A new interpretation of the kinetic model for the imidization reaction of PMDA-ODA and BPDA-PDA poly(amic acid)s - Polyimides and Other High Temperature Polymers - page 38

( peak area at 1380 cm

−

1

)

time = t

( peak area at 1500 cm

−

1

)

(2)

Degree of imidizatio n ( x )

time t

=

=

−

( peak area at 1380 cm

1

)

400 ℃

−

1

( peak area at 1500 cm )

400 ℃

2.3. Evaluation of the parameters of the Seo model
The Seo model was used to correlate the degree of imidization with time [21-22].
In Seo's approach [21], the rate constant was proposed as k(t) = b × sech(-at). In-
serting into a first-order rate equation, the relationship between the degree of
imidization and curing time is obtained as

2 b

− − at

− ln( 1 − x ) = − tan

1

e + constant

(3)

a

The constant in eq. (3) was obtained by fitting with the experimental data to the
original Seo model [21]. However, the constant in eq. (3) was found to be 0.785
by fitting our experimental data at the initial condition (t = 0, x = 0). Hence, the
kinetic equation was expressed as eq. (4).

2 b

− ln( 1 − x ) = − (tan

− 1

e

− at

− 0 785 ) (4)

a

The parameters a and b were expressed in the form of Arrhenius expressions in
this study, which are shown as eqs. (5) and (6).

a = A exp ( − E /RT)

(5)

a a

b A exp ( E /RT )

= −

(6)

b b

The constants A a , A b , E a , and E b were calculated from the Arrhenius plots of the
parameters a and b.

3. RESULTS AND DISCUSSION

Figure 2 shows the FTIR spectra for the PMDA-ODA poly(amic acid) when
cured at 165°C for various curing times of (a) 20 sec, (b) 4 min, (c) 110 min, and
(d) at 400°C for two hours. As the curing progresses, the intensities of the absorp-
tion peaks of polyimide increase while those of the poly(amic acid) and NMP sol-
vent decrease. Hence, it is observed in Figure 2 that the intensities of the peaks at
1680 cm -1 (carbonyl vibration of NMP solvent), 1640-1680 cm -1 (amide I of
poly(amic acid)), and 1550 cm -1 (amide II of poly(amic acid)) decrease with in-
creasing curing time. On the other hand, the peak intensities at 1780 cm -1 , 1720
cm -1 , 725 cm -1 and 1380 cm -1 representing carbonyl symmetric stretching, asym-
metric stretching, bending vibration, and C-N vibration of the imide group, re-
spectively, show an increasing trend with curing time.