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Ceiling temperature ( $T_{c}$ ) is a measure of the tendency of a polymer to revert to its constituent monomers. When a polymer is at its ceiling temperature, the rate of polymerization and depolymerization of the polymer are equal. Generally, the ceiling temperature of a given polymer is correlated to the steric hindrance of the polymer’s monomers. Polymers with high ceiling temperatures are often commercially useful. Polymers with low ceiling temperatures are more readily depolymerizable.

Thermodynamics of polymerization

At constant temperature, the reversibility of polymerization can be determined using the Gibbs free energy equation:

\Delta G_{p}=\Delta H_{p}-T\Delta S_{p}

where $\Delta S_{p}$ is the change of entropy during polymerization. The change of enthalpy during polymerization, $\Delta H_{p}$ , is also known as the heat of polymerization, which is defined by

\Delta H_{p}=E_{p}-E_{dp}

where $E_{p}$ and $E_{dp}$ denote the activation energies for polymerization and depolymerization, respectively, on the assumption that depolymerization occurs by the reverse mechanism of polymerization.

Entropy is the measure of randomness or chaos. A system has a lower entropy when there are few objects in the system and has a higher entropy when there are many objects in the system. Because the process of depolymerization involves a polymer being broken down into its monomers, depolymerization increases entropy. In the Gibbs free energy equation, the entropy term is negative. Enthalpy drives polymerizations. At low temperatures, the enthalpy term is greater than the $T\Delta S_{p}$ term, which allows polymerization to occur. At the ceiling temperature, the enthalpy term and the entropy term are equal, so that the rates of polymerization and depolymerization become equal and the net polymerization rate becomes zero.^[1] Above the ceiling temperature, the rate of depolymerization is greater than the rate of polymerization, which inhibits the formation of the given polymer.^[2] The ceiling temperature can be defined by

T_{c}={\frac {\Delta H_{p}}{\Delta S_{p}}}

Monomer-polymer equilibrium

This phenomenon was first described by Snow and Frey in 1943.^[3] The thermodynamic explanation is due to Dainton and Ivin, who proposed that the chain propagation step of the polymerization is reversible.^[4]^[5]

At the ceiling temperature, there will always be excess monomers in the polymer due to the equilibrium between polymerization and depolymerization. Polymers derived from simple vinyl monomers have such high ceiling temperatures that only a minuscule amount of monomers remain in the polymer at ordinary temperatures. The situation for α-methylstyrene, PhC(Me)=CH₂, is an exception to this trend. Its ceiling temperature is around 66 °C. Steric hindrance is significant in polymers derived from α-methylstyrene because the phenyl and methyl groups are bonded to the same carbon. These steric effects in combination with stability of the tertiary benzylic α-methylstyryl radical give α-methylstyrene its relatively low ceiling temperature. When a polymer has a very high ceiling temperature, it degrades via bond cleavage reactions instead of depolymerization. A similar effect explains the relatively low ceiling temperature for poly(isobutylene).

Ceiling temperatures of common monomers

Monomer	Ceiling temperature (°C)^[6]	Structure
1,3-butadiene	585	CH₂=CHCH=CH₂
ethylene	610	CH₂=CH₂
isobutylene	175	CH₂=CMe₂
isoprene	466	CH₂=C(Me)CH=CH₂
methyl methacrylate	198	CH₂=C(Me)CO₂Me
α-methylstyrene	66	PhC(Me)=CH₂
styrene	395	PhCH=CH₂
tetrafluoroethylene	1100	CF₂=CF₂

References

^ Cowie, J.M.G. (1991). Polymers: Chemistry & Physics of Modern Materials (2nd ed.). New York: Blackie (USA: Chapman & Hall). p. 74. ISBN 0-216-92980-6.
^ Carraher Jr, Charles E (2010). "7". Introduction of Polymer Chemistry (2nd ed.). New York: CRC Press, Taylor and Francis. p. 224. ISBN 978-1-4398-0953-2.
^ R. D. Snow; F. E. Frey (1943). "The Reaction of Sulfur Dioxide with Olefins: the Ceiling Temperature Phenomenon". J. Am. Chem. Soc. 65 (12): 2417–2418. doi:10.1021/ja01252a052.
^ Dainton, F. S.; Ivin, K. J. (1948). "Reversibility of the Propagation Reaction in Polymerization Processes and its Manifestation in the Phenomenon of a 'Ceiling Temperature'". Nature. 162 (4122): 705–707. Bibcode:1948Natur.162..705D. doi:10.1038/162705a0. ISSN 1476-4687. S2CID 4105548.
^ Ivin, Ken. "Baron DAINTON OF HALLAM MOORS" (PDF). Rse.org.uk. Royal Society of Edinburgh : Obituary. Archived from the original (PDF) on 4 October 2006. Retrieved 30 December 2018.
^ Stevens, Malcolm P. (1999). "6". Polymer Chemistry an Introduction (3rd ed.). New York: Oxford University Press. pp. 193–194. ISBN 978-0-19-512444-6.

[1] Cowie, J.M.G. (1991). Polymers: Chemistry & Physics of Modern Materials (2nd ed.). New York: Blackie (USA: Chapman & Hall). p. 74. ISBN 0-216-92980-6.

[2] Carraher Jr, Charles E (2010). "7". Introduction of Polymer Chemistry (2nd ed.). New York: CRC Press, Taylor and Francis. p. 224. ISBN 978-1-4398-0953-2.

[3] R. D. Snow; F. E. Frey (1943). "The Reaction of Sulfur Dioxide with Olefins: the Ceiling Temperature Phenomenon". J. Am. Chem. Soc. 65 (12): 2417–2418. doi:10.1021/ja01252a052.

[4] Dainton, F. S.; Ivin, K. J. (1948). "Reversibility of the Propagation Reaction in Polymerization Processes and its Manifestation in the Phenomenon of a 'Ceiling Temperature'". Nature. 162 (4122): 705–707. Bibcode:1948Natur.162..705D. doi:10.1038/162705a0. ISSN 1476-4687. S2CID 4105548.

[5] Ivin, Ken. "Baron DAINTON OF HALLAM MOORS" (PDF). Rse.org.uk. Royal Society of Edinburgh : Obituary. Archived from the original (PDF) on 4 October 2006. Retrieved 30 December 2018.

[6] Stevens, Malcolm P. (1999). "6". Polymer Chemistry an Introduction (3rd ed.). New York: Oxford University Press. pp. 193–194. ISBN 978-0-19-512444-6.

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@@ Line 6: / Line 6: @@
 :<math>\Delta G_p = \Delta H_p - T \Delta S_p</math>
-where <math>\Delta S_p</math> is the change of [[entropy]] during polymerization.  The change of [[enthalpy]] during polymerization, <math>\Delta H_p</math>, is also known as the [[heat of polymerization]], which is defined by
+where <math>\Delta S_p</math> is the change of [[entropy]] during polymerization. The change of [[enthalpy]] during polymerization, <math>\Delta H_p</math>, is also known as the [[heat of polymerization]], which is defined by
 :<math>\Delta H_p = E_p - E_{dp}</math>
@@ Line 12: / Line 12: @@
 where <math>E_p</math> and <math>E_{dp}</math> denote the activation energies for polymerization and depolymerization, respectively, on the assumption that depolymerization occurs by the reverse mechanism of polymerization.
-Entropy is the measure of randomness or chaos.  A system has a lower entropy when there are few objects in the system and has a higher entropy when there are many objects in the system.  Because the process of depolymerization involves a polymer being broken down into its monomers, depolymerization increases entropy.  In the Gibbs free energy equation, the entropy term is negative.  Enthalpy drives polymerizations.  At low temperatures, the enthalpy term is greater than the <math>T\Delta S_p</math> term, which allows polymerization to occur.  At the ceiling temperature, the enthalpy term and the entropy term are equal, so that the rates of polymerization and depolymerization become equal and the net polymerization rate becomes zero.<ref>{{cite book|last=Cowie|first=J.M.G.|title=Polymers: Chemistry & Physics of Modern Materials|year=1991|publisher=Blackie (USA: Chapman & Hall)|location=New York|isbn=0-216-92980-6|edition=2nd|page=[https://archive.org/details/polymerschemistr0000cowi/page/74 74]|url=https://archive.org/details/polymerschemistr0000cowi/page/74}}</ref>  Above the ceiling temperature, the rate of depolymerization is greater than the rate of polymerization, which inhibits the formation of the given polymer.<ref>{{cite book|last=Carraher Jr|first=Charles E|title=Introduction of Polymer Chemistry|year=2010|publisher=CRC Press, Taylor and Francis|location=New York|isbn=978-1-4398-0953-2|edition=2nd|page=[https://archive.org/details/introductiontopo0000carr/page/224 224]|chapter=7|chapter-url=https://archive.org/details/introductiontopo0000carr/page/224}}</ref>  The ceiling temperature can be defined by
+Entropy is the measure of randomness or chaos. A system has a lower entropy when there are few objects in the system and has a higher entropy when there are many objects in the system. Because the process of depolymerization involves a polymer being broken down into its monomers, depolymerization increases entropy.  In the Gibbs free energy equation, the entropy term is negative. Enthalpy drives polymerizations. At low temperatures, the enthalpy term is greater than the <math>T\Delta S_p</math> term, which allows polymerization to occur. At the ceiling temperature, the enthalpy term and the entropy term are equal, so that the rates of polymerization and depolymerization become equal and the net polymerization rate becomes zero.<ref>{{cite book|last=Cowie|first=J.M.G.|title=Polymers: Chemistry & Physics of Modern Materials|year=1991|publisher=Blackie (USA: Chapman & Hall)|location=New York|isbn=0-216-92980-6|edition=2nd|page=[https://archive.org/details/polymerschemistr0000cowi/page/74 74]|url=https://archive.org/details/polymerschemistr0000cowi/page/74}}</ref> Above the ceiling temperature, the rate of depolymerization is greater than the rate of polymerization, which inhibits the formation of the given polymer.<ref>{{cite book|last=Carraher Jr|first=Charles E|title=Introduction of Polymer Chemistry|year=2010|publisher=CRC Press, Taylor and Francis|location=New York|isbn=978-1-4398-0953-2|edition=2nd|page=[https://archive.org/details/introductiontopo0000carr/page/224 224]|chapter=7|chapter-url=https://archive.org/details/introductiontopo0000carr/page/224}}</ref>  The ceiling temperature can be defined by
 :<math>T_c = \frac{\Delta H_p}{\Delta S_p}</math>
@@ Line 19: / Line 19: @@
 This phenomenon was first described by Snow and Frey in 1943.<ref>{{cite journal | title = The Reaction of Sulfur Dioxide with Olefins: the Ceiling Temperature Phenomenon | author1 = R. D. Snow | author2 = F. E. Frey | journal = J. Am. Chem. Soc. | year = 1943 | volume = 65 | issue = 12 | pages = 2417–2418 | doi = 10.1021/ja01252a052}}</ref> The thermodynamic explanation is due to [[Frederick Dainton|Dainton]] and Ivin, who proposed that the [[chain propagation]] step of the polymerization is reversible.<ref>{{Cite journal|title = Reversibility of the Propagation Reaction in Polymerization Processes and its Manifestation in the Phenomenon of a 'Ceiling Temperature'|journal = Nature|date = 1948|issn = 1476-4687|pages = 705–707|volume = 162|issue = 4122|first1 = F. S.|last1 = Dainton|first2 = K. J.|last2 = Ivin|doi = 10.1038/162705a0|bibcode = 1948Natur.162..705D|s2cid = 4105548}}</ref><ref>{{cite web|url=http://www.rse.org.uk/fellowship/obits/obits_alpha/dainton_lord.pdf|last=Ivin|first=Ken|title=Baron DAINTON OF HALLAM MOORS |publisher=Royal Society of Edinburgh : Obituary|website=Rse.org.uk|accessdate=30 December 2018|url-status=dead|archiveurl=https://web.archive.org/web/20061004122701/http://www.rse.org.uk/fellowship/obits/obits_alpha/dainton_lord.pdf|archivedate=4 October 2006|df=dmy-all}}</ref>
-At the ceiling temperature, there will always be excess monomers in the polymer due to the equilibrium between polymerization and depolymerization.  Polymers derived from simple [[Polyvinyl chloride|vinyl]] monomers have such high ceiling temperatures that only a [[Wikt:minuscule#Adjective|minuscule]] amount of monomers remain in the polymer at ordinary temperatures.  The situation for [[alpha-Methylstyrene|α-methylstyrene]], PhC(Me)=CH<sub>2</sub>, is an exception to this trend.  Its ceiling temperature is around 66 °C. [[Steric hindrance]] is significant in polymers derived from α-methylstyrene because the phenyl and methyl groups are bonded to the same carbon.  These steric effects in combination with stability of the tertiary benzylic α-methylstyryl radical give α-methylstyrene its relatively low ceiling temperature.  When a polymer has a very high ceiling temperature, it degrades via [[bond cleavage]] reactions instead of depolymerization. A similar effect explains the relatively low ceiling temperature for [[Polyisobutylene|poly(isobutylene)]].
+At the ceiling temperature, there will always be excess monomers in the polymer due to the equilibrium between polymerization and depolymerization. Polymers derived from simple [[Polyvinyl chloride|vinyl]] monomers have such high ceiling temperatures that only a [[Wikt:minuscule#Adjective|minuscule]] amount of monomers remain in the polymer at ordinary temperatures. The situation for [[alpha-Methylstyrene|α-methylstyrene]], PhC(Me)=CH<sub>2</sub>, is an exception to this trend. Its ceiling temperature is around 66 °C. [[Steric hindrance]] is significant in polymers derived from α-methylstyrene because the phenyl and methyl groups are bonded to the same carbon. These steric effects in combination with stability of the tertiary benzylic α-methylstyryl radical give α-methylstyrene its relatively low ceiling temperature.  When a polymer has a very high ceiling temperature, it degrades via [[bond cleavage]] reactions instead of depolymerization. A similar effect explains the relatively low ceiling temperature for [[Polyisobutylene|poly(isobutylene)]].
 ==Ceiling temperatures of common monomers==
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