Page 411 - Elements of Chemical Reaction Engineering Ebook

382 Nonefementary Reaction Kinetics Chap. 7

Example 7-6 Determination of Dead Polymer Distribution When Transfer
to Monomer Is the Main Termination Mechanism
Determine an equation for the concentratim of polymer as a function of scaled
time. Once we have the live polymer concentration as a function of time, we can
determine the dead polymer concentration as a function of time. If transfer to mono-
mer is the main mechanism for termination,

Rj+M k’n‘ 1 Pj+ R,

A balance of dead, polymer of chain length j is

Anionic dP- ’ (E7-6.1)
=
polymerization 2 k,,RJM
dt
As a very first approximation, we neglect the rate of transfer to dead polymer from
the live polymer with respect to the rate of propagation:

so that the analytical solution obtained in Equation (7-65) can be used. Then

(E7-6.2)

Integrating, we obtain the dead polymer concentrations as a function of scaled time
from CRC Mathematical Tables integral number 521 :

(E7-6.3)

We recall that the scaled time 0 can be calculated from

In many instances termination of anionic polymerization is brought about by adding
a base to neutralize the propagating end of the polymer chain.

Other Useful Definitions. The number-average kinetic chain length, VN, is
the ratio of the rate of the propagation rate to the rate of termination:

v - ‘P (7-70)
N--
rt
Most often, the PSSH is used so that r, = ri:

I
The long-chain approximation holds when VN is large.