Investigation of synthesis, thermal properties and curing kinetics of fluorene diamine-based benzoxazine by using two curing kinetic methods

Article abstract of DOI:10.1016/j.tca.2013.04.024

A novel diamine-based benzoxazine monomer containing aryl ether and bulky fluorene groups (BEF-p) was prepared from the reaction of 9,9-bis-[4-(p- aminophenoxy)-phenyl]fluorene with paraformaldehyde and phenol. The chemical structure of monomer was confirmed by Fourier-transform infrared (FTIR) and ¹H and ¹³C nuclear magnetic resonance spectroscopy ( ¹H and ¹³C NMR). The polymerization behavior of monomer was analyzed by differential scanning calorimetry (DSC) and FTIR. The curing kinetics was studied by non-isothermal DSC, and the kinetic parameters were determined. The autocatalytic model based on two kinetic methods (Starink-LSR method and direct LSR method) showed good agreement with experimental results. The thermal and mechanical properties of poly(BEF-p) were evaluated with DSC, dynamic mechanical thermal analysis (DMTA), and thermogravimetric analysis (TGA). The results showed that the cured polymer exhibited higher glass transition temperature (T_g) and better thermal stability compared with diaminodiphenylmethane-based benzoxazine(P-ddm), and was slightly lower than those of fluorene diamine-phenol-based polybenzoxazine (poly(BF-p)). Copyright

Full text of DOI:10.1016/j.tca.2013.04.024

Thermochimica Acta 564 (2013) 51–58
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Thermochimica Acta
journal homepage: www.elsevier.com/locate/tca
Investigation of synthesis, thermal properties and curing kinetics of fluorene
diamine-based benzoxazine by using two curing kinetic methods
Xuan-yu Hea, Jun Wanga, Noureddine Ramdania, Wen-bin Liua,∗, Li-jia Liua, Lei Yangb
a Polymer Materials Research Center, College of Materials Science and Chemical Engineering, Harbin Engineering University, Harbin 150001, China
b Key Laboratory of Forest Plant Ecology, Ministry of Education, Northeast Forestry University, Harbin 150040, China
a r t i c l e i n f o
a b s t r a c t
Article history:
A novel diamine-based benzoxazine monomer containing aryl ether and bulky fluorene groups (BEF-p)
was prepared from the reaction of 9,9-bis-[4-(p-aminophenoxy)-phenyl]fluorene with paraformalde-
hyde and phenol. The chemical structure of monomer was confirmed by Fourier-transform infrared (FTIR)
and 1H and 13C nuclear magnetic resonance spectroscopy (1H and 13C NMR). The polymerization behavior
of monomer was analyzed by differential scanning calorimetry (DSC) and FTIR. The curing kinetics was
studied by non-isothermal DSC, and the kinetic parameters were determined. The autocatalytic model
based on two kinetic methods (Starink-LSR method and direct LSR method) showed good agreement
with experimental results. The thermal and mechanical properties of poly(BEF-p) were evaluated with
DSC, dynamic mechanical thermal analysis (DMTA), and thermogravimetric analysis (TGA). The results
showed that the cured polymer exhibited higher glass transition temperature (Tg) and better thermal
stability compared with diaminodiphenylmethane-based benzoxazine(P-ddm), and was slightly lower
than those of fluorene diamine-phenol-based polybenzoxazine (poly(BF-p)).
Received 7 December 2012
Received in revised form 10 April 2013
Accepted 20 April 2013
Available online 3 May 2013
Keywords:
Fluorene diamine-based benzoxazine
Polymerization behavior
Curing kinetics
Thermal properties
© 2013 Elsevier B.V. All rights reserved.
1. Introduction
Lin and coworkers successfully synthesized a series of aromatic
diamine-based benzoxazines by the three-step, two-pot, or one-
Polybenzoxazines, as a class of thermosetting phenolic resins
formed by the cationic ring-opening of the corresponding benzox-
azine monomers without any added initiator, have demonstrated
various attractive properties such as high thermal stability, high
char yields, high glass transition temperature (Tg), near-zero
volumetric change upon curing, good mechanical and dielec-
tric properties, low water absorption, and low flammability.
These unique characteristics make the polybenzoxazines a better
candidate over epoxies and traditional phenolic resins in the
electronics, aerospace, and other industries [1–5]. According to
the related researches, most difunctional benzoxazines were syn-
thesized from bisphenols, monoamines, and formaldehyde. The
large varieties of aromatic bisphenols and monoamines allow for
considerable molecule-design flexibility of benzoxazines [6–12].
Another series of important difunctional benzoxazines were the
pot procedure [15–17]. Agag and Ishida et al. reported a new route
for high yield synthesis of aromatic diamine-based benzoxazines
using the one-step procedure, in which xylenes as a nonpolar,
high-boiling-point solvent, was used at 150 ◦C [18]. Therefore,
various difficult aromatic diamine-based benzoxazines can be
prepared by different synthesis method [19–24]. Furthermore, the
aromatic diamine-based polybenzoxazine can provide higher glass
transition temperature and thermal stability than the conventional
bisphenol-A-based polybenzoxazine [25].
Fluorene molecular contains two benzene rings linked with a
five-membered ring which can provide high overlaps of ␲-orbitals
[26]. Incorporation of bulky pendant groups can impart a significant
increase in both Tg and thermo-oxidative stability by restricting
segmental mobility. Therefore, the development of these polymers
has attracted extensive research interests during the past few
years [27–33]. Recently, researches on synthesis, polymerization
behavior, curing kinetics, and thermal properties of fluorene-based
benzoxazines have been reported. Liu et al. prepared a series of
fluorene-containing benzoxazines from the reaction of 9,9-bis-(4-
hydroxyphenyl)-fluorene, aromatic and aliphatic primary amines,
and formaldehyde [34]. Liu et al. also reported the preparation
of a furan-terminated and fluorene-containing benzoxazine, and
studied their properties [35]. Y.B. Lu et al. subsequently studied
the curing kinetics of fluorene-based benzoxazines [36]. Xu et al.
proved that hydrophobic characteristics of the fluorenyl-based
diamine-based benzoxazines. Allen and Ishida synthesized
a
series of aliphatic diamine-based benzoxazine monomers using
monofunctional phenol with linear aliphatic diamines [13,14]. The
polymerization behavior and curing kinetics of these monomers
and thermal properties of their polymers were also discussed.
∗
Corresponding author. Tel.: +86 451 82589540; fax: +86 451 82589540.
E-mail address: wjlwb@163.com (W.-b. Liu).
0040-6031/$ – see front matter © 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.tca.2013.04.024

52
X.-y. He et al. / Thermochimica Acta 564 (2013) 51–58
polybenzoxazines are due to the low polarity of fluorenyl and
␲–␲ stacking interaction of fluorenyl on the surface [37]. Lin et al.
reported the synthetic route of a benzoxazine based on 9,9-bis(4-
aminophenyl) fluorene, 2-hydroxybenzaldehyde/phenol, and
formaldehyde/paraformaldehyde by using two-pot and one-pot
procedures, and studied the optical and thermal properties of the
monomer and polybenzoxazines [38]. In our previous work, we
also prepared a series of fluorene diamine-based benzoxazine
monomers via the reaction of 9,9-bis-(4-aminophenyl)-fluorene
with paraformaldehyde and unsubstituted or substituted phenols
[39]. The polymerization behavior, regioselectivity, and thermal
properties of monomers and cured polymers were discussed.
However, their further applications were limited considerably
due to brittleness of the formed polymers despite the advanta-
geous properties of fluorene-based benzoxazines. The studies on
performance enhancement of polybenzoxazine mainly include
blending or alloying with other polymers and design of novel
monomers with special properties. Some thermosetting resins
such as polyimide, epoxy, cyanate ester and polyurethane resins
have been blended with benzoxazine resins to improve the tough-
ness of benzoxazine resins [40–43]. Another strategy is to prepare
polybenzoxazines derived from bisphenol and linear aliphatic
amine or phenol and linear aliphatic diamine which achieve high
mechanical performance by incorporating a flexible chain into
the polybenzoxazine matrix. However, the thermal properties of
linear aliphatic amine-based polybenzoxazines generally exhibit
low Tg and poor thermal stability, and decrease with the length
of the aliphatic chains [13,14,44–46]. Introduction of flexible aryl
ether linkages in the backbone is known to toughen polymers
without significant reduction in thermal stability [47–51].
Curing process of benzoxazine resin is very complicated, which
includes gelation, vitrification, subsequent crosslinking, and origi-
nation of three-dimensional networks. Therefore, the fundamental
investigation of benzoxazine curing reaction kinetic is an attrac-
tive topic for a better understanding of the curing behavior as well
as for the control and optimization of production processes and
performance of final products [52]. DSC is based on a phenomeno-
logical method, in which kinetic analysis only need to calculate
the heat variation for a whole reaction process with temperature
or time, without distinguishing the individual reaction in the pro-
cess. So DSC is the most utilized technique to determine kinetic
parameters and rate equation of polymerization of benzoxazine
[36,52–58].
2.2. Monomer synthesis
Scheme illustrates the synthesis of 9,9-bis-[4-(p-nitro-
phenoxy)phenyl]fluorene (BNOFL), 9,9-bis-[4-(p-aminophenoxy)
phenyl]fluorene (BAOFL) and BAOFL-based benzoxazine (BEF-p).
1
2.2.1. 9,9-bis-[4-(p-Nitrophenoxy)phenyl]fluorene (BNOFL)
A
mixture of 9,9-bis-(4-hydroxyphenyl)fluorene (8.76 g,
0.025 mol), p-chloronitrobenzene (8.67 g, 0.055 mol),
anhydrous potassium carbonate (7.95 g, 0.055 mol) and N,N-
dimethylformamide (DMF, 80 mL) was refluxed for 8 h. The
mixture was then cooled and poured into 400 mL of 1:1 ethanol-
water. The precipitated powder were isolated by filtration and
washed thoroughly with water. The product was dried under
vacuum at 80 ◦C for 24 h. A yellow powder (94% yield, m.p.
333–335 ◦C) was obtained. FTIR (KBr, cm−1): 1583 (NO2 asymmet-
ric stretching), 1338 (NO2 symmetric stretching), 1249 (C
O C
asymmetric stretching), 846, 750 (C H out-of-plane bending).
1H NMR (500 MHz, CDCl3, ppm): 6.95–8.19 (m, 24H, Ar H). 13C
NMR (500 MHz, CDCl3, ppm): 117.22–163.11 (36C, the carbons of
benzene ring), 64.53 (1C, quaternary carbon in the fluorene ring).
2.2.2. 9,9-bis-[4-(p-Aminophenoxy)phenyl]fluorene (BAOFL)
Hydrazine monohydrate (60 mL) was added dropwise over a
period of 1 h at 85 ◦C to a mixture of BNOFL (10.5 g, 0.018 mol),
ethanol (150 mL), and a catalytic amount of Pd–C (0.2 g). After the
addition was complete, the reaction was continued at reflux tem-
perature for another 24 h, and the mixture was filtered to remove
Pd–C. After cooling, white-needle crystals were isolated by fil-
tration and washed thoroughly with ethanol. The yield was 81%;
m.p. 177–178 ◦C. FTIR (KBr, cm−1): 3477, 3366 (N–H stretching),
1234 (C
O C asymmetric stretching), 873, 748 (C H out-of-plane
bending). 1H NMR (500 MHz, CDCl3, ppm): 6.62–7.74 (m, 24H,
Ar H), 3.55 (s, 4H, Ar NH2). 13C NMR (500 MHz, CDCl3, ppm):
116.21–157.69 (36C, the carbons of benzene ring), 64.28 (1C, qua-
ternary carbon in the fluorene ring).
2.2.3. BAOFL-based benzoxazine (BEF-p)
BAOFL (10.6 g, 0.02 mol), phenol (3.8 g, 0.04 mol), paraformalde-
hyde (3.6 g, 0.12 mol) and 50 mL mixed isomer xylenes were added
to a 150 mL three neck round-bottomed flask equipped with a mag-
netic stirrer, reflux condenser, and thermometer. The mixture was
stirred at 150 ◦C for 6 h. After that, the reaction mixture was cooled
to room temperature and then poured into hexane. The precip-
itated yellowish powder were isolated by filtration and washed
thoroughly with ethanol and dried under vacuum. The product
was dissolved in dimethylformamide (DMF), precipitated in 1 N
aqueous solution of sodium hydroxide to remove any phenolic
compounds, washed several times with water and finally with
ethanol. The product was dried under vacuum at 60 ◦C for 24 h.
Light yellow powder (82% yield) was provided. FTIR (KBr, cm−1):
In a continuation study on fluorene-based benzoxazine, the
present work describes a successful preparation of diamine-based
benzoxazine monomer without much sacrifice of thermal prop-
erties by incorporating aryl ether and bulky fluorene groups into
the polymer backbone. Chemical structures of monomer were con-
firmed by FTIR, 1H and 13C NMR. The polymerization behavior and
thermal properties of monomer and their cured polymer were dis-
cussed. Non-isothermal DSC was used to investigate the curing
kinetics of BEF-p. Autocatalytic model, Starink method and the least
square regression (LSR) method have been applied to calculate the
kinetic parameters for cure reaction of BEF-p.
1370 (CH2 wagging), 1224 (C
O
C asymmetric stretching), 1139
C symmetric stretch-
(C C asymmetric stretching), 1067 (C
N
O
ing), 950 (C H out-of-plane bending), 823, 747 (C H out-of-plane
bending). 1H NMR (500 MHz, CDCl3, ppm): 6.62–7.74 (m, 32H,
Ar H), 5.30 (s, 4H, O CH2 N), 4.58 (s, 4H, Ar CH2 N). 13C NMR
(500 MHz, CDCl3, ppm): 116.93–156.79 (48C, the carbons of ben-
zene ring), 80.16 (2C, O CH2 N), 64.35 (1C, quaternary carbon in
the fluorene ring), 50.93 (2C, N CH2 Ar).
2. Experimental
2.1. Materials
9,9-bis-(4-Hydroxyphenyl)fluorene was synthesized according
to literature [59]. p-Chloronitrobenzene, anhydrous potassium car-
bonate, hydrazine monohydrate, phenol and paraformaldehyde
were obtained from Shanghai Jingchun Reagent Co., Ltd. (China).
10% palladium on activated carbon (Pd–C) was purchased from
National Pharmaceutical Chemical Co., Ltd. (China). All solvents
were purchased from Tianjin Kermel Chemical Reagent Co., Ltd.
(China), and used without further purification.
2.3. Curing of benzoxazine monomers
BEF-p was polymerized without initiator or catalyst according
to the followings schedule: 180 ◦C/2 h, 200 ◦C/2 h, 220 ◦C/2 h and
240 ◦C/2 h in the air-circulating oven.

X.-y. He et al. / Thermochimica Acta 564 (2013) 51–58
53
Scheme 1. The synthesis route of diamine-based benzoxazine monomer containing aryl ether and bulky fluorene groups (BEF-p).
2.4. Characterization
atmosphere at a flow rate of 50 mL/min. The dynamic mechanical
thermal properties of the obtained polybenzoxazines were carried
out with a TA Q800 dynamic mechanical analyzer. The rectangular
samples (20 mm × 5 mm × 2 mm) were loaded in single cantilever
mode at a temperature ramp of 3 ◦C/min from 30 to 300 ◦C with a
frenquency of 1 Hz under air atmosphere.
Fourier transform infrared (FTIR) spectra were recorded on
a
Perkin-Elmer Spectrum 100 spectrometer in the range of
4000–650 cm−1, which was equipped with a deuterated triglycine
sulfate (DTGS) detector and KBr optics. Transmission spectra were
obtained at a resolution of 4 cm−1 after averaging two scans by
casting a thin film on a KBr plate for monomers and cured sam-
ples. 1H and 13C NMR characterizations were performed on a
Bruker AVANCE-500 NMR spectrometer using deuterated chloro-
form (CDCl3) as the solvent and tetramethylsilane (TMS) as an
internal standard. The average number of transients for 1H and
13C NMR is 32 and 1028, respectively. A relaxation delay time of
1s was used for the integrated intensity determination of 1H NMR
spectra. DSC measurements were evaluated on a TA Q200 differ-
ential scanning calorimeter under a constant flow of a nitrogen
atmosphere of 50 mL/min. The instrument was calibrated with a
high-purity indium standard, and ␣-Al2O3 was used as the refer-
ence material. About 5 mg of sample was weighed into a hermetic
aluminum sample pan at 25 ◦C, which was then sealed, and the sam-
ples were scanned by the non-isothermal method from 20 to 350 ◦C
using 5, 10, 15 and 20 ◦C/min heating rate under nitrogen. Thermo-
gravimetric analysis (TGA) was performed on TA Instruments Q50
at a heating rate of 20 ◦C/min from 30 to 800 ◦C under nitrogen
3. Results and discussion
3.1. Synthesis and structure of the benzoxazine monomers
The diamine 9,9-bis-[4-(p-aminophenoxy)phenyl]fluorene
(BAOFL) was synthesized in two steps from 9,9-bis-(4-
hydroxyphenyl)fluorene [47]. The dinitro compound BNOFL
was prepared by nucleophilic substitution reaction from 9,9-
bis-(4-hydroxyphenyl)fluorene with p-chloronitrobenzene in the
presence of anhydrous potassium carbonate. The catalytic hydro-
genation of BNOFL to the diamine BAOFL was accomplished by
means of hydrazine monohydrate as well as a catalytic amount of
Pd–C. The IR spectrum of BNOFL showed characteristic absorptions
for nitro groups at 1583 and 1338 cm−1. After hydrogenation, the
characteristic absorptions of BNOFL disappeared. New absorptions
at 3477 and 3366 (N H stretching) appeared. Moreover, the
structure of BAOFL was further identified by NMR spectroscopy
Fig. 1. 1H NMR (A) and 13C NMR (B) spectra of BNOFL, BAOFL and BEF-p.

54
X.-y. He et al. / Thermochimica Acta 564 (2013) 51–58
Fig. 2. FT-IR spectra of BEF-p at each cure stage.
Fig. 3. DSC thermograms of BEF-p at each cure stage.
as shown in Fig. 1. These results clearly confirm that the diamine
prepared herein is the proposed structure.
the very strong band assigned to the symmetric stretching modes of
C
N
C around 915 cm−1 appears. These suggest that the crosslink-
The synthesis of BEF-p was accomplished using the one-step
procedure [18]. The formation of oligomers as a result of the poly-
merization of formed benzoxazine was minimal. This ensures that
the benzoxazine monomer synthesized has a high purity, which is
recommended to facilitate the studies of polymerization behavior
and curing kinetics. The 1H and 13C NMR spectra were also recorded
to confirm the structure (Fig. 1). In 1H NMR spectrum (Fig. 1(A)),
the aromatic protons are observed at 6.62–7.74 ppm. The chemical
shifts at 5.30 and 4.58 ppm are attributed to methylene (O CH2 N)
and methylene (Ar CH2 C) of oxazine ring, respectively. In 13C
NMR spectrum (Fig. 1(B)), the resonances at 116.93–156.79 ppm
are assigned to the aromatic carbon atoms. The chemical shifts at
50.93 and 80.16 ppm are ascribed to the carbon atom resonances of
ing reaction further performs and the crosslink density of polyben-
zoxazine increases by the ring-opening polymerization at elevated
temperature. The absorptions at 1584 and 1455 cm−1 assigned
to the ortho-disubstituted benzene ring of benzoxazine monomer
shift to around 1475 cm−1 due to the formation of tetrasubstituted
benzene ring after thermal curing [13,19]. This result indicates that
the crosslinking reaction for BEF-p might also occur at para position
on the phenol besides the ortho position during thermal curing.
As can be seen in Fig. 3, the amount of exotherm gradually
decreases with the increase of heat-treatment temperature, and
the degree of curing gradually increases. From Fig. 3 it may be
observed that the uncured monomer exhibits an exothermal peak
at 271 ◦C assigned to the monomer polymerization. If the monomer
was previously cured at 180 ◦C or 200 ◦C before the DSC tests, the
polymerization process is accelerated probably due to the already
formed OH groups into the polymer chain so that the peak tem-
perature is shifted to lower temperature [58]. When the sample
is cured at 180 ◦C, 200 ◦C, and 220 ◦C, the degree of curing attains
50.4%, 69.5%, and 90.5%, respectively. However, the exothermic
peak completely disappears at 240 ◦C, implying that the polymer-
ization reaction is completed. The step change of the thermogram
assigned to the glass transition temperature (Tg) can be observed
in this stage.
N
CH2 Ar and O CH2 N of oxazine rings, respectively. The sig-
nals located at 64.35 ppm are due to the presence of quaternary
carbon atoms in the fluorene structure [34]. The NMR results con-
firmed the successful synthesis of BEF-p.
FT-IR spectrum of BEF-p monomer is shown in Fig. 2. The absorp-
tion band assigned to the out-of-plane bending vibrations of C
H
located at 950 cm−1 is due to presence of the characteristic mode
of benzene with an attached oxazine ring [24,34]. The absorp-
tions located at 1224 cm−1 and 1067 cm−1 are corresponding to
the asymmetric and symmetric stretching vibrations of C
respectively. The band at 1139 cm−1 is attributed to the asymmetric
stretching vibrations of C C [60]. The absorption bands at 823
O C,
N
3.3. Curing kinetics
and 747 cm−1 are attributed to the C H out-of-plane bending mode
of the para and ortho disubstituted benzene of aniline, aryl ether,
and fluorene ring in BAOFL skeleton, respectively. The CH2 wagging
in the oxazine ring is located at 1370 cm−1 [15,18]. Furthermore,
the characteristic absorption bands of ortho-disubstituted benzene
appear at 1584 cm−1and 1455 cm−1, as well as 750 cm−1 [13].
The curing kinetics analysis is based on the rate Eq. (1) [61]:
d˛
dt
d˛
dT
= ˇ
= k(T) f (˛)
(1)
where k(T) is a temperature-dependent reaction rate constant, f(˛)
is the differential conversion function depending on the reaction
mechanism, and ˇ = dT/dt is a constant heating rate.
3.2. Polymerization behavior of BEP-p
The DSC curves were analyzed on the basis of the following
assumption: the exothermic heat evolved during curing is propor-
tional to the conversion of monomer to polymer. The degree of
curing, ˛, is determined by the following equations:
The polymerization behavior of BEP-p was investigated by DSC
and FTIR. The obtained FTIR spectra and non-isothermal DSC ther-
mograms of BEF-p at each cure stage are shown in Fig. 2 and
Fig. 3, respectively. As can be seen from Fig. 2, as the curing tem-
perature increases, the characteristic absorption bands associated
with the oxazine ring at 950 cm−1, CH2 wagging at 1370 cm−1, the
ꢀHi
˛ =
(2)
ꢀHo
asymmetric and symmetric stretching vibrations of C
O C at 1224
ꢀ
t
and 1067 cm−1 and C
N
C at 1139 cm−1, respectively, gradually
dH
dt
ꢀHi =
dt
(3)
decrease. At 240 ◦C, the characteristic peaks completely disappear,
indicating the completion of ring-opening in this stage. Meanwhile,
0

X.-y. He et al. / Thermochimica Acta 564 (2013) 51–58
55
Fig. 5. Variation of Ea vs. ˛ by Starink method.
Fig. 4. Conversion ˛ as a function of temperature for the BEF-p in different heating
rates.
determination of the reaction order of the BEF-p. This method is
based on Eq. (6) [64].
ꢃ
ꢄ
where ꢀHi is the total amount of heat evolved by the reaction from
the beginning to time t. ꢀHo is the total heat of curing reaction.
The temperature dependence on the rate constant is typically
represented through the Arrhenius equation:
ˇ
Tf1.92
Ea
ln
= Const. − 1.0008
(6)
RTf
ꢁ
ꢂ
where Tf is the temperature at an equivalent (fixed) state of trans-
formation in different heating rate.
−Ea
k T = A exp
( )
(4)
RT
From Eq. (6), a plot of ln(ˇ/Tf1.92) vs. 1/Tf values at the same
where A is the pre-exponential factor. Ea is the activation energy,
which can be determined by Arrhenius law without assuming the
kinetic model function. R is the universal gas constant, and T is the
absolute temperature.
fractional extent of conversion from a series of dynamic DSC exper-
iments at different heating rates would result in a straight line with
a slope of −1.0008Ea/R. Repeating this procedure, the Ea values cor-
responding to different ˛ from the DSC curing curves at different
heating rates can be obtained. The plot of activation energy as a
function of conversion was shown in Fig. 5. It could be clearly seen
that the activation energy values tended to increase with the degree
of conversion. And, the average value of the activation energy of
BEF-p is 117.9 4.2 kJ/mol.
Combining Eq. (1) with Eq. (4) it results:
ꢁ
ꢂ
d˛
dt
d˛
dT
−Ea
= ˇ
= A exp
f (˛)
(5)
RT
Non-isothermal method, more accurate to determine the cur-
ing kinetic parameters, is carried out at different heating rates. In
addition, this method is very attractive because the kinetic data can
be obtained in a relatively short period of time [55]. In this work, a
multiple-heating-rate method for dynamic mode was used to eval-
uate the polymerization reaction kinetic parameters. Fig. 4 shows
the variation of the degree of conversion (˛) as a function of curing
temperature obtained from dynamic DSC.
According to the experimental data and the average activation
energy value obtained from Starink method, we can produce the
plots of ln(d˛/dt) + Ea/RT vs. ln(1 − ˛) as shown in Fig. 6. In Fig. 6,
the peak points of the lines correspond to the peak point of the
DSC curve. It is observed that there is a nonlinear increase before
the peak points and a linear decrease after them. In the n-order
model, the reaction rate is the highest at the beginning of curing,
and it decreases as the reaction proceeds. For autocatalytic pro-
cess, the plot would show a maximum of ln(1 − ˛) approximately
The kinetic parameters of the curing reaction, with special refer-
ence to Ea, can be calculated using various computational methods.
An alternative approach to kinetic analysis is to use model-free
methods that allow the evaluating of Arrhenius parameters with-
out choosing the reaction model. The best known representatives of
the model-free approach are the isoconversional methods [62,63].
These methods are based on the isoconversional principle which
states that the reaction rate at a constant extent of conversion is
only a function of the temperature. They can generally be split in
two categories: differential and integral methods. The differential
isoconversional method presents the most straightforward way to
evaluate the effective activation energy, Ea, as a function of the
extent of reaction. This method can be applied to integral data (e.g.
TG data) only after their numerical differentiation. Because this pro-
cedure may lead to erroneous estimations of the activation energy,
the use of the integral isoconversional methods appears to be a
safer alternative [62]. For non-isothermal conditions, the activa-
tion energy can be calculated by various integral isoconversional
methods such as Ozawa, Kissinger, Starink methods. Compared to
these methods, Straink method offers a significant improvement in
the accuracy of the Ea values [61]. In this work, the average activa-
tion energy value obtained from Starink method was used for the
Fig. 6. The plots of lnd˛/dt + Ea/RT vs. ln(1 − ˛) for different heating rates.

56
X.-y. He et al. / Thermochimica Acta 564 (2013) 51–58
in the range of −0.51 to −0.22, which is equivalent to degree of
curing of about 0.2–0.4. This is due to the autocatalytic nature that
shows the maximum reaction rate at 20–40% conversion [65–67].
Since ln(d˛/dt) + Ea/RT and ln(1 − ˛) were not linearly related and
evidently showed a maximum in the range of the degree of con-
version mentioned above, this suggested that the curing reaction
was autocatalytic in nature. According to other works, the autocat-
alytic nature of reaction kinetics of benzoxazine can be explained
by the generation of free phenol groups while the benzoxazine ring
starts to open. These groups can further accelerate the ring opening
process [53,54].
For
the
benzoxazine
resins,
autocatalytic
model
ˇ
(Sesták–Berggren equation) assumes that the reaction obeys
equation:
f (˛) = ˛m (1 − ˛)n
(7)
Combined with Eq. (5) and Eq. (7), the kinetic model can be
described as follows:
Fig. 7. Comparison of experimental values (symbols) and calculated values (lines)
by Starink-LSR method.
ꢁ
ꢂ
d˛
dt
d˛
dT
−Ea
= ˇ
= A exp
˛
m (1 − ˛n)
(8)
RT
The results of the multiple linear regressions analysis of BEF-p
are Ea ≈ 127.8 2.2 kJ/mol, m ≈ 0.89, n ≈ 1.47, A ≈ exp(29.87). The
curing kinetic equation of the BEF-p with this least square regres-
sion (LSR) method can be expressed as:
where m and n are variables determining the reaction order.
The method of least square regression (LSR) assumes that the
best fit curve of a given type is the curve that has the minimal sum of
the deviations squared (least square error) from a given set of data.
This method is used to deal with the non-isothermal DSC data in
order to obtain the optimum model parameters [68]. Theoretically,
Eq. (8) could be solved by multiple nonlinear regressions. Because
the cure rate was an exponential function of the reciprocal of the
absolute temperature, it was difficult to get a good solution. The
fitting results showed that large errors exist for the kinetic param-
eters obtained by such a method. By taking the logarithm of both
sides of Eq. (8), a linear expression for the logarithm of cure rate
can be obtained:
ꢁ
ꢂ
d˛
dt
d˛
dT
15381
T
= ˇ
= exp(29.87) exp
−
˛
0.89 (1 − ˛)1.47
(11)
The comparisons of the experimental data with the kinetic
model are shown in Fig. 8. The calculated curves were compared
with the experimental curves, and were found to be similar to the
experimental curves.
3.4. Thermal and mechanical properties of polybenzoxazines
ꢁ
ꢂ
ꢁ
ꢂ
ꢁ
ꢂ
d˛
dt
d˛
dT
Ea
Thermal properties of BEF-p after polymerization have been
investigated in comparison to the typical fluorene diamine-
based polybenzoxazine (poly(BF-p)) derived from 9,9-bis-(4-
aminophenyl)-fluorene/phenol bifunctional benzoxazine (BF-p)
without aryl ether [39]. The Tg of poly(BEF-p) was obtained by DSC
and DMA, and shown in Figs. 3 and 9, respectively. As a result,
the Tg value of poly(BEF-p) reaches 240 ◦C by DSC and 253 ◦C
by DMA, respectively, and is 3 ◦C lower than that of poly(BF-p),
but is much higher than that of the diaminodiphenylmethane-
based polybenzoxazine (P-ddm, 200 ◦C by DMA) and bisphenol
fluorene-aniline-based polybenzoxazine (poly(B-pbf), 229 ◦C by
DSC) [17,34]. This is mainly attributed to the backbone rigidity
ln
= ln
ˇ
= ln A −
+ m ln(˛) + n ln(1−˛) (9)
RT
Eq. (9) can be solved by multiple linear regression using the
several different heating rates of data at the same time, in which the
dependent variable is ln[ˇ(d˛/dT)], and the independent variables
are ln˛, ln(1 − ˛), and 1/T. Therefore, the values of A, m, and n can be
obtained using the average activation energy from Starink method.
The degree of curing is chosen to range between ˛ = 0.05 and 0.95.
In all cases, the thermograms obtained at different heating rates
were simultaneously correlated with the same set of kinetic param-
eters. In this way a single set of kinetic parameters is obtained
to fit all the experimental data and no variation of these param-
eters at the heating rate is required. Using this method, the kinetic
parameters are gained: Ea ≈ 117.9 4.2 kJ/mol, m ≈ 0.93, n ≈ 1.45,
A ≈ exp(27.59), respectively. Thus, the curing kinetic equation of
the BEF-p can be expressed as:
ꢁ
ꢂ
d˛
dt
d˛
dT
−14174
= ˇ
= exp(27.59) exp
˛
0.93 (1 − ˛)1.45
(10)
T
The experimental curves and predicted curves based on the
determined kinetic parameters of curing reaction were shown in
Fig. 7. It could be clearly seen that the calculated data from the
model were in good agreement with the experimental results.
For the calculated kinetic parameters described above, we first
need to get Ea, and kinetic parameters cannot be obtained simulta-
neously. Therefore, we will discuss another least square regression
method, which is used to deal with the non-isothermal DSC data
in order to determine the optimum model parameters [68]. In this
method, the values of Ea, n, m and lnA can be calculated by mul-
tiple linear regression model (Eq. (9)), where ln˛, ln(1 − ˛), and
1/T are the independent variable and ln[ˇ(d˛/dT)] is the dependent
variable.
Fig. 8. Comparison of experimental values (symbols) and calculated values (lines)
by direct LSR method.

X.-y. He et al. / Thermochimica Acta 564 (2013) 51–58
57
4. Conclusions
The fluorene diamine-based benzoxazine with aryl ether link-
ages has been prepared and characterized. The polymerization
behavior, mechanical and thermal properties were studied by DSC,
FT-IR, DMA and TGA. With the introduction of bulky fluorenyl moi-
eties, poly(BEF-p) exhibits higher glass transition temperature and
thermal stability than those of P-ddm and bisphenol fluorene-based
polybenzoxazines. Incorporation of flexible aryl ether linkages into
fluorene-based polybenzoxazine slightly affects the thermal stabil-
ity of poly(BEF-p), however, the brittleness of polybenzoxazine is
greatly modified compared with poly(BF-p). The curing kinetics of
BEF-p was investigated using non-isothermal DSC methods. Auto-
ˇ
catalytic model (Sesták–Berggren equation) was used to describe
the cure kinetic phenomena of BEF-p. The model parameters were
estimated by Starink-LSR method and direct LSR method. The
theoretically calculated curves show a good agreement with the
experimental data. In addition, the kinetic parameters can be simul-
taneously obtained from direct LSR method.
Fig. 9. Temperature dependence curves of storage modulus and tan delta for
poly(BEF-p) and poly(BF-p).
Acknowledgements
of polybenzoxazine molecule. Bulky fluorene units have the
high rigidity in the chain backbone, which restrain the internal
rotations and thermal motion of polymer segments. Further-
more, the storage modulus of poly(BEF-p) is about 1.7 GPa,
which is much lower than that of poly(BF-p) (2.6 GPa). The
result shows that the stiffness of polybenzoxazine observably
decreases due to the introduction of flexible ether linkages, and
the brittleness of fluoren-containing polybenzoxazine is greatly
improved.
This work has been funded by the financial supports from
National Natural Science Foundation of China (Project no.
50973022), Specialized Research Fund for the Doctoral Program
of Higher Education (Project no. 20122304110019), Fundamen-
tal Research Funds for the Central Universities (Project nos.
HEUCFT1009, HEUCFR1227, 201310006), Natural Science Founda-
tion of Heilongjiang Province (Project no. E200921), and Innovation
Foundation of Harbin (Project no. 2010RFXXG008).
Thermal stability was evaluated by thermogravimetric analy-
ses (TGA) under nitrogen atmosphere. As can be seen in Fig. 10,
the temperatures corresponding to 5% and 10% weight loss (T5
and T10) are 388 and 420 ◦C, respectively, which are slightly
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