Principles of Free-Radical Polymerization Kinetics

In order for polymerization to take place, we have seen that the monomer has to have double functionality. In step growth polymerization this was provided by the co-reactive functional groups of the monomers. In free radical polymerization the opening of a double bond provides this functionality. The organic molecule reacts with an active species as follows:

Therefore, primary free radicals must be introduced to start the reaction. This is done by the use of an initiator, a thermo-labile compound, typically peroxides or azo-compounds which decompose in the following way:

The primary radicals react with the monomer producing monomer radicals:

Where f is the initiator efficiency or the fraction of radicals that are captured by monomer molecules. From this point, the site of the reactive center changes by the propagation (addition or transfer) reactions:

The rate of addition is not affected by the size of the organic macro-radical, therefore the rate of propagation can be expressed as:

In free radical polymerization, long chains of polymer are formed for a low monomer conversion, since the time life of free radicals is very small.

Chain transfer reactions can occur by transfer of an atom to the macro-radical. The macro-radical is terminated and the new active species can a) add more monomer b) terminate without further addition (inhibition). In any case, the result of chain transfer reactions is a lower molecular weight of the polymer. Schematically, the reaction is shown below:

Transfer reactions may take place from macro-radical to monomer, initiator, solvent or to an agent intentionally introduced to control MW. Only transfer to monomer cannot be controlled and determines the maximum degree of polymerization. The transfer constant is the ratio between the kinetic rates of the transfer reaction with respect to the propagation, where i depends of the nature of the transfer reaction:

The successive addition reactions terminate when two radicals encounter each other. This termination can take place by combination or disproportionation of the two radicals:

It is noteworthy that the termination coefficient is highly dependent on diffusion of the macro-radicals, and when these become entangled with the polymer chains, k_t values decrease significantly, leading to auto-acceleration of polymerization for high monomer concentrations due to lower termination and higher propagation rates (see below).

In order to determine the molecular weight in free radical polymerization, we must calculate the ratio between the depletion of monomer with respect to the production of polymer. For relatively high molecular weight products, the initiation rate is negligible compared to the propagation. If we take the inverse of this ratio:

We obtain the Mayo equation. If we assume the transfer reaction negligible when compared to the termination reactions, and a steady state is reached, the initiation rate is equal to the termination rate. The concentration of radicals can be therefore calculated and introduced in the Mayo equation to determine the degree of polymerization:

We observe that the propagation rate is proportional to k_p and inversely proportional to k_t^1/2 in steady state conditions.

Carlos Arnaiz del Pozo

This summary was elaborated from the outcomes of the course ‘’Polymer Reaction Engineering’’ in the TU/e for the PPD Designers program and from the book: Elements of Polymer Science and Engineering. A.Rudin.