Thermal Decomposition of Silver Carbonate - American Chemical

Article pubs.acs.org/JPCC

Thermal Decomposition of Silver Carbonate: Phenomenology and Physicogeometrical Kinetics Nobuyoshi Koga,*,† Shuto Yamada,‡ and Tomoyasu Kimura† †

Chemistry Laboratory, Graduate School of Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi-Hiroshima 739-8524, Japan Faculty of Arts and Science, Kyusyu University, 744 Motooka, Fukuoka 819-0395, Japan

‡

S Supporting Information *

ABSTRACT: Thermal decomposition of Ag2CO3 to Ag2O was investigated to identify the physicochemical events that occur during the reaction and to reveal the interactions that cause the complex kinetic behavior of the reaction. Based on comparative investigation of thermal decomposition behavior of six different commercially available Ag2CO3, a physicogeometrical reaction model of two partially overlapping reaction stages is proposed. The reaction stages involve the formation of a surface product layer and an internal reaction in the as-produced core−shell structure of the reacting particles. Immediately after the formation of the surface product layer, the structural phase transitions of Ag2CO3 to two different high-temperature phases occur. Under these conditions, the thermal decomposition behavior is controlled by the diffusional removal of CO2 through the surface product layer and/or the increase in internal partial pressure of CO2. The growth of Ag2O particles in the surface product layer produces possible channels for the diffusion of CO2. The relative rates of the formation of the diffusion channels in the surface product layer and the increase in the internal partial pressure determine whether the internal reaction advances at a steady rate or arrests until thermal decomposition of Ag2O of the surface product layer occurs at higher temperatures. The sample and reaction conditions influence the kinetic behavior of different component processes, resulting in the complex thermal decomposition behavior.

1. INTRODUCTION Thermal decomposition of Ag2CO3 has long been the subject of thermoanalytical studies from very early days of kinetic studies of solid-state reactions.1−3 By 1929, Spencer and Topley4 had already reported the kinetic nature of the reaction from the viewpoint of (1) the role of the reaction interface, (2) reversibility of the reaction, (3) influence of atmospheric water vapor, (4) temperature dependence, and (5) influence of sample preparation. They further studied the influence of the atmospheric CO2 on the thermal decomposition, the reaction equilibrium, and the recombination of product Ag2O and CO2.5 All these parameters are fundamental in characterizing the overall reaction kinetics in solid state, even in currently used sophisticated material processing procedures involving solidstate reactions. The respective kinetic aspects have been further investigated in successive periods by novel and advanced physicochemical techniques. The knowledge accumulated by those studies on the kinetics of thermal decomposition of Ag2CO3 forms an important part of the theoretical basis of solid-state reaction kinetics.6−10 Contrary to the expected thermal behavior of the distinct two-step reactions that produce Ag through Ag2O, the reaction pathway is fairly complex and involves several physicochemical events, which influence the kinetics and mechanisms of thermal decomposition. The structural phase transitions to two high© 2012 American Chemical Society

temperature phases of Ag2CO3 occur at the early stage of the first decomposition step of decarbonation.11−17 The formation of a surface product layer at the beginning of thermal decomposition is also responsible for the complex reaction pathway by blocking diffusional removal of CO2, as observed in many different thermal decomposition processes in solids.18−21 The chemical species of the surface product layer are currently identified by detailed spectroscopic analyses.22,23 The reactivity changes depending on sample preparation method24,25 and by the effect of additives.26−28 The reaction rate is accelerated by the effect of atmospheric water vapor.4,29 From these complex phenomena of thermal decomposition, it is highly possible that the influence of such additional physicochemical events on the reaction pathway and mechanisms of thermal decomposition vary depending on the characteristics of the sample particles and the applied and/or self-generated reaction conditions. The change in reactivity depending on the sample and reaction conditions has been mentioned in the study by Spencer and Topley as normal vs abnormal behavior4,5 and later as active vs inactive samples25,29 but is unresolved. Received: September 28, 2012 Revised: December 1, 2012 Published: December 6, 2012 326

dx.doi.org/10.1021/jp309655s | J. Phys. Chem. C 2013, 117, 326−336

The Journal of Physical Chemistry C

Article

subjected to TG-DTA (DTG-50M) measurements at different β (0.5≤ β ≤ 10 K min−1) in flowing N2 (80 cm3 min−1) or in flowing CO2 (80 cm3 min−1). Using an instrument of TG-DTA (TG8120, Rigaku Co.) connected to a quadrupole mass spectrometer (MS: M-200QA, Anelva Co.), TG/DTA-MS measurements were carried out, for about 2.0 mg of each sample weighed into a platinum pan (5 mm ϕ and 2.5 mm in height), in flowing He (200 cm3 min−1) at β = 5.0 K min−1, where the mass spectra of the evolved gases were recorded in the range of 10−50 amu (EMSN: 1.0 A; SEM: 1.0 kV). The influence on the thermal decomposition behavior of the water vapor in the reaction atmosphere was monitored by the mass change under controlled water vapor pressure using the above TG-DTA (TG8120) instrument, which was equipped with a programmable humidity controller (HUM-1, Rigaku Co.). Approximately 10.0 mg of each sample was weighed in a platinum pan (5 mm ϕ and 2.5 mm in height). By keeping the samples at 350 K in the TG-DTA instruments, mixed gases of N2−H2O with a controlled partial pressure of water vapor p(H2O) were introduced into the reaction tube at a rate of approximately 400 cm3 min−1. After stabilizing for 30 min, the samples were heated at β = 5.0 K min−1 for recording TG-DTA curves under controlled p(H2O). Changes in the crystalline phases during the course of thermal decomposition in flowing N2 (100 cm3 min−1) were traced under different heating conditions by high-temperature XRD (HTXRD) using the above RINT2200 V, which was equipped with a programmable heating chamber (TC20, Rigaku Co.). One measurement was performed by stepwise isothermal heating, where the sample was heated at β = 1 K min−1 and maintained at various temperatures from 348 to 723 K in steps of 25 K during the XRD measurements for every 15 min. In the different measurement, XRD measurements were continuously repeated during heating of the the sample at β = 5 K min−1. The HTXRD measurements were also performed in flowing CO2 (100 cm3 min−1) to clarify the possible participation of the structural phase transitions of Ag2CO3 to the thermal decomposition process. The differential scanning calorimetry (DSC: DSC60, Shimadzu Co.) measurements were performed in flowing CO2 (50 cm3 min−1) using approximately 10.0 mg of each sample sealed in an aluminum pan (5 mm ϕ), where cycles of heating and cooling at a rate of ±5 K min−1 were applied below 495 K. 2.3. Collection of the Kinetic Rate Data. Approximately 10.0 mg of each sample was weighed in a platinum pan (6 mm ϕ and 3 mm in height), and the mass-change trace for thermal decomposition of Ag2CO3 to Ag2O was recorded using a hanging-type TG (TGA-50M, Shimadzu Co.) in flowing N2 (80 cm3 min−1) at different constant temperatures and different β. By attaching the homemade controller30,31 of the sample controlled thermal analysis (SCTA)32 to the TGA-50M instrument, the temperature profiles to realize the programmed constant rates of mass loss C, ranging from 7.5 to 15 μg min−1, were recorded for thermal decomposition of Ag2CO3 to Ag2O under conditions otherwise identical to the above isothermal measurements.

This study aims to solve the complex interactions of the respective physicochemical events that occur during thermal decomposition of Ag2CO3 to Ag2O by applying systematic thermoanalytical approaches. Six different commercially available reagents of Ag2CO3 were used in the present study. The reaction pathway and kinetics of thermal decomposition were interpreted using the thermoanalytical results, which were supported by other physicochemical measurements and microscopic observations. A physicogeometrical reaction model of thermal decomposition is proposed by integration of the results from this study and the knowledge accumulated in the last hundred years. The current physicogeometrical approach for the phenomenology of solid-state reaction is rather classical in the age of nanosized particles and atomic ordering but acknowledges the significance of the understanding of solid-state reactions in regulating the properties of solid products by controlling the overall kinetics of the reaction.

2. EXPERIMENTAL SECTION 2.1. Characterization of Samples. Six commercially available reagents of Ag2CO3 listed in Table 1 were used in Table 1. Commercially Available Reagents of Ag2CO3 Utilized in This Study label

manufacturer

code

lot no.

A

31007-12

M1M3634

178647

E

Nacalai tesque, Japan Sigma-Aldrich, U.S. Chempur, Germany STREM CHEM., U.S. Wako, Japan

F

Alfa Aesar, U.S.

B C D

purity description

type III

86096DJ

>98% based on Ag 99%

006972

Ch.290905

99.7%

II

93-4706

A8265048

99+%-Ag

III

198-13162

WKG6395

I

11420

H22S057

1st grade >95% 99.5%-Ag

I

II

this study without any further purification. The starting materials were characterized by powder X-ray diffractometry (XRD, RINT 2200 V, Rigaku Co.) using monochrome Cu−Kα radiation (40 kV, 20 mA) and Fourier transform infrared spectroscopy (FT-IR, FTIR-8400S, Shimadzu Co.) recorded by the diffuse reflectance method after diluting the samples in KBr. For each sample of 15.0 mg weighed in a platinum pan (6 mm ϕ and 3 mm in height), thermogravimetry-differential thermal analysis (TG-DTA, DTG-50M, Shimadzu Co.) in flowing N2 (80 cm3 min−1) at a heating rate of β = 5 K min−1 was carried out to evaluate the composition of the samples from the stoichiometry of the overall thermal decomposition with reference to the following reaction: Ag2CO3 → 2Ag + CO2 + 1/2O2. The morphology of the sample particles was observed by scanning electron microscopy (SEM, JSM-6510, JEOL) after coating the samples with Pt by sputtering. By dispersing the sample particles in distilled water with a small amount of surfactant, the particle size distribution was evaluated by the laser diffraction method (SALD-300 V, Shimadzu Co.). The specific surface area of the samples was measured by a single point method of BET (FlowSorbII-2300, Micromeritics Co.) after a pretreatment of those samples at 373 K in flowing N2 for 1 h. 2.2. Characterization of Thermal Decomposition Behaviors. Approximately 15 mg of each sample was weighed into a platinum pan (6 mm ϕ and 3 mm in height) and

3. RESULTS AND DISCUSSION 3.1. Reactivity of the Samples. The present six samples indicated the practically identical XRD patterns and FTIR spectra; see Figures S1 and S2 in the Supporting Information. All the XRD patterns of the different samples are identical to that reported as the room-temperature (RT) phase of Ag2CO3 327



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(monoclinic, S.G. = P21/m, a = 4.8521, b = 9.5489, c = 3.2536 Å, β = 91.9713°).17 Figure 1 compares the TG-DTA curves of

Figure 2. Mass chromatograms (m/z = 32 and m/z = 44) of the evolved gas during thermal decomposition of samples A, B, and C (m0 = 2.0 mg) at β = 5.0 K min−1 in flowing He (200 cm3 min−1).

Figure 1. Typical TG-DTA curves for samples A, B, and C (m0 = 15.0 mg) at β = 5.0 K min−1 in flowing N2 (80 cm3 min−1).

occurs simultaneously with the evolution of O2 according to reaction 2 at higher temperatures. Thermal behavior of type III samples (A and D) is intermediate between I and II because of the behavior of the gaseous evolutions, in which the simultaneous evolutions of CO2 and O2 at the second massloss step occur in a relatively wider temperature region than that of type II. Such variations in thermal behaviors of Ag2CO3 were noticed very early,4 and the differences between samples of type I and II have been termed as normal vs abnormal or active vs inactive.4,5,25,29 The origin of the variations in reactivity and reaction pathways has been discussed with respect to sample preparation and impurities.25−28 Figure 3 compares typical SEM images of samples B (type I) and C (type II), together with the particle size distribution. One of the major differences between the active and inactive samples is the particle size and its distribution. The specific

−1

the selected samples recorded at β = 5 K min in flowing N2 (80 cm3 min−1). The total mass-loss values as a result of thermal decomposition to Ag were in good agreement with that calculated by assuming the overall reaction as follows: Ag2CO3 → 2Ag + CO2 + 1/2O2, Δm/m0(Ag2CO3) = −21.76%. However, respective samples indicated largely different reaction pathways of thermal decomposition. The patterns of the TGDTA curves of these six samples can be classified into three different types, i.e., types I, II, and III, as shown in Figure 1. The classifications of the present samples based on the characteristics of the reaction pathways of thermal decomposition are also listed in Table 1. The samples of type I, i.e., samples B and E, decompose thermally to Ag through clearly distinct two step reactions by the intermediate compound of Ag2O; see Figure 1. Ag 2CO3 → Ag 2O + CO2 (Δm1/m0(Ag 2CO3) = − 15.96%)

(1)

Ag 2O → 2Ag + 1/2O2 (Δm2 /m0(Ag 2CO3) = − 5.80%)

(2)

A quite different reaction pathway can be expected for type II samples, i.e., samples C and F, where the reaction of the first mass-loss step arrests in the early stage of the reaction 1 and the residual process of the overall thermal decomposition occurs at higher temperatures corresponding to those of reaction 2 of the type I samples. Thermal behavior of type III samples, i.e., samples A and D, is intermediate between type I and II. Figure 2 compares the mass chromatograms (m/z = 32 and 44) of the evolved gas during thermal decompositions of samples A, B, and C, which are classified as type III, I, and II, respectively. For the samples classified as type I (B and E), the evolution of CO2 and O2 are clearly separated in the first and second mass-loss steps, respectively. Thermal decomposition of type II samples starts at slightly lower temperature than that of type I and III samples, but reaction 1, which produces CO2, arrests at the early stages. Thermal decomposition of the residual carbonate

Figure 3. Typical SEM images and the particle size distributions of sample B (type I) and C (type II). 328



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surface areas of samples B and C are 0.37 ± 0.05 and 0.49 ± 0.07 m2 g−1, respectively. It is clearly seen in Figures 1 and 2 that thermal decomposition of type II sample starts at low temperature, as it is generally accepted from a simple consideration of a higher surface energy for smaller particles. However, the reaction of type II sample arrests immediately, indicating the inactive character of the overall reaction. Accordingly, the active or inactive feature of thermal decomposition of Ag2CO3 is not determined by the surface reactivity. The assumption that the change in the reaction pathway is controlled by the physicogeometrical character of the reaction kinetics is also supported by the systematic change in the reaction pathway depending on β, which is typically observed in the reaction of samples A, C, D, and F (types II and III). Figure 4 shows the changes in the TG-DTA curves with β for thermal

according to reaction 1. Because of the lower onset temperature for the samples with smaller particle size, i.e., the samples C and F (type II), the reaction probably starts on the particle surfaces by a nucleation and growth mechanism.33,34 After completion of the surface reaction, reaction 1 proceeds further in types I and III samples, where diffusional removal of CO2 from the interior reaction sites by diffusion through the surface product layer is necessary for the subsequent advancement of the reaction. In type I sample, it is possible that the diffusion path of the evolved CO2 through the surface product layer is preserved during reaction 1. The arrest of the first mass-loss step before completion of reaction 1, observed for types II and III samples, indicates that the internal reactant Ag2CO3 in the particle is stabilized in confinement by the surface Ag2O layer. The impedance effect of the surface product layer on the diffusion of the evolved CO2 is the most probable reason for the arrest of the reaction as it is observed in many thermal decomposition and dehydration processes in solids.10,18,19 Figure 5 compares typical SEM images of partially decomposed samples B and C (approximately 3.2% mass

Figure 4. TG-DTA curves of sample A (m0 = 15.0 mg, type III) at different β values in flowing N2 (80 cm3 min−1).

Figure 5. Typical SEM images of samples B and C decomposed partially (approximately 3.2% mass loss) by heating to 473 K at β = 5.0 K min−1 in flowing N2 (80 cm3 min−1).

decomposition of sample A (type III). With increasing β, the mass loss during the first decomposition step decreases. The decrease in the mass-loss value during the first mass-loss step is compensated by the increase in the mass-loss value in the second mass-loss step, indicating the same total mass loss during the whole course of the two-step reactions. At β = 0.5 K min−1, thermal decomposition proceeds as two reaction steps according to reactions 1 and 2. The same trend of the βdependent change in the reaction pathway was confirmed by high-temperature XRD measurements; see Figures S3 and S4 in the Supporting Information. Under stepwise isothermal condition, Ag2CO3 completely transforms to Ag2O in the temperature range of 448−498 K. However, under linearly increasing temperature at β = 5 K min−1, both the diffraction peaks attributed to Ag2O and a high-temperature phase of Ag2CO3 which will be described below are observed in the temperature range of 498−723 K until the formation of Ag occurs according to reaction 2. The β-dependent change in the reaction pathway of thermal decomposition indicates that the first mass-loss step proceeds in a complex way by the possible participation of more than one kinetic process and physicochemical events. 3.2. Surface Product Layer. From the mass chromatograms shown in Figure 2, it is apparent that the first mass-loss steps of all the samples, regardless of the differences in the mass-loss values, are as a result of the evolution of CO2

loss) by heating to 473 K at β = 5.0 K min−1 in flowing N2 (80 cm3 min−1). The difference in the surface textures of samples B and C is clearly seen. The product layer of sample B is constructed by largely grown product particles, where pores and interstices among the product particles exist. Such pores and interstices are possible diffusion channels for the evolved CO2 by the internal reaction. The surface of sample C is relatively smooth, where the possible channels for CO2 diffusion are very limited. A significant impedance effect of CO2 diffusion is to arrest reaction 1, which is expected from the textures of the surface product layer of sample C. 3.3. Participation of the Structural Phase Transition in Ag2CO3. In Figure 1, two distinct endothermic DTA peaks or shoulders can be observed at the early stage of the first massloss step irrespective of samples. These endothermic events are occurring simultaneously at the early stage of the first decomposition step and seem to be related to the structural phase transitions in the reactant Ag2CO3.12−16 Two hightemperature phases of Ag2CO3, together with the RT phase, have been reported by Norby et al,17 i.e., RT-Ag2CO3 (monoclinic, S.G. = P21/m, a = 4.8521, b = 9.5489, c = 3.2536 Å, β = 91.9713°), β-Ag2CO3 (tetragonal, S.G. = P31c, a = 9.1716, b = 9.1716, c = 6.5176 Å), and α-Ag2CO3 (hexagonal, S.G. = P-62m, a = 9.0924, b = 9.0924, c = 3.3249 Å). The effects of these structural phase transitions on thermal decomposition 329



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sample to 493 K, the two partially overlapping endothermic DSC peaks indicate the transformation from RT phase to βAg2CO3 and from β-Ag2CO3 to α-Ag2CO3, respectively. In sample A (type III), α-Ag2CO3 transforms to β-Ag2CO3 on cooling with a sharp exothermic peak at 459.8 ± 0.4 K. On reheating β-Ag2CO3, the β → α transition occurs at 469.3 ± 0.5 K. The β → α transition temperature does not change by repeated heating and cooling cycles. The transformation of βAg2CO3 to the RT occurs at low temperatures around 370 K with a broad exothermic DSC peak. On reheating the asproduced Ag2CO3 of RT phase, the RT → β phase transition starts at 446.7 ± 0.8 K with a broad endothermic DSC peak. The temperature hysteresis of the reversible transition between the RT and β phase is apparently larger than that of the reversible transition between β and α phase. The RT → β transition occurs at apparently lower temperature than that observed in the first heating of the sample. This is possible because of the reduction in the grain size of Ag2CO3 by the phase transitions, which is supported by the lower intensity of the XRD peaks of the reproduced RT phase in comparison to that of the original RT phase. The transition temperatures and enthalpy changes of the phase transitions of Ag2CO3 of samples A−C are summarized in Table S1 in the Supporting Information. 3.4. Internal Reaction and Formation of Diffusion Channel. On heating the sample in flowing N2, the structural phase transitions of Ag2CO3 from the RT phase to α phase through the β phase occur after partial thermal decomposition of Ag2CO3, and the reactant particles are coated by a surface product layer of Ag2O. Because of the transition of Ag2CO3 inside the particles, the grain size of the reactant substrate decreases. The as-produced grain boundary is a reactive site for thermal decomposition, in addition to the reaction interface between the surface product phase and the internal reactant. Because of the reaction at the grain boundary, the respective grains of the internal α-Ag2CO3 are coated by Ag2O. Because the diffusional removal of CO2 is impeded by the surface product layer of Ag2O, the partial pressure of CO2 in the internal particle increases rapidly. Under these conditions, the internal reaction possibly approaches following equilibrium: Ag2CO3 ⇄ Ag2O + CO2, where the reaction advancement is regulated by the diffusional removal of CO2. On heating type II and III samples at high β, the increase in the partial pressure of CO2 is possibly more significant and results in arrest at this stage; see Figure 1. An aggregate of the Ag2O-coated reactant grains further coated by the surface product layer of Ag2O is assumed as a model for the samples at the arrested stage. The β-dependent change in the mass-loss ratio of the first mass-loss step is interpreted by the variation in the relative rates of CO2 evolution in the internal particle and the diffusional removal of CO2 through the surface product layer. At low β, the rate of CO2 evolution is slow, such that the increase in the internal partial pressure of CO2 is not significant in comparison to that at high β, which promotes the overall thermal decomposition of the first mass-loss step to Ag2O with a relatively smooth massloss behavior. The change in the surface product layer during the reaction has to be considered in the above physicogeometrical interpretation. Figure 8 shows the isothermal mass-loss trace at 458 K for the first mass-loss step of sample A (type III) in flowing N2, together with the time derivative curve. Thermal decomposition proceeds to Ag2O with a relatively smooth mass-loss trace according to reaction 1. The reaction starts with

have to be clarified to understand the overall kinetic behavior of the first mass-loss step. On heating the sample in flowing CO2, reaction 1 shifts to the high-temperature region and endothermic DTA peaks with two distinct peaks appear in the temperature region of the first mass-loss step in flowing N2; see Figure S5 in the Supporting Information. Figure 6 shows the DSC trace during cyclic

Figure 6. Typical DSC traces of sample A (m0 = 10.0 mg) during cyclical heating (β = 5 K min−1) and cooling (β = −5 K min−1) in flowing CO2 (50 cm3 min−1).

heating and cooling of sample A in flowing CO2. Practically the same DSC curves were recorded in all samples. The change in the XRD pattern of sample A during heating and cooling in comparable temperature range with the above DSC measurements in flowing CO2 is shown in Figure 7. Because the XRD pattern changes from the RT phase to α-Ag2CO3 by heating the

Figure 7. Changes in the XRD pattern of sample A during heating (β = 5 K min−1) and subsequent cooling (β = −5 K min−1) in flowing CO2 (100 cm3 min−1), together with the XRD patters of different phases of Ag2CO3 simulated from the reported crystal structures.17 330



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layer is one of the key processes regulating the overall reaction rate behavior. The similar behaviors of the abrupt noise in the DTG curve by pore and/or crack formation during the thermal decomposition of solids are sometimes observed for the reactions which are controlled by the surface reaction and subsequent internal reaction.20,35 3.5. Influence of the Atmospheric Water Vapor. The effect of atmospheric water vapor on thermal decomposition of Ag2CO3 has also been one of the topics of previous kinetic studies. For example, the earliest study on the topic was by Spencer and Topley in the early 20th century.4 It has been reported by many workers that thermal decomposition of Ag2CO3 to Ag2O is accelerated by atmospheric water vapor, as is the case of several other metal carbonates and bicarbonate.36−40 The penetration of water vapor into the surface product layer and the formation of cracks on the surface have been proposed as one of the effects of atmospheric water vapor.4 Based on spectroscopic evidence on the formation of HCO3− on the surface, the catalytic action of HCO3− in the destruction of the crystal structure of the reactant has also been proposed as a possible mechanism. 29 In the present physicogeometrical scenario of thermal decomposition, the influence of atmospheric water vapor on the grain growth of Ag2O in the surface product layer is considered as a probable effect of the catalytic action on the overall kinetics. Figure 10 compares the TG-DTG curves of thermal decomposition of sample A (type III) to Ag2O under different

Figure 8. Typical isothermal mass-change trace at 458 K for the first mass-loss step of sample A (m0 = 9.98 mg) in flowing N2 (80 cm3 min−1).

rapid acceleration in a short period and then immediately decelerates. The rate behavior at the initial stage corresponds to the surface reaction on the respective reactant particle. Taking into account the variation in the transition temperature of RTto β-Ag2CO3 in the repeated DSC runs in Figure 6, the phase transition of the internal reactant seems to occur even during heating at constant temperature. After the surface reaction, the overall rate decelerates moderately indicating a concave derivative curve, which reflects the internal thermal decomposition of β-Ag2CO3 and the diffusional removal of CO2. A reproducible abrupt noise is observed in the derivative curve during the established reaction. Figure 9 compares the SEM

Figure 9. Comparison of the surface textures of sample A heated isothermally at 453 K in flowing N2 (80 cm3 min−1) for (a) 50 and (b) 100 min.

Figure 10. TG-DTG curves for thermal decomposition of sample A (m0 = 10.0 mg) from Ag2CO3 to Ag2O at β = 5 K min−1 under different p(H2O) values.

images of the sample heated isothermally at 458 K for 50 and 100 min, which correspond to the samples before and after the abrupt noise of the derivative mass-loss curve. The grain growth of the solid product on the surface product layer as the reaction advances is apparent. After the abrupt noise, pores appear on the surface product layer. The formation of pores is the most probable cause of the abrupt noise in the derivative mass-loss curve, indicating the rapid escape of internal CO2. The pore formation is observed at around α = 0.70−0.80, which is nearly corresponding to the maximum mass-loss rate due to the internal reaction. This phenomenon also supports the mechanism of the established reaction that is proposed as the thermal decomposition of internal Ag2CO3 under relatively high CO2 pressure, which is controlled by the diffusional removal of CO2 through the surface product layer. Accordingly, the grain growth of the solid product on the surface product

water vapor pressure p(H2O) conditions. The mass-loss value of the first step of reaction 1 increases systematically with increasing p(H2O), accompanied by an increase in the reaction rate and by a shift in the reaction to the low-temperature region. All type II and III samples indicated a similar change in the reaction behavior as a function of p(H2O). This phenomenon is similar to the effect of the heating rate; see Figure 4. It was also confirmed by SEM observations of the surface textures of partially decomposed samples under different p(H2O) that the grain growth of Ag2O in the surface product layer is enhanced by the effect of p(H2O), and pores, as observed in Figure 5 (sample B) and Figure 9b (sample A) for the reaction under isothermal heating in flowing dry N2, are also formed for the reaction of sample A under nonisothermal 331



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procedure.46−49 In Figure S6 in the Supporting Information, the results of the formal kinetic analysis are shown by selecting the reaction of sample A. Apparent activation energy, Ea, evaluated by the isoconversional method50,51 indicated significant dependence on the fractional reaction α. The experimental master plot on the rate behavior could not be fitted by any single kinetic model functions for solid-sate reactions.52,53 The results of the formal kinetic analysis, applied beyond the prerequisite of fundamental kinetic equations, also indicates that the thermal decomposition of Ag2CO3 to Ag2O consists of more than one reaction stage even under the conditions of stoichiometric decomposition at moderate reaction rates. The reaction stages may be characterized by different kinetic parameters and by different physicogeometrical reaction mechanisms. For rigorous kinetic analysis, the formation of the surface product layer and the subsequent internal reaction assumed above have to be treated as two partially overlapping different reaction stages. Along with the physicogeometrical model of the partially overlapping reaction stages for thermal decomposition of Ag2CO3 to Ag2O, the kinetic rate data recorded at constant temperatures were deconvoluted by assuming the following cumulative kinetic equation for the two reaction stages

heating at a higher p(H2O). The apparent acceleration of thermal decomposition is explained by the effect of atmospheric p(H2O) on the enhancement of grain growth of the Ag2O particles in the surface product layer and the consequent reduction in the impedance effect on the diffusional removal of the internal CO2 through the surface product layer. Increase in the mobility of ionic species mediated by the absorbed water molecule on the surface is a probable cause for the acceleration of the grain growth by the atmospheric water vapor, as has been sometimes observed for the sintering and crystallite growth of inorganic oxides.41−45 3.6. Overall Kinetics of Thermal Decomposition. As it is deduced from the TG-DTG curves at low β, Ag2CO3 transforms completely to Ag2O in the first mass-loss step under a moderate reaction rate condition, regardless of the type of samples I−III. The mass-loss measurements at constant temperatures and at constant mass-loss rates allow recording of the kinetic rate data during thermal decomposition of Ag2CO3 to Ag2O. As an example, the mass-loss traces of the thermal decomposition of sample A at different constant temperatures and at different constant rates are shown in Figure 11. Although

dα = dt

N

N

∑ cikifi (αi) i=1

with

∑ ci = 1

and

i=1

N

∑ ciαi = α i=1

(3)

where ci and ki are the mass-loss fractions of the corresponding reaction stages with respect to the total mass-loss of the reaction and the rate constant, respectively. The subscript numbers, i = 1 and 2, indicate the reaction stages. The empirical Sestak−Berggren model,54 SB(m, n, p): f(α) = αm(1−α)n[−ln(1−α)]p, is assumed as the kinetic model function for both reaction stages, in order to accommodate any possible reaction mechanisms.35,55−58 The most appropriate parameters, ci, ki, mi, ni, and pi, of the respective reaction stages were simultaneously optimized by nonlinear least-squares analysis and minimization of the squared sum of the residuals, F, when fitting the experimental curve of (dα/dt)exp vs time by the calculated curve of (dα/dt)cal vs time. 2 ⎡⎛ ⎞ ⎛ dα ⎞ ⎤ d α F = ∑ ⎢⎜ ⎟ −⎜ ⎟ ⎥ ⎢⎝ dt ⎠exp , j ⎝ dt ⎠cal, j ⎥⎦ j=1 ⎣ M

(4)

The default values of ci were estimated preliminarily by conventional peak deconvolution method using a statistical function;59 see Figure S7 and Table S2 in the Supporting Information. Then the order of the default k values were determined graphically by setting the default values of ci and by assuming the first-order equation for f(α), i.e., SB(0, 1, 0). Typical results of the peak deconvolution based on eq 3 for the kinetic rate data of thermal decomposition of the samples B and C at 453 K are compared in Figure 12. The comparable results of kinetic deconvolution were observed for thermal decomposition of the respective samples at different temperatures. The average values of ci and the kinetic exponents in SB(mi, ni, pi) optimized for the reactions at different temperatures are listed in Table 2. The mass-loss fractions, c1 and c2, largely differ in samples B and C. The major portion of the overall reaction of sample B (type I) is regulated by the first reaction stage, and

Figure 11. Typical mass-change traces for thermal decomposition of sample A (m0 = 10.0 mg) from Ag2CO3 to Ag2O recorded in flowing N2 (80 cm3 min−1) at (a) different temperatures T and (b) different controlled rates C.

the abrupt noise as a result of the formation of pores on the surface product layer is observed in all the mass-loss data,20,35 the kinetic rate data of the complete course of reaction 1 can be recorded under isothermal and constant rate conditions. We attempted to formally analyze the kinetic rate data by assuming an ideal single reaction stage after removing the abrupt noise in the derivative curves by a mathematical 332



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Figure 12. Typical decovolution results of the kinetic rate data, recorded isothermally at 453 K, for thermal decomposition of Ag2CO3 to Ag2O. Figure 13. Arrhenius plots for the first and second stages of thermal decomposition of Ag2CO3 to Ag2O.

the second reaction stage covers the residual portion that appeared as reaction tail. The first reaction stage of sample C (type II) arrests in the early stage of the reaction, and the second reaction stage dominates the subsequent reaction. Regardless of the large differences in the values of ci between the samples, the kinetic exponents in SB(mi, ni, pi) are practically identical for the respective reaction stages of the different samples. All the empirical functions of SB(mi, ni, pi) evaluated through optimization indicate a maximum reaction rate in the way of the respective reaction stages, but the physicochemical significance of the respective kinetic exponents is not easy to interpret due to the high flexibility of these kinetic exponents and the complex reaction behavior of the present reaction. The rate constants of the respective reaction stages at different temperatures were recalculated by the nonlinear leastsquares analysis by setting the average values of ci and SB(mi, ni, pi) listed in Table 2 as the fixed values. Figure 13 compares the Arrhenius plots of the respective reaction stages of samples B and C. The apparent Arrhenius parameters evaluated from the plots are also listed in Table 2. For the first reaction stage of the surface reaction, a slightly larger value of Ea is observed for the reaction of sample B (type I). The observation corresponds to the higher onset temperature of the mass-loss process observed in sample B in Figure 1. The values of Ea for the second reaction stages of samples B and C vary in a different way from the respective values of Ea for the first reaction stage. The second reaction stages of samples B and C occur in quite different conditions. Because of the differences in the original

particle size of the reactant and in the fraction of the mass loss as a result of the first reaction stage, the surface product layer was apparently thicker in sample B. The longer diffusion path required for the removal of the evolved CO2 in the interior of the reacting particles is possibly one of the causes for the larger value of the apparent Ea in sample B at the second reaction stage. Using the values of ci and the kinetic parameters of the respective reaction stages under isothermal conditions as the default values, the kinetic rate data recorded under constant mass-loss rate conditions were also subjected to the kinetic deconvolution into two partially overlapping reaction stages of the surface reaction and the internal reaction by assuming the following equation instead of eq 5.60−62 dα = dt

⎛ Ea, i ⎞ ⎟f ( α ) ⎝ RT ⎠ i i

N

N

∑ ciAi exp⎜− i=1

with

∑ ci = 1

and

i=1

N

∑ ciαi = α

(5)

i=1

Typical results of the kinetic deconvolution for the reactions of samples B and C are illustrated in Figure 14. The contributions of the first and second reaction stage on the overall thermal decomposition and of the relation between the two reaction stages indicate the same trends as observed in the

Table 2. Kinetic Parameters for the Respective Reaction Stages of Thermal Decomposition of Samples B and C from Ag2CO3 to Ag2O under Isothermal Conditions, Estimated by the Kinetic Deconvolution Using Nonlinear Least Squares Analysis SB(mi, ni, pi) sample

reaction stage, i

B

1 2 1 2

C

fraction of mass loss, ci 0.77 0.23 0.28 0.72

± ± ± ±

0.04 0.04 0.02 0.02

mi 0.35 0.01 0.17 0.01

± ± ± ±

ni 0.03 0.01 0.02 0.01

1.16 0.97 1.07 0.81

± ± ± ±

R2a

pi 0.15 0.17 0.10 0.10

0.28 0.36 0.18 0.47

± ± ± ±

0.10 0.11 0.01 0.02

0.996 ± 0.001 0.993 ± 0.002

Ea,i kJ mol−1 112 146 104 71

± ± ± ±

9 7 6 2

ln Ai s−1

Rb

± ± ± ±

−0.9941 −0.9978 −0.9946 −0.9994

22.9 29.8 21.3 10.9

2.3 1.8 1.6 0.4

a

The attribution of the nonlinear regression analysis of the kinetic deconvolution according to eq 3. bThe correlation coefficient of the linear regression analysis for the Arrhenius plot. 333



Article

layer and the variations during the course of the reaction regulate the kinetics and equilibrium of the internal reaction by controlling the diffusional removal of CO2 and the partial pressure of CO2. The phenomenology of thermal decomposition, i.e., the impedance effect, arrest, pore formation in the surface product layer, effect of water vapor, and so on, can be interpreted, at least qualitatively, based on the physicogeometrical reaction mechanism.

4. CONCLUSIONS Different commercially available samples of Ag2CO3 indicate different behavior during thermal decomposition to Ag2O and are empirically classified into three types. Regardless of the different overall thermal decomposition behavior of the different samples, the reaction starts at the surfaces of the reactant particles resulting in the formation of a surface product layer. The structural phase transitions of Ag2CO3 to two hightemperature phases occur in the inner core of the reactant just after the formation of the core−shell structure of the reacting particles. The reactivity of the inner reactant increases by the formation of grain boundaries induced by the structural phase transitions. The partial pressure of CO2 inside the particle shell generated by thermal decomposition controls the subsequent kinetic behavior of the reaction. The partial pressure of CO2 is regulated by the diffusional removal of internal CO2 through the surface product layer. The property and the structure of the surface product layer, and variations during the course of the reaction, are the main factors that control the diffusivity of CO2 as well as the pressure gradient between the exterior and interior of the particles. When the impedance effect of the surface product layer on diffusion is relatively low, thermal decomposition of the internal reactant advances at a steady rate to complete the decomposition of Ag2CO3 to Ag2O, as in type I samples. In the reaction of type II samples, the internal reaction arrests at chemical equilibrium, Ag2CO3 ⇄ Ag2O + CO2, where the impedance effect of the surface product layer is significant. The arrest is maintained until thermal decomposition of the surface Ag2O occurs at higher temperatures. The growth of Ag2O in the surface product layer is one of the major factors that control the impedance effect. The surface product layer constructed by well-grown Ag2O particles provides possible channels for the diffusion of CO2, resulting in the advancement of the internal reaction at a steady rate. The growth rate of Ag2O particles in the surface product layer is possibly dependent on the properties of the original reactant particles, where the impurities and the particle size characterize the properties of the reactant particles. The formation temperature of the surface product layer, which depends on the properties of the reactant particles and the reaction atmosphere, is also a factor that controls the growth rate of

Figure 14. Typical decovolution results of the kinetic rate data, recorded under constant mass-loss rates, for thermal decomposition of Ag2CO3 to Ag2O.

respective samples under isothermal conditions; see Figure 12. The optimized parameters in eq 5 are practically identical among those evaluated from the kinetic rate data at different mass-loss rates. Table 3 lists the average values of the optimized parameters for the samples B and C. All of the optimized parameters for the thermal decomposition under the constant mass-loss rates indicate practically the same trend in the relationship among the corresponding values evaluated for those under isothermal conditions. The above results of the kinetic calculations for thermal decomposition process of Ag2CO3 to Ag2O entirely support the proposed physicogeometrical model on the basis of the morphological and phenomenological observations. Thus, it can be concluded that thermal decomposition of Ag2CO3 to Ag2O occurs in the physicogeometrical scheme of the two different mechanistic stages, the formation of the surface product layer and the reactions in the internal core. Furthermore, the property and structure of the surface product

Table 3. Kinetic Parameters for the Respective Reaction Stages of Thermal Decomposition of Samples B and C from Ag2CO3 to Ag2O under Constant Mass-Loss Rate Conditions, Estimated by the Kinetic Deconvolution Using Nonlinear Least-Squares Analysis SB(mi, ni, pi) sample

reaction stage, i

B

1 2 1 2

C

a

fraction of mass loss, ci 0.70 0.29 0.31 0.69

± ± ± ±

0.03 0.03 0.02 0.02

Ea,i/kJ mol−1 116 128 104 70

± ± ± ±

1 1 1 2

Ai/s−1 (1.70 (6.26 (2.22 (3.73

± ± ± ±

0.17) 0.23) 0.04) 0.85)

mi × × × ×

1010 1010 109 104

0.21 0.01 0.14 0.01

± ± ± ±

ni 0.03 0.01 0.07 0.01

0.89 1.17 1.63 0.55

± ± ± ±

R2 a

pi 0.11 0.18 0.11 0.05

0.18 0.25 0.13 0.38

± ± ± ±

0.02 0.04 0.06 0.05

0.988 ± 0.001 0.991 ± 0.002

The attribution of the nonlinear regression analysis of the kinetic deconvolution according to eq 3. 334



Article

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Ag2O particles. Thermal decomposition of type I samples starts at slightly higher temperature than other samples and forms the surface product layer constructed by relatively large Ag2O particles. Because the growth of Ag2O particles is kinetically controlled, the particle size of Ag2O increases with time when heating the sample at appropriate temperatures. Accordingly, the relationship between the two phenomena, i.e., the growth of Ag2O particles in the surface product layer and the increase in the internal pressure of CO2 because of internal thermal decomposition, determines whether the internal reaction arrests, as seen in the variations of the overall reaction behavior of type II and III samples depending on β. A similar trend in the change of the overall reaction behavior as a function of the atmospheric water vapor indicates the catalytic action of the atmospheric water vapor on the growth of the Ag2O particles. In conclusion, thermal decomposition of Ag2CO3 to Ag2O occurs by two reaction stages, i.e., formation of a surface product layer and the reaction of an internal reactant, and these two reaction stages partially overlap, as deduced by the deconvolution of the kinetic rate data. In this geometrical setting, the reaction advances by complex interactions of different kinetic processes. The complex behavior of the overall kinetics of the reaction, which has long been a subject of mechanistic and kinetic studies, can be explained based on the physicogeometrical interpretation of a heterogeneous reaction.

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ASSOCIATED CONTENT

S Supporting Information *

Powder XRD patterns and FT-IR spectra of the samples; changes in the crystalline phases during heating of the sample; thermal behavior of the sample in flowing CO2; structural phase transition of Ag2CO3; formal kinetic analysis of the first massloss step; mathematical deconvolution of the first mass-loss step. This material is available free of charge via the Internet at http://pubs.acs.org.

■

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.

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REFERENCES

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