattices of different sizes, Gibbs free energy minimum for lattices of different sizes, Gibbs free energy for an intermixed lattice restricted to 1,4 substitutions with different enthalpic penalties per substitution, Pseudo-code for generating randomly substituted intermixed matrices, Counterpoise-corrected bond enthalpies for hydrogen-bonded dimers, Enthalpic penalties for single substitutions, Geometry of clusters used to extract bond distances in intermixed lattices, Effect of domain size on the calculated energy penalty per substitution, Spatial distribution of 1,4 TTBTA inclusions in the intermixed TMA/TTBTA lattice, Gibbs free energy for an intermixed lattice restricted to 1,4 substitutions with different enthalpic gains per substitution, Assumptions and limitations in approximating the enthalpic term of the Gibbs free energy. This material is available free of charge via the Internet at http://pubs.acs.org.

ACKNOWLEDGMENT This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) through the Discovery Grants program, by Le Fonds de Recherche du Québec - Nature et technologies (FRQNT), the Ministère du Développement Économique, Innovation et Exportation (MDEIE), and by the Australian Research Council (DE170101170). It has been enabled by the use of computing resources provided by WestGrid and Compute/Calcul Canada, and through the High Performance Computing (HPC) facilities at QUT. F.R. acknowledges the Canada Research Chairs program for funding and partial salary support. F.R. is also grateful to the Government of China for a Chang Jiang scholar short term award and to Sichuan province for a 1,000 talent short term award.


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