Thermochimica Acta 549 (2012) 69–80
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Curing of DGEBA epoxy using a phenol-terminated hyperbranched curing agent: Cure kinetics, gelation, and the TTT cure diagram Qi Li a , Xiaoyu Li b,∗ , Yan Meng a,∗∗ a b
Key Laboratory of Carbon Fiber and Functional Polymers, Ministry of Education, Beijing University of Chemical Technology, Beijing 100029, PR China State Key Laboratory of Organic and Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029, PR China
a r t i c l e
i n f o
Article history: Received 24 June 2012 Received in revised form 4 September 2012 Accepted 5 September 2012 Available online xxx Keywords: Cure kinetics Epoxy Time–temperature-transformation Hyperbranched Gelation Diffusion
a b s t r a c t The cure of diglycidyl ether of bisphenol A (DGEBA) epoxy with a novel phenol-terminated hyperbranched curing agent in stoichiometric ratio was studied comprehensively. The cure behavior was investigated using differential scanning calorimetry (DSC) in both isothermal and dynamic modes. The gelation times were determined by thermal mechanical analysis (TMA). Ramp cure data were analyzed by means of the Vyazovkin’s model free method. The isothermal cure data were analyzed using the Kamal model and the time–temperature-superposition (TTS) kinetic method. In spite of a high ultimate conversion, onset of diffusion control sets in well before vitrification. The effects of diffusion were incorporated into the overall kinetics expression using a diffusion factor. The gel conversion is found to be independent of cure temperature, and an effort has been made to compare the measured gel conversion with the theoretical prediction. In addition, the isothermal time–temperature-transformation (TTT) cure diagram was reported. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Epoxy materials are one of the most versatile thermosetting materials and have good mechanical properties, chemical resistance, and adhesive strength. In addition, free of volatile byproducts during cure and low cure shrinkage make them desirable for structural matrix materials [1,2]. Thus, epoxy materials are widely used in different applications, such as matrix materials, structural adhesives, and protective coatings [1,3]. In order to achieve desirable final properties, the cure kinetics and the changes in physical states during cure must be studied. Several factors can complicate the curing process and lead to different final properties. Cure schedules can not only affect the rate of reaction and the physical states during cure but also change the possible chemical reactions during cure. Gelation, vitrification, as well as possible phase separations, can contribute to the final morphology and properties of cured products. As a result, knowledge of cure kinetics and changes in physical states during cure is crucial for the control and optimization of final properties. In particular, the time–temperature-transformation (TTT) cure diagram [4–6] which summaries the changes in physical states during cure
∗ Corresponding author. Tel.: +86 10 64419631. ∗∗ Corresponding author. Tel.: +86 10 64419631; fax: +86 10 64452129. E-mail addresses:
[email protected] (X. Li),
[email protected] (Y. Meng). 0040-6031/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.tca.2012.09.012
can serve as a powerful tool for optimization. The majority of literature which covers both detailed curing kinetics expressions and TTT cure diagrams of epoxy systems are concerned with linear curing systems. To our knowledge, comprehensive and detailed study of epoxy systems containing hyperbranched reactants has only been explored by Santiago et al. [7] very recently. Dendrimers and hyperbranched polymers (HBPs) are highly branched molecules which have internal cavities and abundant terminal functional groups. The synthesis of monodispersed dendrimers requires cumbersome multiple-step synthesis, making them difficult to be commercialized. In contrast, polydispersed hyperbranched molecules are much easier and cheaper to produce in large quantities. Compared with their linear analogs of same molar mass, the semi-globular shape and ample terminal groups of hyperbranched molecules lead to lower solution viscosity, melt viscosity, and increased solubility [8], which are beneficial for processing. As a result, HBPs have found uses in various applications, such as surface coating [9–11] and drug delivery devices [12]. The abundant functional groups make HBP excellent crosslinking agents for epoxy [13–17] and other thermosetting systems [18–22]. Studies show that hyperbranched curing agents may not only increase crosslink density (if cured effectively) but also improve toughness [23,24]. However, the steric hindrance effects in hyperbranched molecules often lead to a reduced ultimate conversion especially when the primary amine is used as the curing agent [25]. In addition, the wide polydispersity in size [26],
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shape, molecular weight, reactivity [27], and functionality [28] of hyperbranched molecules may lead to different cure behaviors compared with linear curing systems. In order to elucidate the cure behaviors of hyperbranched curing systems, which has rarely been extensively explored, in this paper, a comprehensive cure kinetic study of the epoxy/phenol-terminated-HBP curing system was conducted. In addition, the gel conversion is measured and compared with the theoretical value predicted by Flory–Stockmayer theory [29]. 2. Theoretical background 2.1. Gelation, vitrification and TTT diagram Aside from the cure kinetics, the TTT cure diagram has been proven to be a powerful tool for optimizing the cure process. Central to the TTT diagram are three important temperatures and two lines. The three temperatures are Tg of the ‘uncured’ resin mixture (Tg0 ), the temperature at which gelation and vitrification coincide (gel Tg ), and Tg of the fully (or ultimately) cured resin (Tg∞ ); the two lines are the gelation line and the vitrification line, which require the determination of the gelation time (tgel ) and vitrification time (tvit ) at different cure temperatures (Tc ). The gelation point corresponds to the irreversibly transform from soluble reactants into a three-dimensional, infusible, and insoluble network. After gelation, the curing system loses its ability to flow which may lead to the development of residual stresses [30]. According to the theory of gelation developed by Flory and Stockmayer, assuming equal reactivity and absence of intramolecular reaction, the extent of reaction (or conversion for convenience) at gelation is a fixed value and independent of cure schemes [29]. For curing systems which are composed of nearly monodispersed reactants, the number-average functionalities are used to calculate the theoretical gel conversion (˛gel ). However, for a reacting system involving polydispersed reactants, such as our hyperbranched curing system, ˛gel should be estimated using the weight-average functionalities of the reactants [31,32]: 1 (1) ˛gel = r(fw,A − 1)(fw,B − 1)
where fw,A and fw,B (fw,i = f 2 Ni / i fi Ni ) are weight-average i i functionalities of reactants A and B, respectively, r (≤1) is the ratio of the total functional groups of A to the total functional groups of B. Vitrification is defined as the point when Tg of the reacting system increases to Tc [33]. After vitrification, the rate of reaction usually slows down, and the reaction changes from a chemically controlled stage to a diffusion-controlled stage. In addition, physical aging which is associated with vitrification may lead to a further slow-down of the reaction [34] and inaccurate interpretation of the apparent heat of reaction [35]. 2.2. Cure kinetics Among the various techniques, DSC remains the most popular technique for the determination of cure kinetics, due to the ease of operation and the wide available temperature range. Both isothermal and ramp (or dynamic) cure methods have limitations, thus, a combination of both methods is often needed in order to obtain more reliable cure kinetics. Aside from the mechanistic model which requires details of reaction mechanisms, three ways are often used to analyze the cure data, i.e., the model-fitting kinetics which requires a known kinetic expression, the model-free kinetics (MFK) which is based on isoconversional analysis and the time–temperature-superposition (TTS) kinetics. A brief account of the three methods of analysis is given below.
2.2.1. Model fitting methods The rate of cure reaction could be expressed as the product of a temperature term k(T), which often follows the Arrhenius dependence, and f(˛) which is a function of conversion, ˛ d˛ = k(T ) × f (˛) = A exp dt
−E a
RT
× f (˛)
(2)
where A is the pre-exponential factor, Ea is the apparent activation energy, and R is the universal gas constant. Although various kinetics models have been proposed, for the case of epoxy curing systems, the semi-empirical Kamal model [36] is the most widely used d˛ = (k1 + k2 ˛m )(1 − ˛)n dt
(3)
where k1 and k2 are rate constants for the uncatalyzed and catalyzed reactions, respectively, and m and n are reaction orders. 2.2.2. Model free kinetics methods The MFK methods do not assume any kinetic models in data analysis. Instead, they assume that the activation energy during cure only depends on conversion. Rearranging Eq. (2) yields
d˛ A Ea (˛) = exp − f (˛) RT dt ˇ
(4)
where ˇ (=dT/dt) is the rate of temperature change, Ea (˛) is the conversion-dependent apparent activation energy. Eq. (4) does not have an exact analytical solution, thus numerous approximations have been proposed either in the differential forms or in the integral forms [37]. Recently, an improved and more advanced version, the Vyazovkin’s integral isoconversional method (VA method) [38–40] has been proposed, which offers a better way of interpreting data, especially for complex systems. The VA method can also reduce the coupling errors of different parameters and yield more reliable Ea . Ea (˛) can be determined by numerically evaluating the minimum of the following integral based on the isoconversional principle ˚(Ea ) =
n n I(Ea (˛), T˛,i )ˇj i=1 j = / i
(5)
I(Ea (˛), T˛,j )ˇi
where the temperature integral I(Ea , T) is given by
t˛
I[Ea (˛), T (t˛ )] =
exp t˛−˛
−E (˛) a RT (t)
dt
(6)
The details of the evaluation process can be found elsewhere [41]. In addition, the VA method could yield consistent Ea (˛) values from both ramp cure and isothermal cure and even provide information about the changes in cure mechanisms. 2.2.3. TTS kinetics methods If the change in the apparent activation energy is negligible, the TTS kinetics method provides another way of describing the cure kinetics. In the absence of diffusion control, for a given Tc , the evolution of ˛ can be obtained from the master curve and relationship between Tg and ˛. In order to obtain the conversion-time (˛ ∼ t) relationship, curing reactions are quenched at different cure stages and reheated at a constant heating rate to obtain both Tg of the curing system and the residual heat of reaction, Hres (t), from which the fractional conversion ˛(t) can be calculated ˛(t) = 1 −
Hres (t) Htotal
(7)
where Htotal is the total or ultimate heat of reaction. In most curing systems, one-to-one relationships between Tg and ˛ are often
Q. Li et al. / Thermochimica Acta 549 (2012) 69–80
found. Among the several relationships which relate Tg to ˛ [42,43], the DiBenedetto equation [44] is the most popular choice: Tg (˛) = Tg0 +
˛(Tg∞ − Tg0 ) 1 − (1 − )˛
(8)
where is an adjustable fitting parameter. In order to construct the TTS kinetics master curve, Tg vs. logarithmic time (Tg ∼ ln (t)) curves obtained at different Tc are shifted horizontally with respect to a reference temperature (Tref ). Detailed explanations have been provided by Gillham [45], and a brief derivation is given below. Manipulating Eq. (2) and assuming that one-to-one relationship between Tg and ˛ holds yield
˛
ln 0
d˛ f (˛)
≡ F(Tg ) = ln k(T ) + ln (t)
(9)
If the one-to-one relationship between Tg and ˛ holds, all Tg ∼ ln (t) curves obtained at different Tc can be superposed by shifting horizontally with respect to Tref . The amount of the shift, i.e., the shift factor A(T), is the difference in ln (t) at a constant Tg or ˛ A(T ) = ln(tref ) − ln(tT ) = −
Ea
TTS
R
1 T
−
1 Tref
(10)
2.2.4. Effects of diffusion on cure kinetics In the absence of diffusion control, the Kamal model and the TTS kinetics can provide adequate description of the cure kinetics. However, in the later stages of cure, especially after vitrification, diffusion control may dominate the cure kinetics. In order to incorporate the effects of diffusion on cure kinetics, several ways have been proposed. One way is to invoke the Rabinowitch concept [46], which defines the overall rate constants k1 and k2 in Eq. (3) as a function of the chemically controlled rate constant (kc ) and the diffusion term (kd ) 1 1 1 = + ki kc kd
(11)
where i = 1 and 2. The diffusion term can assume either the modified WLF form [45] or modified Doolittle free volume form [47]. Another way of incorporating the effects of diffusion is to define a diffusion factor (fd ) [48] which equals to the ratio of the measured rate of reaction to the chemically controlled rate of reaction (i.e., in the absence of diffusion). Thus, the overall kinetic expression in form of Eq. (3) can be expressed as d˛ = (k1 + k2 ˛m )(1 − ˛)n fd (˛) dt
(12)
A commonly used expression for fd , which was originally proposed by Chern and Poehlein [49], has the final form [30] of fd (˛) =
1 1 + exp[C(˛ − ˛c )]
(13)
where C and ˛c are temperature-dependent fitting parameters. When ˛ is much lower than the critical conversion ˛c , fd (˛) approaches unity and the effects of diffusion are negligible. However, when ˛ approaches ˛c , fd (˛) decreases and eventually vanishes with further increase in conversion. 3. Experimental 3.1. Materials The diglycidyl ether of bisphenol-A type epoxy, CYD-128, was purchased from Baling Petrochemical Co. Ltd. (China). It has an epoxy equivalent weight of 196 g/eq according to the manufacturer and was used as received. The accelerator 2–ethyl-4-methylimidazole (2E4MI), (99% purity) was purchased from J&K Chemical
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Co. Ltd. and was used as received. The curing agent, the phenolterminated hyperbranched poly(phenylene oxide)s (HPPO), was synthesized in our lab, and the details can be found elsewhere [50]. A schematic drawing of the structure of HPPO is shown in Fig. 1. The number of terminal phenolic group of HPPOs was determined by titration using a Metrohm 848 Titrino plus automatic potentiometric titrator with phenolphthalein as the indicator [51]. Titration results show that every gram of HPPO contains 0.00371 mol of phenolic groups. The molecular weight of HPPO was determined using a Malvern Viscotek GPCmax +270 multi-detector system, in which the reflective index (RI) detector, multi-angle laser light scattering (MALS) detector, and an online viscosity (VIS) detector are coupled to the size exclusion chromatography (SEC) column. Tetrahydrofuran (THF) was used as the solvent in the determination of molecular weights. The number- and weight-average molecular weights are found to be 917 and 2940, respectively. 3.2. Sample preparation and storage The DGEBA epoxy was mixed with stoichiometric amount of HPPO at room temperature in a 50 ml beaker under mechanical stirring; a homogeneous solution is formed after 10 min. Based on the weight of DGEBA, 1 wt% accelerator, 2E4MI, was added into the mixture under mechanical stirring. After another 5 min, the accelerator dissolves completely. The resultant mixture was then degassed for 10 min in a vacuum oven. The degassed mixture was weighted and sealed into separate 40 l standard aluminum DSC pans (crucibles) with sample sizes of approximately 5 mg each. The sealed pans were sealed in zipped plastic bags and stored in a freezer which is set to −25 ◦ C before use. 3.3. Instruments and experimental techniques Both ramp cure and isothermal cure measurements were performed using a DSC-1 DSC (Mettler-Toledo, Switzerland) which is equipped with an intra-cooler under a dry nitrogen atmosphere (50 ml/min). The temperature and enthalpy were calibrated using indium and zinc standards following the manufacturer’s instruction. Before loading sample pans in the DSC, the following procedure is followed to prevent possible moisture condensation. Before the sample pans were taken out form the sealed zipper bags, they were allowed to warm up at room temperature for at least 20 min to avoid possible moisture condensation. The gelation time (tgel ) was determined using a TMA/SDTA841e thermal mechanical analyzer (Mettler-Toledo, Switzerland) which is equipped with a liquid nitrogen cooling system. The temperature, displacement, and force were calibrated with high purity indium and zinc standards, gauge blocks, and weight standards, respectively, following the manufacturer’s instruction. The procedure for the determination of gelation time during isothermal cures is as follows. The furnace of TMA was first equilibrated at the desired isothermal cure temperature. As soon as the furnace was opened, the mixture of the uncured reactants was quickly spread onto the quartz sample support. The furnace was then closed, and the already-started temperature control program will bring the sample to the programmed cure temperature. A periodic force (cycle time = 12 s) of ±0.03 N was automatically applied to the sample [52,53] by a quartz probe. Before gelation, the probe can move freely. Approaching gelation, the probe sticks to the sample and can no longer move freely. As a result, a sudden decrease in the amplitude of the oscillations is observed. The points when the upward movements diminish are taken to be gelation points. The validation of this method is
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Fig. 1. The chemical structures of hyperbranched curing agent (HPPO) and the tetrafunctional counterpart of the HPPO. The weight-average molecular weights of HPPO are found to be 917 and 2940.
illustrated in Section 4.3. After the measurements, samples were burned off with a small flame and the residues brushed away after cooling. 4. Results and discussion 4.1. Determination of Htotal and the MFK analysis of ramp cure measurements The heat of reaction can be obtained by integrating the area between the exothermic peak and the baseline. In this study, the baseline is assumed to be a straight line connecting the beginning and the end points of the exothermic peaks, which are shown as dashed lines in Fig. 2. The total heat of reaction, Htotal , was taken to be the average value from ramp cures at five different heating rates, namely 1, 2, 5, 10 and 15 K/min, from −50 to 250 ◦ C as shown in Fig. 2. As expected, higher heating rates lead to higher peak temperatures and broader peaks. At a heating rate of 15 K/min, signs of thermal degradation are observed at around 245 ◦ C, thus, the maximum heating rate is limited to 15 K/min. All curves show similar features: as temperature increases, the curing system first passes its Tg0 (shown as a step change in heat capacity) and then begins to react (shown as exothermic peaks). After ramp cures, samples
were quenched and reheated at 10 K/min. If Hres is not observed in the second heating run (post cure), the obtained Tg can be taken as Tg∞ . In post cure, no residual heats of reaction were detected. As an example, the second heating run after ramp cure at 10 K/min is also shown in Fig. 2. The values of Tg0 , Tg∞ , and Htotal from the first and post cure scans are reported in Table 1. Tg of cured materials depends on the chemical structure, extent of cure, and heating rates. Because Tg depends on heating rates, the small differences in Tg0 values obtained at different heating rates are insignificant, indicating a consistent initial composition for different samples. The Tg0 value obtained at 10 K/min is −16.5 ◦ C. Tg∞ obtained are very close, indicating that the final structures are not
Table 1 The glass transition temperatures and the heats of reaction at different heating rates. ˇ (K/min)
Tg0 (◦ C)
Htotal (J/g)
Tg∞ (◦ C)
1 2 5 10 15
−18.7 −18.2 −17.8 −16.5 −14.7
204.0 201.2 217.9 216.2 192.1
129.7 128.4 132.7 128.8 129.6
206.3 ± 10.8
129.8 ± 1.7
Average
Q. Li et al. / Thermochimica Acta 549 (2012) 69–80
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Fig. 2. The DSC traces of ramp cures at different heating rates and the 2nd heating scan (at 10 K/min) after ramp cure at 10 K/min.
Fig. 4. Measured conversion (symbols) as a function of time at indicated cure temperatures. Solid curves are the isothermal predictions from the VA method (without diffusion control). Arrows mark the deviation points.
sensitive to the heating rates. The average value of Tg∞ is 129.8 ◦ C. The Htotal value is found to be 206.3 ± 10.8 J/g or 96 ± 5 kJ/mol of epoxide group. This value is slightly higher than the literature value (Htotal = 86.7 kJ/mol) [54–56], suggesting that the phenolic groups in HPPO can react effectively with all epoxide groups. We note that in other curing system which is composed of an epoxy-terminated hyperbranched polymer (based on BoltornTM series) and diamine, a low ultimate conversion was reported due to strong steric hindrance [25]. The high ultimate conversion in our curing system could be attributed to the relatively lower functionalities (compared to other hyperbranched polymers, such as BoltornTM series) and the stiffer backbones which make the terminal phenol groups more accessible to epoxide groups. In ramp cure experiments, the fractional conversion up to a certain time, ˛(t), can be calculated as
reach a given conversion, higher temperature is needed at higher heating rates. If the abscissa is changed from temperature to time, the rate of reaction can be calculated from the 1st derivative of the ˛(t) vs. time (t) curve. Compared with the isothermal cure method, the ramp cure (or dynamic cure) method is easier and faster and can cover a wider temperature range. However, the coupling of time and temperature often makes data analysis more challenging. The advanced MFK developed by Vyazovkin (VA method) offers a better way to analyze ramp cure data as described in the theoretical section. Thus, the VA method was used to analyze the ramp cure data. The calculation is realized using the MFK package in the STARe software from MettlerToledo. The conversion-dependent apparent activation energy curve Ea (˛) in the range of 0.1 ≤ ˛ ≤ 0.9 is roughly a constant value of approximately 76 ± 2 kJ/mol, which is similar to literature values [57–63]. The isothermal predictions from the VA method is shown in Fig. 4 as the solid curves.
˛(t) =
H(t) Htotal
(14)
where H(t) is the heat released up to time (t). The variation of ˛(t) with temperature at different heating rates is shown in Fig. 3. From left to right (along the direct of the arrow), the curves correspond to a heating rate of 1, 2, 5, 10, and 15 K/min, respectively. In order to
Fig. 3. Fractional conversion as a function of the temperature. From left to right along the direction of the arrow, the heating rates are 1, 2, 5, 10, and 15 K/min, respectively.
4.2. Analysis of the isothermal cure data For isothermal measurements, the choice of proper cure temperatures is crucial for obtaining reliable data. At very high temperatures, an appreciable amount of heat is lost during the initial stabilization period; whereas at very low temperatures, the cure time is too long, and the heat released may be too small to be recorded accurately. The suitable isothermal cure temperatures were found to be 60, 80, 100, 120 and 140 ◦ C. Two isothermal methods [54] can be used: (1) load samples at room temperature then heat the sample very quickly to Tc ; (2) preheat the furnace to the Tc , place the sample in the furnace, and start the experiments. In our experiments, the second method was used. After curing isothermally at Tc for different predetermined length of times, ranging from 5 min to 40 h, samples were quenched to the room temperature and subjected to a second scan from −50 ◦ C to 250 ◦ C at 10 K/min to obtain the Tg of the curing system (after curing at Tc for a predetermined time) and the residual heat of reaction (Hres ). Tg was taken as the mid-point of the step change in heat capacity. For the cure measurements longer than 4 h, sealed samples were cured in an oven. After curing in the oven for predetermined time (4 h up to 40 h), the samples were taken out from the oven and transferred to the DSC furnace. The samples were then quenched to −50 ◦ C and reheated at 10 K/min. In order to justify this procedure, the Tg and Hres values obtained samples
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Q. Li et al. / Thermochimica Acta 549 (2012) 69–80
Fig. 5. The second heating runs (post cures) at 10 K/min for samples cured isothermal 80 ◦ C for different times.
which are cured both in the oven and in the DSC for a period of 4 h were compared; and no appreciable difference was found. Thus, for long cure times (>4 h), samples cured in the oven is not different from those cured in the DSC. The second heating scans for samples cured at 80 ◦ C for different cure times are shown in Fig. 5. From top to bottom, the cure time increases as indicated. The curves obtained at other Tc are similar to those obtained at 80 ◦ C and are thus not shown. The conversion (after curing at 80 ◦ C for time t) can be calculated using Eq. (7). As expected, both Tg and ˛ increase monotonically with time. The variations of Tg with ˛ at different cure temperatures are shown in Fig. 6 as symbols. For clarity, not all data points are shown in Fig. 6. In spite of some scattering, the Tg values obtained at different temperatures can collapse into one master curve, indicating that Tg is a unique function of ˛ and does not depend on Tc . In addition, Tg becomes more sensitive to the changes in ˛ at higher conversion, which is typical for thermosetting systems. The relationship between Tg and ˛ can be fitted into the DiBenedetto equation (Eq. (8)), and the fitting parameter is found to be 0.484. The solid curve in Fig. 6 represents the fitting result, which agrees well with experimental data. After obtaining the relationship between Tg and ˛, both variations in Tc and Tg during ramp cures can be obtained as a function of cure time. At all heating rates, Tg is found to be always lower than
Fig. 7. Tg (symbols) as a function of ln (t) at different cure temperatures. The symbols represent experimental data, and the solid curves are trend lines.
Fig. 8. The master curve of Tg vs. ln (t) with respect to 100 ◦ C. The solid curve is drawn to aid the eyes.
Tc . Thus, no vitrification occurs during ramp cures, which means that isothermal prediction (in Section 4.2.1) from the VA method is unlikely to contain the effects of diffusion. 4.2.1. TTS kinetics from isothermal cure data The glass transition temperatures as a function of time at different Tc are shown in Fig. 7. When Tc is low (
