Editing Cage effect

{{short description|Behavior of molecules in solvent as encapsulated particles}}
[[File:CageEffect.tif|thumb|340x340px|Free radicals in solvent can potentially react with a monomer within the solvent cage or diffuse out.]]

In [[chemistry]], the '''cage effect'''<ref>{{Cite journal |last=Chemistry (IUPAC) |first=The International Union of Pure and Applied |title=IUPAC - cage effect (C00771) |url=https://goldbook.iupac.org/terms/view/C00771 |access-date=2022-03-28 |website=goldbook.iupac.org |doi=10.1351/goldbook.c00771|doi-access=free }}</ref> (also known as '''geminate recombination'''<ref>{{Cite web |last=Chemistry (IUPAC) |first=The International Union of Pure and Applied |title=IUPAC - geminate recombination (G02603) |url=https://goldbook.iupac.org/terms/view/G02603 |access-date=2022-03-28 |website=goldbook.iupac.org}}</ref>) describes how the properties of a [[molecule]] are affected by its surroundings. First introduced by [[James Franck]] and [[Eugene Rabinowitch]]<ref>{{Cite journal|last=Rabinowitch, Franck|year=1934|title=Some remarks about free radicals and the photochemisty of solutions|journal=Transactions of the Faraday Society|volume=30|pages=120–130|doi=10.1039/tf9343000120}}</ref><ref>{{Cite journal|last=Rabinowitch|first=E|year=1936|title=The collison{{sic|nolink=y|expected=error is in original}} mechanism and the primary photochemical process in solutions|journal=Transactions of the Faraday Society|volume=32|pages=1381–1387|doi=10.1039/tf9363201381}}</ref> in 1934, the cage effect suggests that instead of acting as an individual particle, [[molecule]]s in [[solvent]] are more accurately described as an encapsulated particle. The encapsulated molecules or [[Radical (chemistry)|radicals]] are called '''cage pairs''' or '''geminate pairs'''.<ref name=":0">{{Cite journal|last=Denisov|first=E.T.|year=1984|title=Cage effects in a polymer matrix|journal=Macromolecular Chemistry and Physics|volume=8|pages=63–78|doi=10.1002/macp.1984.020081984106}}</ref><ref name=":1">{{Cite book|title=Introduction to Polymer Science and Chemistry: A problem solving approach|last=Chanda|first=Manas|publisher=CRC Press|year=2013|location=New York|pages=291, 301–303}}</ref> 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{{sup|-11}}&nbsp;seconds.<ref>{{cite journal | last1 = Herk | first1 = L. | last2 = Feld | first2 = M. | last3 = Szwarc | first3 = M. | year = 1961 | title = Studies of "Cage" Reactions | journal = J. Am. Chem. Soc. | volume = 83 | issue = 14| pages = 2998–3005 | doi=10.1021/ja01475a005}}</ref> Many manifestations of the cage effect exist.<ref>{{Cite web |title=Radical cage effects |url=https://macmillan.princeton.edu/wp-content/uploads/Radical-Cage-Effects-final-no-layering.pdf}}</ref>

In [[Radical polymerization|free radical polymerization]], radicals formed from the decomposition of an initiator molecule are surrounded by a cage consisting of solvent and/or monomer molecules.<ref name=":1" />  Within the cage, the free radicals undergo  many collisions leading to their recombination or mutual deactivation.<ref name=":0" /><ref name=":1" /><ref name=":2">{{Cite journal|last=Braden|first=Dale, A.|year=2001|title=Solvent cage effects. I. Effect of radical mass and size on radical cage pair recombination efficiency. II. Is geminate recombination of polar radicals sensitive to solvent polarity?|journal=Coordination Chemistry Reviews|volume=211|pages=279–294|doi=10.1016/s0010-8545(00)00287-3}}</ref> This can be described by the following reaction:

:<math>
R\!-\!R
\;\;\underset{k_c}{\overset{k_1}{\rightleftharpoons}}\;\;
\underset{\text{cage pair}}{(R^{\,\bullet},^{\bullet}\!R)}
\;\;\underset{k_D}{\overset{k_d}{\rightleftharpoons}}\;\;
\underset{\text{free radicals}}{2R^{\,\bullet}}
\;\rightarrow\;
\text{Products}
</math><ref name=":2" />

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.<ref name=":0" /> In unimolecular chemistry, geminate recombination has first been studied in the solution phase using [[iodine]] molecules<ref>{{Citation |last1=Schwartz |first1=Benjamin J. |title=The Molecular Basis of Solvent Caging |date=1994 |url=https://doi.org/10.1007/978-94-011-0916-1_8 |work=Ultrafast Dynamics of Chemical Systems |pages=235–248 |editor-last=Simon |editor-first=John D. |place=Dordrecht |publisher=Springer Netherlands |language=en |doi=10.1007/978-94-011-0916-1_8 |isbn=978-94-011-0916-1 |access-date=2022-03-28 |last2=King |first2=Jason C. |last3=Harris |first3=Charles B.|url-access=subscription }}</ref> and [[heme]] proteins.<ref>{{Cite journal |last1=Chernoff |first1=D A |last2=Hochstrasser |first2=R M |last3=Steele |first3=A W |date=1980-10-01 |title=Geminate recombination of O2 and hemoglobin. |journal=Proceedings of the National Academy of Sciences |language=en |volume=77 |issue=10 |pages=5606–5610 |doi=10.1073/pnas.77.10.5606 |pmid=6932659 |issn=0027-8424|doi-access=free |pmc=350115 }}</ref><ref>{{Cite journal |last1=Rohlfs |first1=R J |last2=Olson |first2=J S |last3=Gibson |first3=Q H |date=1988-02-05 |title=A comparison of the geminate recombination kinetics of several monomeric heme proteins. |journal=Journal of Biological Chemistry |volume=263 |issue=4 |pages=1803–1813 |doi=10.1016/s0021-9258(19)77948-4 |pmid=3338995 |issn=0021-9258|doi-access=free }}</ref> In the solid state, geminate recombination has been demonstrated with small molecules trapped in [[noble gas]] [[Matrix isolation|solid matrices]]<ref>{{Cite journal |last1=Apkarian |first1=V. A. |last2=Schwentner |first2=N. |date=1999-06-09 |title=Molecular Photodynamics in Rare Gas Solids |url=https://doi.org/10.1021/cr9404609 |journal=Chemical Reviews |volume=99 |issue=6 |pages=1481–1514 |doi=10.1021/cr9404609 |pmid=11849000 |issn=0009-2665|url-access=subscription }}</ref> and in [[triiodide]] crystalline compounds.<ref>{{Cite journal |last1=Cerullo |first1=Giulio |last2=Garavelli |first2=Marco |date=2017-05-27 |title=Caught in the act |url=https://www.nature.com/articles/nchem.2780 |journal=Nature Chemistry |language=en |volume=9 |issue=6 |pages=506–507 |doi=10.1038/nchem.2780 |pmid=28537591 |issn=1755-4349|url-access=subscription }}</ref><ref>{{Cite journal |last1=Poulin |first1=Peter R. |last2=Nelson |first2=Keith A. |date=2006-09-22 |title=Irreversible Organic Crystalline Chemistry Monitored in Real Time |url=https://www.science.org/doi/abs/10.1126/science.1127826 |journal=Science |volume=313 |issue=5794 |pages=1756–1760 |language=EN |doi=10.1126/science.1127826|pmid=16946037 |s2cid=35002522 |doi-access=free |url-access=subscription }}</ref><ref>{{Cite journal |last1=Xian |first1=Rui |last2=Corthey |first2=Gastón |last3=Rogers |first3=David M. |last4=Morrison |first4=Carole A. |last5=Prokhorenko |first5=Valentyn I. |last6=Hayes |first6=Stuart A. |last7=Miller |first7=R. J. Dwayne |date=2017-03-27 |title=Coherent ultrafast lattice-directed reaction dynamics of triiodide anion photodissociation |url=https://www.nature.com/articles/nchem.2751 |journal=Nature Chemistry |language=en |volume=9 |issue=6 |pages=516–522 |doi=10.1038/nchem.2751 |pmid=28537597 |issn=1755-4349|hdl=20.500.11820/52dbea74-99b4-454b-aac2-56c7be20947b |hdl-access=free }}</ref>

== Cage recombination efficiency ==

The cage effect can be quantitatively described as the '''cage recombination efficiency'''  F<sub>c</sub> where:

:<math>F_c = k_c/(k_c + k_d)   </math><ref name=":2" />

Here F<sub>c</sub> is defined as the ratio of the rate constant for cage recombination (k<sub>c</sub>) to the sum of the rate constants for all cage processes.<ref name=":2" /> According to mathematical models, F<sub>c</sub> is dependent on changes on several parameters including radical size, shape, and solvent viscosity.<ref name=":2" /><ref>{{Cite journal|last=Noyes|first=R.M.|year=1954|title=A Treatment of Chemical Kinetics with Special Applicability to Diffusion Controlled Reactions|journal=J. Chem. Phys. |volume=22|issue=8|pages=1349–1359|doi=10.1063/1.1740394|bibcode=1954JChPh..22.1349N}}</ref><ref>{{Cite journal|last=Noyes|first=R.M.|year=1961|title=Effects of diffusion rates on chemical kinetics|journal=Progr. React. Kinet.|volume=1|pages=129–60}}</ref> 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.<ref name=":1" />  Low initiator efficiency, ƒ, is largely attributed to the cage effect. The rate of initiation is described as:

:<math>R_i = 2fk_d[I]   </math> <ref name=":1" />

where R<sub>i</sub> is the rate of initiation, k<sub>d</sub> is the rate constant for initiator dissociation,  [I] 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.<ref name=":1" />

== See also ==
* [[Solvent effects]]
* [[Carrier generation and recombination]]
* [[Rate-determining step]]

== References ==
{{Reflist}}
{{Reaction mechanisms}}

{{DEFAULTSORT:Cage Effect (Chemistry)}}
[[Category:Chemistry theories]]
[[Category:Theoretical chemistry]]
[[Category:Reaction mechanisms]]