Self-assembly of chiral molecules

The relation between twist and chirality remain unclear. Some intriguing phenomenological rules have been developed [59], although a priori calculations of the preferred twist angle between neighbouring molecules is impossible, in contrast to the situation for the tilt, whose relation to the molecular shape is detailed in section 4.1. 

The arrangement of chiral molecules in thermotropic liquid crystals is more complex, since entire volumes of space - rather than the bounded twisted ribbons discussed above - must be ed subject the constraint of a preferred twist between neighbouring molecules. The simplest examples of such mesophases are the cholesteric liquid crystals, discovered last century, (c/. section 5.1.8). This class of thermotropic liquid crystals derives its generic name from chiral cholesterol derivatives (shown below), which were found a century ago to exhibit peculiar optical changes as they were heated. 

Cholesterics are characterised by a single twist , which is characterised by a relative rotation of flat layers of molecules. (These layers are illusory, and useful for illustrative purposes only, since there is no evidence of lamellar ordering perpendicular to the layers.) The optical novelties of these cholesteric phases are due to the pseudo-Bragg reflections from the helical 

The most favourable relative configuration of identical chiral molecules is that where all neighbouring molecules are twisted relative to each other. This is achieved by a double-twist stacking, illustrated in Fig. 4.32. In three-dimensional euclidean space, this double-twist caimot be realised throughout space some disclination singularities must occur [61]. How then can this double twist be most closely approached A simple model, involving nothing more than potatoes, and oven and matches, is useful. The lower- 

This (local) double twist configuration clearly involves a hyperbolic deformation of the imaginary layers. In contrast to the hyperbolic layers found in bicontinuous bilayer lyotropic mesophases, the molecules within these chiral thermotropic mesophases are oriented parallel to the layers, to achieve nonzero average twist. The magnitude of this twist is deternuned by the direction along which the molecules lie (relative to the principal directions on the surface), and a function of the local curvatures of the layers (K1-K2), cf. eq. 1.4. Just as the molecular shape of (achiral) surfactant molecules determines the membrane curvatures, the chirality of these molecules induces a preferred curvature-orientation relation, via the geodesic torsion of the layer. 

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Self-assembly of chiral molecules may result in organized aggregates displaying a remarkable enhancement of ophcal achvity. The best known examples are amino-acid residues that assume a periodic conformation - an a-helix or a p-sheet chain. In this case, the enhancement of optical activity is due to the onset of a parhcular rigid conformation. 

Two characteristics determine the shape of molecular aggregates. The first is the shape of the constituent molecules, which sets the curvature of the aggregate. The second is coupled to the chirality of the molecules, which also determines the curvature of the aggregate, via the geodesic torsion. The bulk of this chapter is devoted to an exploration of the effect of molecular shape on aggregation geometry. An account of the theory of self-assembly of chiral molecules is briefly discussed at the end of this chapter. 

This chapter will review the self-assembly of chiral amphiphiles in aqueous solvents. We will focus on the ways in which individual molecules can pack... 

Figure 5.24 Model of hierarchical self-assembly of chiral rodlike monomers.109 (a) Local arrangements (c-f) and corresponding global equilibrium conformations (c -f) for hierarchical selfassembling structures formed in solutions of chiral molecules (a), which have complementary donor and acceptor groups, shown by arrows, via which they interact and align to form tapes (c). Black and the white surfaces of rod (a) are reflected in sides of helical tape (c), which is chosen to curl toward black side (c ). (b) Phase diagram of solution of twisted ribbons that form fibrils. Scaled variables relative helix pitch of isolated ribbons h hh /a. relative side-by-side attraction energy between fibrils eaur/e. Reprinted with permission from Ref. 109. Copyright 2001 by the National Academy of Sciences, U.S.A.

It was quickly recognized that chirality would play an important role in discotic liquid crystals, not only for the possibility of creating cholesteric and ferroelectric liquid crystals but also as a tool for studying the self-assembly of these molecules as a whole, both in solution and in the solid state. However, initial studies revealed that expression of chirality in discotic liquid crystals was not as straightforward as for liquid crystals derived from calamitic molecules. More recently, with the increase in interest in self-assembly and molecular recognition, considerably more attention has been directed to the study of chiral discotics and their assemblies in solution. The objective of this chapter is... 

Aggeli, A., Nyrkova, I. A., Bell, M., etal., Hierarchical self-assembly of chiral rod-like molecules as amodel for peptide beta-sheet tapes, ribbons, fibrils, and fibers. Proc. Natl. Acad. Sci. U. S. A. 2001,98, 11857-11862. 

Aggeli, A., Nyrkova, I.A., Bell, M., Harding, R., Carrick, L., McLeish, T.C.M., Semenov, A.N., and Boden, N. "Hierarchical self-assembly of chiral rod-like molecules as a model for peptide-sheet tapes, ribbons, bris and bers". Proc. Nat. Acad. Sci. U.S.A. 98,11857-11862 (2001). Attri, A.K., Lewis, M.S., and Korn, E.D. "The formation of actin oligomers studied by analytical ultracentrifugation". ]. Biol. Chem. 266, 6815-6824 (1991). 

Similar 2-D enantiomorphous domains were obtained from the non-chiral nucleic acid base adenine deposited on copper [85] and on M0S2 surface [86,87] and the deposition of cysteine on gold [88]. Evidence for strong chiral preference in interactions of nucleic acid bases and amino acids has been shown for the self-assembly of phenylglycine molecules on gold surfaces on which adenine molecules had been previously deposited [89]. 

The foregoing studies show that chiral supramolecular modules could be obtained from self-assembly of achiral molecule components, and further assembly generates supercoil structures in a mesoscopic dimension, just like the behavior of some chiral molecules. Appropriate manipulation and combination of intermole-cular noncovalent interactions can provide new routes to constructing artificial or-... 

According to R. M. Hazen, these results are in agreement with the postulate that some self-assembly processes of chiral molecules are highly enantioselective (DiGregorio, 2006). 

The experiments discussed in this chapter have shown that a variety of chiral molecules self-assemble into cylindrical tubules and helical ribbons. These are indeed surprising structures because of their high curvature. One would normally expect the lowest energy state of a bilayer membrane to be flat or to have the minimum curvature needed to close off the edges of the membrane. By contrast, these structures have a high curvature, with a characteristic radius that depends on the material but is always fairly small compared with vesicles or other membrane structures. Thus, the key issue in understanding the formation of tubules and helical ribbons is how to explain the morphology with a characteristic radius. 

In this chapter, we have surveyed a wide range of chiral molecules that self-assemble into helical structures. The molecules include aldonamides, cere-brosides, amino acid amphiphiles, peptides, phospholipids, gemini surfactants, and biological and synthetic biles. In all of these systems, researchers observe helical ribbons and tubules, often with helical markings. In certain cases, researchers also observe twisted ribbons, which are variations on helical ribbons with Gaussian rather than cylindrical curvature. These structures have a large-scale helicity which manifests the chirality of the constituent molecules. 

A second example of homochiral columns formed by discotics are the complexes of tetrazoles (59 and 60) with l,3,5-tris(4,5-dihydroimidazol-2-yl)benzene (61).74 Four molecules self-assemble to give a supramolecular disc and these discs subsequently form columns in nonpolar solvents. Chiral discs were obtained from the self-assembly of the chiral tetrazole (60) with 61. The chirality of the side chains was found to induce a bias in the helic-ity of the supramolecular assembly. Sergeants-and-soldiers measurements75 were performed for which chiral (60) and achiral (59) molecules were mixed. The experiments showed no amplification of chirality, thus revealing that in these systems chirality transfer from the side chains into the column is... 

Diverse chiral nanometric ribbons and tubules formed by self-assembly of organic amphiphilic molecules can be transcribed to inorganic... 

Crystallization and reactivity in two-dimensional (2D) and 3D crystals provide a simple route for mirror-symmetry breaking. Of particular importance are the processes of the self assembly of non-chiral molecules or a racemate that undergo fast racemization prior to crystallization, into a single crystal or small number of enantiomorphous crystals of the same handedness. Such spontaneous asymmetric transformation processes are particularly efficient in systems where the nucleation of the crystals is a slow event in comparison to the sequential step of crystal growth (Havinga, 1954 Penzien and Schmidt, 1969 Kirstein et al, 2000 Ribo et al 2001 Lauceri et al, 2002 De Feyter et al, 2001). The chiral crystals of quartz, which are composed from non-chiral Si02 molecules is an exemplary system that displays such phenomenon. 

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