Ceiling temperature

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

:$\backslash Delta\; G\_p\; =\; \backslash Delta\; H\_p\; -\; T\; \backslash Delta\; S\_p$

where $\backslash Delta\; S\_p$ is the change of entropy during polymerization. The change of enthalpy during polymerization, $\backslash Delta\; H\_p$, is also known as the heat of polymerization, which is defined by

:$\backslash Delta\; H\_p\; =\; E\_p\; -\; E\_\{dp\}$

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 $T\backslash Delta\; S\_p$ 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.{{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}} Above the ceiling temperature, the rate of depolymerization is greater than the rate of polymerization, which inhibits the formation of the given polymer.{{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}} The ceiling temperature can be defined by

:$T\_c\; =\; \backslash frac\{\backslash Delta\; H\_p\}\{\backslash Delta\; S\_p\}$

This phenomenon was first described by Snow and Frey in 1943.{{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}} The thermodynamic explanation is due to Frederick Dainton and K. J. Ivin, who proposed that the chain propagation step of the polymerization is reversible.{{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}}{{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}}

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.

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Category:Polymer chemistry

Category:Thermochemistry

Category:Enthalpy