# Ceiling temperature

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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

1. ^ 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.
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.