The Mayo–Lewis equation or copolymer equation in
polymer chemistry
Polymer chemistry is a sub-discipline of chemistry that focuses on the structures of chemicals, chemical synthesis, and chemical and physical properties of polymers and macromolecules. The principles and methods used within polymer chemistry ar ...
describes the distribution of
monomer
In chemistry, a monomer ( ; '' mono-'', "one" + '' -mer'', "part") is a molecule that can react together with other monomer molecules to form a larger polymer chain or three-dimensional network in a process called polymerization.
Classification
...
s in a
copolymer
In polymer chemistry, a copolymer is a polymer derived from more than one species of monomer. The polymerization of monomers into copolymers is called copolymerization. Copolymers obtained from the copolymerization of two monomer species are ...
. It was proposed by
Frank R. Mayo and
Frederick M. Lewis.
[''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.
The ''Journal of the American Chemical Society'' is a weekly peer-reviewed scientific journal that was established in 1879 by the American Chemical Society. The journal has absorbed two other publications in its history, the ''Journal of Analytical ...
; 1944; 66(9) pp 1594 - 1601;
The equation considers 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 (
and
) with their
reaction rate constant In chemical kinetics a reaction rate constant or reaction rate coefficient, ''k'', quantifies the rate and direction of a chemical reaction.
For a reaction between reactants A and B to form product C
the reaction rate is often found to have the ...
s
:
:
:
:
:
The reactivity ratio for each propagating chain end is defined as the ratio of the
rate constant In chemical kinetics a reaction rate constant or reaction rate coefficient, ''k'', quantifies the rate and direction of a chemical reaction.
For a reaction between reactants A and B to form product C
the reaction rate is often found to have the ...
for addition of a monomer of the species already at the chain end to the rate constant for addition of the other monomer.
[Cowie, J.M.G. ''Polymers: Chemistry & Physics of Modern Materials'' (2nd ed., Chapman & Hall 1991) p.106 ]
:
:
The copolymer equation is then:
[Rudin, Alfred ''The Elements of Polymer Science and Engineering'' (Academic Press 1982) p.265 ][
:
with the ]concentration
In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', '' molar concentration'', ''number concentration'', ...
s of the components in square brackets. The equation gives the relative instantaneous rates of incorporation of the two monomers.[
]
Equation derivation
Monomer 1 is consumed with reaction rate
The reaction rate or rate of reaction is the speed at which a chemical reaction takes place, defined as proportional to the increase in the concentration of a product per unit time and to the decrease in the concentration of a reactant per uni ...
:
with