Kinetic relationships in free-radical polymerizations

A kinetic scheme for typical free-radical polymerizations is pictured as follows [2] the rate of propagation is equal to the rate of polymerization R, as all the monomer molecules (except one) are consumed during this step. 

In the above shown kinetic scheme, M stands for the monomer concentration, I is the concentration of the initiator, and [R ] and [P ] mean the concentration of primary and polymer radicals, 

Principles of Polymer Chemistry, DOI 10.1007/978-1 614-2212-9 3, 1st and 2nd editions Kluwer Academic/Plenum Publishers 1995, 2000, 

The equation for the rate of propagation, shown above in the kinetic scheme, contains the term [M ]. It designates radical concentration. This quantity is hard to determine quantitatively because its concentration is usually very low. A steady state assumption is, therefore, made to simplify the calculations. It is assumed that while the radical concentration increases at the very start of the reaction, it reaches a constant value almost instantly. This value is maintained from then on, and the rate of change of free-radical concentration is assumed to quickly become and remain zero during the polymerization. At steady state, the rates of initiation and termination are equal, oxRi = R = 2 i[M ] [4]. This assumption makes it possible to solve for [M ] and can then be expressed as  

The rate of propagation is approximately equal to the total rate of polymerization. The total rate can be designated as R op Because all but one molecule are converted during the step of propagation, we can write  

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