Multistep Kinetic Behavior of the Thermal ... - ACS Publications

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Multistep Kinetic Behavior of the Thermal Decomposition of Granular Sodium Percarbonate: Hindrance Effect of the Outer Surface Layer Takeshi Wada, Masayoshi Nakano, and Nobuyoshi Koga* Chemistry Laboratory, Department of Science Education, Graduate School of Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi-Hiroshima 739-8524, Japan S Supporting Information *

ABSTRACT: The kinetics and mechanism of the thermal decomposition of granular sodium percarbonate (SPC), which is used as a household oxygen bleach, were studied by thermoanalytical measurements under systematically changing conditions and morphological observation of the reactant solids at different reaction stages. A physico-geometrical kinetic behavior of the reaction that occurs in a core−shell structure composed of an outer surface layer and internal aggregates of SPC crystalline particles was illustrated through detailed kinetic analyses using the kinetic deconvolution method. Simultaneously, the hazardous nature of SPC as a combustion improver was evaluated on the basis of the kinetic behavior of the thermal decomposition. It was found that the outer surface layers of the SPC granules hinder the diffusional removal of product gases generated by the thermal decomposition of the internal SPC crystalline particles. The reaction rate decelerates because of an increase in the internal gaseous pressure as the reaction advances. However, the reaction rate accelerates once crack formation occurs in the outer surface layer at the midpoint of the reaction. Therefore, the overall reaction was empirically demonstrated to consist of two overlapping reaction steps owing to the changes in the self-generated reaction conditions in the interior of the SPC granules.

1. INTRODUCTION So-called sodium percarbonate (SPC) [sodium carbonate− hydrogen peroxide (2/3); Na2CO3·1.5H2O2; CAS: 15630-894] is a well-known oxidizer.1 Columnar SPC crystals with an axis length of 20−30 μm and an orthorhombic crystal structure (SG: Cmca, a = 6.7138 Å, b = 15.7407 Å, c = 9.1732 Å)2 are obtained by mixing saturated Na2CO3(aq) and concentrated H2O2(aq). When the solid is heated, oxygen is generated via the thermal decomposition accompanied by an exothermic effect:

They also determined the different kinetic behaviors in the initial, established, and final stages of the thermal decomposition. Galwey and Hood proposed a physico-geometrical interpretation of the kinetic behavior under vacuum characterized by a sigmoidal gaseous evolution rate curve,4,5 that is, the Na2CO3 surface product layer formed in the initial stage of the reaction regulates the diffusional removal of the gases produced by the internal reaction. However, the reaction rate accelerates in the established stage of the reaction. Thus, the overall rate behavior has been explained by a contracting geometry-type reaction with acceleration of the linear advancement rate of the reaction interface toward the center of the reactant particles as the overall reaction advances. Recently, the present authors studied the overall kinetic behavior of the thermal decomposition of SPC crystalline particles from the viewpoint of a physico-geometrical reaction mechanism by focusing on the role of the surface product layer.12 It was revealed through kinetic and morphological studies that the reaction was gradually retarded owing to the hindrance of the diffusional removal of the internal gaseous products by the surface product layer, possibly accompanied by an increase in

Na 2CO3 ·1.5H 2O2 (s) → Na 2CO3(s) + 1.5H 2O(g) + 0.75O2 (g) (1)

Therefore, the substance is a combustion improver and controlled as a hazardous material. The thermal decomposition behavior of SPC and its kinetic characteristics have been extensively studied.3−12 Nagaishi et al.3 suggested that the thermal decomposition of SPC crystalline particles occurs via two successive reaction steps that involve the detachment and decomposition of H2O2(g): Na 2CO3 ·1.5H 2O2 (s) → Na 2CO3(s) + 1.5H 2O2 (g)

(2)

H 2O2 (g) → H 2O(g) + 0.5O2 (g)

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© 2015 American Chemical Society

Received: July 21, 2015 Revised: September 2, 2015 Published: September 7, 2015 9749

DOI: 10.1021/acs.jpca.5b07042 J. Phys. Chem. A 2015, 119, 9749−9760

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The Journal of Physical Chemistry A

outer surface layer of the SPC granules in determining the kinetic behavior of the thermal decomposition is discussed by comparing the present kinetic results with the previously reported physico-geometrical kinetic behavior of the thermal decomposition of SPC crystalline particles.12

the internal gaseous pressure. As the reaction advances, channels for diffusional removal of the gases are formed because of the morphological changes in the surface product layer and possibly the increased internal pressure, resulting in the blowout of the product gases, which leaves traces of the Na2CO3 product as crystalline whiskers. Once the diffusion channels are generated in the surface product layer, the influence of this layer on the internal reaction is reduced. Accordingly, the overall reaction advancement is influenced largely by the self-generated reaction conditions, which change as the reaction proceeds, and empirically characterized as a multistep reaction. The observed rate behavior is understood as a typical kinetic feature of heterogeneous reactions in which solid and gaseous phases are involved, as has been revealed in many thermal decompositions of solids and solid−gas reactions.13−15 For the practical use of SPC as an oxidizing agent in industries, laboratories, and households, SPC is granulated with a core−shell structure composed of Na2CO3 and some other additives in addition to SPC crystalline particles16 as the outer surface layer and aggregates of SPC crystalline particles in the interior.1 The outer surface layer of SPC granules increases the structural strength of the granules and protects the internal SPC crystalline particles from the deterioration via the action of atmospheric water vapor. In addition to this physical shielding effect, the outer surface layer also chemically absorbs atmospheric water vapor via the reaction:17,18 Na 2CO3(s) + H 2O(g) ⇄ Na 2CO3 ·H 2O(s)

2. EXPERIMENTAL SECTION 2.1. Sample and Its Characterization. A commercially available granular SPC for domestic use (Nippon Garlic Corp.) was purchased and used without purification or crushing. The granules were sieved to obtain fractions of different grain sizes using a vibrating sieve instrument (MVS-1, As One). The sieved fraction containing granules with sized ranging from 500 to 1000 μm was selected as the sample. The components of the SPC granules were identified using powder X-ray diffraction analysis (XRD: RINT 2200 V, Rigaku Co., monochrome Cu Kα, 40 kV, 20 mA, 4° min−1, 5° ≤ 2θ ≤ 60°) and Fourier transform infrared spectroscopy (FT-IR: Shimadzu FT-IR 8400S, diffuse reflectance method). The mixture SPC−Na2CO3 composition in the SPC granules was determined from the mass-loss value due to thermal decomposition recorded using thermogravimetry−differential thermal analysis (TG−DTA: DTG-50, Shimadzu Co.). The TG−DTA measurement was performed using approximately 5.0 mg of sample, which was weighed in a platinum pan (6 mm in diameter and 2.5 mm in depth), using a heating rate β of 5 K min−1 in a flow of N2 (80 cm3 min−1). The surface morphology and architecture of the SPC granules were observed using a scanning electron microscope (SEM: JSM-6510, JEOL) after coating the granules and cleaved granules with Pt via sputtering (JFC-1600, JEOL, 20 mA, 60 s). A thin section of the granules was prepared by enclosing several granules in an epoxide-based adhesive (Araldite, NICHIBAN).19−23 One side of the solidified resin body was polished to approximately the center of the enclosed granules using abrasive cloths and papers of different grit numbers (#500− 2000), and then the polished surface was mounted on a glass slide using the synthetic resin. After the resin body was rigidly adhered on the glass slide, the top of the mounted resin body was carefully polished to a thickness of approximately 50 μm using an abrasive paper (#2000) and covered with a thin glass slide using the adhesive resin. The as-prepared thin section was examined under polarized light using an optical microscope (BH-2, Olympus). 2.2. Characterization of the Thermal Decomposition Behavior. SPC granules were preliminarily dried in an electric oven at an ambient temperature of 363 K for 30 min prior to thermoanalytical measurements in order to remove any hydrated water in the outer surface layer. Using a coupled TG−DTA and mass spectroscopy (MS) technique, the thermal decomposition of the SPC granules was investigated by simultaneously tracking the mass-loss behavior and the evolved gases during the thermal decomposition, as well as the thermal effects during the reaction. For these measurements, approximately 5.0 mg (sample mass m0) of SPC granules weighed in platinum pan (5 mm in diameter and 2.5 mm in depth) was heated in a TG−DTA Instruments (TG8120, Rigaku Co.) in flowing He (200 cm3 min−1) at different β values from 2 to 10 K min−1. The outlet gases from the TG−DTA Instruments were continuously introduced into a quadrupole mass spectrometer (M-200QA, Anelva Co.) through a silica capillary tube (0.075 mm internal diameter) heated at 500 K. The mass spectrum of the outlet gas was repeatedly recorded in the range

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Accordingly, the internal SPC crystalline particles are protected, even when the granules are exposed to a high water vapor pressure for an extended time. Considering the thermally induced decomposition of the SPC crystalline particles in the core−shell structure of the granules, the outer surface layer should block the diffusional escape of gaseous products from the granules. It is thus expected that the thermal decomposition of the SPC granules is more significantly influenced by the self-generated reaction conditions and those changes during the reaction. The kinetic interpretation of the overall rate behavior of the thermal decomposition of SPC granules based on a physico-geometrical reaction mechanism that considers the influence of the self-generated reaction conditions is therefore necessary in order to evaluate the thermal stability and reactivity of this hazardous material. The structural characteristics of SPC granules with a secondary core−shell structure also stimulated our interest with respect to the development of the theoretical foundation for the kinetics and mechanism of the thermal decomposition of solids with specific structures.13−15 In this study, the overall rate behavior of the thermal decomposition of SPC granules was investigated under systematically changing reaction conditions, including programmed changes in the temperature and atmospheric water vapor pressure. The characteristics of the rate behavior were then correlated to the morphological changes in the outer surface layer of the SPC granules and SPC crystalline particles in the interior during the reaction. By tracking the changes in the overall rate behavior with the reaction conditions, the variation in the self-generated reaction conditions under the different applied reaction conditions was qualitatively evaluated. On the basis of these phenomenological findings, the kinetic behavior was analyzed by empirically deconvoluting the overall reaction into different reaction steps. The critical role of the 9750


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3. RESULTS AND DISCUSSION 3.1. Sample Characterization. Figure 1 shows typical microscopic images of the as-received SPC granules. The

from 10 to 50 amu (EMSN, 1.0 A; SEM, 1.0 kV) during the TG−DTA measurement. Changes in the crystal structures of the samples that accompanied the thermal decomposition were traced using the powder XRD analysis on a RINT 2200 V system equipped with a programmable heating chamber (PTC-20, Rigaku Co.). After crushing the sample using an agate mortar and pestle and press-fitting onto a platinum plate, the sample was heated in flowing N2 (100 cm3 min−1) according to a stepwise isothermal program: heat at β = 10 K min−1 and then hold for 15 min at selected temperatures from 300 to 525 K in steps of 25 K. The diffraction analyses were performed when the sample was maintained at the constant temperatures. To observe the surface morphologies and architectures of partially decomposed SPC granules, samples were decomposed to different extents by heating in the above TG−DTA Instruments (DTG-50M) under conditions identical to those used for the TG−DTA measurement. The fractional reaction, α, for the partially decomposed sample was calculated from the mass-loss value with reference to the entire mass loss expected for the thermal decomposition of SPC. The partially decomposed samples were immediately cooled to room temperature and observed using SEM. Thin sections of the heat-treated samples were also observed using an optical microscope under polarized light. The influence of atmospheric water vapor on the thermal decomposition of the SPC granules was investigated by the mass-change measurements under different water vapor pressures, p(H2O). For each measurement, approximately 5.0 mg of dried SPC granules weighed in a platinum pan (5 mm in diameter and 2.5 mm in depth) was heated to 333 K in flowing N2 (400 cm3 min−1) in the TG−DTA Instruments (TG8120, Rigaku Co.) and then the flowing gas was switched to a mixed N2−H2O gas (400 cm3 min−1) with a controlled p(H2O) (0.8 ≤ p(H2O) ≤ 10.0 kPa). The mixed N2−H2O gas with the programmed p(H 2O) was generated using a humidity controller (HUM-1, Rigaku Co.), where the flow rates of dry and wet N2 gases for mixing were controlled by monitoring the p(H2O) value in the gas introduced to the reaction chamber of the TG−DTA Instruments. After stabilizing the reaction system for 30 min at 333 K, the sample was heated at β = 5 K min−1, and the mass-loss curves were recorded at different p(H2O). 2.3. Measurement of the Kinetic Rate Data. To analyze the kinetics of the thermal decomposition, the mass-loss curves were recorded using a suspended-type TG (TGA-50M, Shimadzu Co.) in flowing N2 (80 cm3 min−1). For each measurement, approximately 5.0 mg of dried SPC granules weighed in a platinum pan (6 mm in diameter and 2.5 mm in depth) was heated using three different modes: isothermal, linear nonisothermal, and controlled transformation rate thermal analysis (CRTA).24,25 After heating the sample to programmed temperatures at β = 10 K min−1, isothermal massloss traces were recorded at different constant temperatures T (383 ≤ T ≤ 413 K). The linear nonisothermal measurements were performed at different β (1 ≤ β ≤ 10 K min−1). CRTA was performed using the TG instrument equipped with a homemade CRTA controller.26−31 The sample was heated at β = 2 K min−1, and during the mass-loss process, the mass-loss rate was regulated at different constant rates C (5.0 ≤ C ≤ 20.0 μg min−1).

Figure 1. Microscopic images of the as-received SPC granules: (a) SEM image of the exterior; (b) SEM image of the outer surface; (c) SEM image of an internal cleaved surface; and (d) polarizing microscopic view of a thin section of the interior surface.

granules were spherically shaped (Figure 1a), and the surface of each granule consisted of columnar and plate-like crystals (Figure 1b). The columnar crystals are similar to those observed previously in SPC crystalline particles.1,12 The interior of each granule was densely arrayed with crystals radiating from the center (Figure 1c). A polarizing microscopic view of a thin section of a granule clearly revealed that the arrayed structure of the granule interior was rigidly covered by a surface layer of aggregates of fine crystals to form a core−shell structure (Figure 1d). The XRD pattern for the as-received SPC granules is shown in Figure S1 in the Supporting Information. The major diffraction peaks were ascribed to peaks in the XRD pattern for pure SPC crystals.2 However, some minor diffraction peaks were detected that are not observed in the XRD pattern for SPC crystalline particles. These minor peaks are in agreement with some of the typical diffraction peaks for Na2CO3·H2O (orthorhombic, S.G.: Pca21, a = 10.72 Å, b = 5.249 Å, c = 6.469 Å, JCPDS 8-0448). The plate-like crystals observed in the outer surface layer of the SPC granules are the most likely components of this compound, which may have been generated during the granulation process via the decomposition of SPC crystalline particles followed by subsequent hydration in the atmosphere. The formation of Na2CO3·H2O via the decomposition of Na2CO3·1.5H2O2 at room temperature was confirmed by the growth of the corresponding XRD peaks after the exposure of the sample to humid air at ambient temperature for several months (Figure S2). The FT-IR spectrum of the as-received SPC granules exhibited the absorption peaks attributed to H2O2 and CO32− (Figure S3) and agreed with that reported for SPC crystalline particles.12,32 3.2. Thermal Decomposition Behavior. Figure 2 shows typical TG−DTG−DTA curves for SPC granules dried at 363 K for 30 min. The mass-loss due to thermal decomposition of 9751


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chromatographic peaks for m/z = 18 and 32 are not coincident with each other; the mass chromatographic peak for m/z = 18 exhibited a shoulder before the peak maximum, as was observed for the DTG curve, whereas the mass chromatographic peak for m/z = 32 was a smooth single peak. Furthermore, although the chromatographic peaks for m/z = 18 and 32 began to grow simultaneously, the peak maximum for m/z = 18 was detected at a slightly higher temperature than that for m/z = 32, and the evolution of O2 terminated at a slightly lower temperature than that for H2O. These differences in the peak shapes and positions of the mass chromatographic peaks for m/z = 18 and 32 were not observed for the thermal decomposition of SPC crystalline particles.12 It was confirmed by examining the changes in the XRD pattern of the SPC granules during stepwise isothermal heating in flowing N2 (Figure S4) that no crystalline intermediate phase was generated in the temperature range of the thermal decomposition, and Na2CO3 was directly produced, as is the case for SPC crystalline particles. Therefore, physico-geometrical constraints are considered to be a possible cause of the multistep mass-loss behavior, which may occur due to changes in the reaction conditions as the reaction advances. Figure 4 shows the microscopic images of the SPC granules partially decomposed by heating at β = 5 K min−1 to the temperature

Figure 2. TG−DTG−DTA curves for dried SPC granules (sample mass m0 = 4.93 mg) recorded at β = 5 K min−1 in flowing N2 (80 cm3 min−1).

the SPC granules in two mass-loss steps under linear nonisothermal conditions, which were distinguished in the DTG profile as primary shoulder and subsequent peak maximum. A similar two-step mass-loss process has been reported for the thermal decomposition of SPC crystalline particles and explained as a phenomenon caused by the physico-geometrical constraints of the reaction mechanism regulated by the blocking action of the surface product layer in each SPC crystalline particle.12 The observed total mass-loss value during the thermal decomposition of the SPC granules was 30.84 ± 0.32%, which is smaller than the value of 32.48% calculated using eq 1. The difference results from the existence of Na2CO3 in the outer surface layer of the dried SPC granules. From the mass-loss value during thermal decomposition of the SPC granules, the content of Na2CO3 in the sample was calculated to be 7.37 ± 1.37 mol %. Notably, a difference in the thermal decomposition of the SPC granules from that of SPC crystalline particles reported previously was also indicated by the appearance of two well-separated DTA exothermic peaks. Furthermore, the difference in the profiles (shape and peak position) for the exothermic DTA peak and DTG curve is more apparent for the thermal decomposition of SPC granules than for SPC crystalline particles. The mass chromatograms for m/z = 18 (H2O+) and m/z = 32 (O2+) of the evolved gases during the thermal decomposition of the SPC granules at different β are shown in Figure 3. During thermal decomposition, evolution of H2O and O2 was detected. It should be noted that the shapes of the mass

Figure 4. Microscopic images of partially decomposed SPC granules and the final product: (a) SEM image of the external surface (α = 0.55); (b) SEM image of the surface layer (α = 0.55); (c) SEM image of the cleaved surface of the outer layer (α = 0.55); (d) polarizing microscopic view of a thin section of the internal surface (α = 0.40); (e) SEM image of the internal cleaved surface (α = 0.55); and (f) SEM image of the cleaved surface of the outer layer of a granule at the end of the thermal decomposition (α = 1.0).

Figure 3. Mass chromatograms of the gases evolved during the thermal decomposition of SPC granules (m0 = 5.05 ± 0.18 mg) at different β: (a) m/z = 18 (H2O+) and (b) m/z = 32 (O2+). 9752


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The Journal of Physical Chemistry A between the first shoulder and the peak maximum in the DTG curve. At this reaction stage, many cracks were found in the outer surface layer of each granule (Figure 4a), which appeared to result from a significant increase in the internal pressure caused by the blockage by the outer surface layer of the diffusional removal of the gaseous products produced during the internal reaction, as well as the mechanical stress induced by the volume shrinkage in the surface layer. Crack formation in the surface product layer midway through the reaction is rather common for the thermal decomposition of inorganic solids,19,22,33 but a more intensive force appeared to be required for crack formation in the outer surface layer of the SPC granules, indicating a significant increase in the internal gaseous pressure. At this stage, SPC crystalline particles in the outer surface layer had already decomposed to Na2CO3, and Na2CO3 particles aggregated in each original crystal (Figure 4b). The morphology of this Na2CO3 in the outer surface layer of the reacted crystals was identical to that observed for the thermal decompositions of SPC crystalline particles12 and also of sodium hydrogen carbonate.34 In addition, despite the crack formation in the outer surface layer, the core−shell structure was rigidly maintained in the other parts of the granule surface (Figure 4c,d). In the microscopic view observed under polarized light, advancement of the internal reaction occurred along with the boundary lines of aggregate of SPC crystals (Figure 4d). On the internal cleaved surface of a granule, aggregates of the product Na2CO3 particles were observed on the surfaces of each constituent SPC crystalline particle (Figure 4e). Notably, the formation of Na2CO3 whiskers radiating from the interstices of the Na2CO3 aggregates on the surface of the original SPC crystalline particles was also confirmed. Similar whisker formation was observed during the thermal decomposition of SPC crystalline particles and interpreted as resulting from the blowout of gases produced by the internal reaction.12 This phenomenon indicates a temporary increase in the internal pressure in each SPC crystalline particle due to the blocking action of the surface product layer on the diffusional removal of gaseous products and the possible presence of liquid water.12 Figure 4f shows the internal cleaved surface and outer granule surface at the end of the thermal decomposition. In addition to the formation of Na2CO3 whiskers in the interior of the granule, a large number of whiskers were formed on the outer surface of the granule during the final stage of the reaction. These results further indicate that hindrance of the gross diffusion of gaseous products by the outer surface layers of the granules occurred during the course of the thermal decomposition. The increase in the internal pressure of the granules and subsequent recovery to atmospheric pressure following the blowout of gases through the outer surface layer, causing the formation of the whiskers, is thought to have occurred near the maximum mass-loss rate under linearly increasing temperature conditions, which appeared just prior to the completion of the thermal decomposition. The morphological changes observed in the granules indicate that the overall reaction kinetics are largely influenced by the hindrance of the diffusional removal of gaseous products by both the surface product layer of each internal SPC crystalline particle and the outer layers of the core−shell structure of the granules. Examination of the impact of atmospheric water vapor pressure, p(H2O), on the reaction behavior can be used to evaluate the role of the surface layer on the overall kinetics when a reaction is influenced by the diffusional removal of

water vapor through a surface layer.34−39 Figure 5 shows the TG−DTG curves recorded under different p(H2O). No

Figure 5. Influence of atmospheric water vapor pressure p(H2O) on the thermal decomposition of SPC granules (m0 = 5.01 ± 0.03 mg) at β = 5 K min−1: (a) TG−DTG curves under different p(H2O) and (b) changes in Te.o. and Tp in the DTG curves with p(H2O).

distinguishable effect of p(H2O) appeared during the early stage of the reaction (Figure 5a). However, this situation dramatically changed at the point when the shoulder appeared in the DTG curve. Subsequently, the reaction systematically shifted to higher temperatures with increasing p(H2O). This behavior was clearly seen in the changes in the extrapolated onset temperature (Te.o.) and peak top temperature (Tp) of the DTG curve (Figure 5b), where Te.o. was practically constant regardless of p(H2O) and Tp increased with p(H2O). The observed influence of p(H2O) on the thermal decomposition of the SPC granules was also very different from that reported for SPC crystalline particles.12 For the SPC crystalline particles, Te.o. shifted to lower temperature with increasing p(H2O), while Tp remained nearly constant regardless of p(H2O). The acceleration of the early reaction stage in the SPC crystalline particles was attributed to promotion of the dissociation of SPC into Na2CO3 and H2O2 and the decomposition of H2O2 by water vapor absorbed on the crystal surfaces. In the established reaction stage, on the other hand, because the self-generated reaction conditions predominantly controlled the overall reaction rate, the atmospheric p(H2O) did not directly influence the reaction behavior. The outer surface layer in the SPC granules appears to be responsible for the different response to changes in the atmospheric p(H2O). In the SPC granules, the major portion of SPC crystalline particles to be decomposed is protected by the outer surface layer; therefore, atmospheric water vapor does not directly interact with the internal SPC crystalline particles. This function of the outer surface layer, which is in fact designed to protect household SPC granules from degradation due to 9753


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The Journal of Physical Chemistry A atmospheric water vapor during storage, may be the reason for the negligible influence of atmospheric p(H2O) on the kinetic behavior in the early stage of the thermal decomposition. However, as the reaction in the internal SPC crystalline particles advances, this important protective effect of the outer surface layer begins to have opposite influence. Specifically, the outer surface layer significantly hinders the diffusional removal of the gaseous products generated by the thermal decomposition of the internal SPC crystalline particles, resulting in an increase in the internal gaseous pressure. This effect is considered to be more significant than that caused by the surface product layer of the SPC crystalline particles and leads to arrest of the reaction, as indicated by the appearance of the shoulder peak in the DTG curve, due to the thicker Na2CO3 layer on the outer surface. The cracks formed in the outer surface layer in the reaction stage following the appearance of the shoulder peak in the DTG curve (Figure 4a) are believed to be the channels generated to allow release of the high internal gaseous pressure. The shift of the reaction to higher temperatures with increasing atmospheric p(H2O) at this reaction stage is attributed to a delay in crack formation in the outer surface layer due to an increase in the strength of the outer surface layer. Although the architectural strength of the outer surface layer may be weakened by the thermal decomposition of SPC crystalline particles, the degree of weakening depends on the atmospheric p(H2O), which influences the crystal growth of the product Na2CO3 and the interconnection between the constituent particles in the outer surface layer. In addition to physically impeding the gaseous diffusion, the thick Na2CO3 layer also undergoes chemical interaction with the water vapor under when the water vapor pressure is high (eq 4). In fact, when the contribution of the chemical effect of water vapor diffusion through the outer Na2CO3 shell is considered, the difference in the evolution rate behaviors for H2O and O2 during the reaction (Figure 3) can be qualitatively explained. 3.3. Kinetic Characterization of the Multistep Reaction Behavior. As discussed above, the thermal decomposition of SPC granules is significantly influenced by the self-generated reaction conditions, in which continuous changes in the internal gaseous pressure in the granules play a predominant role in regulating the kinetic behavior in the early stage of the reaction. However, the changes in the internal gaseous pressure cannot be experimentally traced during the reaction. In such a situation, it is a challenge to reveal the kinetic characteristic of the reaction and how they change with the reaction conditions by tracking the mass-loss behavior under systematically changing heating conditions, that is, isothermal, linear nonisothermal, and controlled rate conditions. Figure 6 shows the mass-loss curves for the thermal decomposition of SPC granules recorded under isothermal conditions at different temperatures and linear nonisothermal conditions at different β in flowing N2 (80 cm3 min−1). Superficially, a smooth mass-loss behavior with a sigmoidal shape was observed under isothermal conditions (Figure 6a). On the other hand, under linear nonisothermal conditions, the multistep mass-loss behavior expected from the DTG curve with a shoulder before the peak maximum became increasingly apparent with increasing β (Figure 6b). As shown in Figure 7a, under controlled rate conditions, the mass-loss rate was constant during the course of reaction; therefore, the change in the internal gaseous pressure during the reaction was relatively suppressed in comparison to the reactions under conventional isothermal and linear

Figure 6. Mass-loss curves for the thermal decomposition of SPC granules in flowing N2 (80 cm3 min−1): (a) under isothermal conditions at different temperatures (m0 = 5.00 ± 0.05 mg) and (b) under linear nonisothermal conditions at different β (m0 = 5.02 ± 0.05 mg).

Figure 7. Mass-loss measurements at controlled mass-loss rates C for the thermal decomposition of SPC granules (m0 = 5.01 ± 0.05 mg) in flowing N2 (80 cm3 min−1): (a) typical record at C = 10.0 μg min−1 and (b) change in the temperature profile with C.

nonisothermal conditions. In addition, the temperature profile during the reaction under controlled rate conditions exhibited a smooth concave shape independent of the applied controlled mass-loss rate C (Figure 7b). The temperature profile behavior under CRTA conditions is thought to reflect the reverse side of 9754


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The Journal of Physical Chemistry A the kinetic behavior of the sigmoidal mass-loss curve at constant temperature.25,40 The smooth mass-loss and temperature-change behaviors under isothermal and controlled rate conditions, respectively, allowed us to apply a formal kinetic analysis based on the fundamental kinetic equation for a pseudo single step reaction:41,42 ⎛ E ⎞ dα = A exp⎜ − a ⎟f (α) ⎝ RT ⎠ dt

(5)

where α, A, Ea, and f(α) are the fractional reaction, Arrhenius preexponential factor, apparent activation energy, and kinetic model function, respectively. The results of the formal kinetic analysis for the thermal decomposition of SPC granules under isothermal and controlled rate conditions are shown in Figure 8. Initially, the kinetic rate data generated from the mass-loss data under isothermal and controlled rate conditions were simultaneously analyzed using the isoconversional method in differential form, known as the Friedman method,43 because of the applicability of the method to kinetic rate data obtained under any temperature profile:44−46 E ⎛ dα ⎞ ln⎜ ⎟ = ln[Af (α)] − a ⎝ dt ⎠ RT

(6)

The isoconversional relationship or the linear relationship between ln(dα/dt) versus T−1 at a selected α for the kinetic rate data under different reaction conditions is well established for kinetic rate data obtained under isothermal and controlled rate conditions, independent of the selected α (Figure 8a). The slopes of the plots at different α are nearly constant, although the Ea values calculated from the slopes indicated a slight change in the convex shape as the reaction advanced (Figure 8b). The average Ea value for 0.05 ≤ α ≤ 0.95 was calculated to be 112.5 ± 1.2 kJ mol−1, which was larger by approximately 10% than that previously estimated for the thermal decomposition of SPC crystalline particles.12 Because rate behavior under isothermal conditions comparable to that for the thermal decomposition of SPC crystalline particles was observed at a temperature higher approximately 15 K for the SPC granules, the larger Ea value describes the difference in the reaction temperatures with a qualitative meaning. Assuming a constant Ea value during the course of reaction, the rate behavior was reproduced as the hypothetical rate behavior at infinite temperature using the isoconversional relationship:44−50 dα dα ⎛ Ea ⎞ ⎟ = Af (α) = exp⎜ ⎝ RT ⎠ dθ dt

with θ =

∫0

t

Figure 8. Kinetic analysis of the thermal decomposition of SPC granules under isothermal and controlled rate conditions in flowing N2 (80 cm3 min−1): (a) Friedman plots at different α; (b) Ea values at different α; and (c) experimental master plot and fitted curves using SB(m, n, p), SB(m, n, 0), and JMA(m) models.

master plot could not be fitted using the nucleation and growth model JMA(m), f(α) = m(1 − α)[−ln(1 − α)]1−1/m,51−54 even when applying the maximum kinetic exponent m that is theoretically acceptable (JMA(4)). On the other hand, using an empirical kinetic model known as the Šesták−Berggren model55 (SB(m, n, p): f(α) = αm(1 − α)n[−ln(1 − α)]p), the experimental master plot was perfectly fitted with the kinetic exponents SB(−1.61 ± 0.23, 1.40 ± 0.09, 2.26 ± 0.22). This is because of the sufficient flexibility of the empirical model to accommodate the different types of physico-geometric kinetic behaviors and those deviations from the idealized kinetic models.56−58 When applying SB(m, n, 0) to evaluate the behavior as an autocatalytic reaction, the plot was fitted by SB(0.75 ± 0.01, 0.55 ± 0.01, 0). In comparison to the ideal autocatalytic reaction represented by the Prout−Tompkins model59,60 and expressed by SB(1, 1, 0), the rate behavior exhibited greater acceleration because m > n. If JMA(m) was used as the empirical kinetic model without considering the theoretical limitations of the kinetic exponent,61 JMA(6.27 ± 0.23) well fit the experimental master plot. The discrepancy between the geometric behavior of the reaction and the shape

⎛ E ⎞ exp⎜ − a ⎟dt ⎝ RT ⎠

(7)

where θ is Ozawa’s generalized time denoting the hypothetical reaction time at infinite temperature. The experimental master plot of (dα/dθ) versus α for the thermal decomposition of SPC granules shows the maximum rate at α = 0.62 (Figure 8c). Notably, the shape is different from that for SPC crystalline particles (a trapezoidal shape).12 When simple physicogeometrical kinetic models were considered, the shape of the experimental master plot corresponded to a nucleation and growth type reaction model. However, the thermal decomposition of SPC granules is largely regulated by changing, selfgenerated reaction conditions; therefore, the shape of the experimental master plot does not directly reflect the geometrical features of the reaction. In fact, the experimental 47

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of the DTG curve with a shoulder and the fact that the Ea value changed drastically half way through the reaction. For the empirical kinetic modeling of the overlapping reaction steps, all of the kinetic parameters in eq 8 should be determined. A nonlinear least-squares analysis to minimize the residuals F when fitting the experimental kinetic rate data (dα/ dt)exp using the calculated data (dα/dt)cal according to eq 8 was thus performed in order to optimize the kinetic parameters:

of the experimental master plot can be attributed to other factors not considered in the fundamental kinetic equation (eq 5). For the thermal decomposition of SPC granules, a continuous variation in the internal gaseous pressure during the course of reaction likely influences the overall rate behavior. Thus, the experimental master plot (Figure 8c) is interpreted as indicating the apparent rate behavior influenced by changes in the internal gaseous pressure as the reaction advanced. Because a change in the reaction rate behavior in the middle of the reaction was expected from the shape of the DTG curve for the thermal decomposition of SPC granules under linear nonisothermal conditions (Figure 6b), the assumption of a single step reaction for the fundamental kinetic equation is not likely applicable. As shown in Figure 9, a trial application of the

2 ⎡⎛ ⎞ ⎛ dα ⎞ ⎤ d α F = ∑ ⎢⎜ ⎟ −⎜ ⎟ ⎥ ⎢⎝ dt ⎠exp, j ⎝ dt ⎠cal, j ⎥⎦ j=1 ⎣ M

To maintain the kinetic logics and preserve the reliability of the kinetic parameters optimized through this highly mathematical procedure, the initial settings selected for the kinetic parameters in eq 8 are very important. In this study, to determine the initial values for all of the kinetic parameters, a statistical deconvolution method63,71,72 was applied to the experimental kinetic data, and the separated kinetic rate data were analyzed using the formal kinetic analysis method on the basis of the single-step assumption, as was applied to the thermal decomposition under isothermal and controlled rate conditions. The initial values for the kinetic parameters were determined by referencing the kinetic parameters determined for the reaction under isothermal and controlled rate conditions and for the reaction under nonlinear isothermal conditions using the mathematical peak deconvolution procedure. The details of the procedure and the results are described in the Supporting Information. After establishing the initial values for the kinetic parameters (Table S1) in eq 8, all of the kinetic parameters were simultaneously optimized. In this procedure, the JMA(m) model was used as the empirical kinetic model function for both reaction steps in order to detect any variation in the rate behavior using a single kinetic exponent. Figure 10 shows the results of the kinetic deconvolution analysis. As was the case for the thermal decomposition of SPC crystalline particles, the overall process was well fitted assuming the two overlapping reaction steps (Figure 10a). The average kinetic parameters optimized for the reaction at different β are summarized in Table 1. Notably, the Ea values for the first and second reaction steps were practically identical. The sequence of the two reaction steps along the temperature axis was reflected by the smaller A value for the second reaction step. The kinetic model functions estimated for the first and second reaction steps indicated largely different rate behaviors, as can be seen in the normalized master plots for f i(αi)/f i(0.5i,) versus αi (Figure 10b). The kinetic exponents m ≈ 2 and m > 4 in the JMA(m) model obtained for the first and second reaction steps, respectively, may reflect the characteristics of each reaction step. The smaller m value for the first reaction step appears to result from the gradual increase in the hindrance of diffusional removal of the gaseous products by the outer surface layer and consequently the internal gaseous pressure, which impedes the reaction in the interior of the granules. The larger m value determined for the second reaction step indicates an acceleration process possibly caused by the release of the trapped gaseous products accompanied by the formation of diffusion channels in the outer surface layer and reactivation of the impeded internal reaction. Accordingly, the mechanistic change from the first reaction step to the second reaction step is characterized by the variations in the A and m values, while maintaining the Ea value constant. These trends for the

Figure 9. Variation in the Ea value for the thermal decomposition of SPC granules under linear nonisothermal conditions estimated using the Friedman method.

Friedman method to the kinetic rate data under linear nonisothermal conditions resulted in the apparent and systematic variation of the Ea value as the reaction advanced, although the linearity of the Friedman plot at each α was reasonable. The Ea value reached a minimum at α = 0.38, which nearly corresponds to the appearance of the shoulder in the DTG curve. The apparent decrease in the Ea value during the early stage of the reaction is attributed to changes in the selfgenerated reaction conditions, and consequently the rate behaviors depending on β. Because such variation in Ea during the early stage of the reaction was not observed for the thermal decomposition of SPC crystalline particles under identical reaction conditions,12 the apparent variation of Ea indicates significant hindrance of diffusional removal of internal gaseous products by the outer surface layer of the granules. Rigorous kinetic modeling taking into account all of the possible factors is practically difficult for this complex process. Therefore, empirical kinetic modeling assuming an overlapping multistep process that consists of kinetically independent reaction steps is an effective method for understanding the overall kinetic behavior.12,39,62−70 Under this assumption, the overall rate equation can be formalized by the sum of each component reaction step:62,63 dα = dt

n

⎛ Ea, i ⎞ ⎟f (αi) RT ⎠ i

∑ ciAiexp⎜⎝− i=1

n

n

with ∑ ci = 1 and ∑ ciαi = α i=1

(9)

i=1

(8)

where n and c are the number of the component steps and the contribution ratio of each reaction step to the overall process, respectively, and the subscript i denotes each component reaction step. For the present reaction, the number of component reaction steps is n = 2 based on the characteristics 9756


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deconvoluted into two reaction steps using eq 8. The results of the kinetic deconvolution analysis, for which the kinetic parameters determined for the reaction under linear nonisothermal conditions (Table 1) were used as the initial parameter settings, are shown in Figure 11 and the optimized

Figure 10. Results of the kinetic deconvolution analysis for the thermal decomposition of SPC granules under linear nonisothermal conditions: (a) typical result for the reaction at β = 5 K min−1 and (b) experimental master plots for the component reaction steps.

optimized kinetic parameters are quiet similar to those reported for the thermal decomposition of SPC crystalline particles.12 One major difference in the multistep behaviors for the crystalline particles and granules is the apparently larger contribution of the second reaction step in the granular sample. It should also be noted that the difference in the A values for the first and second reaction steps was larger for the granular sample, indicating larger lags of the reaction time and temperature. These differences are ascribed to the larger impedance effect on the internal reaction in the granules due to the presence of both the outer surface layer of the granules and in situ produced surface product layer on each internal crystalline particle. Notably, for the thermal decomposition of SPC granules under isothermal and controlled rate conditions, the evaluated overall rate behavior (Figure 8) resembled that of the second reaction step under linear nonisothermal conditions (Figure 10) in that the rate behavior was characterized by a large m value in the JMA(m) model. Thus, the influence of the blocking action of the outer surface layer and subsequent acceleration were suspected to occur even under moderate reaction conditions. To confirm this suspicion, the kinetic rate data under isothermal and controlled rate conditions were

Figure 11. Results of the kinetic deconvolution analysis for the thermal decomposition of SPC granules under isothermal and controlled rate conditions: (a) isothermal conditions at T = 403 K and (b) controlled rate conditions at C = 10.0 μg min−1.

kinetic parameters are also listed in Table 1. The kinetic rate data under isothermal (Figure 11a) and controlled rate (Figure 11b) conditions were satisfactorily fitted with the practically identical kinetic parameters with that determined for the reaction under linear nonisothermal conditions. The only detectable change in the optimized kinetic parameters was observed for the smaller m value for the JMA(m) model for the second reaction step under isothermal and controlled rate conditions. From these results, it can be concluded that the influence of the blocking of the diffusional removal of internal gaseous products by the outer surface layer on the kinetic behavior of the thermal decomposition is inevitable in the early reaction stage, even under moderate reaction conditions. However, the variation in the reaction conditions as the reaction proceeds depends on the applied reaction conditions. Under moderate reaction conditions, the increase in the internal gaseous pressure is relatively smaller, and thus, subsequent acceleration of the reaction is suppressed, as was

Table 1. Average Kinetic Parameters Optimized for the Thermal Decomposition of SPC Granules JMA(m) condition

i

nonisothermal

1 2 1 2 1 2

isothermal controlled rate

Ea/kJ mol−1

c 0.52 0.48 0.50 0.50 0.52 0.48

± ± ± ± ± ±

0.04 0.04 0.03 0.03 0.03 0.03

114.3 113.9 115.1 114.1 114.9 114.0

± ± ± ± ± ±

0.6 0.5 0.1 0.1 0.2 0.2 9757

A/1011 s−1 6.00 3.05 6.00 3.00 6.00 3.00

± ± ± ± ± ±

0.01 0.01 0.01 0.01 0.01 0.01

R2

m 1.95 5.26 2.04 4.85 1.90 4.78

± ± ± ± ± ±

0.25 1.25 0.07 0.23 0.04 0.17

0.993 ± 0.006 0.987 ± 0.002 0.896 ± 0.120


Article

The Journal of Physical Chemistry A deduced from the decrease in the m value in the JMA(m) model for the second reaction step. It was revealed in this study that the outer surface layer in the core−shell structure and its changes during the reaction play predominant roles in controlling the overall kinetic behavior of the thermal decomposition of SPC granules, as does the primary impedance effect of the surface product layer on the reaction of the SPC crystalline particles that constitute the granules. Such a phenomenological understanding of the reaction kinetics based on a physico-geometrical reaction mechanism is necessary to assess the thermal stability and oxygen release behavior during SPC thermal decomposition. In addition, the exothermic effect observed during the thermal decomposition of this oxidizing solid is also an important feature that characterizes the reaction. Notably, the exothermic effect recorded in the DTA curve during the reaction was not coincident with the mass-loss rate behavior resolved in the DTG curve for the thermal decomposition of SPC (Figure 2). The chemical scheme for successive endothermic and exothermic processes due to detachment and decomposition of H2O2(g) may be responsible for the discrepancy between the features observed in the DTA and DTG curves. The details of this phenomenon will be discussed elsewhere by integrating the findings on the physico-geometrically controlled reaction behavior and the chemical scheme involving successive endothermic and exothermic processes.

the accelerated behavior. Significant effects of the changes in the self-generated reaction conditions are also expected for the reaction under moderate reaction conditions. This assumption is supported by the satisfactory fitting of two overlapping reaction steps as assumed for the decomposition under linear nonisothermal conditions. The revealed kinetic behavior is taken as a typical model for the thermal decomposition of an internal solid protected by an outer surface layer in a core−shell structure. It should also be noted that the performance of SPC granules as a combustion improver is activated in the second half of the reaction following the acceleration of the thermal decomposition triggered by crack formation in the outer surface layer.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b07042. Powder XRD pattern and FT-IR spectrum of SPC granules; changes in XRD pattern of the sample during the thermal decomposition; mathematical deconvolution of the mass-loss data under linear nonisothermal conditions and the formal kinetic analysis of the deconvoluted kinetic data (PDF)

■

4. CONCLUSIONS In the thermal decomposition of SPC granules with a core− shell structure consisting of an outer Na2CO3 surface layer and internal aggregates of SPC crystalline particles, the outer surface layer, which protects the internal SPC crystalline particles, plays a critical role in controlling the apparent overall kinetic behavior. The thermal stability of SPC is improved by the protective action of the outer surface layer, as reflected by an increase in the Ea value for the thermal decomposition by approximately 10% as compared with that for the reaction of SPC crystalline particles. In addition, the influence of the reaction atmosphere on the early stage of the reaction is negligible. On the other hand, the outer surface layer also hinders the diffusional removal of gaseous products generated during the internal reaction, likely resulting in an increase in internal gaseous pressure as the reaction advances. Under linearly increasing temperature conditions, the gradual increase in the internal pressure impedes the reaction of the internal SPC crystalline particles, and the overall reaction is temporary arrested, as indicated by the appearance of a shoulder in the DTG curve. However, the self-generated reaction conditions in the interior of the granules suddenly change following crack formation in the outer surface layer. These cracks act as channels for the diffusional escape of the trapped gases, which then leads to reinitiation of the internal reaction and acceleration of the rate of the overall reaction. In this reaction stage, the blowout of gaseous products from each internal SPC crystalline particle through its surface product layer and from the granule interior through the outer surface layer occurs, leaving many whiskers of Na2CO3 as traces. Therefore, the reaction was empirically deconvoluted into two reaction steps that occur under different self-generated reaction conditions. The reaction apparently proceeds in a smooth manner under isothermal and controlled rate conditions with a constant Ea value of approximately 110 kJ mol−1, but the rate behavior as reproduced by the experimental master plot is characterized by

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel./Fax: +81-82-424-7092. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The present work was supported by JSPS KAKENHI Grant Numbers 25242015, 25350202, and 25350203.

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REFERENCES

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