Chiroptical Differentiation of Twisted Chiral and Achiral Polymer Crystals

Chirality Determination of Nanocrystals by Electron Crystallography

Chirality is a common phenomenon in nature and plays an important role in the properties of matter. The rational synthesis of chiral compounds and exploration of their applications in various fields require an unambiguous determination of their handedness. However, in many cases, determinations of the chiral crystal structure and chiral morphology have been a challenging task due to the lack of proper characterization methods, especially for nanosized crystals. Therefore, it is crucial to develop novel and efficient characterization methods. Owing to the strong interactions between matter and electrons, electron crystallography has become a powerful tool for structural analysis of nanomaterials. In recent years, methods based on electron crystallography, such as high-resolution electron microscopy imaging and electron diffraction, have been developed to unravel the chirality of nanomaterials. This brings new opportunities to the design, synthesis, and applications of versatile chiral nanomaterials. In this perspective, we summarize the recent methodology developments and ongoing research of electron crystallography for chiral structure and morphology determination of nanocrystals, including inorganic and organic materials, as well as highlight the potential and further improvement of these methods in the future.

Leveling up Organic Semiconductors with Crystal Twisting

The performance of crystalline organic semiconductors depends on the solid-state structure, especially the orientation of the conjugated components with respect to device platforms. Often, crystals can be engineered by modifying chromophore substituents through synthesis. Meanwhile, dissymetry is necessary for high-tech applications like chiral sensing, optical telecommunications, and data storage. The synthesis of dissymmetric molecules is a labor-intensive exercise that might be undermined because common processing methods offer little control over orientation. Crystal twisting has emerged as a generalizable method for processing organic semiconductors and offers unique advantages, such as patterning of physical and chemical properties and chirality that arises from mesoscale twisting. The precession of crystal orientations can enrich performance because achiral molecules in achiral space groups suddenly become candidates for the aforementioned technologies that require dissymetry.

Helical Crystals in Aliphatic Copolyesters: From Chiral Amplification to Mechanical Property Enhancement

We demonstrate herein a bottom-up strategy for achieving helical crystals via chiral amplification in copolyesters by incorporating a small amount of (d)-isosorbide into semicrystalline polyester, poly(ethylene brassylate) (PEB). During bulk crystallization of poly(ethylene-co-isosorbide brassylate)s, the molecular chirality of isosorbide in the amorphous region is transferred to PEB crystal chirality and amplified by the formation of right-handed helical crystals. Increasing isosorbide content or reducing crystallization temperature leads to thinner PEB lamellae crystals, strengthening chiral amplification by forming superhelices with a smaller helical pitch. Moreover, the superhelices with smaller helical pitch (larger chiral amplification) endow aliphatic copolyesters with enhanced modulus, strength, and toughness without sacrificing elongation-at-break. The principle outlined here could apply to the design of strong and tough materials.

Model for the depolarizing retarder in Mueller matrix polarimetry

We advance an analytical model describing the polarimetric response of a depolarizing retarder whose retardance varies spatially in magnitude or in orientation. The variation of the retarder parameters may be either of deterministic or of random nature. The model provides both the mean values and the uncertainties of the parameters. Its application is illustrated on two experimental examples, respectively covering the deterministic and the random cases.

Poincaré and his polarization sphere

In a text (1892) on light, Jules Henri Poincaré introduced a geometrical device for tracking the polarization of state of light interacting with matter. Poincaré first mapped all polarization ellipses onto the surface of sphere and changes of state were represented as rotations from one point to another about prescribed axes depending on linear optical properties of the medium. Here, we consider how Poincaré, the mathematician, invented his sphere. Poincaré's professional activities in the service of geodesy appear at first glance to provide a borrowed geometry for his one-to-one mapping of polarization ellipses to global lines of latitude and longitude. However, this association falls apart in the face of a close reading of Poincaré's biography and his influences, especially the research interests of his teachers from the École Polytechnique and the Écoles de Mines. The work of Tissot and Mallard on distortion ellipses in cartography and the etiology of optical activity in crystals, respectively, together with Poincaré's own study of the qualitative theory of differential equations, provide the iconography of, and motivation for, the sphere. Whether Poincaré's mentors were unwitting partners in the invention of the sphere-it is impossible to be sure-Poincaré's otherworldly geometric sensibilities carried him through isometries (rotations) on hyperbolic planes and beyond. The apparent ingenuity behind Poincaré's sphere is diminished in comparison to his fulsome achievements. Moreover, Poincaré's considerations of the psychology of invention further emphasize that sometimes great ideas arrive to those fortunate to receive them by mechanisms that resist interpretation.

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.