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 ...

, the cage effect (also known as geminate recombination) describes how the properties of a

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 ...

are affected by its surroundings. First introduced by

James Franck James Franck (; 26 August 1882 – 21 May 1964) was a German-American physicist who received the 1925 Nobel Prize in Physics with Gustav Hertz "for their discovery of the laws governing the impact of an electron upon an atom". He completed hi ...

and

Eugene Rabinowitch Eugene Rabinowitch (April 27, 1901 – May 15, 1973) was a Russian-born American biophysicist who is known for his work in photosynthesis and nuclear energy. He was a co-author of the Franck Report and a co-founder in 1945 of the ''Bulletin of t ...

in 1934, the cage effect suggests that instead of acting as an individual particle,

s in

solvent A solvent (from the Latin language, Latin ''wikt:solvo#Latin, solvō'', "loosen, untie, solve") is a substance that dissolves a solute, resulting in a Solution (chemistry), solution. A solvent is usually a liquid but can also be a solid, a gas ...

are more accurately described as an encapsulated particle. The encapsulated molecules or

radicals Radical (from Latin: ', root) may refer to: Politics and ideology Politics *Classical radicalism, the Radical Movement that began in late 18th century Britain and spread to continental Europe and Latin America in the 19th century *Radical politics ...

are called cage pairs or geminate pairs. In order to interact with other molecules, the caged particle must diffuse from its solvent cage. The typical lifetime of a solvent cage is 10 seconds. Many manifestations of the cage effect exist. In free radical polymerization, radicals formed from the decomposition of an initiator molecule are surrounded by a cage consisting of solvent and/or monomer molecules. Within the cage, the free radicals undergo many collisions leading to their recombination or mutual deactivation. This can be described by the following reaction: :

R\!-\!R
\;\;\underset\;\;
\underset
\;\;\underset\;\;
\underset
\;\rightarrow\;
\text

After recombination, free radicals can either react with monomer molecules within the cage walls or diffuse out of the cage. In polymers, the probability of a free radical pair to escape recombination in the cage is 0.1 – 0.01 and 0.3-0.8 in liquids. In unimolecular chemistry, geminate recombination has first been studied in the solution phase using

iodine Iodine is a chemical element; it has symbol I and atomic number 53. The heaviest of the stable halogens, it exists at standard conditions as a semi-lustrous, non-metallic solid that melts to form a deep violet liquid at , and boils to a vi ...

molecules and

heme Heme (American English), or haem (Commonwealth English, both pronounced /Help:IPA/English, hi:m/ ), is a ring-shaped iron-containing molecule that commonly serves as a Ligand (biochemistry), ligand of various proteins, more notably as a Prostheti ...

proteins. In the solid state, geminate recombination has been demonstrated with small molecules trapped in

noble gas The noble gases (historically the inert gases, sometimes referred to as aerogens) are the members of Group (periodic table), group 18 of the periodic table: helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), radon (Rn) and, in some ...

solid matrices and in

triiodide In chemistry, triiodide usually refers to the triiodide ion, . This anion, one of the polyhalogen ions, is composed of three iodine atoms. It is formed by combining aqueous solutions of iodide salts and iodine. Some salts of the anion have been ...

crystalline compounds.

Cage recombination efficiency

The cage effect can be quantitatively described as the cage recombination efficiency F_c where: :

F_c = k_c/(k_c + k_d)

Here F_c is defined as the ratio of the rate constant for cage recombination (k_c) to the sum of the rate constants for all cage processes. According to mathematical models, F_c is dependent on changes on several parameters including radical size, shape, and solvent viscosity. It is reported that the cage effect will increase with an increase in radical size and a decrease in radical mass.

Initiator efficiency

In free radical polymerization, the rate of initiation is dependent on how effective the initiator is. Low initiator efficiency, ƒ, is largely attributed to the cage effect. The rate of initiation is described as: :

R_i = 2fk_d

where R_i is the rate of initiation, k_d is the rate constant for initiator dissociation, is the initial concentration of initiator. Initiator efficiency represents the fraction of primary radicals R·, that actually contribute to chain initiation. Due to the cage effect, free radicals can undergo mutual deactivation which produces stable products instead of initiating propagation – reducing the value of ƒ.

References

{{DEFAULTSORT:Cage Effect (Chemistry) Chemistry theories Theoretical chemistry Reaction mechanisms

Cage recombination efficiency

Initiator efficiency

See also

References