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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 ______ _______ _______ ______ __________ __________ ___ ____ __________ ____.
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