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Heterogeneous Kinetic Features of the Overlapping Thermal Dehydration and Melting of Thermal Energy Storage Material: Sodium Thiosulfate Pentahydrate Nao Kameno, and Nobuyoshi Koga J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b02202 • Publication Date (Web): 04 Apr 2018 Downloaded from http://pubs.acs.org on April 4, 2018

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The Journal of Physical Chemistry

Heterogeneous Kinetic Features of the Overlapping Thermal Dehydration and Melting of Thermal Energy Storage Material: Sodium Thiosulfate Pentahydrate Nao Kameno and Nobuyoshi Koga* Department of Science Education, Graduate School of Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi-Hiroshima 739-8524, Japan

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Abstract

The thermal dehydration of sodium thiosulfate pentahydrate (STS-PH), which has been studied as a potential thermal energy storage material, was investigated from the viewpoints of the physico-geometric reaction mechanism, heterogeneous kinetics, and morphologies of the product. Thermoanalytical and microscopic techniques were used to demonstrate the physico-geometric events that control the apparent kinetics of the reaction under different reaction conditions. The thermal dehydration of STS-PH takes place via a two-step reaction that involves a dihydrate intermediate, and the contribution of the melting of STS-PH is a key characteristic. Reaction conditions alter the relative position of the melting of STS-PH with reference to the reaction stage of the thermal dehydration. Depending on the relative position of STS-PH melting, the reaction can occur in the solid state, solid–liquid state, or liquid state. A variety of physico-geometric events contribute to the reaction processes under different reaction conditions, generating different reactant/product configurations and reaction pathways controlled by specific physico-geometric reaction mechanisms. The anhydrides produced via different reaction pathways exhibit largely different morphologies that range from hollow particles to a sponge-like agglomerate. It is expected that the findings presented herein contribute to the theoretical foundations of the complex heterogeneous kinetics in the solid state.


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1. Introduction The thermal dehydration of inorganic salt hydrates has long been studied for elucidating their kinetic properties, which contributed notably to the establishment of the kinetic theory of solid-state reactions.1-3 Because in many thermal dehydration reactions are reversible, the significant impact of environmental water vapor pressure on the thermal dehydration reaction renders the kinetic interpretation difficult.4, 5 In turn, the reversible endothermic dehydration and exothermic rehydration that occur near room temperature can be featured as a potential thermal energy storage material for compensating the seasonal fluctuation of solar energy. The overall reaction of the multistep thermal dehydration of inorganic salt hydrates of formulae MaXb·cH2O to form an anhydrous salt is expressed as follows: MaXb·cH2O(s) ⇄ MaXb(s) + cH2O(g)

(ΔrH > 0)

(1)

The reversible thermal dehydration/rehydration process of several inorganic salt hydrates such as MgSO4·7H2O6-8 has recently been reinvestigated from the thermodynamic and kinetic viewpoints, with the aim of evaluating the practical applicability as thermal energy storage material.9-12 For some inorganic salt hydrates, melting near room temperature precedes their thermal dehydration on heating in a closed system, and the as-produced molten salts recrystallize on cooling. MaXb·cH2O(s) ⇄ MaXb·cH2O(l)

(ΔmH > 0)

(2)

One of the most extensively studied materials regarding eq. (2) is sodium acetate trihydrate.13-20 Both the reversible chemical reaction of eq. (1) and the phase transition of eq. (2) can be involved in thermal energy storage when the chemical and physical processes overlap near room temperature. Sodium thiosulfate pentahydrate (STS-PH, Na2S2O3·5H2O) is an inorganic salt hydrate that undergoes both thermal dehydration and melting near room temperature. Under vacuum and a dynamic flow of inert gas, thermal dehydration proceeds to form an anhydride via a dihydrate intermediate, exhibiting complex kinetic behavior that is controlled by the physico-geometric constraints of the solid-state reaction.21 In a closed system, STS-PH melts at 321.7 K with an enthalpy of melting of ΔmH = 51.82 kJ mol−1.22 The reversible melting and solidification process of STS-PH 3 ACS Paragon Plus Environment


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has attracted attention for its use in thermal energy storage in an open-loop solar water-heating system22 and as a microencapsulated phase change material with an STS-PH/silica core–shell construction.23 Although it has not been reported in previous work on the thermal behavior of STSPH, the thermal dehydration of STS-PH to dihydrate and the melting of STS-PH can be expected to overlap under certain temperature and atmospheric water vapor conditions, because the melting point of STS-PH lies within the temperature region of its thermal dehydration. Rigorous elucidations of this overlapping and the impact that it may have on each thermally induced process are necessary to achieve the most efficient use of STS-PH as a thermal energy storage material. The thermal dehydration of STS-PH appears to be a very complex process from the viewpoint of the kinetics.4, 5 Both reaction steps involved in the dehydration, from pentahydrate to dihydrate and from dihydrate to anhydride, are reversible processes that are controlled by the physicogeometric constraints. Both reactions might initiate on the surface that forms the surface product layer in the early stage of the reaction. The subsequent reaction would occur at the reaction interface, resulting in the progress of the reaction interface toward the center of the solid reactant. This process is accompanied by an increase in the thickness of the surface product layer; therefore, diffusional removal of produced water vapor through the surface product layer becomes gradually difficult as the reaction progresses. Under these conditions, the partial pressure of water vapor that is generated at the reaction interface affects the rate behavior in this region. In some extreme cases, hindrance of the diffusional removal of the evolved gas by the surface product layer causes the reaction to stop, and a stable core–shell structure of residual solid reactant–surface product layer is produced.24-28 Recovery of the reaction is triggered by the generation of a diffusion path in the surface product layer by the formation of pores and cracks. In many cases, the recovered reaction exhibits quite different rate behavior from that of the preceding reaction owing to a dramatic change in the reaction conditions. Condensation of the evolved water vapor is an alternative phenomenon that is expected to take place at the reaction interface and in the surface product layer under high water vapor pressure at temperatures below the boiling point of water. The condensed water interacts with reactant and 4 ACS Paragon Plus Environment

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product solids, leading to their dissolution and gelation. Rapid diffusional removal of the as-produced solution results in the formation of whiskers of the solid product, which are radiating outward from the diffusion path on the surface of the reacting particles.29, 30 The gradual dehydration of the gelated reactant produces, in many cases, a poorly crystalline solid product and sometimes an amorphous solid or glass via the sol–gel process.31-35 In addition to the self-generated reaction conditions at the reaction interface originating from mass transfer phenomena, the temperature at the reaction interface is also influenced by the self-cooling effect owing to the enthalpy change of the reaction,36 which causes fluctuation of the temperature at the reaction interface and the reacting system from the programmed temperature control, producing temperature gradients. It must be noted that the selfgenerated reaction conditions and consequently the rate behavior of the reaction depend largely on the applied sample and measurement conditions.37-40 Therefore, careful setting of the sample and measurement conditions is essential for an accurate recording of the kinetic data for the thermal dehydration of solids in order to reduce the complexity of the kinetic calculation and obtain reliable kinetic parameters.41 The significant difference in the kinetic behaviors of the thermal dehydration of inorganic salt hydrates studied under conventional linear heating and unconventional linear cooling was recently reported by Liavitskaya and Vyazovkin.42,43 Considering the aforementioned physicogeometric features of the thermal dehydration of salt hydrates, the differences in the physicogeometric reaction mechanism and the impacts of mass and heat transfer phenomena should be taken into account for the correct interpretation of the different kinetic behaviors of the reaction under largely different temperature profiles. The melting of the solid reactant that overlaps with the thermal dehydration is logically expected to induce sudden and dramatic changes in the physico-geometric features of the thermal dehydration of STS-PH. A similar phenomenon has been reported for the contribution of the structural phase transition of the reactant solid that overlaps with the thermal decomposition of Ag2CO3 affording Ag2O.26, 27 The structural phase transitions sometimes induce thermal decomposition, as has been reported for the aragonite–calcite phase transition that accompanied by the evolution of 5 ACS Paragon Plus Environment


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water occluded in CaCO3.44, 45 The first-order transitions of the residual solid reactant induce drastic self-cooling of the reaction interface and the overall reacting system, variation of the geometric configuration of reactive sites and area, and enhancement/deterioration of the reactivity of the residual reactant. By the structural phase transition, the grain boundary of the transformed solid can be newly developed as potential reactive sites. By melting, a core–shell structure of the molten reactant–surface product layer is generated.31-35 The thermal decomposition of the molten reactant may also be regulated by the physico-geometric constraints owing to its large viscosity,46 as observed for the thermal degradation of molten polymers.47, 48 The relative position of the melting in the temperature range of the thermal dehydration may change depending on the conditions of the temperature program and reaction atmosphere, because the thermal dehydration temperature depends on the kinetic feature whereas the first-order transition occurs at a specific temperature. In extreme cases, the thermal dehydration occurs in the solid state during the course of the reaction if the reaction temperature is largely below the melting point of the solid reactant. In contrast, if the reaction occurs under a high water vapor pressure, the thermal dehydration probably shifts to higher temperatures and the melting takes place before the thermal dehydration, ensuring thermal dehydration in the liquid state. Differences in the kinetic behaviors of the thermal decomposition of a substance that occurs both in the solid and liquid states are also one of the topics of interest in the kinetic study in order to obtain further insights into the heterogeneous kinetics in the solid state. Recently, Stanford and Vyazovkin reported comparable Arrhenius parameters for the thermal decomposition of malonic acid in the solid, liquid, and supercooled liquid states.49 The surface product layer was not produced during the thermal decomposition of malonic acid, and the mass loss behaviors of the thermal decomposition in the solid, liquid, and supercooled liquid states were tracked successfully in an open system under flowing N2 by changing only the heating conditions. However, when the thermal decomposition of an inorganic salt in solid and liquid occurs under different reaction atmospheric conditions, the relation between the kinetic behaviors in the solid and liquid states may not be so simple because of the influence of the aforementioned physico-geometric constraints and self-generated reaction conditions. 6 ACS Paragon Plus Environment

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The overlapping of the thermal dehydration of STS-PH with its melting involves several physico-geometric phenomena that should be revealed for the rigorous kinetic description of the solid-state reactions. In this study, the thermal dehydration of STS-PH under different reaction conditions was tracked using various thermoanalytical techniques and microscopic observation. Through the complementary interpretation of the kinetic behavior and morphological changes of the sample during the reaction, it was aimed to ascertain the physico-geometric kinetic behaviors from two angles: (1) changes in the overlapping behavior of the thermal dehydration and melting of STSPH depending on the heating and atmospheric conditions and (2) comparison of the kinetic behavior of the thermal dehydration in the solid and liquid states that occurs under different atmospheric conditions. It is expected that the results presented herein will provide fundamental information for the efficient use of STS-PH as a thermal energy storage material and contribute to the theoretical foundations of the complex heterogeneous kinetics in the solid state.

2. Experimental 2.1 Sample and characterization Small and clear single crystals of commercially available STS-PH (Wako Pure Chemical Industries, Ltd., >99.0%) were sieved to different size fractions using stainless steel wire sieves with different mesh sizes and an electrical shaking apparatus (MVS-1, AS ONE). The sieved fraction of 500–1000 μm was stored in a refrigerator at 278 K and used for all the experiments carried out in this study. The sample was characterized by powder X-ray diffractometry (XRD) using a diffractometer (RINT-2200V, Rigaku). The XRD pattern was recorded in a 2θ range from 5° to 60° using a Cu target (monochrome Cu-Kα, 40 kV, 20 mA) by scanning at a rate of 4° min−1. The appearance of the sample particles was observed and photographed using an optical microscope (SZX-7, Olympus).

2.2. Characterization of thermal dehydration behavior



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Differential scanning calorimetry (DSC, DSC-60, Shimadzu) curves were recorded for determining the melting point and the enthalpy change of melting. The sample (approximately 5.0 mg) was weighed in an aluminum pan (5.0 mm in diameter and 2.5 mm in height) and sealed with an aluminum lid by crimping. The sample was heated from room temperature to 353 K at β = 5 K min−1 in flowing N2 (100 cm3 min−1). The DSC measurements were repeated five times for fresh samples. The thermal dehydration behavior of STS-PH was tracked by thermogravimetry–differential thermal analysis (TG–DTA, Thermoplus EVO2, Rigaku). Sample particles of approximately 3.0 mg were weighed in an open platinum pan or in an aluminum cell sealed with a pierced lid (both 5.0 mm in diameter and 2.5 mm in height). To record the TG–DTA curves, the samples were heated from room temperature to 573 K at different heating rates β (= 0.5, 1, 1.5, 2, 3, and 5 K min−1) in flowing N2 (300 cm3 min−1). Mass loss traces under isothermal conditions were also recorded at various temperatures below the melting point of STS-PH using the suspension-type TG (TGA-50, Shimadzu) equipped with a low-temperature furnace. The samples (approximately 3.0 mg) weighed in the platinum pan were heated in flowing N2 (80 cm3 min−1) from 253 K to a predetermined temperature (295 K  T  313 K) at β = 10 K min−1, and this temperature was maintained during the mass loss measurement. Changes in the XRD pattern of the sample during isothermal heating at 308 K in flowing N2 (100 cm3 min−1) were traced using the aforementioned diffractometer with a programmable heating chamber (PTC-20, Rigaku). During the isothermal heating, diffraction measurements were repeated continuously. The sample (approximately 3.0 mg) was weighed into a platinum pan or an aluminum cell. The aluminum cell was sealed with a cover glass. The sample was heated in flowing N2 (100 cm3 min−1) at β = 5 K min−1 from room temperature to 473 K in the DSC instrument. Changes in the morphology of the sample during the DSC measurements were observed by a digital microscope (moticam2000, Shimadzu) equipped with a zoom lens (SKL-Z300C, Saitoh Kogaku), and the snapshots were captured every 1 min. The final solid products of the DSC measurements in the open 8 ACS Paragon Plus Environment

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and sealed systems were also observed by an optical microscope (SZX-7, Olympus) and photographed. Samples dehydrated partially to different degrees were prepared in the aforementioned TG– DTA instrument by heating the sample weighed in the open platinum pan to different temperatures (324, 346, and 384 K) at β = 2 K min−1 in flowing N2 (300 cm3 min−1) and then cooling to room temperature in the instrument. The partially dehydrated samples were observed by a scanning electron microscope (SEM, JSM-6510, JEOL) after being coated with a thin platinum layer by spattering. The cross-sections of the partially dehydrated samples were also examined using an X-ray computed tomography (X-CT, SMX-100CT, Shimadzu). The instruments used for thermal analysis in this study were calibrated by standard methods. Details of the calibration are described in the Supporting Information.

3. Results and Discussion 3.1 Characterization of thermal dehydration behavior Figures S1 and S2 in the Supporting Information show the XRD pattern and outward appearance of the sample particles, respectively. The XRD pattern is in perfect agreement with that reported previously for STS-PH (Na2S2O3(H2O)5, sodium thiosulfate pentahydrate, monoclinic, a = 5.9410, b = 21.5700, c = 7.5250, α = 90.000, β = 103.550, γ = 90.000, ICDD PDF 01-070-0367),50-52 and the sample analyzed exhibits a transparent crystalline form with smooth surfaces. Figure 1 compares the TG–derivative TG (DTG)–DTA curves for the thermal dehydration of STS-PH recorded at  = 2 K min−1 in open and semi-sealed (sealed with a pierced lid) systems. In the open system, the mass loss was found to initiate from room temperature and proceed with three distinguishable mass loss processes. The mass loss value observed during heating from room temperature to 450 K was 35.9 ± 1.1%, which closely corresponds to that of the formation of the anhydride. Na2S2O3･5H2O → Na2S2O3 + 5H2O (Δm = 36.30%) 9 ACS Paragon Plus Environment

(3)


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On the other hand, in the semi-sealed system, a well-shaped endothermic peak that can be attributed to the melting of the sample is observed at approximately 320 K in DTA before the initiation of the mass loss process. Figure S3 shows a typical DSC curve for the corresponding phenomenon recorded for the sample in the sealed cell. The extrapolated onset temperature (Te.o.) and the enthalpy change (ΔmH) were determined from the DSC curves to be Te.o. = 322.0 ± 0.3 K and ΔmH = 51.90 ± 0.98 kJ mol−1, respectively, which are in close agreement to literature values.22 In the subsequent mass loss process, two mass loss processes are clearly distinguishable, with a first mass loss value of 21.5 ± 0.6% attributable to the formation of a stable dihydrate intermediate. Na2S2O3･5H2O → Na2S2O3･2H2O + 3H2O (Δm = 21.77%)

(4)

As the total mass loss during heating from room temperature to 450 K is comparable with that in the open system, the second mass loss process can be assigned to the thermal dehydration of the dihydrate intermediate to anhydride.

Figure 1. Comparison of the TG–DTG–DTA curves for the thermal dehydration of STS-PH (approximately 3.0 mg) in the open and semi-sealed systems recorded at β = 2 K min−1 in flowing N2 (300 cm3 min−1).

Further detailed information of the reaction process can be deduced from Figure 1. In the open system, an endothermic DTA peak of melting is observed at the boundary of the first and second mass loss processes. During the endothermic phenomenon attributed to the melting, the mass loss rate 10 ACS Paragon Plus Environment

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is significantly decelerated, and the mass loss process is interrupted midway through the thermal dehydration from pentahydrate to dihydrate. This is likely due to the self-cooling effect caused by melting. It must also be noted that the mass loss rate behaviors before and after the melting are nearly continuous striding over the break. Therefore, the phase change from solid to liquid is not expected to exert a significant influence on the rate behavior of the thermal dehydration. The formation of the dihydrate explains the boundary between the second and third mass loss processes in the open system. A large difference in the reaction temperature between the measurements in the open and semi-sealed systems is evident in the thermal dehydration both from pentahydrate to dihydrate and from dihydrate to anhydride, with the reaction in the semi-sealed system occurring at higher temperatures. As the reaction occurs in a quasi-isobaric condition of self-generated water vapor in the semi-sealed system, the higher reaction temperature compared with that in the open system indicates that the impact of the water vapor pressure on the gross rate behavior of the reversible reaction process represents as the normal behavior according to chemical equilibrium. Figure S4 shows a typical isothermal mass loss trace of STS-PH recorded in the open system in flowing N2 at 307 K, below the melting point of STS-PH. Even at this lower temperature, the mass loss process proceeding to form the anhydride is evidenced by the total mass loss value of approximately 35%. The shape of the mass loss trace indicates the presence of two different mass loss behavior regions, which can be more clearly seen in the derivative curve that exhibits an initial large peak and a subsequent gradual deceleration step. Changes in the XRD patterns of the crystalline sample during isothermal heating at 308 K in flowing N2 are shown in Figure S5. The XRD peaks of STS-PH exhibit a gradual attenuation with heating time, and an alternative XRD pattern appears during the heating period approximately from 100 to 140 min (Figure S5a). The XRD pattern of the intermediate solid is in approximate agreement with the reported diffraction data for the dihydrate (ICDD PDF 00-036-0696) (Figure S5b). On further heating, the sample loses its crystalline form to some extent exhibiting weak diffraction peaks, but the XRD pattern corresponds to that of the anhydride (ICDD PDF 01-076-2246). The results shown in Figures S4 and S5 indicate that the 11 ACS Paragon Plus Environment


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thermal dehydration of STS-PH to the anhydride occurs via a dihydrate intermediate solid even at the isothermal heating conditions below the melting point of STS-PH, i.e., via the reactions in the solid state.

3.2 Morphological changes Figure S6 shows a series of selected snapshots of the outward appearance of the sample particles recorded during the DSC measurements in the open system in flowing N2. At the very beginning of the measurement around room temperature, the transparent reactant particles immediately lose clarity by the surface reaction. No significant change in the shape and size of the particles is found throughout the overall thermal dehydration process. Figure 2 shows the changes of the detailed surface textures and the internal structure of the particles dehydrated to three selected degrees of dehydration in the open system in flowing N2 as revealed using SEM and X-CT. The three partially dehydrated samples selected were (A) immediately after the melting endotherm (324 K), (B) at the formation of the dihydrate intermediate (346 K), and (C) at the completion of the overall dehydration (385 K) after heating the sample at 2 K min−1 in the open system in flowing N2 using TG–DTA (Figure 2a). For the sample heated to immediately after the melting, SEM images show numerous cracks and– voids on the particle surfaces (Figure 2b(A)). The detailed surface structure exhibits an array of regularly aligned particles with several micrometer sizes in diameter. The surface of the sample dehydrated to dihydrate appears to have been further roughened (Figure 2b(B)). In addition, aggregation and sintering of the surface particles are evident. Immediately after completing the overall dehydration process, the surface is covered with a thin peel of the surface product layer (Figure 2b(C)). This thin peel is constructed with sintered particles, but the component particles are much smaller than those observed for the dihydrate intermediate. The changes of the surface morphology during the thermal dehydration in the open system resemble those observed for the solidstate reactions, even for the process that takes place after the melting. At the same time, contributions of the molten phase can also be deduced from the significant sintering of the product particles on the


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surfaces. The X-CT images of the partially dehydrated sample particles clearly indicate the presence of hollow particles (Figure 2c), whose formation would initiate immediately after the melting (Figure 2c(A)) and would be complete at the formation of dihydrate intermediate (Figure 2c(B)). The construction of the hollow structure is active during the subsequent dehydration process and also in the final dehydration product (Figure 2c(C)).

Figure 2. Changes in the detailed surface textures and the internal structure of particles dehydrated to three selected degrees of dehydration in the open system in flowing N2 (300 cm3 min−1): (a) the reaction stages of the partially dehydrated samples A–C in the TG–DTA curves, (b) SEM images, and (c) X-CT images.

The morphological changes of the sample particles during the thermal dehydration in the open system are indicative of the complex reaction process. Overall, the thermal dehydration initiates at the particle surfaces to produce the surface product layer of dihydrate. Subsequently, the melting occurs in the internal STS-PH structure with a detectable endothermic effect. Then, the reacting 13 ACS Paragon Plus Environment


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particles form the core–shell structure of the molten reactant–surface product layer. The subsequent thermal dehydration of the internal molten reactant accompanies the migration of the molten reactant to the surface product layer and the diffusional removal of water or water vapor through the surface product layer. As a result, the hollow structure is developed during the thermal dehydration of STSPH to dihydrate. During this process, the changes observed in the texture of the surface layer are most likely due to the interaction with water vapor. The subsequent thermal dehydration from dihydrate to anhydride takes place in the geometrical constraint of the hollow construction. On the other hand, in the semi-sealed system, the morphological changes of the reactant during the thermal dehydration differ largely from those in the open system because the reaction proceeds in the liquid state. Figure 3 shows a series of selected snapshots of the outward appearance of sample particles recorded during the DSC measurements in the semi-sealed system. As can be extracted from Figure 3(1)-(3), the outward appearance of the reactant particles remains almost unaltered during the melting, but the molten particles are easily drawn together during the thermal dehydration from pentahydrate to dihydrate (Figure 3(3),(4)). This molten agglomerate is formed in the interval between the first and second mass loss processes (Figure 3(5),(6)). The second mass loss process is characterized by the dehydration from the molten agglomerate of dihydrate forming a surface shell. Effusion of viscous reactant from the crack of the surface shell and bubbling in the molten reactant are the most distinguishing phenomena observed during the second mass loss process that leads to the anhydride (Figure 3(7)). These events are reflected by the abrupt noises in the DSC curve. The agglomerate swells significantly during the second mass loss (Figure 3(7), (8)), which suggests that the thermal dehydration proceeds entirely in the liquid state. However, owing to the high viscosity of the molten reactant and the plausible existence of a thin surface layer over the particles and agglomerate, the reaction in the liquid state still exhibits the typical behavior of a heterogeneous reaction that is regulated by physico-geometric events. Figure S7 compares the solid products of the thermal dehydration in the open and semi-sealed systems. As can be seen, the product obtained in the open system maintains the original particle morphology (Figure S7a), whereas an 14 ACS Paragon Plus Environment

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agglomerate is observed in a side of the sample cell containing the product obtained in the semisealed system (Figure S7b).

Figure 3. A series of selected snapshots of the outward appearance of sample particles in an aluminum cell sealed with a cover glass recorded during the DSC measurements at β = 5 K min1 in flowing N2 (100 cm3 min−1).

3.3 Overlapping of melting with the thermal dehydration process Figure 4 shows the TG–DTG–DTA curves recorded for the open system at different β. In the open system, the mass loss due to thermal dehydration starts at room temperature and proceeds via several mass loss steps to complete the reaction (Figure 4a). Although the curves shift systematically to higher temperatures with β as expected, the number of mass loss steps that can be distinguished from the DTA and DTG peaks tends to increase accordingly. For the DTA curves recorded at a β larger than 1.5 K min−1, a distinguishable DTA endothermic peak of melting was



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observed at the extrapolated onset temperature of Te.o. = 322.0 ± 0.1 K, which indicates that the melting overlaps with the thermal dehydration process. The mass loss ratio before and after the melting with respect to the complete dehydration process changes with β (Figure 4b). A clear tendency of increase in the mass loss ratio before melting with decreasing β is found. Because the thermal dehydration initiates at the surfaces of the reactant particles, each particle is covered with the solid product layer produced by the reaction of solid reactant. In this situation, melting of the internal reactant occurs, giving rise to a molten reactant–surface product layer with a core–shell structure as deduced above from the morphological observations. The results of the TG–DTA measurements indicate that the thickness of the surface product layer increases with decreasing β. At a β lower than 1.0 K min−1, no distinguishable DTA endothermic peak of melting is observed because the dehydration from pentahydrate to dihydrate achieves completion before reaching the melting temperature.


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Figure 4. Changes in the thermal dehydration behavior with β in the open system in flowing N2 (300 cm3 min−1): (a) TG–DTG–DTA curves at different β and (b) changes in the mass loss ratio before and after melting with β.

3.4 Kinetic behavior of thermal dehydration in the liquid state Figure 5 shows the TG–DTG–DTA curves for the thermal dehydration of STS-PH in the semi-sealed system recorded at different β. Irrespective of β, the mass loss process initiates immediately after the DTA endothermic peak of melting and proceeds through two well separated reaction steps via the dihydrate intermediate. The TG–DTG curves for the first mass loss process of molten STS-PH are indicative of the occurrence of a monotonous acceleration with increasing temperature and a systematic shift to higher temperatures with β. During the second mass loss process, abrupt noises appear randomly in the DTG curves, most likely as a result of the bubbling of water vapor produced in the molten reactant as observed microscopically (Figure 3).

Figure 5. Changes in the TG–DTG–DTA curves recorded in the semi-sealed system with β.

The result of the TG–DTG curves for the first mass loss process in the semi-sealed system can be applied to the kinetic calculation. Under the assumption of a single-step reaction,53 the rate behavior can be expressed by the following fundamental kinetic equation.54, 55



d  E   A exp   a  f   dt  RT 

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(5)

where A, Ea, R, and T are the Arrhenius preexponential factor, activation energy, gas constant, and absolute temperature, respectively. The fractional reaction α is defined as the degree of mass loss with reference to the total mass loss during the first mass loss process. The function f(α) is a kinetic model function. Taking the logarithms of eq. (5),

E  d  ln    ln Af    a RT  dt 

(6)

is obtained, which reflects the linear correlation of ln(dα/dt) versus T−1 when applied to the data points at a selected α extracted from a series of kinetic curves at different β. The Ea values at different α are provided by the Friedman plot.56 The results of the Friedman plots applied to the first mass loss process in the semi-sealed system are shown in Figure 6. The Friedman plots at various α show a statistically significant linear correlation (r2 > 0.96 in 0.07 ≤ α ≤ 0.75; Figure 6a). In addition, the slope of the Friedman plots is approximately constant throughout the majority of the reaction (0.05 ≤ α ≤ 0.95). Therefore, the Ea value is constant throughout the wide range of α with the average value of 67.3  2.4 kJ mol−1 (0.05 ≤ α ≤ 0.95; Figure 6b), which supports the validity of the single-step assumption. For a single-step reaction, the rate behavior can be determined using experimental master plots in differential, integral, and combined forms, according to the equations57-60

d d E   exp a   Af ( ) d dt  RT  

g     0

(7)

d  A f  

(8)

d  d

(9)

f  g   

where θ is Ozawa’s generalized time61,62 denoting the hypothetical reaction time at infinite temperature and is defined as 18 ACS Paragon Plus Environment

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t



Ea   dt  RT 

   exp   0

(10)

Figure 6c shows the experimental master plots of (dα/dθ), θ, and (dα/dθ)θ versus α. The reaction rate behavior as reproduced by the (dα/dθ) versus α plot exhibits a gradual deceleration with a slightly concaved shape with the progress of the reaction. At this stage of the reaction in the semi-sealed system, the dehydration occurs in the liquid state and the evaporation of water vapor from the molten surface of each particle constitutes an elementary step of the process. If the reaction rate is controlled by evaporation from the surface with a constant surface area, a zero-order reaction-like rate behavior may be observed.37, 39, 46 However, the molten reactant particles tend to agglomerate during the first mass loss process, and the surface area of the molten reactant decreases as the reaction progresses. The agglomeration, together with the increase in the viscosity of the melt, might possibly account for the deceleration of the rate behavior of the first mass loss process that occurs in the liquid state. The same apparent rate behavior is also deduced from the shapes of the other experimental master plots of θ and (dα/dθ)θ versus α.

Figure 6. Formal kinetic analysis for the first mass loss process of thermal dehydration in a semisealed cell: (a) Friedman plots, (b) Ea values at different α, and (c) experimental master plots.

3.5 Kinetic behavior of thermal dehydration in the solid state Figure 7 shows the isothermal mass loss traces recorded in the open system in flowing N2 at various constant temperatures below the melting point of STS-PH as well as the isoconversional analysis of the isothermal kinetic curves. The mass loss curves indicate a partial overlapping of the



Page 20 of 47

two reaction steps and the overall mass loss value corresponds to the formation of the anhydride (Figure 7a). As a preliminary kinetic approach, the overall reaction affording the anhydride was subjected to Friedman analysis by defining  as the fractional reaction with reference to the overall mass. Although the resulting Friedman plots at different α exhibit an acceptable linearity, the slope of the plot was found to change dramatically during the overall reaction (Figure 7b). The apparent Ea value reaches a maximum at approximately α = 0.6, with concomitant variation of Ea from an increasing to decreasing trend at this α value (Figure 7c). Furthermore, the α value corresponds closely to the overall conversion degree to form the dihydrate intermediate (i.e., α = 0.6).

Figure 7. Formal kinetic analysis for the isothermal dehydration in the open system: (a) isothermal mass-loss traces at different T (selected), (b) Friedman plots, (c) Ea values at different α.

Mathematical peak deconvolution was used as the alternative preliminary kinetic approach to the overlapping reaction process. The DTG curves were separated into two peaks by fitting according to eq. (11).63-65 2 dm   Fi t  dt i 1

(11)

where i denotes the reaction step and F(t) is the statistical function, i.e., the Weibull function in the present case. From the mathematical deconvolution, the average contributions ci of each reaction step i to the overall mass loss were estimated to be (c1, c2) = (0.60  0.05, 0.40  0.05), which correspond closely to the two-step reaction scheme that affords the anhydride via the dihydrate. Further,


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Friedman method was applied to the mathematically separated kinetic curves. Although in both reaction steps a slight but detectable increase in the Ea,i values with the reaction progression was detected, the average Ea,i value in 0.1  i  0.9 was calculated as (Ea,1, Ea,2) = (74.4  11.0, 71.0  4.9) kJ mol−1.

Considering both Ea,1 and Ea,2 values as being nearly constant during each reaction

step, the overall process is interpreted as a combination of two single steps. On the other hand, the large standard deviation in the Ea,1 value indicates the possibility that the first reaction step is further composed of multistep processes. The Ea,1 value shown in Figure S8d changes from approximately 50 kJ mol−1 to 80 kJ mol−1 as the reaction step proceeds, which is the similar trend observed for the first half of the overall reaction in Figure 7c. Details of the mathematical deconvolution and the subsequent formal kinetic analysis of the mathematically separated kinetic curves are described in the section S4 in the Supporting Information. On the basis of preliminary kinetic approaches to the multistep reaction process using isoconversional analysis and the formal kinetic analysis of each reaction step separated by mathematical deconvolution, the kinetic analysis according to the cumulative kinetic equation (kinetic deconvolution analysis (KDA))65, 66 was carried out. 2  E  d   ci Ai exp   a,i  f i ( i ) dt i 1  RT 

2

with

c i 1

i

1

2

and

c i 1

i

i



(12)

As the kinetic model function f(α), an empirical model with three kinetic exponents known as the Šesták-Berggren model SB(m, n, p)67-69 was selected because of its efficiency in accommodating different types of physico-geometric kinetic behaviors. SB(m, n, p) : f ( )   m (1   ) n  ln(1   )

p

(13)

The kinetic description using the cumulative kinetic equation, eq. (12), is directly applicable to the multistep reaction process in which the mutual interaction of the component reaction steps is negligible. For the current reaction in the solid state, both successive reaction steps from pentahydrate 21 ACS Paragon Plus Environment


Page 22 of 47

to dihydrate and from dihydrate to anhydride are expected to proceed with a contraction of the reaction interface. Therefore, no overlapping between the reaction interfaces of each reaction step takes place in the reaction matrix, which may account for the approximate description of the multistep process by the cumulative kinetic equation. For KDA, the contributions of ci and the apparent Ea,i values estimated by the preliminary kinetic analyses were used as the initial values in eq. (12). The initial values of the kinetic exponents in SB(m, n, p) and the Ai values were selected by comparing graphically the experimental kinetic curve and the simulated kinetic curve according to eq. (12). By this graphical method, SB(0, 1, 0) and SB (0, 1, 0.75) were selected as the initial values of the kinetic exponents for the first and second reaction steps, respectively. Then, the initial Ai values were determined so as to fit the position of the peak tops of each reaction step. After setting all the initial kinetic parameters in eq. (12), an optimization run was performed to fit the simulated kinetic curve to the experimental kinetic curve recorded at each constant temperature by the nonlinear least-squares analysis to minimize F value.

 d    d   F        d t d t     cal, j  j 1  exp, j  M

2

(14)

where M is the data point in each kinetic curve. Figure 8 shows the results of the KDA. The overall kinetic curves are satisfactorily fitted by the sum of the contributions of the two reaction steps (Figure 8a) with the determination coefficient r2 better than 0.98. The optimized kinetic parameters are approximately equivalent among those determined for the kinetic curves at different temperatures (Table S2). Table 1 lists the kinetic parameters averaged over those at different constant temperatures. The ci values for the first and second reaction steps (0.62 and 0.38, respectively) closely correspond to those expected for the twostep reaction via the dihydrate intermediate. The Ea,2 value is slightly smaller than the Ea,1 value, but this difference is compensated by a change in Ai value as in the manner of the kinetic compensation effect.70-72 A significant difference was observed between the component reaction steps for the optimized kinetic exponents in SB(m, n, p). This difference is clearly seen in the experimental master 22 ACS Paragon Plus Environment

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plot of (dαi/dθi) versus αi that was reproduced according to eq. (7) using the optimized kinetic exponents (Figure 8b). The rate behavior of the first reaction step is characterized by a nearly linear deceleration as the reaction progresses and can be described by the first-order reaction model. For the second reaction step, the experimental master plot represents the reaction rate that passes through a maximum at α2 = 0.48. This behavior can be superficially described by an autocatalytic reaction model or nucleation and growth model such as JMA(m).73-76 JMA(m) : f ( )  m(1   ) ln(1   )

11/ m

(15)

The experimental master plot for the second reaction step is nearly perfectly fitted with JMA(2.91). Considering the contracting geometry of the reaction interface, the autocatalytic behavior may be described by the Galwey-Hood(n) model30, 77, 78, where the shrinkage of the core with the acceleration of the linear advancement rate of the reaction interface is taken into account.



Galwey  Hood (n) : f ( )  2n(1   )11 / n 1  (1   )1 / n



1/ 2

(16)

The best fit to the experimental master plot using Galway–Hood(n) was observed for n = 3, i.e., threedimensional contraction of the reaction interface with the acceleration of the linear advancement rate.



Page 24 of 47

Figure 8. KDA for the isothermal dehydration in the open system in flowing N2 at various constant temperatures below the melting point of STS-PH: (a) typical result of KDA and (b) the experimental master plots of (dαi/dθi) versus αi drawn using the optimized SB(mi, ni, pi) and fit curves by plausible physico-geometric kinetic model functions.


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Table 1. Average kinetic parameters optimized through KDA for the first and second reaction steps of isothermal dehydration in the open system in flowing N2 at various constant temperatures below the melting point of STS-PH

i

ci

Ea,i / kJ mol

1

0.62 ± 0.02

75.5 ± 0.2

2

0.38 ± 0.02

71.6 ± 0.2

−1

Ai / s

fi(i) = im(1−i)n[−ln(1−i)]p

−1

m

n

p

(1.99 ± 0.01 )×1010

0.02 ± 0.01

1.06 ± 0.08

0.03 ± 0.01

(3.00 ± 0.01) × 109

0.02 ± 0.01

1.05 ± 0.05

0.70 ± 0.03


r2 0.988


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3.6 Variation of the reaction pathway and the physico-geometric mechanism As revealed in this study, the reaction pathway and physico-geometric mechanism of the thermal dehydration of STS-PH vary with the reaction conditions, ensuring the reactions in solid, solid-liquid, and liquid states. This phenomenon is explained by the change in the relative position of the melting of STS-PH with reference to the reaction stage of the thermal dehydration depending on the reaction conditions. The kinetic behaviors and the specific physico-geometric constraints in the respective reactions that occur in different states are summarized in the section S5 in the Supporting Information for comparing the kinetic features and mechanisms to produce largely different morphologies of the final dehydration products.

4. Conclusions The thermal dehydration of STS-PH to form the corresponding anhydride was demonstrated to proceed through a two-step reaction that involves a dihydrate intermediate. The reaction pathway and the physico-geometric mechanism are dramatically affected by heating and atmospheric conditions; these experimental factors alter the relative position of the melting of STS-PH with reference to the reaction stage of the thermal dehydration. At temperatures below the melting point of STS-PH and in an open system, the reaction occurs in the solid state as a partially overlapping two-step process regulated by the contracting geometry of the reaction interface. The first and second reaction steps are characterized by an apparent Ea,i of (Ea,1, Ea,2) = (75.5 ± 0.2, 71.6 ± 0.2) kJ mol−1, respectively. However, their apparent rate behaviors are in disagreement with that expected for the simple geometric models that describe the phase boundary-controlled reaction regulated by the contracting geometry, most likely due to the hindrance of diffusional removal of water vapor through the surface product layer and condensation of evolved water vapor. Under a linear increase of the temperature in the open system, the melting of STSPH overlaps with its thermal dehydration to dihydrate, which causes the latter product to exhibit a


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temporary core–shell structure of the molten STS-PH–surface product layer. Therefore, the influence of the liquid-state reaction of the internal the reacting particles on the apparent rate behavior of the subsequent reaction is not so significant. Consequently, hollow particles of dihydrate are produced as the intermediate product. The continuous second reaction step takes place in the solid state producing hollow particles of anhydride. In the semi-sealed system, the melting of STS-PH occurs before the thermal dehydration; therefore, the reaction occurs in the liquid state. The physico-geometric reaction mechanisms of the two reaction steps of the thermal dehydration exhibit a striking difference because they are dramatically affected by the reaction temperature being below or above the boiling point of water. Evaporation of water vapor from the surface of the molten reactant regulates the apparent rate behavior of the first reaction step with an apparent Ea,1 of 67.3  2.4 kJ mol−1. On the other hand, in the second reaction step, the bubbling of water vapor in the reactant liquid determined the apparent rate behavior, producing the anhydride as a sponge-like agglomerate. In conclusion, a variety of physicogeometric events that depend on the reaction conditions are involved in the thermal dehydration of STSPH. These features create specific geometrical configurations of reactant and product, and regulate the reaction by specific physico-geometric reaction mechanisms. The self-generated reaction geometry and reaction pathway are responsible for the largely different morphologies adopted by the anhydride product.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: ??????????. S1. Calibration of Instruments; S2. Sample Characterization (Figures S1 and S2); S3. Thermal Behavior (Figures S3–S7); S4. Kinetic Behavior of Thermal Dehydration in the Solid State



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(Figure S8, Tables S1 and S2); and S5. Variation of the Reaction Pathway and the Physico-Geometric Mechanism (Figure S9).

AUTHOR INFORMATION Corresponding Author *Tel./fax: +81-82-424-7092. E-mail: [email protected] ORCID Nobuyoshi Koga: 0000-0002-1839-8163 Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS The present work was supported by JSPS KAKENHI Grant Numbers 17H00820 and 16K00966.

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(2)

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(3)

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(12) Donkers, P. A. J.; Sögütoglu, L. C.; Huinink, H. P.; Fischer, H. R.; Adan, O. C. G., A Review of Salt Hydrates for Seasonal Heat Storage in Domestic Applications. Appl. Energy 2017, 199, 4568. (13) Dannemand, M.; Schultz, J. M.; Johansen, J. B.; Furbo, S., Long Term Thermal Energy Storage with Stable Supercooled Sodium Acetate Trihydrate. Appl. Therm. Eng. 2015, 91, 671-678. (14) Dannemand, M.; Johansen, J. B.; Kong, W.; Furbo, S., Experimental Investigations on Cylindrical Latent Heat Storage Units with Sodium Acetate Trihydrate Composites Utilizing Supercooling. Appl. Energy 2016, 177, 591-601. (15) Kong, W.; Dannemand, M.; Johansen, J. B.; Fan, J.; Dragsted, J.; Englmair, G.; Furbo, S., Experimental Investigations on Heat Content of Supercooled Sodium Acetate Trihydrate by a Simple Heat Loss Method. Solar Energy 2016, 139, 249-257. (16) Dannemand, M.; Dragsted, J.; Fan, J.; Johansen, J. B.; Kong, W.; Furbo, S., Experimental Investigations on Prototype Heat Storage Units Utilizing Stable Supercooling of Sodium Acetate Trihydrate Mixtures. Appl. Energy 2016, 169, 72-80. (17) Ma, Z.; Bao, H.; Roskilly, A. P., Study on Solidification Process of Sodium Acetate Trihydrate for Seasonal Solar Thermal Energy Storage. Sol. Energy Mater. Sol. Cells 2017, 172, 99-107. (18) Zhou, G.; Xiang, Y., Experimental Investigations on Stable Supercooling Performance of Sodium Acetate Trihydrate PCM for Thermal Storage. Sol. Energy 2017, 155, 1261-1272. (19) Machida, H.; Sugahara, T.; Hirasawa, I., Relationship between Supercooling Stability and Solution Structure in Sodium Acetate Aqueous Solution. J. Cryst. Growth 2017, 475, 295-299.


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(20) Dannemand, M.; Delgado, M.; Lazaro, A.; Penalosa, C.; Gundlach, C.; Trinderup, C.; Johansen, J. B.; Moser, C.; Schranzhofer, H.; Furbo, S., Porosity and Density Measurements of Sodium Acetate Trihydrate for Thermal Energy Storage. Appl. Therm. Eng. 2018, 131, 707-714. (21) Guarini, G. G. T.; Piccini, S., The Dehydration of Na2S2O3·5H2O Single Crystals as Studied by Thermal Analysis and Optical Microscopy. J. Chem. Soc., Faraday Trans. 1. 1988, 84, (1), 331342. (22) Canbazoğlu, S.; Şahinaslan, A.; Ekmekyapar, A.; Aksoy, Ý. G.; Akarsu, F., Enhancement of Solar Thermal Energy Storage Performance using Sodium Thiosulfate Pentahydrate of a Conventional Solar Water-Heating System. Energy Build. 2005, 37, (3), 235-242. (23) Liu, C.; Wang, C.; Li, Y.; Rao, Z., Preparation and Characterization of Sodium Thiosulfate Pentahydrate/Silica Microencapsulated Phase Change Material for Thermal Energy Storage. RSC Adv. 2017, 7, (12), 7238-7249. (24) Tanaka, H.; Koga, N., Kinetics of the Thermal Dehydration of Potassium Copper(II) Chloride Dihydrate. J. Phys. Chem. 1988, 92, (24), 7023-7029. (25) Koga, N.; Tanaka, H., Kinetic and Morphological Studies of the Thermal Dehydration of Nickel(II) Sulfate Hexahydrate. J. Phys. Chem. 1994, 98, (41), 10521-10528. (26) Koga, N.; Yamada, S.; Kimura, T., Thermal Decomposition of Silver Carbonate: Phenomenology and Physicogeometrical Kinetics. J. Phys. Chem. C 2013, 117, (1), 326-336. (27) Yoshikawa, M.; Yamada, S.; Koga, N., Phenomenological Interpretation of the Multistep Thermal Decomposition of Silver Carbonate to form Silver Metal. J. Phys. Chem. C 2014, 118, (15), 80598070.



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(28) Fujiwara, T.; Yoshikawa, M.; Koga, N., Kinetic Approach to Multistep Thermal Behavior of Ag2CO3–Graphite Mixtures: Possible Formation of Intermediate Solids with Ag2O–Ag and Ag2CO3–Ag Core–Shell Structures. Thermochim. Acta 2016, 644, 50-60. (29) Koga, N.; Maruta, S.; Kimura, T.; Yamada, S., Phenomenological Kinetics of the Thermal Decomposition of Sodium Hydrogencarbonate. J. Phys. Chem. A 2011, 115, (50), 14417-14429. (30) 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, (9), 1880-1889. (31) Koga, N.; Šesták, J., Crystal Nucleation and Growth in Lithium Diborate Glass by Thermal Analysis. J. Am. Ceram. Soc. 2000, 83, (7), 1753-1760. (32) Koga, N.; Criado, J. M.; Tanaka, H., A Kinetic Aspect of the Thermal Dehydration of Dilithium Tetraborate Trihydrate. J. Therm. Anal. Calorim. 2002, 67, (1), 153-161. (33) Koga, N.; Utsuoka, T.; Tanaka, H., Thermal Dehydration of Dipotassium Tetraborate Tetrahydrate and Crystallization of Amorphous Dehydration Product. J. Therm. Anal. Calorim. 2005, 80, (1), 71-75. (34) Koga, N.; Utsuoka, T., Thermal Dehydration of Lithium Metaborate Dihydrate and Phase Transitions of Anhydrous Product. Thermochim. Acta 2006, 443, (2), 197-205. (35) 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, (49), 14477-14486. (36) Tanaka, H.; Koga, N., Self-Cooling Effect on the Kinetics of Nonisothermal Dehydration of Lithium Sulfate Monohydrate. J. Therm. Anal. 1990, 36, (7-8), 2601-2610.


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(37) Koga, N.; Tanaka, H., Effect of Sample Mass on the Kinetics of Thermal Decomposition of a Solid. 1. Isothermal Mass-Loss Process of Molten NH4NO3. Thermochim. Acta 1992, 209, 127-134. (38) Koga, N.; Tanaka, H., Effect of Sample Mass on the Kinetics of Thermal Decomposition of a Solid. 2. Isothermal Dehydration of Li2SO4·H2O. J. Therm. Anal. 1993, 40, (3), 1173-1179. (39) Koga, N.; Tanaka, H., Effect of Sample Mass on the Kinetics of Thermal Decomposition of a Solid. 3. Nonisothermal Mass-Loss Process of Molten NH4NO3. Thermochim. Acta 1994, 240, 141-151. (40) Koga, N.; Criado, J. M., The Influence of Mass Transfer Phenomena on the Kinetic Analysis for the Thermal Decomposition of Calcium Carbonate by Constant Rate Thermal Analysis (CRTA) under Vacuum. Int. J. Chem. Kinet. 1998, 30, (10), 737-744. (41) Vyazovkin, S.; Chrissafis, K.; Di Lorenzo, M. L.; Koga, N.; Pijolat, M.; Roduit, B.; Sbirrazzuoli, N.; Suñol, J. J., ICTAC Kinetics Committee Recommendations for Collecting Experimental Thermal Analysis Data for Kinetic Computations. Thermochim. Acta 2014, 590, 1-23. (42) Liavitskaya, T.; Vyazovkin, S., Discovering the Kinetics of Thermal Decomposition during Continuous Cooling. Phys. Chem. Chem. Phys. 2016, 18, (47), 32021-32030. (43) Liavitskaya, T.; Vyazovkin, S., Delving into the Kinetics of Reversible Thermal Decomposition of Solids Measured on Heating and Cooling. J. Phys. Chem. C 2017, 121, (28), 15392-15401. (44) Koga, N.; Kasahara, D.; Kimura, T., Aragonite Crystal Growth and Solid-State Aragonite–Calcite Transformation: A Physico–Geometrical Relationship via Thermal Dehydration of Included Water. Cryst. Growth Des. 2013, 13, (5), 2238-2246.



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(45) Koga, N.; Nishikawa, K., Mutual Relationship between Solid-State Aragonite–Calcite Transformation and Thermal Dehydration of Included Water in Coral Aragonite. Cryst. Growth Des. 2014, 14, (2), 879-887. (46) Muravyev, N. V.; Koga, N.; Meerov, D. B.; Pivkina, A. N., Kinetic Analysis of Overlapping Multistep Thermal Decomposition Comprising Exothermic and Endothermic Processes: Thermolysis of Ammonium Dinitramide. Phys. Chem. Chem. Phys. 2017, 19, (4), 3254-3264. (47) Yoshikawa, M.; Goshi, Y.; Yamada, S.; Koga, N., Multistep Kinetic Behavior in the Thermal Degradation of Poly(L-Lactic Acid): A Physico-Geometrical Kinetic Interpretation. J. Phys. Chem. B 2014, 118, (38), 11397-11405. (48) Kameno, N.; Yamada, S.; Amimoto, T.; Amimoto, K.; Ikeda, H.; Koga, N., Thermal Degradation of Poly(Lactic Acid) Oligomer: Reaction Mechanism and Multistep Kinetic Behavior. Polym. Degrad. Stab. 2016, 134, 284-295. (49) Stanford, V. L.; Vyazovkin, S., Thermal Decomposition Kinetics of Malonic Acid in the Condensed Phase. Ind. Eng. Chem. Res. 2017, 56, (28), 7964-7970. (50) Taylor, P. G.; Beevers, C. A., The Crystal Structure of Sodium Thiosulphate Pentahydrate. Acta Crystallogr. 1952, 5, (3), 341-344. (51) Padmanabhan, V. M.; Yadava, V. S.; Navarro, Q. O.; Garcia, A.; Karsono, L.; Suh, I. H.; Chien, L. S., Neutron Diffraction Study of Sodium Thiosulphate Pentahydrate, Na2S2O3·5H2O. Acta Crystallogr., Sect. B. 1971, 27, (2), 253-257. (52) Uraz, A. A.; Armagan, N., An X-ray Diffraction Study of Sodium Thiosulphate Pentahydrate, Na2S2O3·5H2O. Acta Crystallogr., Sect. B. 1977, 33, (5), 1396-1399.


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(53) Simon, P., Single-Step Kinetics Approximation Employing Non-Arrhenius Temperature Functions. J. Therm. Anal. Calorim. 2005, 79, (3), 703-708. (54) Koga, N., Ozawa’s Kinetic Method for Analyzing Thermoanalytical Curves. J. Therm. Anal. Calorim. 2013, 113, (3), 1527-1541. (55) Koga, N.; Šesták, J.; Simon, P., Some Fundamental and Historical Aspects of Phenomenological Kinetics in the Solid State Studied by Thermal Analysis. In Thermal analysis of Micro, Nano- and Non-Crystalline Materials, Šesták, J.; Simon, P., Eds. Springer: 2013; pp 1-28. (56) Friedman, H. L., Kinetics of Thermal Degradation of Cha-Forming Plastics from Thermogravimetry, Application to a Phenolic Plastic. J. Polym. Sci. Part C 1964, 6, 183-195. (57) Málek, J., The Kinetic Analysis of Non-Isothermal Data. Thermochim. Acta 1992, 200, 257-269. (58) Koga, N., Kinetic Analysis of Thermoanalytical Data by Extrapolating to Infinite Temperature. Thermochim. Acta 1995, 258, 145-159. (59) Málek, J., A Computer Program for Kinetic Analysis of Non-Isothermal Thermoanalytical Data. Thermochim. Acta 1989, 138, (2), 337-346. (60) Gotor, F. J.; Criado, J. M.; Málek, J.; Koga, N., Kinetic Analysis of Solid-State Reactions: The Universality of Master Plots for Analyzing Isothermal and Nonisothermal Experiments. J. Phys. Chem. A 2000, 104, (46), 10777-10782. (61) Ozawa, T., A New Method of Analyzing Thermogravimetric Data. Bull. Chem. Soc. Jpn. 1965, 38, (11), 1881-1886. (62) Ozawa, T., Non-isothermal Kinetics and Generalized Time. Thermochim. Acta 1986, 100, (1), 109118. 35 ACS Paragon Plus Environment


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(63) Perejón, A.; Sánchez-Jiménez, P. E.; Criado, J. M.; Pérez-Maqueda, L. A., Kinetic Analysis of Complex Solid-State Reactions. A New Deconvolution Procedure. J. Phys. Chem. B 2011, 115, (8), 1780-1791. (64) Svoboda, R.; Málek, J., Applicability of Fraser–Suzuki Function in Kinetic Analysis of Complex Crystallization Processes. J. Therm. Anal. Calorim. 2012, 111, (2), 1045-1056. (65) Koga, N.; Goshi, Y.; Yamada, S.; Pérez-Maqueda, L. A., Kinetic Approach to Partially Overlapped Thermal Decomposition Processes. J. Therm. Anal. Calorim. 2013, 111, (2), 1463-1474. (66) 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, (17), 39984007. (67) Šesták, J.; Berggren, G., Study of the Kinetics of the Mechanism of Solid-State Reactions at Increasing Temperatures. Thermochim. Acta 1971, 3, 1-12. (68) Šesták, J., Diagnostic limits of Phenomenological Kinetic Models Introducing the Accommodation Function. J. Therm. Anal. 1990, 36, (6), 1997-2007. (69) Šesták, J., Rationale and Fallacy of Thermoanalytical Kinetic Patterns. J. Therm. Anal. Calorim. 2011, 110, (1), 5-16. (70) Koga, N.; Šesták, J., Kinetic Compensation Effect as a Mathematical Consequence of the Exponential Rate Constant. Thermochim. Acta 1991, 182, (2), 201-208. (71) Koga, N.; Šesták, J., Further Aspects of the Kinetic Compensation Effect. J. Therm. Anal. 1991, 37, (5), 1103-1108.


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(72) Koga, N., A Review of the Mutual Dependence of Arrhenius Parameters Evaluated by the Thermoanalytical Study of Solid-State Reactions: The Kinetic Compensation Effect. Thermochim. Acta 1994, 244, (1), 1-20. (73) Avrami, M., Kinetics of Phase Change. I. General Theory. J. Chem. Phys. 1939, 7, (12), 11031112. (74) Avrami, M., Kinetics of Phase Change. II. Transformation-Time Relations for Random Distribution of Nuclei. J. Chem. Phys. 1940, 8, (2), 212-223. (75) Avrami, M., Kinetics of Phase Change. III. Granulation, Phase Change, and Microstructure. J. Chem. Phys. 1941, 9, (2), 177-184. (76) Barmak, K., A Commentary on: “Reaction Kinetics in Processes of Nucleation and Growth”. Metall. Mater. Trans. A 2010, 41, (11), 2711-2775. (77) Galwey, A. K.; Hood, W. J., Thermal Decomposition of Sodium Carbonate Perhydrate in the Solid State. J. Phys. Chem. 1979, 83, (14), 1810-1815. (78) Nakano, M.; Fujiwara, T.; Koga, N., Thermal Decomposition of Silver Acetate: PhysicoGeometrical Kinetic Features and Formation of Silver Nanoparticles. J. Phys. Chem. C 2016, 120, (16), 8841-8854.



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Figure 1. Comparison of the TG–DTG–DTA curves for the thermal dehydration of STS-PH (approximately 3.0 mg) in the open and semi-sealed systems recorded at β = 2 K min−1 in flowing N2 (300 cm3 min−1). 51x34mm (300 x 300 DPI)

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Figure 2. Changes in the detailed surface textures and the internal structure of particles dehydrated to three selected degrees of dehydration in the open system in flowing N2 (300 cm3 min−1): (a) the reaction stages of the partially dehydrated samples A–C in the TG–DTA curves, (b) SEM images, and (c) X-CT images. 104x143mm (300 x 300 DPI)


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Figure 3. A series of selected snapshots of the outward appearance of sample particles in an aluminum cell sealed with a cover glass recorded during the DSC measurements at β = 5 K min−1 in flowing N2 (100 cm3 min−1). 107x151mm (300 x 300 DPI)



Figure 4. Changes in the thermal dehydration behavior with β in the open system in flowing N2 (300 cm3 min−1): (a) TG–DTG–DTA curves at different β and (b) changes in the mass loss ratio before and after melting with β. 106x147mm (300 x 300 DPI)


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Figure 5. Changes in the TG–DTG–DTA curves recorded in the semi-sealed system with β. 48x30mm (300 x 300 DPI)



Figure 6. Formal kinetic analysis for the first mass loss process of thermal dehydration in a semi-sealed cell: (a) Friedman plots, (b) Ea values at different α, and (c) experimental master plots. 41x11mm (300 x 300 DPI)


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Figure 7. Formal kinetic analysis for the isothermal dehydration in the open system: (a) isothermal massloss traces at different T (selected), (b) Friedman plots, (c) Ea values at different α. 41x11mm (300 x 300 DPI)



Figure 8. KDA for the isothermal dehydration in the open system in flowing N2 at various constant temperatures below the melting point of STS-PH: (a) typical result of KDA and (b) the experimental master plots of (dαi/dθi) versus αi drawn using the optimized SB(mi, ni, pi) and fit curves by plausible physicogeometric kinetic model functions. 103x141mm (300 x 300 DPI)


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Graphic Abstract 45x25mm (300 x 300 DPI)


Heterogeneous Kinetic Features of the ... - ACS Publications

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