Radical Polymerization - Kinetics

Kinetics

In typical chain growth polymerization, the reaction rate for initiation, propagation and termination can be described as follows.

where f is the efficiency of the initiator and k_d, k_p, and k_t are the constants for initiator dissociation, chain propagation and termination, respectively., and is the concentration of the initiator, monomer and the active growing chain.

Under the steady state approximation, the concentration of the active growing chains remains constant, i.e. the rate of initiation and termination is the same. The concentration of active chain can be derived and expressed in terms of the other known species in the system.

In this case, the rate of chain propagation can be further described using a function of the initiator and monomer concentration

The kinetic chain length v is a measure of the average number of monomer units reacting with an active center during its lifetime and is related to the molecular weight through the mechanism of the termination. Without chain transfer, the dynamic chain length is only the function of propagation rate and initiation rate.

Assuming no chain transfer effect occurs in the reaction, the number average degree of polymerization P_n can be correlated with the kinetic chain length. In the case of termination by disproportionation, one polymer molecule is produced per every kinetic chain:

Termination by combination leads to one polymer molecule per two kinetic chains:

Any mixture of these both mechanisms can be described by using the value δ, and the contribution of disproportionation to the overall termination process:

If chain transfer is considered, then there are other pathways to terminate the growing chain. The equation for dynamic chain length will be modified as the following.

If chain transfer is considered, the kinetic chain length is not affected by the transfer process because the growing free-radical center generated by the initiation step stays alive after any chain transfer event, although multiple polymer chains are produced. However, the number average degree of polymerization decreases as the chain transfers, since the growing chains are terminated by the chain transfer events. Taking into account the chain transfer reaction towards solvent S, initiator I, polymer P, and added chain transfer agent T. The equation of P_n can be expanded:

It is usual to define chain transfer constants C for the different molecules

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