Introduction

Activated carbons (ACs) or analogous biochars are porous materials with well-developed textural properties and high chemical resistance, which are extensively used in several industrial processes, such as adsorption [1,2,3], catalysis [4, 5], sensing [6] and energy storage [7,8,9]. Therefore, the controllable preparation of high-performance AC with specific textural properties has attracted considerable interest from the industrial and academic fields. Carbohydrate [10, 11], biomass waste [12, 13], pitch [14, 15], polymers [16], and coal [17,18,19,20,21,22] are commonly chosen as carbon-containing precursors, and KOH is used as the activating agent. This process usually contains the mixing of precursors and KOH, pyrolysis under an inert atmosphere, and washing the residue with KOH (if necessary). Since precursors such as coal have unique properties, reactions between precursors and KOH during pyrolysis are extremely complicated. Therefore, the research progress has been adversely affected. Understanding activation energies of reactions can help reveal the mechanism of the process. Moreover, an in-depth understanding of the relationship between activation energy and textural properties can be obtained.

In the field of thermal analysis, thermogravimetric (TG) analysis is often used, which measures the mass loss per unit time and/or temperature for solid materials, such as coal and biomass, during the combustion and pyrolysis [10, 23,24,25,26,27,28,29]. In addition, kinetic parameters can be obtained through the quantitative analysis of TG curves. For example, based on the Arrhenius equation, TG experimental data should present a straight line with the slope proportional to the activation energy and the intercept representing the frequency factor [24, 28, 30, 31]. Cumming and Augnin [32] first proposed that the information obtained from the TG profiles could be used for the preliminary assessment of combustion and help in understanding the competitive behavior of coal blends. Knowledge of coal pyrolysis kinetics, such as co-pyrolysis with catalysts or individual pyrolysis, is also crucial for understanding internal reactions [33, 34]. This knowledge is necessary for reaction design and operation temperature control [35]. Thus, understanding coal decomposition and the interaction with KOH is important for understanding the thermochemical transformation process, which is crucial for developing an efficient reaction route. However, recent studies on the co-pyrolysis of coal and KOH in an inert atmosphere still lack information [18, 36].

This work aims to explore the pyrolysis kinetics of coal and KOH blends with different ratios using a TGA device and to reveal the relationship between the kinetic parameters and textural properties of the prepared ACs. These insights can be beneficial for optimizing the pyrolysis process and the preparation conditions of specific ACs with designed textural properties.

Materials and methods

Materials

Reed spring coal, which accounts for a considerable proportion of the proven coking coal reserves in China, was selected for this study due to its low degree of metamorphism and high volatile matter. The coal was ground and sieved to obtain a size range of 180–250 μm, dried at 110 °C for 24 h, and sealed in a glass container at room temperature before use. The proximate and ultimate analysis of the coal samples are listed in Table 1.

Table 1 Proximate and ultimate analysis of coal* (unit: %, in weight)
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KOH was supplied by Sigma-Aldrich (Burlington, MA, USA). KOH and coal were manually mixed in appropriate proportions. The pyrolyzed samples were ground and sieved to obtain a particle size of 180–250 μm, dried at 110 °C for 24 h, and sealed before use. The sample with KOH/coal ratio of x:1 was labeled as AC-x.

TG tests

TG and derivative thermogravimetry (DTG) were used in this study to investigate and analyze the reaction processes and pyrolysis kinetics. Non-isothermal TG was performed using a thermal analyzer DSCQ-1000 (TA Instruments, New Castle, DE, USA) under a 50 mL/min N2 from room temperature to 1000 °C at a heating rates ranging from 5 °C/min to 20 °C/min. To minimize heat and mass transfer effects, for all the samples, 5 mg of sample was dispersed uniformly on a flat crucible with a diameter and depth of 8 mm and 3 mm, respectively. To validate the results, repeated tests were conducted on each sample.

Characterization

The textural properties were characterized by N2 adsorption–desorption at −196 °C using the ASAP 2020 system of Micromeritics Instrument Corporation (Norcross, GA, USA). Before the test, the pyrolyzed samples were degassed at 90 °C for 2 h, and then at 150 °C for 24 h to remove the moisture and other gas impurities adsorbed. The surface area (SBET) was calculated using the Brunauer–Emmett–Teller (BET) equation. The total pore volume (Vtot) was measured at P/P0=0.99. Micropore surface area (Smic) and volume (Vmic) were determined via the t-plot method. The pore size distribution was calculated using density functional theory.

Kinetic analysis

In the non-isothermal kinetics studies, the relationship between temperature (T) and heating rate (\(\beta\)) is as follows [37,38,39,40]:

$$T={T}_{0}+\beta t,$$
(1)

where T0 is the starting temperature, °C, t denotes the time, min, and the unit of β is °C/min.

The specific reaction rate is defined as

$$\frac{{\text{d}}\alpha }{{\text{d}}t}=k{\text{f}}\left(\alpha \right),$$
(2)

where

$$\mathrm{\alpha }=\frac{{W}_{0}-W}{{W}_{0}-{W}_{f}},$$
(3)
$$k=A{\text{exp}}\left(\frac{-E}{{R}_{g}T}\right),$$
(4)

where α is the fraction of the decomposed part; W0, W, and Wf represent the initial mass, the residue mass at time t, and the final mass of the reactant as the reaction is completed, respectively. E denotes the activation energy, Rg indicates the gas constant, T refers to the absolute temperature, and A stands for the pre-exponential factor. f(α) is the hypothetical model of the reaction mechanism function of α.

In this study, Achar differential method and Coats–Redfern integral method were used to obtain kinetic parameters for pyrolysis. Moreover, the Bagchi method was applied to infer the reaction mechanism function.

Achar differential method

On the basis of Eqs. (1)–(4), the following formula can be obtained:

$$\frac{\left({\text{d}}\alpha /{\text{d}}t\right)}{{\text{f}}\left(\alpha \right)}=A{\text{exp}}\left(\frac{-E}{{R}_{g}T}\right).$$
(5)

By taking logarithms on both sides, the Achar equation can be obtained as follows [41,42,43]:

$${\text{ln}}\left[\frac{\left({\text{d}}\alpha /{\text{d}}t\right)}{{\text{f}}\left(\alpha \right)}\right]={\text{ln}}A-\frac{E}{{R}_{g}T},$$
(6)

where the specific reaction rate can be also shown as

$$\frac{{\text{d}}\alpha }{{\text{d}}t}=\frac{\frac{{\text{d}}W}{{\text{d}}t}}{{W}_{0}-{W}_{f}}.$$
(7)

\({\text{ln}}[\frac{({\text{d}}\alpha /{\text{d}}T)\beta }{f(\alpha )}]\) were linearly related to 1/T and kinetic parameters can be obtained from the slope and intercept of the line.

Coats–Redfern integral method

By replacing the integral expression of Eq. (5) with the Coats–Redfern approximate expression, the following formula can be obtained [37,38,39,40]:

$${\text{g}}\left(\mathrm{\alpha }\right)=\frac{A}{\beta }\frac{{{R}_{g}T}^{2}}{E}\left(1-\frac{2RT}{E}\right){\text{exp}}\left(\frac{-E}{{R}_{g}T}\right),$$
(8)

where

$${\text{g}}\left(\mathrm{\alpha }\right)=\underset{0}{\overset{a}{\int }}\frac{{\text{d}}\alpha }{{\text{f}}(\alpha )}.$$
(9)

Considering that 2RT/E<1, Eq. (8) can be simplified as the logarithmic form:

$${\text{log}}\left[\frac{{\text{g}}\left(\mathrm{\alpha }\right)}{{T}^{2}}\right]={\text{log}}\left(\frac{AR}{\beta E}\right)-\frac{E}{{R}_{g}T}.$$
(10)

The kinetic parameters can be obtained from the slope and intercept of the line [g(α)/T2] and [1/T].

Function selection

Table 2 lists mathematical expressions (functions) for different kinetics. Using these functions and the afore-mentioned methods, the reaction mechanisms can be estimated from the DTG curves [40, 41, 43,44,45,46,47,48,49,50,51]. The first-order chemical reaction hypothesis (F1 model) is commonly used in kinetic studies with TGA. In addition to this mechanism, other mechanisms focusing on reaction order (F2–F4 models), geometry (R1–R3 models), diffusion (D1–D4 models), and solid phase reaction (A1–A3 models) are also used to describe gas–solid reactions. According to Bagchi, the E and A values calculated by differential and integral methods should be similar, and correlation coefficients were used to evaluate the fitting results, as well as the optimal function [45, 46].

Table 2 Mathematical expressions of different kinetics
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Single peak fitting

To determine the kinetic parameters of the interaction between KOH and coal, DTG curves of the blend were firstly fitted using the sum of coal pyrolysis and KOH–coal reactions as follows [24, 52]:

$${{\text{d}}m/{\text{d}}t}_{{\text{sum}}}={x}_{1}({\text{d}}m{/{\text{d}}t)}_{{\text{pyrolysis}}}+{x}_{2}({\text{d}}m{/{\text{d}}t)}_{{\text{reaction}}},$$
(11)

where \(({\text{d}}m{/{\text{d}}t)}_{{\text{pyrolysis}}}\) and \(({\text{d}}m{/{\text{d}}t)}_{{\text{reaction}}}\) are the mass loss rates of coal pyrolysis and the reaction of coal and KOH, respectively, and x1 and x2 denote the proportions of coal and KOH in the blend, respectively. Equation (11) was used to exclude the coal pyrolysis, and theoretical DTG curves only containing reactions between coal and KOH were obtained. Then, kinetic parameters could be calculated based on theoretical DTG curves.

Multi-peak fitting

Multipeak Gaussian fitting is often used for spectral or numerical analysis [47, 48]. This type of fitting is simple and effective for decomposing a complex curve containing multiple bumps or convexities into a number of Gaussian fitting peaks. To further understand the reaction mechanism between coal and KOH, multipeak Gaussian fitting method was used to de-convolute DTG curves, and the kinetic analysis was conducted based on each fitting peak to calculate corresponding activation energy.

Results and discussion

TG and DTG curves under N2 atmosphere

Reed spring coal is a typical highly volatile coal with a volatile component accounting for more than 38% (Table 1). High volatiles components can evaporate during the heating process, resulting in considerable original textural properties, which are beneficial for the diffusion and reaction of KOH. Figure 1 shows the experimental TG and DTG curves for coal with/without KOH under N2 atmosphere at different heating rates. The mass loss ratios of the mixtures were significantly higher than that of coal alone, and the ratio increased with increasing KOH ratio. The initial mass loss occurred at around 120 °C due to moisture evaporation, which is not shown in the figures, and the initial mass was defined as the mass after evaporation. The DTG curves demonstrated that two significant mass losses occurred at around 380–500 °C and 700–950 °C in the blended samples (AC-1, AC-2, AC-3), and only one mass loss at around 380–500 °C in the coal sample (AC-0). Mass loss at low temperature was possibly due to the release of volatiles during decomposition. For blended samples, it has been reported that KOH can break the chemical bonds such as the alkyl-aryl bonds, enhancing the removal of some carbon components in the form of volatiles (CH4, CO2 or CO) [12]. Mass loss at high temperature was presumably ascribed to the complex reactions between coal and KOH, including the reduction of KOH, the production of K2CO3 and COx, and the evolution of H2 [17, 19].

Fig. 1
figure 1

TG and DTG curves of coal and KOH blends at different heating rates: TG curves at a 5 °C/min, b 10 °C/min, and c 20 °C/min; DTG curves at d 5 °C/min, e 10 °C/min, and f 20 °C/min (mass ratios of KOH to coal, including 0:1 [AC-0], 1:1 [AC-1], 2:1 [AC-2], and 3:1 [AC-3]). TG thermogravimetric, DTG derivative thermogravimetry

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Table 3 shows the kinetic parameters calculated by Achar and Coats–Redfern methods, including temperature intervals marked as Range, the average temperature as Ta, reaction mechanism function (see Table 2) as Type, activation energy as E, pre-exponential factor as ln A and correlation coefficient as R2. Using 15 functions (Table 2), activation energy and fitting correlation coefficient R2 could be obtained by two methods. The function, which shows the least difference in energies for the two methods and the highest R2, was chosen as the optimal one, and the results are listed in Table 3.

Table 3 Kinetic parameters calculated by the Achar and Coats–Redfern methods with different heating rates
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With the addition of KOH (AC-1), activation energy of the first mass loss significantly decreased, while that of the second mass loss increased compared to that of AC-0. As the content of KOH (AC-2/AC-3) continuously increased, maximum activation energy of the second mass loss increased, and the temperature at which maximum value was reached increased accordingly. In addition, fluctuation of activation energy to the temperature was mainly due to changed mechanism during pyrolysis, while fluctuation of that to the heating rate was ascribed to the temperature gradient from the inner to surface of the sample.

Textural properties of the samples

The literature has shown that different heating rates result in similar specific surface areas [11, 17, 18, 20, 36]. Hence, 5 °C/min was selected. A series of ACs with different KOH ratios were prepared and characterized. In our previous work [53, 54], it was found that during the activation process, pore network generation was mainly caused by redox reactions between carbon and potassium compounds. Moreover, K atoms could also intercalate into carbon lattices, promoting microstructures in the carbon matrix. With increasing KOH content, these effects led to more drastic carbon pore evolution. Table 4 lists the BET analysis results for samples with different mass ratios of KOH to coal. Figure 2 presents the N2 adsorption–desorption isotherms and pore size distributions. AC-0 showed an isotherm of low porosity materials. After mixing with KOH, all the samples exhibited Type I isotherms according to the IUPAC (International Union of Pure and Applied Chemistry) classification. With the increment of KOH content, nitrogen uptake at low relative pressure continuously increased up to AC-2. In addition, hysteresis curves could be observed at high relative pressures for samples AC-1 and AC-2, indicating the considerable mesopore formation. The drop of textural properties in sample AC-3 may be due to the excess transformation from micropore or mesopore to macropore, which is in line with results reported in the literature [55,56,57,58,59]. This speculation could be partially confirmed by the data listed in Table 4.

Table 4 Textural properties of samples (heating rate: 5 °C/min)
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Fig. 2
figure 2

Textural characterization of samples (heating rate: 5 °C/min). (a) Nitrogen adsorption isotherm. (b) Pore size distribution

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Relationship between the textural properties and kinetic parameters of single peak fitting

To further explore the interaction between KOH and coal, DTG curves in Fig. 1 were obtained. The curves show that the overall reaction could be generally divided into two stages. Using Eq. (11), coal pyrolysis was excluded mathematically, and new curves were obtained that mainly reflected reactions between coal and KOH, as shown in Fig. 3.

Fig. 3
figure 3

Theoretical DTG curves only considering interaction between KOH and coal: a 5 °C/min, b 10 °C/min, c 20 °C/min (Mass ratios of KOH to coal, including 1:1 [AC*-1], 2:1 [AC*-2], and 3:1 [AC.*-3])

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DTG results indicated that coal and KOH interacted with each other, and the effects varied with changes in the KOH ratios and heating rates. With the increasing content of KOH, DTG peaks shifted to the high temperature. The variation in heating rate changed the heat transfer, thereby affecting the interior reaction temperature.

Table 5 lists the kinetic parameters calculated by the Achar and Coats–Redfern methods. Figure 4 shows the relationships among activation energy, KOH ratio, and heating rate. The increasing heating rate increased the activation energy but reduced the fluctuation of activation energy. On one hand, as the heating rate increased from 5 °C/min to 20 °C/min, the resistance in heat transfer led to a larger temperature difference between heating furnace and samples, thereby delaying the pyrolysis process and enhancing the pyrolysis temperature [60]. On the other hand, the decreased heating rate could provide additional time for the molten KOH to blend fully with coal [61, 62], thereby facilitating the reaction and decreasing the required activation energy. In addition, the variation of temperature range indicated the change of reaction mechanism, which reflected effect of heating rate on activation energy. Specifically, using 5 °C/min mechanism markedly differed from using the other two heating rates. With the increase of KOH ratio, the activation energy initially decreased and then increased, which indicated that an appropriate amount of KOH could promote the activation process, whereas the excessive addition of KOH would lead to side reactions and increase the activation energy.

Table 5 Kinetic parameters using single peak fitting
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Fig. 4
figure 4

The relationship among activation energy, KOH ratio, and heating rate using single peak fitting

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Figure 5 presents the relationship of activation energy, specific surface area, and pore volume. A good linear correlation between the activation energies and the BET specific surface areas as well as total pore volumes could be observed (R2=0.94/0.99). While as for micropores, a weak correlation is obvious. Thus, activation energies derived from single peak fitting could be used to explain the overall pore formation via reactions between KOH and coal. The increased activation energy required inhibited pore formation, which might be related to the macropores generated by the overreaction.

Fig. 5
figure 5

Relationship among the activation energy of single peak fitting, pore volume, and specific surface area

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Relationship between the textural properties and kinetic parameters of multi peak fitting

In the previous section, the activation energy was correlated with the textural properties to a certain extent. To further analyze the relationship between textural properties and activation energy, the previous method was modified and the curves were deconvoluted by multipeak Gaussian fitting.

The deconvolution process was based on the related reactions. In our previous research [54], we found that the probable reactions between carbon and KOH include: (a) dehydration of KOH and the reaction with oxygen-containing functional groups on surface, as shown in Eqs. (12)–(13); (b) etching the carbon framework by redox reactions from KOH with carbon, as shown in Eqs. (14)–(15); and (c) the formation of K and K2O, as shown in Eqs. (16)–(18).

$$- {\text{COOH}} + {\text{KOH}} \to - {\text{COOK}} + {\text{H}}_2 {\text{O}}$$
(12)
$$2{\text{KOH}} \to {\text{K}}_2 {\text{O}} + {\text{H}}_2 {\text{O}}$$
(13)
$$- {\text{COOK}} + {\text{KOH}} \to {\text{K}}_2 {\text{CO}}_3 + 1/2{\text{H}}_2$$
(14)
$$- {\text{CH}}_2 + 4{\text{KOH}} \to {\text{K}}_2 {\text{CO}}_3 + {\text{K}}_2 {\text{O}} + 3{\text{H}}_2$$
(15)
$${\text{K}}_2 {\text{CO}}_3 \to {\text{CO}}_2 + {\text{K}}_2 {\text{O}}$$
(16)
$${\text{K}}_2 {\text{CO}}_3 {\text{ + 2C}} \to 2{\text{K}} + 3{\text{CO}}$$
(17)
$${\text{K}}_2 {\text{O + C}} \to 2{\text{K}} + {\text{CO}}$$
(18)

Thus, the textural properties may largely depend on these reactions, especially for KOH-activated samples. At 350 °C–550 °C, volatile components began to evaporate (Peak 1#). At the same time, molten KOH (at a fusion temperature of 360 °C) would react with the macromolecular side chain of the coal to produce the initial porosity [61, 62]. At around 600–900 °C, the internal carbon activation reaction (Peak 2#) occurred. The molten KOH entering the pores reacted with the carbon matrix, and gas (CO, CO2, H2O and H2) was produced [61,62,63,64]. Among them, CO2 played a critical role in forming new microporous structures, whereas H2O mainly ensured pore reaming and eventually promoted the formation of new mesopores and macropores [11, 17, 18, 20, 36]. At approximately 750 °C–950 °C, a large amount of metallic K was generated and overflowed (Peak 3#) [17, 63, 65, 66]. At this stage, the metallic K monomer moved through the layers of the carbon matrix, and the aromatic layer was stretched and deformed to form new micropores.

Therefore, on the basis of the reaction characteristics of these three stages, multipeak Gaussian fitting was performed, as shown in Fig. 6. The linear correlation obtained was above 0.98, and the peak temperature obtained roughly conformed to the abovementioned range. From the fitting results, the change in heating rate had minimal influence on the peak height, whereas the change in KOH ratio had a great influence on the peak height.

Fig. 6
figure 6

Deconvolution of DTG curves using Gaussian function. a AC-0, 5 °C/min. b AC-0, 10 °C/min. c AC-0, 20 °C/min. d AC-1, 5 °C/min. e AC-1, 10 °C/min. f AC-1, 20 °C/min. g AC-2, 5 °C/min. h AC-2, 10 °C/min. i AC-2, 20 °C/min. j AC-3, 5 °C/min. k AC-3, 10 °C/min. l AC-3, 20 °C/min

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Table 6 lists the kinetic parameters calculated by the Achar and Coats–Redfern methods. Figure 7 shows the relationship among activation energy, KOH ratio, and heating rate. With the increase of KOH ratio, the activation energy increased accordingly. Previous studies have shown that KOH melts at 360 °C [62, 66], forming a molten layer over coal particles. Then, the alkali species (molecules or ions) diffuse into the particles, and took part in the reactions. Experimental evidences observed in this work and in the literature validated this assumption. For example, the initial temperature for KOH/C reactions was 400 °C [17]. Thus, with the increase of KOH ratio, more energy was needed for melting, resulting in the rising of activation energies, as shown in Fig. 7. In comparison, the low heating rate could provide sufficient time for the full contact of molten KOH with the coal, thereby promoting the reaction. Therefore, the activation energy required was considerably low.

Table 6 Kinetic parameters calculated after deconvolution of DTG curves
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Fig. 7
figure 7

Relationship among activation energy, KOH ratio, and heating rate using multi peak fitting

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As the reactions in different stages had overlapping temperature ranges, the mass change in these stages was used as the weighting coefficient to calculate the activation energy when evaluating the relationship between activation energies and textural properties. Figure 8 shows the relationship among activation energy, specific surface area, and pore volume. The solid points are the combined activation energy values of Peaks 1# and 3#, and the hollow point was the value of Peak 3#. The micropore specific surface area and volume had a good linear correlation with the activation energy of Peak 3#, and the correlation coefficient was significantly improved using the activation energies of Peaks 1# and 3# (R2=0.993/0.996). This result implied that the micropore formation was related to the generation and overflow of metal K. At the same time, the initial pores also played a role in the formation of micropore structures, and the formation of micropores further developed on the initial pores.

Fig. 8
figure 8

Relationship among the activation energy using multi peak fitting, pore volume, and specific surface area

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Conclusion

This work highlights the use of pyrolysis kinetics to determine the pore formation mechanism during coal activation with KOH. By adopting Achar differential and Coats–Redfern integral methods, experimental DTG curves were fitted based on mechanism functions, and kinetic parameters such as activation energies were obtained. The effects of heating rate and KOH ratio on the activation energy showed similar trends when one of the variables was fixed. Another attempt was to correlate the activation energies with the textural properties. The direct fitting was firstly employed, and the obtained activation energies showed little correlation with textural properties. Then, two different methods were used for deconvolution of DTG curves before fitting. The single peak fitting only considered the interaction between KOH and coal, regardless of coal pyrolysis. Linear correlation between the activation energies and total pore volumes/BET surface areas can be obtained (R2=0.94/0.99), implying that the reactions between KOH and C strongly promoted the pore formation. The other multi peak fitting used Gaussian function to deconvolute the DTG curves, and then each theorical DTG peak was fitted using Achar and Coats–Redfern methods. It was found that the summed activation energies derived from surface reactions and metallic K intercalation were linearly related to the micropore volumes/surface areas (R2=0.993/0.996). Moreover, the multi peak fitting revealed that the generation and overflow of metallic K played a vital role in the micropores formation. The proposed methods can be directly applied to the pore analysis and process design for coal activation with KOH.