Ceiling Temperature
and Depropagation
In 1943 Snow and Frey1 observed that the polymerization of alkenes only occurs below a certain temperature, characteristic of the particular alkene, which they termed the ceiling temperature. Generally, the ceiling temperature (Tc) is related to steric strain from interaction of substituents located at alternating cabon atoms on the polymer backbone that interfere with monomers approaching the chain (steric hindrance). The ceiling temperature is also affected by resonance stabilization of monomer double bonds by conjugated substituents as well as by the type of end groups.2
| Polymer | Tc (K) |
| Polyethylene | 883 |
| Poly(oxymethylene) | 398 |
| Poly(1,4-butadiene) | 585 |
| Polyisoprene | 739 |
| Poly(dimethylsiloxane) | 383 |
| Polyisobutylene | 448 |
| Polystyrene | 669 |
| Poly(α-methylstyrene) | 337 |
| Poly(tetramethylene oxide) | 357 |
| Poly(methyl methacyrylate) | 475 |
For most free radical polymerizations with a propagation reaction of the form
Rn· + M → Rn+1·
there exist an elevated temperature at which the chain growth process becomes reversible and depropagation occurs:
Rn· → Rn-1· + M
For this case, the reaction rate is given by
Ri = - d[M] / dt = kp [M] [R·] - ku [R·]
where kp is the reaction constant of propagation and ku that of depropagation. Numerically, the reaction rate may be either positive or negative depending on the concentration of [M] and [R·] and on the rate constants kp and ku which will vary with temperature.
In general, kp and ku have different activation energies. Usually, the activation energy of depropagation Eu is greater than that of polymerization Ep since most vinyl polymerizations are exothermic reactions. For this reason, ku will increase relative to kp as the temperature is raised and the reaction rate will decrease and reach zero when ku = kp [M] or expressed with the Eyring and Polanyi equation:
e-(Ep/Tc - ΔSp)/R [M] = e-(Eu/Tc - ΔSu)/R
where ΔSp and ΔSu are the standard activation entropies of propagation and depropagation reaction. Solving this equation for Tc yields
Tc = (Ep - Eu) / (ΔSp - ΔSu + R log [M])
or
Tc = ΔH / (ΔS0 + R log [M])
where ΔH and and ΔS0 are the molar free enthalpy and entropy of polymerization.3 If both ΔH and ΔS0 are negative (exothermic reaction), then a maximum temperature exists where above polymerization cannot occur. Thus, the polymer will undergo an unzipping reaction and revert to its monomer. If, on the other hand, both ΔH and ΔS0 are positive (endothermic reaction), then a minimum temperature exists where below no polymerization can occur. Thus, the monomer is stable despite the presence of initiators.This critical temperature is called floor temperature. It is a rather rare phenomenon. An examples is molten S8 sulphur, which cannot be polymerized below Tf = 160 °C.
References and Notes
R.D. Snow and F.E. Frey, J. Am. Chem. Soc., 65 (12), p. 2417 (1943)
The temperature at which depolymerization occurs can be raised by converting the less stable end groups into more stable groups. An example is polyacetal; the unstable hydroxyl end groups are usually converted to more stable ester groups by reaction with anhydrides.
If the free enthalpy and entropy of formation of the monomer(s) and the polymer are unknown, they can be predicted with statistical mechanical methods or with group contribution methods.