Ceiling temperature

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

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

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

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

where ${\displaystyle E_{p}}$ and ${\displaystyle E_{dp}}$ 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. It is enthalpy that drives polymerizations. At low temperatures, the enthalpy term is greater than the ${\displaystyle T\Delta S_{p}}$ 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 prevents the formation of the polymer.^[2] Since :${\displaystyle \Delta H_{p}}$ and ${\displaystyle \Delta S_{p}}$ are fairly constant with temperature change, the ceiling temperature can be defined by

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

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.