Ceiling temperature explained

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 byT _{c} = (\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 Frederick Dainton and K. J. 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 small 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 polyisobutylene.

Ceiling temperatures of common monomers

Monomer	Ceiling temperature (°C)^[6]	Structure
	585	CH2=CHCH=CH2
	610	CH2=CH2
	175	CH2=CMe2
	466	CH2=C(Me)CH=CH2
	198	CH2=C(Me)CO2Me
	66	PhC(Me)=CH2
	395	PhCH=CH2
	1100	CF2=CF2

Notes and References

1. Book: Cowie, J.M.G.. Polymers: Chemistry & Physics of Modern Materials. 1991. Blackie (USA: Chapman & Hall). New York. 0-216-92980-6. 2nd. 74.
2. Book: Carraher Jr, Charles E. Introduction of Polymer Chemistry. 2010. CRC Press, Taylor and Francis. New York. 978-1-4398-0953-2. 2nd. 224. 7. https://archive.org/details/introductiontopo0000carr/page/224.
3. The Reaction of Sulfur Dioxide with Olefins: the Ceiling Temperature Phenomenon . R. D. Snow . F. E. Frey . J. Am. Chem. Soc. . 1943 . 65 . 12 . 2417–2418 . 10.1021/ja01252a052.
4. Reversibility of the Propagation Reaction in Polymerization Processes and its Manifestation in the Phenomenon of a 'Ceiling Temperature'. Nature. 1948. 1476-4687. 705–707. 162. 4122. F. S.. Dainton. K. J.. Ivin. 10.1038/162705a0. 1948Natur.162..705D. 4105548.
5. Web site: Baron DAINTON OF HALLAM MOORS . Ivin. Ken. Royal Society of Edinburgh : Obituary. Rse.org.uk. 30 December 2018. dead. https://web.archive.org/web/20061004122701/http://www.rse.org.uk/fellowship/obits/obits_alpha/dainton_lord.pdf. 4 October 2006. dmy-all.
6. Book: Stevens, Malcolm P.. Polymer Chemistry an Introduction. 1999. Oxford University Press. New York. 978-0-19-512444-6. 193–194. 3rd. 6.