Chemistry Reference
In-Depth Information
d½
dt
5
M
M
k
dp
M
R
p
52
k
p
M
½
½
2
½
(8-122)
Since the net rate of polymer production at
T
c
52
d
[M]
/dt
0, then under
5
these conditions
k
p
=k
dp
5
K
5
1
=½M
(8-123)
where
K
is the equilibrium constant.
Analysis of polymerization
depolymerization equilibria makes use of the
reaction isotherm
G
p
1
Δ
G
p
5
Δ
RT
ln
K
(8-124)
G
0
is the Gibbs free-energy change for the polymerization with the
monomer and polymer in appropriate standard states
[23]
. Further, since
Δ
where
G
p
5
Δ
H
p
2
S
p
Δ
T
Δ
(8-125)
and since
ΔG
5
0at
T
5
T
c
, then
H
p
Δ
T
c
5
(8-126)
Δ
S
p
1
R
ln
½
M
e
where [M]
e
is the equilibrium monomer concentration.
It is obvious from the last equation that
T
c
will depend on the monomer con-
centration in the system. Usually [M]
e
is taken as unit concentration and
T
c
, the
ceiling temperature
, is then that temperature above which it is not possible to
form high polymer from unit or lower concentration. In other words, if polymeri-
zation were to be started at
T
c
it would proceed until [M] fell to the value of
[M]
e
. Conversely, if high polymer that is made at some lower temperature is
warmed to
T
c
, depolymerization will ensue until concentration [M]
e
of monomer
is established.
Note in this connection that these last predictions refer to thermodynamic
equilibria and give no information as to how quickly the equilibrium monomer
concentrations will be attained. Macromolecules may in fact be quite useful above
their ceiling temperatures if depolymerization processes are kinetically hindered.
T
c
for poly(formaldehyde) is 126
C, for example, but the polymer can be made
stable enough for melt processing at temperatures above 200
C. This is accom-
plished by esterifying or etherifying the thermolabile hydroxyl ends of the macro-
molecule, copolymerizing with small concentrations of ethylene oxide, and
using basic additives as stabilizers. These expedients all retard the initiation or
propagation steps of chain reactions that could cause the polymer to “unzip” to
monomer.
The equations developed for
T
c
contain no reference to the mode of polymeri-
zation. Although they are presented here in a chapter devoted to radical polymeri-
zation, they are characteristic of the polymer and not of its method of synthesis.
