Mechanism of Free Radical Polymerization

Free radical polymerization consists of three fundamental steps, initiation, propagation, and termination. Initiation, involves the formation of radicals followed by the radical's reaction with a vinyl monomer, propagation is the rapid and progressive addition of monomers to the growing polymer chain without a change of the active center, and termination is the destruction of the growth active center, usually by combination or coupling of the radicals of two growing polymer chains or by disproportionation. In addition to these three processes, chain transfer might occur, which is the transfer of the growth active site from the active chain to a inactive (dormant) one, a monomer or a solvent molecule (transfer agent).

Initiation

This step involves the generation of active species. The free radicals can be produced in a number of ways, including thermal or photochemical decomposition of organic peroxides, hydroperoxides, azo or diazo compounds. Other methods of free radical generation are high-energy radiation and oxidation-reduction (redox) reactions.

The two most common initiators (I) are benzoyl peroxide (BPO) and 2,2'-azo-bis-isobutyrylnitrile (AIBN).¹ Both molecules have a strong tendency to fall apart into two fragments with unpaired electrons, the so-called free radical initiators:

I → 2 R·

Following its generation, the free radical then reacts with a vinyl monomer, that is, it adds to one of the electrons of the double bond of the vinyl monomer and the remaining electron becomes the new free radical:

R· + M → RM·

Thus the process of chain initiation involves two steps; the first being the decomposition of the initiator (e.g. BPO or AIBN) to yield a pair of free radicals R·, and the second the addition of a monomer to the primary radical R· to yield the chain radical, which is called the initiation. It was found that the rate-limiting step is the initiation step, that is, the rate constant for initiator dissociation is much smaller than that for monomer addition.

Some of the monomers may also undergo other reactions such as combination with another radical to form inactive molecules.

The efficiency of the radicals with which they initiate chains can be estimated by comparing the number of initiators decomposed with the number of polymer chains formed. It was found that only a fraction, f, of the initiator molecules initiate a polymerization process. Based on observations, the rate of initiation is proportional to the concentration of initiators [I] and its efficiency f:²

R_i = d[M·] / dt = 2 f k_d [I]

where k_d is the rate constant (velocity coefficient) of initiation.

Propagation

The growth of a polymer chain by successive addition of monomers during propagation can be represented as follows:

RM₁· + M → RM₂·

RM₂· + M → RM₃·

And in general:

RM_x· + M → RM_x+1·

The general assumption is that the radical reactivity is independent of the chain length, this means, that all the propagation steps have the same rate constant  k_p1 = k_p2 = ... =  k_p.² Thus, the rate of polymerization equals the consumption of monomers in the propagation step. Since both a monomer and the growing polymer chain are involved in the reaction, the reaction rate is proportional to both concentrations.

R_p = -d[M] / dt = k_p [M] [M*]

where k_p is the reaction constant or velocity coefficient of the process and [M*] = ∑RM_x, which is the sum of the concentration of all chain radicals.

Termination

The propagation step would theoretically continue until all monomers are consumed. However, pairs of radicals also have a tendency to react with each other and thus annihilate their activities. The termination can occur via combination or disproportionation. In the case of combination or coupling, two growing polymer chains react with each other forming a single nonreactive polymer chain:

M_x· + M_y· → M_x+y

And in the case of disproportionation, a hydrogen atom is transferred from one radical to the other resulting in two polymers, one with a saturated end and the other with an unsaturated end and each with an initiator fragment.

M_x· + M_y· → M_x + M_y

Usually, there is no need to distinguish between these two different types of termination reactions, that is, both reactions can be combined to one rate expression:²

R_t = -d[M·] / dt = 2 k_t [M·]²

Where the factor two occurs as a result of the disappearance of two radicals at each incidence of termination reaction.

Notes & References

1. The initiators are sometimes erroneously called catalysts. Initiators are consumed in the reaction while catalysts are regenerated after the completion of the reaction.

2. Paul L. Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca, New york, 1953