Ideal Copolymerization
(Random or Statistical Copolymers)

In the ideal random vinyl copolymerization, each radical bearing chain has no preference for adding monomers of type M₁ or M₂. Furthermore, both types of radical bearing end groups have the same rate of addition. This means, the probability of the addition of a M₁ monomer to a M₂· radical is the same as the addition of a M₂ monomer to a M₂· radical. The same is true for the addition of monomers to a M₁· radicals. Therefore, the sequence of repeat units in an ideal copolymer is completely random. These polymers are called random or statisitical copolymers.

If r₁ and r₂ are monomer reactivity ratios defined by

r₁ = k₁₁ / k₁₂

r₂ = k₂₂ / k₂₁

then the condition for random copolymerization is

r₁ = 1 / r₂

k₂₁ / k₂₂ = k₁₁ / k₁₂

where k_xy are the rate constants of the four different types of free radical polymerization reactions.

M₁· + M₁ → M₁·      R₁₁ = k₁₁ [ M₁·] [ M₁]

M₁· + M₂ → M₂·      R₁₂ = k₁₂ [ M₁·] [ M₂]

M₂· + M₂ → M₂·      R₂₂ = k₂₂ [ M₂·] [ M₂]

M₂· + M₁ → M₁·      R₂₁ = k₂₁ [ M₂·] [ M₁]

where M₁· and M₂· represent chain radicals having a free radical bearing unit of type 1 and 2. We have to distinguish between two cases:

• Case 1: r₁ > 1 and  r₂ < 1 or r₁ < 1 and  r₂ > 1, r₁r₂ = 1
  Each radical has no preference and the copolymer has a completely random sequence of monomers. However, one monomer is more reactive than the other. Consequently, the copolymer will consist of a greater portion of the more reactive specimen in the random sequence of repeat units.

• Case 2: r₁ =  r₂ = 1
  The sequence is not only random, but the composition is identical with the composition of the monomer blend throughout the range. However, the reactivity of the two radicals might differ, that is, k₁₁ need not be equal to k₂₂.

Incremental Polymer Composition as a Function of Monomer Composition for Ideal Copolymerization

The figure above shows the incremental polymer composition as a function of monomer composition for different reactivity ratios  r₁/r₂ of an ideal copolymerization. The ordinate (F₁) represents the composition of the copolymer increment formed from the monomer blend of composition f₁ shown on the abscissa. The straight line r₁ = 1 is the trivial case in which

r₁= r₂ = 1, ⇒ k₁₂ = k₁₁ and k₂₁ = k₂₂.

This means the two radicals are equally reactive towards each monomer. The radicals sequence is then not only random, but the incremental composition is identical with the mole fractions of the unreacted monomer blend.