Planar chirality, also known as 2D chirality, is the special case of

chirality Chirality () is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek (''kheir''), "hand", a familiar chiral object. An object or a system is ''chiral'' if it is distinguishable fro ...

for two

dimension In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coo ...

s. Most fundamentally, planar

is a

mathematical Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

term, finding use in

chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and chemical compound, compounds made of atoms, molecules a ...

physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

and related physical sciences, for example, in

astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...

optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of optical instruments, instruments that use or Photodetector, detect it. Optics usually describes t ...

and metamaterials. Recent occurrences in latter two fields are dominated by

microwave Microwave is a form of electromagnetic radiation with wavelengths shorter than other radio waves but longer than infrared waves. Its wavelength ranges from about one meter to one millimeter, corresponding to frequency, frequencies between 300&n ...

and terahertz applications as well as micro- and

nanostructure A nanostructure is a structure of intermediate size between microscopic and molecular structures. Nanostructural detail is microstructure at nanoscale. In describing nanostructures, it is necessary to differentiate between the number of dimen ...

d planar interfaces for

infrared Infrared (IR; sometimes called infrared light) is electromagnetic radiation (EMR) with wavelengths longer than that of visible light but shorter than microwaves. The infrared spectral band begins with the waves that are just longer than those ...

and visible

light Light, visible light, or visible radiation is electromagnetic radiation that can be visual perception, perceived by the human eye. Visible light spans the visible spectrum and is usually defined as having wavelengths in the range of 400– ...

In chemistry

This term is used in

contexts, e.g., for a

chiral Chirality () is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek language, Greek (''kheir''), "hand", a familiar chiral object. An object or a system is ''chiral'' if it is dist ...

molecule A molecule is a group of two or more atoms that are held together by Force, attractive forces known as chemical bonds; depending on context, the term may or may not include ions that satisfy this criterion. In quantum physics, organic chemi ...

lacking an asymmetric carbon atom, but possessing two non-

coplanar In geometry, a set of points in space are coplanar if there exists a geometric plane that contains them all. For example, three points are always coplanar, and if the points are distinct and non-collinear, the plane they determine is unique. How ...

rings that are each dissymmetric and which cannot easily rotate about the

chemical bond A chemical bond is the association of atoms or ions to form molecules, crystals, and other structures. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds or through the sharing of electrons a ...

connecting them: 2,2'-dimethylbiphenyl is perhaps the simplest example of this case. Planar chirality is also exhibited by molecules like (''E'')- cyclooctene, some di- or poly-substituted

metallocene A metallocene is a compound typically consisting of two cyclopentadienyl anions (, abbreviated Cp) bound to a metallic element, metal center (M) in the oxidation state II, with the resulting general formula Closely related to the metallocenes are ...

s, and certain monosubstituted paracyclophanes. Nature rarely provides planar chiral molecules,

cavicularin Cavicularin is a natural phenolic secondary metabolite isolated from the liverwort '' Cavicularia densa''. This macrocycle is unusual because it was the first compound isolated from nature displaying optical activity solely due to the presence of ...

being an exception.

Assigning the configuration of planar chiral molecules

To assign the configuration of a planar chiral molecule, begin by selecting the pilot atom, which is the highest priority of the atoms that is not in the plane, but is directly attached to an atom in the plane. Next, assign the priority of the three adjacent in-plane atoms, starting with the atom attached to the pilot atom as priority 1, and preferentially assigning in order of highest priority if there is a choice. Then set the pilot atom to in front of the three atoms in question. If the three atoms reside in a clockwise direction when followed in order of priority, the molecule is assigned as R; when counterclockwise it is assigned as S.

In optics and metamaterials

Chiral diffraction

Papakostas ''et al.'' observed in 2003 that planar chirality affects the polarization of light diffracted by arrays of planar chiral microstructures, where large polarization changes of opposite sign were detected in light diffracted from planar structures of opposite handedness.

Circular conversion dichroism

The study of planar chiral

metamaterial A metamaterial (from the Greek word μετά ''meta'', meaning "beyond" or "after", and the Latin word ''materia'', meaning "matter" or "material") is a type of material engineered to have a property, typically rarely observed in naturally occu ...

s has revealed that planar chirality is also associated with an optical effect in non-diffracting structures: the directionally asymmetric transmission (reflection and absorption) of circularly polarized waves. Planar chiral metamaterials, which are also anisotropic and lossy exhibit different total transmission (reflection and absorption) levels for the same circularly polarized wave incident on their front and back. The asymmetric transmission phenomenon arises from different, e.g. left-to-right, circular polarization conversion efficiencies for opposite propagation directions of the incident wave and therefore the effect is referred to as circular conversion dichroism. Like the twist of a planar chiral pattern appears reversed for opposite directions of observation, planar chiral metamaterials have interchanged properties for left-handed and right-handed circularly polarized waves that are incident on their front and back. In particular left-handed and right-handed circularly polarized waves experience opposite directional transmission (reflection and absorption) asymmetries.

Extrinsic planar chirality

Achiral components may form a chiral arrangement. In this case, chirality is not an intrinsic property of the components, but rather imposed extrinsically by their relative positions and orientations. This concept is typically applied to experimental arrangements, for example, an achiral (meta)material illuminated by a beam of light, where the illumination direction makes the whole experiment different from its mirror image. Extrinsic planar chirality results from illumination of any periodically structured interface for suitable illumination directions. Starting from normal incidence onto a periodically structured interface, extrinsic planar chirality arises from tilting the interface around any axis that does not coincide with a line of mirror symmetry of the interface. In the presence of losses, extrinsic planar chirality can result in circular conversion dichroism, as described above.

Chiral mirrors

Conventional mirrors reverse the handedness of circularly polarized waves upon reflection. In contrast, a chiral mirror reflects circularly polarized waves of one handedness without handedness change, while absorbing circularly polarized waves of the opposite handedness. A perfect chiral mirror exhibits circular conversion dichroism with ideal efficiency. Chiral mirrors can be realized by placing a planar chiral metamaterial in front of a conventional mirror. The concept has been exploited in holography to realize independent holograms for left-handed and right-handed circularly polarized electromagnetic waves. Active chiral mirrors that can be switched between left and right, or chiral mirror and conventional mirror, have been reported.

References

{{DEFAULTSORT:Planar Chirality Stereochemistry Chirality