Chemical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 194

The radicals produced in steps 4.43 and 4.45 can be consumed by termination:

k

(4.47)

t
⋅+ ⋅→

MM M 2.

The rate of the termination step is:

2
[].

(4.48)

r = 2 k

t M

⋅

t

Under the steady-state conditions, the rates of initiation and termination are equal
that allows the concentration of radicals to be expressed as:

1
2

1
2

⋅=

k
k

(4.49)

i

[ MM ] [ MM ] .

2

t

The substitution of Eq. 4.49 into Eq. 4.44 gives the overall rate of depolymerization:

1
2

1
2

1
2

r k k
k

(4.50)

i

= [ MM ] = k [ MM ] .

dp dp ef

2

t

Equation 4.50 can now be used to derive the effective activation energy of polymer
degradation in the usual manner:

ER k
T

d
d

ln

=−

=+−

ef

EEE ( ) /. 2

(4.51)

ef dp i t

− 1

The significance of Eq. 4.51 is that it demonstrates that even when the thermal
degradation of a polymer occurs by simple depolymerization, the activation energy
of the process is a complex value that involves a combination of the activation ener-
gies for depropagation ( E dp ), initiation ( E i ), and termination ( E t ).
The mechanism of thermo-oxidative degradation involves the same initiation
step as thermal degradation (4.45). The macroradical propagates by forming perox-
ide, which abstracts a proton from the polymer yielding hydroperoxide and a new
macroradical:

MM O ⋅+ →⋅

2

MMO

(4.52) 2

MMO MMH MMOOH MM

2 ⋅+

→ + ⋅ . (4.53)

Termination of the radical species occurs by recombination to inert products, P:

2 MM or MMO or MM MMO ⋅ 2 ⋅ ⋅+ 2 ⋅→ . P

(4.54)

2 2