The Mayo–Lewis equation or copolymer equation in polymer chemistry describes the distribution of monomers in a copolymer. It was proposed by Frank R. Mayo and Frederick M. Lewis. The equation considers a monomer mix of two components M 1 {\displaystyle M_{1}\,} and M 2 {\displaystyle M_{2}\,} and the four different reactions that can take place at the reactive chain end terminating in either monomer ( M 1 ∗ {\displaystyle M_{1}^{*}\,} and M 2 ∗ {\displaystyle M_{2}^{*}\,} ) with their reaction rate constants k {\displaystyle k\,} :
M 1 ∗ + M 1 → k 11 M 1 M 1 ∗ {\displaystyle M_{1}^{*}+M_{1}{\xrightarrow {k_{11}}}M_{1}M_{1}^{*}\,}
M 1 ∗ + M 2 → k 12 M 1 M 2 ∗ {\displaystyle M_{1}^{*}+M_{2}{\xrightarrow {k_{12}}}M_{1}M_{2}^{*}\,}
M 2 ∗ + M 2 → k 22 M 2 M 2 ∗ {\displaystyle M_{2}^{*}+M_{2}{\xrightarrow {k_{22}}}M_{2}M_{2}^{*}\,}
M 2 ∗ + M 1 → k 21 M 2 M 1 ∗ {\displaystyle M_{2}^{*}+M_{1}{\xrightarrow {k_{21}}}M_{2}M_{1}^{*}\,}
The reactivity ratio for each propagating chain end is defined as the ratio of the rate constant for addition of a monomer of the species already at the chain end to the rate constant for addition of the other monomer.
r 1 = k 11 k 12 {\displaystyle r_{1}={\frac {k_{11}}{k_{12}}}\,}
r 2 = k 22 k 21 {\displaystyle r_{2}={\frac {k_{22}}{k_{21}}}\,}
The copolymer equation is then:
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