The Mayo-Lewis equation or copolymer equation in polymer chemistry describes the distribution of monomers in a copolymer [1]:
Taking into consideration a monomer mix of two components and and the four different reactions that can take place at the reactive chain end terminating in either monomer () with their reaction rate constants :
and with reactivity ratios defined as:
the copolymer equation is given as:
with the concentration of the components given in square brackets. The equation gives the copolymer composition at any instant during the polymerization.
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From this equation several limiting cases can be derived:
An example is maleic anhydride and stilbene, with reactivity ratio:
Both of these compounds do not homopolymerize and instead, they react together to give exclusively alternating copolymer.
Another form of the equation is:
where stands the mole fraction of each monomer in the copolymer:
and the mole fraction of each monomer in the feed:
When the copolymer composition has the same composition as the feed, this composition is called the azeotrope.
The reactivity ratios can be obtained by rewriting the copolymer equation to:
with
in the feed
and
in the copolymer
A number of copolymerization experiments are conducted with varying monomer ratios and the copolymer composition is analysed at low conversion. A plot of versus gives a straight line with slope and intercept .
A semi-empirical method for the determination of reactivity ratios is called the Q-e scheme.
Monomer 1 is consumed with reaction rate [2]:
with the concentration of all the active centers terminating in monomer 1 or 2.
Likewise the rate of disappearance for monomer 2 is:
Division of both equations yields:
The ratio of active center concentrations can be found assuming steady state with:
meaning that the concentration of active centres remains constant, the rate of formation for active center of monomer 1 is equal to the rate of their destruction or:
or