ARTICLE pubs.acs.org/IECR
Kinetic Study of the Thermal Processing and Pyrolysis of Crosslinked Ethylene Vinyl AcetatePolyethylene Mixtures J. A. Reyes-Labarta,* J. Sempere, and A. Marcilla Departamento of Ingeniería Química, Universidad de Alicante, Apdo. 99, Alicante 03080, Spain
bS Supporting Information ABSTRACT: The different transitions involved in the thermal processing and decomposition of cross-linked ethylene vinyl acetatepolyethylene (EVAPE) mixtures, with different concentrations of PE and peroximon (cross-linking agent), have been analyzed and simultaneously modeled by the application of a mechanistic pseudokinetic model. The model suggested involves all of the fractions susceptible of undergoing transitions or reactions studied by differential scanning calorimetry and thermogravimetric analysis, including complex and overlapped peaks. The model applied is capable of accurately representing the different processes involved and can be of great interest in the understanding and quantification of such phenomena, including the modeling of heat effects involved in the whole processing or pyrolysis of this type of product.
1. INTRODUCTION The family of low-density microcellular compounds obtained by foaming and cross-linking of the ethylene vinyl acetate (EVA) copolymer has a large field of commercial application. Products such as the soles of sports shoes, bicycle helmets, toys, nautical buoys, gymnasium floors, hygienic stable floors, etc. are typical examples of such a wide range of uses, where the density reduction can be turned directly into material/cost savings and more valuable products. The polymer cross-linking consists of the formation of chemical bonds (cross-links) between adjacent molecular chains to form a three-dimensional network. The general effects that this new network provides are stability at higher temperatures and working temperatures (thermal resistance); higher tensile strength, abrasion resistance/cut through, crush resistance and overload characteristics; resistance to (environmental) stress cracking; solvent resistance (only produce a swollen gel in hydrocarbon solutions); solder iron resistance; lower free volume and higher glass transition temperature; slightly better flame resistance; improved chemical and water treeing resistance, fluid resistance (melt viscosity), and high temperature mechanicals (even at 180 °C) such as toughness, impact resistance, longterm hydrostatic strength, creep properties, resistance to slow crack growth and rapid crack propagation; no change of electricals; difficulty of recycling; and a decrease in flexibility and elastic properties. However, extensive cross-linking in a crystalline polymer may cause a loss of crystallinity with deterioration of the mechanical properties on this fraction.13 Thus, other areas of application of cross-linked polymers are insulation and jacketing material in power cables and wires, hot water piping installation, and heat-shrinkable products. Crosslinked polymers can also be coatings, lumber, railroad tires, medical devices, tubing for industrial use (chemically inert and noncorroding, longer service life, lower maintenance costs), adhesives, electronic parts, products employed in the synthesis of ion-exchange resins and stimuli-responsive hydrogels, etc.47 It is even possible to produce a superficial cross-linking in order r 2011 American Chemical Society
to avoid the time migration of the different compounds of the polymer, especially in the packaging of food, pharmaceuticals, or cosmetics,810 and to improve the compatibility of immiscible or incompatible polymers.1113 In addition, there exist several ways to produce cross-linked polymers such as chemical methods, using mainly peroxides14 or silanes,15,16 and high-energy irradiation (electronic-beam) techniques;1719 thermochemical cross-linking involving organic peroxides is widely used because of their controlled decomposition rates, minimal side products, and economical processes.20 Figure 1 shows the general scheme of the cross-linking mechanism of EVA and PE using peroxides to generate free radicals. In previous works,2126 the basis of the kinetic modeling of the transitions involved in the thermal treatment and decomposition of the different components of the ethylene vinyl acetatepolyethylene (EVAPE) foams has been consolidated. Thus, the objective of the present paper is to investigate the interactions among the mixed polymeric matrix (EVAPE) and the cross-linking agent (CA), in order to establish the effect of the cross-linking processes on the thermal behavior and degradation of the system. The study of the actual mechanism of the crosslinking reaction itself is out of the scope the present paper, and its effect on the thermal processing and degradation of the samples will be considered as the result of a single overall process. Thermal properties such as specific melting enthalpy, melting and degradation temperatures of un-cross-linked and crosslinked ternary samples, and their dependence on the PE and CA concentration were studied using differential scanning calorimetry (DSC) and dynamic thermal gravimetric analysis (TGA). The cross-linking degree of the samples was associated with their gel content (GC), determined by a solvent-extraction Received: February 8, 2011 Accepted: May 19, 2011 Revised: May 10, 2011 Published: May 19, 2011 7964
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Industrial & Engineering Chemistry Research method. Also, the density evolution of the cross-linked samples was determined. In addition, a mechanistic and pseudokinetic model is suggested and applied to the analysis and simultaneous correlation of the DSC and TGA data (with various PE and CA contents), including complex or overlapped peaks and apparent heat capacities. This kinetic study is very interesting in regard to the characterization and analysis of the thermal processing and decomposition of the cross-linked materials studied, in order to design the corresponding molds and reactors where the processes take place.2730 On this point, it is important to remark that although the basis for the decomposition of complex or overlapped peaks as well as the consideration of varying specific heat capacities are already studied,31 no references have been found in the literature where the treatment of these peaks had been attempted.
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On the other hand, tertiary recycling of polymeric materials through pyrolysis has received renewed attention in regard to removing plastics, taking advantage of them, due to the possibility of converting their wastes into solid, liquid, and gaseous products with higher value as fuel or chemicals, such as hydrocarbons for the petrochemical industry, and contributing to environmental protection, as well.3235
2. EQUIPMENT AND EXPERIMENTAL PROCEDURE 2.1. Materials. The polymers used were low-density polyethylene (LDPE) PE003 and the EVA PA-539 ALCUDIA copolymer, both supplied by REPSOL YPF. Table 1 shows the properties of these two polymers according to the supplier. The cross-linking agent (CA) was a suitable peroxide frequently used in the production of EVA and PE foams, such as RR0 -bis(tert-butylperoxy)-m/p-diisopropylbenzene, TBPPB, provided by Rusimont Group-Elf Atochem (Peroximon F-40, Table 2). The decomposition of this CA occurs after the melting of the PE and EVA, respectively, that is, in the molten polymer, favoring the cross-linking reactivity. 2.2. Sample Preparation. Ternary mixtures of EVAPECA with three different concentrations of PE (5, 10, and 15 parts per hundred of resin (phr), i.e., 4.76, 9.10, and 13.04 wt %) and TBPPB (0.75, 1.5, and 3 phr, i.e., 0.74, 1.48, and 2.91 wt %) were studied. The concentrations were selected to be close to typical values used in industrial applications.
Table 2. Technical Data for Peroximon F-40 (Rusimont Group-Elf Atochem)
Figure 1. General scheme of the cross-linking mechanism of EVA and PE using peroxides: (a) thermal decomposition of possible peroxides, (b) initiation, (c) cross-linking.
Table 1. Technical Data for LDPE PE003 and EVA PA-539 ALCUDIA (Repsol YPF)
a Measure of the ease of flow of the melt of a thermoplastic polymer. b Temperature at which a flat-ended needle penetrates the material to a depth of 1 mm under a specific load.
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Table 3. General Scheme of Reactions of the Materials Studied (CA, EVA, and PE) in DSC and TGA Experiments DSC
TGA kD, CA
CA sf sCA RCA þ ð1 sCA ÞGCA kT, EVA
kM, EVA
EVA sf EVA ðTÞ sf EVA ðMÞ
kD1, EVA
EVA sf sEVA EVA þ ð1 sEVA ÞGEVA
kM, PE
PE sf PE ðMÞ}
kD2, ED
EVA þ PE sf sED RED þ ð1 sED ÞGED
kM, PE
PE sf PE ðMÞ
The mixtures were prepared, prior to experiments, in a Brabender Plasticorder PL 2000 extruder at 398 K with a speed of 20 rpm, using a single screw. These conditions were chosen to achieve a good homogenization of the mixture but to avoid the thermal decomposition of the peroxide. After the extrusion die, the mixture discharged was cut into pellets, immersed in a water bath, and after that dried at room temperature. 2.3. Thermal Analysis. 2.3.1. Differential Scanning Calorimetry (DSC). DSC tests were performed on a Perkin-Elmer DSC 7 controlled by a PC AT compatible system. Samples of 89 mg were encapsulated in aluminum pans and treated at a heating rate of 10 K/min. The atmosphere used was nitrogen, with a flow rate of 45 STP mL/min. To analyze the influence of the cross-linking agent before and after cross-linking, two consecutive runs to each sample were performed. Initially, a first experiment in the temperature range of 313573 K was run. The sample was then cooled to 293 K, and a second run was performed at the same heating rate, in order to analyze the effect of the cross-linking agent not only before and during the cross-linking process (first run) but also on the final cross-linked polymer (second run), that is, to characterize the postprocessing product. 2.3.2. Thermobalance (TGA). The thermogravimetrical experiments were carried out using a TG209 Netzsch Thermobalance controlled by a PC under the Windows operating system. The tests were performed in a nitrogen environment with a flow rate of 45 STP mL/min. Samples of 5 mg were heated at 10 K/min from 303 to 873 K. In both techniques, the experiments were replicated in order to determine their reproducibility, showing very good results with a maximum deviation between the repeated runs of about 2%. 2.4. Cross-Linking Samples. To obtain the cross-linked product a MECAMAQ DE-200 hydraulic hot plate press was used. The temperature in both plates was 448 K, and the residence time was 10 min. With these conditions, the crosslinking process was complete. 2.4.1. Density Measurement. The density of the different mixtures was measured after processing using a glass picnometer at 298 K. The variation for the measured densities was estimated to be 0.005 g/cm3. 2.4.2. Gel Content Measurement. The degree of cross-linking can be estimated through the gel fraction (i.e., insoluble fraction). The gel content of the cross-linked samples was determined gravimetrically (according UNE 53-381-89) using a 16 h Soxhlet extraction cycle using as a solvent THF (tetrahydrofurane) at 339 K and decaline at 458 K. Approximately 0.30.4 g of the cross-linked polymer (m0) was cut into small pieces. After the extraction cycle, the sample was dried to a constant weight (m1) at 353 K. The gel fraction was calculated as the percentage ratio of the final weight of the polymer to its initial weight, taking
also into account the initial insoluble fraction (f) of the sample. The variation obtained for repeat measurements was lower than 5%. m1 100 ð1Þ GC ¼ 1 m0 ð1 f Þ
3. KINETIC MODELS The pseudokinetic study of the process would be a very important aspect to quantifying and simulating the evolution of the different species present in the sample compounds (with the temperature or time) along the different thermal treatments studied and may help in the optimization of industrial processing. It is widely accepted that cross-linking reactions go through free radical mechanisms. In general, the free radicals generated on thermal decomposition of peroxides can attack the molten polymer chains (abstracting hydrogen atoms to produce alkyl radicals), and cross-linking of the polymer chains may occur. Examples of a radical reaction mechanism of cross-linking are proposed in the literature.3638 But the aim of the present study is to evaluate the effects that the cross-linking process produces on the global pseudokinetic constants of the different thermal transitions and degradation of the systems studied. Therefore, the following pseudokinetic models, which start from a linear combination of the effects that the different components cause, considering the relative concentration of each compound in the different EVAPECA ternary mixtures (m), have been suggested and applied, involving all of the fractions susceptible of undergoing thermal reactions in DSC and TGA experiments (Table 3): DSC dQEVAPECAm dQ DSC dQ DSC ¼ wS CPS þ EVA φEVA, m þ PE φPE, m dT dT dT DSC dQCA þ ð1 φEVA, m φPE, m Þ þ ð1 wS ÞCPM dT
ð2Þ dwTGA dwTGA dwTGA EVAPECAm ¼ EVA φEVA, m þ PE φPE, m dt dt dt dwTGA þ CA ð1 φEVA, m φPE, m Þ dt
ð3Þ
where φi,m represents the mass fraction of polymer i in the sample m. To obtain better correlation to fit all of the experimental data of the whole DSC curve, due to the existence of a strong baseline variation, the contributions of the apparent heat capacities (CP) 7966
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Table 4. Composition, Code, Density (g/cm3), and Gel Content (% of Insoluble Fraction in THF at 339 K and Decaline at 458 K) of EVAPECA Mixtures (Pressed Samples at 175 °C over 10 min) compositions (phr) EVA
PE
CA
measurements code
3
samples
density (g/cm )
% GC (THF)
% GC (decal.)
100
0
0
EVA
0.938
0
100
0
100
0
PE
0.923
100
0
100 100
0 5
1.5 1.5
(b.1) I
ET(1.5) EP(5)T(1.5)
0.944 0.944
95.2 97.1
95.9
100
10
1.5
II
EP(10)T(1.5)
0.943
96.3
94.4
100
15
1.5
III
EP(15)T(1.5)
0.941
95.2
93.8
100
10
0
(b.2)
EP(10)
0.932
8.2
100
10
0.75
IV
EP(10)T(0.75)
0.938
92.4
90.2
100
10
3
V
EP(10)T(3)
0.949
99
97.5
Table 5. DSC Results (First and Second Run) of Pure Compounds and Studied EVAPECA Mixtures sample code
DSC run
ΔHmelt.EVA (J/g)
Ttrans.EVA (K)
Tmelt.EVA (K)
ΔHmelt.PE (J/g)
Tmelt.PE (K)
EVA
1st
57.3
321.8
345.3
0.8
386.1
2nd
52.7
321.5
346.6
0.8
386.1
PE
1st
81.3
387.8
2nd 1st
79.7
387.8
CA (b.1)
1st
58.6
320.5
345.0
0.8
386.2
2nd
36.9
321.0
340.5
0.7
381.0
1st
55.6
320.3
345.2
4.3
386.2
2nd
36.1
321.3
340.1
3.3
380.3
I II
1st
56.5
320.5
345.2
8.2
385.8
2nd
36.8
321.3
340.6
6.1
380.8
III
1st 2nd
57.7 37.2
320.6 321.4
345.3 341.2
11.2 9.1
385.8 380.8
(b.2)
1st
59.4
319.5
345.0
8.3
386.8
2nd
55.8
322.0
345.3
8.6
386.8
1st
56.3
320.5
345.3
8.4
385.8
2nd
41.2
321.5
343.1
7.1
380.8
1st
56.1
320.3
345.1
8.6
386.5
2nd
31.8
321.1
339.3
5.1
380.8
IV V
of the global solid (wS) and melted (1 wS) fractions with the temperature have also been included in the model as a second degree polynomial for each global fraction (solid or melted): CP = (aT2 þ bT þ c) (J/(g K)). In previous papers, Marcilla et al. suggested and applied a pseudokinetic model and a methodology to model and explain the thermal transitions and fusions involved in the thermal treatment of polymers (such as PE and EVA) prior to their decomposition21,22 and the thermal (and catalytic) pyrolysis of PE, PP, and EVA polymers.3944 These previous models use n-order kinetics and Arrhenius type behavior of the rate constant and can be developed and applied in an equivalent way for our analysis to model the different individual contributions in the ternary samples studied, following the corresponding scheme of reactions (Table 3). Additionally, Table S1 (in the Supporting Information) shows a summary of the kinetic equations used. The total number of parameters that have to be fitted depends on the thermal treatment studied (number of peaks). Thus, in the
ΔHdecomp.CA (J/g)
Tdecomp.CA (K)
432.2
458.6
8.7
468.5
7.8
469.8
7.6
469.5
7.6
468.6
2.9
462.5
14.7
473.3
DSC experiments, where four parameters are used per single reaction peak (ΔH, kref, Ea, and n), the proposed model for an EVAPECA mixture has 23 parameters (4 reactions þ 2 line base correction þ 1 unknown fraction). In the case of the TGA, the total number of parameters to be optimized is 11 for an EVAPECA ternary mixture (3 kD, 3 (Ea/R), 3 n, and the coefficients sEVA and sCA). This number of parameters may appear too high but the high number of separate processes/peaks analyzed must be considered, taking into account the evolution of the apparent heat capacities and that no simplifying linearizations have been made. In the case of the correlation of the second DSC run, where the samples are already cross-linked and no more CA is present in the sample, the corresponding CA term in eq 2 is removed, and therefore, the number of parameters is 19. 3.1. Mathematical Treatment. The pseudokinetic parameter unknowns of the kinetic models proposed in this work have been optimized using the tool “Solver” included in the spreadsheet Excel for Windows. In all of the calculations, the objective 7967
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Figure 2. DSC results (first runs) for the pure polymers and ternary mixtures EVAPECA with various PE contents (5, 10, and 15 phr).
Figure 3. DSC results (first runs) for the pure EVA and ternary mixtures EVAPECA with various CA contents (0.75, 1.5, and 3 phr of TBPPB).
function considered was OF ¼
4
N
∑ ∑
m¼1 i¼1
"
dY dX
expt
dY dX
#2 ð4Þ
calcd
where m represents the different samples simultaneously fitted (with different PE or CA contents), i represents the experimental data at temperature Ti and at time ti, N is the number of experimental points, (dY/dX)expt represents the experimental heat or mass derivative with respect to the temperature or time, as obtained from the DSC or TGA apparatus respectively, and
(dY/dX)calcd is the calculated value from the corresponding proposed kinetic model (eq 2 or 3). To compare different kinetic models, a relative standard deviation is introduced pffiffiffiffiffiffiffi OF ðN PÞ ð5Þ RSD ð%Þ ¼ 100 Dexpt_av where P is the number of parameters to be fitted and Dexpt_av is the average of the experimental derivatives. The integration of the kinetic equations was carried out using the Euler method. 7968
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Figure 4. DSC results (second runs) for the pure polymers and ternary mixtures EVAPECA with various PE contents (5, 10, and 15 phr).
Figure 5. DSC results (second runs) for the pure polymers and ternary mixtures EVAPECA with various CA contents (0.75, 1.5, and 3 phr of TBPPB).
4. RESULTS AND DISCUSSION In this section, the EVAPE cross-linking process through chemical reactions with a different amount of PE and TBPPB used as cross-linking agent is discussed. 4.1. Physical Properties of the Cross-Linked Samples. The results of density and gel content for the cross-linked samples are shown in Table 4 to confirm the effect of the cross-linking reaction. The densities of the pure polymers (PE and EVA) without CA and some binary sample are also given as a reference in comparison with the samples cross-linked with different
amounts of PE and peroxide. As expected, the presence and increase in CA concentration produces an increase in the final density and gel content of the sample as a consequence of a larger cross-linking degree of the new structure generated, keeping also in mind the effect of the lower density of the PE in the samples. 4.2. Thermal Properties and Analysis. 4.2.1. DSC Experiments. Table 5 shows the melting temperatures (or reaction temperature in the case of the cross-linking agent) and heats (i.e., area under the corresponding peak), determined by DSC measurements, for all of the non-cross-linked samples (first 7969
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Figure 6. Experimental TGA curves for the CA, pure polymers, and ternary EVAPECA mixtures with various PE contents (5, 10, and 15 phr).
Figure 7. Experimental TGA curves for the CA, pure polymers, and ternary EVAPECA with various CA contents (0.75, 1.5, and 3 phr of TBPPB).
DSC run) and cross-linked samples (second DSC run) studied, including pure components and same binary mixtures. DSC for First Runs. Analyzing the first run for all of the EVA PECA ternary mixtures studied, the peaks corresponding to
the thermal transitions of the polymeric matrix are similar (number of peaks, reaction temperatures, and heat) to those corresponding to the pure polymers used and their binary mixtures reported in the literature,21,22,45 which means two 7970
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Table 6. TGA Peak Temperatures (K) of the Pure Compounds and Studied Samples sample code
peak CA
EVA PE CA
peak EVA 639
peak PE 747 747
445
(b.1)
490
655
759
I
472
651
754
II
472
650
752
III
472
648
751
(b.2)
643
749
IV
472
645
749
V
472
661
765
endothermic peaks corresponding to the transition and melting of the EVA domains at 322 and 340 K, respectively, and one endothermic peak for the melting of the PE domains at 385 K. The decomposition of the cross-linked agent (TBPPB) only presents an exothermic peak corresponding to the decomposition of this peroxide from 400 to 490 K and, therefore, after the thermal transitions of both polymers (Figures 2 and 3). The variation of the PE content in the samples only seems to slightly affect the temperature interval where the thermal decomposition of the CA takes place. However, the temperature observed of the peak corresponding to the thermal decomposition of the CA increases gradually when increasing the content of the CA. As can be seen in Figure 3 and Table 5, the presence of the cross-linked agent also produces a relative increase of the slope of the final baseline (at high temperatures), which means an increase of the apparent heat capacities of the sample, due to a larger viscosity of the melted and cross-linked polymeric matrix. Obviously, the peak area (J/g of sample) corresponding to the thermal decomposition of the PE and cross-linking agent increases with the concentration of the corresponding compound in the mixture, but the lineal increase observed does not mean any variation of their specific decomposition enthalpies (J/g of PE or J/g of CA), as will be shown in the quantitative kinetic analysis. DSC for Second Consecutive Runs. If the second consecutive heating run of the EVAPECA mixtures is considered (Figures 4 and 5 and Table 5), we can observe that the first peaks corresponding to the EVA contributions present a decrease in their height and total area, in the same way as happens in pure EVA,21 and appear at similar temperatures when increasing the PE content. However, they undergo a noticeable (and progressive) decrease in their height and total area when increasing the CA content, as a consequence of the increase of the corresponding cross-linking degree, previously commented upon in the gel content study. The third peak also undergoes a continuous decrease in the peak temperature and area, compared with the first run, when the cross-linking agent is increased. Furthermore, this third peak corresponding to the melting of the ethylene domains of the EVAPE polymeric matrix presents a much lesser variation than the previous peaks (corresponding to the vinyl acetate domains). The acetate groups of the EVA copolymer help the formation of radicals to a larger extent than in the case of the PE;4648 therefore, the EVA domains undergo a larger modification as a consequence of the cross-linking process than the PE domains. The progressive decrease in the heat of the different transitions observed when increasing the CA content (that is, increasing the
cross-link density) is due to the reduction in the structural regularity that the created cross-links introduce, impeding or disturbing the reorganization and also the folding of macromolecular chains, decreasing in general the size and content of crystals.14,15,36 The base lines after the polymer peaks, for both runs of each sample, are very similar. Therefore, the baseline slope should depend mainly on the cross-linking process, certifying the new structure formed. Finally, it can also be observed that for all of the second run experiments no more CA decomposition peaks appear, indicating that TBPPB was consumed completely during the first runs. 4.2.2. TGA Experiments. The general shape of the thermal degradation of the polymeric matrix of the ternary samples studied is similar to that corresponding to pure polymers, presenting two steps.26 However, there is a progressive shift of all decomposition processes to higher temperatures when increasing the peroxide content in the samples, due to the larger molecular weight of the polymer that the cross-linking reaction produces. As an example, Figures 6 and 7 show the TGA curves for the pure components and EVAPECA ternary samples (peak temperatures for all of the mixtures studied are shown in Table 6). As expected, the CA presents a thermal degradation with only one step, around 460 K, and a final solid residue corresponding to 60% of the initial weight. The EVAPECA samples show a first peak corresponding to the VA loss and a second peak corresponding to the decomposition of the polyolefin chain resulting from the first decomposition process of the EVA and the PE present in the sample. A magnification of the range of temperatures where the CA undergoes decomposition is presented, clearly showing that this process is visually proportional to the amount of CA used. 4.3. Kinetic Modeling Results. 4.3.1. DSC Kinetic Model Analysis. In the simultaneous correlation of the first DSC run for all of the ternary EVAPECA samples studied (varying the PE and CA content), where no differences in the peak temperatures have been observed, all of the pseudokinetic parameters (ΔH, k0ref, Ea, and n) are constant (validating the linear combination of the individual behavior of the components), except that corresponding to the CP contributions (for global solid and melted species) that necessarily have been fitted independently for each ternary sample, indicating the nonlinear influence of the cross-linking agent in the internal heat transfer (Table S2 in Supporting Information). Figure 8 shows an example of the deconvolution of the calculated curves and the satisfactory degree of the correlation obtained, bearing in mind the complexity of the curves studied. In Figure 8b, we can also observe the contribution of the different components and reactions to the global DSC curve. The evolution of the CP contribution (for global solid and melted species) in the DSC (first run) of the different EVAPECA samples (with different CA content) is shown in Figure 9. It is possible to observe that the contribution of CPM increases when increasing the CA content, especially at high temperatures, due to the decrease in thermal conductivity that the larger viscosity of the cross-linked samples produces. The contribution of CPS is lower, as can be seen by the absence of important slope variations before the corresponding EVA peaks. In the case of the second DSC run, that is, once the EVAPE polymeric matrix is already cross-linked, there exists a change in the location and area of the peaks associated with the melting processes of the corresponding polymers only when changing the 7971
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Figure 8. Experimental and calculated DSC curves for the mixture EP(10)T(3): (a) first and second runs and (b) first run with the different contribution of each component.
CA content. This feature shows that in these cases, the linear combination no longer applies, and thus, it is necessary to allow variation of the corresponding pseudokinetic parameters with the cross-linking agent concentration (apart from those corresponding to the CP contributions), in order to obtain a satisfactory fit. The parameters that have been fitted independently for each curve (ternary samples II, IV, and V) are ΔHT,EVA, ΔHM,EVA, ΔHM,PE, k0ref,M,EVA, k0ref,M,PE, Ea M,EVA, and nM,EVA. The parameters ΔH, log k0ref, and Ea present an approximate parabolic dependence on the CA content, and only the parameter nM,EVA presents a linear dependence (Table S3 in Supporting Information). Figure 8a shows, as an example, the excellent results obtained for the ternary samples EVAPECA, with 10 and 3 phr of PE and CA, respectively. The increase of the apparent heat capacity shows the effect of the new structure (with greater viscosity and
molecular weight) generated by the cross-linking reaction, decreasing the thermal conductivity inside the cross-linked sample. The second consecutive DSC run for the samples with different PE contents has not been simultaneously modeled because it does not present any remarkable difference in the peak temperatures (Figure 4). The averages of the relative standard deviations obtained are 0.15 and 0.17 for all the DSC curves (1200 points), first and second runs, respectively. At this point, it is necessary to remark that the comparison of the kinetic parameters must be carefully considered since the three parameters are highly interrelated.21 Thus, the order of reaction is related to the shape and symmetry of the peaks, being almost symmetric for first order reactions. The activation energy and the pre-exponential factor are both related to the peak location and width, the width of the peak being more sensitive to Ea. 7972
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Figure 9. Evolution of the Cp contribution (for global solid and melted species) and the CA decomposition in the DSC (first run) of the EVAPECA samples with different CA contents: 0.75, 1.5, and 3 phr.
Figure 10. Experimental and calculated TGA curves for the mixtures EVAPECA, with various CA (TBPPB) contents: 0.75 and 3 phr.
In the case of the melting heat, the values obtained from the kinetic analysis presented are always lower than the values obtained by the direct integration of the DSC curves, because, in the direct integration calculations, the contributions of the heat capacities are included in the melting heat. 4.3.2. TGA Kinetic Model Analysis. As commented upon before, a progressive displacement in the decomposition temperatures to higher values can be observed in the cross-linked samples, when increasing the cross-linking degree. This variation causes, necessarily, variation of the corresponding pseudokinetic parameters with the concentration of the CA, as in the correlation of the second DSC run, since in TGA the decomposition of
the polymer is studied, and this happens after the CA decomposition, so the sample is therefore already cross-linked. In this case, we have considered this effect in the pre-exponential factors that are directly related with the temperature of maximum degradation, while Ea and n have been kept constant for each series of samples. Therefore, these pre-exponential factors for all of the related reactions have to be independently optimized for each sample (IV), in order to obtain a simultaneous and satisfactory fit of all of the cross-linked samples studied (varying the PE and CA content). It is necessary to observe that all of the pseudokinetic parameters corresponding to the pure EVA have also been optimized independently, due to the effect of 7973
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Industrial & Engineering Chemistry Research the cross-linking process introduced in the initial polymeric matrix. In this case, the logarithm of the pre-exponential factors kref,D1,EVA and kref,D,ED present an almost linear tendency of decreasing with the PE and CA content of the cross-linked samples (Table S4 in the Supporting Information). As an example, Figure 10 presents the experimental and calculated TGA curves for the ternary samples with 10 phr of PE and 0.75 and 3 phr of CA showing an excellent degree of coincidence. The average of the relative standard deviations obtained is 0.51 for all of the TGA experiments (1679 points).
5. CONCLUSIONS Investigation on the thermal properties of non-cross-linked ternary samples showed that the melting point and heat of fusion of the pure polymer are not significantly modified by the presence of the peroxide before the cross-linking process (DSC first run). In the cross-linked samples (second DSC run), the increase of the cross-linking degree also produces a decrease of the melting point and heat of fusion, and on the other hand, an increase of the density, gel content, and the thermal decomposition temperature (TGA). Therefore, cross-linking produces a delay or a stability effect on the main decomposition process of the EVA mixtures studied. The models proposed satisfactorily fit the different calorific processes that occur in the different non-cross-linked and crosslinked materials studied by the DSC and TGA techniques, even when complex and overlapped peaks are present. These models specially include the evolution of the apparent heat capacities, the decrease of the melting point and heat of fusion in the crosslinked samples (second DSC run), and the increase of the thermal decomposition temperature (TGA). These results can be used to control the thermochemical cross-linking process, to optimize the energy requirements and the properties of crosslinked polymers, and to simulate the thermal degradation of cross-linked samples. ’ ASSOCIATED CONTENT
bS
Supporting Information. (Table S1) Resume of the pseudokinetic equations used in the DSC and TGA modeling. (Table S2) Pseudokinetic parameters obtained from the simultaneous fit of the experimental data of the DSC curves (first run) of all of the ternary mixtures EVAPECA studied (varying the PE and CA content). (Table S3) Pseudokinetic parameters obtained from the simultaneous fit of the experimental data of the DSC curves (second run) of all the ternary mixtures EVAPECA studied (varying the PE and CA content). (Table S4) Pseudokinetic parameters obtained from the simultaneous fit of the experimental data of the TGA curves of all the ternary mixtures EVAPECA studied (varying the PE and CA content). This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION
ARTICLE
’ NOTATION a, b, c = parameters of the heat capacity second-degree polynomial CA = cross-linking agent (peroximon) CP = heat capacity of the global solid (S) or melted (M) fractions (J/gK) dQj/dT = Heat derivative with respect to the temperature of process j, with dQj dwj ΔHj dwj ¼ ΔHj ¼ dT dT vH dT kref , j ni Eaj 1 1 wj exp ¼ ΔHj vH R T Tref DSC = differential scanning calorimetry dwi/dt = mass derivative with respect to the time of species i Eaj = activation energy of reaction j ED = ethylene domains EVA = polyethylene vinyl acetate copolymer Gi = gas produced in the thermal decomposition of species i ΔHj = constant latent heat of reaction j kref,j = pre-exponential factor of reaction j at Tref (373 K) k0ref = k0ref = kref,j/vH M = melt state N = number of experimental points n = reaction order OF = objective function P = number of parameters to be fitted PE = polyethylene or polyethylene domains in EVA phr = parts per hundred of resin PP = polypropylene R = perfect gas constant Ri = solid residue produced in the thermal decomposition of species i RSD = relative standard deviation S = solid state sj = yield coefficients for the solid residue produced in the thermal decomposition j T = temperature TBPPB = R-R0 -bis(tert-butylperoxy)-m/p-diisopropylbenzene Ti = temperature at a given time ti = time (s) TGA = thermogravimetric analysis Tp = peak temperature VA = vinyl acetate domains in the EVA copolymer w = mass fraction of nontransformed polymer (or nonreacted material; g/gsample) wS = global solid fraction (g/gsample) Greek Symbols
vH = constant heating rate φi,m = weight percentage of polymer i in the corresponding sample m γ = vinyl acetate fraction in EVA copolymer
Corresponding Author
*E-mail:
[email protected].
’ REFERENCES
’ ACKNOWLEDGMENT Support for this work was provided by the Vice-Presidency of Research (University of Alicante): VIGROB099.
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