Kinetics and Mechanism of the Thermal Decomposition of Sodium

Article pubs.acs.org/JPCA

Kinetics and Mechanism of the Thermal Decomposition of Sodium Percarbonate: Role of the Surface Product Layer 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 S Supporting Information *

ABSTRACT: The reaction mechanism and overall kinetics of the thermal decomposition of sodium percarbonate crystals were investigated by thermoanalytical measurements and morphological observations. The reaction proceeds via a surface reaction and subsequent advancement of the asproduced reaction interface toward the center of the crystals, where the seemingly smooth mass-loss behavior can be described by the apparent activation energy Ea of ca. 100 kJ mol−1. However, considering the rate behavior, as the reaction advances, it is expected that the secondary reaction step characterized by an autocatalytic rate behavior takes part in the overall reaction. The hindrance of the diffusional removal of the evolved gases by the surface product layer, Na2CO3, is the most probable reason for the change in the reaction mechanism. In the deceleration part of the first reaction step, the second reaction step is accelerated due to an increase in the water vapor pressure at the reaction interface inside the reacting particles. We also expect the self-generated reaction condition of the high water vapor pressure and the existence of liquid phase due to the formation of Na2CO3 whiskers as the solid product and the insensitive rate behavior of the second reaction step to a higher atmospheric water vapor pressure. A relevant reaction model for the thermal decomposition of SPC crystals are discussed by focusing on the role of the surface product layer.

1. INTRODUCTION Sodium percarbonate (SPC), with the formula Na2CO3·1.5H2O2, is the adduct of hydrogen peroxide and sodium carbonate1 and is a major component of oxygen bleach utilized industrially and domestically.2 Granular SPC is utilized in conventional oxygen bleach,3 in which the surface layer of the granule such as Na2CO3 has an important role, i.e., to protect the internal SPC crystals from decomposition by the effects of atmospheric water vapor. SPC crystals are elongated columnar shapes with the crystallographic structure of an orthorhombic system (S.G.: Cmca, a = 6.7138 Å, b = 15.7407 Å, c = 9.1732 Å).4 In many thermal decomposition reactions of solids, the reaction initiates at the surface, producing a surface product layer, which sometimes influences the kinetic behavior of the subsequent thermal decomposition.5−11 Na2CO3 as the surface solid product layer is formed by the thermal decomposition of SPC crystals. Similar to the surface Na2CO3 layer of granular SPC, the surface product layer of Na2CO3 formed during decomposition of SPC crystals would be expected to afford significant interactions with atmospheric water vapor and the water vapor produced by the internal reaction. Accordingly, the thermal decomposition of SPC crystals is one of the most suitable reactions for investigating the role of the surface product layer on the overall kinetics of the thermal decomposition of solids. The elucidation of the mechanism and kinetics of thermal decomposition would also contribute to the evaluation of the thermal stability and oxygengeneration behavior of this compound.12−17 In addition, Na2CO3 © 2013 American Chemical Society

is studied as a potential capture medium for CO2 separation technologies.18,19 The surface product layer, formed during the thermal decomposition of SPC crystals, is rich with water vapor and free from CO2; thus, it comprises potential reaction sites for CO 2 absorption. The kinetic approach to the thermal decomposition of SPC crystals is also expected to provide some fundamental information for such technological applications, together with information of the daily use chemical in relation to chemical safety as an oxidative solid and an oxygen generator. The mechanism and kinetics of the thermal decomposition of SPC crystals have been reported by Nagaishi et al.20 and Galwey and Hood.21,22 Nagaishi et al.20 explained the occurrence of the thermal decomposition of SPC crystals via two reaction steps, which include the detachment of H2O2 and its subsequent decomposition. The kinetic behaviors of the three distinct stages of the reaction, i.e., the initial, established, and final stages, were separately analyzed, leading to different kinetic descriptions. Galwey and Hood21 interpreted sigmoidal mass−loss curves for the thermal decomposition of SPC crystals under vacuum from the standpoint of a physico-geometrical mechanism. They suggested complex consecutive and/or concurrent processes for the surface reaction and subsequent advancement of the asReceived: December 16, 2012 Revised: February 10, 2013 Published: February 12, 2013 1880

dx.doi.org/10.1021/jp3123924 | J. Phys. Chem. A 2013, 117, 1880−1889

The Journal of Physical Chemistry A

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Shimadzu Co.) under different heating conditions in flowing N2 (80 cm3 min−1). The partially decomposed samples were immediately cooled to room temperature and observed by SEM. 2.4. Measurement of Kinetic Rate Data. The kinetic rate data for the thermal decomposition of the sample (5.00 ± 0.05 mg weighed in a 6 mmϕ × 2.5 mm platinum cell) were collected by a hanging-type TG (TGA-50M, Shimadzu Co.) in flowing N2 (80 cm3 min−1). Sampling was carefully executed without pressing the needle-like crystals. Three different modes of temperature programs, isothermal, linear nonisothermal, and controlled transformation rate thermal analysis (CRTA)25,26 modes, were applied for recording the mass-loss data of thermal decomposition. The isothermal mass-loss data were recorded at different temperatures, 368 ≤ T ≤ 393 K, after heating the sample to the programmed temperature at β = 10 K min−1. For linear nonisothermal measurement, the samples were heated at different β (1 ≤ β ≤ 10 K min−1). CRTA measurements, a technique of sample controlled thermal analysis (SCTA),26 were performed by attaching the homemade controller to the TG instrument. The sample was heated at β = 2 K min−1, while the mass-loss rate C was regulated at different constant values (5.0 ≤ C ≤ 20.0 μg min−1) during the mass-loss process. 2.5. Influence of Atmospheric Water Vapor. The influence of atmospheric water vapor on the reaction behavior was monitored by TG-DTA measurements under a controlled water vapor pressure p(H2O). Keeping the sample (5.00 ± 0.05 mg weighed in a 5 mmϕ × 2.5 mm platinum cell) at 333 K in the TG-DTA instruments (TG8120, Rigaku Co.), mixed N2−H2O gases with a controlled p(H2O) were introduced into the reaction tube at an approximate rate of 400 cm3 min−1. After stabilizing the reaction system for 30 min, the sample was heated at β = 5 K min−1 under different p(H2O) levels (0.8 ≤ p(H2O) ≤ 10.0 kPa). Under the selected p(H2O) levels, 0.8, 4.1, and 10.0 kPa, the TG-DTA curves were recorded at different β (0.5 ≤ β ≤ 5 K min−1).

produced reaction interface, where the internal reaction is accelerated by the self-generated water vapor. They also considered a possible inhabitation effect of the surface product layer on the diffusional removal of the product gases. These studies demonstrate the different mechanistic interpretations and kinetic behaviors of the reaction. The present study demonstrates the mechanism and kinetics of the thermal decomposition of freshly prepared SPC crystals by focusing on the role of the surface product layer. The reaction was traced by thermoanalytical measurements under systematically adjusted heating and atmospheric water vapor conditions. On the basis of kinetic analyses of the thermoanalytical curves and interpretation of the kinetic results complemented by morphological and structural observations, we propose a relevant reaction model for the thermal decomposition of SPC crystals.

2. EXPEIRMENTAL SECTION 2.1. Sample Preparation. SPC crystals were synthesized according to previous reports.4,20−24 All chemicals used for sample preparation were reagent grade and purchased from Nacalai Tesque (Japan). A saturated aqueous solution of Na2CO3 was prepared by adding an excess amount of Na2CO3 to distilled water, stirring for 24 h at ambient temperature, and filtering the final mixture. The saturated Na2CO3 (aq) solution (20 cm3) was mixed at once with H2O2 (∼15% aq, 20 cm3), and the resulting mixture was left standing at room temperature for 5 min. Absolute ethanol (approximately 100 cm3) was then added to the precipitated mixture, and the diluted mixture was stirred mechanically. The precipitates were isolated by suction filtration and washed several times using absolute ethanol. The isolated precipitates were dried in a vacuum desiccator for 24 h. 2.2. Characterization of the Sample. The powder X-ray diffraction (XRD) pattern of the sample was recorded using a diffractometer (RINT 2200 V, Rigaku Co.) with Cu-Kα radiation (40 kV, 20 mA). A Fourier transform infrared (FT-IR) spectrum was recorded by a diffuse reflectance method using a spectrometer (FT-IR 8400S, Shimadzu Co.) after diluting the sample with KBr powder. The morphology of the sample particles was observed by scanning electron microscopy (SEM; JSM-6510, Jeol) after coating the sample with Pt by sputtering (20 mA, 60 s). 2.3. Characterization of Thermal Decomposition. Thermal decomposition of the sample was recorded by simultaneous measurements of thermogravimetry-differential thermal analysis (TG-DTA; TG8120, Rigaku Co.). The evolved gases during thermal decomposition were analyzed using a quadrupole mass-spectrometer (MS; M-200Q, Anelva Co.), which was connected to the TG-DTA instruments using a silica capillary tube (0.075 mm internal diameter) heated at 500 K. The sample (5.0 mg weighed in a 5 mmϕ × 2.5 mm platinum cell) was heated at a heating rate β = 5 K min−1 in flowing He (200 cm3 min−1) for recording TG-DTA curves, where the mass spectra of the evolved gases were monitored continuously in the range 10− 50 amu (EMSN: 1.0 A; SEM: 1.0 kV). Changes in the crystalline phase of the sample, press-fitted on a platinum plate without grinding, were traced by repeated measurements of XRD patterns during isothermal heating at 373 K in flowing N2 (100 cm3 min−1) using the above XRD instrument, which was equipped with a programmable heating chamber (PTC020, Rigaku Co.). The diffraction measurements were initiated every 15 min after heating the sample to 373 K at β = 10 K min−1. The sample (m0 = 5.0 mg) was partially decomposed to different fractional reaction α in a TG-DTA instruments (DTG-50M,

3. RESULTS AND DISCUSSION 3.1. Sample Characterization. Figure 1a shows typical SEM images of the sample particles. The crystals are columnar with an axis length of ca. 20−30 μm. The XRD pattern of the sample corresponded to the simulated pattern of Na2CO3·1.5H2O2 (orthorhombic, S.G.: Cmca, a = 6.7138 Å, b = 15.7407 Å, c = 9.1732 Å).4 All IR absorption peaks reported for SPC24 were confirmed in the FT-IR spectrum of the sample. The XRD pattern and FT-IR spectrum of the sample are shown in Figures S1 and S2, respectively, in the Supporting Information (SI). Figure 2 shows the TG-DTG-DTA curves for the thermal decomposition of SPC crystals. Superficially, the reaction, initiated at approximately 375 K, proceeds in a single mass-loss process accompanied by an exothermic DTA peak. The total mass loss during the course of the reaction, 32.32 ± 0.33%, is in good agreement with the calculated value, 32.48%, derived assuming the following reaction: Na 2CO3 ·1.5H 2O2 (s) → Na 2CO3(s) + 1.5H 2O(g) + 0.75O2 (g)

(1)

3.2. Thermal Decomposition Process. The DTG curve in Figure 2 indicates continuous acceleration of the mass-loss rate until the mass-loss reaches approximately 25.7% (α = 0.80), but a shoulder is observed at a mass loss of approximately 12.3% (α = 0.38). Similar behavior is observed in the DTA exothermic peak, although the shoulder and maximum peak shift slightly to a 1881



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Nagaishi et al20 reported a two-step reaction consisting of the dissociation of H2O2 (g) from SPC and the decomposition of H2O2 (g) into H2O (g) and O2 (g). Na 2CO3 ·1.5H 2O2 (s) → Na 2CO3(s) + 1.5H 2O2 (g)

(2)

2H 2O2 (g) → 2H 2O(g) + O2 (g)

(3)

In this study, evolution of only H2O and O2 were detected in the MS spectra of the evolved gases, possibly indicating immediate decomposition of gaseous H2O2. Figure 2 also shows the mass chromatograms of m/z 18 (H2O+) and m/z 32 (O2+) during the thermal decomposition of the SPC crystals. The mass-chromatogram peaks have a shape similar to the DTG and DTA, having a shoulder preceding the maximum peak. Figure 3 shows the changes in the XRD pattern of the sample during isothermal heating at 373 K in flowing N2, Figure 3a, and

Figure 1. Changes in the texture of SPC crystals during thermal decomposition in flowing N2 (80 cm3 min−1): (a) reactant crystals; (b) α = 0.03 (isothermal, T = 378 K, 5 min); (c) α = 0.28 (isothermal, T = 378 K, 15 min); (d) cleaved surface of (c); (e) α = 0.78 (nonisothermal, β = 5.0 K min−1, 413 K); and (f) α = 1.00 (isothermal, T = 378 K, 100 min).

Figure 3. (a) Changes in the powder XRD pattern during isothermal heating at 373 K and (b) XRD pattern after heating at 373 K for 270 min.

the XRD pattern after heating for 270 min, Figure 3b. The diffraction peaks attributed to the SPC crystals gradually attenuate accompanied by the growth of those attributed to the product Na2CO3, and no additional diffraction peak due to a possible intermediate crystalline phase is detected. In Figures 1b−f, changes in the SEM images of the sample crystals during thermal decomposition are shown. The reaction initiates on the surface of the particle by nucleation and growth of the solid product, Figure 1b (α = 0.03). The surface becomes covered by the product layer as the reaction advances, Figure 1c (α = 0.28). The cleaved surface of the partially decomposed sample (α = 0.28) exemplifies the surface product layer which covers the internal reactant crystal, Figure 1d. Accordingly, the surface reaction is completed in the early stages of the reaction, and the subsequent reaction proceeds by the advancement of the reaction interface toward the center of the crystal, similar to a shrinking core model.27,28 In the established reaction, the product gases that evolve at the reaction interface must be removed by diffusion through the surface product layer. If the diffusional removal of the evolved gases at the reaction interface

Figure 2. Typical TG-DTG-DTA curves and mass chromatograms of m/z 18 and 32 for the evolved gas during the thermal decomposition of SPC crystals (m0 = 5.03 mg) at β = 5 K min−1 in flowing He (200 cm3 min−1). Arrows indicate shoulders.

higher temperature. The findings in the DTG and DTA curves indicate possible contribution of a physico-geometrical event to impede the mass-loss process and accelerate the reaction after a brief arrest. 1882



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until nearly the reaction end. Figure 5 shows a typical record of the mass-loss data under a controlled constant mass-loss rate of C

is impeded by the surface product layer, the reaction is decelerated due to the chemical equilibrium established at the reaction interface, as observed in many thermal decompositions of solids.5,6,10 Such hindrance afforded by the surface product layer can be a possible cause of the shoulder observed in the DTG and DTA curves and mass chromatograms of the evolved gases, Figure 2. The product platelet crystals that formed on the particle surface and/or in the surface product layer gradually grow as the reaction advances, Figure 1e (α = 0.78). As a result, pores develop in the surface product layer, which potentially become diffusion channels for the evolved gases during the established reaction. Especially for the reaction under nonisothermal conditions, whiskers radiate from the pores at the reaction stage. Rapid escape of a liquid through the pores followed by the immediate evaporation of water are postulated as a probable mechanism for whisker formations.8 In this case, the whisker formation is a positive evidence of the existence of a liquid phase and a high water vapor pressure at the reaction interface. Under such condition, the destruction of the reactant crystal structure and the decomposition of H2O2 are accelerated.22 The maxima of DTG, DTA, and MS peaks, observed at α ≈ 0.80, probably appear as the reaction is accelerated by water vapor or liquid phase. The final solid product is the agglomerate of Na2CO3 platelet crystals, Figure 1f (α = 1.00). 3.3. Overall Kinetics of Thermal Decomposition. Figure 4 shows the mass-loss traces at different constant temperatures, Figure 4a, and under linear nonisothermal heating conditions at different β, Figure 4b, for the thermal decomposition of SPC crystals in flowing N2 and the corresponding time derivative curves. The major portion of the isothermal mass-loss process indicates linear mass-loss behavior. Under linearly increasing temperatures, the mass-loss process continuously accelerates

Figure 5. Typical results of mass-loss measurements under a controlled mass-loss rate C for the thermal decomposition of SPC crystals (m0 = 5.0 mg) in flowing N2 (80 cm3 min−1): (a) typical record at C = 10.0 μg min−1 and (b) reaction temperature profiles at different C.

= 10.0 μg min−1, Figure 5a, and the temperature profiles of the reaction at different C values, Figure 5b. The mass-loss rate is successfully regulated to maintain a constant rate. The temperature profile during the reaction is concaved and shifts systematically to higher temperatures with increasing C. The nearly constant temperature observed for the main portion of the reaction under a constant mass-loss rate corresponds to the constant mass-loss rate under a constant temperature observed in the isothermal mass-loss traces, Figure 4a. To evaluate the overall kinetics of the thermal decomposition of SPC crystals, we assumed the following derivative kinetic equation for a single-step reaction, that is, for the reaction regulated by a specific rate-limiting step in a physico-geometrical mechanism with constant apparent Arrhenius parameters during the reaction.29 ⎛ E ⎞ dα = A exp⎜ − a ⎟f (α) ⎝ RT ⎠ dt

(4)

where A, Ea, and f(α) are the Arrhenius pre-exponential factor, apparent activation energy, and kinetic model function, respectively. All kinetic rate data converted from the mass-loss data under different temperature program modes, isothermal, linear nonisothermal, and CRTA modes, were analyzed simultaneously based on eq 4.8,9 The results from the kinetic calculation are illustrated in Figure 6. A relationship between dα/dt and T at a restricted α is derived by taking the logarithm of eq 4.30

Figure 4. Typical mass-loss traces and their time-derivative curves for the thermal decomposition of SPC crystals (m0 = 5.0 mg) in flowing N2 (80 cm3 min−1) (a) under isothermal heating at different T and (b) under linearly increasing temperature at different β. 1883



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temperature, were calculated by extrapolating the rate data at fixed α to infinite temperature according to31−34 ⎛E ⎞ dα dα = exp⎜ a ⎟ ⎝ RT ⎠ dθ dt

with

θ=

∫0

t

⎛ E ⎞ exp⎜ − a ⎟ dt ⎝ RT ⎠ (6)

where θ is Ozawa’s generalized time. Based on the shape of the experimental master plot, the hypothetical reaction rate at infinite temperature increases continuously until α ≈ 0.3 and remains nearly constant over the main portion of the reaction, 0.3 ≤ α ≤ 0.8, followed by deceleration till the reaction end. In comparison with the morphological change of the sample shown in Figure 1, it is clearly seen that arrest of the acceleration behavior observed at α ≈ 0.3 corresponds to the reaction stage in which the surface reaction is completed and the surface product layer is formed, Figure 1c,d. Ideally for a well-defined single step reaction, the experimental master plot is correlated to the kinetic model function and the pre-exponential factor as31−34,37 35,36

dα = Af (α) dθ

Because the trapezoidal shape of the experimental master plot cannot be fitted by any conventional kinetic model functions derived for a solid-state reactions, an empirical kinetic model function known as the Sestak−Berggren model,38 SB(m, n, p), f(α) = αm(1 − α)n[−ln(1 − α)]p, which fits to various physicogeometric reactions and the deviated cases,29,39,40 was applied to fit the experimental master plot. The most appropriate kinetic exponents in the kinetic model functions and the A value were estimated simultaneously by a nonlinear regression analysis by applying the Levenberg−Marquardt optimization algorithm.41 The apparent best fit was obtained with SB (0.95 ± 0.34, 0.12 ± 0.12, −0.56 ± 0.32) and A = (4.7 ± 0.2) × 1010 s−1 having the attribution R2 = 0.9562. For isothermal decomposition under vacuum, Galwey and Hood confirmed an apparent kinetic fit to a nucleation and growth type model known as the Johnson-MehlAvrami equation,42−45 JMA(m): f(α) = m(1 − α)[−ln(1 − α)]1−1/m, in the range 0.05 ≤ α ≤ 0.70.21 To compensate for the discrepancy in the final stage of the reaction, they proposed the following empirical equation in integral form by combining the contracting area equation and an appropriate form of Fick’s law applied to allow for the increasing difficulty of the removal of the active catalyst, i.e., water molecules.21

Figure 6. Kinetic results for the thermal decomposition of SPC crystals under isothermal, nonisothermal, and controlled rate conditions in flowing N2 (80 cm3 min−1): (a) Friedman plots at different α from 0.1 to 0.9 in steps of 0.1, (b) Ea values at different α, and (c) the experimental master plot and curves fitted by SB(m, n, p) and Galwey-Hood(n) models.

E ⎛ dα ⎞ ln⎜ ⎟ = ln[Af (α)] − a ⎝ dt ⎠ RT

(7)

g (α ) =

(5)

When the overall kinetic behavior is fully satisfied by eq 4, the plot of ln(dα/dt) vs T−1 for the data points at a restricted α, i.e., Freidman plot,30 forms a straight line, regardless of the temperature program modes applied to measure the kinetic rate data. The plots of ln(dα/dt) vs T−1 at different α in the range 0.1 ≤ α ≤ 0.9 in steps of 0.1 are shown in Figure 6a. At the selected α, all data points recorded under different temperature program modes form a straight line. The slopes of the Friedman plot at different α are approximately constant, indicating a constant Ea value over a wide range of α, Figure 6b. The averaged Ea value over 0.05 ≤ α ≤ 0.95 was 103.0 ± 0.7 kJ mol−1, which is slightly smaller than those reported previously, approximately 110−115 kJ mol−1.20,21 The α-dependence of the rate behavior was evaluated by drawing an experimental master plot of dα/dθ vs α, Figure 6c. The dα/dθ values, a hypothetical reaction rate at infinite

∫0

α

dα = [1 − (1 − α)1/2 ]1/2 f (α )

(8)

The differential form of eq 8 with a nonintegral or fractal dimension of contracting geometry n can be derived as f (α) = 2n(1 − α)1 − 1/ n [1 − (1 − α)1/ n ]1/2

(9)

The apparent best fit of eq 9 to the experimental master plot in Figure 6c is obtained using n = 2.30 ± 0.08 and A = (1.76 ± 0.02) × 1010 s−1 with R2 = 0.8106. The Galwey-Hood model abstractly describes the overall rate behavior, but the fit is apparently inferior to that of SB(0.95, 0.12, −0.56) and arrest of acceleration observed at α ≈ 0.3 and the subsequent constant rate process over 0.3 ≤ α ≤ 0.8 cannot be described appropriately. The discrepancy indicates that the deceleration of the surface induced reaction of contracting geometry type and the acceleration of the internal reaction afforded by the increase in the water vapor pressure are not necessarily continuous phenomena. 1884



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3.4. Deconvolution of Thermal Decomposition. As a possible model for describing the trapezoidal shape of the experimental master plot shown in Figure 6c, we propose an overlapping two-step reaction which consists of the surface induced reaction of contracting geometry type and the internal reaction which occurs at the reaction interface inside the reactant particles under the self-generated condition of high water vapor pressure. This is based on the morphological changes of the reactant particles during the reaction, Figure 1. This assumption is also supported by experimental evidence, i.e., the appearance of shoulders in DTG, DTA, and MS curves observed in Figure 2. As described in the next section, the shoulders become more apparent with increasing atmospheric water vapor. In addition, the thermal decomposition of granular SPC used in industry and at home indicates the two-step reaction more clearly. Under the assumption of the overlapping two-step reaction, the kinetic rate data recorded under linearly increasing temperatures were deconvoluted by assuming the following kinetic equation for the overall mass-loss process:46−49 dα = dt

N

⎛ Ea, i ⎞ ⎟f ( α ) ⎝ RT ⎠ i i

∑ ciAi exp⎜− i=1

N

with

∑ ci = 1

and

i=1

N

∑ ciαi = α i=1

Figure 7. Typical results of kinetic deconvolution for the thermal decomposition of SPC crystals in flowing N2 (80 cm3 min−1) under different heating modes; (a) nonisothermal at β = 5 K min−1, (b) isothermal at T = 378 K, and (c) controlled mass-loss rate at C = 5.0 μg min−1.

(10)

where the overall reaction rate, dα/dt, is expressed by the summation of the reaction rates of the different reaction steps, i, with the fractional mass loss of the different reaction steps, ci. The values of ci, Ai, and Ea,i and the kinetic exponent in f i(αi) are the parameters to be optimized. These parameters are simultaneously optimized by a nonlinear least-squares analysis for minimizing the square sum of the residue when fitting the calculated curve (dα/dt)cal vs time to the experimental curve (dα/dt)exp vs time.46−49 2 ⎡⎛ ⎞ ⎛ dα ⎞ ⎤ α d −⎜ ⎟ ⎥ F = ∑ ⎢⎜ ⎟ ⎢⎝ dt ⎠exp , j ⎝ dt ⎠cal, j ⎥⎦ j=1 ⎣

deconvoluted into two overlapping reaction steps with R2 values from the nonlinear least-squares analysis better than 0.99. The deconvoluted curves indicate that the first reaction step contributes for entire reaction, and the second reaction step overlaps to the deceleration part of the first reaction step. Table 1 lists the average values of the optimized parameters for the thermal decomposition of the SPC crystals at different β. According to the acceptable standard errors of the respective average values among different β, the optimized parameters are independent of β. The optimized values of c1 and c2 are practically identical to those estimated by the conventional mathematical deconvolution. The optimized values of the apparent Ea for different reaction steps are comparable and nearly correspond to that estimated for the overall reaction in Figure 6b. The kinetic results for the first and second reaction steps differ in the values of A and m in JMA(m). A smaller A value for the second reaction step corresponds to a higher reaction temperature of the second reaction step than that of the first reaction step. The kinetic model functions estimated for the first and second reaction steps are graphically compared in Figure 8. The kinetic model function JMA(1.93) estimated for the first reaction step is ideally interpreted as a nucleation and growth controlled process, where several interpretations regarding the contributions of nucleation and growth dimension are possible. However, it is difficult to correlate the JMA(6.55) function estimated for the second reaction step to the theoretical model of the nucleation and growth process. The maximum reaction rate of the second reaction step appears at the second-half of the mass-loss process, indicating autocatalytic behavior with a long acceleration period. Figure 8 shows the curve fitted by the autocatalytic kinetic equation, known as the Prout-Tompkins equation,53,54 which corresponds to SB(1, 1, 0). In comparison with the ProutTompkins model, the experimental master plot for the second

M

(11)

To estimate the default values for parameter optimization based on eqs 10 and 11, we performed a conventional mathematical deconvolution of the kinetic rate data under linearly increasing temperatures using the Weibull function.49−52 The results from mathematical deconvolution and subsequent formal kinetic analyses for the deconvoluted kinetic rate data are described in the SI. By mathematical deconvolution, the values of c1 and c2were estimated, 0.70 ± 0.04 and 0.30 ± 0.04, respectively, as shown in Figures S3 and S4. The apparent Ea values evaluated for the deconvoluted rate data were practically identical between the different reaction steps indicating Ea ≈ 100 kJ mol−1, Figure S5, which corresponds to a constant Ea value, 103.0 ± 0.7 kJ mol−1, evaluated for the overall reaction by assuming a single-step reaction, see Figure 6b. The experimental master plots drawn for the deconvoluted kinetic rate data were apparently fitted by JMA(m), Figure S6. Kinetic deconvolution of the rate data based on eq 10 was performed by setting the default values of ci and Ea,i, estimated by the above mathematical deconvolution, and mi = 3 in JMA(m). The order of the default Ai values was estimated graphically by comparing the experimental and calculated curves of the kinetic rate data. Figure 7a shows a typical result of kinetic deconvolution for the nonisothermal decomposition at β = 5 K min −1 . The rate data at different β were successfully 1885



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Table 1. Average Values of the Mass-Loss Fraction c and Apparent Kinetic Parameters of Different Reaction Steps Evaluated for the Thermal Decomposition of SPC Crystals under Dry N2 (80 cm3 min−1) Optimized by Kinetic Deconvolution measurement

reaction step

R2

c

Ea/kJ mol−1

A/109 s−1

m in JMA(m)

nonisothermal

1st 2nd 1st 2nd 1st 2nd

0.997 ± 0.004

0.69 ± 0.02 0.31 ± 0.02 0.65 ± 0.01 0.35 ± 0.01 0.67 ± 0.02 0.33 ± 0.02

97.3 ± 0.2 98.6 ± 0.1 97.2 ± 0.2 98.6 ± 0.2 97.5 ± 0.1 98.9 ± 0.1

10.0 ± 0.1 8.00 ± 0.01 9.00 ± 0.01 8.10 ± 0.01 9.00 ± 0.01 8.10 ± 0.01

1.93 ± 0.03 6.55 ± 0.15 1.86 ± 0.11 5.05 ± 0.39 1.95 ± 0.04 5.50 ± 0.28

isothermal controlled rate

0.938 ± 0.011 0.954 ± 0.023

dimensional shrinkage of the as-produced reaction interface toward the center of the crystal in the deceleration period. However, the rigorous mathematical formalism for such a process is left for future studies. The possible increase in the partial pressure of the product gases, i.e., O2 and H2O, at the reaction interface is also a cause for deceleration, considering the effects of chemical equilibrium, because the diffusional removal of the product gases from the reaction interface through the surface product layer becomes difficult as the reaction advances. Under such a high water vapor pressure, formation of a liquid phase at the reaction site is very probable. The liquid phase may be an alkaline solution of H2O2; therefore, the advancement of the reaction interface accompanied by the destruction of the reactant crystals and the decomposition of the liberated H2O2 are significantly accelerated, appearing as the second reaction step. The escape of the liquid phase through pores in the surface product layer and the evaporation of water result in the formation of the solid product whiskers, Figure 1e. Formation of Na2CO3 whiskers has also been observed during the thermal decomposition of NaHCO3,8 in which the possible existence of a liquid phase during the second-half of the reaction was anticipated. The expected physico-geometrical mechanism of the formation of the liquid phases and whiskers in both thermal decomposition processes are comparable, but the acceleration afforded by the liquid phase is probably more significant for the thermal decomposition of SPC crystals because of the acceleration of exothermic H2O2 decomposition mediated by the liquid phase. The change in the acceleration effect of the liquid phase results in a different rate behavior observed in the second-half of the reaction, i.e., the appearance of the autocatalytic process as the second reaction step in the thermal decomposition of SPC crystals and the contracting geometry process continuing during the entire thermal decomposition of NaHCO3. Accordingly, the surface product layer plays a predominant role in controlling the overall kinetics of the thermal decomposition of SPC crystals since it governs the diffusional removal of product gases and the formation of the liquid phase. 3.5. Influence of Atmospheric Water Vapor. In the above physico-geometrical reaction model, the first and second reaction steps proceed under different conditions with respect to the selfgenerated water vapor pressure p(H2O). To evaluate the validity of the reaction model, the influence of atmospheric p(H2O) on the respective reaction steps was investigated. Figure 9a shows the influence of atmospheric p(H2O) on the mass-loss curve and its derivative curve for the thermal decomposition of SPC crystals under a linearly increasing temperature at β = 5 K min−1. With increasing atmospheric p(H2O), the onset temperature Te.o. of the derivative curve systematically shifts to a lower temperature, whereas the peak temperature Tp remains unchanged, Figure 9b. From the shift in Te.o. observed with increasing atmospheric p(H2O), it is inferred that the surface reaction is accelerated by the atmospheric p(H2O). The constant Tp that is independent of

Figure 8. Experimental master plots of the respective reaction steps drawn using JMA(m) functions evaluated by kinetic deconvolution and curves for the second reaction step fitted by Prout-Tompkins and SB(m, n, 0) models.

reaction step indicates a further autocatalytic characteristic, which is fitted by SB(0.90, 0.69, 0) with values n < m < 1. The kinetic rate data recorded under isothermal and controlled rate conditions were also kinetically deconvoluted similar to those in nonisothermal decomposition, where the optimized parameters for the nonisothermal decomposition process were utilized as the default values for the kinetic optimization for the reactions under isothermal and controlled rate conditions. Typical results of the kinetic deconvolution for the reactions under isothermal and controlled rate conditions are shown in Figure 7b,c, respectively. The optimized parameters are also listed in Table 1. The optimized parameters for the reaction under isothermal and controlled rate conditions are practically identical with those estimated for nonisothermal decomposition. These results indicate that the relationship between the two distinguishable reactions with comparable Ea values is maintained unchanged under different heating modes, resulting in the ideal isoconversional relationship with the constant Ea values for the overall reaction during main portion of the reaction, as was seen in Figure 6a,b. The above results for kinetic deconvolution of thermal decomposition into two reaction steps can be interpreted from the viewpoint of physico-geometrical kinetics, which is supported by the morphological observations of the reacting particles shown in Figure 1. The first reaction step, which contributes during the entire overall reaction, is unambiguously characterized by the surface reaction and subsequent advancement of the as-produced reaction interface toward the center of the crystals, where crystallites of the solid product, Na2CO3, grow two-dimensionally forming a stacking layer of platelets as the surface product layer. The observed apparent fitting to the nucleation and growth type model JMA(m) with m ≈ 2.0 can potentially be interpreted as the rate process regulated by a complex routine causing a two-dimensional growth of the product crystals in the acceleration period and subsequent two1886



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reported values.21 The optimized Arrhenius parameters for the second reaction step decrease with an increase in atmospheric p(H2O) and the advancement of reaction, where the change in the Ea value is compensated by the change in the A value. By drawing the Arrhenius plots using the Ea and A values, it was confirmed that the reaction rate at a temperature in the reaction temperature region increases in the first reaction step due to the effect of atmospheric p(H2O), whereas no distinguishable change was found for the second reaction step. The apparent values of the kinetic exponent m in JMA(m) are also smaller than those determined for the reactions in flowing dry N2 and they fluctuate among the reactions under different atmospheric p(H2O). Figure 10 graphically compares the kinetic model

Figure 9. Influence of p(H2O) on the thermal decomposition of SPC crystals (m0 = 5.0 mg): (a) mass-loss traces and their derivative curves recorded under linearly increasing temperature at β = 5 K min−1 and (b) changes in Te.o. and Tp of DTG curves with p(H2O).

the atmospheric p(H2O) suggests that the internal reaction is not influenced by the atmospheric p(H2O). By selecting three different p(H2O) values, 0.76, 4.05, and 10.0 kPa, the nonisothermal mass-loss data at different β were recorded for the kinetic calculation. The TG-DTG curves are illustrated in Figure S7 in the SI. The apparent Ea values at different α evaluated according to eq 5 are compared among the reactions under different p(H2O) in Figure S8 in the SI. For the first- and second-half of the reaction, the influence of atmospheric p(H2O) appears as a larger fluctuation of the Ea values and a detectable decrease in the Ea values as the reaction advances, respectively. Kinetic deconvolution according to eq 10 was applied to evaluate the influence of atmospheric p(H2O) on the kinetic behavior of the respective reaction steps, where default values of the parameters were set similar to the manner described above. Typical results of kinetic deconvolution for the reactions under different atmospheric p(H2O) are compared in Figure S9 in the SI. Table 2 lists the average values of the optimized parameters for the reactions at the respective β under different p(H2O). The values of Ea and A optimized for both reaction steps are slightly larger than those determined for the reaction in flowing dry N2, which correspond to previously

Figure 10. Change in the experimental master plots of the respective reaction steps, drawn using JMA(m) functions evaluated by kinetic deconvolution, associated with the effect of atmospheric water vapor: (a) first reaction step and (b) second reaction step.

functions estimated under different atmospheric p(H2O). A distinguishable change dependent on the atmospheric p(H2O) can be observed for the initial part of the first reaction step, Figure 10a, but the experimental master plots of the second reaction step under different atmospheric p(H2O) are practically identical, Figure 10b. With increasing atmospheric p(H2O), the acceleration component of the first reaction step is completed in an earlier stage of the reaction. Considering the above physico-geometrical reaction model of the surface reaction and subsequent advancement of the reaction interface toward the center, the change in the initial stage of the

Table 2. Average Values of the Mass-Loss Fraction c and Apparent Kinetic Parameters of Different Reaction Steps Evaluated for the Thermal Decomposition of SPC Crystals under Different p(H2O) Optimized by Kinetic Deconvolution p(H2O)/kPa

reaction step

c

Ea/kJ mol−1

A/1011 s−1

m in JMA(m)

0.76

1st 2nd 1st 2nd 1st 2nd

0.69 ± 0.02 0.31 ± 0.02 0.68 ± 0.01 0.32 ± 0.01 0.68 ± 0.01 0.32 ± 0.01

109.7 ± 0.3 109.8 ± 0.1 109.8 ± 0.2 106.9 ± 0.1 107.4 ± 0.3 102.1 ± 0.2

11.6 ± 0.1 7.14 ± 0.01 14.2 ± 0.1 2.52 ± 0.01 7.02 ± 0.01 0.526 ± 0.001

1.49 ± 0.04 3.73 ± 0.27 1.45 ± 0.05 4.24 ± 0.30 1.36 ± 0.04 4.37 ± 0.26

4.05 10.0

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reaction, which is dependent on atmospheric p(H2O), can be rationalized by the acceleration effect of p(H2O) on the surface reaction.55,56 Because the second reaction step takes place under a higher p(H2O) generated by the reaction itself, no practical influence of atmospheric p(H2O) is observed. These findings on the effect of atmospheric water vapor also support the overlapping two-step reaction proposed in this study.

AUTHOR INFORMATION

Corresponding Author

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

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The present work was partially supported by a grant-in-aid for scientific research (B) (21360340 and 22300272) from the Japan Society for the Promotion of Science.

4. CONCLUSIONS Apparently, the thermal decomposition of SPC crystals proceeds with a smooth mass-loss behavior irrespective of the applied heating modes. The overall kinetics is characterized by the constant Ea value of ∼100 kJ mol−1, which is independent of α. However, a change in the rate behavior with the advancement of reaction is indicated by the experimental master plot, which has a trapezoidal shape. It reflects arrest of initial acceleration and a subsequent constant mass-loss rate over the main part of the reaction. Considering the physico-geometry of the process, the thermal decomposition of SPC crystals proceeds via a surface reaction and subsequent advancement of the as-produced reaction interface toward the center of the crystals. The asproduced surface product layer of Na2CO3 impedes the diffusional removal of the evolved H2O and O2, resulting in a possible increase in the partial pressures of H2O and O2 at the internal reaction interface. Based on the formation of Na2CO3 whiskers radiating from the pores in the surface product layer observed during the second-half of the reaction, we expect a potential existence of a liquid phase at some area inside the reacting particles. The aqueous solution is an alkaline solution of H2O2; therefore, the internal reaction is significantly accelerated. Accordingly, the overall rate behavior of thermal decomposition is explained by the basal reaction of the surface induced reaction of contracting geometry type, composed of the surface reaction and the subsequent advancement of the as-produced reaction interface toward the center of crystal, and the additional autocatalytic reaction mediated by the liquid phase in the secondhalf of the reaction. The two distinguishable reactions are characterized by the comparable value of Ea, ∼100 kJ mol−1, and the contribution of the respective reaction steps is approximately in the ratio 7:3, irrespective of the applied heating program modes. The initial part of the basal reaction (the first reaction step) is accelerated by atmospheric p(H2O), whereas the additional autocatalytic reaction (the second reaction step) is independent of the atmospheric p(H2O). This observation indicates an acceleration effect of water vapor on the reaction and also a high p(H2O) in the internal reaction site generated by the reaction itself. The surface product layer plays an important role in inducing the self-generated reaction conditions in the secondhalf of the reaction by governing the diffusional removal of the evolved gases at the internal reaction sites and the subsequent increase in the internal p(H2O).

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ASSOCIATED CONTENT

S Supporting Information *

Powder XRD patter and FT-IR spectrum of the reactant crystals. Mathematical deconvolution of the thermal decomposition under linearly increasing temperature and formal kinetic analysis of the deconvoluted kinetic rate data. TG-DTG curves under different atmospheric p(H2O) and kinetic analysis for the reactions under selected p(H2O). This material is available free of charge via the Internet at http://pubs.acs.org. 1888



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Kinetics and Mechanism of the Thermal Decomposition of Sodium

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