J. Phys. Chem. C 2010, 114, 19425–19432
19425
Resolution of Binary Enantiomeric Mixtures in Two Dimensions Irina Paci* Department of Chemistry, UniVersity of Victoria, Victoria, British Columbia, V8P 5C2, Canada ReceiVed: August 4, 2010; ReVised Manuscript ReceiVed: October 5, 2010
The chirality of a molecule can play an important role during surface self-assembly. For example, adsorption on an achiral surface can lead to chiral resolution of enantiomeric mixtures. The resulting structures are often extended homochiral domains or two-dimensional chiral aggregates. Such processes hold promise not only as a means of directly achieving enantiomeric resolution but also for use in asymmetric catalysis and for building chiral surfaces for further chiral adsorption. We examined the mixing phase behavior of two model chiral molecules, in intermediate-density monolayers, restricted to assemble in two dimensions. In bulk solutions, the separation of enantiomers may occur at crystallization. On surfaces, the relevant phase change is a twodimensional condensation. We found that this dimensional restriction led to higher-entropy phase separation regimes and resulted in a rich phase behavior for these systems. One chiral model is a two-dimensional chiral conglomerate which behaves similarly to, but with more nuanced transitions than, respective bulk analogues. The second model exhibits a more complex structural evolution with enantiomeric excess and a hybrid “racemic compound”/pseudoracemic mixing behavior. 1. Introduction Over the past two decades, developments in surface science have resulted in the design of functionalized surfaces of everincreasing complexity. These developments have been paralleled by the advent of new visions for the bottom-up creation of nanostructured application devices, for everything from everyday electronics to biomedical sensing. Self-assembly of chiral species and the enantiomeric surface structures that result have many foreseeable applications. Chiral resolution, patterning for chiral catalysis, biochemical sensing, and drug delivery are just a few of the possibilities.1-5 Chirality in condensed phases has long been a subject of intense study because of its importance in the pharmaceutical industry. At the molecular level, chirality is conferred by the nonsuperimposability of mirror-image isomers due to a lack of improper rotation symmetry elements, such as an inversion center or a symmetry plane. This facilitates chiral recognition, that is, a differentiation of interactions between a chiral molecule and the two possible enantiomers of another. It results in the preferential orientation of molecules, according to interactions that involve short-range repulsions, attractive van der Waals dispersion, and electrostatic forces between groups possessing partial or full charges.6-9 The complexity of the intermolecular interactions necessary to achieve chiral recognition is diminished when the molecules are constrained to evolve predominantly in a plane, such as in the case of surface-supported self-assembly.10-14 However, in this case, the surface itself influences the recognition process, through changes in molecular conformation, binding to relevant sites, or changes in diffusional patterns. A telling example is the formation of chiral macroscopic arrays upon adsorption of homochiral tartaric acid (from a racemic mixture) on Ni(111), but not on Ni(110) surfaces, where racemic arrays are formed instead.15 The development of an understanding of the effects that lead to such pattern formation is still in its infancy. Nevertheless, chiral resolution upon adsorption is the two* To whom correspondence should be addressed. E-mail:
[email protected].
dimensional analogue of spontaneous resolution upon crystallization and is thus of significant interest. The outcome of the absorbed-phase self-assembly process is ultimately determined by the free energy surface defined by a combination of these interactions with thermodynamic conditions, such as temperature and density. Two types of surfaceadsorbed chiral patterns have been observed experimentally: small clusters of homochiral molecules forming at low surface coverages and extended chiral domains forming at full monolayer densities. In homochiral clusters, molecular alignment confers chirality and a helical direction to the self-assembled structure.16-18 Clusters comprising molecules of opposite chirality are often in mirror-image relationships themselves. At higher coverage, extended homochiral surfaces have been observed.19-25 The entire surface can be homochiral only when a pure enantiomer is adsorbed. When adsorption occurs from racemic mixtures, extended mirror-image domains may be observed, but the monolayer is racemic overall. Binary melting-point phase diagrams, which are graphs of the dependence on mixture composition of the thermodynamic properties of relevant associated phase changes, are a useful tool for chiral-system analysis. In bulk mixtures, which may separate at crystallization, these diagrams are compositiondependence plots of the fusion temperature. They are important for understanding the behavior of enantiomeric mixtures and for developing procedures for the separation of individual enantiomers from them.26-32 In bulk chiral systems, the shape of a diagram facilitates the categorization of a mixture as a conglomerate, racemate, or solid solution/pseudoracemate. Conglomerates crystallize as mechanically separable homochiral structures and exhibit an eutectic point at the racemic (50:50) mixture, thus melting like a pure substance. Chiral molecules classified as “racemic compounds” exhibit two eutectic points in their diagrams. Crystals of such compounds incorporate both enantiomers in a unit cell. The enantiomers are mixed in solid solution/pseudoracemic crystals. Establishing a category for any given compound is thus an important step in devising a separation method.26
10.1021/jp107326c 2010 American Chemical Society Published on Web 10/22/2010
19426
J. Phys. Chem. C, Vol. 114, No. 45, 2010
Paci
In a previous publication, we showed that restriction to two dimensions can lead in some systems to chiral resolution of racemic mixtures at condensation.10 Here, we examine the twodimensional analogues of binary melting-point phase diagrams and their usefulness in the characterization of enantiomeric mixtures. We used parallel-tempering Monte Carlo (PTMC) simulations to examine the interplay between temperature and composition and to examine the binary diagrams of two model chiral molecules. The models themselves were not designed to resemble any specific real molecules. Instead, they illustrate the types of interplay of electrostatic and steric interactions that lead to chiral recognition in real systems. The two associated racemic mixtures have been shown to exhibit distinctive chiral self-assembly when the molecules were restricted to evolve in two dimensions.10 Here, we extend our calculations to include mixtures of different compositions, as a means of identifying similarities and differences from bulk categories of analogous mixing diagrams. The remainder of this paper is organized as follows. The PTMC methodology, model systems, and computational details are described in section 2. The results and discussion are presented in section 3. Our conclusions are summarized in section 4.
Figure 1. Model molecules investigated in this paper. Each atom is not necessarily representative of a C, N, O, H, or another actual atom, but rather of a particular Lennard-Jones interacting species. Atoms colored in yellow and green carry partial charges. Chiral centers are indicated in yellow.
TABLE 1: Physical Characteristics of the Racemic Systems moleculea
nat
i
position (x*,y*,z*)
qi
σ*ii
*ii
A
5
B
7
1 2 3 4 5 1 2 3 4 5 6 7
(0,0,0) (0.55,0,0) (0,1.05,0) (0,-0.55,0) (0,0,0.7) (0,0,0) (0.55,0,0) (0,2.15,0) (0,-0.55,0) (0,1.4,0) (-0.55,1.4,0) (0,0.7,0)
0.6 -0.6 0 0 0 0.6 -0.6 0 0 0.6 -0.6 0
1.0 0.5 2.0 0.5 1.0 1.0 0.5 2.0 0.5 1.0 0.5 1.0
1.0 1.0 1.5 3.5 0.5 1.0 0.7 0.25 3.0 1.0 0.7 0.25
2. Method Parallel tempering Monte Carlo is one of several methods in modern statistical mechanics that are frequently used to avoid trapping in metastable configurations. It has been shown to work well for simulations of clusters because of its inherent ergodicity.33-36 Briefly, replicas of the system are simultaneously equilibrated at different temperatures, using canonical (constant number of particles, volume, and temperature) Monte Carlo moves. Ergodicity is sought by periodically performing configurational swaps between replicas with different temperatures. Our simulations, described in detail elsewhere,10 consisted of a Markov chain of the following types of moves: (i) MC translational moves, based on the standard Metropolis acceptance criterion;35 (ii) Stochastic temperature swap moves, where two replicas of the system at different temperatures, i and j ) i + 1, were randomly selected and their configurations swapped with a probability based on a Boltzmann factor acceptance ratio; and (iii) swaps between the positions of pairs of nonidentical molecules, were accepted based on their Boltzmann factors. The racemates were composed of 200 rigid molecules. They were confined to a simulation box, made large enough so as to not impact the resulting structures. Evaporative events (particles leaving the simulation box) were forbidden, by rejecting moves that led to evaporation. Intermolecular interactions were defined with pairwise atom-based Lennard-Jones and electrostatic potentials, given by nat
Uab )
∑
i,j)1 j
