polymers Article
An Insight into the Flammability of Some Bio-Based Polyesters Loïc Dumazert and Rodolphe Sonnier * Ecole des Mines d’ Alès, Centre des Matériaux des Mines d’ Alès—Pôle Matériaux Polymères Avancés, 6 Avenue de Clavières, 30319 Alès CEDEX, France;
[email protected] * Correspondence:
[email protected] Received: 29 November 2017; Accepted: 8 December 2017; Published: 12 December 2017
Abstract: The heat release capacity of polymers can be generally predicted using a method based on the additivity of group contributions (the Van Krevelen approach). Nevertheless, there are some exceptions, evidencing that this approach is insufficient and must be completed. In this study, the kinetic triplet accounting for the description of pyrolysis is identified for 11 polymers. Activation energy and the frequency factor are calculated using Kissinger’s method. Reaction models are chosen among the Avrami–Erofeev functions. The high flammability of poly(3-hydroxybutyrate) and the underestimation of its heat release capacity using the Van Krevelen approach are explained from these parameters. The results highlight the possibility of improving the model, using additional but easily accessible data. Keywords: polyesters; poly(3-hydroxybutyrate); flammability; pyrolysis; pyrolysis-combustion flow calorimeter
1. Introduction Recently, methods based on the Van Krevelen approach have been proposed to assess the flammability of a polymer at microscale, using a pyrolysis-combustion flow calorimeter (PCFC) [1–5]. A PCFC is an apparatus that allows the heating of a few milligrams of a polymer to 750 ◦ C, according to a linear heating rate (1 K/s) under nitrogen. Pyrolytic gases are continuously sent to a combustor at 900 ◦ C in an excess of oxygen, and combustion is completed. The amount of heat released is calculated according to the oxygen depletion method, allowing some important flammability properties to be measured, such as Heat Release Capacity (HRC) or Total Heat Release (THR). HRC is the ratio between the peak of Heat Release Rate (pHRR) and the heating rate (typically 1 K/s). The pHRR is one of the main parameters used to assess the flammability of a polymer. THR corresponds to the area under the Heat Release Rate (HRR) curve. In previous works [4,5], the contributions to HRC and THR were calculated for more than 45 chemical groups, and the properties of around 130 polymers were predicted with good accuracy (Figure 1). Unfortunately, some predictions failed, in particular for several aliphatic polyesters, including polyglycolide (PG), poly(lactic acid) (PLA), and poly(3-hydroxybutyrate) (PHB). These three polymers exhibit experimental HRCs much higher than the calculated ones. This failure may be partly due to the limits of the method for PG and PLA. Indeed, the negative contributions assigned to the ester groups become irrelevant when the ester mass fraction in the polymer is too high. Nevertheless, PHB has the same ester fraction as poly(butylene succinate) (PBS), but its HRC is much higher than for PBS and other polyesters (Figure 2).
Polymers 2017, 9, 706; doi:10.3390/polym9120706
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Figure versus release capacity (HRC) for more 100 polymers (data Figure1.1Experimental – Experimental versuscalculated calculatedheat heat release capacity for more than than one hundred polymers drawn from [4]). White circles correspond the 11 polymers studied in this work. (data to drawn from [SON16])
Unfortunately, some predictions failed, in particular for several aliphatic polyesters including polyglycolide (PG), poly(lactic acid) (PLA) and poly(hydroxybutyrate) (PHB). These three polymers exhibit experimental HRC much higher than the calculated ones. The failure may be partly assigned to the limits of the method for the two first mentioned ones. Indeed, the negative contributions assigned to the ester groups become irrelevant when the ester mass fraction in the polymer is too high. Nevertheless, PHB has a same ester fraction than poly(butylene succinate) (PBS) but the value of its pHRR is very uncommon (Figure 2).
Figure 2. 2Correlation capacity and andtotal totalheat heatrelease release (THR) measured Figure – Correlationbetween betweenheat heat release release capacity measured in PCFC forin a pyrolysis-combustion flow calorimeter for(data around 150from pure[SON16]) polymers (data drawn from [4]). around 150 pure(PCFC) polymers drawn White circles correspond to the 11 polymers studied in this work.
The reason behind this failure is obviously related to specific pyrolysis mechanisms. Indeed, HRC depends on heat of combustion and pyrolysis kinetics parameters, i.e. the so-called kinetic triplet (Ea, The reason behind this failure is obviously related to specific pyrolysis mechanisms. Indeed, HRC A, f(α)). This kinetic triplet (Ea, A, f(α)) is used to adequately describe pyrolysis kinetics through the 2 depends on the heat of complete combustion (∆h) and pyrolysis kinetics parameters, i.e., the so-called equation 1. kinetic triplet (Ea , A, f (α)). This kinetic triplet (Ea , A, f (α)) is used to adequately describe pyrolysis kinetics through Equation (1): = 𝐴𝑒 𝑓(𝛼) − Ea equation 1 dα = Ae RT f (α) (1) dt With α the extent of the reactant conversion, R the gas constant, Ea the activation energy, A the frequency (or preexponential) factor, f(α) the reaction model (It exists many reaction models available [6-7]). In order to understand why some predictions failed and to improve our model, the knowledge of the triplet for each polymer would be useful, even if the physical meaning of the kinetic triplets is
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in the equation, α is the extent of the reactant conversion (i.e., the reacted fraction), R is the gas constant, Ea is the activation energy, A is the frequency (or pre-exponential) factor, and f (α) is the reaction model (there are many reaction models available [6,7]). In order to understand why some predictions failed, and to improve our model, the knowledge of the triplet for each polymer would be useful, even if the physical meaning of the kinetic triplets is controversial, for a couple of reasons comprehensively discussed in the literature [6]. There are many articles dealing with the pyrolysis mechanisms, in great detail, for almost all polymers. Several authors have already studied the pyrolysis of PHB in great detail [8–11], and a step of auto-catalytic degradation was reported [9]. Nevertheless, the quantitative data (namely, the kinetic triplet to describe the pyrolysis) vary greatly from one study to another. Even the activation energy must be considered only as apparent, and its value for a same polymer may vary to a large extent. As an example, Ariffin et al. have listed the activation energy values for PHB obtained by various research teams [9]. The activation energy ranges from 110 to 380 kJ/mol, according to the authors and the heating rate methods. The same discrepancy can be found for PLA or polycaprolactone (PCL), for example. From a practical point of view, it is hardly possible to use these data for an initial quick assessment of the thermal stability and flammability of polymers, only based on their chemical structure. The objective of this work is to use a simple and standardized procedure to identify a kinetic triplet, allowing for the correct calculation (i.e., with good accuracy) of the temperature and the intensity of the pHRR, measured in a PCFC, even if the whole HRR curve is not perfectly described. Our motivation is purely to improve the model previously proposed, based on the additivity of group contributions. More specifically, we would like to identify why PHB but also PLA and PG exhibit surprisingly high HRC values, from the knowledge on their kinetic triplets. The procedure is based on Kissinger’s method for calculating the activation energy and the frequency factor, and considers only the Avrami-Erofeev functions as reaction models. No knowledge of the precise pyrolysis mechanisms is required. The first results on a set of 11 polymers show that the high HRC measured for PHB is highlighted well by the calculated kinetic triplet. 2. Methodology 2.1. Materials The2017, commercial Polymers 9, 706 Polymers Polymers 2017, 2017, 9, 9, 706 706
polymers used in this study are listed in Table 1. Seven of them are polyesters. 44 of 14 4 of of 14 14 The four remaining ones are commonly used polymers. Table 1. Polymers studied in this work. Table Table 1. 1. Polymers Polymers studied studied in in this this work. work. Table 1. Polymers studied in this work. Polymer Polymer Polymer Polymer
Manufacturer Manufacturer Manufacturer Manufacturer
(High (Highdensity) density) (High (High density) density) Polyethylene Polyethylene Polyethylene Polyethylene
Eraclene FCFC 92 92 Eraclene Eraclene Eraclene FC FC 92 92 Polimeri Europa Polimeri Europa Polimeri Europa Polimeri Europa 3100 MT3 1P2381 3100 MT3 1P2381 3100 MT3 1P2381 3100 MT3 1P2381 Atofina Atofina Atofina Atofina
Polypropylene Polypropylene Polypropylene Polypropylene Polyethylene Polyethylene Polyethylene Polyethylene terephthalate terephthalate terephthalate terephthalate
Arnite D04 300 Arnite D04 300 Arnite D04 Arnite D04 300300
Chemical structure Chemical structure Chemical Chemical structure structure
Heat of Heat Heat of of complete complete complete Heat of complete combustion combustion combustion(kJ/g) combustion (kJ/g) (kJ/g) (kJ/g) 42 42 42 42
39 39 39 39
16 16 1616
Polybutylene Polybutylene Polybutylene Polybutylene terephthalate terephthalate terephthalate terephthalate
ValoxGE 325F GE Valox 325F Plastics Valox Valox 325F 325F GE GE Plastics Plastics Plastics
Polycaprolactone Polycaprolactone Polycaprolactone
CAPA 6800 Perstorp CAPA CAPA 6800 6800 Perstorp Perstorp
26.5 26.5 26.5
Polybutylene Polybutylene Polybutylene succinate succinate succinate
2003F Xinfu Pharm 2003F 2003F Xinfu Xinfu Pharm Pharm
21.5 21.5 21.5
Poly(3-hydroxybu Poly(3-hydroxybu Poly(3-hydroxybu tyrate) tyrate) tyrate)
Biocycle 1000 Biocycle Biocycle 1000 1000
20 20 20
20 20 2020
Polymer Polymer (High density) density) (High (High density) Polyethylene (High density) Polyethylene (High density) Polyethylene Polyethylene Polyethylene Polypropylene Polymers Polypropylene 2017, 9, 706 Polypropylene Polypropylene Polypropylene Polyethylene Polyethylene Polyethylene terephthalate Polyethylene terephthalate Polyethylene terephthalate terephthalate terephthalate Polybutylene Polybutylene Polymer Polybutylene terephthalate Polybutylene terephthalate Polybutylene terephthalate terephthalate terephthalate Polycaprolactone Polycaprolactone Polycaprolactone Polycaprolactone Polycaprolactone Polycaprolactone
Manufacturer Manufacturer
Chemical structure Chemical structure
Eraclene FC FC 92 92 Eraclene Eraclene FC 92 Polimeri Europa Eraclene FC 92 Polimeri EracleneEuropa FC 92 Polimeri Polimeri Europa Europa Polimeri 3100 MT3Europa 1P2381 3100 MT3 1P2381 3100 MT3 1P2381 Atofina 3100 Atofina MT3 1P2381 3100 Atofina MT3 1P2381 Atofina Atofina Arnite D04 300 Arnite D04 300 Arnite Arnite D04 D04 300 300 Arnite D04 300
Table 1. Cont.
Valox 325F GE Plastics Manufacturer Valox 325F GE Plastics Valox Valox 325F 325F GE GE Plastics Plastics Valox 325F GE Plastics
Chemical structure
CAPA 6800 CAPA 6800 Perstorp Perstorp CAPA 6800 Perstorp CAPA CAPA 6800 6800 Perstorp Perstorp CAPA 6800 Perstorp
Polybutylene 2003F Xinfu Pharm Polybutylene Polybutylene succinate 2003F 2003F Xinfu Pharm Polybutylene Xinfu Pharm succinate Polybutylene 2003F Xinfu Pharm Polybutylene succinate 2003F Xinfu Pharm succinate 2003F Xinfu Pharm succinate succinate Poly(3-hydroxybu Poly(3-hydroxybu Biocycle 1000 Poly(3-hydroxybutyrate) Biocycle 1000 Poly(3-hydroxybu tyrate) Biocycle 1000 Poly(3-hydroxybu Biocycle 1000 tyrate) Poly(3-hydroxybu Biocycle 1000 tyrate) Biocycle 1000 tyrate) tyrate)
combustion (kJ/g) combustion combustion (kJ/g) (kJ/g) (kJ/g) (kJ/g) 42 42 42 42 42 39 39 39 39 39 16 16 16 16 16
Heat of 20 complete 20 combustion (kJ/g) 20 20 20 26.5 26.5 26.5 26.5 26.5 26.5
21.5 21.5 21.5 21.5 21.5 21.5 2020 20 20 20 20
Polylactic acid acid Polylactic Polylactic acid Polylactic Polylactic acid acid Polylactic acid
Unitika 6201-D 6201-D Unitika Unitika 6201-D Unitika Unitika 6201-D 6201-D Unitika 6201-D
16 16 16 16 16 16
Polyglycolide Polyglycolide Polyglycolide Polyglycolide Polyglycolide Polyglycolide
Sigma Aldrich Sigma Aldrich Sigma Aldrich Sigma Aldrich Sigma Aldrich Sigma Aldrich
10.5 10.5 10.5 10.5 10.5 10.5
Polymethyl Polymethyl Polymethyl methacrylate Polymethyl Polymethyl methacrylate Polymethyl methacrylate methacrylate methacrylate methacrylate
Altuglas V825T V825T Altuglas Altuglas V825T Altuglas V825T Altuglas V825T Altuglas V825T
23 23 23 2323 23
Polystyrene Polystyrene Polystyrene Polystyrene Polystyrene Polystyrene
Lacqrène 1340 1340 Atofina Atofina Lacqrène Lacqrène 1340 Lacqrène 1340 Lacqrène 1340 Atofina Atofina Lacqrène 1340 Atofina Atofina
4 of 15
35 35 35 35 3535
2.2. Experiments 2.2. Experiments 2.2. Experiments 2.2. 2.2. Experiments Experiments The thermal thermal stability stability of of the the samples samples was was determined determined using using thermogravimetric thermogravimetric analysis analysis (TGA (TGA The 2.2. Experiments thermal stability of the samples was determined using thermogravimetric analysis (TGA PyrisThe 1, Perkin-Elmer, Waltham, MA, USA). The sample weights were approximately 5 mg. The thermal of was using thermogravimetric analysis The thermal stability stability of the the samples samples was determined determined using thermogravimetric analysis5(TGA (TGA Pyris 1, Perkin-Elmer, Waltham, MA, USA). The sample weights were approximately mg. Pyris 1, Perkin-Elmer, Waltham, MA, USA). The sample weights were approximately 5 mg. The thermal stability of the samples was determined using thermogravimetric analysis (TGA Pyris Pyris Waltham, MA, The weights were approximately 55 mg. Experiments were performed between 30USA). and 750 °Csample at different heating rates (5, 10, 20, and 40 Pyris 1, 1, Perkin-Elmer, Perkin-Elmer, Waltham, MA,30 USA). The°C sample weights wererates approximately mg. Experiments were performed between and 750 at different heating (5, 10, 20, and 40 Experiments were performed between 30 and 750 °C at different heating rates (5, 10, 20, and 40 1,K/min) Perkin-Elmer, Waltham, USA). The sample weights were approximately 5 mg.20, Experiments Experiments performed between 30 and different rates (5, and underwere nitrogen (20 MA, mL/min). The temperature used with Kissinger’s method Experiments were performed between 30decomposition and 750 750 °C °C at attemperature different heating heating ratesKissinger’s (5, 10, 10, 20,method and 40 40 K/min) under nitrogen (20 mL/min). The used with ◦ C decomposition K/min) under nitrogen (20 mL/min). The decomposition temperature used with Kissinger’s method were performed between 30 and 750 at different heating rates (5, 10, 20, and 40 K/min) under K/min) under nitrogen (20 mL/min). The decomposition temperature used with Kissinger’s method was determined as the temperature of the peak of mass loss rate on a dTG (derivative was determined as the the peak oftemperature mass loss used rate with on aKissinger’s dTG (derivative K/min) under nitrogen (20 temperature mL/min). Theof decomposition method was determined as the temperature oftemperature the peak of mass rate onmethod a dTGwas (derivative thermogravimetric) curve. was determined as the temperature mass loss rate nitrogen (20 mL/min). The used withloss Kissinger’s determined thermogravimetric) was determined ascurve. the decomposition temperature of of the the peak peak of of mass loss rate on on aa dTG dTG (derivative (derivative thermogravimetric) curve. The flammability of the polymers listed in Table 1 was analyzed using a PCFC (FTT, Derby, asthermogravimetric) the The temperature ofcurve. the peak of mass loss rate on a dTG (derivative thermogravimetric) curve. thermogravimetric) curve. flammability of the polymers listed in Table 11 was analyzed using aa PCFC (FTT, Derby, The flammability of the polymers listed in Table was analyzed using PCFC (FTT, Derby, The flammability the polymers listed in Table was analyzed using PCFC (FTT, Derby, UK)The under standard conditions, i.e., anaerobic pyrolysis from 25 to 750using °C at 1aaa°C/s in (FTT, nitrogen, andUK) ofof listed Table PCFC Theflammability flammability ofthe thepolymers polymers listedin in Table111was wasanalyzed analyzed using PCFC (FTT,Derby, Derby, UK) under standard conditions, i.e., anaerobic pyrolysis from 25 to 750 °C at 11 °C/s in nitrogen, and UK) under standard conditions, i.e., anaerobic pyrolysis from 25 to 750 °C at °C/s in nitrogen, and ◦ ◦ UK) under standard conditions, i.e., anaerobic pyrolysis from 25 to 750 °C at 1 °C/s in nitrogen, and complete combustion in an excess of oxygen at 900 °C [12]. under standard conditions, i.e., i.e., anaerobic pyrolysis from C at at 11°C/s C/s nitrogen, UK) under standard conditions, anaerobic pyrolysis from2525toto750 750 °C in in nitrogen, andand complete combustion in an excess of oxygen at 900 °C [12]. complete combustion in an excess of oxygen at 900 °C [12]. ◦ complete combustion in an excess of oxygen at 900 °C [12]. complete oxygen at at900 900°CC[12]. [12]. completecombustion combustionin inan an excess excess of oxygen
2.3. Method The objective of this work is to compare the kinetic triplets of an extended set of polymers, in order to understand why some aliphatic polyesters exhibit a higher pHRR than expected. The description of pyrolysis mechanisms is out of the scope of this work. A purely mathematical description of the pyrolysis correctly predicting the HRR is the main task. HRR is closely related to mass loss rate (MLR) through Equation (2): HRR = MLR × ∆h
(2)
here, ∆h represents the heat of complete combustion (in the case of a PCFC, the combustion is complete). The heat of complete combustion is measured using a PCFC in standard conditions. For the studied polymers, it is reasonable to consider that this value remains constant throughout the whole pyrolysis
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process. The measured values are listed in Table 1. HRR and ∆h are calculated in W/g and J/g g/g respectively, therefore MLR is calculated in s = s−1 . Both in TGA and in a PCFC, the sample is heated using a constant heating rate under nitrogen flow. In theory, both devices allow the calculation of the same kinetic triplet using the same methods. However, the ability to modify the heating rate is more limited in a PCFC, and the accuracy of the temperature is lower. Therefore, we decided to first determine the activation energy and the frequency factor using TGA. In the first step, TGA was carried out to calculate the activation energy of pyrolysis, through a procedure involving multiple heating rates. Two methods were used and compared: the Flynn-Wall-Ozawa method and Kissinger’s method. Details about these methods can be found elsewhere [13–15]. The latter also allows the calculation of the frequency factor. TGA provides inconsistent data at the highest heating rates, for unknown reasons, especially in the case of polyglycolide. Therefore, for that polymer, the selected heating rates were 2, 5, and 10 K/min. The MLR curve in a PCFC can be deduced from the HRR curve using Equation (2). From this curve, and the knowledge of Ea and A, a reaction model f (α) can be identified to determine the whole kinetic triplet (Ea , A, f (α)). The interpretation of f (α) as a reaction mechanism is probably irrelevant in many cases [6]. Some authors have used a combination of reaction models to accurately fit the TGA curves [16]. Our approach was different and purely practical. Only first-order reaction and Avrami-Erofeev models were considered. A reasonably good fit was obtained using these models for all polymers, as shown in the following. Moreover, this choice allowed for comparing the reaction models of the different polymers through only one parameter (n). The general form of the chosen models is shown in Equation (3): 1
f (α) = n(1 − α)(− Ln(1 − α))1− n
(3)
in this equation, n ranges between 1 and 4 [17]. Corresponding to the first-order reaction, n = 1, and the other cases correspond to Avrami–Erofeev models. If the triplet (Ea , A and f (α)) is correctly identified, then the MLR curve is well-fitted, i.e., the HRR curve can be rebuilt by multiplying the calculated MLR by the heat of complete combustion (Equation (2)). Note that the heating rate in a PCFC is 1 K/s (60 K/min). Therefore, the activation energy and the frequency factor calculated using TGA are used to extrapolate the pyrolysis kinetics outside the temperature experimental range, as recommended by Vyazokin [6]. However, we have found a slight but systematic shift of activation energy. Indeed, the activation energy Ea(PCFC) , used to simulate the mass loss rate at 1 K/s (i.e., to simulate in fine the HRR curve measured in PCFC), is slightly lower E
than the activation energy Ea(TGA) , calculated by Kissinger’s method from TGA data ( Ea(PCFC) ≈ 0.95). a(TGA)
The comparison is shown in the supporting information (Figure S1). 3. Results and Discussion 3.1. Activation Energy of Pyrolysis Table 2 presents the activation energies calculated from the Flynn-Wall-Ozawa and Kissinger methods. The activation energy using the Flynn-Wall-Ozawa method was calculated only for the conversion range 0.2–0.8. The values for lower or higher conversions are often less reliable. The values for activation energy are highly constant over the whole conversion range for some polymers (PE (polyethylene), PP (polypropylene), PHB (poly(3-hydroxybutyrate), PG (polyglycolide), and PS (polystyrene)). For other polymers, the activation energy tends to increase when conversion increases. Both cases are common. For example, Aoyagi et al. have observed that apparent activation energies for PCL and PHB remain constant, while activation energy for PLA increases from 80 to 160 kJ/mol [8].
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Table 2. Kinetic parameters measured for all studied polymers. Flynn-Wall-Ozawa method Ea (kJ/mol)
Polymer PE PP PET PBT PCL PBS PHB PLA PG PMMA PS
Kissinger method
α = 0.2
α = 0.4
α = 0.6
α = 0.8
Mean
210 202 169 157 139 125 98 109 95 164 159
217 194 177 163 163 140 93 100 89 170 158
210 192 182 165 166 148 89 116 91 174 159
209 187 193 172 172 151 84 120 94 193 162
211 194 180 164 160 141 91 111 92 175 159
Ea (kJ/mol)
LnA
221 198 180 174 151 154 91 126 86 176 160
29.2 26.9 24.7 25.6 21.3 21.8 15.4 18.2 10.4 27.4 22.0
Figure 3 shows the agreement between the activation energies measured using both methods (the mean activation energy for the conversion range 0.2–0.8 was used for the Flynn-Wall-Ozawa method).
Figure 3. activation valuesfrom obtained from the Kissinger and Figure 3Comparison – Comparison ofofactivation energyenergy values obtained Kissinger and Flynn-Wall-Ozawa Flynn-Wall-Ozawa methods. methods Figure 4 illustrates how the ester group fraction or the presence of CH3 pendant group onto the
As explained in the introduction, activation values in the literature arefrom not consistent, polymer backbone, influence the the activation energy energy value. The activation energy calculated and the reliability of the comparison of values from different works limited. Flynn-Wall-Ozawa method decreases when increasing the fraction of theisester group.However, For CH3-freeit is notable that the values obtained in this energy work are in quite good agreement from some other reports polymers, this activation decreases linearly from 211 kJ/mol with for PE those (ester fraction 0) to 92 kJ/mol for methods. polyglycolideFor (ester fraction 0.76). A similar energies decrease is between observed for polymers containing that used the same example, activation 100 and 120 kJ/mol for PHB a CH3 group thevalues activation energyin is systematically a given ester fraction. For example, (slightly higher thanbut the found our work) lower haveforbeen measured using multiple heating the activation energy is 194 kJ/mol for PP (versus 211 kJ/mol for PE) and 91 kJ/mol for PHB (versus rates [8,9]. Table S1 in the supporting information gives an overview of the activation energies found 141 kJ/mol for PBS – for both polymers the ester fraction is 0.51). in literature. that the dependence activation energy measured usingpresence Kissinger method on 3the presence group of FigureNote 4 illustrates how theofester group fraction or the of a CH pendant on the a CH3 group is less obvious even if both energy methods value. (Flynn-Wall-Ozawa and Kissinger) well from the polymer backbone influences the activation The activation energyprovide calculated correlated results. Flynn-Wall-Ozawa method decreases when increasing the fraction of the ester group. For CH3 -free polymers, the activation energy decreases linearly from 211 kJ/mol for PE (ester fraction 0) to 92 kJ/mol for polyglycolide (ester fraction 0.76). A similar decrease is observed for polymers containing a CH3
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group, but whose activation energy is systematically lower for a given ester fraction. For example, the activation energy is 194 kJ/mol for PP (versus 211 kJ/mol for PE) and 91 kJ/mol for PHB (versus 141 kJ/mol for PBS). For these last two polymers, the ester fraction is 0.51. Note that the dependence of activation energy measured using the Kissinger method with the presence of a CH3 group is less obvious, even if both methods (Flynn-Wall-Ozawa and Kissinger) provide well-correlated results.
Figure 4. Activation energy (from the Flynn-Wall-Ozawa method) versus ester group fraction/ for Figure 4 – Activation energy (from Flynn-Wall-Ozawa method) versus ester group function for polymers with or without a CH3 group. polymers with or without a CH3 group
It is known well known frequency factor thethe activation energy energy are oftenare correlated It is well thatthatthethefrequency factorand and activation often correlated (compensation effect) [6]. This typical relation is also observed with our results (Figure 5). However, (compensation effect) [6]. This typical relation is also observed with our results (Figure 5). However, the pair (Ea, A) is offset from the straight line for PHB. The frequency factor is higher than expected. A the pair (Eahigher , A) isfrequency offset from the straight line for PHB. The frequency factor is higher than expected. factor leads to a faster degradation, all other factors being equal. A higher frequency factor leads to a faster degradation, all other factors being equal.
9 Figure 5 – Activation energy LnA versusfrom Ln(A) the fromKissinger Kissinger method (straight is calculated Figure 5. Activation energy versus method. The line straight line is calculated considering all polymers except PHB) considering all polymers except poly(3-hydroxybutyrate) (PHB).
Calculation of activation energies from chemical structure Van Krevelen approach has been used to predict a huge number of polymer properties including those related to thermal degradation [18]. To the best of our knowledge, this method has never been
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3.2. Calculation of Activation Energies from Chemical Structure The Van Krevelen approach has been used to predict a huge number of polymer properties, including those related to thermal degradation [18]. To the best of our knowledge, this method has never been used to calculate the activation energy for pyrolysis. There are other, more refined methods for assessing the activation energy, but they need knowledge of the pyrolysis pathway. Ariffin et al. give an example of the calculation of β-elimination in PHB, using the molecular orbital calculation method [9]. The present section is an attempt to show that the frequency factor and the activation energy may be well-predicted from the contributions of only four chemical groups. The activation energy Ea (respectively LnA) is calculated from the contributions of Eai (respectively LnAi ) to the activation energy of the chemical groups, as well as their molar masses Mwi (Equations (4) and (5)). Ea = LnA =
∑i Mwi Eai ∑i Mwi
(4)
∑i Mwi LnAi ∑i Mwi
(5)
Frequency factor and activation energy are both calculated using the Kissinger method for nine polymers among the eleven studied ones. Table 3 lists the contributions of the four chemical groups present in these nine polymers. PS and PMMA (poly(methyl methacrylate)) were not included in this calculation, because they contain additional chemical groups. Polymers Polymers 2017, 2017, 9, 9, 706 706 Polymers 2017, 9, 706 Polymers 2017, 9, 706
Table 3. Contributions to the activation energy and frequency factor for four chemical groups.
99 of of 14 14 of 14 99 of 14
Table Table 3. 3. Contributions Contributions to to the the activation activation energy energy and and frequency frequency factor factor for for four four chemical chemical groups. groups. Table 3. Contributions to the activation energy and frequency factor for four chemical groups. Table 3. Contributions to the activation energy and frequency factor for four Contribution tochemical groups. Chemical groups M w (g/mol) Contribution Contribution to to Contribution to Chemical Mw to EContribution (kJ/mol) LnA Chemical groups groups Mw (g/mol) (g/mol) a Chemical groups Mw (g/mol) Ea (kJ/mol) LnA Chemical groups Mw (g/mol) Ea (kJ/mol) LnA Ea (kJ/mol) (kJ/mol) LnA Ea LnA 14 1414 14 14
220 220 220 220 220
29 2929 29 29
29 2929 29 29
170 170 170 170 170
27 2727 27 27
76 7676 76 76
280 280 280 280 280
38 3838 38 38
44 44 44 44 44
60 60 60 60 60
10 10 10 10 10
Figures 6 and 7 show the correlation between the experimental values (i.e., obtained from the Kissinger method) and the calculated values, using values in Table 3. The correlation is quite good between the activation energy and the frequency factor. Note that the discrepancy between the experimental data and the calculated frequency factor concerns mainly the PHB, but also the PG (for the frequency factor). The contributions to activation energy and frequency factor are logically correlated (see Figure S3 in Supplementary Materials).
Figure Figure 6. 6. Experimental Experimental versus versus calculated calculated activation activation energies energies for for the the studied studied polymers. polymers. Figure 6. Experimental versus calculated activation energies for the studied polymers. Figure 6. Experimental versus calculated activation energies for the studied polymers.
Figures 6 and 7 show the correlation between the experimental values (i.e. obtained from Kissinger method) and the calculated ones using values in Table 3. The correlation is quite good concerning for the activation energy and for the frequency factor. Note that the discrepancy between the experimental data and the calculated frequency factor concerns mainly the PHB but also the PG (for frequency Polymers 2017, 9, 706factor). The contributions to activation energy and frequency factor are logically 9 of 15 correlated (see Figure S3 in supporting information).
Figure 6. Experimental versus calculated activation energies for the studied polymers.
Figure 6 – Experimental versus calculated activation energies for the studied polymers
11
Figure 7. Experimental versus calculated LnA for the studied polymers.
Figure 7 – Experimental versus calculated Ln(A) for the studied polymers
4. Reaction Model As explained above, the MLR curve in a PCFC is deduced from an HRR curve. For each polymer, Reaction model we used the activation energy and frequency factor already calculated, as well as the parameter n listed in Table 4, to fit this MLR curve. Noteisthat the activation energyThe hasbest been slightly modified, As explained above, MLR curve in PCFC deduced from HRR curve. reaction model able toas explained in MLR the section The reaction models (Equation (3), i.e., models) fit the curve is“Method”. chosen using slightly corrected activation energy and Avrami-Erofeev frequency factor already for the various polymers differ only from the parameter n. Note the values listed in Table 4 are also the calculated. The reaction models (equation 3) differ only from the parameter n. Table 3 lists the parameter n used for each polymer. Note these values are also the best ones to fit the TGA curves (except PP for which n value may be closer to 2). In other words, the kinetic triplet used to fit PCFC curves is fully defined from thermogravimetric analyses. Table 3 – Values of the parameter n for all studied polymers
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best ones to fit the TGA curves (except PP, for which the n value may be closer to 2). In other words, the kinetic triplet used to fit MLR curves obtained from PCFC is fully defined from TGA. Figures 8 and 9 show the experimental and calculated mass loss rate curves for PLA and PHB, respectively. Experimental curves have been obtained from HRR curves in a PCFC, using Equation (2). The curves for other studied polymers can be found in the Supplementary Materials. It is noticeable that the reaction models fit the mass loss rate curves quite well, at least when the mass loss rate is moderate to high (>0.005–0.01 s−1 ). The temperature and the intensity of the peak of mass loss rate are both well-fitted. The accuracy of the experimental curve is lower at low and high conversions, in particular for PHB. The calculated MLR curve for PCL is less satisfying, but the temperature and the intensity of the peak of the MLR remain well-fitted. Using Equation (2), and the value of the heat of complete combustion listed in Table 1, it is easy to rebuild the HRR curves, and to compare the calculated and experimental pHRR. Figure 10 shows the good agreement between the pHRRs calculated using the kinetic triplets determined previously and the experimental pHRR. Table 4. Values of the parameter n for all studied polymers. Polymer
n
PE 2 PP 1.5 PET 1.5 1.5 mass loss rate curves for PLA and PHB Figures 8 and 9 show the experimentalPBT and calculated PCL 1.5be found in supporting information. It is respectively. The curves for other studied polymers can PBS 1.5 noticeable that the reaction models fit quite well the mass loss rate curves, at least when mass loss PHB 3.5 rate is moderate to high (> 0.005-0.01 s-1PLA ). The temperature and the intensity of the peak of mass 2 2.5 high conversions, in particular for PHB. loss rate are well fitted. The accuracy is PG lower at low and PMMAbut the temperature 1 Calculated MLR curve for PCL is less satisfying and the intensity of the peak of PS 2
MLR remain well fitted.
Figure 8 – Experimental and mass calculated mass loss rate curves for PLA 1 K/s at 1 K/s. Figure 8. Experimental and calculated loss rate curves for poly(lactic acid)at(PLA)
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It is quite surprising that such a result was obtained for only one type of reaction model (the Avrami-Erofeev model), which allows for an easy comparison between polymers. The simple approach developed here (based on Kissinger’s method and the Avrami-Erofeev model) should be extended to other polymers, in order to check its applicability. The main interest of this approach is to allow an easy comparison between polymers, as well as the identification of polymers for which pyrolysis kinetics appears unexpected and needs further research. The last section illustrates the usefulness of the method.
Figure9.9 –Experimental Experimentaland andcalculated calculatedmass massloss lossrate ratecurves curvesfor forPHB PHBat at11K/s. K/s Figure Using equation 2 and value of heat of combustion listed in Table 1, it is easy to rebuild the HRR curves and to compare the calculated and experimental pHRR. Figure 10 shows that the agreement between calculated and experimental pHRR is very good. It is quite surprising that such a result is obtained for only one type of reaction models (AvramiErofeev models) allowing an easy comparison between polymers. The simple approach developed here (based on Kissinger’s method and Avrami-Erofeev models) should be extended to other polymers in order to check its applicability. Its main interest is to allow an easy comparison between polymers and the identification of polymers for which pyrolysis kinetics appears unexpected and needs further researches. The last section illustrates the usefulness of the method.
Figure 10.10 Comparison between thecalculated calculatedand andexperimental experimentalpHRR peakfor of the Heat (pHRR) Figure – Comparison between 11Release studiedRate polymers for the 11 studied polymers.
Discussion about the flammability of PHB The above comparison of kinetic triplets allows establishing some relations between the chemical structure and some parameters. In particular, the influence of ester group into the polymer backbone or the presence of methyl group as pendant group is highlighted. Both cases contribute 14 to lower the activation energy which leads to a low thermal stability. PG and PLA exhibit low activation
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5. Discussion about the Flammability of PHB The above comparison of kinetic triplets allows for establishing some relationships between the chemical structure of polymers and some parameters. In particular, the influence of an ester group on the polymer backbone, or the presence of a methyl group as a pendant group is highlighted. Both cases contribute to lowering the activation energy, which leads to a low thermal stability. PG and PLA exhibit low activation energy due to a high ester fraction. PHB has the same ester fraction as PBS, but a lower activation energy due to the presence of a CH3 pendant group. Nevertheless, due to the compensation effect, the frequency factor decreases together with activation energy. Therefore, the influence of activation energy on thermal stability is real, but limited. However, for PHB, the frequency factor is higher than expected, promoting a faster decomposition. Figure 11 shows the MLR curve of PHB if the compensation effect was respected, i.e., if the frequency factor was correlated with the activation energy through the relationship in Figure 5. In that case, the peak of MLR would be lower and shifted to higher temperature. The reason PHB does not respect the compensating effect is unknown. Finally, PG, PLA, and PHB also exhibit a high value for parameter n (2–2.5 and even 3.5 for PHB versus 1.5 for all other polyesters). A high value for n is also responsible for an increase of the pyrolysis rate. Figure 12 shows the calculated mass loss rate curves of PHB for different values of n. An increase in the n value does not influence the temperature of the peak, but increases significantly its intensity (i.e., also the intensity of pHRR).
Figure11 11.– Experimental mass lossloss raterate curves at 1 K/s a PCFC). Figure Experimentaland andcalculated calculated mass curves at 1for K/sPHB for (in PHB (PCFC).Calculation Calculation was done with andwas without compensation effect. donerespecting with and the without respecting compensation effect.
Finally PG, PLAthese and two PHB sources also exhibit a high valuefor forPHB parameter (2-2.5 and factor even 3.5 forexpected PHB versus Note that of discrepancy (highernfrequency than and 1.5 for all other A high value forHRC n is also forconsidering an increaseaofvalue pyrolysis high n value) are polyesters). enough to explain why its is soresponsible high. When for nrate. = 1.5 Figure 12 shows calculated mass lossthe rate curves of PHB different An increase in n and respecting thethe compensation effect, HRC is only 380for J/(g ·K). Thisvalues valueofisn. close to the dotted line in Figure 2, and in agreement with theof calculated value using asignificantly Van Krevelen value does not influence the temperature the peak but increases its method intensity(Figure (i.e. also1). Inthe theintensity case of PLA and PG, the calculation with n = 1.5 (versus 2 and 2.5 respectively) leads to an HRC of pHRR). Note that these two sources of discrepancy for PHB (higher frequency factor than expected and high n value) are enough to explain why its HRC is so high. When considering a value for n = 1.5 and respecting the compensation effect, the HRC is only 380 J/g.K. This value is close to the dotted line in Figure 2 and in agreement with the calculated value using a Van Krevelen method (Figure 1). In the case of PLA and PG, the calculation with n = 1.5 (versus 2 and 2.5 respectively) leads to HRC equal to
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equal to 320 and 145 J/(g·K) respectively. These values are also close to those expected from the rough correlation between HRC and THR seen in Figure 2.
Figure Experimentaland andcalculated calculated mass curves at 1atK/s (in (PCFC) a PCFC)with withdifferent different values values for Figure 12 –12.Experimental massloss lossrate rate curves 1 K/s for n for PHB. n for PHB
6. Conclusions The originality of this work is obviously not the use of very classical methods to calculate the Conclusion kinetic triplet. However, the procedure described here should allow the main flammability properties ofThe polymers to be accurately. originality ofpredicted this work more is obviously not the use of very classical methods to calculate the kinetic Indeed, the contribution to the HRC of ester functions to predict the correctly HRC of all aliphatic triplet. But the procedure described here should allow fails predicting more the main polyesters on its own. On the other hand, taking into account the kinetic triplet—Activation energy, flammability properties of polymers. frequency factor, and the n parameter (from the Avrami-Erofeev model)—Accounts for the surprising behavior Indeed, this polymer is the main exception, which the predicted much Indeed, of thePHB. contribution to HRC of ester function fails on its for own to predict the HRCHRC of allwas aliphatic lower than the experimental value. polyesters. Whereas taking into account the kinetic triplet: activation energy, frequency factor and n Moreover, it may be possible calculate the activation energy using the Vanbehavior Krevelenof method, parameter (from Avrami-Erofeev tomodel), allows to account for the surprising PHB. based on the additivity of group contributions. Calculating the contributions of chemical groups Indeed this polymer is the main exception, for which the predicted HRC was much lower than theto activation energy, as well as establishing the relations between the chemical structure and the values of experimental value. the frequency factor and n parameter, are the next steps to improve the model. Of course, such Van Krevelen method can appear to be using too simplistic. Moreover, the used Moreover, it may beapossible to calculate the activation energy a Van Krevelen method based parameters are a purely mathematical description, and probably have no physical meaning. Therefore, on the additivity of group contributions. Calculating the contributions of chemical groups to there are obvious approach. approach could be structure powerfuland if itthe allows the activation energylimits as wellforasthis establishing theHowever, relations the between the chemical values flammability of polymers to be assessed quickly, and with good accuracy.
of frequency factor and n parameter, are the next steps to improve the model.
Supplementary Materials: The following are available online at www.mdpi.com/2073-4360/9/12/706, Figure S1: Of course,between such a Van Krevelen method can appear as too simplistic.analysis Moreover, the used parameters Comparison activation energies calculated from thermogravimetric (TGA) data using Kissinger’s method and activation energies used to fit the pyrolysis-combustion flow calorimeter (PCFC) results; Figure S2: are a purely mathematical description and have probably no physical meaning. Therefore there are Correlation between the contributions to activation energy and frequency factor; Figure S3: Experimental versus obvious mass limitsloss forrate thiscurves approach. it can be powerful if it allows assessing flammability of calculated for PE But at 1 K/s; Figure S4: Experimental versus calculatedthe mass loss rate curves for PP at 1 K/s; Figure Experimental polymers quickly withS5: a good accuracy.versus calculated mass loss rate curves for PET at 1 K/s; Figure S6: Experimental versus calculated mass loss rate curves for PBT at 1 K/s; Figure S7: Experimental versus calculated
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mass loss rate curves for PBS at 1 K/s; Figure S8: Experimental versus calculated mass loss rate curves for PCL at 1 K/s; Figure S9: Experimental versus calculated mass loss rate curves for PG at 1 K/s; Figure S10: Experimental versus calculated mass loss rate curves for PS at 1 K/s; Figure S11: Experimental versus calculated mass loss rate curves for PMMA at 1 K/s; Table S1: Activation energies from literature for studied polymers. Acknowledgments: The authors thank Belkacem Otazaghine and Benjamin Gallard for their help. Author Contributions: For research articles with several authors, a short paragraph specifying their individual contributions must be provided. The following statements should be used “Loïc Dumazert and Rodolphe Sonnier conceived and designed the experiments; Loïc Dumazert performed the experiments; Loïc Dumazert and Rodolphe Sonnier analyzed the data; Rodolphe Sonnier wrote the paper.” Authorship must be limited to those who have contributed substantially to the work reported. Conflicts of Interest: The authors declare no conflict of interest.
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