J. ZHANG et al.: ISOTHERMAL IMIDATION KINETICS OF POLYMETHACRYLIMIDE BASED ON IN-SITU FTIR
865–871
ISOTHERMAL IMIDATION KINETICS OF
POLYMETHACRYLIMIDE BASED ON IN-SITU FTIR
IZOTERMALNA IMIDACIJSKA KINETIKA POLIMETAKRILIMIDA
NA OSNOVI IN SITU FTIR
Jing Zhang
1,2*
,XuMa
1
, Bao-Yu Huang
2
, Song Lv
2
, Yi-Fan Zhou
1
,
Jiao-Xia Zhang
1
1
School of Materials Science and Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China
2
Changzhou Sveck Photovoltaic New Material Co., Ltd, Changzhou 213200, China
Prejem rokopisa – received: 2019-03-31; sprejem za objavo – accepted for publication: 2019-07-12
doi:10.17222/mit.2019.070
The isothermal imidation process of polymethacrylimide (PMI) prepared from acrylonitrile (AN), methacrylic acid (MAA) and
alpha-methylstyrene (AMS) was investigated by "in-situ" Fourier transform infrared spectroscopy (FTIR) at different
temperatures, ranged between 180 °C and 200 °C. The bending vibration absorption peak of hydrogen on the benzene ring in
AMS at 700 cm
–1
was selected as the internal standard. The extent of the imidation was defined by the area ratio of the
characteristic absorption peak of the nitrile groups at 2243 cm
–1
to the internal standard. The plots of imidation extent versus
time were analyzed by the Friedman method and the Avrami equation. The activation energy at the imidation extent between 0
and 0.2 was 60.4 kJ/mol to 65.1 kJ/mol, which was ascribed to the reaction of the forming imide ring structures. The increase of
the activation energy from 65.1 kJ/mol to 92.3 kJ/mol at the imidation extent between 0.2 and 0.4 can be ascribed to the reaction
of forming polyimine cyclic structures. At the imidation extent higher than 0.4, the activation energy decreased from
92.3 kJ/mol to 52.1 kJ/mol and the frequency factor (lnA) fell from 20.5 s
–1
to 12.6 s
–1
. At this stage, the reaction was controlled
by diffusion. Moreover, the Avrami curves were in good agreement with the experimental data of the imidation, except for the
late stage. The decrease of the kinetic constant from 2.14×10
4
s
–1
to 0.92 s
–1
and activation energy from 54.05 kJ/mol to
20.39 kJ/mol further indicated that the imidation mechanism of the AN/MAA/AMS co-polymer system changed from
kinetically controlled at the prophase to diffusion controlled at the anaphase.
Keywords: polymethacrylimide, isothermal imidation kinetics, in-situ FTIR
Avtorji ~lanka so raziskovali izotermi~ni imidacijski proces polimetakrilimida (PMI), pripravljenega iz akrilonitrila (AN),
metakrilne kisline (MAA) in alfa-metilstirena (AMS) z in situ Fourierjevo transformacijsko infrarde~o spektroskopijo (FTIR) v
temperaturnem obmo~ju med 180 °C in 200 °C. Za interni standard so izbrali pregibni vibracijski absorpcijski vrh vodika na
benzenskem obro~u v AMS pri 700 cm
–1
. Obseg imidacije so definirali z razmerjem med presekom karakteristi~nih
absorpcijskih vrhov nitrilnih skupin pri 2243 cm
–1
in internim standardom. Grafi~ni prikaz obsega imidacije v odvisnosti od ~asa
so analizirali s Friedmanovo metodo oziroma Avramijevo ena~bo. Aktivacijska energija pri obsegu imidacije med 0 in 0,2 je bila
od 60,4 kJ/mol do 65,1 kJ/mol, kar so avtorji pripisali reakciji strukturne tvorbe imidnih obro~ev. Pove~anje aktivacijske
energije z 65,1 kJ/mol na 92,3 kJ/mol, pri obsegu imidacije med 0,2 in 0,4, so pripisali reakciji tvorbe cikli~ne poli-iminske
strukture. Pri obsegu imidacije nad 0,4 se je aktivacijska energija zmanj{ala z 92,3 kJ/mol na 52,1 kJ/mol in frekven~ni faktor
(lnA) je padel z 20,5 s
–1
na 12,6 s
–1
. V tem stadiju je reakcijo nadzorovala difuzija. Nadalje so se Avramijeve krivulje dobro
ujemale z eksperimentalnimi rezultati imidacije, razen v zadnjem stadiju. Zmanj{anje kineti~ne konstante z 2,14×10
4
s
–1
na
0,92 s
–1
in aktivacijske energije z 54,05 kJ/mol na 20,39 kJ/mol, je nato pokazalo, da se je imidacijski mehanizem
AN/MAA/AMS kopolimernega sistema spremenil iz kineti~no kontroliranega v profazi v difuzijsko kontroliranega v anafazi.
Klju~ne besede: polimetakrilimid, izotermi~na imidacijska kinetika, in situ FTIR
1 INTRODUCTION
PMI foam is a kind of high-performance thermo-
setting resin developed by Degussa, a German company,
in 1972. It is applied widely because of its superior per-
formance, such as 100 % closed cellular structure, high
thermal resistance, wide range of density control, and
excellent mechanical properties. Up to now, PMI foam
has developed over 165 specifications in sandwich
structures all over the world, including aerospace,
shipping, railcar manufacturing, and radome applica-
tions.
1,2
PMI foam was usually prepared by the heat treatment
of block copolymers of methacrylonitrile (MAN) or
acrylonitrile (AN) and methacrylic acid (MAA) in the
presence of crosslinking agents and foaming agents.
3,4
Great effort has been made to research the preparation
methods, properties, cellular structures and applications
of PMI.
15
However, there are few researches about the
imidation kinetics of PMI. In order to achieve satisfying
mechanical and thermal properties, it is necessary to
figure out the imidation mechanism of PMI clearly. In
our early work, the isothermal curing of PMI has been
studied through dynamic mechanical analysis (DMA).
6
Fourier transform infrared spectroscopy (FTIR) is a
conventional analysis technique employed to study the
imidation and curing process.
712
It has the advantages of
Materiali in tehnologije / Materials and technology 53 (2019) 6, 865–871 865
UDK 67.017:669.715-026.5 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 53(6)865(2019)
*Corresponding author's e-mail:
zhangjing@just.edu.cn (Jing Zhang)

a high signal-to-noise ratio, fast scanning speed and
simple operation. However, FTIR cannot evaluate the
imidation process of traditional PMI, because no
functional group could be taken as an internal standard.
In this paper, AMS was introduced as the third monomer
to prepare a new PMI. The benzene ring in AMS didnot
participate in the imidation reaction, so that the surface
bending vibration absorption peak of hydrogen on the
mono-substituted benzene ring at 700 cm
–1
could be
selected as the internal standard. Moreover, the Friedman
isoconversional method and Avrami equation were
employed to quantify the isothermal imidation kinetics
of the PMI.
2 EXPERIMENTAL PART
2.1 Materials
AN was supplied by Sinopec QiLu Petrochemical
Company (China). MAA was supplied by Sinopharm
Chemical Reagent Co. Ltd. (China), while AMS was
purchased from Shanghai Macklin Biochemical Co. Ltd.
(China). Azobisisobutyronitrile (AIBN), supplied by
Shanghai Macklin Biochemical Co. Ltd. (China), was
used as the initiator. Acrylamide (AM) supplied by
Sinopharm Chemical Reagent Co. Ltd. (China) was used
as the crosslinking agent.
2.2 Preparation of AN/MAA/AMS copolymer board
The preparation of the MAA/AN/AMS copolymer
board was carried out via bulk casting. Firstly, the
mixture of 210 g of AN, 155 g MAA, 40 g AMS, 1 g
AIBN, and 11 g AM was pre-polymerized in a three-
necked flask in a water bath at 70 °C for 100 min.
Secondly, the prepolymer with a certain viscosity was
poured into a vitreous mould, having dimension of 45.0
mm × 45.0 mm × 10.0 mm. Afterwards, the mould was
sunk into the water bath at 60 °C for 72 h. Finally, a
transparent and uniform board of AN/MAA/AMS
co-polymer was obtained. The samples for the FTIR test
were scraped as a fine powder, having the dimension of
200 mesh from the AN/MAA/AMS copolymer board.
2.3 Measurement
The FTIR measurement was performed with a
homogenized mixture of sample and potassium bromide.
The KBr spectrum was measured for automatic back-
ground subtraction to obtain the background contri-
bution. All the spectra were obtained with a resolution of
4cm
–1
in the wavenumber range from 4000 cm
–1
to 400
cm
–1
, averaging 32 scans, using the FTIR Nicolet iS10 of
Thermo Scientific (USA). The samples were placed
between two 32-mm-diameter KBr windows in a tem-
perature-controlled sample holder equipped with an
electrical heating jacket that allowed the in-situ FTIR
analysis. The FTIR spectra were taken at intervals of 5
min at 180 °C, 185 °C, 190 °C, 195 °C and 200 °C for
4h.
3 RESULTS AND DISCUSSION
3.1 FTIR spectroscopy data
Figure 1 shows the FTIR curves of the
AN/MAA/AMS co-polymer at 190 °C during the
imidation process. The peak at 700 cm
–1
is attributed to
the surface bending vibration of the hydrogen on the
mono-substituted benzene ring in AMS units. The
characteristic absorption peak assigned to nitrile groups
appeared at 2243 cm
–1
, which can be utilized to
quantitatively evaluate the imidation behavior of
AN/MAA/AMS co-polymer system.
The intensity of the band at 2243 cm
–1
decreases with
the imidation time significantly, which is ascribed to the
decrease of the number of nitrile groups. This is mainly
attributed to the reaction of the forming imide ring
structures between the adjacent monomeric units of AN
and MAA (Scheme 1).
5,13
Moreover, the reaction of the
forming polyimine cyclic structures (ladder polymer)
could also consume nitrile groups (Scheme 2).
5,13,14
However, the absorption peak of the nitrile groups does
not disappear entirely, which indicates that the iso-
thermal imidation of the AN/MAA/AMS copolymer
would not achieve a fully imidation system.
15,16
Scheme 1
Scheme 2
Furthermore, the absorption peak of the carbonyl
groups at 1694 cm
–1
splits and the second carbonyl group
absorption peak appears at 1630 cm
–1
, due to the reaction
of forming imide ring structures (Scheme 1).
13
Simult-
J. ZHANG et al.: ISOTHERMAL IMIDATION KINETICS OF POLYMETHACRYLIMIDE BASED ON IN-SITU FTIR
866 Materiali in tehnologije / Materials and technology 53 (2019) 6, 865–871

aneously, a new band at 2337 cm
–1
is observed, which
could be related to the amination reaction of the PAN
block that -NH
2
was grafted onto the PAN (H
2
Ow a s
generated from dehydration reaction of adjacent AM).
The reaction equation is given in Scheme 3.
13,17
Scheme 3
The extent of the imidation,  , is determined quanti-
tatively according to Equation (1):
 =−
=
1
0
(/* )
(/* )
SS
SS
t
t
(1)
where S represents the area of characteristic absorption
peak of the nitrile group at 2243 cm
–1
and S
*
represents
the area of the out-of-plane bending vibration peak of
hydrogen on a monosubstituted benzene ring at 700
cm
–1
. The subscript t denotes the time of the imidation
reaction, whilet=0 means the ratio of the the area at
initial time. Figure 2 shows the extent of the imidation
( ) versus time (t) curves for the imidation reaction at
different temperatures. The conversion achieved 59.30
% to 61.03 % in 4 h. Figure 3 shows the rate of
imidation (d /dt) as a function of the extent of imidation
( ) of the AN/MAA/AMS copolymer at different
temperatures. The reaction rate was obtained by
differentiating the – t curves. Obviously, there is only
one peak on the curves at 180 °C to 195 °C. The maxi-
mum rate of imidation occurs at a certain intermediate
extent between 0.1 and 0.2. Then the reaction rate
undergoes a decrease with the increase of extent when is higher than 0.2 and approaches zero at the end.
Interestingly, there are two peaks on the curve at
200 °C. The difference indicates that the imidation
mechanism of the AN/MAA/AMS copolymer system
changes at temperatures over 200 °C. The second peak
can be ascribed to the reaction of forming a ladder
polymer between the adjacent AN monomeric unit
(Scheme 2).
3.1 Model-free study
The isothermal imidation kinetics of the
AN/MAA/AMS copolymer system is described by a
J. ZHANG et al.: ISOTHERMAL IMIDATION KINETICS OF POLYMETHACRYLIMIDE BASED ON IN-SITU FTIR
Materiali in tehnologije / Materials and technology 53 (2019) 6, 865–871 867
Figure 3: The rate of imidation (d /dt) as a function of extent of
imidation ( ) of the AN/MAA/AMS copolymer at different tempera-
tures
Figure 1: FTIR spectra in the 4000 cm
–1
to 400 cm
–1
wavenumber
range of AN/MAA/AMS copolymer at 190 °C during the imidation
process
Figure 2: The extent of imidation ( ) as a function of time (t)ofAN/
MAA/AMS copolymer at different temperatures

general rate equation as a function of temperature and
conversion of the imidation, as follows in Equation (2):
dd atk Tf / ()() =  (2)
where f( ) is the kinetic model in accord with the
reaction mechanism, and k is the reaction rate constant
as a function of temperature T (absolute scale) due to
the Arrhenius equation, in Equation (3):
kT A
E
RT
() e x p =−
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ a
(3)
where A is the pre-exponential factor (also known as
frequency factor, reflecting the number of collisions
between functional groups), E
a
the activation energy of
the imidation reaction and R is the universal gas
constant (8.314 J/mol·K). Substituting Equation (3) into
the Equation (2) can yield a new expression as:
dd
a
atA
E
RT
f /e x p( ) =−
⎛ ⎝ ⎜ ⎞ ⎠ ⎟  (4)
Then, applying logarithmic properties to two sides of
Equation (4), the classical form of the Friedman equation
about E
a
and can be obtained, as:
18
[] ln ln ( )
d
d
a
a
t
Af
E
RT
⎛ ⎝ ⎜ ⎞ ⎠ ⎟=−  (5)
with the assumption that both the activation energy and
the pre-exponential factor are the functions of the
imidation extent, the significance of the Friedman
isoconversional method is that no knowledge of the
reaction model and the kinetic rate expression are
assumed for the data evaluation.
19
It is a typical way to
describe variations in the curing or imidation kinetics of
many thermosetting systems. The activation energy is
determined from the slope of the plot of ln(d /dt) versus
1/T when  takes a constant value. For the n
th
-order
reaction, the value of lnA can be obtained from the
known values of ln (d /dt) and E
a
/RT from Equation
(6).
19–21
[] ln ( ) ln ln ln ( ) Af
a
t
E
RT
An f  =
⎛ ⎝ ⎜ ⎞ ⎠ ⎟+=+
d
d
a
(6)
Figure 4 exhibits the Friedman plots of the iso-
thermal imidation process in the  range between 0.1
and 0.5 by Equation (5). The difference of  value is
0.05. Figure 5 shows the variation of the activation
energy and the pre-exponential factor obtained by the
Friedman method at various extent of imidation. For the
AN/MAA/AMS copolymer system, the imidation
process underwent a rearrangement of the molecular
segments, and then the imide ring structure generated
between the adjacent acid and the nitrile units (Scheme
1). It has been reported that the cyclization reaction takes
place at a temperature of about 150 °C.
5
The value of E
a
increases from 60.4 kJ/mol to 65.1 kJ/mol slowly at the
extent lower than 0.2 is a vivid evidence. At a higher
extent of imidation ( range between 0.2 and 0.4), the
activation energy increased from 65.1 kJ/mol to
92.3 kJ/mol. Due to the carboxyl groups adjacent to the
nitrile groups have been exhausted, the intermolecular
cross-linking of the AN can form a ladder polymer
(Scheme 2). The AN monomeric units in copolymer
system form ladder polymer structures at high
temperatures over 200 °C.
5
As for the stage that  is
higher than 0.4, it is noteworthy that the frequency factor
decreased quite steeply (Figure 5) The mobility of the
unreacted nitrile groups is hindered due to the significant
increase of the imidation extent and the crosslinking
degree. Moreover, the steric hindrance of the benzene
ring in the third monomer AMS restricts the motion of
the PMI chain segments. The imidation in the late stage
is difficult to take place, and the reaction is controlled by
diffusion rather than chemical factors.
J. ZHANG et al.: ISOTHERMAL IMIDATION KINETICS OF POLYMETHACRYLIMIDE BASED ON IN-SITU FTIR
868 Materiali in tehnologije / Materials and technology 53 (2019) 6, 865–871
Figure 5: Plots of activation energy (E
a
) and frequency factor (lnA)of
AN/MAA/AMS copolymer system against the extent of imidation ( )
obtained by Friedman method
Figure 4: Friedman plots of isothermal imidation process of
AN/MAA/AMS copolymer system in the interval 0.1 =  = 0.5 (the
difference of value is 0.05)

3.2 Model-fitting study
The Avrami equation is an alternative approach to
evaluate the activation energy of the imidation reaction
of the AN/MAA/AMS copolymer system, which has
been applied to analyze the curing of PMI in our pre-
vious work.
6
The classical form of the Avrami equation
can be expressed as Equation (7):
22
[] 1
0
−= −  exp kt
n
(7)
where k
0
is the kinetic constant related with the tem-
perature and n is the Avrami exponent reflecting the
growth mechanism. Applying logarithmic properties to
both sides of Equation (7), the following Equation (8)
can be obtained.
[] ln ln( ln ln −−=+ 1
0
 knt (8)
The kinetic parameters can be calculated from the
curves by using the modified Avrami equation. Figure 6
shows the ln[–ln(1 – )] versus lnt curves of AN/MAA/
AMS co-polymer system at different temperatures
obtained by Equation (8). According to the difference of
slope, each curve in Figure 6 can be divided into two
segments. Therefore, the linear fitting should be carried
out for each segment independently. The kinetic para-
meters obtained by the Avrami equation are listed in
Table 1. The difference of the Avrami exponent values at
different temperatures indicates that the reaction
mechanism changes during the imidation process.
Table 1: Fitting results to the Avrami exponent (n) and kinetic
constant (k
0
) of AN/MAA/AMS copolymer system at different tem-
peratures
T/°C 180 185 190 195 200
n1
0.616 0.511 0.340 0.494 0.743
k0,1
0.078 0.138 0.268 0.155 0.078
n2
0.275 0.192 0.122 0.160 0.191
k0,2
0.222 0.352 0.518 0.425 0.368
Note: the subscripts 1 and 2 denote segments 1 and 2 in Figure 6
The curves derived by Equation (6) are compared
with the experimentally measured data in Figure 7.
Obviously, the modelled curves are in good agreement
with the experimental data. While the final degree of
fitting shows a poor prediction between 57 % and 60 %
conversion. It has been reported that the experimental
extent of the imidation was lower than the value
calculated by the kinetic model when the reaction
became diffusion controlled for a higher extent.
23
As
shown in Figure 7, it became evident that the consi-
deration of the diffusion control in the Avrami model
allowed an improved curve description at the latter stage
of the imidation.
The correlation between the kinetic constant (k
0
) and
temperature (T) can be shown as the following empirical
Equation (9):
24
kA
E
RT
n
0
1/
exp =−
⎛ ⎝ ⎜ ⎞ ⎠ ⎟ a
(9)
Applying the logarithmic properties to both sides of
Equation (9), the modified Equation (10) can be ob-
tained, from which the value of E
a
and k can be calcul-
ated from the slope and intercept of the fitting curve,
respectively:
1
0
n
kk
E
RT
ln ln =−
a
(10)
Figure 8 shows the (1/n)lnk
0
versus 1/T relationship
for the linear segments of the ln[–ln(1 – )]–ln t curves.
The kinetic constant (k) and activation energy (E
a
)
calculated by Equation (10) are listed in Table 2.Inthe
temperature range 180 °C to 200 °C, the value of the
kinetic constant decreased from 2.14×10
4
s
–1
to 0.92 s
–1
.
The four magnitude orders difference indicated that the
imidation of AN/MAA/AMS copolymer system was
dominated by a kinetic-controlled reaction in the early
stage. While the difusion control became operative with
the reaction process and the E
a
value decreased from
J. ZHANG et al.: ISOTHERMAL IMIDATION KINETICS OF POLYMETHACRYLIMIDE BASED ON IN-SITU FTIR
Materiali in tehnologije / Materials and technology 53 (2019) 6, 865–871 869
Figure 7: Fitting results of isothermal conversion curves of PMI cal-
culated through the Avrami equation
Figure 6: The ln[-ln(1- )] versus lnt curves of AN/MAA/AMS
copolymer system at different temperatures

54.05 kJ/mol to 20.39 kJ/mol. This result is consistent
with the conclusion from the Friedman method. The
results are in agreement with a previous study that the
activation energy of the thermosetting system would
decrease after becoming diffusion controlled.
25,26
Table 2: Activation energy of the evolution of  during the imidation
process of PMI by Avrami equation
T/°C k
1
/s
–1
E
1
/(kJ·mol
–1
)
k
2
/s
–1
E
2
/(kJ·mol
–1
)
180~200 2.14×10
4
54.05 0.92 20.39
Note: the subscripts 1 and 2 denote segments 1 and 2 in Figure 6
4 CONCLUSIONS
The isothermal imidation process of the AN/MAA/
AMS co-polymer system was investigated by in-situ
FTIR at 180 °C, 185 °C, 190 °C, 195 °C and 200 °C. The
bending vibration absorption peak of hydrogen on the
mono-substituted benzene ring was selected as the
internal standard. The extent of the imidation was
defined by the area ratio of the characteristic absorption
peak of the nitrile groups to the internal standard. At the
imidation extent between 0 and 0.2, the activation energy
was 60.4 kJ/mol to 65.1 kJ/mol, which was ascribed to
the reaction of forming imide ring structures between
adjacent AM and MAA. The increase of the activation
energy from 65.1 kJ/mol to 92.3 kJ/mol at the imidation
extent between 0.2 and 0.4 could be ascribed to the
reaction of polyimine cyclic structures between adjacent
AN. At the imidation extent higher than 0.4, the
activation energy and the frequency factor decreased
steeply, and the reaction rate approached zero. At this
stage, the imidation of the AN/MAA/AMS co-polymer
was controlled by diffusion. Moreover, the predicted
curves from the Avrani models fitted well with the
experimental data, except for the late stage of the
reaction. The decrease of the kinetic constant from
2.14×10
4
s
–1
to 0.92 s
–1
and activation energy from
54.05 kJ/mol to 20.39 kJ/mol further indicated that the
imidation of the AN/MAA/AMS copolymer system was
dominated by a kinetic-controlled reaction in the early
stage, and the diffusion control became operative in the
later stage.
Acknowledgement
This work was supported by the National Natural
Science Foundation of China (Grant No. 51603094), and
the Natural Science Foundation of Jiangsu Province
(Grant No. BK20160562).
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