Ees

Ma

b

c

a

ARRAA

KEPNCDN

1

oecpcftenIepmgawh

0d

Thermochimica Acta 533 (2012) 10– 15

Contents lists available at SciVerse ScienceDirect

Thermochimica Acta

jou rna l h omepage: www.elsev ier .com/ locate / tca

valuation of curing kinetic parameters of anpoxy/polyaminoamide/nano-glassflake system by non-isothermal differentialcanning calorimetry

ehdi Ghaffari a,b,c, Morteza Ehsania,∗, Hossein Ali Khonakdara, Guy Van Asscheb, Herman Terrync

Iran Polymer and Petrochemical Institute, P.O. Box: 14965-115, Tehran, IranResearch Group Physical Chemistry and Polymer Science, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, BelgiumResearch Group Electrochemical and Surface Engineering, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium

r t i c l e i n f o

rticle history:eceived 22 November 2011eceived in revised form 3 January 2012ccepted 7 January 2012vailable online 16 January 2012

a b s t r a c t

The curing kinetics of diglycidyl ether of bisphenol-A epoxy resin cured with a polyaminoamide in theabsence and presence of nano-glassflakes were studied by means of non-isothermal differential scanningcalorimetry experiments at four heating rates. The data were analyzed by different approaches. Theexperimental data for both neat and nano-glassflakes filled systems are well-represented by an nth-orderbehavior. The calculated ln(A/s−1), Ea, and n for the neat system and nano-glassflakes filled systems are

−1 −1

eywords:poxyolyaminoamideano-glassflakesuring kineticsifferential scanning calorimetry

9.52, 49.6 kJ mol , and 1.00, and 8.98, 47.83 kJ mol , and 0.97, respectively. Model-free methods showthat the activation energy is roughly constant in both with and without NGF. In all analyses, Ea valuesof the nano-glassflake filled system are lower than those of the neat epoxy/polyaminoamide throughoutthe curing reaction, despite lower differences.

© 2012 Elsevier B.V. All rights reserved.

on-isothermal

. Introduction

Epoxy resins are often used for industrial applications becausef their good chemical, mechanical, thermal, and electrical prop-rties [1]. However, the application of epoxy resins is sometimesonstrained owing to their high viscosity and, especially, theiroor impact resistance [2]. One of the most important appli-ations of epoxy coatings is the protection of metal surfacesrom environmental attack. Thus, an improved corrosion resis-ance and enhanced mechanical properties are important factors inpoxy coating preparation. Recently, epoxy coatings with inorganicanofillers are being studied for improved coating performance [3].

n this work, we focus on the addition of nano-glassflake (NGF) in anpoxy coating. The incorporation of glass flakes into coatings andlastics offers significant performance advantages compared withany other forms of reinforcement, hence the increasing use of

lass flake reinforced materials for high performance engineeringnd commodity products. Property enhancements include reduced

arpage and shrinkage, improved dimensional stability, surfaceardness and wears resistance, and increased tensile and flexural

∗ Corresponding author. Tel.: +98 21 44580027; fax: +98 21 44580027.E-mail address: m.ehsani@ippi.ac.ir (M. Ehsani).

040-6031/$ – see front matter © 2012 Elsevier B.V. All rights reserved.oi:10.1016/j.tca.2012.01.009

stiffness. Glass flake reinforced products also display good resis-tance to weathering and chemical attack [4].

One of the most important steps of epoxy coating preparationis the curing process, as it has a major influence on the final prop-erties of the coating. Thus, understanding the curing mechanismand kinetics is an essential step in the evaluation of the processing-property relationships of these nanocomposites. During the curingprocess of an epoxy resin, the system changes from a viscous liq-uid to a highly crosslinked network. Since the reaction occurs inthe condensed phase, the rate of the curing reaction is controlledby the activity of the functional groups and their mobility. Dur-ing the first stages of the reaction, when the rate of displacementof the groups is much faster than the rate of the actual chemicalreaction, the reaction is controlled by the chemistry of the reactinggroups. As the reaction proceeds, chain branching increases untilthe system reaches gelation. As the reaction and crosslinking pro-gresses, the glass transition temperature (Tg) of the reacting systemincreases until curing temperature (Tc) is reached, at which the sys-tem reaches a glassy state and vitrifies [5–11]. In these conditions,the mobility of the reactive centers is progressively restricted, andthe reaction may turn into a diffusion or mobility-controlled pro-

cess. As a result, the kinetics slow down, limiting the degree ofconversion that can be reached at curing temperatures, Tc, belowthe maximum glass transition of the fully cured epoxy Tg,x = 1. Con-sequently, Tg plays an important role in the curing process of an

chimi

eecv(k

ftkpwnaiii[oItbktttOtopteictn

oECgk

2

2

pE(drUi23Nt

wfspa

M. Ghaffari et al. / Thermo

poxy. In coating processes, often solvent is combined with thepoxy to reduce the viscosity. This solvent decreases the Tg andonsequently affects the curing kinetics and the degree of con-ersion at which vitrification occurs. The resin used in this studyEpikote1001) includes 25% solvent, which can affect the curinginetic [12,13].

In the presence of additives in general, and high specific sur-ace nanofillers in particular, effects on curing kinetics and glassransition could be envisaged. Xie et al. [14] studied the curinginetics of multiwall carbon nanotubes (MWNT)/epoxy nanocom-osites with isothermal differential scanning calorimetry (DSC). Itas observed that the initial reaction rates of the epoxy/MWNTanocomposites were comparatively higher than that of neat epoxyt all curing temperatures, whereas the time span to the max-mum reaction rate of the nanocomposites decreased with anncrease in MWNT content. Other researchers investigated the cur-ng kinetics of epoxy/nanoclay systems. Whereas Ton-That et al.15] and Montserrat et al. [16] reported that the presence of nan-clay facilitates the curing reaction of epoxy/nanoclay composites,vankovic [17] indicated that nanoclay has a very small effect onhe epoxy cure kinetics. Xie et al. [18] showed that presence of car-on nanofibers (CNF) leads to a negligible effect on the epoxy curinginetics. On the other hand, Aussawasathien et al. [19] showed thathe curing reaction rates of CNF-epoxy nanocomposites are higherhan that for neat epoxy resin at low curing temperatures. At higheremperatures, the effect of CNF on the curing rate was insignificant.verall, the CNF-epoxy composite exhibited slightly lower activa-

ion energy than that of the neat epoxy system at the beginningf the curing. Other researchers studied the effect of nano-silicaarticles on the curing kinetics. Ranjbara et al. [20] showedhat the presence of nano-silica particles reduces the activationnergy of the curing kinetics of an acrylic-melamine clearcoat andncreases the total heat of the reaction. Rosso and Ye [21] indi-ated that upon the addition of silica nanoparticles to neat resin,he degree of conversion increases with an increasing amount ofanoparticles.

The objective of the present work is to study the curing kineticsf the commercial and widely used corrosion resistant epoxy resinpikote1001-X-75 (containing 25% Xylene) with polyaminoamiderayamid115 as curing agent, in the absence and presence of nano-lassflake by means of non-isothermal DSC experiments. The cureinetics data will be analyzed using different methods.

. Experimental

.1. Materials

The epoxy resin used in this study, Epikote1001-X-75, wasrovided by Hexion Specialty Chemicals Co., The Netherlands.pikote1001-X-75 consists of diglycidyl ether of bisphenol-ADGEBA) with a epoxide equivalent weight of 450–500 g equiv−1,iluted with xylene to an epoxy-xylene weight ratio of 75/25. Theesin was cured with Crayamid115 supplied by Cray Valley Co.,K. Crayamid115 is a liquid polyaminoamide resin with a viscos-

ty of 55,000 mPa s and an active hydrogen equivalent weight of40 g equiv−1. Milled nano-glassflakes (NGF) with a thickness of50 nm (GF 350 nmM) were obtained from Glassflake Ltd., UK. TheGF was stored in a sealed plastic bag to prevent moisture absorp-

ion.The epoxy resin and the curing agent were mixed at a 65:35

eight ratio, without and with NGF. The neat resin samples (NGF

ree) were prepared in a small bottle using a high speed mechanicaltirrer at 2500 rpm for 3 min. The samples containing 1% NGF wererepared starting from a dispersion of NGF in epoxy, mixed using

high speed mechanical stirrer at 2500 rpm for 15 min. Next, the

ca Acta 533 (2012) 10– 15 11

equivalent amount of Crayamid115 was added into the mixture,and mixing was continued for another 3 min.

2.2. Instruments

Calorimetric studies were carried out on a Mettler-Toledo DSC-821 thermal analyzer in covered high pressure stainless steelpans under nitrogen atmosphere at heating rates of 1, 2.5, 5 and10 K min−1. The instrument was calibrated for temperature andenthalpy using indium. Samples of about 10 mg of the reactive sys-tems were put in hermetically sealed aluminum DSC pans (Mettler).The cure process and the glass transition temperature of partiallycured and fully cured samples were determined in non-isothermalexperiments.

3. Theoretical background

There are several approaches to measure and analyze the cur-ing kinetics by DSC [22]. A first experimental approach is to useexperiments at multiple heating rates (non-isothermal method).Alternatively, one can perform isothermal experiments at differ-ent temperatures (and compositions). Next, the non-isothermal orisothermal kinetic data, or a combination of both, can be mod-eled using (semi-)empiric or mechanistic models to describe thereaction kinetics, which often requires detailed information on thecomposition of the resins. Alternatively, model-free methods [23]permit one to get an idea of the overall activation energy of thecure process, without requiring a more detailed chemical kineticsmodel.

In this work, we used non-isothermal experiments for a firstinvestigation of the curing kinetics of the epoxy/polyaminoamideand the epoxy/polyaminoamide/nano-glassflake systems, both inthe presence of xylene. For analyzing the non-isothermal DSC data,the assumption can be made that Ea (apparent activation energy) isconstant, or it can be considered to be variable during the process.

3.1. Kinetic analysis of the non-isothermal DSC data withvariable Ea assumption

3.1.1. Friedman methodThe kinetic analysis of non-isothermal resin-cured system is

based on the rate equation as follows [24]:

ln(

d˛

dt

)= ln A −

(E

RT

)+ ln f (˛) (1)

where ̨ is the degree of conversion, t is the time, (d˛/dt) is thecuring rate (rate of conversion), A is the pre-exponential factor, Ris the ideal gas constant, T is the absolute temperature and f(˛)describes the conversion dependence and is related to the reactionmechanism.

During the curing of resin, the reaction rate is only a functionof temperature at any given conversion ̨ and the plot of ln (d˛/dt)against 1/T should be a straight line with slope −Ea(˛)/R, with Ea(˛)the activation energy corresponding with conversion ˛.

3.2. Kinetic analysis of the non-isothermal DSC data with theconstant Ea assumption

3.2.1. Ozawa methodOzawa method can be applied to the thermal data, using the

following Eq. (2) [25]:( ) ( )

log ̌ = 12.303

ln ̌ = −0.4567Ea

RTp

+[

log(

AEa

R

)− log F(˛) − 2.315

](2)

1 chimica Acta 533 (2012) 10– 15

wtF

ltp

3

ir

l

(bfieolcieam

4

mm[c

˛

wtb�poit1

Fe

44

46

48

50

52

0,0 0,2 0,4 0,6 0,8 1,0

α

Ea

(k

J/m

ol)

EC

EC1%NGF

2 M. Ghaffari et al. / Thermo

here ̌ is the heating rate, Tp is the temperature corresponding tohe exothermic peak and F(˛) is a constant function, described as:(˛) =

∫1/f(˛) d˛

Ozawa’s method is based on the linear relationship between theogarithm of the heating rate and the inverse of the peak tempera-ure expressed in Eq. (2). The overall activation energy of the curingrocess can be estimated from the resultant slope.

.2.2. Modified Borchardt and Daniels methodIn the Borchardt and Daniels (B/D) method [26], a DSC exper-

ment at a single heating rate is analyzed assuming the curingeaction obeys an nth order kinetics, as expressed by Eq. (3).

n(

d˛

dt

)= ln A −

(E

RT

)+ n ln(1 − ˛) (3)

In later forms, the equation was extended with a contribution+m ln ˛) representing autocatalysis. The parameters in Eq. (3) cane estimated through non-linear parameter optimization methods,tting the evolution of d˛/dt and/or ̨ as determined from one DSCxotherm. In this case, one set of parameters (A, Ea, n, and m) isbtained at each heating rate. However, the results show that Ea andn A values change markedly with an increase in heating rate, indi-ating the parameters obtained are not reliable, as is also reportedn other works [24,27,28]. While the B/D method is based on thevaluation of a single non-isothermal DSC experiment, Eq. (3) canlso be fitted to the four experiments simultaneously (modified B/Dethod).

. Results and discussion

In a non-isothermal DSC run, the total area �Htot of the exother-al peak (using a suitable baseline) is directly proportional to theolar reaction enthalpy �rH released during the curing reaction

29]. The fractional extent of conversion ̨ at any temperature Tan be expressed as:

= �HT

�Htot(0 ≤ ̨ ≤ 1) (4)

here �HT is the partial integral of the exothermal peak upo temperature T. By differentiating ̨ versus time, or preferablyy dividing the heat flow rate with respect to the baseline byHtot, one obtains the experimental reaction rate (d˛/dt). Fig. 1

resents the evolutions of d˛/dt versus temperature for the reaction

f neat and NGF-filled Epikote1001 with Crayamid115 at heat-ng rate of 2.5 K min−1. The average cure reaction heat values ofhe epoxy/polyaminoamide system with and without NGF were08.32 ± 6.71 J/g and 110.5 ± 5.65 J/g, respectively.

0,000 E+00

2,000E- 04

4,000E- 04

6,000E- 04

8,000E- 04

1,000E- 03

0 50 10 0 15 0 20 0

Temperature (°C)

dα

/dt

(1/s

)

EC

EC1%NGF

ig. 1. Plots of d˛/dt vs. temperature at heating rates of 2.5 K min−1: forpoxy/polyaminoamide with (EC1%NGF) and without (EC) nano-glassflake.

Fig. 2. Plots of activation energy as function of conversion forepoxy/polyaminoamide system with and without NGF.

The reaction of epoxy resins with polyaminoamide is rathermildly exothermic compared to that of epoxy resin with aliphaticshort-chain amines. At 10 K min−1, the reaction exotherm startsaround 50 ◦C. At room temperature, the curing of epoxy resins withpolyaminoamide generally requires longer curing times than withshort-chain (aliphatic) amines [30]. As commonly observed, forboth systems the exothermic peaks shift to higher temperatures athigher heating rates, which results in an increase in the exothermalpeak temperature, which is exploited in the Ozawa methods.

4.1. Friedman method

To exploit Eq. (1), series of ln(d˛/dt) versus (1000/T) values atthe same conversion ˛, obtained from a set of non-isothermal DSCexperiments at different heating rates. In this case, a straight linewith a slope of −Ea/R is obtained. An advantage of this method todetermine Ea compared to other methods is that this method is amodel-free process, which enables one to determine the evolutionof Ea with conversion without assuming a certain reaction model.The plot in Fig. 2 presents the evolution of the activation energywith the extent of reaction for both resin systems. Variation of Ea

for ̨ < 0.1 and ̨ > 0.9 is not automatically a major concern, becauseit parameters can be affected greatly by possible minor errors inbaseline determination [24].

The differences between the maximum and minimum activa-tion energies are 1.69 kJ mol−1 and 2.4 kJ mol−1 for the systemswith and without NGF, respectively. Since the variation of Ea

values with ̨ is negligible compared to the expected Ea error,it can be concluded that Ea is roughly constant over the entireconversion range of both systems. The average values of Ea are46.8 kJ mol−1 and 48.8 kJ mol−1 for the systems with and withoutNGF, respectively. Throughout the curing reaction, Ea is 2 kJ mol−1

lower for the nano-glassflake filled system compared to the neatepoxy/polyaminoamide.

Sbirrazzuoli and Vyazovkin [31,32] showed a significantdecrease in Ea values occurs upon the transition from a kinetic-controlled to diffusion-controlled regime during vitrification.Vitrification of a reacting thermosetting system occurs when itsTg rises to the reaction temperature. Although, this phenomenonis not only restricted to isothermal conditions, for highly reactivesystems, or when the applied heating rate is sufficiently small, vit-rification occurs in non-isothermal conditions as well [7]. It is notlikely that diffusion limitations are responsible for the variations

in activation energy observed in the current systems: as infiniteglass transition temperatures (Tg′ = 1) are 18.75 ◦C and 19.79 ◦C forepoxy/polyaminoamide with and without NGF, respectively, theminor difference of Ea and the negligible decrease of Ea verifies that

M. Ghaffari et al. / Thermochimica Acta 533 (2012) 10– 15 13

0

0,0004

0,0008

0,0012

0,0016

0,00 0,2 0 0,4 0 0,6 0 0,8 0 1,0 0

α

dα

/dt

(1/s

)EC

EC1%NGF

Fs

tmi

odcr

4

vNrpmEcOcsi

vcic

a

Fw

0,00

0,20

0,40

0,60

0,80

1,00

0 50 0 100 0 150 0 200 0 250 0 300 0

Time (s)

α

EC

EC1%NGF

ig. 3. Plots of d˛/dt vs. ̨ at heating rate of 5 K min−1 for epoxy/polyaminoamideystem with and without NGF.

here is no vitrification in both systems. The influence of increasingobility restrictions is thought to be negligible during our non-

sothermal experiments.Since Ea does not vary significantly with ̨ and no shoulders are

bserved in the reaction rate curve, the process can be adequatelyescribed as single-step kinetics, i.e., by a single kinetic triplet. Thisan be accomplished through linear model-fitting for determiningeaction models and pre-exponential factors [24].

.2. Ozawa method

Fig. 3 shows the relation between the reaction rate and con-ersion for the epoxy/polyaminoamide systems with and withoutGF at different heating rates. As shown in Fig. 3, the conversion ˛

eached at the peak exotherm is nearly constant (0.6) for both sam-les. Therefore, these and the isoconvertional method (Friedmanethod) results together with the reaction rate curve show that

a can be considered as a constant value, and the Ozawa equationan be used to estimate the curing kinetic parameters. Fig. 4 showszawa plots for the neat resin and the resin containing NGF. Thealculated activation energy for the neat epoxy/polyaminoamideystem is 53.8 kJ mol−1, while these value decrease to 51.3 kJ mol−1

n the presence of NGF.To select a proper reaction model, it is necessary to plot con-

ersion versus time in isothermal run. Fig. 5 shows the isothermaluring at 50 ◦C for both systems. It can be seen that reaction models a decelerating type. It is known that the nth-order is the most

ommon reaction model of decelerating type [24].

Assuming an nth-order kinetics for this system, the Borchardtnd Daniels approach can be used using (Eq. (3)). To reduce the

0,0

0,5

1,0

1,5

2,0

2,5

2,4 2,5 2,6 2,7 2,8 2,9

1000/Tp

Ln

β

EC

EC1%NGF

ig. 4. Ozawa’s and Kissinger’s plots for epoxy/polyaminoamide system with andithout NGF.

Fig. 5. Plots of ̨ vs. time at 50 ◦C for epoxy/polyaminoamide system with andwithout NGF.

calculation errors arising from the linear regression, errors mainlyarising from the small heat flow rates attained at conversionsapproaching unity (most negative ln(1 − �)), Eq. (3) can be trans-formed using its value at a second conversion �’ approximatelyequal to 1 − �:

ln(

d˛

dt

)|˛′∼1−˛ = ln A − E

RT ′ + n ln ˛′ (5)

Subtraction leads to:

I =[(

E

RT

)+ ln

(d˛

dt

)]−

[E

RT ′ + ln(

d˛

dt

)|˛′∼1−˛

]

= n ln ˛′ − n ln(˛) = n ln[

˛′

˛

](6)

The reaction order n equals the slope of the left-hand side expres-sion in Eq. (6) (I) plotted against ln[˛′/˛]. To do this, one needs avalue for E. The reaction order n, given by the slope, equals 1.19 and1.15, using the activation energies obtained by the Ozawa methodfor the neat resin and the NGF-filled resin, respectively. Eq. (3)can be solved with the obtained results of E and n to estimate thecorresponding value of ln A for every ˛. Fig. 6 shows that ln A isalmost constant from 10% to 90% of conversion. Thus, accordingto Ozawa method, the average ln(A/s−1) values are 10.89 ± 0.85and 10.06 ± 0.73 for the neat resin and the system including NGF,respectively (Table 1). Both systems show small changes of the ln Avalues. Sbirrazzuoli et al. [33] showed that adding the nano par-ticles can increase A values. It was proposed that the increase of

A value for the epoxy/amine system can be due to the efficiencymodification of the collisions during the amine addition. This canbe initiated by a proton donor that leads to the stimulation of thering opening procedure [33].

Fig. 6. Plot of ln A (1/s) vs. ˛. for epoxy/polyaminoamide system with (EC1%NGF)and without NGF (EC) systems.

14 M. Ghaffari et al. / Thermochimica Acta 533 (2012) 10– 15

Table 1Kinetic parameters based on Ozawa and modified B/D method.

Epikote/Crayamid Epikote/Crayamid/1%NGF

Ea (kJ mol−1) n ln A (s−1) Ea (kJ mol−1) n ln A (s−1)

Ozawa 53.8 1.19 10.89 51.3 1.15 10.06Modified B/D 49.62 1.00 9.52 47.83 0.97 8.98

e at 1

4

tpfnl1v

oaoeraiBewofit

5

ssoractpw

cN

[

[

[

[

[

[

[

Fig. 7. curing rate versus temperature: (a) epoxy/polyaminoamid

.3. Modified Borchardt and Daniels (B/D) method

Modeling the set of DSC data at different heating rates simul-aneously, results in a single (optimum) set of curing kineticarameters that minimizes the sum of the squares of the dif-erences between measured and calculated values for all fouron-isothermal experiments. According to the results, the calcu-

ated ln(A/s−1), Ea, and n using this method are 9.52, 49.62 kJ mol−1,.00 for the neat resin, while for the system including NGF thealues are 8.98, 47.83 kJ mol−1, and 0.97, respectively (Table 1).

The success of any model-based curing control system dependsn the accuracy of the prediction of the conversion and curing ratet any time/temperature of the curing process. Thus, the resultsf Ozawa and the modified B/D methods were compared with thexperimental data. Fig. 7a and b shows the evolution of the reactionate with temperature for the epoxy/polyaminoamide system withnd without NGF at 10 K min−1. It can be see that both methods aren good agreement with the experimental data. Nevertheless, the/D modified model shows a slightly superior agreement with thexperimental data around the maximum reaction rate. Of course,hile the Ozawa method only utilize the peak temperature values

f the curing curves to determine the activation energy, the modi-ed B/D method makes a more extensive use of all information inhe curing curves.

. Conclusions

The curing kinetic parameters of the epoxy/polyaminoamideystem Epikote1001/Crayamid115 containing 25% xylene and theame system in the presence of 1 wt% of nano-glassflake wasbtained by several approaches. The analysis results show that theesults of the Ozawa and modified Borchardt and Daniels methodsll fit the obtained experimental data, although the modified Bor-hardt and Daniels methods presents the best agreement aroundhe maximum reaction rate. The results of the Friedman analysisoint out that the activation energy is roughly constant in both

ith and without NGF.

In all cases, the activation energy is lower for the systemontaining nano-glass flakes. Nevertheless, the difference is low.otwithstanding the decreased activation energy, the shape of the

[

0 K min−1 and (b) epoxy/polyaminoamide/1%NGF at 10 K min−1.

reaction exotherm is not markedly affected, indicating that thereaction mechanism is not strongly affected.

References

[1] M. Akatsuka, Y. Takezawa, S. Amagi, Influences of inorganic fillers on curingreactions of epoxy resins initiated with a boron trifluoride amine complex,Polymer 42 (2001) 3003–3007.

[2] Y. Zheng, K. Chonung, G.L. Wang, P. Wei, P. Jiang, Epoxy/nano-silicacomposites: curing kinetics, glass transition temperatures, dielectric andthermal–mechanical performances, J. Appl. Polym. Sci. 111 (2009) 917–927.

[3] K. Kowalczyk, T. Spychaj, Frequency dependent heat capacity in the cure ofepoxy resins, Prog. Org. Coat. 62 (4) (2008) 425–429.

[4] W.R. Broughton, M.J. Lodeiro, G.D. Pilkington, Influence of coupling agents onmaterial behaviour of glass flake reinforced polypropylene, Composites A 41(2010) 506–514.

[5] M.T. Aronhime, J.K. Gillham, Time–temperature–transformation (TTT) cure dia-gram of thermosetting polymeric, Adv. Polym. Sci. 78 (1986) 83–113.

[6] G. Van Assche, A. Van Hemelrijck, H. Rahier, B. Van Mele, Modulated differ-ential scanning calorimetry isothermal cure and vitrification of thermosettingsystems, Thermochim. Acta 268 (1995) 121–142.

[7] G. Van Assche, A. Van Hemelrijck, H. Rahier, B. Van Mele, Modulated differentialscanning calorimetry: non-isothermal cure, vitrification and devitrification ofthermosetting systems, Thermochim. Acta 286 (1996) 209–224.

[8] G. Van Assche, A. Van Hemelrijck, H. Rahier, B. Van Mele, 8 Modulated temper-ature differential scanning calorimetry. Cure, vitrification, and devitrificationof thermosetting systems, Thermochim. Acta 304/305 (1997) 317–334.

[9] G. Van Assche, B. Van Mele, Y. Saruyama, Frequency dependent heat capacityin the cure of epoxy resins, Thermochim. Acta 372 (2001) 125–130.

10] G. Van Assche, S. Swier, B. Van Mele, Modeling and experimental verificationof the kinetics of reacting polymer systems, Thermochim. Acta 388 (2002)327–341.

11] L. Calabrese, A. Valenza, Effect of CTBN rubber inclusions on the curing kineticof DGEBA–DGEBF epoxy resin, Eur. Polym. J. 39 (2003) 1355–1363.

12] Y. Tanaka, H. Kakiuchi, Study of epoxy compounds. Part I. Curing reactions ofepoxy resin and acid anhydride with amine and alcohol as catalyst, J. Appl.Polym. Sci. 7 (1963) 1063–1081.

13] L. Mascia, T. Tang, Curing and morphology of epoxy resin–silica hybrids, J.Mater. Chem. 8 (1998) 2417–2421.

14] H. Xie, B. Liu, Z. Yuan, J. Shen, R. Cheng, Cure kinetics of carbonnanotube/tetrafunctional epoxy nanocomposites by isothermal differentialscanning calorimetry, J. Polym. Sci. B: Polym. Phys. 42 (2004) 3701–3712.

15] M.T. Ton-That, T.D. Ngo, P. Ding, G. Fang, K.C. Cole, S.V. Hoa, Epoxy nanocom-posites: analysis and kinetics of cure, Polym. Eng. Sci. 44 (2004) 1132–1141.

16] S. Montserrat, F. Roman, J.M. Hutchinson, L. Campos, Analysis of the cure ofepoxy based layered silicate nanocomposites: reaction kinetics and nanostruc-

ture development, J. Appl. Polym. Sci. 108 (2008) 923–938.

17] M. Ivankovic, I. Brnardic, H. Ivankovic, H.J. Mencer, DSC study of thecure kinetics during nanocomposite formation: epoxy/poly(oxypropylene)diamine/organically modified montmorillonite system, J. Appl. Polym. Sci. 99(2006) 550–557.

chimi

[

[

[

[

[

[

[

[

[

[

[

[

[[

[

M. Ghaffari et al. / Thermo

18] H. Xie, B. Liu, Q. Sun, Z. Yuan, J. Shen, R. Cheng, Cure kinetic study of carbonnanofibers/epoxy composites by isothermal DSC, J. Appl. Polym. Sci. 96 (2005)329–335.

19] D. Aussawasathien, E. Sancaktar, Effect of non-woven carbon nanofiber matpresence on cure kinetics of epoxy nanocomposites, Macromol. Symp. 264(2008) 26–33.

20] Z. Ranjbara, A. Jannesaria, S. Rastegarb, Sh. Montazeri, Study of the influence ofnano-silica particles on the curing reactions of acrylic-melamine clear-coats,Prog. Org. Coat. 66 (2009) 372–376.

21] P. Rosso, L. Ye, Epoxy/silica nanocomposites: nanoparticle-induced cure kinet-ics and microstructure, Macromol. Rapid. Commun. 28 (2007) 121–126.

22] J. Menczel, in: J. Menczel, R.B. Prime (Eds.), Thermal Analysis of Polymers, Wiley,2009.

23] S. Vyazovkin, N. Sbirrazzuoli, Isoconversional kinetic analysis of thermallystimulated processes in polymers, Macromol. Rapid. Commun. 27 (18) (2006)1515–1532.

24] S. Vyazovkin, A.K. Burnham, J.M. Criado, L.A. Pérez-Maqueda, C. Popescu,

N. Sbirrazzuoli, ICTAC kinetics committee recommendations for performingkinetic computations on thermal analysis data, Thermochim. Acta 520 (2011)1–19.

25] C.S. Wang, C.H. Lin, Novel phosphorus-containing epoxy resins. Part II: curingkinetics, Polymer 41 (2000) 8579–8586.

[

ca Acta 533 (2012) 10– 15 15

26] H.J. Borchardt, F. Daniels, The application of differential thermal analysis to thestudy of reaction kinetics, J. Am. Chem. Soc. 79 (1956) 41.

27] D. Rosu, F. Mustata, C.N. Cascaval, Investigation of the curing reactions of somemultifunctional epoxy resins using differential scanning calorimetry, Ther-mochim. Acta 370 (2001) 105–110.

28] M.V. Alonso, M. Oliet, J.M. Pérez, F. Rodrıguez, J. Echeverrı, Determination ofcuring kinetic parameters of lignin–phenol–formaldehyde resol resins by sev-eral dynamic differential scanning calorimetry methods, Thermochim. Acta 419(2004) 161–167.

29] Y. Zhang, S. Vyazovkin, Comparative cure behavior of DGEBA and DGEBP with4-nitro-1,2-phenylenediamine, Polymer 47 (2006) 6659–6663.

30] D. Peerman, W. Tolberg, D. Floyd, Ind. Eng. Chem. 49 (7) (1957) 1091–1094.31] N. Sbirrazzuoli, S. Vyazovkin, Learning about epoxy cure mechanisms

from isoconvensional analysis of DSC data, Thermochim. Acta 388 (2002)289–298.

32] N. Sbirrazzuoli, S. Vyazovkin, A. Mititelu, C. Sladic, L. Vincent, A study of epoxyamine cure kinetics by combining isoconversional analysis with temperature

modulated DSC and dynamic rheometry, Macromol. Chem. Phys. 204 (2003)1815–1821.

33] C. Alzina, N. Sbirrazzuoli, A. Mija, Hybrid nanocomposites: advanced nonlinearmethod for calculating key kinetic parameters of complex cure kinetics, J. Phys.Chem. B 114 (2010) 12480–12487.