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Kinetic study of the pyrolysis of neoprene
J. Anal. Appl. Pyrolysis 74 (2005) 231–237 www.elsevier.com/locate/jaap
Kinetic study of the pyrolysis of neoprene J.A. Caballero *, J.A. Conesa, I. Martı´n-Gullo´n, R. Font Department of Chemical Engineering, University of Alicante, Ap. 99, E-03080 Alicante, Spain Received 11 June 2004; accepted 11 November 2004 Available online 7 April 2005
Abstract Kinetics of neoprene thermal decomposition has been performed under dynamic conditions at different heating rates, between 5 and 80 8C/ min in a TG apparatus. The same kinetic model has been applied simultaneously to runs performed at different heating rates and different atmospheres allowing a good correlation of the weight loss data. A mechanism based on three independent reactions has been used to model the thermal decomposition. The first reaction is of an order close to two, and the other two reactions are of order below one, similar to other plastic materials. Different alternatives for the mathematical treatment for fitting TG data were considered. The accuracy of the calculated kinetic parameters was studied by means of a sensibility analysis. # 2004 Elsevier B.V. All rights reserved. Keywords: Neoprene; Pyrolysis; Thermogravimetry
1. Introduction Pyrolysis has become an interesting alternative for converting the gradual increase of plastics disposals in valuable chemicals, which can be used either as fuels or valuable raw materials for the chemical and petrochemical industry. Thermogravimetric analysis is one of the most used techniques to study the primary reactions of decomposition of solids. In the case of tyres, the use of thermogravimetric techniques has been used for the identification of the polymers present in the material, and their proportions. Different rubbers were thermogravimetrically analysed by Conesa and Marcilla [1], and the authors were able to predict the behaviour of rubber mixtures, as well as the composition of some other samples. Brazier and Schwartz [2], Sircar and Lamond [3], Brazier and Nickel [4], and Yang et al. [5] state that the use of Derivative ThermoGravimetry (DTG) instead of TG makes * Corresponding author. Tel.: +34 96 5903400x2322; fax: +34 96 5903826. E-mail address: [email protected] (J.A. Caballero). 0165-2370/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jaap.2004.11.007
easier the identification of the polymers, mainly because small changes in TG curves are magnified in the corresponding DTG curves. These researchers show that there are two characteristic zones in the DTG of a rubber: in the first, the decomposition of the processing oil, plastifier and additives takes place, whereas in the second, the polymer is decomposed. Sircar and Lamond [3] showed that the temperature of maximum rate of volatilization (Tmax) is 365 8C for natural rubber (NR, polyisoprene), 447 8C for the styrene–butadiene rubber (SBR), and 465 8C for butile rubber (BR), when heating at 10 8C/min. According to Yang et al. [5], the Tmax would be 377, 444 and 465 8C for NR, SBR and BR, respectively, at the same heating rate. These authors showed that the Tmax can vary, depending on the sample where the polymers are contained. These researchers showed that the experimental curve can be simulated by means of a fit of the experimental data to a kinetic scheme that assumes the independent decomposition of each polymer by means of a n-order reaction. By means of this fit, Yang et al. [5] calculated the initial amount of each polymer and oil in the original tyre. Maurer [6] proposed the calculation of the
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J.A. Caballero et al. / J. Anal. Appl. Pyrolysis 74 (2005) 231–237
Nomenclature e Ei Fi Gi I ki kio OF Su wio u
unitary vector activation energy (kJ/mol) i fraction of the sample gases from fraction i contribution of inorganic fraction to the weight of the non-pyrolyzed sample kinetic constant (s1) pre-eponential factor (s1) objective function sensitivity parameter contribution of each organic fraction to the weight of the non-pyrolyzed sample optimized parameter
polymer composition by means of the peak height in DTG obtained in an air atmosphere, but Sircar and Lamond [3] indicate that the reproducibility in an air atmosphere is not as good as in a nitrogen atmosphere. Literature available about thermogravimetric studies of solids under inert atmosphere is widely extent. Some of the recent papers published on this subject show the usefulness of TGA to characterize refuses (as recycled cellulose by Devallencourt et al. [7]), study decomposition mechanisms of biomass [8], calculate decomposition kinetic constants to predict the overall rate of volatile release [9] or as a previous step in refuse incineration (PVCC and polyamide-6 by Bockhorn et al. [10] or epoxy resin by Chen and Yeh [11]). In the same way, TGA is a useful tool to study charcoal gasification, since it provides accurate data about charcoal reactivities under active atmospheres (CO2, oxygenated mixtures or steam). Literature about this subject is also extent [12–15]. Neoprene is noted for a unique combination of properties, which has led to its use in thousands of applications in diverse environments. The basic chemical composition of neoprene synthetic rubber is polychloroprene. The polymer structure can be modified by copolymerizing chloroprene with sulfur and/or 2,3dichloro-1,3-butadiene to yield a family of materials with a broad range of chemical and physical properties. For this study, we have selected Neoprene AD-10 (DuPont Dow), which is a solid cloroprene homopolymer. Neoprene was the original coating used in automotive airbags production. Nowadays, primary use of neoprene is in contact adhesives that require high initial and ultimate bond strength and ability to form bonds with minimum pressure after long open assembly periods. Neoprene can be dissolved without milling, or can be milled before solution (for reology control), to cover a broad range of solution viscosity. It is soluble in solvents with various evaporation rates. Neoprene has no known health hazards, but it should be handled in accordance with good industrial hygiene
practices. However, flame chemistry in incineration systems involves the formation of many organic products of incomplete combustion, including chlorinated species (specially important in compounds like neoprene) such as polychlorinated biphenyls (PCB), polychlorinated dibenzo-p-dioxins (PCDD), and polychlorinated dibenzofurans (PCDF). The presence of a high amount of chlorine in the atmosphere will cause the formation of such a pollutants if a good control of the conditions does not exists, which is a point to take into account in any process in which neoprene is implied [16,17]. Neoprene decomposition has been investigated for long time. In 1948, Skinner and McNeal [18] investigated the decomposition of different elastomers at high temperatures, being neoprene one of the polymers used. The authors showed that neoprene undergoes an exothermic decomposition when rapidly heated, and that an increase in the heating rate enhances the abruptness and magnitude of the exothermic rise. The authors demonstrate that the exothermic activity is ascribed primarily to the existence of residual double bond in the polymer structure. More recently, Gupta et al. [19] studied the decomposition of nylon impregnated with different flame-retardant rubbers, also including polychloroprene (neoprene). It has been demonstrated in many cases, that the appropriated kinetic model can explain a set of TG dynamic data with a single set of kinetic parameters, regardless the heating rate [20]. It seems evident that if a kinetic model can explain the results obtained in different operating conditions with a single set of kinetic parameters, there is no reason to admit a change in the reaction mechanism, unless other independent evidence of such a change exists [21]. It is known that, for an adequate design and/or operation of the equipment involved in the energetic valorization of materials, it is necessary to know the kinetics of the processes, i.e., reaction rates. The aim of the present work is to present and discuss the thermogravimetric behaviour of the neoprene in inert atmosphere. A kinetic scheme able to correlate simultaneously (with no variation of the kinetic constants) runs performed at different heating rates is presented.
2. Equipment and experimental procedure The material used in this paper is Neoprene AD-10 made by DuPont Dow. Technical data could be easily found in www.dupont-dow.com. The thermobalance used in the study was a SETARAM 92-16.18 Model TGA. The atmosphere used was helium with a flow rate of 60 ml min1. The temperature control was made by a Pt/Pt–Rh thermocouple located directly below the sample basket (0.4 mm i.d.; 0.7 mm high). The carrier gas flow used in the experiments was introduced in the thermobalance from the upper side of the equipment
J.A. Caballero et al. / J. Anal. Appl. Pyrolysis 74 (2005) 231–237
causing this way a small buoyancy force downwards. This effect brings a small error to the weight measurements, which is corrected with blank runs. The equipment itself can make an assumption of the quantity of this buoyancy, which it then quits automatically from the resulting experimental data. The experimental data presented in this paper corresponding to the different operating conditions, are the mean values of runs carried out twice or thrice. The results obtained in all these cases were very similar. The experiments were carried out at five different heating rates (5, 10, 30, 40 and 80 8C/min). The initial sample weight was always lower than 4 mg with particles previously milled to powder; under these conditions heat transfer effects are minimized. 2.1. Mathematical treatment of the data Each run, at the different heating rates has the same number of points to be fitted (70 points), in such a way that all the runs contribute in the same proportion to the objective function. The objective function used considers the data of all the experiments made at different heating rates, as has been proposed previously [1,21], and is the following: XX OF ¼ ½wexpi j wcalci j 2 j
i
where i represents the experimental data at time t in the experiment with a heating rate j. In this objective function, all the points in each fit contribute in the same proportion.
3. Results and discussion Fig. 1 shows the evolution of the weight loss of each sample at the different heating rates used. As heating rate increases, the weight loss curves are displaced to higher temperatures. 3.1. Kinetic model The kinetic model applied to the TG data considers three organic fractions that decompose independently producing volatiles. In the original polymer exists a fraction that cannot be decomposed at the temperatures studied in the present work; besides it is possible some char formation. Non decomposed fraction and char cannot be differentiate in a TG experiment in which we only have information about weight loss. This fraction (an inorganic fraction and char) will be represented by I. Remark that kinetic equations are the same independent if the I fraction comes from the inorganic fraction or from the char. A similar model has been used to explain the decomposition of other rubber samples [1]. The decomposition of each organic fraction has been considered to follow the reaction Eq. (S1):
233
Fi ! Gi ; i ¼ 1; 2; 3 I !I ðno mass loss in the given temperature domainÞ (S1) where Fi is the i fraction of the sample and Gi is the gases (or volatiles) produced by this fraction. wio is the contribution of each organic fraction to the weight of the non-pyrolyzed sample. Consequently: w1o þ w2o þ w3o þ I ¼ 1
(1)
where I is the inorganic plus char fraction (determined by the residue at the maximum temperature of the runs). As in the thermobalance it is not possible to distinguish between the non-decomposed sample and the solid residue formed, it is usual to study the global weight-loss kinetics. The kinetic equations representing the process (S1) are: dFi ¼ ki Fini ; i ¼ 1; 2; 3 (2) dt The boundary condition of this differential equation is F i = wio at t = 0. Bearing in mind that the weight measured is the non-decomposed fraction and the inorganic fraction it can be written: w ¼ F1 þ F2 þ F 3 þ I
(3)
Then, the global mass loss kinetic equation for (S1) is deduced to the Eq. (1), and the weight of sample is: X w¼ wi þ I (4) i
The kinetic constant ki can be expressed by an Arrhenius law: Ei ki ¼ kio exp (5) RT There is a broad literature about mathematical treatment for fitting experimental data to a given TG curve, see for example [22]. Some of the methods tray to adjust each point of the curve assuming a variation of activation energy with conversion. Although, this approach could be justified due to the fact that single thermal decomposition could involve a large number of individual reactions, in practice is preferred to assume that these reactions can be lumped in a single one, in other case the physical meaning is lost and the model becomes a correlation model with no practical applications. Another approach consists in the linearization of kinetic equations using graphical representations like for example for a first order reaction: dw=dt 1 ln (6) versus w T However, this approach produces very inaccurate results. On one hand, the data should be filter in order to get a smooth representation of the derivative, introducing some error. On the other hand, the method is very sensitive to small errors in experimental data. The parameters obtained with this approach can be considered a good starting point for more sophisticated methods.
Fig. 1. TG obtained at different heating rates. Experimental and calculated values.
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The most common approach for solving this problem consists of coupling an ordinary differential equation solver (ODE) with an optimizer for a minimum square fit. In order to avoid numerical problems with the calculation of derivatives a direct search solver is usually chosen, the most used are probably those based on the simplex flexible method or in simulated annealing. This last approach is very reliable and easy to use (and to program). The major drawback is that in some cases, the number of function evaluations (number of times that the ODE solver is invoked) is very high. Even with modern computers if the number of parameters is not small, the calculation could take a considerable amount of time. There are different ways to avoid this difficulty. The most straightforward is change to an optimizer that uses information of the derivatives. Successive Quadratic Programming (SQP) or Generalized Reduced Gradient (GRG) codes are the most used. In this case, the tolerances of the ODE solver must be tightened in order to get accurate numerical derivatives (at least first derivatives: the Hessian matrix can be approximated by an update formula like BFGS or DFP [23]), in other case, the rate of convergence can dramatically decrease due to a bad selection in the search directions or even converge to spurious optimal values. Although, the ODE system is solved more times in each iteration to calculate the derivatives, the total number of iterations dramatically decreases reducing considerably the total calculation time. One more step is even possible. Differential equations can be discretized using orthogonal collocation or any other method. The system becomes in a nonlinear programming problem with only algebraic equations [24]. This last approach is the faster, however, a large number of algebraic equations appear and a solver that can deal with sparse systems of equations is usually required. The mathematical calculations have been done using the software Matlab 6.0. The integration of the kinetic equations was carried out using the ODE45 method implemented in Matlab, and the optimisation performed using a SQP algorithm. For each of the reactions, a total of four different parameters are used: the pre-exponential factor ki, activation energy Ei, the reaction order ni and the initial contribution to the weight wio . A value of wio could be calculated using Eq. (3) so the total number of parameters is 11. In order to scale the different parameters, the following was used in the optimization: logðkoi; 1000K Þ E =R=1000 i (7) ni w io The corresponding parameters are presented at Table 1, together with a sensibility parameter defined as: OFðu þ ei eTi DuÞ OFðuÞ Sui ð%Þ ¼ 100 OFðuÞ
(8)
235
Table 1 Optimal value of the adjusted parameters and sensitivity parameter S a
log (ko1) E1 (kJ/mol) n1 w1o
18.65 166.8 2.1 0.042
8.40 0.30 3.03 35.43
log (ko2)a E2 (kJ/mol) n2 w2o
6.62 100.0 0.70 0.404
1.31 0.31 1.50 122.0
log (ko3)a E3 (kJ/mol) n3
11.39 148.6 0.45
5.81 0.82 3.44
Objective function: 0.0124 a
1
ko (min ).
where OF makes reference to the objective function and u makes reference to a vector containing each one of the adjusted parameters given in Eq. (7). ei is an unitary vector (a column vector of zeros except in the i position in where there is a 1). For example: 12 2 3 02 3 3 Du1 u1 1 C6 Du 7 6 u 7 B6 0 7 C6 2 7 6 2 7 B6 7 T B 6 7 6 7 6 7 u þ e1 e1 Du ¼ 6 . 7 þ B6 . 7½ 1 0 0 C C6 .. 7 A4 . 5 4 .. 5 @4 .. 5 0 un 3 u1 þ Du1 6 7 u2 6 7 6 7 ¼6 .. 7 4 5 . 2
Dun
(9)
un Sensibilities defined by Eq. (8) provide information about the effect of locally variations of any parameter around the optimal solution on the quality of the fit. Larger sensitivities indicate important influence of those parameters over the quality of the fit. Note that a classical confidence interval analysis loss their physical meaning due to the fact that errors in TG–DTG experiments are neither independent nor random and, although, they can provide some qualitative information they also can produce ‘‘confused information’’ (the interval of variation in the parameter do not correspond with the postulated confidence). Sensibility parameters defined by Eq. (8) provided information about the effect of the parameters variation without the limitations of confidence analysis. In order to the effect of each parameter on the objective function be comparable with the effect of other parameters, we calculate the sensitivities according to previous equation for a fixed relative perturbation of the parameters: Dui ¼ cte ui
(10)
Data presented in Table 1 include the sensitivity parameters as defined by Eq. (9) with a relative variation of each parameter (Eq. (10)) of 102.
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Fig. 2. Contribution of each fraction to the TG of neoprene. 5 8C/min.
It is worth to mention that when we perform a sensibility analysis usually, we are interested in the sensitivity coefficients. In our case, the sensitivity coefficients are @w/@u. In other words, ‘how each experimental point is affected by the variation of each parameter’. Although, in some circumstances, it could be of interest (for instant to detect parameters affecting only to a part of a curve). In general, the global information given by the sensitivity parameters defined by Eq. (8) are enough. In any case, calculating the sensitivity coefficients can be performed together with the calculation of derivatives if a gradient based algorithm is used. Writing in a more general form the kinetic equations as: dw ¼ Fðt; w; uÞ (11) dt Differentiating Eq. (9) with respect to u and using the chain rule we have: @ dw @F @F @w þ (12) ¼ @u dt @u @w @u Interchanging the order of differentiation we get: d @w @F @F @w þ ¼ dt @u @u @w @u
(13)
Table 2 Tmax (8C) of each fraction at the different heating rates Fraction 1 Fraction 2 Fraction 3
In order to obtain @w/@u, we must solve the set of differential and algebraic equations (DAE) together with the set of equations given by Eq. (13) with the quantities @F/@u and @F/@w obtained by simple differentiation. Eq. (13) is called sensitivity equations and the values @w/@u are called, as previously mentioned, sensitivity coefficients. Note that the parameter with major sensibility is w2o due to the fact that small deviations in this parameter change the position in which the second decomposition takes places and then all the TG curve is displaced respect to the experimental. Same comments are valid for w1. Note also that the TG curves are especially insensitive to activation energies and that small variations in log (ki) have a considerable effect. Fig. 1 shows the experimental and calculated weight loss curves. A very good agreement can be observed with the same kinetic constants at the three heating rates. Fig. 2 shows the contribution of each fraction to the total weight loss curve, for the experiment at 5 8C/min. From this figure, and from the corresponding to the other samples, the temperatures Tmax corresponding to each fraction can be deduced, and are presented at Table 2. The first fraction being decomposed corresponds to the plastifier decomposition (process that takes place in the range 220–260 8C). The values calculated of initial amount of plastifier are in these case 4.2%.
4. Conclusions
5 8C/min
10 8C/min
30 8C/min
40 8C/min
80 8C/min
235 366 448
236 367 448
237 369 449
238 371 451
237 380 455
Very good representation of the weight loss of neoprene has been obtained by a kinetic model involving three organic fractions representing the three main steps of neoprene
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decomposition, and using kinetic parameters independent of the heating rate.
Reference [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
J.A. Conesa, A. Marcilla, J. Anal. Appl. Pyrolysis 37 (1996) 95. D.W. Brazier, N.V. Schwartz, J. Appl. Polym. Sci. 22 (1978) 113. A.K. Sircar, T.G. Lamond, Rubber Chem. Technol. 48 (1975) 301. D.W. Brazier, G.H. Nickel, Rubber Chem. Technol. 48 (1975) 661. J. Yang, S. Kaliaguine, C. Roy, Rubber Chem. Technol. 66 (1993) 213. J.J. Maurer, J. Macromol. Sci. Chem. A8 (1974) 73. C. Devallencourt, J.M. Saiter, D. Capitaine, Polym. Degrad. Stab. 52 (1996) 327. G. Varhegyi, P. Sza´ bo, F. Till, B. Zelei, M.J. Antal Jr., X. Dai, Energy Fuels 12 (1998) 969. H. Teng, H.C. Lin, J.A. Ho, Ind. Eng. Chem. Res. 36 (1997) 3975. H. Bockhorn, A. Hornung, U. Hornung, S. Teepe, J. Weichmann, Combust. Sci. Techol. 116–117 (1996) 129. K.S. Chen, R.Z. Yeh, J. Hazard. Mater. 49 (1996) 105.
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[12] I. Martı´n-Gullo´ n, M. Asensio, A. Marcilla, R. Font, Ind. Eng. Chem. Res. 35 (1996) 4139. [13] S. Dutta, C.Y. Wen, R.J. Belt, Ind. Eng. Chem. Process Des. Dev. 16 (1977) 20. [14] S. Dutta, C.Y. Wen, Ind. Eng. Chem. Process Des. Dev. 16 (1977) 31. [15] P. Salatino, O. Senneca, S. Masi, Carbon 36 (1998) 443. [16] B.R. Stanmore, Combust. Flame 136 (2004) 398. [17] J.A. Conesa, A. Fullana, R. Font, J. Anal. Appl. Pyrolysis 58–59 (2001) 555. [18] G.S. Skinner, J.H. McNeal, Ind. Eng. Chem. 40 (1948) 2303. [19] Y.N. Gupta, A. Chakraborty, D.K. Setua, J. Appl. Polym. Sci. 89 (2003) 2051. [20] E. Avni, R.W. Coughlin, Thermochim. Acta 90 (1985) 157. [21] J.A. Conesa, J.A. Caballero, A. Marcilla, R. Font, Thermochim. Acta 254 (1995) 175. [22] J.A. Conesa, J.A. Caballero, A. Marcilla, R. Font, J. Anal. Appl. Pyrolysis 58–59 (2001) 617. [23] S.G. Nash, A. Soler, Linear and nonlinear programming, Series in Industrial Engineering and Management Sciences, McGrawHill, 1996. [24] J.E. Cuthrell, L.T. Biegler, AIChE J. 33 (8) (1987) 1257.
Kinetic study of the pyrolysis of neoprene J.A. Caballero *, J.A. Conesa, I. Martı´n-Gullo´n, R. Font Department of Chemical Engineering, University of Alicante, Ap. 99, E-03080 Alicante, Spain Received 11 June 2004; accepted 11 November 2004 Available online 7 April 2005
Abstract Kinetics of neoprene thermal decomposition has been performed under dynamic conditions at different heating rates, between 5 and 80 8C/ min in a TG apparatus. The same kinetic model has been applied simultaneously to runs performed at different heating rates and different atmospheres allowing a good correlation of the weight loss data. A mechanism based on three independent reactions has been used to model the thermal decomposition. The first reaction is of an order close to two, and the other two reactions are of order below one, similar to other plastic materials. Different alternatives for the mathematical treatment for fitting TG data were considered. The accuracy of the calculated kinetic parameters was studied by means of a sensibility analysis. # 2004 Elsevier B.V. All rights reserved. Keywords: Neoprene; Pyrolysis; Thermogravimetry
1. Introduction Pyrolysis has become an interesting alternative for converting the gradual increase of plastics disposals in valuable chemicals, which can be used either as fuels or valuable raw materials for the chemical and petrochemical industry. Thermogravimetric analysis is one of the most used techniques to study the primary reactions of decomposition of solids. In the case of tyres, the use of thermogravimetric techniques has been used for the identification of the polymers present in the material, and their proportions. Different rubbers were thermogravimetrically analysed by Conesa and Marcilla [1], and the authors were able to predict the behaviour of rubber mixtures, as well as the composition of some other samples. Brazier and Schwartz [2], Sircar and Lamond [3], Brazier and Nickel [4], and Yang et al. [5] state that the use of Derivative ThermoGravimetry (DTG) instead of TG makes * Corresponding author. Tel.: +34 96 5903400x2322; fax: +34 96 5903826. E-mail address: [email protected] (J.A. Caballero). 0165-2370/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jaap.2004.11.007
easier the identification of the polymers, mainly because small changes in TG curves are magnified in the corresponding DTG curves. These researchers show that there are two characteristic zones in the DTG of a rubber: in the first, the decomposition of the processing oil, plastifier and additives takes place, whereas in the second, the polymer is decomposed. Sircar and Lamond [3] showed that the temperature of maximum rate of volatilization (Tmax) is 365 8C for natural rubber (NR, polyisoprene), 447 8C for the styrene–butadiene rubber (SBR), and 465 8C for butile rubber (BR), when heating at 10 8C/min. According to Yang et al. [5], the Tmax would be 377, 444 and 465 8C for NR, SBR and BR, respectively, at the same heating rate. These authors showed that the Tmax can vary, depending on the sample where the polymers are contained. These researchers showed that the experimental curve can be simulated by means of a fit of the experimental data to a kinetic scheme that assumes the independent decomposition of each polymer by means of a n-order reaction. By means of this fit, Yang et al. [5] calculated the initial amount of each polymer and oil in the original tyre. Maurer [6] proposed the calculation of the
232
J.A. Caballero et al. / J. Anal. Appl. Pyrolysis 74 (2005) 231–237
Nomenclature e Ei Fi Gi I ki kio OF Su wio u
unitary vector activation energy (kJ/mol) i fraction of the sample gases from fraction i contribution of inorganic fraction to the weight of the non-pyrolyzed sample kinetic constant (s1) pre-eponential factor (s1) objective function sensitivity parameter contribution of each organic fraction to the weight of the non-pyrolyzed sample optimized parameter
polymer composition by means of the peak height in DTG obtained in an air atmosphere, but Sircar and Lamond [3] indicate that the reproducibility in an air atmosphere is not as good as in a nitrogen atmosphere. Literature available about thermogravimetric studies of solids under inert atmosphere is widely extent. Some of the recent papers published on this subject show the usefulness of TGA to characterize refuses (as recycled cellulose by Devallencourt et al. [7]), study decomposition mechanisms of biomass [8], calculate decomposition kinetic constants to predict the overall rate of volatile release [9] or as a previous step in refuse incineration (PVCC and polyamide-6 by Bockhorn et al. [10] or epoxy resin by Chen and Yeh [11]). In the same way, TGA is a useful tool to study charcoal gasification, since it provides accurate data about charcoal reactivities under active atmospheres (CO2, oxygenated mixtures or steam). Literature about this subject is also extent [12–15]. Neoprene is noted for a unique combination of properties, which has led to its use in thousands of applications in diverse environments. The basic chemical composition of neoprene synthetic rubber is polychloroprene. The polymer structure can be modified by copolymerizing chloroprene with sulfur and/or 2,3dichloro-1,3-butadiene to yield a family of materials with a broad range of chemical and physical properties. For this study, we have selected Neoprene AD-10 (DuPont Dow), which is a solid cloroprene homopolymer. Neoprene was the original coating used in automotive airbags production. Nowadays, primary use of neoprene is in contact adhesives that require high initial and ultimate bond strength and ability to form bonds with minimum pressure after long open assembly periods. Neoprene can be dissolved without milling, or can be milled before solution (for reology control), to cover a broad range of solution viscosity. It is soluble in solvents with various evaporation rates. Neoprene has no known health hazards, but it should be handled in accordance with good industrial hygiene
practices. However, flame chemistry in incineration systems involves the formation of many organic products of incomplete combustion, including chlorinated species (specially important in compounds like neoprene) such as polychlorinated biphenyls (PCB), polychlorinated dibenzo-p-dioxins (PCDD), and polychlorinated dibenzofurans (PCDF). The presence of a high amount of chlorine in the atmosphere will cause the formation of such a pollutants if a good control of the conditions does not exists, which is a point to take into account in any process in which neoprene is implied [16,17]. Neoprene decomposition has been investigated for long time. In 1948, Skinner and McNeal [18] investigated the decomposition of different elastomers at high temperatures, being neoprene one of the polymers used. The authors showed that neoprene undergoes an exothermic decomposition when rapidly heated, and that an increase in the heating rate enhances the abruptness and magnitude of the exothermic rise. The authors demonstrate that the exothermic activity is ascribed primarily to the existence of residual double bond in the polymer structure. More recently, Gupta et al. [19] studied the decomposition of nylon impregnated with different flame-retardant rubbers, also including polychloroprene (neoprene). It has been demonstrated in many cases, that the appropriated kinetic model can explain a set of TG dynamic data with a single set of kinetic parameters, regardless the heating rate [20]. It seems evident that if a kinetic model can explain the results obtained in different operating conditions with a single set of kinetic parameters, there is no reason to admit a change in the reaction mechanism, unless other independent evidence of such a change exists [21]. It is known that, for an adequate design and/or operation of the equipment involved in the energetic valorization of materials, it is necessary to know the kinetics of the processes, i.e., reaction rates. The aim of the present work is to present and discuss the thermogravimetric behaviour of the neoprene in inert atmosphere. A kinetic scheme able to correlate simultaneously (with no variation of the kinetic constants) runs performed at different heating rates is presented.
2. Equipment and experimental procedure The material used in this paper is Neoprene AD-10 made by DuPont Dow. Technical data could be easily found in www.dupont-dow.com. The thermobalance used in the study was a SETARAM 92-16.18 Model TGA. The atmosphere used was helium with a flow rate of 60 ml min1. The temperature control was made by a Pt/Pt–Rh thermocouple located directly below the sample basket (0.4 mm i.d.; 0.7 mm high). The carrier gas flow used in the experiments was introduced in the thermobalance from the upper side of the equipment
J.A. Caballero et al. / J. Anal. Appl. Pyrolysis 74 (2005) 231–237
causing this way a small buoyancy force downwards. This effect brings a small error to the weight measurements, which is corrected with blank runs. The equipment itself can make an assumption of the quantity of this buoyancy, which it then quits automatically from the resulting experimental data. The experimental data presented in this paper corresponding to the different operating conditions, are the mean values of runs carried out twice or thrice. The results obtained in all these cases were very similar. The experiments were carried out at five different heating rates (5, 10, 30, 40 and 80 8C/min). The initial sample weight was always lower than 4 mg with particles previously milled to powder; under these conditions heat transfer effects are minimized. 2.1. Mathematical treatment of the data Each run, at the different heating rates has the same number of points to be fitted (70 points), in such a way that all the runs contribute in the same proportion to the objective function. The objective function used considers the data of all the experiments made at different heating rates, as has been proposed previously [1,21], and is the following: XX OF ¼ ½wexpi j wcalci j 2 j
i
where i represents the experimental data at time t in the experiment with a heating rate j. In this objective function, all the points in each fit contribute in the same proportion.
3. Results and discussion Fig. 1 shows the evolution of the weight loss of each sample at the different heating rates used. As heating rate increases, the weight loss curves are displaced to higher temperatures. 3.1. Kinetic model The kinetic model applied to the TG data considers three organic fractions that decompose independently producing volatiles. In the original polymer exists a fraction that cannot be decomposed at the temperatures studied in the present work; besides it is possible some char formation. Non decomposed fraction and char cannot be differentiate in a TG experiment in which we only have information about weight loss. This fraction (an inorganic fraction and char) will be represented by I. Remark that kinetic equations are the same independent if the I fraction comes from the inorganic fraction or from the char. A similar model has been used to explain the decomposition of other rubber samples [1]. The decomposition of each organic fraction has been considered to follow the reaction Eq. (S1):
233
Fi ! Gi ; i ¼ 1; 2; 3 I !I ðno mass loss in the given temperature domainÞ (S1) where Fi is the i fraction of the sample and Gi is the gases (or volatiles) produced by this fraction. wio is the contribution of each organic fraction to the weight of the non-pyrolyzed sample. Consequently: w1o þ w2o þ w3o þ I ¼ 1
(1)
where I is the inorganic plus char fraction (determined by the residue at the maximum temperature of the runs). As in the thermobalance it is not possible to distinguish between the non-decomposed sample and the solid residue formed, it is usual to study the global weight-loss kinetics. The kinetic equations representing the process (S1) are: dFi ¼ ki Fini ; i ¼ 1; 2; 3 (2) dt The boundary condition of this differential equation is F i = wio at t = 0. Bearing in mind that the weight measured is the non-decomposed fraction and the inorganic fraction it can be written: w ¼ F1 þ F2 þ F 3 þ I
(3)
Then, the global mass loss kinetic equation for (S1) is deduced to the Eq. (1), and the weight of sample is: X w¼ wi þ I (4) i
The kinetic constant ki can be expressed by an Arrhenius law: Ei ki ¼ kio exp (5) RT There is a broad literature about mathematical treatment for fitting experimental data to a given TG curve, see for example [22]. Some of the methods tray to adjust each point of the curve assuming a variation of activation energy with conversion. Although, this approach could be justified due to the fact that single thermal decomposition could involve a large number of individual reactions, in practice is preferred to assume that these reactions can be lumped in a single one, in other case the physical meaning is lost and the model becomes a correlation model with no practical applications. Another approach consists in the linearization of kinetic equations using graphical representations like for example for a first order reaction: dw=dt 1 ln (6) versus w T However, this approach produces very inaccurate results. On one hand, the data should be filter in order to get a smooth representation of the derivative, introducing some error. On the other hand, the method is very sensitive to small errors in experimental data. The parameters obtained with this approach can be considered a good starting point for more sophisticated methods.
Fig. 1. TG obtained at different heating rates. Experimental and calculated values.
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The most common approach for solving this problem consists of coupling an ordinary differential equation solver (ODE) with an optimizer for a minimum square fit. In order to avoid numerical problems with the calculation of derivatives a direct search solver is usually chosen, the most used are probably those based on the simplex flexible method or in simulated annealing. This last approach is very reliable and easy to use (and to program). The major drawback is that in some cases, the number of function evaluations (number of times that the ODE solver is invoked) is very high. Even with modern computers if the number of parameters is not small, the calculation could take a considerable amount of time. There are different ways to avoid this difficulty. The most straightforward is change to an optimizer that uses information of the derivatives. Successive Quadratic Programming (SQP) or Generalized Reduced Gradient (GRG) codes are the most used. In this case, the tolerances of the ODE solver must be tightened in order to get accurate numerical derivatives (at least first derivatives: the Hessian matrix can be approximated by an update formula like BFGS or DFP [23]), in other case, the rate of convergence can dramatically decrease due to a bad selection in the search directions or even converge to spurious optimal values. Although, the ODE system is solved more times in each iteration to calculate the derivatives, the total number of iterations dramatically decreases reducing considerably the total calculation time. One more step is even possible. Differential equations can be discretized using orthogonal collocation or any other method. The system becomes in a nonlinear programming problem with only algebraic equations [24]. This last approach is the faster, however, a large number of algebraic equations appear and a solver that can deal with sparse systems of equations is usually required. The mathematical calculations have been done using the software Matlab 6.0. The integration of the kinetic equations was carried out using the ODE45 method implemented in Matlab, and the optimisation performed using a SQP algorithm. For each of the reactions, a total of four different parameters are used: the pre-exponential factor ki, activation energy Ei, the reaction order ni and the initial contribution to the weight wio . A value of wio could be calculated using Eq. (3) so the total number of parameters is 11. In order to scale the different parameters, the following was used in the optimization: logðkoi; 1000K Þ E =R=1000 i (7) ni w io The corresponding parameters are presented at Table 1, together with a sensibility parameter defined as: OFðu þ ei eTi DuÞ OFðuÞ Sui ð%Þ ¼ 100 OFðuÞ
(8)
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Table 1 Optimal value of the adjusted parameters and sensitivity parameter S a
log (ko1) E1 (kJ/mol) n1 w1o
18.65 166.8 2.1 0.042
8.40 0.30 3.03 35.43
log (ko2)a E2 (kJ/mol) n2 w2o
6.62 100.0 0.70 0.404
1.31 0.31 1.50 122.0
log (ko3)a E3 (kJ/mol) n3
11.39 148.6 0.45
5.81 0.82 3.44
Objective function: 0.0124 a
1
ko (min ).
where OF makes reference to the objective function and u makes reference to a vector containing each one of the adjusted parameters given in Eq. (7). ei is an unitary vector (a column vector of zeros except in the i position in where there is a 1). For example: 12 2 3 02 3 3 Du1 u1 1 C6 Du 7 6 u 7 B6 0 7 C6 2 7 6 2 7 B6 7 T B 6 7 6 7 6 7 u þ e1 e1 Du ¼ 6 . 7 þ B6 . 7½ 1 0 0 C C6 .. 7 A4 . 5 4 .. 5 @4 .. 5 0 un 3 u1 þ Du1 6 7 u2 6 7 6 7 ¼6 .. 7 4 5 . 2
Dun
(9)
un Sensibilities defined by Eq. (8) provide information about the effect of locally variations of any parameter around the optimal solution on the quality of the fit. Larger sensitivities indicate important influence of those parameters over the quality of the fit. Note that a classical confidence interval analysis loss their physical meaning due to the fact that errors in TG–DTG experiments are neither independent nor random and, although, they can provide some qualitative information they also can produce ‘‘confused information’’ (the interval of variation in the parameter do not correspond with the postulated confidence). Sensibility parameters defined by Eq. (8) provided information about the effect of the parameters variation without the limitations of confidence analysis. In order to the effect of each parameter on the objective function be comparable with the effect of other parameters, we calculate the sensitivities according to previous equation for a fixed relative perturbation of the parameters: Dui ¼ cte ui
(10)
Data presented in Table 1 include the sensitivity parameters as defined by Eq. (9) with a relative variation of each parameter (Eq. (10)) of 102.
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Fig. 2. Contribution of each fraction to the TG of neoprene. 5 8C/min.
It is worth to mention that when we perform a sensibility analysis usually, we are interested in the sensitivity coefficients. In our case, the sensitivity coefficients are @w/@u. In other words, ‘how each experimental point is affected by the variation of each parameter’. Although, in some circumstances, it could be of interest (for instant to detect parameters affecting only to a part of a curve). In general, the global information given by the sensitivity parameters defined by Eq. (8) are enough. In any case, calculating the sensitivity coefficients can be performed together with the calculation of derivatives if a gradient based algorithm is used. Writing in a more general form the kinetic equations as: dw ¼ Fðt; w; uÞ (11) dt Differentiating Eq. (9) with respect to u and using the chain rule we have: @ dw @F @F @w þ (12) ¼ @u dt @u @w @u Interchanging the order of differentiation we get: d @w @F @F @w þ ¼ dt @u @u @w @u
(13)
Table 2 Tmax (8C) of each fraction at the different heating rates Fraction 1 Fraction 2 Fraction 3
In order to obtain @w/@u, we must solve the set of differential and algebraic equations (DAE) together with the set of equations given by Eq. (13) with the quantities @F/@u and @F/@w obtained by simple differentiation. Eq. (13) is called sensitivity equations and the values @w/@u are called, as previously mentioned, sensitivity coefficients. Note that the parameter with major sensibility is w2o due to the fact that small deviations in this parameter change the position in which the second decomposition takes places and then all the TG curve is displaced respect to the experimental. Same comments are valid for w1. Note also that the TG curves are especially insensitive to activation energies and that small variations in log (ki) have a considerable effect. Fig. 1 shows the experimental and calculated weight loss curves. A very good agreement can be observed with the same kinetic constants at the three heating rates. Fig. 2 shows the contribution of each fraction to the total weight loss curve, for the experiment at 5 8C/min. From this figure, and from the corresponding to the other samples, the temperatures Tmax corresponding to each fraction can be deduced, and are presented at Table 2. The first fraction being decomposed corresponds to the plastifier decomposition (process that takes place in the range 220–260 8C). The values calculated of initial amount of plastifier are in these case 4.2%.
4. Conclusions
5 8C/min
10 8C/min
30 8C/min
40 8C/min
80 8C/min
235 366 448
236 367 448
237 369 449
238 371 451
237 380 455
Very good representation of the weight loss of neoprene has been obtained by a kinetic model involving three organic fractions representing the three main steps of neoprene
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decomposition, and using kinetic parameters independent of the heating rate.
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