R7.1 Polymerization
R7.1 Polymerization
R7.1 Polymerization
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381<br />
The first moment is<br />
�1 I0 1 e � � � � l<br />
l !<br />
-----<br />
⎛ � ⎞<br />
� ⎜ �<br />
⎝ � ⎟ � I 0 ( 1�<br />
e���e�)<br />
⎠<br />
l�0<br />
�1 � I0 ( 1� �)<br />
The number-average length of growing polymer radical (i.e., live polymer) is<br />
� n<br />
�<br />
j�0<br />
�1 �0 � ---- �1��<br />
2 � j�1<br />
�2 I0 j 2 � R � j � I0<br />
j -----------------<br />
� ( j � 1)<br />
!<br />
Chap.<br />
(RE7-3.7)<br />
(RE7-3.8)<br />
(RE7-3.9)<br />
(RE7-3.10)<br />
Realizing that the j � 0 term in the summation is zero and after changing the index<br />
of the summation and some manipulation, we obtain<br />
(RE7-3.11)<br />
(RE7-3.12)<br />
(RE7-3.13)<br />
Plots of �n and �w along with the polydispersity, D,<br />
are shown in Figure RE7-3.1.<br />
We note from Equation (<strong>R7.1</strong>-48) that after a long time the maximum value<br />
of �, �M , will be reached:<br />
The distributions of live polymer species for an anionic polymerization carried out<br />
in a CSTR are developed in Problem P7-19.<br />
Example R7–4 Determination of Dead Polymer Distribution When Transfer<br />
to Monomer Is the Main Termination Mechanism<br />
Determine an equation for the concentration of polymer as a function of scaled<br />
time. After we have the live polymer concentration as a function of time, we can<br />
determine the dead polymer concentration as a function of time. If transfer to monomer<br />
is the main mechanism for termination,<br />
�<br />
j�0<br />
�2 I0 1 3� �2 � ( � � )<br />
� w<br />
�2 ----<br />
�1 1 3� �2 � �<br />
� � -----------------------------<br />
1� �<br />
D �w 1 3� �<br />
-----<br />
2 � �<br />
( 1� �)<br />
2<br />
� � -----------------------------<br />
R j<br />
� n<br />
� M<br />
M0 � ------<br />
I0 k<br />
tm<br />
�M ⎯⎯→ P j�<br />
R1
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