Introduction

Industrially epoxy resins are very important thermoset materials [1] and find their usefulness in the field of coatings [2, 3], high-performance composites [4], insulating materials [5], microelectronics [6] and encapsulants [7]. For excellent engineering performance, materials must satisfy high-temperature performance [8], creep resistance [9], high stiffness [10], high electrical and mechanical properties [11]. Superior thermal, mechanical, electrical, chemical resistance, adhesive and low shrinkage properties of epoxy resins make them high-performance materials for various applications. For optimum process parameters and high production rate with satisfactory properties, precise understanding of curing process is essential [12]. Curing kinetics is useful for the comparison of curing behavior of different compositions of different matrices, catalysts, fillers, additives, etc. [13]. Both degree of cure and reaction rate strongly affect processing and physical properties of the cured epoxy resins [14].

Differential scanning calorimetry (DSC) is the most useful technique in understanding curing kinetics and key process parameters [15]. Recently, several investigators had used DSC technique to understand non-autocatalytic and autocatalytic curing of epoxy resins by different curing agents [12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27] and discussed autocatalysis mechanism. With the advancement of the technology, several researchers had attempted to enhance thermal stability of epoxy resins by introducing various aromatic ring structures such as biphenyl, naphthalene, fluorine, anthrone, heterocycles, etc., in the epoxy skeleton [28,29,30].

To the best of our knowledge, no work has been reported on dynamic DSC curing kinetics of epoxy resin of 9,9′-bis(4-hydroxyphenyl)anthrone-10 (Scheme-1). In this study, an attempt has been made to understand dynamic DSC curing kinetics of epoxy resin of 9,9′-bis(4-hydroxyphenyl)anthrone-10 at four different heating rates using three different curing agents such as 4,4′-diaminodiphenylsulphone (DDS), 4,4′-diaminodiphenylmethane (DDM) and tetrahydrophthalicanhydride (THPA). The derived results are discussed in light of the structure of curing agents on kinetic behavior.

Scheme 1
scheme 1

Epoxy resin of 9,9′-bis(4-hydroxyphenyl) anthrone-10 (EAN)

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Experimental

Materials

The materials used in this study were of laboratory grade and were purified prior to their use [31]. 4,4′-Diaminodiphenylmethane (DDM) (Spectrochem, Mumbai), 4,4′-diaminodiphenylsufone (DDS) (National Chemicals, Vadodara) and tetrahydrophthalicanhydride (THPA) (Merck, Germany) were used as received. Epoxy resin of 9,9′-bis(4-hydroxyphenyl)anthrone-10 (EAN) was synthesized and purified according to our recent publication [32]. Epoxy equivalent weight of the resin used in the present study was 940.

Measurements

Dynamic differential scanning calorimetric (DSC) curing study of EAN was studied on a Shimadzu DSC60 at four different heating rates: 5, 10, 15 and 20 °C min−1 in N2 atmosphere (100 mL min−1). DSC was calibrated by pure indium metal prior to the study of EAN. The samples were prepared thoroughly by grinding 20% of hardeners and EAN. Known mass of the samples was taken in aluminum pans covered by aluminum lids and sealed using a crimper. DSC curves were scanned over temperature range from room temperature to 400 °C. TG curves of cured and uncured samples were scanned on a Shimadzu DTG 60H at 10 °C min−1 heating rate in N2 atmosphere.

Curing kinetics

Many kinetic models such as nth-order reaction, the autocatalytic reaction and the diffusion control models have been developed to investigate the curing kinetics of the epoxy resins [17,18,19,20]. All kinetic studies rely on the fundamental equation that governs the rate of conversion at constant temperature as a function of the concentration of the reactants [21]:

$$\frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = \beta \frac{{{\text{d}}\alpha }}{{{\text{d}}T}} = k f\left( \alpha \right)$$
(1)

where α is the degree of cure, β = dT/dt is the heating rate, k is a temperature-dependent reaction rate constant, f(α) is the differential conversion function, and it depends on the reaction mechanism. Generally, k assumes to have the Arrhenius form:

$$k = A{\text{e}}^{{ - {\text{E}}_{\text{a}} /{\text{RT}}}}$$
(2)
$$f\left( \alpha \right) = \left( {1 - \alpha } \right)^{{\text{n}}}$$
(3)
$$A = \frac{{E_{\text{a}} \beta }}{{RT^{2} }}{\text{e}}^{{{\text{E}}_{\text{a}} /{\text{RT}}}}$$
(4)

where A is the pre-exponential factor, E a is the activation energy, R is the gas constant, T is the absolute temperature and n is the order of reaction.

Nonisothermal method is more precise method to evaluate the curing kinetic parameters. This method is very simple and rapid for the determination of kinetic parameters. The isothermal method renders the destabilization of the DSC heat flow at the beginning of the measurement, which leads to experimental errors. The two methods cover different temperature domains as discussed by Sbirrazzuoli et al. [22]. The shape of curing peak, the number of peaks and/or shoulders in the isothermal and nonisothermal DSC curves may be different. Although there is only a single peak in the isothermal DSC curve, a peak and a shoulder may appear in the nonisothermal DSC curve. Consequently, the kinetic parameters obtained from an isothermal cure study may not be good in predicting the nonisothermal curing behaviors [23]. Nonisothermal method involves either single or multiple dynamic temperatures scans in the study of the curing reactions of thermosets [24,25,26]. Kissinger, Ozawa, Friedman and Flynn–Wall–Ozawa methods are widely used to study dynamic kinetics of thermosetting polymers.

The Kissinger method

The Kissinger method is widely used for the estimation of the kinetic parameters such as E a and A from dynamic DSC data. At the peak temperature, the rate of curing is maximum [33]. Using peak temperature data, activation energy can be determined according to Eq. 5:

$$\ln \frac{\beta }{{T_{\text{p}}^{2} }} = \ln \frac{{Q_{\text{p}} AR}}{{E_{\text{a}} }} - \frac{{E_{\text{a}} }}{RT}$$
(5)

where

$$Q_{\text{P }} = - \frac{{{\text{d}}f\left( \alpha \right)}}{{{\text{d}}\alpha }} = \alpha_{\text{p}}$$
(6)

The plot of ln β/T 2p against 1/T should be a straight line with slope equal to − E a/R.

The Ozawa method

The Ozawa method [34] relates the logarithm of the heating rate and the inverse of the exothermic peak temperature.

$$\ln \beta = \ln \left( {\frac{{AE_{\text{a}} }}{R}} \right) - \ln f\left( \alpha \right) - 5.331 - 1.052 \frac{{E_{\text{a}} }}{RT}$$
(7)
$$f\left( \alpha \right) = \mathop \int \limits_{0}^{\alpha } \frac{{{\text{d}}\alpha }}{f\left( \alpha \right)}$$
(8)

where f(α) is a constant function. The plot of ln β against 1/T should be a straight line with slope equal to − 1.052 E a/R.

Isoconversional method

The isoconversional method assumes that both of the activation energy (E a) and pre-exponential factor (A) are the functions of the degree of curing (α). In addition, the isoconversional approach can be used to evaluate both simple and complex chemical reactions. The significance of this technique is that no kinetic rate expression is assumed for the data evaluation [34]. Two different isoconversional methods are as follows.

Friedman method

This method is one of the isoconversional methods based on the assumption that kinetic parameters E a and A vary with extent of the reaction (α) [35]. The Friedman method for nth-order reaction is based on Eq. 9:

$$\ln \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = \ln \beta \frac{{{\text{d}}\alpha }}{{{\text{d}}T}} = \ln \left[ {Af\left( \alpha \right)} \right] - \frac{{E_{\text{a}} }}{RT}$$
(9)

Upon substituting Eq. 4 in Eq. 9 gives Eq. 10:

$$\ln \left[ {Af\left( \alpha \right)} \right] = \ln \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} + \frac{{E_{\text{a}} }}{RT} = { \ln } A + n { \ln } \left( {1 - \alpha } \right)$$
(10)

The values of ln [Af (α)] can be obtained from the known values of ln [dα/dt] and E a/RT. Therefore, the plot of ln [Af (α)] and ln(1 − α) yields a straight line with slope equal to n and the intercept equal to ln A.

The Flynn–Wall–Ozawa method

The isoconversional integral method was proposed independently by Flynn, Wall and Ozawa [36] using Doyle’s approximation of the temperature integral.

$$\ln \beta = \ln \left( {\frac{{AE_{\text{a}} }}{R}} \right) - \ln g\left( \alpha \right) - 5.331 - 1.052 \frac{{E_{\text{a}} }}{RT}$$
(11)
$$g\left( \alpha \right) = \mathop \int \limits_{0}^{\alpha } \frac{{{\text{d}}\alpha }}{f\left( \alpha \right)}$$
(12)

where g(α) is the integral conversion function. The isoconversional method assumes that both of the activation energy and pre-exponential factors are the functions of the degree of curing. In addition, the isoconversional approach can be used to evaluate both simple and complex chemical reactions. The significance of this technique is that no kinetic rate expression is assumed for the data evaluation [37].

For a constant degree of conversion α, the plot of ln β versus 1/T should be a straight line with slope equal to − 1.052 E a/R. The apparent activation energy derived from the Flynn–Wall–Ozawa method is more reliable than that of the Friedman method owing to its integrating character exhibiting less sensitivity to noise than the Friedman method. The later, however, provides a better visual separation of more reaction steps as well as information concerning the existence of an autocatalytically activated process [38]. The advantage of nonisothermal method is that they do not require prior knowledge of the reaction mechanism in order to quantify kinetic parameters [39]. Pre-exponential factor (A) can be determined according to Eq. 4.

Kinetic models

The mechanism of nonisothermal curing kinetics for epoxy resins is based on nth-order and autocatalytic models [40]. In case of nth-order model, conversion rate is proportional to concentration of unreacted material. The reaction rate is dependent only on the amount of unreacted material remaining, and the reaction products are not involved in the reaction. On the other hand, autocatalyzed model assumes that at least one of the reaction products is involved in propagating reaction and characterized by maximum degree of conversion between 20 and 60%. To predict the cure kinetics over the whole range of conversion, the Friedman isoconversional method can be employed for nonisothermal dynamic DSC data.

For nth-order kinetics, the rate of the reaction can be expressed as:

$$\frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = A \left( {1 - \alpha } \right)^{{\text{n}}} {\text{e}}^{{ - {\text{E}}_{\text{a}} /{\text{RT}}}}$$
(13)

For autocatalyzed reaction, the rate of reaction can be expressed as

$$\frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = A \alpha^{{\text{m}}} \left( {1 - \alpha } \right)^{{\text{n}}} {\text e}^{{ - {\text{E}}_{\text{a}} /{\text{RT}}}}$$
(14)

where n and m are the orders of the two independent reactions. According to nth-order kinetic model, the maximum reaction rate will be observed at t = 0 and for autocatalytic model, the reaction rate is zero initially and attains the maximum value at some intermediate conversion.

Logarithmic forms of Eqs. 13 and 14 can be expressed as

$$\ln \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = \ln A - \frac{{E_{\text{a}} }}{RT} + n\ln \left( {1 - \alpha } \right)$$
(15)
$$\ln \frac{{{\text{d}}\alpha }}{{{\text{d}}t}} = \ln A - \frac{{E_{\text{a}} }}{RT} + n\ln \left( {1 - \alpha } \right) + m \ln \alpha$$
(16)

Equations 15 and 16 can be solved by multiple linear regression method. The dependent variable is ln dα/dt, and the independent variables are ln α, ln (1 − α) and 1/T. The values of A, m and n can be obtained using the average activation energy from Flynn–Wall–Ozawa method. The degree of curing is chosen between the beginning of the reaction and the maximum peak of degree of curing (α = 0.2–0.6).

Results and discussion

DSC curves of EAN, EAN-DDM, EAN-DDS and EAN-THPA at four different heating rates: 5, 10, 15 and 20 °C min−1 in nitrogen atmosphere are presented in Figs. 1–4, respectively. From Figs. 1–4, it is observed that melting and peak exotherms are shifted toward higher-temperature range with increasing heating rate. The onset of curing temperature (T o), peak maximum temperature (T p) and curing range is reported in Table 1. Heat of curing at each heating rate for each sample was determined by the measurement of area under exothermic peak (dH T) and is also reported in Table 1. From Table 1, it is observed that no systematic trend was observed for dH with increasing β.

Fig. 1
figure 1

DSC curves for EAN at 5, 10, 15 and 20 °C min−1 heating rates in nitrogen atmosphere

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Fig. 2
figure 2

DSC curves for EAN-DDM at 5, 10, 15 and 20 °C min−1 heating rates in nitrogen atmosphere

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Fig. 3
figure 3

DSC curves for EAN-DDS at 5, 10, 15 and 20 °C min−1 heating rates in nitrogen atmosphere

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Fig. 4
figure 4

DSC curves for EAN-THPA at 5, 10, 15 and 20 °C min−1 heating rates in nitrogen atmosphere

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Table 1 Dynamic DSC curing data of EAN, EAN-DDM, EAN-DDS and EAN-THPA at multiple heating rates
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In order to evaluate E a, DSC data were analyzed according to Kissinger (Eq. 5) and Ozawa (Eq. 7) methods from which it is observed that E a values derived according to Ozawa method are somewhat higher than that of the Kissinger method due to approximation made in Ozawa method. Kissinger and Ozawa plots of all the four samples are shown in Figs. 5 and 6, respectively. The values of E a were derived from the slopes and are shown in Table 2. Observed trend of E a is EAN-DDS > EAN > EAN-THPA > EAN-DDM due to different nature of matrix and hardeners. The low values of E a for EAN-DDM and EAN-THPA indicated flexible nature of cured resin, while high values of E a for EAN and EAN-DDS suggested rigid nature of the cured resin.

Fig. 5
figure 5

Kissinger plots for EAN, EAN-DDM, EAN-DDS and EAN-THPA

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Fig. 6
figure 6

Ozawa plots for EAN, EAN-DDM, EAN-DDS and EAN-THPA

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Table 2 Activation energies of EAN, EAN-DDM, EAN-DDS and EAN-THPA derived according to Kissinger and Ozawa methods
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In order to evaluate E a and A, DSC data were analyzed according to Flynn–Wall–Ozawa (Eq. 11) isoconversional method. For that various degrees of curing (α) for a given sample and for a given heating rate were evaluated by measuring total area (dH T) under the DSC curve and partial area (dH) at definite temperature. The degree of curing (α) is the ratio of dH to dH T. Degree of conversion against temperature plots for these samples at multiple heating rates are shown in Figs. 7–10 from which it is observed that in the beginning and toward the end of the curing reaction α−T correlation is nonlinear in accordance with epoxies studied by several investigators [12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]. Flynn–Wall–Ozawa isoconversional curves for EAN, EAN-DDM, EAN-DDS and EAN-THPA are shown in Figs. 11–14, respectively. Derived values of E a and A are presented in Tables 3–6 from which it is observed that both E a and A are decreased considerably with increasing degree of curing for EAN, EAN-DDM and EAN-DDS, while they increased slowly up to α = 0.3 and then decreased with increasing α values for EAN-THPA system. Observed trend in E a and A is EAN-DDS > EAN > EAN-THPA > EAN-DDM. For epoxy-amine systems, decrease in E a and A with increasing α is due to intermolecular cross-linking breaking resulting in increasing chain flexibility. Such behavior is also observed in epoxy-amine systems [22, 27, 41, 42]. Increasing values for E a and A for EAN-THPA systems (α < 0.4) indicated further cross-linking reaction of double bonds in THPA ring or thermal polymerization of allylic double bonds formed as a result of dehydration of secondary alcoholic groups. Thus, for epoxy-amine systems dependency of E a with α is observed, which suggested that curing mechanism is kinetically complex.

Fig. 7
figure 7

Plots of degree of conversion against temperature at 5, 10, 15 and 20 °C min−1 for EAN

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Fig. 8
figure 8

Plots of degree of conversion against temperature at 5, 10, 15 and 20 °C min−1 for EAN-DDM

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Fig. 9
figure 9

Plots of degree of conversion against temperature at 5, 10, 15 and 20 °C min−1 for EAN-DDS

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Fig. 10
figure 10

Plots of degree of conversion against temperature at 5, 10, 15 and 20 °C min−1 for EAN-THPA

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Fig. 11
figure 11

Flynn–Wall–Ozawa plots for EAN at various degrees of curing

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Fig. 12
figure 12

Flynn–Wall–Ozawa plots for EAN-DDM at various degrees of curing

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Fig. 13
figure 13

Flynn–Wall–Ozawa plots for EAN-DDS at various degrees of curing

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Fig. 14
figure 14

Flynn–Wall–Ozawa plots for EAN-THPA at various degrees of curing

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Table 3 Activation energies and pre-exponential factors derived for EAN according to Flynn–Wall–Ozawa method
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Table 4 Activation energies and pre-exponential factors derived for EAN-DDM according to Flynn–Wall–Ozawa method
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Table 5 Activation energies and pre-exponential factors derived for EAN-DDS according to Flynn–Wall–Ozawa method
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Table 6 Activation energies and pre-exponential factors derived for EAN-THPA according to Flynn–Wall–Ozawa method
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Friedman method is an important tool in understanding autocatalytic mechanism. DSC data for all the systems were analyzed by Friedman method (Eq. 16). The Friedman plots for EAN, EAN-DDM, EAN-DDS and EAN-THPA are shown in Figs. 15–18 from which it is observed that nonlinear increase in ln [A dα/dt] with ln (1 − α) for epoxy-amine systems and a maximum (α = 0.3) for EAN-THPA systems implied autocatalytic nature of the reaction kinetics. The values of n and m for EAN-THPA system are reported in Table 7 from which it is observed that nth and mth reaction orders are 1.34 and 0.34, respectively, i.e., they followed fractional-order curing kinetics.

Fig. 15
figure 15

Plots of ln [Af (α)] against ln(1 − α) for EAN at 5, 10, 15 and 20 °C min−1 heating rates

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Fig. 16
figure 16

Plots of ln [Af (α)] against ln(1 − α) for EAN-DDM at 5, 10, 15 and 20 °C min−1 heating rates

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Fig. 17
figure 17

Plots of ln [Af (α)] against ln(1 − α) for EAN-DDS at 5, 10, 15 and 20 °C min−1 heating rates

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Fig. 18
figure 18

Plots of ln [Af (α)] against ln(1 − α) for EAN-THPA at 5, 10, 15 and 20 °C min−1 heating rates

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Table 7 Order of the reactions derived according to Friedman’s method for EAN-THPA
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In order to confirm the validity of the kinetic model used, simulated conversion curves at multiple heating rates were constructed using obtained kinetic constants for EAN-THPA. Simulated conversion curves along with experimental curves at multiple heating rates are presented in Fig. 19 from which it is observed that the calculated and experimental curves are in good agreement between α = 0.2 and 0.6. At higher degree of conversion, i.e., after onset of vitrification, the observed deviation is probably due to change in curing mechanism (diffusion controlled) [43]. At lower degree of conversion, the observed deviation is due to slow rate of curing and then after catalytic effect led to agreement between calculated and experimental results. In case of EAN-DDM and EAN-DDS, peak maxima were not observed in ln [Af(α)] against ln (1 − α) curves, and therefore, simulation analysis was not performed.

Fig. 19
figure 19

Simulated conversion and experimental curves for EAN-THPA at 5, 10, 15 and 20 °C min−1 heating rates

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TGA curves of EAN, EAN-DDM, EAN-DDS and EAN-THPA at the heating rate 10 °C min−1 in nitrogen atmosphere are presented in Fig. 20 from which it is observed that EAN-DDM and EAN-DDS followed apparently single-step degradation, while EAN and EAN-THPA followed two-step degradation kinetics. Initial decomposition temperature T o, decomposition range, the  % mass loss involved and the  % residue remained at 700 °C are reported in Table 8. Observed thermal stability order of cured resin is EAN-DDS > EAN-DDM > EAN-THPA > EAN. A considerable amount of residue left at 700 °C (14.6–33.5%) confirmed the formation of highly cross-linked products. Degradation process of a polymer is a complex process and involves a variety of reactions, namely cross-linking, branching, rearrangement, etc. Ether, hydroxyl, ester/amide linkages are weak linkages in the cured resin, which degrade selectively to form new products which further degrade at elevated temperatures. Considerably higher residue at 700 °C confirmed the formation of highly cross-linked materials.

Fig. 20
figure 20

Plots of % mass against temperature for EAN, EAN-DDM, EAN-DDS and EAN-THPA at 10 °C min−1 heating rate under N2 atmosphere

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Table 8 TG data of EAN, EAN-DDS, EAN-DDM and EAN-THPA cured resins
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Conclusions

Dynamic DSC curing study was carried out to understand autocatalytic behavior of epoxy-amines and epoxy-anhydride systems. Flynn–Wall–Ozawa method showed E a and A order as EAN-DDS > EAN > EAN-THPA > EAN-DDM. Both E a and A decreased with increasing conversion in case of epoxy-amine systems. Friedman’s autocatalytic model showed autocatalytic behavior of resin-hardener systems. Simulated conversion and experimental curves are found in good agreement between α = 0.2–0.6 for EAN-THPA. Cured and uncured resins showed good thermal stability. Observed thermal stability order is EAN-DDS > EAN-DDM > EAN-THPA > EAN.