Handbook of Size Exclusion Chromatography and Related ...

decreases smoothly and monotonically after the booster, and there is no obvious
indication that abimodal population is actually present. When Eq. (12) is applied
toMw,however,thecurveofMw,inst givesdramaticevidencethatMw fallsabruptly
to the predicted lower value, and remains constant. Histograms of the evolving
massdistributioncanbebuiltupateachpointinconversion,whichresembleGPC
chromatogram-based mass distributions. Two of these are shown in the insets to
Fig. 5. The first shows the unimodal, large Mw distribution prevailing just before
the booster initiator was added. The second inset, to the right, shows the bimodal
character of the population at 90% conversion, weighted heavily towards the small
masses that began to be produced after the initiator boost.
2.1.3 Free Radical Polymerization in a Continuous Reactor
It is advantageous in many industrial situations to produce polymers in a continuous
process. This allows a steady state of production to be reached, with a continuous
input of reactants and output of product. We recently adapted ACOMP to a common
type of continuous reactor, a homogeneous, continuously stirred tank reactor (34). In
this arrangement a solution of monomer/initiator was continuously fed at a flow rate
r (mL/s) to a reactor thermostatted to a desired temperature, from which reactor
liquid was continuously withdrawn at the same rate.
If a given monomer/initiator mix is fed into a reactor of volume V at flow
rate r, and fluid is pumped from the reactor at the same rate, then the steady-state
value of conversion reached is
fsteady state ¼ kp[R]
p þ kp[R]
and the number-average, steady-state degree of polymerization is
Nn,steady state ¼
pkp[m] s
kt[R]( p þ kp[R])
where p is the reciprocal of the average residence time, given by
(13)
(14)
p ¼ r=V (15)
and [m] s is the molar concentration of monomer in the reservoir that feeds the
reactor at rate p, [R] is the concentration of propagating free radical, and kp and kt
are the propagation and termination rate constants, respectively. The concentration
of monomer in the reactor reaches its steady-state value according to
p[m] s
[m](t) ¼ [m] r
p þ kp[R] exp{ (p þ kp[R])t}
p
þ
p þ kp[R] [m] s (16)
where [m] r is the concentration of monomer initially in the reactor.
© 2004 by Marcel Dekker, Inc.