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 from ...

for two

dimension In physics and mathematics, the dimension of a Space (mathematics), mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any Point (geometry), point within it. Thus, a Line (geometry), lin ...

s. Most fundamentally, planar

is a

mathematical Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

term, finding use in

chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...

physics Physics is the natural science that studies matter, its 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 which r ...

and related physical sciences, for example, in

astronomy Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...

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

and

metamaterials A metamaterial (from the Ancient Greek, Greek word Meta, μετά ''meta'', meaning "beyond" or "after", and the Latin word ''materia'', meaning "matter" or "material") is any material engineered to have a property that is not found in naturally ...

. Recent occurrences in latter two fields are dominated by

microwave Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ran ...

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 dimens ...

d planar interfaces for

infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around ...

and visible

light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...

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 (''kheir''), "hand", a familiar chiral object. An object or a system is ''chiral'' if it is distinguishable from ...

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

lacking an

asymmetric carbon An asymmetric carbon atom (chiral carbon) is a carbon atom that is attached to four different types of atoms or groups of atoms. Le Bel-van't Hoff rule states that the number of stereoisomers of an organic compound is 2n, where n represents the num ...

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. Howe ...

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

chemical bond A chemical bond is a lasting attraction between atoms or ions that enables the formation of molecules and crystals. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds, or through the sharing of ...

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

cyclooctene Cyclooctene is the cycloalkene with a formula . Its molecule has a ring of 8 carbon atoms, connected by seven single bonds and one double bond. Cyclooctene is notable because it is the smallest cycloalkene that can exist stably as either the '' ...

, 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

paracyclophane In organic chemistry, a cyclophane is a hydrocarbon consisting of an aromatic unit (typically a benzene ring) and a chain that forms a bridge between two non-adjacent positions of the aromatic ring. More complex derivatives with multiple aromati ...

s. 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 o ...

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 any material engineered to have a property that is not found in naturally occurring materials. ...

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 In electrodynamics, circular polarization of an electromagnetic wave is a polarization state in which, at each point, the electromagnetic field of the wave has a constant magnitude and is rotating at a constant rate in a plane perpendicular to t ...

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