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R7.1 Polymerization

R7.1 Polymerization

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Rate of<br />

disappearance<br />

of monomer<br />

Rate of formation of<br />

dead polymers<br />

Monomer<br />

balance<br />

Initiator<br />

balance<br />

367<br />

Using Equation (<strong>R7.1</strong>-14) to substitute for<br />

monomer is<br />

The rate of disappearance of monomer,<br />

agation, :<br />

r<br />

p<br />

�rM � k p M R �<br />

�r M<br />

j�1<br />

Finally, the net rate of formation of dead polymer<br />

r P j<br />

The rate of formation of all dead polymers is<br />

rP<br />

� 0.5kta(<br />

R�)<br />

2<br />

<strong>R7.1</strong>.3 Modeling a Batch <strong>Polymerization</strong> Reactor<br />

Chap.<br />

(<strong>R7.1</strong>-15)<br />

R�,<br />

the rate of disappearance of<br />

(<strong>R7.1</strong>-16)<br />

�rM,<br />

is also equal to the rate of prop-<br />

Pj<br />

by addition is<br />

(<strong>R7.1</strong>-17)<br />

To conclude this section we determine the concentration of monomer as a<br />

function of time in a batch reactor. A balance on the monomer combined with<br />

the LCA gives<br />

�<br />

A balance on the initiator I2<br />

gives<br />

dM<br />

------- � k p M ∑ R j � k p MR�<br />

�<br />

dt<br />

Integrating and using the initial condition<br />

tion of the initiator concentration profile:<br />

�<br />

�<br />

�<br />

j<br />

k p MR�<br />

k p M 2k0<br />

( I2)<br />

f<br />

� --------------------<br />

r p<br />

0.5k ta<br />

r P<br />

� �rM<br />

�<br />

k�j�1<br />

�<br />

k�1<br />

�<br />

�<br />

j�1<br />

r P j<br />

� dI2 ------- �<br />

k0 I2 dt<br />

k<br />

t<br />

Rk<br />

R j�k<br />

k<br />

p<br />

M 2k0<br />

( I2)<br />

f<br />

--------------------<br />

k<br />

t<br />

(<strong>R7.1</strong>-18)<br />

I2<br />

� I20<br />

at t � 0, we obtain the equa

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