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The Mayo–Lewis equation or copolymer equation in polymer chemistry describes the distribution of monomers in a copolymer:[1] It is named for Frank R. Mayo and Frederick M. Lewis.

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.

Limiting cases

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.

Calculation of reactivity ratios

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.

Equation derivation

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

External links

  • copolymer equation applet @eng.utah.edu Link
  • copolymers @zeus.plmsc.psu.edu Link

References

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  1. Copolymerization. I. A Basis for Comparing the Behavior of Monomers in Copolymerization; The Copolymerization of Styrene and Methyl Methacrylate Frank R. Mayo and Frederick M. Lewis J. Am. Chem. Soc.; 1944; 66(9) pp 1594 - 1601; Electronic Instrument Positions Staff (Standard ) Cameron from Clarence Creek, usually spends time with hobbies and interests which include knotting, property developers in singapore apartment For sale and boomerangs. Has enrolled in a world contiki journey. Is extremely thrilled specifically about visiting .
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