Exothermic Behavior of Thermal Decomposition of Sodium Percarbonate

Article pubs.acs.org/JPCA

Exothermic Behavior of Thermal Decomposition of Sodium Percarbonate: Kinetic Deconvolution of Successive Endothermic and Exothermic Processes Masayoshi Nakano, Takeshi Wada, and Nobuyoshi Koga* Chemistry Laboratory, Department of Science Education, Graduate School of Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi-Hiroshima 739-8524, Japan ABSTRACT: This study focused on the kinetic modeling of the thermal decomposition of sodium percarbonate (SPC, sodium carbonate−hydrogen peroxide (2/3)). The reaction is characterized by apparently different kinetic profiles of mass-loss and exothermic behavior as recorded by thermogravimetry and differential scanning calorimetry, respectively. This phenomenon results from a combination of different kinetic features of the reaction involving two overlapping mass-loss steps controlled by the physico-geometry of the reaction and successive endothermic and exothermic processes caused by the detachment and decomposition of H2O2(g). For kinetic modeling, the overall reaction was initially separated into endothermic and exothermic processes using kinetic deconvolution analysis. Then, both of the endothermic and exothermic processes were further separated into two reaction steps accounting for the physico-geometrically controlled reaction that occurs in two steps. Kinetic modeling through kinetic deconvolution analysis clearly illustrates the appearance of the net exothermic effect is the result of a slight delay of the exothermic process to the endothermic process in each physico-geometrically controlled reaction step. This demonstrates that kinetic modeling attempted in this study is useful for interpreting the exothermic behavior of solid-state reactions such as the oxidative decomposition of solids and thermal decomposition of oxidizing agent.

1. INTRODUCTION Many reaction processes of inorganic solids involving thermal decomposition are predominantly regulated by geometrical constraints in the relationship between the surface layer produced in an early stage of the reaction and the inward advancement of the reaction interface generated at the boundary between the surface product layer and internal reactant.1−5 The surface product layer inhibits the diffusional removal of the gaseous products generated at the internal reaction interface. Consequently, this causes self-generated reaction conditions at the reaction interface. The overall reaction kinetics of thermal decomposition tracked by mass-loss behavior occasionally indicate a partially overlapping multistep reaction feature caused by these physico-geometrical factors and changes in the self-generated reaction conditions during the reaction.6−10 In addition, reactions in solids can be composed of multiple constituent chemical processes that occur successively. Examples include the oxidative decomposition of solids,11,12 the thermal decomposition of oxidizing solids,13,14 and the successive thermal decomposition and reaction of the solid product with atmospheric gases.15 In this type of reaction, each constituent chemical process contributes differently to the overall thermal effect of the reaction determined to be either exothermic or endothermic. When the constituent chemical processes proceed consecutively, having satisfied the steady-state approximation, the reaction is treated kinetically as a pseudo-single-step reaction. In these © 2015 American Chemical Society

cases, the time- or temperature-resolved thermal effect is approximated as the sum of the time derivatives of each thermal effect of the constituent chemical processes that proceed by regulating the same kinetic regime. If these constituent chemical reactions occur with a significant time lag and in different places within the reaction system, the time- or temperature-resolved thermal effect of the overall reaction becomes the sum of the time derivative of the thermal effects of the constituent chemical processes that proceed according to different kinetic regimes and reflect a multistep chemical reaction scheme. However, the actual reaction can be more complex because some reactions proceed in a combination of multistep behaviors controlled by physico-geometrical features of solid-state reactions and successive chemical reaction schemes. The kinetic solution of complex reaction has practical significance for solid-state reaction processes such as assessing the stability and reactivity of materials, evaluating the effectiveness of energetic materials involved in safety assessment, and controlling the material synthesis process. One probable reaction involving solids that exhibit this complex multistep behavior controlled by physico-geometrical and successive chemical reaction schemes is the thermal decomposition of sodium percarbonate (SPC; sodium Received: July 21, 2015 Revised: September 2, 2015 Published: September 7, 2015 9761

DOI: 10.1021/acs.jpca.5b07044 J. Phys. Chem. A 2015, 119, 9761−9769

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The Journal of Physical Chemistry A carbonate−hydrogen peroxide (2/3); Na2CO3·1.5H2O2; CAS No. 15630-89-4):13,14,16−24

the physico-geometrical constraint and the chemical scheme of the successive reaction. This study evaluated the chemical scheme of successive reactions in thermal decomposition of SPC from the differences in the rate behaviors measured using thermogravimetry (TG) and differential scanning calorimetry (DSC). Separation of calorimetric data into endothermic and exothermic effects attributed to the successive reactions of eqs 2 and 3, respectively, was attempted using an empirical kinetic deconvolution procedure. Then, both of the endothermic and exothermic effects were further separated into two reaction steps by considering the two overlapping reaction steps controlled by physico-geometrical constraints revealed in our previous studies.13,14 Based on the empirical kinetic model of the thermal decomposition of SPC, the kinetic meaning of the time- or temperature-resolved thermal effects recorded using DSC measurements is evaluated and the differences between reactions of SPC crystalline particles and granules are illustrated. This example of kinetic modeling demonstrates the usefulness of applying the kinetic procedure to additional relevant reactions.

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

(1)

This compound is widely used in industries and laboratories as an oxidizing agent and also as household oxygen bleach.25 Because of the oxygen generation by the thermal decomposition (eq 1), this compound is controlled as a hazardous material due to a combustion improver. Galwey and Hood17,18 reported that thermal decomposition of SPC crystalline particles proceeds in a contraction geometrical scheme involving the initial formation of the surface product layer and subsequent advancement of the reaction interface inward. The gaseous products are removed from the interior of the reactant crystals through the surface product layer. A physicogeometrical model of a contracting geometry type of reaction with an acceleration of the linear advancement rate of the reaction interface was proposed to interpret the overall kinetic behavior of a deformed autocatalytic-type reaction. The present authors recently revealed through systematic thermoanalytical measurements under different conditions and morphological investigations of the thermal decomposition of SPC crystalline particles (columnar with an axis length of 20−30 μm) that the overall rate behavior is explained by two distinguishable reaction steps.13 In the first half of the reaction, the hindrance effect of the surface product layer on the diffusional removal of the gaseous product results in a gradual increase in the internal gaseous pressure and the retardation of the internal reaction. Formation of diffusion channels in the surface product layer for the internal gaseous products halfway through the reaction shifts the reaction into acceleration behavior. Traces of the blowout of gaseous products are visible as Na2CO3 whiskers radiating outward from the diffusion channels in the surface product layer. The thermal decomposition of granulated SPC, which is the general form of the compound for practical use, was also studied recently and compared with crystalline particles of SPC.14 The outer surface layer of the granulated SPC that plays a protective role of the internal crystalline particles exhibits a significant hindrance effect on the diffusional removal of gaseous products during the thermal decomposition. The duplex hindrance effects of the outer surface layer and the surface product layer of each internal crystalline particle arrested the reaction halfway through and then crack formation in the outer surface layer of the granules reactivated it. Accordingly, the thermal decomposition of SPC crystalline particles and granules can be empirically described by the two overlapping reaction steps separated by the physico-geometrical constraints and the changes in the self-generated reaction conditions during the reaction. In addition, the thermal decomposition of SPC is considered a successive process of the detachment and subsequent decomposition of H2O2(g).16 Na 2CO3 ·1.5H 2O2 (s) → Na 2CO3(s) + 1.5H 2O2 (g)

(2)

H 2O2 (g) → H 2O(g) + 1 2 O2 (g)

(3)

2. EXPERIMENTAL SECTION 2.1. Samples. The same crystalline and granular SPC samples used in previous studies13,14 were used after confirming that no detectable change was found in composition, structure, or thermal decomposition behavior. Figure 1 shows the

Figure 1. Scanning electron microscopic images of the SPC samples: (a) SPC crystalline particles and (b) a SPC granule.

scanning electron microscopic images of the SPC samples. The crystalline SPC was precipitated by mixing a saturated Na2CO3 solution and approximately 15% H2O2 solution at room temperature.13 The precipitate was separated and washed with absolute ethanol and dried in a vacuum desiccator. The granular SPC was purchased as commercially available domestic oxygen bleach (Nippon Garlic Corp.).14 A sieved fraction of 500−1000 μm was sampled without any further purification or crushing. Samples were characterized using powder X-ray diffraction, Fourier transform infrared spectroscopy, and various thermoanalytical measurements.13,14 The morphology of the samples was observed and characterized with a scanning electron microscope. The SPC crystalline particles were columnar crystals approximately 20−30 μm in axis length (Figure 1a) and characterized as orthorhombic crystals (S.G. = Cmca, a = 6.712 Å, b = 15.7407 Å, c = 9.1732 Å)26 with a composition corresponding to Na2CO3·1.5H2O2.13 The SPC granules were spherically shaped (Figure 1b) and consisted of a core−shell structure with internal aggregates of SPC crystalline particles radiating from the center and covered by a surface layer

The respective reactions are endothermic and exothermic processes. The net reaction heat of thermal decomposition is the sum of the thermal effects generated by these constituent reactions according to Hess’s law. However, the profile of timeor temperature-resolved thermal effects during the reaction depends on the combination of kinetic features controlled by 9762


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particles indicates the distinguishable exothermic effect during the latter half of the reaction, and the clearly separated two exothermic DTA peaks are characteristic of the reaction in SPC granules. It has also been confirmed that the characteristic of the DTA peak shape does not change significantly by the effect of the flow rate of N2 applied as one of the reaction conditions. The differences between the DTG and DTA curves are probably due to the overall thermal decomposition process that consists of successive endothermic and exothermic processes. The successive reactions of SPC dissociation into Na2CO3 and H2O2 (eq 2) and subsequent H2O2 decomposition into H2O and O2 (eq 3) that occur separately in time and space are possible reasons for the phenomena observed for the thermal decomposition of SPC. Because there was an exothermic effect during the preparation of SPC crystalline particles by mixing the saturated Na2CO3(aq) and approximately 15% H2O2(aq) even after accounting for the heat of dilution of both solutions, the dissociation reaction of SPC (eq 2) might appear to be an endothermic process. The exothermic behavior of the H2O2 decomposition (eq 3) is well-known.27 Therefore, the DTA signal at any given time or temperature during the reaction was recorded as the sum of the endothermic and exothermic effects at that particular time or temperature. DSC measurements of the thermal decomposition of SPC recorded additional quantitative calorimetric data under conditions comparable to those of the mass-change measurements for kinetic calculation in previous studies.13,14 Parts a and b of Figure 3 show the DSC curves, recorded at different β, for the thermal decomposition of SPC crystalline particles and granules, respectively. The DSC curves indicate trends that correspond to the DTA curves of the respective samples. With increasing β, the DSC curves shift to higher temperatures, but no significant change in the shape of the DSC exothermic peaks is observed. After considering the purity of the SPC samples,

composed of SPC crystalline particles and sodium carbonate. The molar fraction of Na2CO3 in SPC granules used in our studies was calculated to be 7.37 ± 1.37 mol % from the massloss value during the thermal decomposition of SPC granules.14 Both samples decomposed to Na2CO3 on heating, without producing intermediate crystalline phases. Detailed descriptions of the samples are provided in previous studies.13,14 2.2. Thermoanalytical Measurements. Thermogravimetric−differential thermal analysis (TG−DTA) measurements for both samples (sample mass m0 = 5.00 mg; weighed into a platinum cell of 6 mm i.d. and 2.5 mm in height) were performed at a heating rate of 5 K min−1 in an atmosphere of N2 (80 cm3 min−1) using a top-loading instrument (TGD-50M, Shimadzu Co.). DSC was used for recording the kinetic rate data of the thermal decomposition. Each sample of 5.00 ± 0.05 mg was weighed in an aluminum pan (6 mm in diameter and 2.5 mm in depth). The DSC curves were recorded using a DSC instrument (DSC-60, Shimadzu Co.) in N2 flowing at a rate of 50 cm3 min−1 at different β (1 ≤ β ≤ 10 K min−1).

3. RESULTS AND DISCUSSION 3.1. Preview of the Thermal Decomposition Process. Parts a and b of Figure 2 show typical TG−derivative TG

Figure 2. TG−DTG−DTA curves for the thermal decomposition of SPC recorded at β = 5 K min−1 in N2 (80 cm3 min−1): (a) SPC crystalline particles (m0 = 5.00 mg) and (b) SPC granules (m0 = 5.00 mg).

(DTG)−DTA curves, recorded at β = 5 K min−1 in N2 (80 cm3 min−1), for the thermal decomposition of SPC crystalline particles and granules, respectively. In previous studies,13,14 the overall mass-loss process of SPC crystalline particles and granules was characterized by an overlapping multistep process regulated by physico-geometric constraints of surface layers produced during thermal decomposition and granule generation. The thermal decomposition characteristics of the samples have noticeable differences in the peak shape and maximum peak position between the DTG and DTA curves. With reference to the mass-loss rate behavior expected from the DTG curves, the DTA curve for the reaction of SPC crystalline

Figure 3. DSC curves for the thermal decomposition of SPC recorded at different β in N2 (50 cm3 min−1): (a) SPC crystalline particles (m0 = 5.01 ± 0.02 mg) and (b) SPC granules (m0 = 4.99 ± 0.04 mg). 9763


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Therefore, the application of the kinetic deconvolution analysis is understood as an empirical kinetic approach for finding the kinetic characteristics of the component processes and their mutual relationship. Through the kinetic deconvolution analysis based on eq 5, many kinetic parameters are simultaneously optimized. For such mathematical processing, a large effort must be paid for keeping the physicochemical significance of each optimized parameter. In this study, the initial kinetic parameters used for the subsequent optimization were carefully determined through logically designed preliminary kinetic considerations and analyses for keeping the physicochemical significance of the kinetic deconvolution analysis. The initial Qexo value of the H2O2 decomposition for the thermal decomposition of 1 mol of SPC is calculated to be 158.27 kJ from the standard enthalpy of the reaction, ΔrH°298 = −105.51 kJ mol−1.28 Thus, the initial cexo value is determined according to eq 6, with reference to the enthalpy change of the overall reaction calculated from the DSC peak area. Once the initial cexo is determined, the initial cendo is determined according to eq 7. The initial values of (cendo, cexo) averaged over those determined for each DSC curve recorded at different β were (−11.83 ± 0.64, 12.83 ± 0.64) and (−12.05 ± 0.35, 13.05 ± 0.35) for the thermal decomposition of SPC crystalline particles and granules, respectively. No practical method was found to experimentally determine the initial Ea,endo and Ea,exo values. Therefore, an attempt was made to adopt the apparent activation energy Ea for the overall reaction into both the initial Ea,endo and Ea,exo values. The Kissinger method34 is a possible method to determine the apparent activation energy for the overall reaction from DSC curves recorded at different β:

the enthalpy change of the overall thermal decomposition (eq 1) was calculated to be −12.36 ± 0.60 and −12.14 ± 0.32 kJ mol−1 for SPC crystalline particles and SPC granules, respectively. These values represent good agreement between the samples. It was also confirmed that the experimentally determined enthalpy changes for the overall reaction do not change by the effect of the flow rate of N2. However, the enthalpy change values are smaller compared to those of H2O2 decomposition (ΔrH°298 = −105.51 kJ mol−1),28 even though the decomposition of 1.5 mol of H2O2 contributes to the thermal decomposition of 1 mol of SPC. The endothermic processes that contribute to the overall reaction should compensate for the difference. 3.2. Kinetic Deconvolution of Endothermic and Exothermic Processes. The heat flow (dQ/dt) by the reaction and overall heat of reaction Q are obtained from the experimentally resolved DSC curve after subtracting the baseline. The overall reaction rate (dα/dt) is expressed using the values29−31 dQ 1 dα = dt dt Q

(4)

where α is the fractional reaction of the overall process. When DSC curves for thermal decomposition of SPC are assumed to result from the contributions of successive endothermic dissociation of SPC and exothermic H2O2 decomposition, the overall reaction rate recorded using DSC is the sum of these two kinetic processes:32,33 ⎛ Ea,endo ⎞ dα = cendoAendo exp⎜ − ⎟f (α ) ⎝ RT ⎠ endo endo dt ⎛ Ea,exo ⎞ + cexo A exo exp⎜ − ⎟f (α ) ⎝ RT ⎠ exo exo

⎛ β⎞ ⎡ f (αp) AR ⎤ E ⎥− a ln⎜⎜ 2 ⎟⎟ = ln⎢ − ⎢⎣ dα Ea ⎥⎦ RTp ⎝ Tp ⎠

(5)

where c, A, Ea, and f(α) are the contribution ratio, Arrhenius preexponential factor, apparent activation energy, and kinetic model function in differential forms, respectively. The subscripts endo and exo indicate the endothermic and exothermic process components, respectively. The contributions, cendo and cexo, are defined as follows: cendo =

Q endo Q

0

where Tp is the peak maximum temperature characteristic for the overall reaction. For the reaction of SPC crystalline particles, the change in Tp in the DSC curve with β can be examined for the Kissinger plot. There are three possibilities to apply the Kissinger plot to the reaction of SPC granules: the first exothermic peak maximum, the subsequent endothermic peak maximum positioned between the first and second exothermic peaks, and the second exothermic peak maximum. The Kissinger plots ln (β/Tp2) versus Tp−1 are shown in Figure 4. For the reaction of SPC crystalline particles, the Ea value of 100.2 ± 1.4 kJ mol−1 was determined from the Kissinger plots (Figure 4a). In our previous kinetic study of the thermal decomposition of SPC crystalline particles,13 the Ea value for the overall mass-loss process under isothermal, linear nonisothermal, and controlled transformation rate conditions indicated the constant value of 103.0 ± 0.7 kJ mol−1 in the range of 0.05 ≤ α ≤ 0.95, even though the multistep reaction was revealed from the mass-loss behavior. The agreement of the Ea value determined by the Kissinger plot for the DSC curves with that reported for the mass-loss process provided justification for the designation of the Ea value of 100.2 ± 1.4 kJ mol−1 as the initial value of Ea,endo and Ea,exo for the thermal decomposition of SPC crystalline particles. For the reaction of SPC granules, three different values of Ea were obtained from the Kissinger plots (Figure 4b). The Ea values determined in reference to the first exothermic peak maximum, the endothermic peak maximum between the two exothermic peaks, and the second exothermic peak maximum were 181.6 ±

(6)

where Qendo and Qexo are the heats of the endothermic and exothermic process components, respectively. The following relationship must concurrently be satisfied by cendo and cexo: cendo + cexo =

Q endo + Q exo Q

=1

(9)

(7)

Furthermore, the αendo and αexo at a time or temperature are correlated to α: α = cendoαendo + cexoαexo (8) Due to the experimental difficulty of separately tracking the endothermic and exothermic process components, deconvolution of the overall kinetic information into process components is the only possible method for interpreting the reaction scheme of the successive processes. The kinetic deconvolution analysis based on eq 5 assumes that the overlapping processes are kinetically independent. However, a certain mutual kinetic correlation between the endothermic and exothermic processes is inevitable in this reaction as in many solid-state reactions. 9764


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Parts a and b of Figure 5 show typical results of the kinetic deconvolution into the endothermic and exothermic process

Figure 4. Kissinger plots applied to DSC curves recorded at different β: (a) SPC crystalline particles and (b) SPC granules. Figure 5. Typical results of kinetic deconvolution of the thermal decomposition of SPC into the endothermic and exothermic process components (β = 5 K min−1): (a) SPC crystalline particles and (b) SPC granules.

4.8, 158.3 ± 5.4, and 119.6 ± 2.0 kJ mol−1, respectively. In previous study,14 the mass-loss process of the thermal decomposition of SPC granules under nonisothermal conditions was also characterized by the two overlapping reaction steps with Ea values of 114.3 ± 0.6 and 113.9 ± 0.5 kJ mol−1. This indicated a close correspondence to the constant Ea value of 112.5 ± 1.2 kJ mol−1 (0.05 ≤ α ≤ 0.95) determined for the mass-loss process under isothermal and controlled transformation rate conditions.14 Because the Ea value determined in reference to the second exothermic peak maximum, 119.6 ± 2.0 kJ mol−1, is the closest to those values determined for the overall mass-loss process, that value was used as the initial values of Ea,endo and Ea,exo for the thermal decomposition of SPC granules. An empirical kinetic model function that accommodates different types of physicochemical characteristics of the kinetic behavior of each process component is provided as f(α) in eq 5. The Šesták−Berggren model with three kinetic exponents,35−37 SB(m,n,p): f(α) = αm(1 − α)n[−ln(1 − α)]p, is an empirical kinetic model applicable to different types of solid-state reactions.38−40 Initially, the first-order reaction was assumed for f(α) for both the endothermic and exothermic process components by introducing SB(0,1,0) into fendo(αendo) and fexo(αexo). After the initial values of c, Ea, and f(α) were set in eq 5, the order of initial Aendo and Aexo was determined by graphically comparing the experimentally resolved kinetic rate data and those calculated according to eq 5. Subsequently, all of the kinetic parameters in eq 5 were simultaneously optimized for each kinetic curve at different β to minimize the square root of the residuals F when fitting the calculated (dα/dt) versus t curve to the experimental (dα/dt) versus t curve:32,33 2 ⎡⎛ ⎞ ⎛ dα ⎞ ⎤ α d −⎜ ⎟ ⎥ F = ∑ ⎢⎜ ⎟ ⎢⎝ dt ⎠exp, j ⎝ dt ⎠cal, j ⎥⎦ j=1 ⎣

components for the thermal decomposition of SPC crystalline particles and granules, respectively. The results clearly illustrate the reaction model composed of the endothermic and exothermic processes. The experimentally resolved DSC curves were recorded as the residuals when the endothermic and exothermic effects canceled each other out at a particular time or temperature. In the thermal decomposition of SPC crystalline particles, a residual exothermic effect mainly appears during the second half of the reaction. Two partially overlapping DSC exothermic peaks observed during the thermal decomposition of SPC granules are interpreted as residual exothermic effects and appear in the acceleration and deceleration stages of the reaction under linearly increasing temperature conditions. Table 1 lists the averaged kinetic parameters determined for the separated endothermic and exothermic processes. For each SPC sample, the nearly identical Ea values were determined for the endothermic and exothermic processes. The slightly smaller A value for the exothermic process indicates a detectable delay of the exothermic process from the endothermic process, which is in agreement with the reaction sequence of the dissociation of SPC and the decomposition of H2O2. Differences in the kinetic behavior of the endothermic and exothermic processes also appear in the kinetic exponents of the SB(m,n,p) model. Therefore, the net difference of the endothermic and exothermic effects was detected by the DSC exothermic peak as the results of the difference in the kinetics of the endothermic and exothermic processes characterized by the differences in the A value and the kinetic model function. 3.3. Kinetic Deconvolution Considering Chemical and Physico-geometrical Constraints. Further refinement of the kinetic modeling for the endothermic and exothermic processes in the thermal decomposition of SPC is needed, because the

M

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0.990 ± 0.006

0.994 ± 0.005

1.9 2.3 3.0 2.8 ± ± ± ±

dα = dt

−146.2 158.6 −148.2 160.3

R2 Q/kJ (mol SPC)−1

overlapping two mass-loss steps are the physico-geometrical characteristics of the reaction.13,14 Thus, the endothermic and exothermic processes separated in the primary kinetic deconvolution (Figure 5) must be further separated into two reaction steps by considering the physico-geometrical characteristics of the reaction. Then the overall reaction rate at a time or temperature is expressed by the sum of each two-step endothermic and exothermic process:32,33 ⎛ Ea,endo, i ⎞ (αendo, i) ⎟f ⎝ RT ⎠ endo, i

2

∑ cendo, iAendo, i exp⎜− i=1

⎛ Ea,exo, i ⎞ ⎟ f (α ) ⎝ RT ⎠ exo, i exo, i

2

+

∑ cexo, i A exo, i exp⎜−

± ± ± ±

2

2

∑ cendo,i + ∑ cexo, i = 1 0.06 0.06 0.03 0.08

2

± ± ± ± 0.96 1.02 0.79 0.70

n

i=1

0.05 0.06 0.06 0.08 ± ± ± ± 10 1010 1012 1012

× × × × 0.72) 0.54) 0.87) 1.34) ± ± ± ± (5.50 (4.80 (5.42 (5.27 0.5 0.5 0.6 0.8 ± ± ± ± 98.4 98.1 118.0 118.1 0.6 0.6 0.6 0.6 ± ± ± ± −11.8 12.8 −12.2 13.2 granules

endo exo endo exo crystalline particles

2 i=1

(12)

The initial kinetic parameters in eq 11 were set with the kinetic parameters determined through the primary kinetic deconvolution into the endothermic and exothermic processes (Table 1) and those determined for the two overlapping massloss steps in our previous studies. Table 2 summarizes the reported kinetic parameters for the respective mass-loss steps of the thermal decomposition of SPC.13,14 The four contributions (cendo,i, cexo,i)i=1or2 in eq 11 were calculated using the values of cendo and cexo in Table 1 and ci values in Table 2 as (cendoci, cexoci)i=1or2. Irrespective of the endothermic and exothermic processes, the initial Ea values for the first and second reaction steps were adopted from those determined for each mass-loss step (Table 2). The two overlapping mass-loss steps have been empirically described by a nucleation and growth-type kinetic model function, JMA(m): f(α) = m(1 − α)[−ln(1 − α)]1−1/m,41−44 as shown in Table 2. The JMA(m) functions for the first and second mass-loss steps were transformed to each SB(m,n,p) function35−37 and used as the initial setting of f(α) for the first and second reaction steps in eq 11 irrespective of the endothermic and exothermic processes. After this initial setting, the order of the initial A values was determined graphically, where the equivalent values were set to each reaction step irrespective of the endothermic and exothermic processes. The optimization run was subsequently performed for the respective kinetic rate data at different β using the same procedure described for the primary kinetic deconvolution into the endothermic and exothermic processes. Figure 6 shows typical results of the kinetic deconvolution of the thermal decomposition of SPC into four reaction processes involving each two-step endothermic and exothermic process. The calculated temperature range of the overall reaction for each sample corresponds well to that of the mass-loss process of the thermal decomposition at the same β.13,14 The optimized kinetic parameters were practically independent of β, as seen from the acceptably small standard deviations of the average kinetic parameters for those at different β shown in Table 3. Irrespective of the reaction step i, the optimized kinetic parameters do not have a large deviation from those determined for the mass-loss processes of thermal decom-

0.07 0.15 0.08 0.33

m

and

i=1

∑ cendo, iαendo, i + ∑ cexo, iαexo, i = α

10

A/s Ea/kJ mol c process sample

SB(m,n,p)

i=1

−1

(11)

where subscript i denotes the physico-geometrical reaction step. In eq 11, the following relationships must be fulfilled:

0.15 0.08 0.37 0.09

p

0.07 0.05 0.07 0.07

i=1

−1

Table 1. Average Kinetic Parameters Optimized through Kinetic Deconvolution of the Thermal Decomposition of SPC into the Endothermic and Exothermic Process Components (1 ≤ β ≤ 10 K min−1)


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Table 2. Previously Reported Kinetic Parameters of the Two Overlapping Mass-Loss Steps of the Thermal Decomposition of SPC Utilized as the Initial Values for the Kinetic Deconvolution into Each Endothermic and Exothermic Process13,14 JMA(m) sample

mass-loss step

crystalline particles

first second first second

granules

Ea/kJ mol−1

ci 0.69 0.31 0.52 0.48

± ± ± ±

0.02 0.02 0.04 0.04

97.3 98.6 114.3 113.9

± ± ± ±

0.2 0.1 0.6 0.5

m 1.93 6.55 1.95 5.26

± ± ± ±

ref 0.03 0.15 0.25 1.25

13 14

first reaction step and is apparently delayed from the beginning of the overall reaction. However, it is attenuated halfway through the first reaction step by the beginning of the second reaction step. The second overall exothermic effect starts to appear on the midway through the second reaction step and continues until the end of the second reaction step. Here, the maximum exothermic effect in the DSC is observed during the final stage of the second reaction step and the overall reaction. Therefore, the relationship of the reaction behavior of thermal decomposition and the experimentally resolved DSC curve is clearly seen from the modeling through kinetic deconvolution considering the physico-geometrical reaction steps and the successive endothermic and exothermic processes. In addition, the differences in the profiles of the DSC curves for the thermal decomposition of SPC crystalline particles and SPC granules are also explained by the results of the kinetic deconvolution. This study demonstrates that the overlapping multistep solidstate reactions involving endothermic and exothermic processes are successfully modeled through the kinetic deconvolutions combined with attention to overlapping multistep reaction behavior controlled by the physico-geometrical kinetics and chemical sequence of the endothermic and exothermic process components. Kinetic modeling results provide information concerning the relationship between the physico-geometrical reaction mechanism and the thermal effect through the overall reaction. This type of reaction is common in the oxidative decomposition of solids and the reaction of oxidizing solids. These reactions are widely used in material synthesis and as energy sources. Therefore, the kinetic modeling procedure presented based on the thermoanalytical measurement and kinetic deconvolution of experimental data is a possible method for obtaining detailed kinetic information for assessing the stability and reactivity of materials, evaluating effectiveness of energetic materials involved in safety assessment, and controlling material synthesis processes, etc.

Figure 6. Typical results of kinetic deconvolution of the thermal decomposition of SPC accounting for chemical and physico-geometrical constraints (β = 5 K min−1): (a) SPC crystalline particles and (b) SPC granules.

position. In addition, the differences in the optimized kinetic parameters between the endothermic and exothermic processes in each reaction step are also very minimal. However, the appearance of the exothermic effect during the reaction as resolved by the DSC signal is largely dependent on the physicogeometrically controlled multistep reaction behavior and chemical scheme of the successive endothermic and exothermic processes. In the initial reaction stage, the cancellation of the endothermic and exothermic effects caused by the slight delay of the exothermic process is deduced, which results in no detectable exothermic effect in the DSC curves of either the crystalline or granular samples. The delayed exothermic effect is also apparent from the evidence that the major exothermic effect is disproportionally represented in the latter half of the overall thermal decomposition. In the thermal decomposition of SPC crystalline particles (Figure 6a), the overall exothermic effect starts to appear halfway through the first reaction step and continues until the end of the reaction. The DSC exothermic peak was observed in the reaction stage empirically described by the overlapping of the first and second reaction steps. In comparison, the thermal decomposition of SPC granules (Figure 6b) has the characteristic of more separation between first and second reaction steps and a larger contribution from the second reaction step. The overall exothermic effect begins to appear in the earlier stage of the

4. CONCLUSIONS The thermal decomposition of SPC is kinetically characterized as successive endothermic and exothermic processes regulated by a physico-geometrical reaction mechanism. The physicogeometrical reaction mechanism of the two overlapping reaction steps, caused by the inhabitation effect of the surface product layer of Na2CO3 on the diffusional removal of the gaseous products produced by the internal reaction, has been revealed by the kinetic deconvolution analysis of the mass-loss data during thermal decomposition. The calorimetric data of the thermal decomposition resolved with DSC produce a profile different from the mass-loss data. This is because the overall exothermic effect appears as a result of the cancellation of the endothermic effect of the detachment process of H2O2(g) by the exothermic effect of the decomposition of H2O2(g). Thus, the calorimetric data were separated into the endothermic and exothermic processes through the kinetic 9767


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0.997 ± 0.003

0.992 ± 0.007

2.0 2.5 4.8 7.7 4.0 4.7 4.1 4.2 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 0.02 0.02 0.14 0.11 0.03 0.06 0.04 0.05 ± ± ± ± ± ± ± ± 1.01 1.01 1.05 1.05 0.96 1.05 1.00 1.03

n

■

AUTHOR INFORMATION

0.01 0.01 0.08 0.09 0.02 0.03 0.04 0.03

Notes

± ± ± ± ± ± ± ±

■ ■

The authors declare no competing financial interest.

0.00 0.00 0.04 0.04 0.01 0.02 0.03 0.03

m

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

0.40) 0.38) 1.29) 1.29) 0.28) 0.30) 0.16) 0.29)

× × × × × × × ×

10 1010 1010 1010 1012 1012 1012 1012

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

10

(2.63 (2.64 (6.15 (6.15 (2.83 (2.81 (2.79 (2.75 0.6 0.4 1.8 1.8 0.4 0.6 0.3 0.5 ± ± ± ± ± ± ± ± 96.9 97.0 97.6 97.7 114.0 113.9 113.4 113.3 granules

endo(1) exo(1) endo(2) exo(2) endo(1) exo(1) endo(2) exo(2) crystalline particles

−8.16 9.01 −3.53 3.68 −6.33 6.80 −5.78 6.31

± ± ± ± ± ± ± ±

0.30 0.51 0.30 0.53 0.25 0.29 0.25 0.26

Ea/kJ mol c process (step) sample

REFERENCES

(1) Tanaka, H.; Koga, N.; Galwey, A. K. Thermal Dehydration of Crystalline Hydrates: Microscopic Studies and Introductory Experiments to the Kinetics of Solid-State Reactions. J. Chem. Educ. 1995, 72, 251−256. (2) Galwey, A. K. Structure and Order in Thermal Dehydrations of Crystalline Solids. Thermochim. Acta 2000, 355, 181−238. (3) Koga, N.; Tanaka, H. A Physico-Geometric Approach to the Kinetics of Solid-State Reactions as Exemplified by the Thermal Dehydration and Decomposition of Inorganic Solids. Thermochim. Acta 2002, 388, 41−61. (4) Koga, N.; Goshi, Y.; Yoshikawa, M.; Tatsuoka, T. PhysicoGeometrical Kinetics of Solid-State Reactions in an Undergraduate Thermal Analysis Laboratory. J. Chem. Educ. 2014, 91, 239−245. (5) Pijolat, M.; Favergeon, L.; Soustelle, M. From the Drawbacks of the Arrhenius-f(α) Rate Equation towards a More General Formalism and New Models for the Kinetic Analysis of Solid−Gas Reactions. Thermochim. Acta 2011, 525, 93−102. (6) Tanaka, H.; Koga, N. Kinetics of the Thermal Dehydration of Potassium Copper(II) Chloride Dihydrate. J. Phys. Chem. 1988, 92, 7023−7029. (7) Koga, N.; Tanaka, H. Kinetic and Morphological-Studies of the Thermal Dehydration of Alpha-Nickel(II) Sulfate Hexahydrate. J. Phys. Chem. 1994, 98, 10521−10528. (8) Koga, N.; Suzuki, Y.; Tatsuoka, T. Thermal Dehydration of Magnesium Acetate Tetrahydrate: Formation and in Situ Crystallization of Anhydrous Glass. J. Phys. Chem. B 2012, 116, 14477− 14486. (9) Koga, N.; Yamada, S.; Kimura, T. Thermal Decomposition of Silver Carbonate: Phenomenology and Physicogeometrical Kinetics. J. Phys. Chem. C 2013, 117, 326−336. (10) Yoshikawa, M.; Yamada, S.; Koga, N. Phenomenological Interpretation of the Multistep Thermal Decomposition of Silver

± ± ± ± ± ± ± ±

A/s

−1

SB(m,n,p)

0.48 0.48 0.83 0.82 0.49 0.48 0.81 0.81

p

0.01 0.01 0.05 0.05 0.01 0.01 0.02 0.01

−100.7 111.1 −43.7 45.6 −78.0 83.8 −71.3 77.7

R2 Q/kJ (mol SPC)−1

deconvolution analysis. The results indicate that the overall profile of exothermic effect recorded by DSC was the result of a slight delay in the exothermic process from the endothermic process. Furthermore, the calorimetric data were separated into each of the two endothermic and exothermic processes by considering the physico-geometrical reaction mechanism of the two overlapping reaction steps. Kinetic modeling through kinetic deconvolution analysis by considering the physicogeometrical reaction mechanism and the chemical sequence of the endothermic and exothermic process components provided detailed kinetic information. This information concerning the relationship between the physico-geometrical reaction mechanism and the resulting exothermic effect from the overall reaction explains the differences in the DSC profiles of the thermal decomposition of SPC crystalline particles and SPC granules. Kinetic modeling demonstrated for the thermal decomposition of SPC is applicable to many multistep solidstate reactions that involve both endothermic and exothermic processes as the component reactions. These include the oxidative decomposition of solids and the thermal decomposition of oxidizing solids.

Corresponding Author

−1

Table 3. Average Kinetic Parameters Optimized by Kinetic Deconvolution of the Thermal Decomposition of SPC into Each Endothermic and Exothermic Process by Considering Chemical and Physico-geometrical Constraints (1 ≤ β ≤ 10 K min−1)


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The Journal of Physical Chemistry A Carbonate to Form Silver Metal. J. Phys. Chem. C 2014, 118, 8059− 8070. (11) Koga, N.; Sato, Y. Formation and Transformation Kinetics of Amorphous Iron(III) Oxide During the Thermally Induced Transformation of Ferrous Oxalate Dihydrate in Air. J. Phys. Chem. A 2011, 115, 141−151. (12) Kitabayashi, S.; Koga, N. Physico-Geometrical Mechanism and Overall Kinetics of Thermally Induced Oxidative Decomposition of Tin(II) Oxalate in Air: Formation Process of Microstructural Tin(IV) Oxide. J. Phys. Chem. C 2014, 118, 17847−17861. (13) Wada, T.; Koga, N. Kinetics and Mechanism of the Thermal Decomposition of Sodium Percarbonate: Role of the Surface Product Layer. J. Phys. Chem. A 2013, 117, 1880−1889. (14) Wada, T.; Nakano, M.; Koga, N., Multistep Kinetic Behavior of the Thermal Decomposition of Granular Sodium Percarbonate: Hindrance Effect of the Outer Surface Layer. J. Phys. Chem. A 2015, DOI: 10.1021/acs.jpca.5b07042. (15) Noda, Y.; Koga, N. Phenomenological Kinetics of the Carbonation Reaction of Lithium Hydroxide Monohydrate: Role of Surface Product Layer and Possible Existence of a Liquid Phase. J. Phys. Chem. C 2014, 118, 5424−5436. (16) Nagaishi, T.; Kaneda, T.; Kotsubo, A.; Matsumoto, M.; Yoshinaga, S. Thermal Decomposition of the Addition Compound of Sodium Carbonate with Hydrogen Peroxide (Na2CO3·1.5H2O2). Kogyo Kayaku 1976, 37, 84−90. (17) Galwey, A. K.; Hood, W. J. Thermal Decomposition of Sodium Carbonate Perhydrate in the Solid State. J. Phys. Chem. 1979, 83, 1810−1815. (18) Galwey, A. K.; Hood, W. J. Thermal Decomposition of Sodium Carbonate Perhydrate in the Presence of Liquid Water. J. Chem. Soc., Faraday Trans. 1 1982, 78, 2815−2827. (19) Lunghi, A.; Cattaneo, M.; Cardillo, P. Thermal Stability of Sodium Percarbonate: Kinetic Data. Riv. Combust. 1996, 50, 229−234. (20) Qin, F.-y.; Gu, D. Thermal Decomposition Reaction Kinetics of Sodium Percarbonate. Huadong Ligong Daxue Xuebao 2001, 27, 214− 216. (21) Zhao, H.-k.; Wang, H.-x.; Du, M.-j. Research on Thermal Decomposition Kinetics of Sodium Percarbonate. Shangqiu Shifan Xueyuan Xuebao 2002, 18 (79−81), 85. (22) Wang, H.-x.; Zhao, H.-k.; Du, M.-j.; Bai, Y.-j. Research on Thermal Decomposition Kinetics of Sodium Percarbonate. Shangqiu Shifan Xueyuan Xuebao 2003, 19, 94−97. (23) Wang, H.-x.; Zhao, H.-k. Theoretical Analysis of the Thermal Decomposition Kinetics of Sodium Percarbonate and Its Experimental Verification. Nantong Daxue Xuebao, Ziran Kexueban 2006, 5, 43−46. (24) Gigante, L.; Dellavedova, M.; Pasturenzi, C.; Lunghi, A.; Mattarella, M.; Cardillo, P. Study of the Decomposition Mechanism of Sodium Carbonate Perhydrate by Thermal Analysis. Riv. Combust. Ind. Chim. 2008, 62, 279−284. (25) Wada, T.; Koga, N. Chemical Composition of Sodium Percarbonate: An Inquiry-Based Laboratory Exercise. J. Chem. Educ. 2013, 90, 1048−1052. (26) Pritchard, R. G.; Islam, E. Sodium Percarbonate between 293 and 100 K. Acta Crystallogr., Sect. B: Struct. Sci. 2003, 59, 596−605. (27) Tatsuoka, T.; Koga, N. Energy Diagram for the Catalytic Decomposition of Hydrogen Peroxide. J. Chem. Educ. 2013, 90, 633− 636. (28) Haynes, W. M., Ed. CRC Handbook of Chemistry and Physics, 95th ed.; CRC Press: Boca Raton, FL, USA, 2014. (29) Málek, J. A Computer Program for Kinetic Analysis of NonIsothermal Thermoanalytical Data. Thermochim. Acta 1989, 138, 337− 346. (30) Málek, J. The Kinetic Analysis of Non-Isothermal Data. Thermochim. Acta 1992, 200, 257−269. (31) Málek, J. Kinetic Analysis of Crystallization Processes in Amorphous Materials. Thermochim. Acta 2000, 355, 239−253. (32) Sánchez-Jiménez, P. E.; Perejón, A.; Criado, J. M.; Diánez, M. J.; Pérez-Maqueda, L. A. Kinetic Model for Thermal Dehydrochlorination of Poly(Vinyl Chloride). Polymer 2010, 51, 3998−4007.

(33) Koga, N.; Goshi, Y.; Yamada, S.; Pérez-Maqueda, L. A. Kinetic Approach to Partially Overlapped Thermal Decomposition Processes. J. Therm. Anal. Calorim. 2013, 111, 1463−1474. (34) Kissinger, H. E. Reaction Kinetics in Differential Thermal Analysis. Anal. Chem. 1957, 29, 1702−1706. (35) Šesták, J.; Berggren, G. Study of the Kinetics of the Mechanism of Solid-State Reactions at Increasing Temperatures. Thermochim. Acta 1971, 3, 1−12. (36) Šesták, J. Diagnostic Limits of Phenomenological Kinetic Models Introducing the Accommodation Function. J. Therm. Anal. 1990, 36, 1997−2007. (37) Šesták, J. Rationale and Fallacy of Thermoanalytical Kinetic Patterns. J. Therm. Anal. Calorim. 2012, 110, 5−16. (38) Málek, J.; Criado, J. M. Empirical Kinetic Models in Thermal Analysis. Thermochim. Acta 1992, 203, 25−30. (39) Pérez-Maqueda, L. A.; Criado, J. M.; Sánchez-Jiménez, P. E. Combined Kinetic Analysis of Solid-State Reactions: A Powerful Tool for the Simultaneous Determination of Kinetic Parameters and the Kinetic Model without Previous Assumptions on the Reaction Mechanism. J. Phys. Chem. A 2006, 110, 12456−12462. (40) Koga, N.; Mako, A.; Kimizu, T.; Tanaka, Y. Thermal Decomposition of Synthetic Antlerite Prepared by Microwave-Assisted Hydrothermal Method. Thermochim. Acta 2008, 467, 11−19. (41) Avrami, M. Kinetics of Phase Change. I. General Theory. J. Chem. Phys. 1939, 7, 1103−1112. (42) Avrami, M. Kinetics of Phase Change. II. Transformation-Time Relations for Random Distribution of Nuclei. J. Chem. Phys. 1940, 8, 212−223. (43) Avrami, M. Kinetics of Phase Change. III. Granulation, Phase Change, and Microstructure. J. Chem. Phys. 1941, 9, 177−184. (44) Barmak, K. A Commentary On: “Reaction Kinetics in Processes of Nucleation and Growth. Metall. Mater. Trans. A 2010, 41, 2711− 2775.

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Exothermic Behavior of Thermal Decomposition of Sodium Percarbonate

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