Coverage and Enantiomeric Excess Dependent Enantiomorphism in Two-Dimensional Molecular Crystals† Manfred Parschau,‡ Roman Fasel,§ and Karl-Heinz Ernst*,‡ Nanoscale Materials Science Laboratory and nanotech@surfaces Laboratory, Empa, Swiss Federal ¨ berlandstrasse 129, CH-8600 Du¨bendorf, Laboratories for Materials Testing and Research, U Switzerland
CRYSTAL GROWTH & DESIGN 2008 VOL. 8, NO. 6 1890–1896
ReceiVed NoVember 7, 2007; ReVised Manuscript ReceiVed December 17, 2007
ABSTRACT: The question of racemate versus conglomerate stability is tremendously important for chiral resolution via crystallization methods. Scanning tunneling microscopic studies with molecular resolution on two-dimensional (2D) model systems contribute at large to solve problems on complex crystallization phenomena. The dependence of lattice polymorphism and enantiomorphism on coverage and enantiomeric excess has been investigated for monolayers of enantiopure and racemic heptahelicene on a Cu(111) surface in ultrahigh vacuum. The densest packing is achieved in a homochiral lattice structure. This should favor 2D conglomerate formation for the racemate, since a higher coverage leads to an overall lower energy. However, only heterochiral structures are observed. Small enantiomeric excess (ee) induces lattice homochirality by suppressing one enantiomorph. At larger ee, we observe crystals disordered at the molecular level. Long-range ordered homochiral structures are suppressed due to small chiral impurities. The preference of a 2D racemic compound formation, the induction of lattice homochirality at small ee, and the solid solution formation at larger ee are discussed in the light of energetic, entropic, and kinetics effects.
1. Introduction When a racemic mixture condenses it may form (i) a racemic compound, in which both enantiomers are present in the same single crystal; (ii) a conglomerate, in which the single crystals contain only one enantiomer, but the sample as a whole is racemic; and (iii) a solid solution, in which the condensate contains the two enantiomers in a nonordered arrangement.1 Racemic crystals outnumber by far conglomerate-formers, and even fewer tend to form solid solutions.1,2 The latter is also called a pseudoracemate3 and sometimes is obtained by seeding the racemic liquid with pure enantiomers.4 In his famous experiment in 1848, Pasteur separated left- and right-handed ammonium sodium tartrate crystals manually and observed opposite optical activity for their aqueous solutions.5 His insight that the origin of chirality is based on molecular structure laid the foundation of modern structural organic chemistry. In particular two important aspects in his experiment allowed the manual separation: (i) Handedness was transferred from molecular structure into the macroscopic shape of the crystal (hemihedrism), and (ii) the racemate precipitated into a conglomerate of homochiral crystals. The underlying mechanisms of both processes are still poorly understood. We are neither able to predict the shape of a crystal from molecular structure6 nor do we know why just 10% of all racemates crystallize into conglomerates.1 One reason for the difficulty to understand and investigate these processes is their cooperative nature. Extremely small structural influences govern the macroscopic result while becoming amplified by many cooperating units. This lack of insight has also economical consequences, since separation of enantiomers via crystallization is still the most important means.7 Cooperativity among different homochiral biomolecules is also of fundamental importance in life.8 A promising approach to gain insight into this complex field is studying two-dimensional (2D) crystallization and self†
Dedicated to Prof. Jack Dunitz on the occasion of his 85th birthday. * To whom correspondence should be addressed. Tel.: +41-44-823 43 63 Fax: +41-44-823 40 34. E-mail:
[email protected]; www.empa.ch/mss. ‡ Nanoscale Materials Science Laboratory. § nanotech@surfaces Laboratory.
Figure 1. Ball and stick models of (M)- and (P)-heptahelicene.
assembly phenomena on well-defined substrates with a scanning tunneling microscope (STM), whereby position and orientation of the molecules are revealed at submolecular resolution. Various aspects of 2D chiral surface science have been investigated via this technique,9–11 including homochiral and diasteriomeric recognition.12 Moreover, it has been predicted that 2D enantioseparation on a surface should occur more easily than in three-dimensional (3D) crystals.13 Because of confinement in the plane certain symmetry elements, like center of inversion or the glide plane parallel to the surface, are precluded,14 and a higher probability for spontaneous resolution is therefore expected.15 Here we present a STM study on the 2D crystallization of the chiral aromatic hydrocarbon heptahelicene (Figure 1, C30H18, [7]H) on a Cu(111) surface. For the pure enantiomers, we previously found a pronounced transfer of chirality into the monolayer, manifested by the formation of extended chiral motifs.16 Interestingly, mirror domains have been observed for the racemate at the same surface, indicating at a first glance a lateral resolution of the enantiomers.17 However, STM experiments in combination with molecular modeling calculations (MMC) showed that heterochiral M-P pairs become aligned in a chiral configuration, leading to the observed enantiomorphism.18 A switch to the opposite enantiomorph requires only a small rearrangement of the enantiomers in the heterochiral pair. This leads to the induction of lattice homochirality via cooperative amplification of a small chiral bias in nonracemic mixtures.18 Amplification of chirality in two dimensions,
10.1021/cg701100r CCC: $40.75 2008 American Chemical Society Published on Web 05/17/2008
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Table 1. Matrix Notation and Exact Lattice Properties for One Set of Enantiomorphous Structuresa lattice R (P) β (P) (6&3) γ (P) (clover) ε F′ F
matrix notation
( ( ( ( (
) ) ) ) )
12 -2 2 14 8 2 -2 6 3 -2 7 8 4 -1 6 10 4 -1 5 8
molec per unit cell
a [Å]
b [Å]
Ra,b
β[11j0]
A/molec[Å2]
θlocalrel (%)
3 9
22.5 ( 0.5 33.48 33.3 ( 0.2 18.41 18.4 ( 0.2 11.13 11.7 ( 0.6 11.69 11.9 ( 0.3 11.69 11.7 ( 0.5
22.5 ( 0.5 33.48 33.3 ( 0.2 18.41 18.4 ( 0.2 19.27 19.6 ( 0.5 22.25 22.4 ( 0.3 17.87 18.0 ( 0.2
120° ( 2.5 120° 119.9° ( 2.0° 120° 13.3° ( 2.7° 90° 90.7° ( 2.6° 94.31° 94.8° ( 1.1° 92.67° 92.7° ( 1.6°
≈ -22° -7.6° -7.7 ( 0.6 +13.89° 13.3° ( 2.7° -23.41° -22° ( 2.2° -10.89° -10.5° ( 0.8° -10.89° -10.5° ( 0.8°
146 107.9
67 90.7
3 2 2 2
97.8
100
107.2
91.3
129.6
75.3
104.4
93.7
a The experimental results are given in italic with error margins. Enantiopure R(P), β(P) and γ(P) as well as racemic F′, δ and F structures. a, b: length of adlattice unit cell vectors; R: angle between a and b; β: adlattice tilt angle w. r. t. the [11j0] substrate direction; A: occupied area per molecule; θlocal: relative coverage of the structure (γ ≡ 100%). The corresponding mirror structures are denoted as R(M), β(M), γ(M), λ′, ε, and λ (see Supporting Information for unit cells).
corresponding to the “sergeants-and-soldiers” principle observed for chirally doped helical polymers,19 has been first observed in racemic monolayers layers of prochiral succinic and mesotartaric acid after doping with intrinsically chiral (R,R)- or (S,S)tartaric acid.20–22 The amplification in helical copolymers with small enantiomeric excess (ee) in the side chains has been coined as “majority rule”.23 In this paper we report for the monolayer system [7]H/ Cu(111) how lateral density (i.e., coverage) and the ee influence expression of long-range chirality (enantiomorphism), lateral enantiospecific separation, and cooperative interactions in 2D crystal lattices. This includes lattice structures formed by the racemic mixture and a chiral phase transition with varying coverage, the enantiomorphism in layers of the pure enantiomers, and the influence of ee on the long-range order. Besides the previously reported amplification of chirality with small ee at monolayer saturation coverage,18 this effect is now observed for the other racemic structures at lower coverages. In addition, we report here the suppression of long-range order due to enantiomeric impurities. These disrupt the lattice of the pure enantiomers via cooperative interactions, not allowing chiral expression or enantiomorphism. Finally, we discuss why nonpolar molecules prefer racemic crystal formation in 2D, although their homochiral opponents can be packed more densely and should be therefore more favored by adsorption energetics.
2. Experimental Section Experiments have been carried out in an ultrahigh vacuum (UHV) chamber, base pressure of 1 × 10-10 mbar, equipped with a variabletemperature STM (Omicron Nanotechnology). The Cu(111) surface was prepared by repeated cycles of Ar+ sputtering and subsequent annealing at 800 K for 10 min. Racemic [7]H has been synthesized as described previously.24 Separation into the enantiomers was performed via HPLC on a Chiracel OD column. The achieved enantiomeric purity (ee > 0.999) has been determined also via HPLC on a Chiracel OD-H column. The [7]H molecules, racemate and pure enantiomers, were evaporated in vacuo from a homemade twin Knudsen cell at a temperature of 433 K onto a Cu(111) substrate held at room temperature during deposition, if not stated otherwise. The deposition rate for racemic [7]H was about 0.1 monolayers/min under these conditions. Enantiomeric excess25 at the surface was achieved via different evaporation times of the two pure enantiomers at identical sublimation temperatures. After deposition the sample was transferred into the STM and cooled with a cooling rate of about 10 K/min to a temperature of 50 K. The STM images were acquired at this temperature. All shown images were recorded in constant current mode. The given bias voltage always refers to the sample with respect to the tip; that is, a positive value indicates tunneling from the tip to the sample. We used bias voltages that allowed low currents and larger tunneling distances, thus causing minimal interference of the molecular crystal. The structural parameters (Table 1) of
Figure 2. Phase diagram of [7]H on Cu(111) with varying coverage and ee. the lattices have been determined from the average of 20 drift corrected STM images of the respective structure. Molecular modeling was performed using the AMBER force field of the Hyperchem 7 package.26 The molecular conformation of [7]H on Cu(111) was assumed as previously determined from XPD experiments27 and successfully applied in earlier studies.16,18 The Cu(111) surface geometry was included such that it provided a static “checkerboard”, defining the possible molecular adsorption sites. The minimum total energy configurations of the close-packed monolayer system were determined by considering all possible molecular configurations within the experimentally determined unit cells. Total energies were calculated for all possible combinations of the enantiomeric identities of the molecules, their lateral positions within the unit cell, and their azimuthal orientations. The periodicity of the adsorbate lattice was considered by applying periodic boundary conditions. The viability of this approach for this system has been demonstrated by us previously.16,18
3. Results An overview of all structures depending on ee and coverage and where they coexist is given in the form of a schematic phase diagram in Figure 2. Overall six different phases are observed, all existing in two mirror symmetric forms: R, β, and γ for the pure enantiomers and ε/δ, λ′/F′, and λ/F for the racemic mixture. The density of these structures and the orientation of their lattice with respect to the metal substrate are different. Experimental values and the theoretical lattice parameters are listed in Table 1. The adlattice periodicities are presented in matrix notation,28 applying the rules for the appropriate choice of unit cell vectors.29 Also listed are the number of molecules per unit cell, the lengths of the unit cell vectors and their apex angle, the tilt angle β of the adlattice with respect to the [11j0] substrate direction, andsas measures for the densities of the structuressthe area occupied by one molecule as well as the corresponding local coverage of the particular lattice. We use
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relative coverage values with the highest coverage set to 100%, which is only achieved by enantiopure [7]H in the γ structure (formerly called 3-structure or clover leaf structure16). The maximum coverage of 100%, that is, θrel ) 1.0, corresponds to an absolute coverage of 3/52, that is, θ abs ) 0.0577 molecules per Cu surface atom. We distinguish between global and local coverage, which are the experimentally controlled average coverage on the entire crystal surface and the coverage of a particular lattice structure induced by the self-assembly process, respectively. The lattice unit cells for all observed structures are shown in the Supporting Information Figures S2 and S3. 3.1. Zero Enantiomeric Excess: The Racemic Monolayer. After deposition of the racemic mixture of [7]H on Cu(111) no ordered superstructures are observed up to coverages close to half a monolayer. Even at 50 K, single molecules are too mobile to be imaged via STM on the flat Cu(111) terraces. Hence, the diffusion barrier for the individual molecule is either low enough to allow the molecules to diffuse to the step edges where they get pinned, or they are moved by the STM tip. The molecules are only observed to decorate the lower part of step edges, forming one-dimensional chains. The apparent height of the molecules is about 2.8 to 3.0 Å. Consequently, the molecules are imaged brighter than a Cu(111) single step with a height of 2.08 Å. This molecular height agrees with the dimension previously determined via X-ray photoelectron diffraction (XPD) for the pure enantiomers on Cu(111).27 Since the [7]H molecules exhibit no chemical groups to form stronger directional intermolecular bonds, they do not coalesce into 2D islands at small coverage and are imaged as unstable patterns by the STM. The apparent molecular height on flat terraces is comparable with the height of the molecules pinned at step edges. This mobile phase (2D gas) starts to condensate at about 50% of the saturated monolayer coverage, and short chains of [7]H molecules appear to nucleate randomly over the terraces (see Supporting Information Figure S1). With increasing coverage enantiomorphous lattice structures embedded in areas of short-ranged ordered features are observed. Figure 3 presents STM images for the racemate from medium coverage to saturation. Overall, three pairs of enantiomorphous structures, denoted as ε/δ, λ′/F′, and λ/F, are observed. All these adlattices successively form with increasing global coverage and have a common feature, that is, the molecules are aligned in zigzag double rows (see insets of Figure 3a,d, for example). At θglobalrel ) 0.59 the racemate shows only small islands of ε and δ domains (Figure 3a). The majority of the surface area is covered with short-range ordered molecules, mainly in form of short zigzag rows. Although the domain size of the ε and δ domains increase with coverage, already at θglobalrel ) 0.70 these domains coexist with the newly formed λ′/F′ phase (Figure 3b). While with increasing coverage the ε/δ domain size decreases, the λ′/F′ domains grow in size. In addition, the latter simultaneously get denser (Figure 3c). When finally the saturation coverage for the racemate is reached, the molecular layer shows only the two enantiomorphous λ/F-domains (Figure 3d). There is another interesting observation to note: With increasing coverage, the probability of finding coexisting mirror domains on the same terrace decreases. This becomes also clear from Figure 3: While small ε and δ domains (Figure 3a) may coexist, their larger domains tend to occupy exclusively a single terrace (Figure 3b). Coexistence of λ′ and F′ on the same terrace is observed as well. However, Figure 3b shows this situation with a δ domain in between λ′ and F′, avoiding the direct mirror domain boundary. At higher coverages mirror domain boundaries on one terrace are rarely observed.30
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Figure 3. STM images (150 × 150 nm2) of different enantiomorphous phases of racemic [7]H on Cu(111) with increasing global coverage (θglobal rel ) 0.59 (a), 0.71 (b), 0.85 (c), 0.93 (d)). Domains are colored according to the phase diagram shown in Figure 2 (measurement parameters: (a) U ) +2.72 V, I ) 20 pA; (b) U ) +2.80 V, I ) 18 pA; (c) U ) +2.67 V, I ) 24 pA; (d) U ) +2.61 V, I ) 20 pA).
Figure 4. High resolution STM image (-1.67 V, 1.28 nA) from a F/F′ domain boundary. The only difference between both structures is the distance between the zigzag double rows formed by heterochiral pairs. The double row in the middle has a translational mismatch to both structures. The overlap of molecular frames with the electron density is indicated for two heterochiral pairs.
We have shown previously via molecular modeling calculations for the λ/F phase that the zigzag rows are composed of heterochiral pairs.18 Highly resolved STM images supported by extended Hückel simulations allow determining the absolute configuration of the enantiomers.18 High resolution STM performed on both high coverage phases indicate that we can safely make the same conclusion for the λ′/F′ phase, since the zigzag rows appear to be identical (Figure 4). From these images and extended Hückel simulations the absolute configuration of the enantiomers is obtained.18 The only difference between the λ′/F′ and λ/F structures is the distance between the zigzag rows, while the distance between adjacent heterochiral pairs within the rows as well as the tilt of the zigzag row with respect to the substrate lattice are identical (Table 1). For the ε/δ phase, we
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Figure 5. Coverage series for enantiopure [7]H: (a) P - [7]H, θglobalrel ) 0.63 (-3.1 V, 24 pA); (b) M - [7]H, θglobalrel ) 0.84 (2.18 V, 43 pA); (c) M - [7]H, θglobalrel ) 0.96 (2.05 V, 19 pA).
do not have STM data that allow conclusions on a detailed adsorbate structure, but its similarity to the better resolved zigzag structures and the difference to the enantiopure phases are a strong hint for a heterochiral phase. This is confirmed by MMCs, which give the lowest total energy for a M-P zigzag chain structure with a 60° relative azimuthal orientation of the M and P enantiomers. Detailed structure models will be discussed in section 4. 3.2. Enantiopure Monolayers: ee ) 1.0. As observed for the racemate, only from medium to high coverage ordered structures have been observed in STM for the pure enantiomers. Figure 5 summarizes the development with increasing coverage. At about two-thirds of the saturated monolayer coverage, clusters composed of three molecules form an ordered array (Figure 5a). With increasing coverage the β phase forms, with the repeating unit appearing as 6&3 molecule feature. Finally, the densest of all observed structures, the γ phase is generated. This structure appears in STM as built up by clusters of three molecules as well. Figure 5b,c actually shows intermediate coverages at which the respective structures coexist. The completed monolayer at θglobalrel ) 1.0 (not shown here), however, shows the surface completely covered with the γ structure, just like the green area in Figure 5c.16 As indicated by the oblique tilt angles in Table 1, all structures of the pure enantiomers are enantiomorphous, that is, opposite enantiomers express the opposite tilt in their lattices. However, the lattices are truly hexagonal. Taking only the topmost Cu surface layer into account, these adsorbate structures can be characterized as enantiomorphous composition of two 2D hexagonal lattices. 3.3. Small Enantiomeric Excess: Chirality Amplification. With an ee of a few percent in the monolayer and at saturation coverage, the ratio between terraces occupied by λ and F domains is not equal anymore. For ee g |0.08| the formation of one enantiomorph is completely suppressed and lattice homochirality on the entire surface is installed (Figure 6). Only domains of the same handedness are observed. Because the composition of the domains is still racemic, the ee must be located outside the domains (gray area).18 In two dimensions here, this phenomenon is also observed for the enantiomorphous phases at lower coverages. One example, representative for all other areas of the surface, is shown in Figure 7. Only “lefthanded” λ′ and ε domains are observed at positive ee ([M] > [P]). Although the domains are of racemic composition, the entire surface exhibits homochirality due to the single chiral alignment of all heterochiral pairs. 3.4. Large Enantiomeric Excess: Disorder Induced By Chiral Impurity. While with increasing ee the 1:1 heterochiral domains shrink in size, the poorly ordered areas containing the ee become larger (gray areas in Figure 7). With 20% of the opposite enantiomer in the monolayer, only small islands of
Figure 6. STM images for coverages of θglobalrel ) 0.93 and ee ) -0.08 (a) and ee ) +0.08 (b). Either exclusively clockwise tilted F (a) or counterclockwise tilted λ domains (b) are observed for negative or positive ee, respectively (measurement parameters: (a) +2.56 V, 26 pA; (b) +2.56 V, 23 pA).
Figure 7. STM image for a coverage of θglobalrel ) 0.70 at ee ) +0.20. Only single enantiomorphism is observed for the particular phase (150 × 150 nm2, +2.72 V, 21 pA).
the enantiomorphous heterochiral features are left (Figure 8a). Simultaneously, characteristic features of the enantiomerically pure β structure, the so-called 6&3 pinwheel clusters, appear. With increasing ee the number of enantiopure 6&3 clusters increases slightly and the racemic zigzag rows become shorter. However, even at rather large ee, long-range lattice order is not established. Just 9% of P-molecules in the monolayer are sufficient to avoid the M-[7]H long-range lattice order observed for the pure enantiomers (Figure 8b).
4. Discussion Similar to the interpretation of the observed handed supramolecular structures of the pure enantiomers of [7]H, the structures
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Figure 8. STM images at a coverage of θglobalrel ) 0.90 ( 0.02 and ee ) +0.60 (a) and ee ) +0.81 (b). Only few single 6&3 clusters (a, inset) of the pure M-[7]H are observed (examples marked with circles) (measurement parameters: 40 × 40 nm2, (a) 2.89 V, 21 pA; (b) 2.83 V, 20 pA).
of the racemic mixture can be explained within a simple topographic model.16 From the aforementioned XPD study we know that [7]H is adsorbed with the first three benzene rings parallel to the Cu(111) surface and spirals away from the surface.27 Assuming that the brightest feature in the constantcurrent STM image corresponds to the uppermost part of the molecule, the [7]H molecule can be approximated as a disk with an off-center protrusion (Figure 9). An arrow, aligned in the same plane as the C2 axis of the free molecule, is also plotted into each disk.31 The actual orientation of the molecule for the respective appearance is printed in Figure 9f. Except for the β structure, the models shown in Figure 9 are strongly favored from MMCs over other possibilities. The model for the β structure is based on the STM appearance only, since MMCs are prohibitive due to nine independent molecules per unit cell. We were not able to make reliable conclusions for the R structure of the pure enantiomers. Different lateral density induces a change of relative azimuthal orientations from the β to the γ structure. Remarkably, the latter represents a frustrated structure, as observed in crystals of parallel aligned helical polymers, like poly(L-hydroxyproline)32 or poly(L-lactide).33 This shows that, although the packing is mediated by the Cu substrate grid, our “one-pitch” helices apparently follow the same sterically controlled packing rules as extended helical molecules in 3D crystals. In the racemic ε/δ and the λ/F structures (Figure 9a,c), the molecules in a heterochiral pair are aligned differently with respect to their relative azimuthal orientations. ε/δ domains are favored at low coverage, while the λ/F domains are favored at closer packing. The alignment of the adlattice with respect to the substrate lattice is one kind of chiral expression at surfaces,10 and it is interesting to follow the ε/δ-to-λ/F-transition at the molecular level. This phase transition not only includes a realignment of the zigzag rows with respect to the substrate lattice, but also involves the change of relative azimuthal alignment in a heterochiral pair. Quite remarkable is that the intermediate λ′/F′ phase has a lower density (Table 1) and, according to the MMCs (Supporting Information, Figure S4), the lowest stability. In order to form the densest and most stable λ/F packing at saturation coverage, the transition from the dense ε/δ phase goes through the loosely packed, but, with respect to the final phase, equally aligned λ′/F′ phase. We must keep in mind here that only certain adsorbate sites provided by the substrate crystal and certain azimuthal orientations due to the steric interaction between the helices are allowed. This explains the more or less abrupt switch in orientation in the transition from ε/δ to λ/F. With increasing lateral pressure the relative
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azimuthal alignment of the molecules in the ε/δ phase apparently becomes destabilized. This leads to the (counterintuitive) situation that locally a less favored structure is formed (Figure 3b), while globally the energy of the system decreases due to minimizing lateral pressure. This allows maintaining the dense ε/δ phase as part of the monolayer. The λ′/F′ phase is truly an intermediate structure. As defined in Table 1, it can only coexist together with the ε/δ phase. With further increasing coverage the ε/δ phase disappears, while the λ′/F′ phase converts stepby-step into λ/F domains. Only if the molecular coverage is high enough, the molecules crystallize from the 2D disordered phase into an ordered arrangement. Under these conditions, that is, when short-range repulsive forces are significant, discrimination between homoand heterochiral ordering has been predicted to be more likely.34 Together with the preclusion of certain symmetry elements at surfaces, this should actually favor a lateral separation into domains of pure enantiomers. However, we clearly observe heterochiral structures for the racemate. In addition, they are enantiomorphous, because the M-P pairs are aligned into a chiral unit and close-packing occurs in an oblique angle to the substrate lattice, thus forming two mirror-like possibilities. Improper symmetry operations, like inversion and glide reflections, are believed to make the 3D racemic crystal more stable than the homochiral ones, since they lead to more densely packed crystals.1b The glide plane perpendicular to the surface has then been put forward as symmetry element allowing 2D racemate formation at surfaces;14b however, it rarely gives 2D closepacking.35 A glide plane between single heterochiral pairs parallel to the [11j0] substrate direction can be identified here, but it is not a symmetry element of the whole lattice, because the adlattice vectors run in an oblique angle to the [11j0] direction. The λ and F domains at saturation coverage are closer packed than the β structure of the pure enantiomers, but their density is below the one of the γ structure. This is reverse to the 3D case, where the [7]H racemic lattice (P21/c space group) packs closer than the pure enantiomer (P21 space group).36 It is thus an example for Wallach’s rule, stating that racemic crystals tend to be denser than the homochiral ones.1b,37 Denser packing on a metal surface, in general, does imply a higher gain of adsorption enthalpy with respect to the free molecules in the gas phase as long as repulsive forces at high coverages are prevailed.17,38 One should therefore expect a 2D conglomerate formation here, that is, the pure γ phases of both enantiomers form separately after exposure to the racemate. Although our MMCs do not take the interaction with the surface into account, they yield a lower energy for homochiral γ domains than for the racemic λ/F domains (see Figure S4, Supporting Information), which again favors 2D conglomerate formation. Therefore, we must assume that either entropic effects or a kinetic bias, as previously mentioned for 3D racemate crystallization,39 has to be taken into account. There are different kinetic barriers that may favor heterochiral structures in dense 2D layers: (1) MMCs for small clusters consisting of 2-5 molecules consistently yield the lowest energies for heterochiral configurations (see Supporting Information Figure S4). These seed clusters provide an intrinsic bias toward growing heterochiral structures. (2) In order to grow an enantiopure domain, on average every second molecule arriving has to be removed, while in case of the racemic crystal it just has to slip into right site in a right orientation nearby. (3) The 2D crystals rather form at higher coverages. In that situation, enantiopure structures would require separation via lateral mass transport. But diffusion of molecules
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Figure 9. Structure models for three racemic structures δ (a), λ′ (b), λ (c) and the two well-ordered enantiopure structures β (d) and γ (e). Unit cells are indicated. The molecules are approximated by a disk with an off-center protrusion corresponding to the brightest feature observed in STM. The arrow indicates the C2 axis of the free molecule (f).
through the dense layer at those temperatures is expected to be substantially hindered. Consequently, the observed structures are preferred at that limited diffusion path length. A similar situation has been observed for tartaric acid on Cu(110): Although the pure enantiomer can be packed into a denser structure than the racemate, no conglomerate formation is observed at saturation coverage.40 (4) Once the λ/F phase has formed the energy to squeeze either enantiomer into the heterochiral domains exceeds the value of the desorption energy,18 making a reorganization from heterochiral into homochiral domains via adsorption impossible. There is no difference in entropy between 2D heterochiral and homochiral domains. Even for 3D crystals, it has been made clear by Brock et al. that there is no entropy contribution favoring a racemic lattice over chiral conglomerate formation.1b Perfect homochiral and racemic crystals have the same entropy, which is zero at 0 K according to the third fundamental law of thermodynamics; and entropy differences due to grain boundary effects can safely be neglected. Moreover, both crystals are also in contact with the same racemic 2D liquid. However, adsorption has been performed at temperatures where no ordered lattices are observed. Although the coverage is high, the molecules are allowed to move around. For this system at our deposition conditions, the mixing entropy must be considered. For a disordered 2D phase, the racemate is favored by RT ln 2, that is, by 1.73 kJ/mol at 300 K. The MMC-determined energy advantage for the pure γ structure over the λ/F phase amounts only to roughly 1 kJ/mol (Supporting Information Figure S4). Therefore, at the disordered state during adsorption, the entropic contribution does not allow the lateral separation in order to reach the higher coverage required for enantiopure γ structure formation! Intriguingly, no larger enantiopure domains are formed at large ee. Only enantiopure lattice features on a local scale are observed, even at ratios of 9 to 1 (ee ∼ 0.8). These features are the pinwheel structures of the β structure. If we apply again
the argument of close-packing, the racemic δ/ε and λ/F structures are favored over β but not over γ. The latter, however, is not observed at all with the opposite enantiomer present even at large ee. As discussed for ee ) 0, the high coverage (lateral pressure) to overcome the repulsive forces in order to form the γ structures might be never installed under deposition conditions for entropic reasons as long as a chiral impurity is coadsorbed. Thus, the maximum coverage for mixed structures always stays below the one achievable for the enantiopure γ structure. During crystallization upon cooling, the racemic zigzag structure is more stable than the less dense β structure and its formation is preferred. In other words, since locally mixed configurations over enantiopure configurations are favored, one opposite handed molecule is able to disrupt formation of pure enantiomeric structures of at least nine other enantiomers. During nucleation and growth, a wrong-handed majority enantiomer, on the other hand, is unlikely to be replaced by a minority enantiomer, and further growth of the zigzag row is quickly terminated for kinetic reasons. The fact that there are always small zigzag parts in the structure with different alignment vectors avoids a uniform structure. This leads to a 2D crystal that is disordered at the molecular scale, and now the entropic contribution becomes substantial even for a crystalline solid. Such a system resembles an ideal 3D solid solution with static disorder.41 Those compounds have usually molecules with a nearly spherical shape.2 In two dimensions, the disk-shaped [7]H and the possibility to be 6-fold azimuthally oriented on Cu(111) are apparently ideal for the observed miscibility. However, a similar observation has been made for an elongated chiral formamide on a graphite surface.42 At zero ee, the phase diagram in Figure 2 shows the coexistence of mirror domains. This is, however, an approximation for our macroscopic sample and not valid on a small scale. The coexistence of mirror domains on a single terrace is only observed at lower coverage with small domains, surrounded by low-ordered areas. Mirror domain boundaries (MDBs) have
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higher energy content since they do not allow dense packing. Nevertheless, the formation of both domains at different places of a terrace cannot a priori be excluded. So if ever formed during crystallization, MDBs migrate to the steps by rearrangement of one mirror domain. Since this rearrangement only takes small site changes of the enantiomers at the less dense MDB, they can therefore easily disappear during crystal growth. This finally leads to spontaneous local symmetry breaking on a single terrace with an equal chance of forming either enantiomorph. In the presence of a small chiral bias, that is, ee, one domain becomes more stable than the other, due to enantioselective interactions between enantiomers at the enantiomorphous domain edges. While at larger ee, the minority domain probably never forms, this scenario cannot be excluded for small ee. But now the rearrangement on the terrace occurs with the ee present at the MDB. This will always stabilize the “majority-domain” over the “minority-domain” in the restructuring process. This plausible scenario beautifully shows how adjacent molecules cooperatively work for equal alignment of heterochiral pairs. As shown here, this amplification mechanism works at smaller coverages for the λ′/F′ and δ/ε domains with lower densities as well. The possibility that only short-range rearrangements between cooperating units are needed in order to have longrange effects makes this amplification process so effective.
5. Conclusions Oblique alignment of adlattice to substrate lattice is not only a form of chiral expression at surfaces, it also plays a role in 2D chiral phase transitions and the formation of long-range order. Chiral impurities disturb the formation of the majority lattice. That is, large ee causes small lattice segments to be wrongly aligned with respect to the long-range enantiopure lattice. Considering the lower dimension and the denser packing of pure enantiomers, chiral resolution is believed to be favored, but racemic lattices are formed due to kinetic hindering. In addition, the mixing entropy in disordered layers does not allow the highest possible coverage at deposition conditions. Single enantiomorphism of heterochiral lattices is observed at small ee for all racemic phases. Mirror domain boundaries between opposite chiral structures are very rare. The pure enantiomer structure at highest packing density shows a frustrated 2D crystal lattice, as known for 3D crystals of helical polymers. Acknowledgment. Financial support from the Schweizerischer Nationalfonds is gratefully acknowledged. Supporting Information Available: Additional STM data for lower coverages, schematic representations of the unit cells of the lattices for the enantiopure β and γ structures as well as for the racemic ε/δ, λ′/F′, and λ/F phases, and interaction energies for small seed clusters and extended lattice structures as determined from MMCs. This information is available free of charge via the Internet at http:// pubs.acs.org.
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