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MayoLewis equationThe MayoLewis 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 ratio's 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. Additional recommended knowledge
Limiting casesFrom 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. Calculation of reactivity ratio'sThe reactivity ratio's 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 ratio's and the copolymer composition is analysed at low conversion. A plot of versus gives a straight line with slope and intercept . A semiempirical method for the determination of reactivity ratio's is called the Qe scheme. ProofMonomer 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
References


This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "MayoLewis_equation". A list of authors is available in Wikipedia. 