Copolymerization: Difference between revisions

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== Copolymerization Equation ==
The Mayo-Lewis equation (also called the copolymerization equation) gives the molar ratios of the two monomers M<sub>1</sub> and M<sub>2</sub> in the resulting polymer as follows:
 
<math>\frac {d\left [M_1 \right ]}{d\left [M_2\right ]}=\frac{\left [M_1\right ]\left (r_1\left[M_1\right ]+\left [M_2\right ]\right)}{\left [M_2\right ]\left (\left [M_1\right ]+r_2\left [M_2\right ]\right)}</math>
 
where r<sub>1</sub> and r<sub>2</sub> are the reactivity ratios of the individual monomers and r<sub>1</sub> = k<sub>11</sub>/k<sub>12</sub> & r<sub>2</sub> = k<sub>22</sub>/k<sub>21</sub>, i.e. ''r'' = the rate of reaction with another monomer of itself / the rate of reaction with a different monomer. ''r'' is also called the copolymerization parameter.
 
k<sub>11</sub> and k<sub>22</sub> are the rate constants for the homopolymerization of the two monomers. k<sub>12</sub> or k<sub>21</sub> are the rate constants for the reaction between the two different monomers.
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F<sub>1</sub>=1-F<sub>2</sub>=d[M<sub>1</sub>]/(d[M<sub>1</sub>]+d[M<sub>2</sub>])
 
and ''f''<sub>1</sub>, ''f''<sub>2</sub> are the mole fractions of monomers M<sub>1</sub>, M<sub>2</sub> in the feed:
 
''f''<sub>1</sub>=1-''f''<sub>2</sub>=M<sub>1</sub>/(M<sub>1</sub>+M<sub>2</sub>)
 
== Examples ==