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Kinetics, Catalysis, and Reaction Engineering

Characterization of Carbon/Carbon Composites by Kinetic Deconvolution Analysis for a Thermal Oxidation Process: An Examination Using a Series of Mechanical Pencil Leads Daichi Hara, Kazuyuki Nishikawa, and Nobuyoshi Koga Ind. Eng. Chem. Res., Just Accepted Manuscript • Publication Date (Web): 08 Oct 2018 Downloaded from http://pubs.acs.org on October 8, 2018

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Industrial & Engineering Chemistry Research

Characterization of Carbon/Carbon Composites by Kinetic Deconvolution Analysis for a Thermal Oxidation Process: An Examination Using a Series of Mechanical Pencil Leads

Daichi Hara, Kazuyuki Nishikawa, 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 behaviors of carbon/carbon (C/C) composites in flowing air were investigated on the basis of mechanical pencil leads with different hardness values and diameter sizes as a model system. Two separated mass-loss processes were observed during heating the mechanical pencil leads in air, which are attributed to the evaporation/decomposition of an impregnation agent and the subsequent thermal oxidation of the residual C/C composite. The thermal behaviors were invariant among the mechanical pencil leads with different diameter sizes, but they systematically changed with hardness. Variations in the thermal behaviors can be quantified by the mass-loss value during the evaporation/decomposition of the impregnation agent, in addition to the kinetic deconvolution analysis that was applied to the multistep thermal oxidation process of carbon components with different reactivities. These results correlate the thermal behavior with the compositional and structural characteristics of C/C composites, which can be useful for characterization and product control.

Keywords: Carbon/carbon composite, Mechanical pencil lead, Thermal analysis, Multistep thermal oxidation, Kinetic deconvolution analysis


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1. Introduction Carbon/carbon (C/C) composites have attracted great attention as a promising material having various potential applications. Research is still in progress to further sophisticate their physical properties, such as lightness, strength, and conductivity, by examining novel component carbon materials with different crystallographic and morphological characteristics and configuring these carbon materials.1-5 Simultaneously, improving the thermal stability of C/C composites in an oxidizing atmosphere is necessary to expand its practical applicability. The kinetics and mechanisms of thermal oxidation of C/C composites are thus necessary for characterizing and improving their thermal stability, which also provide a guide for a safety assessment of applications. Therefore, huge efforts have been made to gain reasonable kinetic descriptions for thermal oxidation processes.6-22 Thermal oxidation of carbon materials is a class of complex heterogeneous processes in solid–gas systems. Even the thermal oxidation of graphite, which is well defined in view of crystallography and morphology, is not necessarily a simple single-step reaction.23-34 The reaction process is controlled by the mass transfer phenomena of the reactant and product gases, that is, O2 and CO2, respectively, in the geometrical constraint of reactant solid–gas contact and diffusional removal of product gas.35 In addition, the heat transfer phenomena that originated from the great exothermic effect of the reaction make it challenging to collect reliable data for kinetic calculations.36 These situations are further complicated in C/C composites.9,11-13 Multiple carbon components with different reactivities, which are bonded with each other, are configured with a regulated or random orientation to form a composite. In addition to the intrinsic reactivity of each carbon material, the reactivity and thermal oxidation kinetics of C/C composites are controlled by the characteristics of carbon–carbon junctions and pore structures as well. Therefore, secondary physicogeometric constraints are introduced into the kinetics and mechanisms of the overall thermal oxidation reaction. As a result, multistep thermal oxidation behaviors are reported for many C/C composites.6,15,18,20,21 For example, Guo and Xiao20 illustrated well the complexity of the multistep thermal oxidation of a carbon fiber/carbon composite. The two-step thermal oxidation comprises reactions of matrix carbon 3 ACS Paragon Plus Environment


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components and carbon fibers. The rate-limiting step also changes from the chemical reaction to gaseous diffusion by increasing the reaction temperature. Furthermore, multistep thermal oxidation occurs with partial overlapping between the component reaction steps. As a possible kinetic approach to such a multistep heterogeneous process of the thermal oxidation of C/C composites, the applicability of the kinetic deconvolution analysis (KDA)37,38 was examined in our previous study.39 KDA is based on the cumulative kinetic equation and the kinetic calculations of multiple nonlinear least squares analysis. Mechanical pencil leads, which were manufactured by two different companies, were used as typical C/C composites. The mechanical pencil leads can be treated as a class of C/C composite comprising graphite particles and the pyrolytic carbon matrix produced by the calcination of the shaped graphite–polymer mixture in an inert atmosphere. The results of KDA revealed the contributions and kinetic characteristics of each reaction step of the two partially overlapping thermal oxidation steps that are attributed to the component pyrolytic carbon and graphite in mechanical pencil leads. In addition, the differences in the kinetic behavior between two mechanical pencil leads were expected to originate from the compositional and structural characteristics. If the kinetic results of the multistep thermal oxidation process could be correlated to the compositional and structural characteristics of C/C composites, such correlation can be a useful index for improving their thermal stability and a measurement of their quality control. In this study, a series of mechanical pencil leads with different hardness values and diameter sizes, manufactured by one company, were used as the test system. It was expected that these mechanical pencil leads were manufactured using the same starting materials and comparable processing methods. Different mixing ratios of graphite and polymer binder, however, were used for preparing the mechanical pencil leads with different hardness values. The compositions of graphite/pyrolytic carbon were thus systematically changed. The thermal behaviors of these mechanical pencil leads in flowing air were initially investigated. Then, the systematic changes in the rate behavior of the two-step thermal oxidation process with the hardness of the mechanical pencil lead were quantified through a kinetic analysis using KDA. The correlation of the changes in 4 ACS Paragon Plus Environment

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contributions and kinetic parameters of each component oxidation step with the compositional and structural characteristics of the mechanical pencil leads was examined in order to discuss the possibility of using semiempirical relationships as one measure for characterizing C/C composites.

2. Experimental 2.1. Samples and characterization Mechanical pencil leads with different hardness values (4B–4H, diameter size: 0.5 mm) and different diameter sizes (0.3–0.9 mm, hardness: HB) manufactured by a Japanese company was used as the samples. One of these samples (diameter: 0.5 mm, hardness: HB) has been characterized in our previous work39 using pyrolysis-gas chromatography/mass spectroscopy (Py-GC/MS), powder X-ray diffractometry, optical microscopy, scanning electron microscopy (SEM), energy-dispersive X-ray (EDX) spectroscopy, and thermogravimetry–differential thermal analysis (TG–DTA). The lead surface that was coated with wax showed regularly arranged valleculae along the direction of length. The cleaved surfaces of the lead also indicated a linearly arranged architecture along the direction of length, which were constructed with aggregates of plate-like graphite crystals. By heating the lead in flowing air, a silicon oil impregnated in the calcined C/C composite of the mechanical pencil lead as the lubricant oil to increase the smoothness for drawing, was evolved at a low temperature before the thermal oxidation of the C/C composite. The thermal oxidation of the C/C composite was characterized as the partially overlapping two-step reaction process, producing detectable residues of impurity ash. The morphological characteristics of the present samples were compared by SEM observation (JSM-6510, JEOL). The atomic compositions of the sample were determined by EDX spectroscopy using an instrument (X-act, Oxford Instruments) equipped with the scanning electron microscope.

2.2. Thermal behavior



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TG–DTA measurements were carried out for a single sample rod (approximately 4 mm in length and approximately 2 mg (m0) in mass), weighed on a platinum pan (5 mm in diameter and 2.5 mm in height) using an instrument (SSC/5200, SII). A series of TG–DTA curves were recorded by heating the sample in flowing air (300 cm3 min−1) to 1173 K at different heating rates  (0.5 ≤  ≤ 10 K min−1). During TG–DTA measurements, the outlet gas from the instrument was continuously introduced into an infrared CO2 meter (LX-720, IIJIMA). The CO2 concentration was monitored as the evolved gas analysis for CO2 (EGA(CO2)). Similarly, the sample was heated in the TG–DTA instrument at  = 10 K min−1 to different temperatures T (873 ≤ T ≤ 923 K) and then maintained at a specific temperature for recording isothermal mass-change traces. Sample controlled thermal analysis (SCTA)40 was also applied to trace the thermal oxidation of the samples. A suspension-type TG (TGA-50, Shimadzu) equipped with a homemade SCTA controller41-45 was used for the measurements. A series of rod samples (0.5 mm in diameter) with different hardness values (4B–4H) were heated at 5 K min−1 in flowing air (80 cm3 min−1). In the temperature range higher than 723 K, the rate of mass loss ascribed to the thermal oxidation was controlled to be a constant value C at 7.5 g min−1. A pair of SCTA measurements were carried out: one using a single rod and the other using two pieces of sample rods.

3. Results and Discussions 3.1. Sample characterization and thermal behavior Figures S1 and S2 in the Supporting Information compare SEM images of the samples that have different hardness values and diameter sizes, respectively. Regularly arranged valleculae along the direction of length were observed on the outer surface of the samples. The interval of the valleculae decreased by increasing the hardness, which did not change with the diameter size. A linearly arranged architecture was found in the cleaved surfaces of the samples. The densely arranged smaller graphite particles became more particular as the sample’s hardness increased. The difference in the architecture of the cleaved surfaces was not distinguishable for the samples with different 6 ACS Paragon Plus Environment

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diameter sizes among those having the same hardness. The EDX spectra of the samples with different hardness values and diameter sizes are compared in Figs. S3 and S4, respectively. The contents of component elements are listed in Tables S1 and S2 in the Supporting Information. Carbon was the major element, whereas silicon, oxygen, and sodium were observed as minor elements. The content of silicon tended to decrease by increasing the hardness because of the change in the content of silicon oil as an impregnation agent. Figure S5 shows typical TG/derivative TG(DTG)–DTA curves for a mechanical pencil lead recorded in flowing air. Irrespective of hardness and diameter, all pencil leads examined in this study exhibited similar thermal behaviors. The first mass-loss process accompanied by a well-shaped endothermic peak in DTA is attributed to the evaporation and decomposition of silicon oil.39 Subsequently, the thermal oxidation of the sample rod occurred, accompanied by exothermic peaks in DTA. Two distinguishable peak tops were observed in both DTG and DTA during the thermal oxidation process, indicating a partially overlapping two-step process. As a result, all sample rods were nearly burned out completely, leaving detectable solid residues (ash). In Fig. 1, TG/DTG–DTA–EGA(CO2) curves for the mechanical pencil leads with different hardness and diameter sizes are compared. While the thermoanalytical curves systematically varied with the hardness (Fig. 1(a)), no distinguishable difference can be observed for the samples with different diameter sizes (Fig. 1(b)). The changes of the thermoanalytical curves with the hardness were observed for the mass-loss value of the first mass-loss process and the contributions and overlapping features of two peaks during the second mass-loss process attributed to the thermal oxidation as highlighted in Figures S6 and S7, respectively. A two-step reaction behavior was more clearly observed by the temperature profile during the thermal oxidation, which was recorded by controlling the mass-loss rate to be constant using SCTA (Figure S8). The detailed analyses of the thermoanalytical curves are described in the section S2 in the Supporting Information. The comparable C/C composite structures among the samples with different diameter sizes were deduced from the practically identical thermoanalytical curves. Therefore, the preparation 7 ACS Paragon Plus Environment


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conditions appeared to be the same for the samples with different diameter sizes. On the other hand, the change in the thermoanalytical curves with the pencil’s hardness could be attributed to the different compositional and structural characteristics of C/C composites. It is expected from the variations that the composition ratio of graphite and polymer as well as the calcination temperature of the mixture will be different during the preparation of mechanical pencil leads with different hardness values.

Figure 1. Changes in TG/DTG–DTA–EGA(CO2) curves recorded at  = 5 K min1 in flowing air (300 cm3 min1) depending on the (a) hardness (diameter size 0.5 mm) and (b) diameter size (hardness 2B) of the mechanical pencil leads.

3.2. Kinetic data for the thermal oxidation process Figures 2 and 3 show the mass-loss curves recorded under linear nonisothermal and isothermal conditions for the thermal oxidation process of two samples with hardness of 4B and 4H, 8 ACS Paragon Plus Environment

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respectively. In the case of the 4B sample, the mass-loss curves that were recorded under linear nonisothermal conditions (Fig. 2(a)) exhibited two well distinguishable reaction steps as evidenced by the two peak tops in DTG curves. The mass-loss curves shifted systematically to high temperatures with  without changing the shape of the curves. Under isothermal conditions (Fig. 2(b)), the two reaction steps was distinguished by a change in the slop of the mass-loss curves that occurred midway through the overall reaction. In the case of 4H sample (Fig. 3), the feature of the multistep process was less significant in both mass-loss curves recorded under linear nonisothermal (Fig. 3(a)) and isothermal (Fig. 3(b)) conditions.

Figure 2. The mass-loss traces for the thermal oxidation process of the 4B sample (m1 = m0 – m1 = 1.73 ± 0.04 mg) recorded under (a) linear nonisothermal and (b) isothermal conditions.



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Figure 3. The mass-loss traces for the thermal oxidation process of the 4H sample (m1 = m0 – m1 = 2.10 ± 0.06 mg) recorded under (a) linear nonisothermal and (b) isothermal conditions.

As seen in Fig. S8, the features of the two reaction steps were more clearly seen by the measurements under SCTA conditions. Figure 4 shows the temperature profiles of SCTA for the thermal oxidation process of the 4B and 4H samples. By comparing the temperature profiles for the 4B (Fig. 4(a)) and 4H (Fig. 4(b)) samples, difference in the contributions of each reaction step to the overall reaction were evident between the samples. The contribution of the first reaction step was larger for the 4H sample. In both samples, the temperature profile showed parallel shift to low temperatures when the measurement was performed using two pieces of sample rods with the same length, because the actual rate of the thermal oxidation in each piece of sample rod was diminished to be the half of that in the measurement for the single piece of sample rod.


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Figure 4. The temperature profiles of SCTA measurements (C = 7.5 g min1) for the thermal oxidation process of pencil leads: (a) 4B and (b) 4H samples.

3.3 Preliminary kinetic approach to the overlapping thermal oxidation process Prior to the kinetic approach to the two partially overlapping reaction steps, we tried to estimate the overall kinetic feature using an idealized kinetic equation for a single-step reaction. Due to the fact that the above thermoanalytical measurements were carried out under flowing air and thus a constant concentration of O2, the term of O2 concentration in the kinetic equation can be treated as a constant. Therefore, the formal kinetic equation (Eq. (1)) was applied to the overall thermal oxidation process:46

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

(1)

where α is the fractional reaction calculated as the fraction of mass-loss with respect to the total mass loss during the thermal oxidation, A is the Arrhenius pre-exponential factor, Ea is the apparent



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activation energy, R is the gas constant, and f(α) is the kinetic model function that describes physicogeometric mechanism of the reaction. It is noted that Eq. (1) can be applied to the kinetic rate data recorded under different temperature change conditions including nonisothermal, isothermal, and SCTA conditions. A linear correlation might be given by plots of ln(dα/dt) versus T1 examined for the data points at a fixed α selected from the series of kinetic rate data recorded under nonisothermal, isothermal, and SCTA conditions (Friedman plot47-50). From the slope of the plot, the values of Ea at a selected α were calculated. The results exhibited a systematic change in the apparent Ea value as the reaction advances in all the samples with different hardness values. An initial increase in the Ea value and change in the variation trend midway through the reaction were observed as a general trend. An increase in the α range of the initial Ea increase and the change in the variation trend at a larger α value were found by increasing the hardness from 4B to 4H. The apparent change in the variation trend with the pencil’s hardness can be interpreted in relation with the change in the contributions of each oxidation step and the overlapping feature of two reaction steps. Detailed results of the conventional isoconversional analysis based on eq. (1) are described in Section S4 in the Supporting Information. Another possible preliminary approach to the overall kinetic data having partially overlapping reaction features may be the peak deconvolution using statistical functions. In the procedure, the overall reaction rate is assumed to be expressed by37,38,51,52

dm N   F ti  dt i 1

(2)

where N and F(t) are the number of component reaction steps and a statistic function to fit derivative kinetic data of each component step i, respectively. The mathematical deconvolution of the overall DTG peak recorded under nonisothermal conditions estimates the contribution ci of each reaction step i with reference to the overall reaction from the ratio of the separated peak area to the overall peak area. Table S3 lists the contribution ci of each reaction step i that was estimated from the mathematical deconvolution for the samples with different hardness values. In addition, empirically separated 12 ACS Paragon Plus Environment

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kinetic curves under nonisothermal conditions were obtained, which were subsequently subjected to a formal kinetic analysis for each reaction step. Details of the mathematical deconvolution according to Eq. (2) and the formal kinetic analysis of the mathematically separated kinetic data are described in Sections S4 and S5 in the Supporting Information, respectively.

3.4. KDA for the overlapping thermal oxidation process When the component reaction steps are kinetically independent and each reaction step is simply described by the function of  and T, the overlapping process is expressed by the cumulative kinetic equation37,38,53,54

 E  d N   ci Ai exp  a ,i  f i  i  with dt i 1  RT 

N

c i 1

i

 1 and

N

c  i 1

i

i



(3)

where the subscript i identifies the component reaction step. As seen in Fig. S14, it is provable that the apparent Arrhenius parameters for each reaction step changed systematically as the reaction advanced. The variation of the self-generated reaction conditions during the reaction is expected as one of the possible causes of the change in Arrhenius parameters. In that case, an accommodation function of a parameter other than α and T has to be introduced to satisfactorily describe the kinetic behavior of each reaction step. However, formalization of such accommodation function is impossible except in some simple cases. Therefore, the direct application of Eq. (3) to the present reaction is understood as a semiempirical method to separate the overlapping processes into net kinetic behaviors of each reaction step. Application of an empirical kinetic model function is thus preferable for accommodating any deviation of the net kinetic behavior from the ideal kinetic model for the single-step reaction. In this study, Šesták–Berggren model55-57 with three kinetic exponents (SB(m, n, p)) was employed.

f     m 1     ln 1    n

p

(4)

Because the kinetic calculation based on Eq. (3) (KDA) requires simultaneous optimization of a total of 12 parameters for two overlapping reaction steps, the reliability of the initial values is the 13 ACS Paragon Plus Environment


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most important factor for obtaining meaningful kinetic parameters. In this study, the initial values of ci were substituted with the values determined by the mathematical deconvolution analysis (Table S3). Considering ci values and Ea variation trend estimated through the Friedman method, for example, those shown in Fig. S14, two distinguishable  regions in the overall thermal oxidation process were determined. The average Ea values within each  region were used for the initial values of Ea,i. SB(0,1,0), which is equivalent to the first order reaction law, was assumed for the initial kinetic exponents. After setting those initial values, the order of initial Ai values was determined by graphically comparing the experimental kinetic data with those calculated according to Eq. (3). The initial values used for the optimization run are listed in Table S4 in the Supporting Information. Then, the optimization was run to minimize the squares sum of the residues when fitting the experimental kinetic curve recorded under a specific reaction condition.  da   da   F        j 1   dt  exp , j  dt  cal, j  M

2

(5)

where M is the number of data points of the kinetic data. Figures 5 and 6 represent the typical fitting of the experimental kinetic data by Eq. (3) as two overlapping reaction steps for the thermal oxidation process of 4B and 4H samples, respectively, under different temperature program modes. The optimized kinetic parameters for each sample did not indicate a great change depending on the applied heating modes (linear nonisothermal, isothermal, and SCTA) and heating parameters (, T, and C). This result implies that the KDA as a semi-empirical method of kinetic analysis can be successfully applied to the thermal oxidation process of the mechanical pencil leads. Table 1 lists the average kinetic parameters optimized for the thermal oxidation process of the 4B and 4H samples under different heating parameters. The detailed results of the KDA for all the samples with different hardness values are listed in Table S6.


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Figure 5. Typical results of KDA for the 4B sample under (a) nonisothermal, (b) isothermal, and (c) SCTA conditions.



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Figure 6. Typical results of KDA for the 4H sample under (a) nonisothermal, (b) isothermal, and (c) SCTA conditions.


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Table 1. Average kinetic parameters optimized for each reaction step of the thermal oxidation of the 4B and 4H samples under different temperature program modes

Hardness

Condition

Nonisothermal

4B

Isothermal

SCTA

Nonisothermal

4H

Isothermal

SCTA

Ea,i

SB(mi, ni, pi)

Ai / s1

i

ci

1

0.50  0.09

129.4  3.4

2

0.50  0.09

1

1

mi

ni

pi

(4.5  0.1) × 104

0.11  0.09

1.04  0.11

0.10  0.03

152.0  1.9

(4.0  0.1) × 105

0.20  0.05

0.87  0.10

0.32  0.06

0.48  0.06

130.6  1.9

(4.4  0.1) × 104

0.01  0.04

1.17  0.26

0.09  0.04

2

0.52  0.06

150.5  1.1

(3.9  0.1) × 105

0.26  0.01

0.98  0.12

0.34  0.05

1

0.42  ---

128.5  ---

(4.5  ---) × 104

0.08  ---

1.10  ---

0.12  ---

2

0.58  ---

151.8  ---

(3.9  ---) × 105

0.25  ---

1.06  ---

0.26  ---

1

0.70  0.04

111.1  2.6

(2.5  0.1) × 103

  0.09

1.04  0.20

  0.03

2

0.30  0.04

159.1  2.1

(7.1  0.1) × 105

0.13  0.05

0.79  0.16

0.22  0.08

1

0.68  0.02

109.3  1.1

(2.5  0.1) × 103

0.19  0.09

1.16  0.17

  0.04

2

0.32  0.02

158.4  1.7

(6.9  0.1) × 105

0.20  0.07

0.88  0.18

0.29  0.05

1

0.70  ---

113.1  ---

(2.5  ---) × 103

  ---

1.10  ---

  ---

2

0.30  ---

161.9  ---

(7.1  ---) × 105

0.16  ---

0.75  ---

0.26  ---

/ kJ mol


r2 0.999 0.002



0.958 0.020



0.930  ---

0.999 0.001



0.993 0.002



0.898  ---


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3.5 Correlation of the kinetic results with the hardness of the pencil lead Figure 7 compares the values of ci, Ea,i and Ai of the samples with different hardness values. The c1 value increased by increasing hardness, counterbalanced with the decrease in the c2 value (Fig. 7(a)). The trend of variation in the Ea,i value changed in the HB sample irrespective of the reaction steps (Fig. 7(b)). In the first reaction step, the Ea,1 value was approximately constant in the range from 4B to HB samples, which decreased from HB to 4H samples. An opposite trend can be found for the second reaction step. The variation trend in Ai followed that of Ea,i (Fig. 7(c)), probably because of the mutual dependence in Arrhenius parameters, which is known as the kinetic compensation effect.5860

As shown in Fig. 8, the kinetic exponents in SB(mi, ni, pi) for each reaction step also changed with

the hardness of the pencil leads. For the first reaction step, the values of m1 and p1 increased systematically by increasing the hardness, whereas the value of n1 stayed approximately the same. The systematic decreases in n2 and p2 values from 2B to 4H were distinguishable, whereas the m2 value stayed approximately constant irrespective of the hardness.


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Figure 7. Change in the optimized kinetic parameters depending on the sample’s hardness: (a) contribution ci, (b) apparent activation energy Ea,i, and (c) pre-exponential factor Ai.



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Figure 8. Change in the kinetic exponents in SB(mi, ni, pi) with the hardness of the pencil lead: (a) the first reaction step (i =1) and (b) the second reaction step (i = 2).

Using the optimized kinetic exponents in SB(mi, ni, pi), the experimental master plots for each reaction step were reproduced according to the following isoconversional relationship:49,61-63

E  d i d i  exp a ,i   Ai fi  i  di dt  RT 

t

 E 

i   exp   a ,i dt 0  RT 

with

(6)

where θ is Ozawa’s generalized time,64,65 which is the hypothetical reaction time at infinite temperature calculated through extrapolating the reaction rates at a fixed  according to the Arrhenius relationship. The experimental master plots of (di/dθi) versus i of the samples with different hardness values are compared in Fig. 9. The experimental master plots for the first reaction step abstractly indicate deceleration profiles and a systematic change from convex to concave shapes by increasing the hardness. For the HB and 2H samples, a rate behavior with nearly linear deceleration was observed, which corresponds to the first order reaction law. Considering the heterogeneous 20 ACS Paragon Plus Environment

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kinetic behavior of the thermal oxidation process, the variation of the rate behavior of the first reaction step with the hardness of the sample was interpreted qualitatively because of the systematic changes in the structural characteristics of the C/C composite. All experimental master plots for the second reaction step showed the maximum (d2/dθ2) value midway through the reaction and the detectable shift of 2 value at the maximum to the low values by increasing the hardness. Similar shapes of the experimental master plots observed for the second reaction step have been reported for the thermally induced oxidation of natural and synthetic graphite samples.30 On the basis of a well-defined physicogeometric consideration of the reaction mechanism, this type of rate behavior is described by a nucleation–growth type66-70 or an autocatalytic type71 reaction model, which are accommodated in the SB(m, n, p) model as SB(0, 0, p) or SB(m, n, 0), respectively. The correspondence in the rate behavior also supports the assumption that the second reaction step was originated from the thermal oxidation of the originally mixed graphite particles during the preparation of mechanical pencil leads.

Figure 9. Normalized master plots of (di/dθi) versus i reproduced using the optimized SB(mi, ni, pi): (a) the first reaction step (i =1) and (b) the second reaction step (i = 2). 21 ACS Paragon Plus Environment


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The systematic changes in ci values and other kinetic parameters with the hardness of mechanical pencil leads demonstrate that the KDA that was applied to the thermal oxidation process is a useful tool for characterizing the compositional and structural characteristics of C/C composites. This kinetic calculation is expected to be applicable to the thermal oxidation process of other C/C composite materials as a semiempirical method, for example, for product control during manufacturing.

4. Conclusions By heating mechanical pencil leads in flowing air, two mass-loss processes were observed in well-separated temperature regions to form a considerably detectable amount of ash. The first mass-loss process accompanied by an endothermic effect was due to the evaporation/decomposition of an impregnation agent such as silicon oil. The second mass-loss process accompanied by an exothermic effect and evolution of CO2 was the thermal oxidation of C/C composite. The second mass-loss process was further comprised of two partially overlapping reaction steps ascribed to the thermal oxidation of two different sources of carbon: one was produced by the carbonization of polymer binders during the calcination process while manufacturing pencil leads, and the other is the originally mixed graphite particles. The special emphasis of the present article is on the systematic changes in the thermal behaviors of mechanical pencil leads with different hardness values and these invariances among different diameter sizes of mechanical pencil leads with the same hardness. The mass-loss value during the thermally induced evaporation/decomposition of an impregnation agent reflected indirectly the spaces of pores and interstices in the C/C composites. The kinetic behavior of the two-step thermal oxidation process can be correlated to the compositional and structural characteristics of C/C composites. Therefore, the systematic changes in the thermal behaviors with the hardness are interpreted as the results of the changes in their compositional and structural characteristics. In addition to the qualitative analysis of the mass-loss value during the 22 ACS Paragon Plus Environment

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evaporation/decomposition of an impregnation agent using TG, the kinetic analysis of the thermal oxidation process comprising two partially overlapping reaction steps can be a possible method to quantitatively correlate the thermal behavior with the compositional and structural characteristics of C/C composites. The KDA based on a cumulative kinetic equation (Eq. (3)) is practically applicable for characterizing the complex heterogeneous kinetics in a solid–gas system. The results of KDA provide the contributions and kinetic parameters of each reaction step of the thermal oxidation process. The variations of these values can be correlated semiempirically to the changes in the compositional and structural characteristics of C/C composites as demonstrated for the thermal oxidation process of the mechanical pencil leads with different hardness values. At the same time, the contributions and the kinetic parameters determined for a specific C/C composite can be used as the empirical index to control its quality. The KDA is equally useful for many other C/C composite materials when thermal oxidation occurs as the partially overlapping multistep process.

Supporting Information The Supporting Information is available free of charge on the ACS Publications website. S1. Sample Characterization (Figures S1–S4, Tables S1 and S2) S2. Thermal Behavior (Figures S5– S8) S3. Conventional Isoconversional Analysis (Figures S9 and S10) S4. Mathematical Deconvolution Analysis (Figure S11, Table S3) S5. Formal Kinetic Analysis of the Mathematically Separated Data (Figures S12-S14) S6. Kinetic Deconvolution Analysis of the Thermal Oxidation Process (Tables S4 and S5).

AUTHOR INFORMATION Corresponding Author *Tel./fax: +81-82-424-7092. E-mail: [email protected] 23 ACS Paragon Plus Environment


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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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(36) 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. (37) Koga, N.; Goshi, Y.; Yamada, S.; Pérez-Maqueda, L. A. Kinetic Approach to Partially Overlapped Thermal Decomposition Processes. J. Therm. Anal. Calorim. 2013, 111, 14631474. (38) Koga, N. Physico-Geometric Approach to the Kinetics of Overlapping Solid-State Reactions. In Handbook of Thermal Analysis and Calorimetry, 2nd ed.; Vyazovkin, S.; Koga, N.; Schick, C., Eds. Elsevier: Amsterdam, 2018; Vol. 6, pp 213-251. (39) Nishikawa, K.; Ueta, Y.; Hara, D.; Yamada, S.; Koga, N. Kinetic Characterization of Multistep Thermal Oxidation of Carbon/Carbon Composite in Flowing Air. J. Therm. Anal. Calorim. 2017, 128, 891-906. (40) Sørensen, O. T.; Rouquerol, J. Sample Controlled Thermal Analysis: Origin Goals, Multiple Forms, Applications and Future; Kluwer: Dordrecht, 2003. (41) Alcalá, M. D.; Real, C.; Criado, J. M. Application of Constant Rate Thermal Analysis (CRTA) to the Synthesis of Silicon Nitride by Carbothermal Reduction of Silica. J. Therm. Anal. 1992, 38, 313-319. (42) Pérez-Maqueda, L. A.; Criado, J. M.; Gotor, F. J. Controlled Rate Thermal Analysis Commanded by Mass Spectrometry for Studying the Kinetics of Thermal Decomposition of Very Stable Solids. Int. J. Chem. Kinet. 2002, 34, 184-192.


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Figure 1. Changes in TG/DTG–DTA–EGA(CO2) curves recorded at β = 5 K min-1 in flowing air (300 cm3 min1)

depending on the (a) hardness (diameter size 0.5 mm) and (b) diameter size (hardness 2B) of the mechanical pencil leads. 113x169mm (300 x 300 DPI)

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Figure 2. The mass-loss traces for the thermal oxidation process of the 4B sample (m1 = m0 – Δm1 = 1.73 ± 0.04 mg) recorded under (a) linear nonisothermal and (b) isothermal conditions. 76x98mm (300 x 300 DPI)



Figure 3. The mass-loss traces for the thermal oxidation process of the 4H sample (m1 = m0 – Δm1 = 2.10 ± 0.06 mg) recorded under (a) linear nonisothermal and (b) isothermal conditions. 76x98mm (300 x 300 DPI)


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Figure 4. The temperature profiles of SCTA measurements (C = 7.5 μg min-1) for the thermal oxidation process of pencil leads: (a) 4B and (b) 4H samples. 76x106mm (300 x 300 DPI)



Figure 5. Typical results of KDA for the 4B sample under (a) nonisothermal, (b) isothermal, and (c) SCTA conditions. 76x145mm (300 x 300 DPI)


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Figure 6. Typical results of KDA for the 4H sample under (a) nonisothermal, (b) isothermal, and (c) SCTA conditions. 76x146mm (300 x 300 DPI)



Figure 7. Change in the optimized kinetic parameters depending on the sample’s hardness: (a) contribution ci, (b) apparent activation energy Ea,i, and (c) preexponential factor Ai. 76x146mm (300 x 300 DPI)


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Figure 8. Change in the kinetic exponents in SB(mi, ni, pi) with the hardness of the pencil lead: (a) the first reaction step (i =1) and (b) the second reaction step (i = 2). 76x112mm (300 x 300 DPI)



Figure 9. Normalized master plots of (dαi/dθi) versus αi reproduced using the optimized SB((mi, ni, pi) ): (a) the first reaction step (i =1) and (b) the second reaction step (i = 2). 76x110mm (300 x 300 DPI)


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For Table of Contents Only 47x26mm (300 x 300 DPI)


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