Derivation of the copolymerisation equation

We limit the discussion to copolymerisations where two monomers are built in unbranched polymers via the free radical mechanism. If the penultimate unit in the radical chain end does not influence the reactivity of the radical and Flor/s principle for constant reactivity is valid, only four propagation steps are involved in the copolymerisation reaction  

The reactivity ratios represent the preference of the chain end radical —Mi for addition of monomer 1 to monomer 2 (ri) and of chain end radical —M2 for addition of monomer 2 to monomer 1 (r2). 

We can define the probability that a certain chain end radical reacts with a certain monomer  

The mole fraction of blocks M i with length i (mole fraction relative to all other blocks M i) is  

If n 00, or more precisely formulated, if there are many —MiM2 and —M2M1 — transitions per copolymer chain, there are as many Mi blocks as there are M2 blocks. Consequently, at any time the following holds for the composition of the instantaneously formed copolymer  

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