Dendritic crystal growth, differential circular scattering, and the origin of biomolecular homochirality

Chiroptical anisotropy of crystals and molecules

Optical activity, a foundational part of chemistry, is not restricted to chiral molecules although generations have been instructed otherwise. A more inclusive view of optical activity is valuable because it clarifies structure-property relationships however, this view only comes into focus in measurements of oriented molecules, commonly found in crystals. Unfortunately, measurements of optical rotatory dispersion or circular dichroism in anisotropic single crystals have challenged scientists for more than two centuries. New polarimetric methods for unpacking the optical activity of crystals in general directions are still needed. Such methods are reviewed as well as some of the 'nourishment' they provide, thereby inviting to new researchers. Methods for fitting intensity measurements in terms of the constitutive tensor that manifests as the differential refraction and absorption of circularly polarized light, are described, and examples are illustrated. Single oriented molecules, as opposed to single oriented crystals, can be treated computationally. Structure-property correlations for such achiral molecules with comparatively simple electronic structures are considered as a heuristic foundation for the response of crystals that may be subject to measurement.

Polarized light through polycrystalline vaterite helicoids

Vaterite helicoids [W. Jiang et al., Nat. Commun., 2017, 8, 15066] are chiral, polycrystalline suprastructures grown in the presence of the amino acids, aspartic (Asp) or glutamic (Glu) acid, that are abundant in proteins regulating biomineralization. These complex objects are composed of hexagonal vaterite nanocrystals assembled as curved-edge platelets that form chiral ensembles. The sense stacked platelets is correlated with the stereochemistry of the amino acid additive: l-Asp gives counterclockwise architectures while d-Asp gives the clockwise enantiomorphs. As new layers stack, platelets become progressively inclined with respect to the substrate suface. The growth and structure of vaterite helicoids was originally evidenced by electron microscopy and atomic force microscopy. Here, we develop an optical model for describing polarized light transmission through helicoids as measured by Mueller matrix polarimetry. The close agreement between experimental measurements and simulation confirms that the propellor-like organization of inclined platelets creates optically active structures determined by growth additive stereochemistry. The microscopy employed demonstrates the information that can be obtained by complete polarimetry using a camera as a light detector, a technique that could be applied profitably to all manner of complex structures organized from anisotropic particles.

Bernauer's bands

Ferdinand Bernauer proposed in his monograph, "Gedrillte" Kristalle (1929), that a great number of simple, crystalline substances grow from solution or from the melt as polycrystalline spherulites with helically twisting radii that give rise to distinct bull's-eye patterns of concentric optical bands between crossed polarizers. The idea that many common molecular crystals can be induced to grow as mesoscale helices is a remarkable proposition poorly grounded in theories of polycrystalline pattern formation. Recent reinvestigation of one of the systems Bernauer described revealed that rhythmic precipitation in the absence of helical twisting accounted for modulated optical properties [Gunn, E. et al. J. Am. Chem. Soc. 2006, 128, 14234-14235]. Herein, the Bernauer hypothesis is re-examined in detail for three substances described in "Gedrillte" Kristalle, potassium dichromate, hippuric acid, and tetraphenyl lead, using contemporary methods of analysis not available to Bernauer, including micro-focus X-ray diffraction, electron microscopy, and Mueller matrix imaging polarimetry. Potassium dichromate is shown to fall in the class of rhythmic precipitates of undistorted crystallites, while hippuric acid spherulites are well described as helical fibrils. Tetraphenyl lead spherulites grow by twisting and rhythmic precipitation. The behavior of tetraphenyl lead is likely typical of many substances in "Gedrillte" Kristalle. Rhythmic precipitation and helical twisting often coexist, complicating optical analyses and presenting Bernauer with difficulties in the characterization and classification of the objects of his interest.

Amplification of chirality at solid surfaces

Symmetry-breaking phenomena in two-dimensional crystallization at surfaces are reviewed and the potential impact to chiral amplification in three-dimensional systems in connection with the origin of homochirality in the biomolecular world is discussed. Adsorption of prochiral molecules leads to two-dimensional conglomerates, i.e., on a local scale spontaneously to homochiral crystal structures. Small enantiomeric excess or chiral impurities in this environment install homochirality on a global scale, that is, on the entire surface.