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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Kinetics and Mechanisms of the Thermal Decomposition of Copper(II) Hydroxide: A Consecutive Process Comprising Induction Period, Surface Reaction, and Phase Boundary-Controlled Reaction Masahiro Fukuda, and Nobuyoshi Koga J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b03260 • Publication Date (Web): 29 May 2018 Downloaded from http://pubs.acs.org on May 30, 2018

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The Journal of Physical Chemistry

Kinetics and Mechanisms of the Thermal Decomposition of Copper(II) Hydroxide: A Consecutive Process Comprising Induction Period, Surface Reaction, and Phase Boundary-Controlled Reaction

Masahiro Fukuda 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

This study focused on the kinetics and mechanisms of the thermal decomposition of Cu(OH) 2 as a potential processing route to produce CuO nanoparticles. The physico-geometric reaction behaviors were studied using available physicochemical techniques and microscopic observation. The kinetic modeling of the reaction process to produce CuO nanoparticles was examined via the kinetic analysis of the mass-loss data recorded under different heating conditions. The reaction exhibited specific physico-geometric kinetic characteristics, including an evident induction period, a subsequent sigmoidal mass-loss behavior under isothermal conditions, and a long-lasting reaction tail under linearly increasing temperature conditions. During the first mass-loss step characterized by the sigmoidal mass-loss behavior, the crystallite size of the produced CuO was constant, and the specific surface area increased systematically. The second mass-loss step during the reaction tail was accompanied by the crystal growth of CuO. Therefore, the end of the first mass-loss step was the most efficient reaction stage to obtain CuO nanoparticles. The overall kinetic process that reaches this reaction stage was successfully demonstrated as consecutive physico-geometric processes comprising the induction period, surface reaction, and one-dimensional phase boundary-controlled reaction, providing the kinetic parameters for each component step.


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1. Introduction The syntheses of CuO nanoparticles and nanostructures have attracted significant attentions because of their potential applications as catalysts,1-5 electrodes,6-9 sensors,10-14 and so on. Various synthetic methods and conditions have been examined to obtain CuO with specific sizes and structures for successful applications.15 These synthetic methods involve wet chemical precipitation methods,16-22 thermal decomposition of copper(II) compounds,23-27 thermal oxidation of copper in a solid–gas system,28-31 hydrothermal methods,32-36 electrochemical methods,37, 38 and sonochemical methods.39, 40 Various CuO nanoparticles and nanostructure have been synthesized, e.g., nanoparticles having different sizes23, 25, 41,42 and microstructures with rod,4, 34, 38, 43 needle/fiber,5, 24, 30, 39, 44 wire,28,29, 45,46

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ribbon,16, 47 film/sheet/plate,27, 33, 48, 49 spherical,26, 50 cage,51 dendrite-like,52 flower-like,18-19, 36, 53-

and urchin-like20 shapes. Although the CuO synthetic route in solid–gas systems involving the

thermal decomposition of copper(II) compounds and the thermal oxidation of Cu is classical, the reaction processes are fundamentally important when a large scale and cost effective synthesis of CuO with desired properties is considered. Furthermore, the thermal decomposition of copper(II) compounds in solid state is an important processing step in many newly proposed synthetic methods via the controlled synthesis of precursors using various methods.41-43, 45, 47, 50, 51, 56 Therefore, the precise control of the thermal decomposition processes of copper(II) compounds should be achieved for the successful synthesis of CuO nanoparticles and nanostructures. Cu(OH) 2 and basic copper(II) compounds are the most frequently used precursors for the controlled preparation of CuO. The fundamental information of the thermal decomposition of these



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compounds to form CuO has been reported in views of reaction pathway57-60 and kinetics.61-68 The reaction pathway of the thermal decomposition of these compounds can be classified into two types. One is the single-step reaction of the simultaneous dehydroxylation and decomposition of other anions to produce CuO as observed for Cu(OH) 2 (spertiniite),61 Cu 2 CO 3 (OH) 2 (malachite),60, 63-66, 68 Cu 3 (CO 3 ) 2 (OH) 2 (azurite),65 and Cu 2 NO 3 (OH) 3 (gerhardtite). The other is the successive dehydroxylation and decomposition of the component anions via the stable intermediate mixtures of CuO and dehydroxylated compounds, similar to Cu 4 SO 4 (OH) 6 (brochantite)57-59,

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and

Cu 3 SO 4 (OH) 4 (antlerite).67 Given that the desulfation reactions during the thermal decomposition of basic copper(II) sulfates occur at higher temperatures than the dehydroxylation reaction, the crystal growth of the CuO product is more prompted than those produced by the single-step thermal decomposition of Cu(OH) 2 and other basic copper(II) compounds. For the controlled preparation of CuO nanoparticles and nanostructures via the thermal decomposition of precursors, the successful control of CuO crystal growth is the key factor. Therefore, compounds that decompose to CuO in a single-step reaction and at possibly low temperatures are preferable. The kinetics of the thermal decomposition of Cu(OH) 2 and basic copper(II) compounds are generally very complex in the physico-geometric scheme of the reactions in solid–gas systems.69, 70 The overall rate behavior is controlled by the consecutive and/or concurrent processes of surface reaction (SR), the advancement of the reaction interface, the diffusion of product gas through the surface product layer, the crystal growth of the CuO product, and so on. The reaction proceeds as a result of the mutually interacted behavior and under the as-produced self-generated reaction conditions with geometric constraints.


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Therefore, kinetic behaviors can be largely affected by the morphological characteristics of the reactant (precursor) and the reaction conditions, such as heating and atmospheric conditions. This may lead to variations in the morphology and particle characteristics of the CuO product. Therefore, it is important to investigate the kinetic behavior and its relation to the morphological characteristics of the CuO product in a complex reaction system. The aim is to understand the thermal processing of copper(II) compound precursors to produce CuO with desired morphologies and physicochemical properties. This study focused on the thermal decomposition of Cu(OH) 2 to study the kinetic modeling of the formation process of CuO nanoparticles and nanostructures that possess the simplest composition and reaction pathway. Cu(OH) 2 is a promising precursor for preparing CuO nanoparticles and nanostructures,46 and Cu(OH) 2 itself has the potential to be used as catalyst.71-73 The thermal decomposition of Cu(OH) 2 occurs at lower temperatures than the decomposition temperature region of basic copper(II) compounds. Considering the low crystal growth rate of CuO at low temperatures, it is expected that the relation between the dehydroxylation and crystal growth processes can be more clearly observed than that during the thermal decomposition of basic copper(II) compounds. The physico-geometric reaction behaviors of the thermal decomposition of Cu(OH) 2 in flowing inert gas were revealed using available physicochemical techniques and microscopic observations. Thereafter, the kinetic modeling of the reaction process for the efficient production of CuO nanoparticles was examined through the systematic kinetic analysis of mass-loss data recorded under different heating conditions. The results presented in this article provide useful information for



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studying the thermal decomposition of Cu(OH) 2 with different morphological characteristics and under different reaction conditions. Furthermore, this work is to be a useful index for a comparative studies of the formation kinetics of CuO nanoparticles and nanostructures by the thermal decompositions of different copper(II) compounds.

2. Experimental 2.1 Sample preparation and characterization Stock solutions of CuSO 4 (aq), NH 3 (aq), and NaOH(aq) were prepared by dissolving reagent grade CuSO 4 ·5H 2 O (special grade, > 99.5%, Kishida Chem.), NH 3 (aq) (special grade, 28%, Nacalai Tesque), and NaOH(aq) (special grade, Sigma-Aldrich Japan) into deionized–distilled water, respectively. 4.6 M-NH 3 (aq) was added dropwise at a rate of 2 cm3 min−1 into 0.5 M-CuSO 4 (aq) (100 cm3) until the pH reached approximately 11. The solution was kept at 323 K in a temperature programmable water bath. By mechanically stirring the solution, 1.0 M-NaOH(aq) was added dropwise at a rate 2 cm3 min−1 to the solution until the pH reached 12. The precipitates were collected by suction filtration and washed using deionized–distilled water repeatedly. The precipitates were dried in a vacuum desiccator at ambient temperature for 24 h. The sample was stored in a refrigerator at 278 K before being subjected to various measurements. The morphologies of the samples were observed by scanning electron microscopy (SEM; JSM-6510, JEOL) after coating the sample with a thin platinum layer by sputtering (30 mA, 30 s). The samples were characterized using powder X-ray diffractometry (XRD; RINT 2200V, Rigaku,


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Cu–K α , 40 kV, 20 mA) at a scan speed of 4° min−1. Fourier-transform infrared spectroscopy (FT-IR; FT-IR 8400S, Shimadzu) was also performed by the diffuse reflectance method after diluting the samples with KBr. Thermogravimetry (TG)–differential thermal analysis (DTA) was recorded using a horizontal type TG–DTA instrument (TG/DTA220, SII) for the sample, weighed approximately 5.0 mg into a platinum pan (5 mm in diameter and 2.5 mm in height), by heating at a heating rate β of 5 K min−1 in flowing N 2 (300 cm3 min−1).

2.2 Tracking of thermal decomposition behavior The changes in the crystalline phases of sample during heating under a stepwise isothermal program were investigated using the aforementioned XRD instrument by equipping a programmable heating chamber (PTC-20A, Rigaku). The sample was press-fitted on the platinum plate and heated at β = 2 K min−1 in flowing N 2 (100 cm3 min−1). During the heating program, the sample temperature was maintained at different temperatures for 15 min for XRD measurements (Cu-K α , 40 kV, 20 mA): in steps of 15 K from 353 to 473 K and in steps of 50 K from 473 K to 773 K. The time resolved XRD measurements were also performed at 403 K by repeating XRD measurements at every 15 min for 5 h. A portion of evolved gas during heating the sample (approximately 5.0 mg), weighed in a platinum pan (5 mm in diameter and 2.5 mm in height), at β = 10 K min−1 in flowing He (200 cm3 min−1) in a horizontal type TG–DTA instrument (Thermoplus TG-8120, Rigaku) was introduced into a mass spectrometer (M-200QA, Anelva) via a silica capillary tube (0.075 mm internal diameter)



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heated at 500 K. The mass spectra (MS) of the evolved gas were measured repeatedly in a mass range of 10–50 amu (EMSN 1.0 A, SEM 1.0 kV). To obtain partially decomposed samples to different fractional reaction α, which is defined by the fraction of mass loss with respect to the total mass loss during the overall thermal decomposition, the sample was heated at a constant temperature of 373 K in a TG–DTA instrument (Thermoplus Evo2, Rigaku) under the same conditions for the kinetic measurements described below. The samples that were partially decomposed to α = 0.02, 0.10, 0.25, 0.50, 0.75, and 0.90 were then obtained. Similarly, the samples were heated to different temperatures at β = 3 K min−1 to obtain the samples that were partially decomposed to α = 0.91, 0.94, 0.97, and 1.00. The thermally treated samples were cooled to room temperature in the instrument by confirming no detectable change in the mass by the possible hydration and subsequently observed using the aforementioned SEM instrument after the pretreatments described above were conducted. The samples of 300 ± 5 mg were weighed in an alumina boat (SSA-A, 13.5 mm × 80 mm × 10 mm). The samples were heated in an electric tube furnace (Isuzu) at a constant temperature of 373 K in flowing N 2 (200 cm3 min−1) for different duration times to obtain the samples that were partially decomposed to α = 0.18, 0.39, 0.61, and 0.75. Furthermore, the samples were heated linearly to different temperatures at β = 3 K min−1 to obtain the samples that were partially decomposed to α = 0.89, 0.91, 0.95, and 1.00. After cooling the thermally treated samples to room temperature, each sample was heated in a U-tube sample holder at 323 K for 30 min in flowing mixed gas of He–N 2


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(30% N 2 ). Subsequently, the specific surface area was measured using an instrument (FlowSorb2300II, Micromeritics) via the single-point method of Brunauer–Emmett–Teller (BET).

2.3 Measurement of kinetic data The sample (3.00 ± 0.05 mg) was weighed into a platinum pan (5 mm in diameter and 2.5 mm in height). TG–derivative TG (DTG) measurements were performed using a horizontal TG–DTA instrument (Thermoplus Evo2, Rigaku) by heating the sample in N 2 flow (300 cm3 min−1) under different temperature program modes, including isothermal, linear nonisothermal, and controlled transformation rate thermal analysis (CRTA)74,75 modes. The isothermal mass-loss curves were recorded at different constant temperatures in the range of 380–410 K in steps of 5 K after heating the sample to the temperatures at β = 10 K min−1. Five different β ranging from 0.5 to 5 K min−1 were employed for recording the mass-loss curves by heating the sample from room temperature to 773 K under linearly increasing temperature conditions. The measurements under CRTA modes were performed by heating the sample at β = 1 K min−1, and the mass-loss rate was controlled to be seven different constant transformation rates C ranging from 3.0 to 12.0 μg min−1 during the course of the mass-loss process via the feedback control of the heating/cooling rate through monitoring the DTG signal.74, 75 All TG–DTA instruments used in this study were preliminarily calibrated with regard to temperature and mass change by using the standard procedures as described in the Supporting Information.



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3. Result and discussions 3.1 Characterization of sample Figure S1 shows the typical SEM images of the sample. The sample is an aggregate of needle-like crystals and each needle-like crystal has a length of approximately 3–5 μm. The specific surface area (S BET ) of the sample was 5.28 ± 0.03 m2 g−1. Figures S2 and S3 show the XRD pattern and FT-IR spectrum of the sample, respectively. The XRD pattern agrees perfectly with that reported previously for Cu(OH) 2 (orthorhombic, S.G. = Cmc21(36), a = 2.9471, b = 10.5930, c = 5.2564, α = β = γ = 90.000, ICDD-PDF 01-080-0656).76,77 The FT-IR spectrum exhibits the absorption peaks of O–H stretching vibrations at 3572 and 3300 cm−1 as free and hydrogen bonded O−H groups, respectively.78 The absorption peaks that appeared in the range of 400–1000 cm−1 are attributed to the Cu–O–H bond.78 The absorption peaks attributed to sulfate and ammonium ions were not observed; these ions were the components of the mother solution used for preparing the sample. Figure S4 shows the TG–DTG–DTA curves for the thermal decomposition of the sample. The TG curve exhibits rapid mass loss initiated at approximately 405 K, and an evident reaction tail continued to 650 K. The total mass-loss value during thermal decomposition was 18.67 ± 0.19%, which is slightly larger than the calculated value (18.45%) for the reaction. Cu(OH) 2 → CuO + H 2 O

(1)

The observed difference is related to the absorbed water released at a temperature lower than that of the main thermal decomposition. The mass-loss values of the major part with rapid mass-loss process


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(the first mass-loss step) and the reaction tail with gradual mass-loss process (the second mass-loss step) were 16.90 ± 0.09% and 1.77 ± 0.12%, respectively.

3.2 Thermal behavior Figure 1 shows the results of the TG/DTA–MS measurements. The evolved gas during thermal decomposition was exclusively water vapor for both the first and second mass-loss steps.

Figure 1. TG–DTA curves and the MS ion thermogram for m/z =18 recorded during heating the sample (m 0 = 5.027 mg) at β = 10 K min−1 in flowing He (200 cm3 min−1).

Figure 2 shows the changes in the XRD pattern during isothermal heating at 403 K in flowing N 2 (100 cm3 min−1). The attenuation of the diffraction peaks attributed to Cu(OH) 2 was first observed after heating the sample at 403 K for approximately 100 min (Figure 2a), thus indicating the possible existence of the induction period (IP) for the reaction. The diffraction peaks of Cu(OH) 2 completely disappeared in the XRD pattern at 255 min. Instead, the diffraction peaks of CuO (monoclinic, S.G. ACS Paragon Plus 11 Environment


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= C2/c(15), a = 4.6840, b = 3.4273, c = 5.1316, α = γ = 90.000, β = 99.510, ICDD-PDF 01-0777716)77,

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grow gradually as the reaction advances, and the XRD pattern at 285 min perfectly

corresponds to CuO (Figure 2b). The changes in the crystallite sizes of Cu(OH) 2 and CuO were estimated roughly using the Scherrer equation80, and the results indicated gradual decrease in the crystallite size of Cu(OH) 2 as the reaction advances (Figure 2c). However, the crystallite size of asproduced CuO by thermal decomposition did not change during the reaction. Therefore, it is speculated that the crystal growth of CuO is neglected during the reaction under isothermal conditions.


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Figure 2. Changes in the XRD pattern of the sample during isothermal heating at T = 403 K in flowing N 2 (100 cm3 min−1): (a) XRD patterns at different heating times, (b) XRD pattern of the product, and (c) changes in Cu(OH) 2 and CuO crystallite sizes with heating time.

Figure 3 shows the changes in the XRD pattern of the sample during stepwise isothermal heating in flowing N 2 (100 cm3 min−1). The XRD pattern attributed to Cu(OH) 2 gradually diminishes from a temperature of 398–413 K, thus indicating the initiation of the thermal decomposition (Figure



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3a). At the same time, the XRD peaks of CuO start to appear in the same temperature region. The XRD peaks of Cu(OH) 2 perfectly disappear at a temperature in the range of 428–443 K, which corresponds to the end of the first mass-loss step. During further heating, the intensity of the diffraction peaks of CuO increases gradually. A rough estimation of the crystallite size using the Scherrer equation indicates a continuous increase in the CuO crystallite size in the temperature range of the second mass-loss step by increasing the sample temperature (Figure 3b). Thus, the second mass-loss step observed as the reaction tail can be correlated with the crystal growth of CuO and accompanied release of H 2 O trapped in the pores, interstices, and cores of the CuO crystallite agglomerates in the poorly crystalline CuO.


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Figure 3. Changes in the XRD pattern of the sample during stepwise isothermal heating in flowing N 2 (100 cm3 min−1): (a) XRD patterns at different temperatures and (b) changes in CuO crystallite size with temperature.

Figure 4 shows the changes in the S BET of the sample heated isothermally at 373 K for different duration times and nonisothermally to different temperatures at β = 3 K min−1 in flowing N 2 (200 cm3 min−1). Under the isothermal condition, S BET value starts to increase after heating the sample for 120 min (Figure 4a). This result also indicates the existence of the IP. During the nonisothermal heating, S BET increases in the temperature range of the first mass-loss step and reaches the maximum of 65.3 m2 g−1 at 473 K, which approximately corresponds to the end of the first mass-loss step (Figure 4b). The S BET decreases by further heating to the higher temperatures via the crystal growth of CuO during the second mass-loss step observed as the reaction tail.



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Figure 4. Changes in the S BET of the sample during heating in flowing N 2 (200 cm3 min−1): (a) under isothermal conditions at T = 373 K and (b) under nonisothermal conditions at β = 3 K min−1.

Figure S5 compares the SEM images of the surface textures of the sample decomposed to different α under isothermal and nonisothermal conditions. The sample that decomposed to α = 0.50 under isothermal conditions at 373 K for 120 min represents the cleavage of original needle-like crystals in the length direction and the branching (Figure S5a). Each branch approximately constricted the regular interval. The cleavage and branching of the needle-like crystals may be induced by the reaction on the original surface, and the reaction on the surface promotes their constriction. These phenomena may occur because of the mechanical stress accompanying the formation of the solid product layer on the surface of the original needle-like crystals and branches. After further heating at the constant temperature, the branches fracture at the constrictions as seen from the surface texture of the sample that decomposed isothermally to α = 0.90 at 373 K for 220 min (Figure S5b). The morphological changes of the sample crystals, including cleavage, constriction, and fracture, can also explain the gradual increase in S BET during isothermal heating (Figure 4a). The surface texture of the sample heated under nonisothermal conditions at β = 3 K min−1 up to the end of the first mass-loss step (Figure S5c, 473 K, α = 0.94) also indicates the cleavage and branching. The diameter size of the branch is smaller in comparison with that produced by the isothermal heat treatment. The more evident cleavage and branching under nonisothermal conditions can explain the maximum S BET of the sample at the end of the first mass-loss step (Figure 4b). After further heating to the end of the ACS Paragon Plus 16 Environment

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second mass-loss step, the branches aggregate by sintering (Figure S5d, 673 K, α = 1.00), which is accompanied by the gradual decrease in S BET during the second mass-loss step (Figure 4b). Figure S6 shows the mass-loss curves recorded under different temperature program modes of isothermal, linear nonisothermal, and CRTA. The isothermal mass-loss curves recorded at different constant temperatures (Figure S6a) clearly exhibit the existence of the IP. A long IP is observed for the measurement at low constant temperatures. The IP observed during the thermal decomposition of solids is understood as the time required for the formation of possible nucleation sites on the reactant surface.81-85 The mass-loss values did not vary practically with the measured constant temperature and was determined to be 17.00 ± 0.30%, which closely corresponds to the mass-loss value of the first mass-loss step. The mass-loss curves recorded under linear nonisothermal conditions at different β (Figure S6b) indicate two mass-loss steps as described above. The mass-loss values of each massloss step did not change with β and had average values of 16.36 ± 0.29% and 1.87 ± 0.50%. The mass-loss measurements under controlled mass-loss rates (Figure S6c) were not very successful, particularly in the initial part of the reaction because the mass-loss rate cannot be controlled precisely owing to the rapid mass loss at the beginning of the reaction. However, the residual mass-loss process during the first mass-loss step was approximately controlled at the programed C. The two-step massloss behavior was also observed by the measured temperature profile that indicated the gradual temperature change and the subsequent rapid temperature increase regions. The mass-loss values for the first and second steps recorded under CRTA conditions were 16.95 ± 1.02% and 2.40 ± 0.17%, respectively, which are in agreement with those determined under linear nonisothermal conditions.



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3.3 Kinetic analysis of the induction period Figure 5 illustrates the kinetic analysis for the IP using the isothermal mass-loss curves at different temperatures. The duration time for the IP (t IP ) was determined empirically as the intersection point of two tangent lines drawn before initiating the mass loss and at a mass-loss value of 0.1%. The t IP value was decreased exponentially by increasing the temperature (Figure 5a). The reciprocal value of t IP can be treated as the average rate of the kinetic process during the IP. The kinetic equation for the IP is expressed by assuming the Arrhenius type temperature dependence of the average rate. 83-87  E  1 = AIP exp − a, IP  f (α IP ) t IP  RT 

(2)

where A IP and E a,IP are the apparent pre-exponential factor and activation energy for the IP, respectively. R and α IP are the gas constant and fractional conversion of a chemical process that occurs during the IP, respectively. The function f(α IP ) is the kinetic model function for the IP. By taking logarithms of both sides of eq. (2), eq.(3) is obtained: E  1  ln  = ln[AIP f (α IP )] − a, IP RT  t IP 

(3)

Given that the α IP value at the point indicating the same conversion rate as the average rate should be the same for all data at different temperatures, the logarithmic term in the right hand of eq. (3) can be treated as a constant. The Arrhenius-type plot of ln(1/t IP ) versus 1/T for the IP of the thermal decomposition indicates an statistically significant linear correlation (r2 > 0.98, Figure 5b). From the slope of the plot, E a,IP value was estimated to be 196.8 ± 16.7 kJ mol−1. ACS Paragon Plus 18 Environment

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Figure 5. Kinetic analysis for the IP of the thermal decomposition of Cu(OH) 2 : (a) changes in the duration time of the IP with temperature and (b) the Arrhenius-type plot for the IP.

3.4. Kinetic analysis for the first mass-loss step Figure 6 shows the kinetic data for the first mass-loss step (the first reaction step), measured under isothermal (Figure 6a), linear nonisothermal (Figure 6b), and CRTA (Figure 6c) conditions. The fractional conversion α 1 for the first reaction step was defined by referencing the total mass-loss value for the isothermal mass-loss data and to the mass-loss value during the first mass-loss step for the mass-loss data under linear nonisothermal and CRTA conditions. For the isothermal kinetic data (Figure 6a), the reaction time was defined by setting the time of initial mass-loss observed to be zero.



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Figure 6. Kinetic data for the first reaction step of the thermal decomposition of Cu(OH) 2 converted from the mass-loss curves recorded under different temperature profiles in flowing N 2 (300 cm3 min−1): (a) under isothermal conditions at different T, (b) under linear nonisothermal conditions at different β, and (c) under controlled transformation rate conditions at different C.

The kinetic data under different temperature profiles were simultaneously analyzed using the fundamental kinetic equation for the single-step reaction.88-91

 E  dα 1 = A1 exp − a, 1  f (α1 ) dt  RT 

(4)


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where A 1 and E a,1 are the apparent Arrhenius parameters, i.e., the pre-exponential factor and activation energy, respectively. The kinetic model function f(α 1 ) describes the physico-geometric reaction mechanism of the thermal decomposition of solids. The apparent E a,1 values at different α 1 were determined by the Friedman plot92 on the basis of the logarithmic form of eq. (4).

E  dα  ln 1  = ln[A1 f (α1 )] − a, 1 RT  dt 

(5)

When the reaction mechanism does not change within the temperature conditions under investigation, the ln (dα 1 /dt) versus T−1 plot for the data points at the selected α 1 represents a straight line with the slope of –E a,1 /R because the constancy of ln[A 1 f(α 1 )] is preserved. The results of formal kinetic analysis using the Friedman and master plot88-89, 93-95 methods are shown in Figure 7. The plots for the data points at the selected α 1 , including all kinetic data under different temperature profiles, exhibit excellent linear correlation with the correlation coefficient of the linear regression analysis better than −0.99 (0.08 ≤ α 1 ≤ 0.92, Figure 7a). The E a,1 values at different α 1 calculated from the slopes indicate a constant value during the main part of the reaction with an average value of 119.0 ± 2.0 kJ mol−1 (0.10 ≤ α 1 ≤ 0.80, Figure 7b). This indicates the uniform reaction mechanism within the measured temperature conditions. The gradual decrease in the E a,1 value observed in the initial part of the reaction can be explained by the contribution of the surface nucleation and growth process, which is expected from the evident IP of this reaction. The variation in the E a,1 value in the final part of the first reaction step is likely attributed to the phenomena related to the diffusional removal of water vapor. As mentioned above, the subsequent reaction step is the removal of water vapor accompanied by the growth of CuO crystallites. Therefore, the diffusional ACS Paragon Plus 21 Environment


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removal of water vapor trapped in the pores, interstices, and cores of the CuO crystallite agglomerates of the CuO product seems to become gradually difficult during the final part of the first reaction step.

Figure 7. The results of formal kinetic analysis for the first reaction step of the thermal decomposition of Cu(OH) 2 using the Friedman and master plot methods: (a) Friedman plots at different α 1 , (b) E a,1 values at different α 1 , and (c) experimental master plot of (dα 1 /dθ 1 ) versus α1 .


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By using the average E a,1 value for the main part of the first reaction step (0.10 ≤ α 1 ≤ 0.80), the rate behavior at the infinite temperature was simulated as the experimental master plot of (dα 1 /dθ 1 ) versus α 1 .88, 89, 93-95

E  dα 1 d α 1 = exp a, 1  = A1 f (α1 ) with dθ1 dt  RT 

t



θ1 = ∫ exp − 0



Ea, 1  dt RT 

(6)

where θ 1 is the generalized time proposed by Ozawa96, 97 and denotes the hypothetical reaction time at infinite temperature. The experimental master plot indicates superficially an autocatalytic-type reaction behavior and correctly reflects the feature of the sigmoidal mass-loss curves at constant temperatures (Figure 7c). The apparent shape of the experimental master plot was fitted using an empirical kinetic model function known as Šesták–Berggren model with three kinetic exponents (SB(m, n, p)).98-100 SB(m, n, p): f (α ) = α m (1 − α )n [− ln (1 − α )]p

(7)

The best fit was obtained using SB(1.00, 0.94, −0.30), which slightly deviated from the homogeneous autocatalytic model expressed by SB(1, 1, 0). An alternative possible model applicable to the sigmoidal mass-loss curves is a nucleation–growth model, e.g., Johnson–Mehl–Avrami model (JMA(m)).101-103 JMA(m): f (α ) = m(1 − α )[− ln (1 − α )]1−1/ m

(8)

The experimental master plot was fitted by JMA(1.91). However, the fit was not superior to that of SB(1.00, 0.94, −0.30). Given the systematic change in the apparent E a,1 during the initial part of the reaction (Figure 7b), the overall process of the first reaction step cannot fully be described by the well-defined physico-geometric kinetic model.



Page 24 of 58

3.5. Kinetic analysis based on the induction period–surface reaction–phase boundary-controlled reaction model The sigmoidal shape of the integral kinetic curve for the first reaction step, as revealed by the isothermal mass-loss curves (Figure 6a) and experimental master plot (Figure 7c), is also interpreted as the physico-geometric consecutive process of SR and subsequent phase boundarycontrolled reaction (PBR) regulated by contracting geometry. The consecutive SR–PBR reaction is also supported by the existence of the evident IP and the systematic decrease in the apparent E a,1 value in the initial part of the reaction observed for the present reaction. This type of kinetic interpretation has been proposed by Mampel,104 and the integral kinetic approach based on the Mampel’s model has been examined.105-108 A detailed theoretical consideration for this type of consecutive reaction was made by Favergeon et al. as nucleation and anisotropic reaction.109 Recently, Ogasawara and Koga developed a differential kinetic approach to this type of reaction by deriving a combined kinetic equation for an IP–SR–PBR model with different contracting dimensions n at a constant temperature.85 For example, for the first-order SR and subsequent one-dimensional PBR, i.e. IP–SR–PBR(1), the overall reaction rate (dα 1 /dt) is expressed by eq. (9) and (10): a) t − t IP ≤ 1 / k PBR :

dα1 = kPBR [1 − exp(−kSR (t − tIP ))] dt

b) t − t IP ≥ 1 / k PBR :

  k dα1 = k PBR exp(−kSR (t − t IP )) exp SR dt   k PBR

(9)

   − 1  

(10)

where k SR and k PBR are the rate constants for the SR and PBR, respectively. Similar sets of kinetic equations at constant temperature are available for the respective shrinkage dimensions n.108 The ACS Paragon Plus 24 Environment

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kinetic equations of the IP–SR–PBR(n) with n = 2 and 3 are listed in Table S1. The results of the preliminary kinetic analyses for the IP and first reaction step can be used to determine the initial t IP and k PBR values at each reaction temperature. After setting the t IP and k PBR values in the kinetic equations for the IP–SR–PBR model, the initial k SR value was determined by comparing the calculated curve on the basis of the kinetic equation with the experimental kinetic curve. Thereafter, the optimization of the three rate constants was performed to minimize the sum of the squares of the residues by nonlinear least squares analysis.

 dα  F = ∑  1  j =1   dt  exp, j M

 dα   − 1    dt  cal, j 

2

(11)

where M is the number of data points. Figure 8 shows the typical results of the nonlinear least squares analysis based on the IP– SR–PBR models performed for the IP and first reaction step of the thermal decomposition of Cu(OH) 2 at 389 K. The optimized rate constants of t IP −1, k SR , and k PBR at different temperatures based on the IP–SR–PBR models with different interface advancement dimensions n are listed in Table S2, together with the determination coefficient of the nonlinear least squares analysis (r2). Irrespective of reaction temperature, the most statistically significant fit to the experimental kinetic curve was obtained for the IP–SR–PBR model with the one-dimensional advancement of the reaction interface. The t IP value optimized via kinetic analysis was practically identical with that of preliminary kinetic analysis (Figure 5). The optimized k SR and k PBR values varied systematically with reaction temperature. Figure 9 shows the Arrhenius plots for k SR and k PBR values determined using the IP– SR–PBR model with one-dimensional interface advancement. Both Arrhenius plots exhibited good ACS Paragon Plus 25 Environment


Page 26 of 58

linearity with a correlation coefficient better than −0.995. The apparent Arrhenius parameters for IP, SR, and PBR steps are summarized in Table 1. Both the E a values for SR and PBR were much smaller than the E a for IP and were practically identical within the standard error. The values were also close to the E a value of the main reaction part of the first reaction step evaluated by the isoconversional method (Figure 7b).

Figure 8. The results of kinetic analysis based on IP–SR–PBR models for the reaction at 389 K: (a) one-dimensional, (b) two-dimensional, and (c) three-dimensional interface shrinkage.


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Figure 9. The Arrhenius plots for k SR and k PBR determined through the kinetic analysis based on IP– SR–PBR model with one-dimensional interface advancement.

Table 1. Apparent Arrhenius parameters for IP, SR, and PBR(n =1) for the IP and first reaction step of the thermal decomposition of Cu(OH) 2 Step

E a / kJ mol−1

ln (A / s−1)

γa

IP

196.8 ± 16.7

54.3 ± 5.1

−0.9894

SR

127.0 ± 6.0

32.9 ± 1.8

−0.9967

PBR

124.6 ± 6.0

31.4 ± 1.8

−0.9966

a

correlation coefficient of the linear regression analysis of the Arrhenius plot.

The results of the kinetic analysis based on the IP–SR–PBR model are indicative of the possible distribution of the reaction initiation time among needle-like crystals. The decrease in the apparent E a value in the initial part of the first reaction step evaluated by the isoconversional method (Figure 7b) can be interpreted by correlating the variations in the number of reacting crystals with the heating conditions. The E a,SR value evaluated for the SR (Table 1) approximately corresponds to the



Page 28 of 58

average E a,1 value in the range α 1 ≤ 0.1. When assuming that the PBR in each crystal initiated immediately after the nucleation in that crystal, the expected one-dimensional PBR may indicate the advancement of the reaction interface to the length direction of the needle-like crystals. The E a,PBR value for PBR (Table1) was comparable with the average E a value for the main part of the reaction evaluated by the isoconversional method (Figure 7b).

4. Conclusion The thermal decomposition of needle-like Cu(OH) 2 crystals exhibited specific kinetic features involving an evident IP, sigmoidal mass-loss curves under isothermal conditions, and a longlasting reaction tail that continues to the temperature higher by approximately 200 K than the end of the main mass-loss process under linearly increasing temperature conditions. When the IP was considered as the period in the chemical process wherein the first nucleation site was formed, the apparent E a,IP value was estimated to be approximately 197 kJ mol−1 from the Arrhenius-type temperature dependence of the average rate of the chemical process, as deduced from the duration time of the IP at different constant temperatures. During the subsequent mass-loss process under isothermal conditions, the specific surface area of the sample increased systematically as the reaction advanced, while the crystallite size of the as-produced CuO remained unchanged. The isothermal mass-loss process was terminated, leaving approximately 10% mass loss to complete the thermal decomposition. The first mass-loss step, which was the main reaction part before the termination, was described by a nearly constant E a,1 value of 119.0 ± 2.0 kJ mol−1 (0.10 ≤ α 1 ≤ 0.80). The experimental


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master plot exhibited a nucleation and growth-type shape expected from the sigmoidal mass-loss curve under isothermal conditions. The subsequent process occurred in a wide temperature range to complete the thermal decomposition of Cu(OH) 2 under linearly increasing temperature conditions. During the second mass-loss step, the gradual mass loss was accompanied by the growth of the crystallite size of the CuO product and by the decrease in the specific surface area. Therefore, the second mass-loss step can be interpreted as the evolution of trapped water molecules in the pores, interstices, and cores of the CuO crystallite agglomerates regulated by the crystal growth of the CuO product. From the view point of CuO nanoparticle formation, the end of the first mass-loss step was considered as the most appropriate stage. For the consecutive processes of the IP and the sigmoidal first mass-loss step of the thermal decomposition of Cu(OH) 2 for producing a CuO nanoparticle, a combined kinetic model comprising the IP–SR–PBR was applicable. The model for the onedimensional reaction interface advancement was selected as the most appropriate model to describe the experimental kinetic data under isothermal conditions. In this scheme, the reaction in the needlelike Cu(OH) 2 crystal initiated randomly on the surfaces, after the IP with the distribution of the reaction initiation time. Once the reaction initiated in each crystal, the reaction interface advanced in a one-dimensional manner from the initial nucleation sites. The Arrhenius parameters (E a kJ mol−1, ln (A / s−1)) for IP, SR, and PBR were estimated to be (196.8 ± 16.7, 54.3 ± 5.1) IP , (127.0 ± 6.0, 32.9 ± 1.8) SR , and (124.6 ± 6.0, 31.4 ± 1.8) PBR , respectively.



Page 30 of 58

ASSOCIATED CONTENT Supporting Information

The Supporting Information is available free of charge on the ACS Publications website at DOI: ????????.

S1. Calibration for Thermal Analysis; S2. Sample Characterization (Figures S1–S4); S3. Thermal Behavior (Figures S5 and S6); S4. Kinetic Analysis Based on the IP–SR–PBR model (Tables S1 and S2).

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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Figure 1. TG–DTA curves and the MS ion thermogram for m/z =18 recorded during heating the sample (m0 = 5.027 mg) at β = 10 K min−1 in flowing He (200 cm3 min−1). 59x46mm (300 x 300 DPI)

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Figure 2. Changes in the XRD pattern of the sample during isothermal heating at T = 403 K in flowing N2 (100 cm3 min−1): (a) XRD patterns at different heating times, (b) XRD pattern of the product, and (c) changes in Cu(OH)2 and CuO crystallite sizes with heating time. 154x313mm (300 x 300 DPI)


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Figure 3. Changes in the XRD pattern of the sample during stepwise isothermal heating in flowing N2 (100 cm3 min−1): (a) XRD patterns at different temperatures and (b) changes in CuO crystallite size with temperature. 117x179mm (300 x 300 DPI)



Figure 4. Changes in the SBET of the sample during heating in flowing N2 (200 cm3 min−1): (a) under isothermal conditions at T = 373 K and (b) under nonisothermal conditions at β = 3 K min−1. 73x70mm (300 x 300 DPI)


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Figure 5. Kinetic analysis for the IP of the thermal decomposition of Cu(OH)2: (a) changes in the duration time of the IP with temperature and (b) the Arrhenius-type plot for the IP. 60x48mm (300 x 300 DPI)



Figure 6. Kinetic data for the first reaction step of the thermal decomposition of Cu(OH)2 converted from the mass-loss curves recorded under different temperature profiles in flowing N2 (300 cm3 min−1): (a) under isothermal conditions at different T, (b) under linear nonisothermal conditions at different β, and (c) under controlled transformation rate conditions at different C. 129x220mm (300 x 300 DPI)


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Figure 7. The results of formal kinetic analysis for the first reaction step of the thermal decomposition of Cu(OH)2 using the Friedman and master plot methods: (a) Friedman plots at different α1, (b) Ea,1 values at different α1, and (c) experimental master plot of (dα1/dθ1) versus α1. 156x323mm (300 x 300 DPI)



Figure 8. The results of kinetic analysis based on IP–SR–PBR models for the reaction at 389 K: (a) onedimensional, (b) two-dimensional, and (c) three-dimensional interface shrinkage. 104x143mm (300 x 300 DPI)


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Figure 9. The Arrhenius plots for kSR and kPBR determined through the kinetic analysis based on IP–SR–PBR model with one-dimensional interface advancement. 55x40mm (300 x 300 DPI)



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