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Sec. 7.3   Polymerization                                      379





















                                   Figure 7-9 Live polymer concentration as a function of  chain length at different
                                   scaled times.

                                   Neglecting the rate of  chain transfer to the monomer with respect to  the
                               rate of propagation, a =ole  balance on the monomer gives


                                                                                            (7  -67)


                               Knowing the initial monomer concentration, Mo, we  can solve for the mono-
                               mer concentration at any time:



                               We  can also evaluate the scaled time 0:









                    Relationship
               between tlhe scaled
                 time, 0, and real                                                          (7-69)
                        time t
                               One can now  substitute Equation (7-69) into Equation (7-66) to determine the
                               live polymer concentrations at any time 1.
                                    For  anionic  polymerization,  termination  can  occur  by  neutralizing  the
                               live polymer RJ lo PJ.


                                 Example 7-5  Calculating the Distribution Parameters @om Analytical
                                             Expressions for Anionic Polymerization
                                 Cdculi%te pn , pm , and D for the live polymer chains I?,.
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