Role of Molecular Orientational Anisotropy in the Chiral Resolution of

Jul 2, 2012 - Separation of chiral molecules using achiral inputs is an interesting alternative to traditional techniques based on the chiral recognit...
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Role of Molecular Orientational Anisotropy in the Chiral Resolution of Enantiomers in Adsorbed Overlayers Paweł Szabelski* and Aleksandra Woszczyk Department of Theoretical Chemistry, Maria-Curie Skłodowska University, Pl. M. C. Skłodowskiej 3, 20-031 Lublin, Poland S Supporting Information *

ABSTRACT: Separation of chiral molecules using achiral inputs is an interesting alternative to traditional techniques based on the chiral recognition mechanism. In this article we propose a lattice gas Monte Carlo model of two-dimensional chiral segregation induced by breaking of molecular orientational symmetry. Simulations were performed on a square lattice for rigid chain molecules composed of four and five identical segments. Mirror-image flat chain conformations resulting in different enantiomeric pairs were considered for each probe molecule. The enantiomers were assumed to interact via short-ranged segment−segment interaction potential limited to nearest neighbors on the lattice. We considered two qualitatively different situations in which (1) the molecules were allowed to rotate on the surface and adopt any of the four planar orientations and (2) the rotation was blocked, so that only one planar orientation was possible. The results obtained for the racemic overlayers showed clearly that the orientational symmetry breaking can induce spontaneous segregation of the enantiomers into large enantiopure domains. However, this effect was observed only for molecules with sufficiently long linear fragment. In the case of kinked bulky molecules a mixed assembly was formed, demonstrating the role of molecular shape in the orientationally biased segregation of enantiomers in adsorbed films. The insights from this study can be useful in developing strategies for 2D chiral separations in which external directional fields are used.

1. INTRODUCTION Spontaneous self-organization of organic molecules in adsorbed overlayers has been recently recognized as a promising method to create chiral nanostuctured surfaces with unique physicochemical properties. Controlled adsorption of molecular building blocks on solid substrates either in ultra-high-vacuum conditions or from liquid phase allows for fabrication of highly ordered 2D superstructures with predefined morphology.1−3 This refers to both compact monolayers and planar porous molecular networks comprising cavities with nanometer size.4 Suitable choice of the shape, size, and functionality of the chiral or prochiral molecular bricks at play enables fine tuning of the symmetry and periodicity of the resulting overlayer, including the shape and size of the adsorbed molecular assemblies.4,5 These structural properties are especially important for adsorption and catalytic processes in which guest molecules interact preferentially with the complementary local nanostructures of the overlayer. A telling example in this field is enantioselective heterogeneous catalysis based on selective interaction of chiral reactants with a chirally templated surface.6−8 A special property of such a surface is that it is nonsuperimposable with its mirror image, and thus it can, for example, adsorb preferentially one enantiomer of a chiral reagent, leading to formation of a specific product. Homochiral adsorbed overlayers can be also used as templates for growth of columnar 3D phases, for example, chiral liquid crystal phases.9 © 2012 American Chemical Society

In this case, adsorbed molecules forming a domain of a given rotation direction can serve as nucleation points for growth of molecular stacks. In practice, creation of chiral adlayers is based on preadsorption of either chiral or prochiral organic modifier molecules which self-organize to form domains.8 Desirable features of those domains are maximum area and, ideally, unique rotation direction (homochirality), both of which promote highly enantiospecific performance of the overlayer. Although spontaneous separation of homochiral domains on solid surfaces has been observed in many cases,1−3 controlling this process is usually difficult as it is strongly temperature and coverage dependent and, moreover, many subtle factors related to intermolecular interactions and surface−molecule interactions are at play. This refers especially to those chiral assemblies which are formed at a liquid/solid interface where solvent molecules coadsorb, so that they can strongly interfere with structure formation.10−12 Other problems are the kinetic trapping which hinders formation of thermodynamically stable ordered phases and the existence of polymorphic homochiral domains.12 Received: April 30, 2012 Revised: June 30, 2012 Published: July 2, 2012 11095

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2. MODEL AND SIMULATION

To understand and control the self-segregation in racemic adlayers, Monte Carlo (MC) computer simulations and statistical mechanical calculations have been performed for different simplified molecular structures adsorbed on energetically homogeneous surfaces. These include bent hard needles,13 flat tripods,14,15 and more complex polyatomic Lennard−Jones molecules.16,17 It has been shown that molecular geometry and adsorbate density,13 intermolecular interactions,14,15 and the relation between steric and electrostatic interactions16 strongly influence chiral phase separation, so that careful manipulation of these factors can be used to induce or enhance the segregation process. Recently, it has been also demonstrated that both the structure and the composition of the adsorbing surface can have a substantial influence on formation of enantiopure molecular assemblies.18,19 For example, using a simple MC lattice model we were able to show that a complete chiral resolution of enantiomers can be achieved on a hybrid chiral surface with periodic distribution of active sites.18 In this case, the main factor responsible for separation was the compatibility of the molecular footprint of a given enantiomer with the corresponding local chiral motif of active adsorption sites. Interestingly, spontaneous chiral resolution has been observed experimentally in organic overlayers adsorbed on totally achiral metallic surfaces, demonstrating the role of interplay between intermolecular interactions and subtle differences in bonding of the enantiomers with the achiral surface. Usually an essential prerequisite for formation of enantiopure domains is the strict adsorption mode of a chiral molecule in which its translational and rotational degrees of freedom are largely reduced. This molecular confinement can be provided by different atomic nanostructures, like, for example, the parallel rows on (110) metallic crystal faces.8 Recently, it has been shown that the atomic rows of the Cu(110) surface help the adsorbed molecules of a prochiral quinacridone derivative to segregate and form homochiral domains with two enantiomorphous orientations.20 Another possibility of creation of homochiral adlayers by means of achiral inputs can be the use of external uniaxial fields. For example, Berg et al. demonstrated that a preferred in-plane orientation of prochiral molecules adsorbed on a graphite surface can be induced by the combined use of a liquid crystal (LC) solvent and a directional magnetic field.21 In this technique, called LC imprinting, the unidirectional orientation of the bulk LC solvent molecules induced by the external magnetic field was transmitted to the dissolved prochiral molecules adsorbing on graphite. The obtained breaking of the orientational symmetry of the adsorbed molecules allowed for continuous control over absolute handedness and enantiomeric excess in the system. The recent experimental results mentioned above motivated us to examine whether the orientational confinement of adsorbed chiral molecules that is induced by external factors can directly promote their enantioseparation in two dimensions. To answer this question, in this work we propose a simple MC model of chiral segregation occurring in a racemic mixture of interacting rigid chain enantiomers adsorbed on a solid surface. The major purpose of the present study is to understand the effect of molecular orientational anisotropy on structure formation in the racemic overlayers and identify key structural molecular properties promoting segregation.

We consider model chiral molecules adsorbed on a planar surface represented by a square lattice of equivalent adsorption sites. In a more general sense the enantiomers in our model can be treated as mirrorimage footprints of a molecule which can be either chiral or prochiral in bulk phase. In this simplified description only that part of the bulk chiral molecule which directly contacts the surface is considered. The remaining part of the molecule which is not involved in the adsorption is disregarded and assumed to be responsible only for preservation of chirality in the bulk phase. As in our previous studies, the chiral molecules were assumed to consist of identical segments which are interconnected to form a rigid chain lying on a plane.18,22−26 A molecular segment can be an atom or a functional group which occupies one adsorption site. In this work we focus on model enantiomers which comprise four and five segments. In the case of the four-membered chains these are the S-shaped (A) and Γ-shaped (B) structures shown in the top part of Figure 1.

Figure 1. Schematic view of the model enantiomers comprising four segments (A and B) adsorbed on a square lattice (top). Selected molecular orientation used in the directional model is shown in black for each structure. Remaining orientations allowed in the isotropic model are shown in gray. (Bottom) Six possible chiral planar structures built of five segments (a−f) used in the simulations. One enantiomeric form, called arbitrarily R, is shown for molecules a−f. For the larger molecules built of five segments the six nonsuperimposable chain conformations a−f shown in the bottom part of Figure 1 were considered. The corresponding enantiomers of types A, B, and a−f were arbitrarily marked by R and S, as indicated in the figure. The molecules from Figure 1 were allowed to interact via short-ranged segment−segment interaction potential limited to nearest neighbors on a square lattice. The energy of interaction between a pair of neighboring segments was characterized by the parameter ω, which was assumed to take negative values for attractive segment−segment interactions. To examine the effect of molecular orientational anisotropy in our system we consider two qualitatively different situations related to the number of allowed orientations of the enantiomers on a square lattice. In the first case, which we call orientationally isotropic, the molecules of A and B were allowed to adopt the four orientations which are shown in Figure 1 in black and gray. We stress that the term isotropic used here refers to the four directions on a square lattice which are related to the position of neighboring vertices. It shall not be confused with the usual meaning, in which infinitely many orientations are 11096

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Figure 2. Equilibrium configurations of the enantiopure (R) overlayers comprising 1800 molecules of A (left) and B (right) simulated for the directional model at T = 0.5. White arrow in the left part shows the (−1,1) direction of the parallel rows formed by molecules of A. Insets in both parts are magnified fragments of the corresponding overlayers. Thick white lines in the insets connect neighboring molecules aligned in the (−1,1) direction. Two bimolecular A clusters with equal number of bonds between neighboring segments (red lines) are shown on the right. Black arrows indicate the direction in which the corresponding molecular row propagates. allowed. A similar assumption was made for the five-membered molecules a−f (possible orientations not shown). Note that for molecules B and d there are in fact only two different orientations (vertical and horizontal), as these molecules are centrosymmetric. In the second case called directional the molecules were restricted to adopt only one orientation, for example, that shown in black for A and B. To make the model general we do not provide any specific physical origin of the orientational preference assumed here. However, as mentioned previously, there is clear experimental evidence that such factors as external magnetic field21 or unidirectional nanostructure of the substrate can promote a specific planar orientation of adsorbed enantiomers.8,20 Simulations were performed on a 100 by 100 lattice using the conventional canonical ensemble Monte Carlo method for rigid polyatomic molecules with Metropolis sampling.27 To eliminate edge effects periodic boundary conditions in both directions were applied. Briefly, the simulation algorithm was organized as follows. In the first step, molecules of a selected type were distributed randomly on the lattice. Next, the adsorbed layer was equilibrated by a series of attempts to move each molecule to a new position. In the case of the isotropic model a selected molecule was randomly translated and its new orientation was randomly chosen out of the four allowed cases. For the directional model the molecular orientation was always fixed. In the new position a cluster of adsorption sites matching the shape of the molecule was probedif none of the selected cluster sites was occupied, the molecule was inserted with the probability p = min[1, exp(−ΔE /kT )], where ΔE = En − Eo

rotate for the isotropic model) a molecule to a new position on the lattice.

3. RESULTS AND DISCUSSION Molecules Comprising Four Segments. Figure 2 shows enantiopure equilibrium overlayers comprising molecules of A and B (R enantiomers) simulated for the directional model at T = 0.5. A noticeable difference between the structures formed by the enantiomers of A and B is the range of ordering which is much longer for the first adsorbate, as demonstrated by the white lines in the insets in Figure 2. In particular, the molecules of A self-assemble into an extended closely packed domain without any defect or dislocation. The resulting chevron-like superstructure is made up of long parallel rows aligned in the (−1,1) direction, and it is characterized by a rectangular (√2 × √8)R45° unit cell. For molecules of B we can also observe formation of a compact extended domain, but in this case the assembled structure is not globally periodic. The main reason for that is the presence of two kinks in a molecule of B which enable formation of two types of bimolecular clusters with the same potential energy. These clusters are shown in the right part of Figure 2, of which the first (top right) can initiate propagation of a vertical molecular row and the second can start up propagation of a diagonal molecular row. In consequence, the adsorbed overlayer is a mixture of domains of variable size in which molecules of B belong to rows aligned in the (1,0) and (−1,1) directions (see the insets in Figure 2). One important factor which stabilizes the mixed structure is the lack of energy penalty associated with formation of walls between domains. Note that the B domains of both types are perfectly interlocked, so that the potential energy of a molecule of B within a domain (either vertical or diagonal) is essentially the same as that of a molecule of B located at the domain periphery. This allows for creation of a molecular overlayer without void spaces, in which the two linear patterns can coexist. In the case of adsorbate A the chevron-like structure shown in Figure 2 is a unique structure which guarantees full coordination of a molecule (10 foreign molecular segments per molecule), and thus, it is characterized by the lowest potential energy (see Figure S5, Supporting Information). As we will show later, the structural degeneracy created by molecules of B has serious consequences to the chiral resolution in a racemic phase.

(1)

The potential energy of a molecule in the new and old position, En and Eo, respectively was calculated using the simple summation n

4

El = ω ∑ ∑ sij for l = n, o i=1 j=1

(2)

where the first sum runs over n segments of a selected molecule (in our case n = 4 and 5) and the second sum runs over the four nearest neighbors of the segment i on a square lattice. The occupation variable sij is equal to 1 if sites i and j are occupied by segments belonging to a pair of neighboring molecules. Otherwise, it is equal to 0. The symbols k and T have their usual meanings, that is, the Boltzmann constant and the system temperature. In the orientationally isotropic case we additionally used the orientation-biased MC simulation technique.28 For the sake of convenience we assumed that the energy of interaction between a molecule and the surface is equal to zero. All of the results described here were obtained for ω = −1.0, assuming that ω, k, and T are dimensionless parameters. To equilibrate the systems we used up to 108 MC steps, where one MC step is a single attempt to move (and 11097

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Figure 3. Equilibrium configurations of the racemic overlayers comprising 900 R + 900 S molecules of A (left) and B (right) simulated for the isotropic model at T = 0.5. Magnified fragments show the closely packed structures formed by randomly oriented enantiomers R (blue) and S (red).

Figure 4. Equilibrium configurations of the racemic overlayers comprising 900 R + 900 S molecules of A (left) and B (right) simulated for the directional model. Results shown in the top part correspond to T = 0.5, while those from the bottom part were obtained at T = 1.5. Insets in the top part show magnified fragments of the enantiopure domains R and S (A) and of the mixed overlayer (B). White arrows in the left-upper panel show the orthogonal directions in which the enantiomers of A are aligned.

Figure 3 presents equilibrium racemic overlayers (900 R + 900 S) simulated for the isotropic model at T = 0.5 for molecules of A (left) and B (right). As it is seen in the figure, both overlayers are compact but contrary to the corresponding one-component systems are disordered with sparse void spaces.

The obtained result shows clearly that the chiral resolution cannot occur when tetramers A and B are allowed to take the four planar orientations assumed in the isotropic model. Despite the fact that the tendency for local clustering of like enantiomers can be observed in both systems, formation of 11098

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Figure 5. Changes in the average number of bonds of type R−R, S−S, and R−S during the simulation obtained for the isotropic (left) and directional model (right). Results shown in the figure were calculated for racemic mixtures comprising 900 R + 900 S molecules of A (top) and B (bottom). They are averages over 10 independent runs performed at T = 0.5.

Figure 2 for the R enantiomer). In the case of adsorbate B the racemic overlayer is disordered but contains much less defects (void spaces) compared to its counterpart from Figure 3 obtained with the isotropic model. Note also that like enantiomers of B tend to form rows aligned in the (−1,1) (R, blue) and (1,1) (S, red) directions, and this effect is a result of perfect interlocking of diagonal domains R and S which run perpendicular to each other. To explain the effect of orientational anisotropy on the phase behavior in systems A and B let us focus on the associated domain growth mechanisms. The bottom part of Figure 4 shows the mixed racemic overlayers comprising molecules of A (left) and B (right) simulated at a higher temperature T = 1.5 at which initial formation of enantiopure domains can be easily observed. For both systems the optimal domain growth is based on incorporation of that enantiomer which fits best the domain boundary. In the case of the racemate of A, the orientational anisotropy forces the molecules to self-assemble via the kink-tokink attachment which minimizes the potential energy and results in the densest molecular packing. Note that this mechanism is very effective for like enantiomers, but it drastically reduces the chance of incorporation of an enantiomer of one handedness into a domain of the opposite handedness. Because of the self-sorting process the enantiopure domains of A grow relatively fast and are the largest among the aggregates shown in the bottom-left part of Figure 4. On the other hand, the most stable configuration of a pair of neighboring opposite enantiomers of A is that one in which their long vertical arms are in full contact. Even though the energy of this configuration (3 bonds between a pair of enantiomers) is exactly the same as that for the kink-to-kink

large enantiopure domains is strongly limited. This originates mainly from the interlocking of randomly oriented enantiopure clusters R and S in which peripheral molecules have the same potential energy as those placed within the clusters. The magnified fragments of the simulated racemic overlayers displayed in Figure 3 show how the surface can be completely covered by the interlocking molecular clusters comprising enantiomers R and S. These local disordered structures ensure full coordination of a molecule of A and B (minimum energy per molecule) and largely promote mixing in both systems. In consequence, the racemic overlayers formed by molecules of A and B are qualitatively very similar. Indeed, our separate simulations showed that in each system the number of vertically oriented molecules is equal to the number of horizontally oriented molecules (see Figure S4, Supporting Information). Moreover, the structure of the overlayer B from Figure 3 is also very similar to that which has been recently obtained by Barnes et al. for the racemic mixture of noninteracting S-shaped tetrominoes on a square lattice.31 A totally different situation is encountered when the enantiomers in the racemic overlayers A and B are restricted to adopt only one planar orientation. The top part of Figure 4 shows equilibrium overlayers (900 R + 900 S) obtained with the directional model at T = 0.5 for molecules of A (left) and B (right). A striking difference between the two overlayers is that for A we observe a complete chiral segregation while for B the molecules form a mixed structure with interpenetrating enantiopure domains. The compact mirror-image domains created by the enantiomers of A run in the orthogonal (−1,1) and (1,1) directions, and their periodicity is identical with that observed for the corresponding one-component systems (see 11099

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shown in the top-right part of Figure 5. Here, the curve corresponding to the heterogeneous bonds drops almost to zero and the R−R and S−S curves reach a value close to 2.4. Obviously, this is an explicit manifestation of the chiral segregation process that produces compact enantiopure domains. In this case, the dense packing of enantiomers in the extended domains whose magnified fragments are shown in the insets to Figure 4 is responsible for the saturated homochiral coordination of a single molecule of R or S. In this coordination mode each molecule is surrounded by 6 molecules of the same chirality, so that it forms 10 R−R or S−S bonds. The resulting average number of bonds per segment for a molecule placed within the domain R or S is then equal to 2.5. Of course, because of the existence of phase boundaries in which the molecules are coordinated in a different way, this number is slightly lower on average. An interesting perspective related to the effect of orientational confinement of the molecules of A is the possibility of controlling the chiral segregation temporally by switching on/ off external factors which induce unidirectional alignment of the enantiomers. To illustrate this possibility in Figure 6 we showed

configuration of like enantiomers, the mixed bimolecular structure cannot propagate. This can be easily seen at the boundary between the large enantiopure domains from the topleft part of Figure 4. In this case enantiomers R and S whose short arms point in opposite directions are the starting points for the corresponding diagonal enantiopure rows. No further repetition of the interfacial bimolecular pattern takes place along the growth directions. For molecules of type B this situation is more diversified, as the vertically oriented enantiomers R and S can easily fit the boundary of domains comprising their antipodes. In the right part of Figure 4 we notice that the overlayer obtained for T = 1.5 consists of a considerable number of heterogeneous clusters in which enantiomers R and S are interlocked. The self-sorting mechanism is ineffective here because of the structural degeneracy introduced by molecules of B, which we discussed previously for the enantiopure overlayer (R). For the mixed system this structural degeneracy is additionally amplified by the presence of the second enantiomer. To quantify the effect of orientational anisotropy on the chiral resolution in the systems comprising molecules of A and B we calculated the average number of virtual segment− segment bonds in the simulated overlayers. These include bonds between like enantiomers (R−R and S−S, homogeneous) and opposite enantiomers (R−S, heterogeneous). Precisely, this quantity was obtained by reckoning the bonds of types R−R, S−S, and R−S that can be drawn between the selected molecule (R or S) and its nearest-neighbor sites occupied by foreign molecules R or S. The calculated values were next averaged over the number of adsorbed molecules of a given chirality (R or S) and divided by the number of segments in the considered molecular structure. Figure 5 shows changes in the average number of homogeneous and heterogeneous bonds per one molecular segment during the simulation run at T = 0.5. Remember that for a fully coordinated molecule of A and B, each of which comprises 4 segments, there are 10 bonds connecting the molecule with neighboring foreign segments. This gives 2.5 bonds per segment for the maximum coordination mode. As it can be seen in the bottom part of Figure 5, the relative positions of the curves corresponding to the homogeneous and heterogeneous bonds in the overlayer B are very similar for both models, namely, in both cases the average number of heterogeneous bonds, being equal to ∼1.14 for the isotropic model and ∼1.04 for the directional model, is close to the average number of homogeneous bonds (∼1.28 and ∼1.40, respectively). Because the average number of R−S bonds is proportional to the interface width in the overlayer, the obtained results prove that enhanced phase mixing occurs in the system, regardless of whether molecules of B are orientationally confined or not. In the right-bottom part of Figure 5 we also observe that the breaking of orientational symmetry causes a noticeable lowering of the average number of heterogeneous bonds which is accompanied by a slight increase in the average number of R−R and S−S bonds. This effect is a consequence of formation of connected enantiopure domains which reduces the number of small R and S clusters in the system (compare Figures 3B and 4B). In the case of molecule A, the results simulated for the isotropic model reflect clearly the mixing occurring in the racemic phase and they are not much different from the analogous results obtained for molecule B. For the directional model we can, however, observe a completely different relation between the curves

Figure 6. Reversibility of the mixing-segregation process illustrated by the cyclic changes in the average number of R−S bonds per segment in the racemic mixture comprising 900 R + 900 S enantiomers of A. Black and red lines correspond to the directional and isotropic models, respectively. Arrows indicate the allowed molecular orientation within a given period of the simulation run at T = 0.5.

the results of one simulation run at T = 0.5 in which the orientational confinement was periodically switched on every 2 × 106 MC steps. This period was carefully chosen to ensure complete equilibration of the adsorbed overlayer in both modes. As it can be seen in the figure, introduction of the orientational anisotropy into the system causes a rapid decrease in the average number of R−S bonds, from ∼1.1 to ∼0.04 (black lines). In this case, the adsorbed enantiomers selforganize quickly into mirror-image domains, so that the equilibrium structure is formed yet within one-quarter of the simulation period. On the other hand, relaxation of the overlayer is a considerably slower process which requires at least one simulation period (red lines). The disordering observed when removing the orientational restriction takes place due to gradual peripheral melting of the enantiopure domains R and S. The molecules released form the R(S) side of the domain are incorporated (through large displacement 11100

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Figure 7. Snapshots of the overlayers comprising racemic mixtures of enantiomers a, b, and c; 650 R + 650 S molecules at T = 0.5. Top part shows the results obtained for the isotropic model, while the bottom part corresponds to the directional model. Insets in the bottom part show magnified fragments of the ordered domains of the R enantiomer of the corresponding molecule. White arrows indicate the direction of enantiopure domains R and S.

Figure 8. Snapshots of the racemic overlayer comprising enantiomers of d; 650 R + 650 S molecules at T = 0.5. Left part corresponds to the isotropic model, while the middle and right parts correspond to the directional model. Two possible packings of the R enantiomer (d and d*) are shown for the isotropic model. Magnified fragments show the alignment of enantiomer R within homochiral domains denoted by R and R*.

moves across the R−S interface) into the mixed cluster growing on the opposite S(R) side of the domain (see Figure S1, Supporting Information). The driving force for the mixing is the entropy gain associated with the increased number of relative molecular orientations in the densely packed overlayer obtained with the isotropic model. The result shown in Figure 6 demonstrates two things: the immediate effect of the

orientational anisotropy on the chiral resolution in the adsorbed overlayer and the full reversibility of the observed structural changes. Both properties indicate that external directional forces can be effectively used for precise triggering of the chiral segregation process. The results obtained for molecules A and B show that the chain conformation influences heavily phase behavior in the 11101

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Figure 9. Snapshots of the racemic overlayer comprising enantiomers of e (left) and f (right); 650 R + 650 S molecules at T = 0.5. Top part corresponds to the isotropic model, while the bottom part corresponds to the directional model. Insets in both parts show magnified fragments of the corresponding overlayers. White arrows in the bottom-right part indicate the directions in which enantiomers R and S are aligned.

corresponding racemic overlayers. One question which arises here is what is the main structural factor which makes the enantiomers of A able to segregate into mirror-image domains? The molecules of A and B have the same aspect ratio (3:2) but differ in symmetry (A is asymmetric and B is centrosymmetric). Additionally, a molecule of A contains a long straight fragment (3 segments in line), while a molecule of B has two kinks. To test whether the structural properties of A are general prerequisites for the 2D chiral resolution in racemic overlayers we performed analogous simulations for the larger structures a−f from Figure 1. Molecules Comprising Five Segments. Figure 7 presents the equilibrium racemic overlayers comprising molecules of a, b, and c (650 R + 650 S) simulated at T = 0.5. The results shown in the top part were obtained for the isotropic model, while those from the bottom part correspond to the directional model. As it follows from the figure, the structure of the adsorbed layer obtained with the isotropic model (top) is very similar for each molecule, namely, a common effect involving enhanced mixing leading to formation of dispersed domains can be observed and the number of vertically and horizontally oriented molecules in each overlayer is approximately equal. However, when the molecules are forced to orient in one direction a complete chiral resolution occurs in each system. For molecules of a and b we observe formation of compact

chevron-like mirror-image domains with diagonal molecular rows, resembling those obtained for molecule A (see Figure 4). The enantiopure domains of a and b are characterized by the same parallelogram (√2 × √13)R ± 56° unit cell. In the case of molecule c the closely packed enantiopure domains have a somewhat different periodic pattern with a square (√5 × √5) R ± 27° unit cell. Note that the molecules discussed above belong the same class, that is they are all asymmetric with the same aspect ratio (3:1) and are equipped with a long linear arm. To examine whether segregation occurs also for the more compact molecules d−f we performed additional simulations whose results are shown in Figures 8 and 9. The snapshots presented in both figures were obtained for the corresponding racemates (650 R + 650 S) at T = 0.5. Let us start with molecule d, which is the only centrosymmetric molecule among molecules a−f. As it is seen in the left part of Figure 8, the structure of the mixed overlayer simulated with the isotropic model is very similar to that observed for molecules a−c. For the directional model, a spontaneous chiral resolution occurs, leading to formation of closely packed enantiopure domains with dichotomic structure. These two packing possibilities are illustrated for enantiomer R in the middle (d) and right (d*) part of Figure 8. The spatial arrangement of the molecules shown in the middle part follows the normal chevron-like pattern, and it is characterized by a 11102

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Figure 10. Changes in the average number of R−S bonds during the simulation obtained for the isotropic (right) and directional model (left) for molecules a−f. results shown in the figure were calculated at T = 0.5 for racemic mixtures comprising 650 R + 650 S molecules. They are averages over 10 independent runs.

parallelogram (√2 × √13)R ± 56° unit cell. In the domain R* shown in the right part the enantiomers are, however, packed in a different way, such that they form a more isotropic structure with a square (√5 × √5)R ± 27° unit cell. Note that the results obtained for the orientationally confined molecule d are entirely different compared to its smaller analog B. This clearly shows that molecular centrosymmetry has no effect on the possibility of chiral resolution in the isotropic model.13 The structural degeneracy associated with formation of enantiopure domains with different packing motifs originates from the lowered aspect ratio (3:3) of a molecule of d compared to the three molecules from Figure 7. Indeed, our separate simulations showed that elongation of the central linear part of a molecule of d causes segregation of the enantiomers into mirror-image domains with exclusive chevron-like pattern (results not shown). The racemic overlayers simulated for the two asymmetric molecules e and f are presented in Figure 9. Because the morphologies of the mixed overlayers obtained for e and f using the isotropic model (top part) are similar to the analogous results discussed previously, we focus on the orientationally confined case. As it is seen in the left part, a new type of phase behavior can be observed in the system comprising molecules of e. Contrary to molecule d having the same aspect ratio (1:1), chiral resolution does not occur here but the obtained overlayer is porous and partially ordered. Note that molecule e is more ramified than molecule d. This structural property prevents close packing of the enantiomers of e aligned in one direction. In consequence, a locally periodic mixed layer with void defects forms. One example of the mixed periodic structure consisting of alternate rows of R and S is shown in the inset in the bottomleft part of Figure 9. This pattern, in which the enantiomers are in racemic proportion, is characterized by a rectangular (√8 × √18)R45° unit cell. In the case of molecule f having the same aspect ratio (2:1) as the smaller molecules A and B we observe a complete chiral segregation leading to creation of mirrorimage domains with a square (√5 × √5)R ± 27° unit cell. To compare the effect of orientational anisotropy on the chiral resolution in the racemic overlayers comprising molecules with five segments in Figure 10 we plotted the average number of heterogeneous (R−S) bonds calculated for each molecule. The left part of Figure 10 shows the results

obtained with the directional model, while the right part shows analogous data obtained with the isotropic model. As follows from the left part, the orientational anisotropy is responsible for the decrease in the number of the R−S bonds in all of the systems, except for e. This common tendency is directly related to the chiral resolution occurring in the overlayers simulated for the orientationally confined molecules a−d and f. Although the initial decline of the curves calculated for molecules a, f, and d is steeper than for molecules b and c, all these curves drop below 0.2, which indicates efficient enantiomer separation. The different shape of the curve calculated for molecule e originates from formation of the locally ordered mixed structure shown in the bottom-left panel in Figure 9. In the magnified fragment inset we notice that a single molecule of type R(S) has 7 bonds with neighboring molecules of type S(R). This agrees well with the value of 1.34 reached by the corresponding curve (blue line) from Figure 10. Indeed, according to the obtained value a single R(S) enantiomer of the five-membered molecule e has 6.70 heterogeneous bonds on average. In the case of the results calculated for the isotropic model which are plotted in the right part of Figure 10, we observe that the average number of heterogeneous bonds is in general much larger than for the directional model. The only exception is again molecule e. These results show clearly that mixing of enantiomers occurs in the considered overlayers, and additionally, they provide some information about the tendency for clustering. For example, for molecule e, whose enantiomers form the compact mixed structure shown in the top part of Figure 9, the tight packing of randomly oriented molecules enables creation of small enantiopure domains. This effect is reflected in the lower average number of R−S bonds compared to the result simulated with the isotropic model. In the case of the remaining five-membered molecules, from the left part of Figure 10 we conclude that the tendency for formation of enantiopure domains in the corresponding randomly mixed overlayers increases in the order e, c, a, f, b, and d. From visual inspection of the snapshot presented in the left part of Figure 8 it follows that the enantiomers of d form homochiral clusters of a cruciform shape and that the corresponding interconnected domains are less dispersed, compared to the remaining cases. This results in the lowest average number of R−S bonds in the mixed overlayer comprising molecules of d. 11103

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The above findings show that the main structural factor which is responsible for the chiral segregation is the presence of a sufficiently long straight arm in a molecule. For the molecular structures considered here the arm should be at least three segments long. Indeed, all of the considered molecules meeting this criterion (A, a−d, f) were found to undergo spontaneous chiral resolution when orientationally confined. On the other hand, for branched (e) or kinked (B) compact molecules breaking of the orientational symmetry does not induce chiral segregation.

segregation process which we demonstrated here can have potential application in steering optical, adsorptive, catalytic, or biological properties of chiral functional surfaces.

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ASSOCIATED CONTENT

S Supporting Information *

Snapshots of the racemic overlayer comprising molecules of A taken during the relaxation procedure; changes in the potential energy of the racemic overlayer A during the relaxation procedure; mechanism of the formation of different domain walls by the centrosymmetric molecules B and d; proportions between verticaly and horizontally oriented molecules in the racemic overlayers A and B; and selected bimolecular clusters with different relative orientation of the enantiomers. This material is available free of charge via the Internet at http:// pubs.acs.org.

4. CONCLUSIONS The results of this work demonstrate that the orientational confinement of chiral molecules adsorbed on solid surfaces can strongly promote their segregation into extended enantiopure domains. Our MC simulations show that the chiral resolution process is largely dependent on molecular geometry, including both the shape and the aspect ratio. With the simple MC lattice model we were able to indicate those molecular architectures for which the resolution is effective. The most prominent selfsegregation effect was observed for molecules equipped with a straight chain fragment built of at least three segments. This finding indicates that rod-like chiral molecules with a minimal number of kinks are best candidates for 2D chiral separations induced by breaking of the orientational symmetry. On the other hand, the presence of multiple kinks in the molecular chains considered here reduces drastically the chances of segregation, as shown clearly for the short four-membered Sshaped chain B. In the case of the longer chains this structural feature can lead to formation of enantiopure domains with more than one pattern. This was demonstrated for the centrosymmetric molecule d, for which the simulations revealed also that the asymmetry of the molecular chain is not necessary for chiral resolution. Moreover, our simulations showed that segregation of enantiomers is fully reversible and can be programmed by suitable manipulation of external factors which induce unidirectional alignment of the enantiomers. Remember, however, that in real situations it is often observed that the adsorbing surface, especially a metallic surface, has a serious impact on the resolution/mixing of adsorbed organic enantiomers. This is because of subtle differences in the interaction patterns of the enantiomers with the surface, leading to formation of enantiopure domains. For that reason our model relates mainly to those systems in which the surface− molecule interactions are relatively weak and are identical or very similar for both enantiomers. One potential case meeting this criterion could be adsorption of big organic molecules on the liquid/graphite interface, in which the adsorbate structure matches the symmetry of the substrate.21 The insight from this theoretical study can be useful in developing new experimental techniques in which directional magnetic or electric fields are used to induce controlled resolution of enantiomers in adsorbed overlayers. For example, this approach can be used for those chiral or prochiral molecules which possess electric or magnetic dipole moment and exhibit strong coupling with the corresponding external field parallel to the substrate. When strong enough, the applied field can induce unidirectional positioning of the adsorbed molecules, as they tend to align parallel to the field lines. In consequence, due to the fixed molecular orientation in the adsorbed phase the intermolecular interaction pattern between enantiomers can change significantly, so that their spontaneous resolution can occur. The possibility of triggering the self-

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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