Copolymerisation is the polymerisation of two or more different monomers to produce a copolymer containing chemically distinct repeating units. In the chemistry of materials, copolymerisation is an important method for controlling the physical, chemical, thermal, and mechanical properties of polymers. By changing the nature and proportion of the monomers and controlling their arrangement along the polymer chain, materials with desired flexibility, strength, chemical resistance, glass-transition temperature, and other properties can be obtained. The kinetics of copolymerisation describes the relative rates at which the different monomers react with the growing polymer radicals and determines the sequence distribution of monomer units in the final copolymer. Consider the free-radical copolymerisation of two monomers, M₁ and M₂. The growing polymer chain may possess either an active radical derived from M₁ or one derived from M₂. Therefore, four propagation reactions are possible: M₁• + M₁ → M₁–M₁• M₁• + M₂ → M₁–M₂• M₂• + M₁ → M₂–M₁• M₂• + M₂ → M₂–M₂• The rates of these four propagation reactions are represented by the corresponding rate constants k₁₁, k₁₂, k₂₁, and k₂₂. Here, k₁₁ represents the reaction of a radical ending in M₁ with monomer M₁, while k₁₂ represents its reaction with M₂. Similarly, k₂₁ and k₂₂ describe reactions involving a radical ending in M₂. The kinetics of copolymerisation is commonly described using the Mayo–Lewis copolymerisation equation. The reactivity ratios are defined as r₁ = k₁₁/k₁₂ and r₂ = k₂₂/k₂₁. These ratios provide information about the preference of a growing radical for the two monomers. If r₁ is greater than one, a radical ending in M₁ tends to add M₁ preferentially. If r₁ is less than one, it tends to add M₂. The same interpretation applies to r₂. The instantaneous composition of the copolymer can be expressed in terms of the monomer concentrations and reactivity ratios. In simplified form, the fraction of M₁ units entering the copolymer depends on [M₁], [M₂], r₁, and r₂. The Mayo–Lewis equation is F₁ = (r₁f₁² + f₁f₂)/(r₁f₁² + 2f₁f₂ + r₂f₂²), where f₁ and f₂ are the mole fractions of M₁ and M₂ in the monomer mixture, respectively, and F₁ is the mole fraction of M₁ units in the instantaneous copolymer. This relationship demonstrates that the composition of a copolymer is not necessarily the same as the composition of the initial monomer mixture. The