Physical world and mathematics

Photoredox-generated iminyl radical chemistry

Photoredox-generated iminyl radical chemistry is a branch of organic synthesis that uses visible-light photoredox catalysis to generate iminyl radicals from oxime derivatives for C–N and C–C bond formation.

Photoredox-induced 1,2-metalate migration of boronate complexes

Photoredox-induced 1,2-metalate migration of boronate complexes is a family of visible-light-driven reactions, first reported in 2017, in which a radical adds to a boronate complex and a carbon substituent then migrates from boron.

Photoredox-mediated Giese addition

Photoredox-mediated Giese addition is a visible-light-driven form of the Giese reaction: a photocatalyst generates a carbon-centered radical under mild conditions, and it adds to an electron-deficient alkene to form a carbon–carbon bond.

Photoredox/nickel-catalyzed C(sp3)–H arylation

Photoredox/nickel-catalyzed C(sp3)–H arylation is a dual-catalytic organic reaction, first reported in 2014, in which a photocatalyst and nickel convert alkyl C–H bonds into carbon–aryl bonds using aryl halides.

Photoreflectance

Photoreflectance is a contactless modulation spectroscopy technique that measures pump-induced changes in a sample's optical reflectance, used to characterize semiconductor band structure, transition energies, and built-in electric fields at room temperature.

Photorefractive effect

The photorefractive effect is a light-induced change in a material's refractive index, produced when redistributed charge builds an internal field via the electro-optic effect, first observed in 1966.

Photoresponsive hydrogels

Photoresponsive hydrogels are crosslinked, water-rich polymer networks that change stiffness, structure, or drug release when illuminated, used in drug delivery, tissue engineering, and soft robotics.

Photosensitization

Photosensitization is the process in which a molecule called a photosensitizer absorbs light and transfers energy or an electron to another molecule, driving reactions it could not undergo directly.

Photosphere

The photosphere is the visible surface of the Sun, the lowest layer of the solar atmosphere, which emits most of the Sun's light at about 5,500 °C.

Photostimulated luminescence

Photostimulated luminescence is delayed luminescence in which a material exposed to ionizing radiation releases stored energy as light when later stimulated by red or infrared light.

Photostriction

Photostriction is the generation of mechanical strain in a material by the absorption of light, a nonthermal deformation often combining the photovoltaic and converse piezoelectric effects, promising wireless light-driven actuators.

Phototactic Janus particles

Phototactic Janus swimmers are micrometer-scale Janus particles that convert light into self-propulsion, steering along light gradients through phoretic mechanisms and forming light-switchable collective states such as living crystals.

Photothermal catalysis

Photothermal catalysis is a catalytic approach in which photocatalysis and thermal catalysis operate together, offering milder conditions and higher activity for CO2 reduction, ammonia synthesis, and hydrogen production.

Photothermal catalytic CO2 conversion

Photothermal catalytic CO2 conversion is the use of catalysts that absorb sunlight to drive carbon dioxide reduction, combining photon-to-heat conversion with photochemical processes in one system.

Photothermal deflection spectroscopy

Photothermal deflection spectroscopy, also called the mirage effect, is a sensitive optical technique that measures a sample's absorption by detecting a probe laser beam's deflection.

Photothermal effect

The photothermal effect is the conversion of absorbed light into heat through nonradiative processes in the absorbing material, a universal effect behind photothermal spectroscopy, solar steam generation, and photothermal cancer therapy.

Photothermal microscopy

Photothermal microscopy is a label-free optical imaging technique that detects light absorbed by a sample through the local heating it produces, visualizing non-fluorescent nanoscale absorbers in cells and materials.

Photothermal radiometry

Photothermal radiometry (PTR) is a contactless measurement technique in which a modulated or pulsed light beam heats a sample and an infrared detector records the resulting thermal emission.

Photothermal spectroscopy

Photothermal spectroscopy is a family of techniques that measures the heat a sample releases after absorbing light, recovering absorption spectra and thermal properties of opaque solids, liquids, and gases.

Photothermoelectric effect

The photo-thermoelectric effect (PTE) generates a voltage when light heats charge carriers at a boundary between regions with different Seebeck coefficients, a key photocurrent mechanism in graphene photodetectors.

Photovoltage spectroscopy

Photovoltage spectroscopy is an optoelectronic characterization technique that measures surface photovoltage as a function of illumination wavelength, probing charge separation and band structure in semiconductors and solar-cell materials.

Photovoltaic effect

The photovoltaic effect, also called the Becquerel effect, is the generation of voltage or current in a material exposed to light, first observed in 1839.

Phragmén–Lindelöf principle

The Phragmén–Lindelöf principle, also known as the Phragmén–Lindelöf theorem, is a result in complex analysis extending the maximum modulus principle to unbounded domains, proved by Phragmén and Lindelöf in 1908.

Phrase structure rules

Phrase structure rules are rewrite rules in generative grammar, formalized by Noam Chomsky in the 1950s, that expand categories like S → NP VP to build sentence trees.

Phthalaldehyde

Phthalaldehyde, also known as ortho-phthalaldehyde or OPA, is an aromatic dialdehyde used as a fluorescent reagent for primary amines in HPLC and, since 1999, as a high-level disinfectant for endoscopes, replacing glutaraldehyde.

Phthalate

A phthalate is an ester of phthalic acid, made industrially by reacting phthalic anhydride with alcohols, used above all as a plasticizer that softens otherwise brittle polyvinyl chloride (PVC).

Phthalates

Phthalates, also called phthalate esters, are esters of phthalic acid used mainly as plasticizers that make PVC flexible; 6 to 8 million tons are produced yearly.

Phthalic acid

Phthalic acid, also called benzene-1,2-dicarboxylic acid or o-phthalic acid, is the ortho isomer of benzenedicarboxylic acid, with two carboxyl groups on adjacent positions of a benzene ring.

Phthalic anhydride

Phthalic anhydride, also known as isobenzofuran-1,3-dione, is the cyclic anhydride of phthalic acid, a white crystalline solid with formula C8H4O3 made by oxidizing o-xylene and used mainly in phthalate plasticizers, polyester resins, and alkyd resins.