Ceiling Temperature
For most free-radical polymerization reactions, there are some elevated temperatures at which the chain-growth process becomes reversible and depropagation takes place:
where, kd·p is the rate constant for depropagation or depolymerization. The equilibrium for the polymerization–depolymerization reaction is temperature dependent. The reaction isotherm can be written:
In the above equation DF0 is the free energy of polymerization of both, monomer and polymer, in appropriate standard states [88]. The standard state for the polymer is usually solid (amorphous or partly crystalline). It can also be a one molar solution. The monomer is a pure liquid or a one molar solution. The relationships of monomer concentration to heat content, entropy, and free energy are shown by the following expression. This applies over a wide range of temperatures [5].
In the above equation, Tc is the ceiling temperature for the equilibrium monomer concentration. It is a function of the temperature of the reaction. Because the heat content is a negative quantity, the concentration of the monomer (in equilibrium with polymer) increases with increasing temperatures. There are a series of ceiling temperatures that correspond to different equilibrium monomer concentrations. For any given concentration of a monomer in solution, there is also some upper temperature at which polymerization will not proceed. This, however, is a thermodynamic approach. When there are no active centers present in the polymer structure, the material will appear stable even above the ceiling temperature in a state of metastable equilibrium. The magnitude of the heat of polymerization of vinyl monomers is related to two effects: (1) Steric strains that form in single bonds from interactions of the substituents. These substituents, located on the alternate carbon atoms on the polymeric backbones, interfere with the monomers entering the chains. (2) Differences are in resonance stabilization of monomer double bonds by the conjugated substituents [70].
Most 1,2 disubstituted monomers, as stated earlier, are difficult to polymerize. It is attributed to steric interactions between one of the two substituents on the vinyl monomer and the b-substituent on the ultimate unit of the polymeric chain [94]. A strain is also imposed on the bond that is being formed in the transition state. The propagation reaction usually requires only an activation energy of about 5 kcal/mol. As a result, the rate does not vary rapidly with the temperature. On the other hand, the transfer reaction requires higher activation energies than does the chain-growth reaction. This means that the average molecular weight will be more affected by the transfer reaction at higher temperature. When allowances are made for chain transferring, the molecular weight passes through a maximum as the temperature is raised. At temperatures below the maximum, the product molecular weight is lower because the kinetic chain length decreases with the temperature. Above the maximum, however, the product molecular weight is also lower with increases in the temperature. This is due to increase in the transfer reactions. The above assumes that the rate of initiation is independent of the temperature. The relationship of the kinetic chain length to the temperature can be expressed as follows [5]:
where, EP, ET, and EI are energies of propagation, termination, and initiation, respectively. A large EI means that if the temperature of polymerization is raised, the kinetic chain length decreases. This is affected further by a greater frequency of chain transferring at higher temperatures. In addition, there is a possibility that disproportionation may become more significant.
