Thermochimica Acta 547 (2012) 53–61
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Thermal degradation kinetics of poly(trimethylol propane triacrylate)/poly(hexane diol diacrylate) interpenetrating polymer network Ankur Goswami a , Geetika Srivastava a , A.M. Umarji a , Giridhar Madras b,∗ a b
Materials Research Centre, Indian Institute of Science, Bangalore 560012, India Department of Chemical Engineering, Indian Institute of Science, Bangalore 560012, India
a r t i c l e
i n f o
Article history: Received 24 March 2012 Received in revised form 5 August 2012 Accepted 7 August 2012 Available online 16 August 2012 Keywords: Thermogravimetric analysis Kinetic parameters Interpenetrating polymer network Degradation Model-free method Microstereolithography
a b s t r a c t Interpenetrating polymer networks (IPNs) of trimethylol propane triacrylate (TMPTA) and 1,6-hexane diol diacrylate (HDDA) at different weight ratios were synthesized. Temperature modulated differential scanning calorimetry (TMDSC) was used to determine whether the formation resulted in a copolymer or interpenetrating polymer network (IPN). These polymers are used as binders for microstereolithography (MSL) based ceramic microfabrication. The kinetics of thermal degradation of these polymers are important to optimize the debinding process for fabricating 3D shaped ceramic objects by MSL based rapid prototyping technique. Therefore, thermal and thermo-oxidative degradation of these IPNs have been studied by dynamic and isothermal thermogravimetry (TGA). Non-isothermal model-free kinetic methods have been adopted (isoconversional differential and KAS) to calculate the apparent activation energy (Ea ) as a function of conversion (˛) in N2 and air. The degradation of these polymers in N2 atmosphere occurs via two mechanisms. Chain end scission plays a dominant role at lower temperature while the kinetics is governed by random chain scission at higher temperature. Oxidative degradation shows multiple degradation steps having higher activation energy than in N2 . Isothermal degradation was also carried out to predict the reaction model which is found to be decelerating. It was shown that the degradation of PTMPTA follows a contracting sphere reaction model in N2 . However, as the HDDA content increases in the IPNs, the degradation reaction follows Avrami–Erofeev model and diffusion governed mechanisms. The intermediate IPN compositions show both type of mechanism. Based on the above study, debinding strategy for MSL based microfabricated ceramic structure has been proposed. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Microstereolithography (MSL) is an emerging rapid prototyping technique by which complex three dimensional micro-objects can be fabricated from a predeﬁned Computer Aided Design (CAD). Multifunctional acrylates have been used extensively in MSL based rapid prototyping technique for their extremely high reactivity under UV exposure . This process involves a UV laser, which is focused on a motorized stage that moves in the X–Y–Z direction based on a predeﬁned CAD algorithm [2,3]. A liquid multifunctional acrylate or epoxy monomer is kept on the top of X–Y–Z stage and subsequently polymerization takes place depending on the selective exposure of the UV laser. 1,6-Hexane diol diacrylate (HDDA) rapidly photopolymerizes under UV exposure and therefore, has been extensively used for applications such as the fabrication of microgear, microcantilever
∗ Corresponding author. Tel.: +91 80 22932321; fax: +91 80 22932321. E-mail addresses: [email protected]
, [email protected]
(G. Madras). 0040-6031/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.tca.2012.08.006
and microturbine [3–5]. Although the thermal and mechanical properties of PHDDA have been discussed earlier [6,7], no signiﬁcant attempts have been made with trimethylol propane triacrylate (TMPTA). Since TMPTA is a highly viscous monomer ( = 100 mPa s at 25 ◦ C) as compared to HDDA ( = 9 mPa s at 25 ◦ C) , it is not experimentally conducive for these applications. Nevertheless, the rate of photopolymerization (Rp ) of the former (110 s−1 ) is much faster than the latter (25 s−1 ) due to its extra unsaturated acrylate functional group . In order to optimize the thermal and mechanical properties, considerable effort is being made by blending these two monomers and to polymerize them under UV. Both of the monomers are multifunctional and consist of more than one unsaturated double bond. Therefore, both can crosslink under UV irradiation and form an interpenetrating polymer network (IPN) . Despite the prospect of these polymers for the above mentioned applications, the thermal and mechanical aspects of these respective IPNs have not been investigated. Further, in order to fabricate ceramic micro-objects by this technique, ceramic particles have to be suspended in the desired monomer with appropriate solvent, dispersant and plasticizers [3,11]. As the laser is focused on the suspension of the monomer,
A. Goswami et al. / Thermochimica Acta 547 (2012) 53–61
polymerization occurs, which results in binding the green ceramic body. After the net shape is obtained, it is important to remove the organic from the ceramic–polymer matrix without any shape deformation before reaching the sintering temperature. The uncontrolled removal of polymer during binder burn off can lead to different defects e.g. microcracks, hotspot, delamination, etc. Therefore, it is important to understand the kinetics of degradation of these IPNs under thermally activated process at different environmental conditions (either inert or oxidative). The decomposition of polymeric materials has been widely characterized by thermogravimetric technique. Numerous kinetic methods (e.g. Friedman, Chang, Chatterjee-Conrad, Flynn, Kissinger, Freeman-Carroll, and Horowitz-Metzger) have been developed in order to determine the kinetic triplet of a reaction (i.e. apparent activation energy (Ea ), reaction order (n) and collision factor (Z)) depending upon the experimental conditions (isothermal or non-isothermal) involved in the thermal analysis [12–14]. Non-isothermal methods are more popular and authentic in the case of determining kinetic parameters. Further, the International Confederation for Thermal Analysis and Calorimetry (ICTAC) has suggested to avoid the non-isothermal single heating rate kinetic methods because of the limitations pertained in the presumption of the kinetic model . It has been recommended to adopt non-isothermal multiple heating rate methods for the computation of reliable kinetic parameters where no assumption of kinetic model is required. Brief analyses of the adopted kinetic methods in this work have been dealt in Section 3. In this report, the thermal stability and thermokinetic parameters of different compositions of TMPTA–HDDA IPNs have been investigated by “model free kinetic methods” using multiple heating rate programs. The thermokinetic parameters are analyzed and reported both in N2 and air by the above kinetic methods using nonisothermal conditions. Isothermal conditions are adopted to predict the reaction model of the degradation mechanism of these polymers. Further, their application in choosing the conditions (such as heating rate and environment) in binder removal kinetics are also discussed. 2. Experimental 2.1. Materials The monomers 1,6-HDDA (80%), TMPTA and the photoinitiator, 2,2-dimethyl 2 phenyl acetophenone (DMPA) (99%) were obtained from Sigma–Aldrich, USA. The monomers possess the following molecular structure as shown in Scheme 1. Both the monomers were puriﬁed by washing with 5 mol l−1 NaOH solution (maintaining a (1:3) volume ratio of monomer to caustic soda) followed by washing with deionized water, in order to make the monomers free from inhibitor. The monomers were dried over MgSO4 and stored in dark at 0 ◦ C. The composition of HDDA in TMPTA monomer was varied from 0 to 80 wt%. The codes given to the samples are PTMPTA, TH8020, TH5050, TH2080 and PHDDA based on the composition as shown in Table 1. 1 g l−1 photoinitiator was mixed with all the compositions of monomer at 25 ◦ C. 2.2. Photopolymerization An in-house built UV photochemical reactor was used and all the mixtures were kept together for bulk polymerization for 30 min at an equal distance from the UV source. A jacketed quartz tube with inner and outer diameter of 3.4 cm and 4 cm was used. The reactor was 20 cm length, and housed a high pressure 125 W mercury vapor lamp (Phillips, India). Cold water circulation through the jacketed quartz tube was maintained to ensure the temperature at 35 ◦ C.
The lamp radiates predominantly at 365 nm (3.4 eV). The photon ﬂux of the lamp measured by UV light meter probe (Digital Instruments) was 40 W m−2 . The semisolid polymers were the product of photopolymerization reaction and were thoroughly washed in isopropanol and kept in the hot plate at 100 ◦ C for 10 h in order to remove the unconverted monomer oligomers and solvents. The degradation of copolymer compositions was studied by thermal analysis in N2 and air. 2.3. TG/DTA and TMDSC The thermogravimetric measurements were carried out in SDT Q600 (TA Instrument Inc.). TG/DTA experiments have been carried out for all the samples (PTMPTA, TH8020, TH5050, TH2080, and PHDDA) in N2 and air gas ﬂow with varying heating rates 2, 5, 10, 15, 20, 25 ◦ C min−1 . The sample weight was taken around 10 ± 2 mg. The isothermal TG analyses of all the polymers are performed at 400 ◦ C both in N2 and air. The temperature was raised to the respective isothermal temperature at 100 ◦ C min−1 heating rate in order to avoid the weight loss during this period. In all the cases the ﬂow rate of the gas was kept at 100 ml min−1 . Temperature modulated DSC (TMDSC) was carried out to determine the glass transition and the curing behavior of these polymers. In TMDSC, a small periodic perturbation in heating rate can be used to probe glass transition and curing in a single run. By this technique, the total heat ﬂow signal can be separated in reversing and non-reversing heat ﬂow and thus separate the thermodynamic (reversing heat ﬂow) and kinetic events (non-reversing heat ﬂow). TMDSC was carried out using Q100 DSC (TA Instrument Inc.) and the amount of samples used was in the range of 10 ± 2 mg. All the ﬁve samples were equilibrated at −20 ◦ C and heated up to 280 ◦ C at an underlying heating rate (q0 ) of 1 ◦ C min−1 with modulation amplitude (Aq ) of ±2 ◦ C for every 80 s. Liquid nitrogen was used to keep the ﬂange temperature of the DSC cell at −175 ◦ C. The gas ﬂow rate of N2 was maintained at 50 cm3 min−1 . The heat–cool–heat cycle was repeated for all the runs of TMDSC. In all the experiments, hermetic sealed aluminum pans with the pinholes were used for the gases to evolve. The heat ﬂow rate and heat capacity calibration were carried out by running a standard sapphire followed by indium standard over a wide range of temperature (−50 to 400 ◦ C). The determined heat capacities were compared with the literature value to obtain the calibration constant. 3. Methods for kinetic studies by thermal degradation The kinetics of heterogeneous condensed phase reactions can be modeled by deﬁning a function f (˛). It designates the degree of reaction or fractional conversion at any time t and is given by ˛=
x0 − xt x0 − xf
where xt is the measured value for extensive variables (e.g. mass, volume, enthalpy, etc.) at any given time t, x0 and xf are the initial and ﬁnal values at the start and the end of the reaction . The rate of a reaction can be described by differential form as shown in Eq. (2) d˛ = f (˛)k(T ) dt
The integrated form of the reaction model is given by the following Eq. (3)
g(˛) = 0
d˛ = f (˛)
k(T ) dt
The function f (˛) and g(˛) govern the model of the reaction which can have various mathematical forms depending upon the
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Scheme 1. Table 1 Comparative degradation temperatures of the polymers in (a) N2 and (b) air. Compositions
wt% HDDA feed in the (TMPTA–HDDA) IPN
Char yield (550 ◦ C) (%)
(a) PTMPTA TH8020 TH5050 TH2080 PHDDA (b) PTMPTA TH8020 TH5050 TH2080 PHDDA
0 20 50 80 100 0 20 50 80 100
426.8 410.0 403.9 399.1 383.3 372.6 347.8 366.2 375.9 364.2
447.5 438.8 424.9 415.2 402.3 419.8 397.7 405.4 406.4 394.3
464 460.8 453.1 433.9 417.7 453.5 448.1 447.2 429.0 415.5
476.8 475.0 470.7 460.7 431.7 467.7 468.0 465.5 453.9 429.5
4.5 6.4 4.0 3.8 Trace 0.93 2.2 2.5 1.7 1.40
mechanism involved in the reaction pathway. Some of these pathways are summarized by Vyazovkin et al. and it has been recommended to use multiple heating rates to obtain the kinetic data . Most of the reaction models that exist in literature are speciﬁc to the solid state reaction only. A brief discussion on the choice of reaction model will be dealt in Section 3.2. The temperature dependent parameter, k(T ) can be expressed by the following Arrhenius equation: k(T ) = Z exp
in which Z and Ea represent the collision or frequency factor and the apparent activation energy of the reaction, respectively. Therefore, Eq. (2) can be expressed as d˛ = Z exp dt
The kinetics of thermal degradation has been extensively studied by dynamic and isothermal thermogravimetry and is most commonly modeled by Eq. (5). The thermogravimetric data obtained by thermal degradation in different atmosphere (N2 and air) have been analyzed by using model-free kinetic methods based on multiple heating rates and are discussed in the following section.
3.1.1. Differential isoconversional methods The assumption for all isoconversional methods is that the reaction rate is only a function of temperature at constant extent of conversion. Eq. (6) is obtained by taking logarithmic derivative of Eq. (2) at constant ˛ with subsequent algebraic operations .
∂ ln(d˛/dt) ∂(1/T )
(Ea )˛ R
where (Ea )˛ is the apparent activation energy at different conversion (˛). Therefore, Eq. (6) can be used to estimate the activation energy of any thermally activated reaction with the function of conversion (˛) without assuming any particular reaction model and thus these termed as model-free methods. Further, the uncertainty in estimating Arrhenius parameter is avoided in the isoconversional method compared to the model ﬁtting method where kinetic models are assumed . 3.1.2. Integral isoconversional methods The other way of determining the activation energies can be accomplished by the integral form of the isoconversional method such as Ozawa and Kissinger–Akahira–Sunose (KAS) [19–21]. Compared to the former, the latter method shows signiﬁcant accuracy in determining Ea . Eq. (7) is obtained by substituting k(T ) from Eq. (4) in Eq. (3) followed by subsequent Doyle’s approximation ,
3.1. Model free methods ln There are two main isoconversional methods described in the literature depending on their approaches of solution i.e. differential and integral methods. The formulation and advantages of these methods are critically reviewed elsewhere . However, a brief discussion is as follows.
f (˛) −
(Ea )˛ RT˛
where ˇi (= dT/dt) is heating rate used during thermal analysis. The subscript i denotes various temperature programs at which TGA is performed. This method is named as KAS method.
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3.2. Determination of reaction model from model ﬁtting and model free analyses It is equally important to know the reaction model of any kinetic process apart from the activation energy. Even though several reaction models are discussed in the literature, they all can be reduced to three major types of models i.e. accelerating, decelerating and sigmoidal (or autocatalytic) . All the individual type has the characteristic reaction proﬁle and can be expressed as ˛ (or d˛/dt) vs. t (or T). The isothermal method is one way to estimate the reaction model roughly since at isothermal condition k(T ) will be constant in Eq. (2) and the kinetic curve can be determined by the reaction model only. The isothermal kinetic proﬁle of the above reaction models which are governed by the following equations : Accelerating model : f (˛) = n˛(n−1)/n Decelerating model : f (˛) = (1 − ˛)
Sigmoidal model : f (˛) = n(1 − ˛)[− ln(1 − ˛)]
Therefore, in order to analyze any reaction model, it is required to perform an isothermal experiment in addition to experiments at constant heating rate (non-isothermal). However, an appropriate method can be chosen based on plotting ln(1 − ˛) or ln(d˛/dt) vs. t of the isothermal data . If the plot is linear then the sample follows ﬁrst order kinetics whereas the reaction model follows contracting sphere/cylinder model (R2 and R3) if the plot is concave downwards. On the other hand, if the plot becomes concave upwards, the reaction is increasing diffusion resistance (D2/D3). However if the plot shows a maxima, then the reaction follows the Avrami–Erofeev (A2/A3) model . The other method to determine the reaction model is to plot the master curve of y(˛) vs. ˛ and z(˛) vs. ˛ where KAS isoconversional method is used to determine (Ea )˛ . In order to plot y(˛) vs. ˛, master plot the average E0 is chosen from all the E˛ and substituted in the following Eq. (11) to determine the function y(˛). y(˛) =
E 0 RT˛
The z(˛) master plots are obtained by multiplying the differential and integral form of the reaction models and shows the following form. z(˛) = f (˛)g(˛) =
One can determine the characteristic kinetic model depending on the variation of y(˛) and z(˛) with ˛ as discussed in the literature [15,23,24]. Reaction models determined from isothermal conditions are termed as model ﬁtting method, whereas, parameters determined from the master plot of y(˛) and z(˛) with conversion from non-isothermal data are called as model free method. 4. Results and discussion 4.1. TMDSC study of the homopolymer and IPNs of TMPTA and HDDA TMDSC experiments were carried out in order to determine the glass transition of the homopolymer (PTMPTA and PHDDA) and their IPNs. Due to extensive crosslinking in the matrix, no Tg was found in the reversing heat ﬂow curve, as shown in Fig. 1(a). However, PTMPTA undergoes curing from 160 to 260 ◦ C, which is indicated by the exothermic peak in the non-reversing heat ﬂow, as depicted in Fig. 1(b). With the increment of HDDA content in the matrix, this curing peak disappears. The curing of
Fig. 1. (a) Reversing and (b) non-reversing heat ﬂow of TMPTA–HDDA homopolymer and IPN compositions.
PTMPTA, TH8020 and TH5050 compositions indicates that they undergo further crosslinking on heat treatment due to the presence of trifunctional groups in the matrix. TH2080 and PHDDA compositions showed no curing as the number of functional groups are lesser compared to TMPTA rich phases. TMDSC conﬁrms that these compositions are not usual copolymers but they are interpenetrating polymer network having no distinct glass transition (Tg ). 4.2. Non-isothermal thermal degradation of homopolymer and IPNs of TMPTA and HDDA in inert and air atmosphere The extent of conversion (from TGA) and the rate of conversion (DTG) with the function of temperature at different heating rates for PTMPTA in N2 atmosphere are presented in Fig. 2(a) and (b). Figs. 3(a), (b) and 4(a), (b) show the same plot of PTMPTA and PHDDA homopolymer and their IPNs at a heating rate of 10 ◦ C min−1 in N2 and air respectively. The DTG plot of both PTMPTA and PHDDA in Figs. 2(b) and 3(b) show that they degrade in a single step during thermally activated processes in inert atmosphere. However, PHDDA shows a small shoulder in its DTG curve at 450 ◦ C (Fig. 3(b)). Both PTMPTA and PHDDA are thermoset and degrade by random chain scission leaving a carbon residue but their IPNs degrade in two steps. Fig. 3(b) indicates both the peaks of the DTG curve of these IPNs lie approximately at the same temperature of individual homopolymer (PTMPTA and PHDDA). Since both the monomers are multifunctional and can crosslink upon UV irradiation, a possible micro-phase separation is involved during the polymerization, which exhibits two-step degradation during thermal decomposition depending on the thermal stability of their respective homopolymers. However, in air, the degradation is oxidative and by random chain scission leaving no carbon residue as char. Both the
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Fig. 2. (a) Extent of conversion (˛) and (b) rate of conversion (DTG) with temperature of PTMPTA at different heating rates (2, 5, 10, 15, 20 and 25 ◦ C min−1 ) in N2 .
Fig. 3. (a) Extent of conversion (˛) and (b) rate of conversion (DTG) with temperature of TMPTA–HDDA IPNs at 10 ◦ C min−1 heating rate in N2 .
4.3. Kinetic study of TMPTA–HDDA homopolymer and their IPN by model-free isoconversional method homopolymers and IPN compositions exhibit degradation in three steps, as shown in Fig. 4(b). T10 , T25 , T50 and T75 are the characteristic thermal degradation temperatures at which 10%, 25%, 50% and 75% mass loss occurred, respectively, and these temperatures are reported in Table 1(a) and (b). It can be observed that the degradation temperature decreases with an increase in the HDDA content in the matrix. However, the overall compositions are less stable in air as compared to N2 atmosphere. Recently, Krongauz  extensively studied the mechanism of polyacrylates degradation in N2 and air and described that the degradation of these polymers occurs through decarboxylation, formation of monomers and alcohols in nitrogen. However, in air, these polymers degrade through peroxide formation, radical reactions with oxygen, depolymerization, alcohol formation and liberation of carbon dioxide. The degradation of polyacrylate in air occurs in three steps. Initially, molecular oxygen attacks the tertiary carbon atom of the polymer chain, which results in the formation of hydroperoxide groups and can be seen as the ﬁrst step in the DTG plot. Subsequently, the decomposition of hydroperoxides leads to random chain scission and produces low molecular weight polymeric units followed by volatilization of these units . This is indicated by further two steps of the DTG plot, as shown in Fig. 3(b). The increase of thermal stability of TMPTA rich phases is due to the higher crosslink density, which slows down the mobility of the radicals, reduces oxygen diffusion and lowers the valency transfer .
4.3.1. Thermal degradation (in N2 atmosphere) The apparent activation energies (Ea ) have been extracted from the TGA experiments for all the homopolymers and IPNs using model free isoconversional method and are discussed in this study. Fig. 5(a) and (b) shows the variation of Ea with conversion (˛) of both the homopolymers and IPNs in N2 determined from differential isoconversional (Eq. (6)) and KAS method (Eq. (7)), respectively. It is observed from Fig. 5(a) that in N2 atmosphere, the variation of apparent activation energy with conversion degree indicates complex process in PTMPTA and IPNs. Initially, Ea increases with the conversion and reaches the maxima and reduces. In case of PTMPTA the drop of Ea with the conversion is fairly lesser than the other IPNs. All the IPNs show complex Ea vs. ˛ curve which is concave downwards. Vyazovkin argued that concavity signiﬁes the process undergoes a limiting stage of degradation . On the other hand, PHDDA shows a slow increment in Ea in the initial conversion, however, it increases steadily after ˛ = 0.5 denoting the process involves several parallel reactions. These parallel reactions consist of decomposition of side chains in the initial stage followed by the breaking of polymer backbone . A similar trend was observed in Ea vs. ˛ plot determined by KAS method (Integral method). However, the Ea values calculated by KAS method are slightly different as obtained by differential method. This difference between the two methods is attributed to their intrinsic nature of calculation of activation energy. The calculation of the temperature integral (Eq. (7)) by Doyle’s
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Fig. 4. (a) Extent of conversion (˛) and (b) rate of conversion (DTG) with temperature plot of TMPTA–HDDA IPNs at 10 ◦ C min−1 heating rate in air.
approximation assumes that the activation energy is not dependent on the degree of conversion, therefore a systematic error in computation might be introduced in KAS method . Nevertheless, differences in the activation energies determined by the single method are more than 10% indicating the processes are complex . As discussed earlier, initially, the degradation of both homopolymer and IPNs in absence of air occurs through depolymerization, decarboxylation and alcohol formation. The initial lower values of activation energy are associated with the initiation process that occurs due to the chain end scission of the polymer chain. With further heating, chain ends are consumed and subsequently, the limiting step of degradation shifts toward the random chain scission, which shows higher values of activation energy . However, after certain conversion, all the IPNs show a steady decrease in the activation energies. PHDDA degrades in a single stage and shows steady increase in activation energy with conversion. Therefore, it is observed that the maxima of the activation energy of all the IPNs shifts towards higher conversion with the increment of HDDA content in the matrix. It signiﬁes that there are two reversible processes involved in the degradation of IPNs. The ascending part of the dependence of Ea with conversion suggests that the reaction with higher activation largely contributes to the heat release. However, after reaching the maxima, the dependence becomes lower indicating relatively decreasing contribution of the reaction with the higher activation energy . 4.3.2. Thermo-oxidative degradation (in air atmosphere) Fig. 6(a) and (b) shows the Ea vs. ˛ plot determined from isoconversional–differential and KAS method for TMPTA and HDDA
Fig. 5. Dependence of apparent activation energy (Ea ) with the degree of conversion (˛) of all TMPTA–HDDA homopolymer and IPNs determined by isoconversional (a) differential method and (b) KAS method in N2 atmosphere.
homopolymers and their IPNs in oxidative atmosphere. It is observed that for all the compositions the activation energy (Ea ) initially shows a lower value at low conversion compared to the thermal degradation in N2 . After ˛ = 0.3 Ea increases monotonously for PTMPTA, TH8020 and TH5050 compositions. However, the slopes change after ˛ = 0.5 indicates rate limiting kinetics . PHDDA also shows similar behavior but its Ea increases up to ˛ = 0.5 and shows an inﬂection in the Ea vs. ˛ plot. This feature of the plot signiﬁes that the process undergoes an intermediate stage where the reaction changes over from diffusion controlled to kinetic controlled regime . TH2080 shows a slightly different behavior than the other compositions wherein the activation energy steadily increases with conversion. A careful observation from both Fig. 6(a) and (b) indicates that PTMPTA, TH8020 and TH5050 show three inﬂection points in the Ea –˛ plot indicating all these homopolymer and IPNs degrade through three stages. These indicates multiple processes are involved whereas PHDDA shows two inﬂection points, which suggests that PHDDA may degrade through two simultaneous reversible mechanisms. On the other hand, the Ea vs. ˛ plot of TH2080 shows lesser crest and trough compared to the other compositions indicating the process involves parallel reactions . The polymer degrades in oxygen through the initiation resulting in radical precursors. This reacts with oxygen to form a peroxy (ROO*) radical intermediate. This highly reactive ROO* abstracts labile hydrogen from the adjacent polymer molecule to yield the hydroperoxide . Fig. 6(a) and (b) shows at ˛ ≤ 0.2, the rate controlling step involves the peroxy radical in the propagation
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Fig. 6. Dependence of apparent activation energy (Ea ) with the degree of conversion for (˛) TMPTA–HDDA homopolymer and IPNs determined by isoconversional (a) differential method and (b) KAS method in air atmosphere.
step of degradation which is in the range of 80–110 kJ mol−1 . This hydroperoxide can undergo either bimolecular or monomolecular decomposition. At medium conversion (˛ < 0.5), the activation energy in the Ea vs. ˛ show 155–170 kJ mol−1 indicating the process involve bimolecular decomposition. At higher conversion (˛ = 0.5–0.8), the activation energy (Ea ) increases up to 250–280 kJ mol−1 . The increase in activation energy at higher conversions can be attributed to the rate limiting step of random chain scission, as observed for the thermo-oxidative degradation of PE and PP . This is also similar to the three stage degradation observed for the degradation of polyacrylates . 4.4. Isothermal degradation Fig. 7(a) and (b) shows the isothermal degradation at 400 ◦ C of all the homopolymers and IPNs in N2 and air, respectively. Fig. 7(a) shows that in N2 , degradation is smooth having no multiple stages whereas degradation in air shows multiple stages (Fig. 7(b)) and the number of stages decreases with increasing HDDA content.
Fig. 7. Isothermal TGA of all TMPTA–HDDA homopolymer and IPNs at 400 ◦ C in (a) N2 and (b) air atmosphere. Inset shows the extent of conversion vs. time of same isothermal plot at same condition.
reveals that ln(1 − ˛) vs. t curve is concave downward signiﬁes that the reaction follows contracting geometry model (R2 and R3) . Therefore, the order varies from 1/2 to 2/3 for all the homopolymers and IPNs discussed in this study. However, in order to determine the reaction model at nonisothermal conditions in N2 y(˛) vs. ˛ and z(˛) vs. ˛ have been plotted, as shown in Fig. 8(a) and (b). Based on the peak position of z(˛) and the shape of y(˛), it is observed that PTMPTA shows contracting sphere model (R3) at higher conversion. However, TH8020 exhibits diffusion controlled (D2/D3) model at low conversion and R3 at higher conversion. TH5050 shows Avrami–Erofeev model below 20% conversion and follows R3 model at higher conversion. TH2080 exhibits a diffusion controlled process, as clearly seen in y(˛) vs. ˛ plot. The peak of z(˛) vs. ˛ indicates this might follow the D4 model. PHDDA shows diffusion controlled process throughout the entire regime which is apparent from the shape of the curve of y(˛) vs. ˛. However, the above master plot is not applicable for the degradation of all the homopolymers and IPNs in air since their activation energy signiﬁcantly varies with conversion.
4.5. Model prediction by isothermal kinetic curve and model free method from non-isothermal master curve
4.6. DTA study
It is important to know the reaction model that governs the reaction mechanism of thermal degradation. The inset in Fig. 7(a) and (b) shows the ln(1 − ˛) vs. t plot from which it is discerned that the reaction mechanism is decelerating and therefore the decelerating model should be used i.e. f (˛) = (1 − ˛)n . A careful observation also
Fig. 9(a) and (b) depicts the DTA of PTMPTA and PHDDA homopolymers and their IPNs in N2 and air ambient. It is observed that all the homopolymers and IPNs degrade in N2 with an endothermic reaction however they degrade evolving large amount of heat in air. Fig. 9(b) depicts that all the compositions exhibit three
A. Goswami et al. / Thermochimica Acta 547 (2012) 53–61
Fig. 8. (a) y(˛) vs. ˛ and (b) z(˛) vs. ˛ master curve for the degradation of all the homopolymers and IPNs in N2 .
exothermic peaks in oxidative degradation. They range approximately from 350 to 425 ◦ C (ﬁrst exotherm), 425 to 500 ◦ C (second exotherm) and 500 to 600 ◦ C (third exotherm). However, the ﬁrst exotherm is relatively less intense in TH2080 and TH5050 compositions. 4.7. Debinding strategy The above kinetic study has been carried out to optimize the debinding operation of ceramic material fabricated by MSL technique. Debinding is a diffusion controlled process through which binder is removed in a controlled way . The atmosphere (N2 /air) and the heating rate are two important parameters, which are to be optimized in order to make the process faster and feasible. The primary requirement of any binder is its thermal stability up to high temperatures so that when the binder is removed, the ceramic attains an adequate green strength before reaching the sintering temperature. PTMPTA shows higher thermal stability than other compositions studied in this work. However, the degradation of PTMPTA at non-isothermal conditions (2–25 ◦ C min−1 in N2 ) occurs through decomposition controlled process in N2 and air because of its high activation energy involved in the degradation. In addition, it follows a contracting geometry model where material shrinks during removal, which is detrimental for any debinding operation. Among the other compositions, PHDDA and TH2080 show relatively low activation energy in N2 up to ˛ = 0.5 and follow diffusion controlled degradation throughout the entire degradation regime. On the other hand, in case of oxidative degradation, PHDDA and TH2080 show higher activation energies with
Fig. 9. DTA of TMPTA–HDDA homopolymers and IPNs in (a) N2 atmosphere (b) air atmosphere.
conversion than that of any other compositions. Therefore, the strategy of binder removal can be as follows: (a) using a very low heating rate (