In chemistry, the cage effect<ref>Template:Cite journal</ref> (also known as geminate recombination<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>) describes how the properties of a molecule are affected by its surroundings. First introduced by James Franck and Eugene Rabinowitch<ref>Template:Cite journal</ref><ref>Template:Cite journal</ref> in 1934, the cage effect suggests that instead of acting as an individual particle, molecules in solvent are more accurately described as an encapsulated particle. The encapsulated molecules or radicals are called cage pairs or geminate pairs.<ref name=":0">Template:Cite journal</ref><ref name=":1">Template:Cite book</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 10-11 seconds.<ref>Template:Cite journal</ref> Many manifestations of the cage effect exist.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref>
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.<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">Template:Cite journal</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>Template:Citation</ref> and heme proteins.<ref>Template:Cite journal</ref><ref>Template:Cite journal</ref> In the solid state, geminate recombination has been demonstrated with small molecules trapped in noble gas solid matrices<ref>Template:Cite journal</ref> and in triiodide crystalline compounds.<ref>Template:Cite journal</ref><ref>Template:Cite journal</ref><ref>Template:Cite journal</ref>
Cage recombination efficiencyEdit
The cage effect can be quantitatively described as the cage recombination efficiency Fc where:
- <math>F_c = k_c/(k_c + k_d) </math><ref name=":2" />
Here Fc is defined as the ratio of the rate constant for cage recombination (kc) to the sum of the rate constants for all cage processes.<ref name=":2" /> According to mathematical models, Fc is dependent on changes on several parameters including radical size, shape, and solvent viscosity.<ref name=":2" /><ref>Template:Cite journal</ref><ref>Template:Cite journal</ref> It is reported that the cage effect will increase with an increase in radical size and a decrease in radical mass.
Initiator efficiencyEdit
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 Ri is the rate of initiation, kd 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" />