KINETICS OF ADDITION POLYMERIZATION

January 10, 2023
by Bhoomika Sheladiya

The catalytic polymerization of a monomer, M says, CH2 = CHX here, X = halogen. The following steps are involved in this process:

The initiator molecule I yields a free radical R

\[\displaystyle I\underset{{}}{\overset{{{{k}_{1}}}}{\longrightarrow}}R\]

The rate of production of the free radical is,

\[\displaystyle r={{k}_{1}}\left[ I \right]---(1)\]

Now, the free radical R adds to the double bind of the monomer molecules, generating new free radicals;

\[\displaystyle C{{H}_{2}}=CHX+R\underset{{}}{\overset{{{{k}_{2}}}}{\longrightarrow}}RC{{H}_{2}}CHX\]
\[\displaystyle RC{{H}_{2}}CHX+C{{H}_{2}}=CHX\to R-(C{{H}_{2}}-CHX)\]

The rate of disappearance of the monomer M is given by,

\[\displaystyle -\frac{{d\left[ M \right]}}{{dt}}={{k}_{2}}\left[ R \right]\left[ M \right]---(2)\]

The recombination of two free radicals achieves chain termination,

\[\displaystyle R-{{(C{{H}_{2}}-CHX)}_{n}}+\left( {XCH-C{{H}_{2}}} \right)-R\]
\[\displaystyle \underset{{}}{\overset{{{{k}_{3}}}}{\longrightarrow}}\]
\[\displaystyle R-{{(C{{H}_{2}}-CHX)}_{n}}-{{\left( {XCH-C{{H}_{2}}} \right)}_{{n-R}}}\]

The free radicals have very low concentration, and we can assume that their rate of production is equal to their rate of disappearance so that,

\[\displaystyle {{k}_{1}}\left[ I \right]={{k}_{3}}{{\left[ R \right]}^{2}}---(3)\]
\[\displaystyle \left[ R \right]={{\left( {\frac{{{{k}_{1}}}}{{{{k}_{3}}}}} \right)}^{{\frac{1}{2}}}}{{\left[ I \right]}^{{^{{\frac{1}{2}}}}}}---(4)\]

Substituting for [R] into equation (2), we get,

\[\displaystyle -\frac{{d\left[ M \right]}}{{dt}}={{k}_{2}}{{\left( {\frac{{{{k}_{1}}}}{{{{k}_{3}}}}} \right)}^{{\frac{1}{2}}}}{{\left[ I \right]}^{{^{{\frac{1}{2}}}}}}\left[ M \right]\]

The kinetics chain length, γ, s the ratio of the overall rate to the rate of the initiation step. It can also define the number of repeating chain units in the polymer chain.

\[\displaystyle \gamma =\frac{{-\frac{{d\left[ M \right]}}{{dt}}}}{r}=\frac{{-\frac{{d\left[ M \right]}}{{dt}}}}{{{{k}_{1}}\left[ I \right]}}---(6)\]

Also, the probability of another monomer to the growing chain radical is given by,

\[\displaystyle P=\frac{{{{k}_{2}}\left[ M \right]}}{{{{k}_{2}}\left[ M \right]+{{k}_{3}}\left[ R \right]}}=\frac{1}{{\frac{{1+{{{\left( {{{k}_{1}}{{k}_{3}}} \right)}}^{{\frac{1}{2}}}}{{{\left[ I \right]}}^{{^{{\frac{1}{2}}}}}}}}{{{{k}_{1}}\left[ M \right]}}}}----(7)\]

Vinyl polymerization, p is the order of 0.999.

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About the author

Bhoomika Sheladiya

BSc. (CHEMISTRY) 2014- Gujarat University
MSc. (PHYSICAL CHEMISTRY) 2016 - School of Science, Gujarat University

Junior Research Fellow (JRF)- 2019
AD_HOC Assistant Professor-(July 2016 to November 2021)

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