Ceiling temperature

Ceiling temperature ( $T_{c}$ ) is a measure of the tendency of polymers to revert to their 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.

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.

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. Above the ceiling temperature, the rate of depolymerization is greater than the rate of polymerization, which inhibits the formation of the given polymer.^[1] The ceiling temperature can be defined by

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

Monomer-polymer equilibrium

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)^[2]	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

↑ 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.
↑ 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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