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Scientific Reports volume 14, Article number: 2076 (2024 ) Cite this article Compostable Plates Wedding
In this study, thermogravimetric and thermo-kinetic analysis of sugarcane bagasse pith (S.B.P.) were performed using a robust suite of experiments and kinetic analyses, along with a comparative evaluation on the thermo-kinetic characteristics of two other major sugarcane residues, namely sugarcane straw (S.C.S.) and sugarcane bagasse (S.C.B.). The thermogravimetric analysis evaluated the pyrolysis behavior of these residues at different heating rates in a nitrogen atmosphere. The Kissinger, advanced non-linear isoconversional (ANIC), and Friedman methods were employed to obtain effective activation energies. Moreover, the compensation effect theory (CE) and combined kinetic analysis (CKA) were used to determine the pre-exponential factor and pyrolysis kinetic model. Friedman's method findings indicated that the average activation energies of S.C.S., S.C.B., and S.B.P. are 188, 170, and 151 kJ/mol, respectively. The results of the ANIC method under the integral step Δα = 0.01 were closely aligned with those of the Friedman method. The CKA and CE techniques estimated ln(f(α)Aα) with an average relative error below 0.7%. The pre-exponential factors of S.C.S., S.C.B., and S.B.P. were in the order of 1014, 1012, and 1011 (s−1), respectively. From a thermodynamic viewpoint, positive ∆G* and ∆H* results provide evidence for the non-spontaneous and endothermic nature of the pyrolysis process, indicating the occurrence of endergonic reactions.
Over the past few decades, the availability of agro-food wastes, particularly sugarcane by-products (S.C.B.) and waste (S.C.S. and S.B.P.), in large quantities on one hand, and the global tendency to address the energy crisis and invest in the renewable bioenergy sector, on the other hand, have led the scientists to identify a number of traditional and sophisticated thermochemical pathways to utilize and convert lignocellulosic materials, commonly referred to as biomass, into higher value-added products1,2. Among the various thermochemical processes, researchers have highly considered and evaluated the pyrolysis process3,4,5,6.
Pyrolysis of biomass and other degradable compounds is a multi-scale complicated process consisting of a large number of physicochemical interactions7,8,9. The physical changes at micro/particle and macro/reactor scales during pyrolysis can be described using the comprehensive transport phenomena formulations, while chemical conversions are predicted using various simple to detailed kinetic models10,11,12. Understanding the pyrolysis kinetics of a feedstock is important for the design, optimization, control, feasibility assessment, and scale-up of the pyrolysis reactors in industrial applications13,14.
In recent decades, several studies have used thermal analysis techniques such as differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) to collect non-isothermal data and identify reaction mechanisms and compute kinetic parameters of thermal conversion processes15,16,17,18,19,20.
Generally, two commonly employed approaches to mathematical explanation for solid-state decomposition kinetics are model-free and model-fitting techniques. Model-fitting methods are the most frequently used to describe the conversion rate of the pyrolysis feed to product (i.e., global model) or a set of pseudo-component products (i.e., semi-global model). Pre-assumed reaction models and collected experimental data are used to approximate distinct kinetic parameters (also known as ‘kinetic triplets’) for each reaction through the application of linear or non-linear regression techniques21,22,23. Usually, the conversion mechanism and its reaction model differ depending on the feedstock properties and the reaction conditions.
In contrast to the model-fitting approach, model-free methods, commonly referred to as isoconversional methods24,25, operate under the premise that, at a predetermined conversion level, temperature is the sole variable influencing the reaction rate26. This implies that the activation energy (Ea) values for each specific conversion can be directly obtained without making assumptions about the underlying nature of the reaction model27.
Within the well-known realm of "model-free" methodologies, the determination of activation energy involves employing either a linear or nonlinear isoconversional procedure. The choice between these approaches depends on the assumptions underlying the selection of integral or differential isoconversional methods. It is worth mentioning that the differential isoconversional methods, owing to their reliance on instantaneous rate values, are susceptible to experimental noise, resulting in numerical instability. This issue can be effectively mitigated by adopting integral isoconversional approaches22,28.
Moreover, the pre-exponential factor (A) can be determined with noteworthy precision using sophisticated methods that adhere to a model-free approach29,30,31,32. Subsequently, the identification of activation energy and the pre-exponential factor allows for the generation of a tabular representation depicting an explicit version of the reaction model27,32.
International Confederation for Thermal Analysis and Calorimetry (ICTAC) kinetic researches shows that both model-fitting and isoconversional approaches can adequately describe the kinetics of single-step and multi-step processes, provided that the models in the model-fitting method are simultaneously fitted to several datasets gathered under various temperature programs21,22,33. However, when modeling multi-step reactions using model-fitting methods, various nontrivial issues arise, which is not the case when employing the model-free approaches22. In other words, isoconversional techniques can reduce the risk of mistakes in the model selection and parameter estimation.
Estimating the kinetic parameters of the pyrolysis process often involves the utilization of a model-free approach, which encompasses several methods, including Kissinger34, as well as various differential and integral isoconversional techniques such as Friedman35, Ozawa36, Ozawa-Flynn-Wall (OFW)36,37, Kissinger–Akahira–Sunose (KAS)38, and advanced non-linear (NLN) isoconversional (ANIC) methods39,40.
It was shown by Vyazovkin et al.27,28 that the OFW and KAS methods might produce relatively good values of the activation energy at E/RT > 13 due to the approximations made in these approaches. They also demonstrated that the ANIC and Friedman approaches are essentially independent of the E/RT value and can produce exceptionally low errors in the activation energy. As a result, ANIC and Friedman methods can be recommended to compute the activation energy necessary for the predictions and solve the other issues sensitive to activation energy accuracy27,28.
The pyrolysis kinetics of various biomass and agriculture waste materials have been extensively studied in the literature. These materials include sugarcane straw41, sugarcane bagasse41, soybean hull17, rice and corn18, tobacco waste42, plum and fig pomace43, olive mill solid waste44, coconut shell straws45, poplar wood46, pinewood sawdust47, bamboo sawdust48, maize straw, invasive lignocellulosic biomasses (i.e., Prosopis juliflora and Lantana camara)49 and digested organic fractions50. These studies employ a wide range of techniques, both model-fitting and model-free methods such as Kissinger, KAS, OFW, Friedman, ANIC, distributed activation energy model (DAEM) and other hybrid approaches51. To the best of our knowledge, the kinetic analysis of the pyrolysis reaction for S.B.P. has not been specifically discussed in the literature.
In this study, thermogravimetric and thermo-kinetic analysis of sugarcane bagasse pith (S.B.P.) was performed using a robust suite of experiments and kinetic analyses along with a comparative evaluation on the thermo-kinetic characteristics of two other major sugarcane residues, namely sugarcane straw (S.C.S.) and sugarcane bagasse (S.C.B.). In this regard, the thermogravimetric analysis is used to evaluate the pyrolysis behavior of sugarcane residues at seven distinct heating rates in a nitrogen atmosphere. The Kissinger34, Friedman35, and ANIC39,40 methods were utilized to obtain the activation energies. Moreover, the compensation effect theory29,32 and the combined kinetic analysis52 were employed to determine the samples pre-exponential factor and pyrolysis kinetic model using TG data. Simultaneously, a procedural and repeatable workflow for analyzing the results of the selected convergent approaches, in terms of determining the proper pyrolysis reaction model and estimating the kinetic parameters, is proposed based on the successful agreement between the study outcomes and the experimental data.
The materials and experimental procedures utilized in this study have been previously described in our recent publication1. Sugarcane residues were collected from the CP69-1062 variety obtained from Karun Agro-Industry in Iran's Khuzestan province. It is important to mention that these materials are waste or by-products of the harvesting, juice extraction, and milling industrial processes of sugarcane, and do not involve the collection or utilization of live sugarcane plants. The use of these industrial residues complies with relevant institutional, national, and international guidelines and legislation governing the utilization of agricultural waste products for research purposes. All samples were prepared according to ASTM E1757-01 (2015) standards. Dry samples were crushed using a Retsch PM 100 planetary ball mill, sieved to a particle size of ≤ 212 μm (US Mesh 70), and then analyzed using a Mettler-Toledo TGA 1 thermal analyzer under high-purity nitrogen at a flow rate of 50 mL/min. The heating protocol involved ramping the temperature at 10 °C/min up to 105 °C, followed by a 10 min hold and further heating to 800 °C. Heating rates ranging from 10 to 40 °C/min were tested with approximately 10.7 mg of each sample. The entire TGA procedure was repeated three times, with an average deviation of less than 1.45%.
In thermogravimetric analysis (TGA), the degree of conversion (α) is defined as the mass fraction of the decomposed solid throughout the process. The degree of conversion (α) is calculated using the initial mass (m0), final residual mass (mf), and mass at any given time (mt) according to Eq. (1):
Assuming that all of the components in solid or many condensed phases have the same reactivity and ignoring the influence of pressure on thermal analysis kinetics22,53, the kinetics of a single-step reaction can typically be described by the following rate equation. This equation can be considered as a product of two independent functions22:
where in Eq. (2) α is the degree of conversion, t is the conversion time, dα/dt is the rate of the reaction process, k(T) is the reaction rate constant, T is the reaction temperature, and f(α) is a conversion function that demonstrates the reaction model used and relies on the controlling mechanism.
The effect of temperature on the reaction rate is typically assumed to follow the Arrhenius equation, as shown below22:
where A, Ea and R are the Arrhenius pre-exponential factor, the activation energy, and the universal gas constant, respectively.
In certain conditions, the non-isothermal reaction rate expressions can be represented under constant heating rate (β), alongside corresponding superficial transformation equations, as follows:
By combining Eqs. (2), (3), and (5), Eq. (2) turns into:
In the case where A remains a constant, the integral form of Eq. (6) can be represented by the following equation22,28:
Alternatively, Eq. (7) can be concisely reformulated as the temperature integral function:
In these expressions, g(α) signifies the integral representation of the reaction model, while I(Ea, T) or J(Ea, T(t)) denote temperature integral functions. Table 1 comprises a well-known set of the reaction models and their integral counterparts, highlighting the dependence on α in the reaction kinetics22,32. Equations (6) and (7) are considered as the basic equations of differential and integral methods, respectively.
If the degree of conversion is kept constant, then f (α) is fixed at any temperature or temperature regime. In this scenario, the process mechanism becomes exclusively dependent on the conversion instead of the temperature22,28. Isoconversional methods, based on these assumptions, facilitate the estimation of activation energy without being constrained by a specific reaction model.
In accordance with the selected approach and associated hypotheses, various isoconversional methods have been extensively detailed in existing literature32,34,35,37,38,39,40. These techniques commonly determine the activation energy at a predetermined conversion degree using data obtained through a series of TG runs.
The Kissinger method relies on obtaining the maximum reaction peak temperature and the corresponding maximum reaction rate from each heating rate series generated by thermal analysis instruments, such as DSC and TGA. The method's basic equation is Eq. (6), where the maximum rate takes place when d2α/dt2 is zero22,34:
here, f′(α) = df(α)/dt, and the subscript m specifies the variables related to the maximum reaction rate. If the reaction model is assumed to be first order (Table 1) and the natural logarithm is used, Eq. (9) can be stated as follows22,34:
where i represents the index of the individual heating rate (β). The activation energy (Ea) and pre-exponential factor (A) can be determined by plotting ln(β/T2m,i) against 1/Tm,i and fitting all the data with a straight line.
Performing a natural logarithmic transformation to Eq. (6) gives:
in Eq. (11), known as Friedman’s method35, i is the individual heating rate (β) index, and Tα,i is the temperature at which the degree of conversion α is accomplished. For any specified value of α, the slope of a plot of ln(dα/dt)α,i against 1/Tα,i yields the value of Ea, and the mathematical function f(α), which describes the reaction model, can be determined from the intercept of the plot. Equation (11) can be used with any temperature program, in addition to its applicability to linear heating programs.
Integrating Eq. (7) over small time intervals (tα-Δα) → tα provides the following results for each given value of α27,40:
Equation (12) lacks a fully analytical solution; hence Ea,α must be calculated numerically. Following the isoconversional method assumptions, it is presumed that g(α) is constant at equivalent conversions (at each heating rate). In other words, the response reaction model remains mostly unchanged and maintains a consistent structure at the given conversion. Consequently, based on Eqs. (8) and (12), for a particular conversion and relying on the outcomes of a series of experiments conducted at a discrete heating rate (βi), the following can be expressed:
under a constant heating rate, one could express:
This implies that for a given conversion and a set of experiments performed at nth arbitrary heating rates, the following results could be obtained, according to Eqs. (8) and (12):27,54
Equation (16) can be generalized by dividing both sides of Eq. (15) by one another and summing. The result is54:
In Eq. (17), the optimization indicator is designated by the symbol Ωα, signifying the minimum achievable value of the equation. Additionally, the temperature integral functions (J) can be calculated using the trapezoidal rule40, or the Senum and Yang approximation27,39,55,56. Eα can be determined as the value that minimizes Ωα by repeating the optimization procedure for each α value using Eq. (17)40,54. Equation (17) is applicable to a wide range of temperature programs, and its accuracy depends on the size of the integral step28,57.
In the following, the integral methods can be employed to obtain the mathematical function that describes the reaction model through the application of Eq. (18):31
By applying the presumption that the reaction model is constant over a small conversion interval and is independent of the heating rate to the integral function on the left side of Eq. (18), the mathematical function f(α) describing the reaction model can be obtained from Eq. (19):
Finding the reaction model and pre-exponential factor may be accomplished by combining the outcomes of a model-free approach and a model-fitting method for a particular heating rate22. Several methods exist in the model-free and isoconversional computations to estimate the pre-exponential factor. These methods can be classified as model-based or model-free22,29. Researchers28,29,30,31 have demonstrated that when the Eα varies significantly with α, as it does in a multi-step process, the application of model-free based procedures leads to outstanding results, notably for the Friedman and ANIC methods. The objective is to take advantage of the compensation effect (CE), expressed as follows58:
In order to compute the pre-exponential factor, after evaluating Ea using an isoconversional technique, several values of Ea and A could be determined by the model-fitting method based on TG experimental data gathered at a single heating rate for each reaction model presented in Table 1. Finally, by utilizing these values and Eq. (20), and obtaining values for a and b, the pre-exponential factor can be calculated based on each pre-evaluated value of Ea.
Adaptable theoretical models are commonly utilized to accurately represent and justify deviations from idealized processes28,59,60. The most well-known model is a modified form of Sestak and Berggren's truncated equation (tSB)22,52.
Pérez-Maqueda52 revealed that the findings of the combined kinetic analysis (CKA) (i.e., Ea, A, and f(α)), obtained from linear model-fitting of TG analysis data collected from arbitrary temperature programs to the tSB reaction model, could be reconciled with a number of theoretical reaction models (e.g., Table 1). This method has the advantage that the reaction model is not confined to Table 1 or comparable kinetic models. Considering the CKA approach, the following generic form is used to determine the kinetic model52:
In fact, Eq. (21) could be adjusted by modifying the values c, n, and m to match different ideal kinetic models developed under particular mechanistic assumptions52.
The combined kinetic analysis is relied on rearranging Eq. (6) and replacing f(α) with Eq. (21):
The unknown kinetic parameters of Eq. (22) can be effectively determined using the nonlinear optimization method and thermogravimetric data collected at one or more heating rates. Afterwards, the optimization results are employed to evaluate the maximum correlation coefficient (R2). This assessment is carried out using the linear representation of Eq. (22), within specific conversion (α) ranges. The indicated evaluation provides the values of n and m, along with the intercept (ln(cA)) and slope (Ea) of Eq. (22) over the specified conversion (α) range. If the values of n and m do not fall within the expected range of one of the ideal kinetic models (see Table 1), it becomes impossible to separate the variables c and A in the intercept (ln(cA)) of Eq. (22). However, studies have demonstrated that the impact of c on the pre-exponential factor, commonly denoted as ln(A), is negligible and can be disregarded under certain conditions due to the relatively small value of c22.
In conclusion, it can be stated that although the effect of conversion on the reaction rate as determined by the CKA method (i.e., f(α)) may not be entirely consistent with any ideal kinetic model, the results obtained can still be used to compare isoconversional methods for identifying a correct reaction model22.
The following general equation can be written using Eyring's active complex theory to derive the thermodynamic parameters61:
In Eq. (23), \(\frac{{\kappa }_{B}T}{h}\) is the frequency of vibration of the high-energy, active complex surmounting the transition state energy barrier62. The probability that a chemical reaction will occur once the system has attained the active state is indicated by the transmission coefficient (κ). The transmission coefficient quantifies the probability that a complex would dissociate into products rather than reactants61,63. Theoretically, κ might range from zero to one, but it often takes unity61.
Whether the reaction is monomolecular or bimolecular, the difference between ∆H* in Eq. (23) and Ea in Eq. (3) is only one or two R.T. values. Since this discrepancy typically falls within the expected range of experimental activation energy uncertainty, which is around 5–10%, it can be overlooked29,64. By comparing Eqs. (3) and (23) and assuming ∆H*≈ Ea, the change of the activation entropy at the formation of an activated complex from the reactant is obtained:
The following thermodynamic relationship is used to calculate the Gibbs free energy of the activated complex formation:
In contrast, by substituting Eq. (3) in Eq. (23) and considering Eq. (26), the value of \(\Delta {G}^{*}\) can also be obtained from the following equation:
According to the equations, two approaches for determining the thermodynamic parameters are compared in Eqs. (24)–(27). Method I, consists of Eqs. (24)–(26), while Method II consists of Eqs. (25)–(27). In Eqs. (23)–(27) κB is the Boltzmann constant (1.38065 × 10–23 J/K), h is the Planck constant (6.62607 × 10–34 J.s), the value of κ is assumed to be one, ∆S* (J/mol.K), ∆H* (kJ/mol) and ∆G* (K.J./mol) are the entropy, enthalpy and Gibbs free energy of activation, respectively. All thermodynamic parameters based on Method I or II can be obtained by substituting T = Tp, the maximum decomposition temperature from the differential thermogravimetry (DTG) data, in Eqs. (24)–(27).
In this section, following a thorough examination and analysis of laboratory results, the investigation unfolds in a systematic sequence. Firstly, the outcomes related to the activation energy and the ‘ln(f(α)Aα)’ quantity, derived through the application of the Friedman and ANIC isoconversional methods, are presented. Subsequently, the assessment of the reaction model is conducted using the CKA procedure. Employing the CE methodology, the values of the pre-exponential factor are scrutinized. Additionally, using both the CKA and CE results, the ‘ln(f(α)Aα)’ quantity is computed and compared with the values obtained through the isoconversional methods. Finally, the thermodynamic parameters of the process are computed and examined using the final results in all three tested samples. The procedural workflow of the kinetic analysis in this study is shown in Fig. 1.
Procedural workflow of the kinetic analysis.
The summary of the experimental analysis of sugarcane residues is presented in Table 2 [In the table, the reported values represent the average of three replicate experiments, ‘ ± S.D.’ indicates standard deviation, ‘db.’ denotes the dry basis, fixed carbon calculated by difference (dry basis): 100-VM-Ash, and oxygen content calculated by difference (dry basis): 100-(C + H + N + Ash)]. These experimental results are derived from our recent study1.
The composition of biomass polysaccharides and their monosaccharide components significantly impact both the rate of thermal decomposition and the thermal stability of biomass1. Thermogravimetric analysis (TGA) findings (see Fig. 2) have allowed the categorization of the thermal decomposition of three biomass samples, namely S.C.S., S.C.B., and S.B.P., into four distinct stages1:
Dehydration Stage (< 423 K): This stage involves the removal of internal and external water from the biomass.
Torrefaction Stage (423–548 K): During this stage, extractives and a portion of hemicellulose undergo decomposition.
Active Pyrolysis Stage (548–673 K): In this zone, hemicellulose, cellulose, and a portion of lignin are decomposed. The derived thermogravimetry (DTG) curve typically exhibits two prominent peaks, with the dominant peak attributed to the devolatilization of cellulose.
Passive Pyrolysis Stage (673–1073 K): This stage primarily involves the decomposition of lignin.
TG and DTG curves of (a) S.C.S., (b) S.C.B., and (c) S.B.P. at various heating rates.
According to Fig. 2 and Table 3 [In the table, ‘ ± S.D.’ indicates standard deviation], comparing weight changes at different temperature ranges, it was observed that S.C.S. and S.B.P. experienced greater weight loss than S.C.B. during the torrefaction stage. The weight loss in S.C.S. was mainly attributed to extractive materials, while in S.B.P., the type of hemicellulose and its interactions with other polysaccharides affected the rate of weight loss within this stage1. In the active pyrolysis zone, S.C.B. demonstrated the highest weight loss and thermal degradation rate due to its elevated levels of hemicellulose and cellulose content1,41.
The peak temperature analysis of the DTG profile for S.C.S., S.C.B., and S.B.P. at the different heating rates in the active pyrolysis zone is shown in Table 4. Accordingly, the decomposition rate and peak temperature are increased with increasing the heating rate for all samples. The results showed that the average first and second peak temperature (mainly related to the hemicellulose and cellulose, respectively) of S.C.B. is equal to 602 and 644 K and are higher than the average peak temperature of S.B.P. (i.e., 600 and 642 K) and S.C.S. (i.e., 576 and 619 K), respectively. Accordingly, a similar result can be obtained for the decomposition rate at the different heating rates as follows: S.C.S. < S.B.P. < S.C.B.
In this investigation, the kinetic parameters were determined employing the in-house kinetic calculation software known as XTKinetic, developed on the Python platform. The results of the linear regression parameters obtained using the Kissinger method are shown in Table 5 [In the table, the uncertainty ( ±) was determined using the traditional standard error approach with 95% confidence intervals65]. Additionally, Tables 6 and 7 [In the table, \({\Omega }_{\alpha }^{*}={\Omega }_{\alpha }-n\left(n-1\right)\) ] present outcomes for activation energies (Ea) and ln(f(α)Aα, along with their error metrics (i.e., R2 and \({\Omega }_{\alpha }\) ), for S.C.S., S.C.B., and S.B.P. samples determined using Friedman and ANIC methods. Both methodologies involved computing Ea within a conversion factor (α) range of 0.1–0.7 and a heating rate (β) of 10–40 K/min.
It is worth mentioning that, in this study, the conversion factors greater than 0.7 were not considered due to their potential non-linear behavior and the increased likelihood of precision loss, particularly in the vicinity of the TGA/DTG peak tail20. A critical observation suggests that an accurate assessment of the Ea dependency is achievable by approximating the temperature integral with a small Δα, specifically 0.0228,30. Therefore, in our research, the computation was executed for every α value within the range of 0.1 to 0.7, utilizing a step size of 0.01.
Furthermore, the uncertainty of the activation energy (Ea) obtained from the Friedman method was estimated using the traditional linear regression standard error approach, in line with 95% confidence intervals65. This analysis was performed in conjunction with Vyazovkin and Sbirrazzuoli modifications66. Also, the uncertainty in the Ea value calculated by the ANIC method was assessed by applying the approach recommended by Vyazovkin and Wight67, incorporating 95% confidence intervals. Figure 3 depicts the dependency of the activation energy (Ea) on the conversion factor and its uncertainty for three samples.
Dependence of activation energy (Ea) on conversion factor (α) of (a) S.C.S., (b) S.C.B., and (c) S.B.P.
As can be observed in Fig. 3, the pyrolysis activation energies of each biomass sample increase until the conversion degrees of 0.45, then decrease slightly until the conversion degrees of 0.6 before increasing significantly for the conversion degrees higher than 0.7. The likelihood of an accelerated decomposition process for the primary composition, which approaches equilibrium at early stages, is inferred by the minor increase in activation energy (Ea) for S.C.S. and S.C.B. before the conversion value of 0.2. It should be highlighted that this expedited degradation process may differ from the one at the start of the thermal conversion, which is mainly caused by the degradation of low-molecular composition68. The decrease in the activation energy (Ea) for S.B.P. at α < 0.2 could be attributed to the type of hemicellulosic material present in this biomass1,69,70 as well as the depithing process71, which involves the lignin softening and rearrangement of fibers. Furthermore, the larger drop in activation energy (Ea) for S.C.B. and S.B.P. at α > 0.45 may be attributed to the reduced lignin concentration of S.C.B. and S.B.P. compared to S.C.S. The limited deviation of activation energy (Ea) values at 0.15 < α < 0.3 for S.C.S. indicates that the hemicellulose degradation mechanism in S.C.S. remains similar throughout the selected conversion range. Moreover, the deviation from linearity in the final conversions of S.C.S., S.C.B., and S.B.P. can be ascribed to intricate multi-step reaction mechanisms unfolding across a spectrum of temperatures under various heating rates, all influenced by heat and mass transport mechanisms68,72. The Friedman plot for S.C.S., S.C.B., and S.B.P. are shown in Fig. 4. The conversion factors of 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, and 0.7 were employed in the regression analyses. All potential conversions produce almost parallel fitted lines, consistent with similar activation energy across the conversions. Besides, when the fitting lines are not parallel, it can be inferred that a shift from one set of reaction mechanisms to another has occurred68,73.
Friedman plot of (a) S.C.S., (b) S.C.B., and (c) S.B.P. at different conversion factor (α).
The findings of the Friedman method indicated that the activation energies of S.C.S., S.C.B., and S.B.P. are around 171–199 (avg., 188), 144–185 (avg., 170), and 136–164 (avg., 151) kJ/mol, respectively. As can be seen, the application of the ANIC method leads to results that are extremely close to the specified ranges. Specifically, Kissinger74 demonstrated that his approach causes the Ea values to be underestimated. The results presented in Table 5 confirm this proposition. Investigations show that the obtained Ea values are comparable and close to the values reported in the literature for thermal decomposition of S.C.S. and S.C.B.41,60,72,73,75. However, no analogous results were found for the pyrolysis of S.B.P. As shown in Fig. 3, if the conversion step (Δα) in the ANIC method is lower than 0.02 (here 0.01 is chosen), then the values of the activation energy and ln(f(α)Aα) obtained will be quite near to those obtained from Friedman method, even though the trend and Ea values deviate significantly from Friedman method for larger values of Δα (e.g., Δα > 0.02).
Table 8 [The uncertainty ( ±) was determined using the traditional standard error approach with 95% confidence intervals65] and Fig. 5 present the findings of the combined kinetic analysis (CKA) for S.C.S., S.C.B., and S.B.P. across seven heating rates. According to the results for S.C.B., a conversion factor (α) of 0.1–0.75 yields the highest R2 value, whereas, for S.C.S. and S.B.P., the corresponding ranges were 0.1–0.7. Comparing the results of activation energies in Table 6 and Table 8 show that the activation energies (Ea) obtained using CKA for S.C.S., S.C.B., and S.B.P. differ by 4.78%, 2.62%, and 1.66%, from the average Friedman method results, respectively. Similarly, comparable outcomes can be achieved through the application of the ANIC method. In this context, it becomes evident that the outcomes from both the Friedman and ANIC methods are in close agreement. Based on this and the findings already described, also by ignoring the calculation of c in Eq. (22), the optimization outcomes will be analysed and compared in the following sections.
Combined kinetic analysis plot for (a) S.C.S., (b) S.C.B., and (c) S.B.P.
In order to determine the pre-exponential factor, TGA data and a model-fitting method were used to evaluate 15 reaction models presented in Table 1 in accordance with the compensation effect (CE) study described in Section "Determining the pre-exponential factor". The statistical parameters mentioned in Table 9 [In the table, in Eqs. (28)–(34), n: number of data points, \({\omega }_{i}\) : the weight corresponding to ith value of the variable, p: number of model parameters, \({y}_{i}\) : ith value in a sample, \({\widehat{y}}_{i}\) : ith value of the variable to be predicted, \(\overline{y }\) : mean value of a sample] were utilized to compare the obtained results. It was also shown that one of the most useful metrics for the model selection and statistical analysis is the normalized root means square error (nRMSE) parameter. Accordingly, besides Bayesian information criterion (BIC) and Akaike's information criterion (AIC), nRMSE has also been utilized as an accuracy metric in the model selection76,77,78. In this analysis, the model accuracy has been marked as “outstanding” when nRMSE was less than 10%, “good” when nRMSE was between 10 and 20%, “fair” when nRMSE was between 20 and 30%, and “poor” when nRMSE was greater than 30%77.
To achieve the maximum possible R2 from the model-fitting procedure, the optimal range of conversion factor (α) of TGA data for S.C.S. was 0.1–0.7, while the corresponding ranges for S.C.B. and S.B.P. were 0.1–0.75 and 0.1–0.8, respectively.
In the present study, the best set of the calculated model-fitting kinetic parameters based on the heating rate that leads to the appropriate CE-dependent parameters was chosen. This decision was made based on comparing the relative error between ln(f(α)Aα) calculated from CE parameters at different heating rates and the reaction model obtained from CKA with the results obtained from the Friedman and ANIC method. On the basis of this information, the heating rate of 15 K/min was found to produce the best results considering the agreement with the TGA experiments. It should be noted that, a comparative analysis revealed that the values of the pre-exponential factor (ln(Aα)), obtained through the compensation effect methodology and involving fitting 15 reaction models at different heating rates, exhibit a standard deviation ranging from 0.02 to 0.1 for all three samples.
Figure 6 and Table 10 illustrate the CE plot and the outcomes of the model-fitting method for the heating rate of 15 K/min across all three samples. Also, Table 11 provides the acquired CE parameters. From Table 10 and in accordance with the defined range for nRMSE, it can be seen that the results of the reaction models F1, F2, A2, A3, and A4 for S.C.S., F1, F2, A2, A3, A4, R2, and R3 for S.C.B., and F1, A2, A3, A4, R2, R3 and D3 for S.B.P., have “good” accuracy compared to other models, while the results from other models do not. It is worth noting that the related conclusions can be deduced for other heating rates.
Compensation effect plot (dot line) for (a) S.C.S., (b) S.C.B., and (c) S.B.P. The data points on the graph represent the ln(A) and Ea values that were determined for the 15-reaction models in Table 1 using a heating rate of 15 K/min.
The AIC, BIC, and R2 all confirm the accuracy evaluation. The results indicate that nRMSE can be used to select the optimal model for all three samples, whereas the level of empirical support of the model (e.g., AIC-AICmin) with different selection ranges, as well as the R2, could only verify the selected model. Additionally, while certain models assessed in this work have an AIC-AICmin that does not meet the threshold of acceptability (less than 10), it has been shown that for the non-nested models, this threshold might be greater79. It should be emphasized that although the R2 comparison results are compatible with other statistical metrics, caution should still be taken when relying on R2 alone since it is defined as a pseudo-R283 and is not directly attainable from the nonlinear optimization techniques.
A comparison of the results obtained in the previous three sections reveals that the ln(f(α)Aα) values, calculated using the CE and CKA procedures for S.C.S., S.C.B., and S.B.P. are, on average, approximately 5% higher, 6% higher, and 7% lower than those obtained through Friedman and ANIC methods, respectively. However, the trend of ln(f(α)Aα) calculated based on ln(Aα) derived from the chosen reaction models and that of f(α) produced by CKA are consistent with the outcomes obtained using these methods. Furthermore, according to Sbirrazzuoli31, using the 4-reaction models Avrami-Erofeev (A2, A3, A4) and Mampel (F1) for CE parameter computation can result in trustworthy values. This study demonstrates that while all of the 4-reaction models are among all of the selected reaction models, calculating ln(f(α)Aα) with the 4-reaction approach could increase its value by as much as 18% for S.C.S., 6% for S.C.B., and 20% for S.B.P. compared to the ln(f(α)Aα) obtained using Friedman and ANIC methods.
In general, it can be stated that using a 4-reaction or the selected reaction model based on the statistical metrics of the model-fitting findings to calculate the CE parameters yields the final results of ln(f(α)Aα) with the same trend as those of the model-free methods. However, the final values of ln(f(α)Aα) might be produced with an absolute relative error of 5–20% due to the type of raw material, the accuracy of the experimental results, and the error-prone nature of the non-linear optimization approaches. This could be supported by similar findings in the published literature84.
According to the provided explanations and the experimental TG data of the present study (see Fig. 2), the optimal ln(f(α)Aα) is resulted by selecting all 15 reaction models for CE parameters computation and employing the CKA reaction model for f(α) calculation.
Assuming that c is equal to one, Fig. 7 and Table 12 depict the comparison between the results obtained from the Friedman method (see Table 6) and the computed value for the quantity ln(f(α)Aα) with CE-CKA findings. To calculate ln(f(α)Aα), Aα is computed using Eq. (20), with the CE parameters obtained from the 15 and 4-reaction models, as shown in Table 11. Additionally, values of f(α) are determined based on the CKA results presented in Table 8 and Eq. (21).
Comparison of ln(f(α)Aα) based on the Friedman method and CE + CKA results for (a) S.C.S., (b) S.C.B., and (c) S.B.P.
Based on these findings, it can be concluded that the average relative error for ln(f(α)Aα) estimated using the CKA and CE methods for S.C.S., S.C.B., and S.B.P., compared to the values obtained using the Friedman method, is 0.407%, 0.526%, and 0.492%, respectively. The application of ANIC method yields comparable results; however, there is a slight increase in the average relative error for the estimated ln(f(α)Aα), which is 0.507%, 0.565%, and 0.698% for S.C.S., S.C.B., and S.B.P., respectively.
To calculate the thermodynamic parameters, it is necessary to determine the reaction's kinetic characteristics at first and then assess the reaction's maximum peak or the decomposition temperature. The maximum peak temperature (Tp) value can be obtained in a few different ways: (1) using the highest possible degradation temperature in the DTG curve at each heating rate or at the lowest heating rate, (2) by taking the average of the highest possible temperatures across all heating rates85,86. In this research, the maximum peak temperature is considered corresponding to β → 0, and it is determined by solving the quadratic equation, a0 + a1.β + a2.β2, where a0, a1, and a2 are the numerical coefficients, and the reciprocal value of the a0 coefficient is identical to Tp at β → 068,87,88. In this regard, the value of maximum peak temperature according to Table 4 for S.C.S., S.C.B., and S.B.P. has been calculated as 591.38, 612.13, and 605.52 K, respectively.
Table 13 presents the average values of ∆S*, ∆H*, and ∆G* that were obtained by two distinct methods (Method I and II) based on the findings of the Friedman method. It should be noted that similar outcomes to those of the Friedman method could be obtained using the ANIC method.
The values of ∆S* and ∆H* are seen to increase up to the range of conversion 0.45, then decrease relatively up to the conversion reaches of 0.6, after which they rise again. In contrast, ∆G* exhibits a relative decline up to the conversion range of 0.45, then increases up to the range of 0.6 before declining again. Singh et al.89 have also observed a similar trend in this regard.
The value of ∆S* signifies the extent to which a reaction tends to be in either the transition state or the ground state. A decreased or negative value of ∆S* indicates that the reaction can proceed with less energy and difficulty. In such cases, ∆S* often suggests an associative mechanism in which two reactants form a single active complex90.
∆S* values close to zero (e.g., S.C.B.) during pyrolysis indicate that the feedstock experienced only slight chemical or physical change, resulting in a new condition close to its thermodynamic equilibrium. A low value of ∆S* lengthens the time required for the pyrolysis reaction (referred to as "slow" reactions)91,92.
Larger negative values of ∆S* (e.g., S.B.P.) indicate that the degree of disorder in the products is significantly lower compared to the initial reaction state, while positive values reveal the opposite93. In these circumstances, the reaction can involve a bimolecular step and is most likely a second-order reaction. ∆S* in such instances indicates the entropy loss caused by the unification of the two reaction partners into a single transition state90. The devolatilization stage of all three samples produced negative ∆S* values, which is a significant finding. A high or positive value of ∆S* indicates that the activated complex, which is about to dissociate, has a high reactivity (associated with “fast” reactions) and is distant from the thermodynamic equilibrium state. Naturally, if the value of ∆S* is more positive (e.g., S.C.S.), a fast reaction can have a higher activation energy90,91,92.
A significant factor in assessing whether a decomposition process is endothermic or exothermic is the value of the enthalpy change parameter ∆H*, which may be positive or negative. Moreover, ∆H* is an important thermodynamic parameter for determining the energy required to convert the biomass into bioenergy products. Positive values of ∆H* indicate that an external heat source is necessary for biomass pyrolysis to produce biofuels and bio-based compounds, as is typical of an endothermic reaction92. The activation energies are consistent with the value of ∆H* being equal to the difference between the reagent and the activated complex94. The difference between activation energy (Ea) values and ∆H* reveals the likelihood of the pyrolysis reaction93. More specifically, a lower ∆H* value suggests that the product formation was easier, whereas a larger ∆H* value shows that the product formation was more complex95.
∆G* is a parameter that reveals the amount of energy available from the feedstock throughout the pyrolysis process. It is also used to determine the spontaneity of the decomposition process, which is another essential factor92,93,94,95. Positive results for ∆G* and ∆H* in the thermodynamic parameters of S.C.S., S.C.B., and S.B.P. support the conclusion that the pyrolysis process is non-spontaneous, endothermic, and the event was also endergonic.
This research explored the thermo-kinetic characteristics of sugarcane bagasse pith (S.B.P.) and conducted a comparative evaluation with two other significant sugarcane residues, namely sugarcane straw (S.C.S.) and sugarcane bagasse (S.C.B.), throughout the pyrolysis process. The study utilized rigorous thermogravimetric analysis and kinetic computations. Key findings include the robust agreement between the ANIC and Friedman methods, demonstrating consistency in ln(f(α)Aα) and activation energy values. Furthermore, the study demonstrates that if a small step size (e.g., Δα ≈ 0.01) is chosen for the ANIC method, the activation energy range calculated for S.C.S. (171–199 kJ/mol), S.C.B. (144–185 kJ/mol), and S.B.P. (136–164 kJ/mol) using Friedman's method were vin close agreement with ANIC results.
The method of calculating the ln(f(α)Aα) quantity using two different methodologies, including CE and CKA, and comparing the results with those of the isoconversional method, along with accuracy assessments, exhibits scalability and precision in our approach. Additionally, the study shows that the application of different reaction models in the CE method to obtain the pre-exponential factor may lead to final results of ln(f(α)Aα) with an absolute relative error of 5–20%.
Thermogravimetric analysis in the study reveals an accelerated decomposition process in the early stages, shaped by factors such as low-molecular composition and the influence of hemicellulosic material, providing qualitative insights into the distinctive thermal characteristics of each sample.
Thermodynamic analysis affirms the non-spontaneous and endothermic nature of pyrolysis for S.B.P., S.C.S., and S.C.B. Moreover, a distinct trend is revealed through the results obtained from activation energy and thermodynamic calculations, indicating that S.B.P. has lower thermal stability compared to S.C.B. and S.C.S. These findings align with physicochemical characterizations, emphasizing operational considerations for samples and highlighting the bioenergy potential of S.B.P., S.C.S., and S.C.B.
It should be justified that “All data generated or analyzed during this study are included in this published article”.
Najafi, H., Golrokh Sani, A. & Sobati, M. A. A comparative evaluation on the physicochemical properties of sugarcane residues for thermal conversion processes. Ind. Crops Prod. 202, 117112 (2023).
Aguiar, A. et al. Sugarcane straw as a potential second generation feedstock for biorefinery and white biotechnology applications. Biomass and Bioenergy 144, 105896 (2021).
Sharma, A., Pareek, V. & Zhang, D. Biomass pyrolysis—A review of modelling, process parameters and catalytic studies. Renew. Sustain. Energy Rev. 50, 1081–1096 (2015).
Dhyani, V. & Bhaskar, T. A comprehensive review on the pyrolysis of lignocellulosic biomass. Renew. Energy 129, 695–716 (2018).
Pawar, A., Panwar, N. L. & Salvi, B. L. Comprehensive review on pyrolytic oil production, upgrading and its utilization. J. Mater. Cycles Waste Manag. 22, 1712–1722 (2020).
Sharma, G., Kaur, M., Punj, S. & Singh, K. Biomass as a sustainable resource for value-added modern materials: A review. Biofuels Bioprod. Biorefining 14, 673–695 (2020).
Pecha, M. B., Arbelaez, J. I. M., Garcia-Perez, M., Chejne, F. & Ciesielski, P. N. Progress in understanding the four dominant intra-particle phenomena of lignocellulose pyrolysis: Chemical reactions, heat transfer, mass transfer, and phase change. Green Chem. 21, 2868–2898 (2019).
Wang, G. et al. A review of recent advances in biomass pyrolysis. Energy & Fuels 34, 15557–15578 (2020).
Wang, S., Dai, G., Yang, H. & Luo, Z. Lignocellulosic biomass pyrolysis mechanism: A state-of-the-art review. Prog. Energy Combust. Sci. 62, 33–86 (2017).
Ranzi, E. et al. Chemical kinetics of biomass pyrolysis. Energy & Fuels 22, 4292–4300 (2008).
Di Blasi, C. Modeling chemical and physical processes of wood and biomass pyrolysis. Prog. Energy Combust. Sci. 34, 47–90 (2008).
Houston, R., Oyedeji, O. & Abdoulmoumine, N. Detailed biomass fast pyrolysis kinetics integrated to computational fluid dynamic (CFD) and discrete element modeling framework: Predicting product yields at the bench-scale. Chem. Eng. J. 444, 136419 (2022).
Xing, J. et al. Predictive single-step kinetic model of biomass devolatilization for CFD applications: A comparison study of empirical correlations (EC), artificial neural networks (ANN) and random forest (RF). Renew. Energy 136, 104–114 (2019).
Lu, L. et al. Multiscale CFD simulation of biomass fast pyrolysis with a machine learning derived intra-particle model and detailed pyrolysis kinetics. Chem. Eng. J. 431, 133853 (2022).
Díez, D., Urueña, A., Piñero, R., Barrio, A. & Tamminen, T. Determination of hemicellulose, cellulose, and lignin content in different types of biomasses by thermogravimetric analysis and pseudocomponent kinetic model (TGA-PKM Method). Processes 8, 1048 (2020).
Morya, R. et al. Recent advances in black liquor valorization. Bioresour. Technol. 350, 126916 (2022).
Article CAS PubMed Google Scholar
Miranda, M. I. G., Bica, C. I. D., Nachtigall, S. M. B., Rehman, N. & Rosa, S. M. L. Kinetical thermal degradation study of maize straw and soybean hull celluloses by simultaneous DSC–TGA and MDSC techniques. Thermochim. Acta 565, 65–71 (2013).
Yao, C. et al. Thermogravimetric analysis and kinetics characteristics of typical grains. J. Therm. Anal. Calorim. 143, 647–659 (2021).
Cano-Pleite, E., Rubio-Rubio, M., Riedel, U. & Soria-Verdugo, A. Evaluation of the number of first-order reactions required to accurately model biomass pyrolysis. Chem. Eng. J. 408, 127291 (2021).
Kumar, A. & Reddy, S. N. Study the catalytic effect on pyrolytic behavior, thermal kinetic and thermodynamic parameters of Ni/Ru/Fe-impregnated sugarcane bagasse via thermogravimetric analysis. Ind. Crops Prod. 178, 114564 (2022).
Brown, M. E. et al. Computational aspects of kinetic analysis Part A: The ICTAC kinetics project-data, methods and results. Thermochim. Acta 355, 125–143 (2000).
Vyazovkin, S. et al. ICTAC Kinetics Committee recommendations for performing kinetic computations on thermal analysis data. Thermochim. Acta 520, 1–19 (2011).
White, J. E., Catallo, W. J. & Legendre, B. L. Biomass pyrolysis kinetics: A comparative critical review with relevant agricultural residue case studies. J. Anal. Appl. Pyrolysis 91, 1–33 (2011).
Vyazovkin, S. & Sbirrazzuoli, N. Isoconversional Kinetic Analysis of Thermally Stimulated Processes in Polymers. Macromol. Rapid Commun. 27, 1515–1532 (2006).
Vyazovkin, S. Computational aspects of kinetic analysis: Part C. The ICTAC Kinetics Project—The light at the end of the tunnel?. Thermochim. Acta 355, 155–163 (2000).
Sbirrazzuoli, N. Advanced isoconversional kinetic analysis for the elucidation of complex reaction mechanisms: A new method for the identification of rate-limiting steps. Molecules 24, 1683 (2019).
Article CAS PubMed PubMed Central Google Scholar
Vyazovkin, S. & Dollimore, D. Linear and nonlinear procedures in isoconversional computations of the activation energy of nonisothermal reactions in solids. J. Chem. Inf. Comput. Sci. 36, 42–45 (1996).
Vyazovkin, S. Isoconversional Methodology. In Isoconversional Kinetics of Thermally Stimulated Processes 27–62 (Springer, 2015). https://doi.org/10.1007/978-3-319-14175-6_2.
Vyazovkin, S. Determining preexponential factor in model-free kinetic methods: How and why?. Molecules 26, 3077 (2021).
Article CAS PubMed PubMed Central Google Scholar
Sbirrazzuoli, N. Determination of pre-exponential factor and reaction mechanism in a model-free way. Thermochim. Acta 691, 178707 (2020).
Sbirrazzuoli, N. Determination of pre-exponential factors and of the mathematical functions f(α) or G(α) that describe the reaction mechanism in a model-free way. Thermochim. Acta 564, 59–69 (2013).
Vyazovkin, S. Modern isoconversional kinetics: From misconceptions to advances. Handb. Therm. Anal. Calorim. 6, 131–172 (2018).
Vyazovkin, S. et al. ICTAC Kinetics Committee recommendations for analysis of multi-step kinetics. Thermochim. Acta 689, 178597 (2020).
Kissinger, H. E. Reaction kinetics in differential thermal analysis. Anal. Chem. 29, 1702–1706 (1957).
Friedman, H. L. Kinetics of thermal degradation of char-forming plastics from thermogravimetry: Application to a phenolic plastic. J. Polym. Sci. Part C Polym. Symp. 6, 183–195 (1964).
Ozawa, T. A New Method of Analyzing Thermogravimetric Data. Bull. Chem. Soc. Jpn. 38, 1881–1886 (1965).
Flynn, J. H. & Wall, L. A. General treatment of the thermogravimetry of polymers. J. Res. Natl Bur. Stand. Sect. A Phys. Chem. 70A, 487–523 (1966).
Akahira, T. & Sunose, T. Method of determining activation deterioration constant of electrical insulating materials. Res. Rep. Chiba Inst. Technol. (Sci. Technol.) 16, 22–31 (1971).
Vyazovkin, S. Advanced isoconversional method. J. Therm. Anal. 49, 1493–1499 (1997).
Vyazovkin, S. Modification of the integral isoconversional method to account for variation in the activation energy. J. Comput. Chem. 22, 178–183 (2001).
de Palma, K. R., García-Hernando, N., Silva, M. A., Tomaz, E. & Soria-Verdugo, A. Pyrolysis and combustion kinetic study and complementary study of ash fusibility behavior of sugarcane bagasse, sugarcane straw, and their pellets—Case study of agro-industrial residues. Energy Fuels 33, 3227–3238 (2019).
Wu, W., Mei, Y., Zhang, L., Liu, R. & Cai, J. Kinetics and reaction chemistry of pyrolysis and combustion of tobacco waste. Fuel 156, 71–80 (2015).
Katnić, Đ et al. Characterization and kinetics of thermal decomposition behavior of plum and fig pomace biomass. J. Clean. Prod. 352, 131637 (2022).
Guida, M. Y. et al. Thermochemical treatment of olive mill solid waste and olive mill wastewater. J. Therm. Anal. Calorim. 123, 1657–1666 (2016).
Ali, I., Bahaitham, H. & Naebulharam, R. A comprehensive kinetics study of coconut shell waste pyrolysis. Bioresour. Technol. 235, 1–11 (2017).
Article CAS PubMed Google Scholar
Slopiecka, K., Bartocci, P. & Fantozzi, F. Thermogravimetric analysis and kinetic study of poplar wood pyrolysis. Appl. Energy 97, 491–497 (2012).
Article ADS CAS Google Scholar
Mishra, R. K. & Mohanty, K. Pyrolysis characteristics and kinetic parameters assessment of three waste biomass. J. Renew. Sustain. Energy 10, 013102 (2018).
Alam, M., Bhavanam, A., Jana, A., Viroja, J. & Kumar, S. & Peela, N. R.,. Co-pyrolysis of bamboo sawdust and plastic: Synergistic effects and kinetics. Renew. Energy 149, 1133–1145 (2020).
Sahoo, A., Kumar, S., Kumar, J. & Bhaskar, T. A detailed assessment of pyrolysis kinetics of invasive lignocellulosic biomasses (Prosopis juliflora and Lantana camara) by thermogravimetric analysis. Bioresour. Technol. 319, 124060 (2021).
Article CAS PubMed Google Scholar
Wen, Y. et al. Pyrolysis of raw and anaerobically digested organic fractions of municipal solid waste: Kinetics, thermodynamics, and product characterization. Chem. Eng. J. 415, 129064 (2021).
Xu, L. et al. Pyrolysis characteristics and kinetic reaction parameters estimation of sassafras wood via thermogravimetric modeling calculation coupled with hybrid optimization methodology. Energy 263, 125936 (2023).
Pérez-Maqueda, L. A., Criado, J. M. & Sánchez-Jiménez, P. E. Combined kinetic analysis of solid-state reactions: A powerful tool for the simultaneous determination of kinetic parameters and the kinetic model without previous assumptions on the reaction mechanism. J. Phys. Chem. A 110, 12456–12462 (2006).
Vyazovkin, S. Kinetic effects of pressure on decomposition of solids. Int. Rev. Phys. Chem. 39, 35–66 (2020).
Campbell, J. S., Grace, J. R., Lim, C. J. & Mochulski, D. W. A new diagnostic when determining the activation energy by the advanced isoconversional method. Thermochim. Acta 636, 85–93 (2016).
Senum, G. I. & Yang, R. T. Rational approximations of the integral of the Arrhenius function. J. Therm. Anal. 11, 445–447 (1977).
Órfão, J. J. M. Review and evaluation of the approximations to the temperature integral. AIChE J. 53, 2905–2915 (2007).
Cai, J. et al. Processing thermogravimetric analysis data for isoconversional kinetic analysis of lignocellulosic biomass pyrolysis: case study of corn stalk. Renew. Sustain. Energy Rev. 82, 2705–2715 (2018).
Vyazovkin, S. & Linert, W. Thermally induced reactions of solids: Isokinetic relationships of non-isothermal systems. Int. Rev. Phys. Chem. 14, 355–369 (1995).
Burnham, A. K., Zhou, X. & Broadbelt, L. J. Critical review of the global chemical kinetics of cellulose thermal decomposition. Energy Fuels 29, 2906–2918 (2015).
Wang, J. et al. Understanding pyrolysis mechanisms of pinewood sawdust and sugarcane bagasse from kinetics and thermodynamics. Ind. Crops Prod. 177, 114378 (2022).
Eyring, H. The activated complex and the absolute rate of chemical reactions. Chem. Rev. 17, 65–77 (1935).
Chang, R. Physical Chemistry for the Biosciences. (University Science Books, 2005).
Eyring, H. The activated complex in chemical reactions. J. Chem. Phys. 3, 107–115 (1935).
Article ADS CAS Google Scholar
Benson, S. W. Thermochemical Kinetics. (Wiley, 1976).
Beyer, W. H. Handbook of Tables for Probability and Statistics. (CRC Press, Inc., 1968).
Vyazovkin, S. & Sbirrazzuoli, N. Confidence intervals for the activation energy estimated by few experiments. Anal. Chim. Acta 355, 175–180 (1997).
Vyazovkin, S. & Wight, C. A. Estimating realistic confidence intervals for the activation energy determined from thermoanalytical measurements. Anal. Chem. 72, 3171–3175 (2000).
Article CAS PubMed Google Scholar
Yao, F., Wu, Q., Lei, Y., Guo, W. & Xu, Y. Thermal decomposition kinetics of natural fibers: Activation energy with dynamic thermogravimetric analysis. Polym. Degrad. Stab. 93, 90–98 (2008).
Collard, F. & Blin, J. A review on pyrolysis of biomass constituents: Mechanisms and composition of the products obtained from the conversion of cellulose, hemicelluloses and lignin. Renew. Sustain. Energy Rev. 38, 594–608 (2014).
Varhegyi, G., Antal, M. J., Szekely, T. & Szabo, P. Kinetics of the thermal decomposition of cellulose, hemicellulose, and sugarcane bagasse. Energy & Fuels 3, 329–335 (1989).
Rainey, T. J. & Covey, G. Pulp and paper production from sugarcane bagasse. in Sugarcane-Based Biofuels and Bioproducts (eds. O’Hara, I. M. & Mundree, S. G.) 259–280 (John Wiley & Sons, Inc, 2016). https://doi.org/10.1002/9781118719862.ch10.
Benitez, A. M. C. Thermal processing of michanthus, sugarcane bagasse, sugarcane trash and their acid hydrolysis residues (PhD Thesis, Aston University, 2014).
Santos , KG , Malagoni , RA , Lira , TS , Murata , VV & Barrozo , MAS Isoconversional kinetic analysis of pyrolysis of sugarcane bagasse .Mater.Sci.Forum 727–728, 1830–1835 (2012).
Kissinger, H. E. Variation of peak temperature with heating rate in differential thermal analysis. J. Res. Natl. Bur. Stand. 1934(57), 217–221 (1956).
Ounas, A., Aboulkas, A., El harfi, K., Bacaoui, A. & Yaacoubi, A. Pyrolysis of olive residue and sugar cane bagasse: non-isothermal thermogravimetric kinetic analysis. Bioresour. Technol. 102, 11234–11238 (2011).
Article CAS PubMed Google Scholar
Göçken, M., Özçalıcı, M., Boru, A. & Dosdoğru, A. T. Integrating metaheuristics and artificial neural networks for improved stock price prediction. Expert Syst. Appl. 44, 320–331 (2016).
Li, M.-F., Tang, X.-P., Wu, W. & Liu, H.-B. General models for estimating daily global solar radiation for different solar radiation zones in mainland China. Energy Convers. Manag. 70, 139–148 (2013).
Heinemann, A. B., van Oort, P. A. J., Fernandes, D. S. & de Maia, A. H. N. Sensitivity of APSIM/ORYZA model due to estimation errors in solar radiation. Bragantia 71, 572–582 (2012).
Burnham, K. P. & Anderson, D. R. Model Selection and Multimodel Inference: A Practical Information- Theoretic Approach. (Springer New York, 2004). https://doi.org/10.1007/b97636.
Ingdal , M. , Johnsen , R. & Harrington , DA The Akaike information criterion in weighted regression of immittance data .Electrochem.Acta 317, 648–653.
Wu, L. & Qiu, J. Linear and Nonlinear Regression Models. in Applied Multivariate Statistical Analysis and Related Topics with R 111–130 (EDP Sciences, 2021). https://doi.org/10.1051/978-2-7598-2602-5.c009.
Iqbal, M. F. et al. Sustainable utilization of foundry waste: Forecasting mechanical properties of foundry sand based concrete using multi-expression programming. Sci. Total Environ. 780, 146524 (2021).
Article ADS CAS PubMed Google Scholar
Schabenberger, O. & Pierce, F. J. Contemporary statistical models for the plant and soil sciences. (CRC Press LLC, 2002). doi:https://doi.org/10.5860/CHOICE.40-0345.
Liavitskaya, T. & Vyazovkin, S. Discovering the kinetics of thermal decomposition during continuous cooling. Phys. Chem. Chem. Phys. 18, 32021–32030 (2016).
Article CAS PubMed Google Scholar
Hii, S. W. et al. Iso-conversional kinetic and thermodynamic analysis of catalytic pyrolysis for palm oil wastes. in Value-Chain of Biofuels Fundamentals, Technology, and Standardization (eds. Yusup, S. & Rashidi, N. A.) 277–300 (Elsevier Inc., 2022). doi:https://doi.org/10.1016/B978-0-12-824388-6.00025-7.
Gouda, N. & Panda, A. K. Determination of kinetic and thermodynamic parameters of thermal degradation of different biomasses for pyrolysis. Biocatal. Agric. Biotechnol. 21, 101315 (2019).
Ma, H. et al. Molecular structure, thermal behavior and adiabatic time-to-explosion of 3,3-dinitroazetidinium picrate. J. Mol. Struct. 981, 103–110 (2010).
Article ADS CAS Google Scholar
Janković, B., Stopić, S., Bogović, J. & Friedrich, B. Kinetic and thermodynamic investigations of non-isothermal decomposition process of a commercial silver nitrate in an argon atmosphere used as the precursors for ultrasonic spray pyrolysis (USP): The mechanistic approach. Chem. Eng. Process. Process Intensif. 82, 71–87 (2014).
Kumar Singh, R., Patil, T. & Sawarkar, A. N. Pyrolysis of garlic husk biomass: Physico-chemical characterization, thermodynamic and kinetic analyses. Bioresour. Technol. Reports 12, 100558 (2020).
Espenson, J. H. Chemical Kinetics and Reaction Mechanisms. (McGraw-Hill, Inc., 1995).
Kumar Singh, R., Patil, T., Pandey, D. & Sawarkar, A. N. Pyrolysis of mustard oil residue: A kinetic and thermodynamic study. Bioresour. Technol. 339, 125631 (2021).
Article CAS PubMed Google Scholar
Mumbach, G. D. et al. Prospecting pecan nutshell pyrolysis as a source of bioenergy and bio-based chemicals using multicomponent kinetic modeling, thermodynamic parameters estimation, and Py-GC/MS analysis. Renew. Sustain. Energy Rev. 153, 111753 (2022).
Shahbeig, H. & Nosrati, M. Pyrolysis of municipal sewage sludge for bioenergy production: Thermo-kinetic studies, evolved gas analysis, and techno-socio-economic assessment. Renew. Sustain. Energy Rev. 119, 109567 (2020).
Sronsri, C., Noisong, P. & Danvirutai, C. Isoconversional kinetic, mechanism and thermodynamic studies of the thermal decomposition of NH4Co0.8Zn0.1Mn0.1PO4·H2O. J. Therm. Anal. Calorim. 120, 1689–1701 (2015).
Yang, J., Liang, Q. & Hou, H. Thermal decomposition mechanism and kinetics of Pd/SiO2 nanocomposites in air atmosphere. J. Therm. Anal. Calorim. 135, 2733–2745 (2019).
XThermo Research Group, No.117, Somayeh Street, Tehran, 158176-8511, Iran
Hamidreza Najafi & Ahmad Golrokh Sani
School of Chemical Engineering, Iran University of Science and Technology (IUST), Postal Box 16765-163, Tehran, Iran
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Authorship statement: H.N.: Experimental design, software, modeling, and analysis of the generated data. H.N. and A.G.S.: Investigation, visualization, validation, writing-original draft. H.N., A.G.S., and M.A.S.: Conceptualization, methodology, writing-review and editing. M.A.S.: Supervision. All authors read and approved the submitted version.
Correspondence to Mohammad Amin Sobati.
The authors declare no competing interests.
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Najafi, H., Golrokh Sani, A. & Sobati, M.A. Thermogravimetric and thermo-kinetic analysis of sugarcane bagasse pith: a comparative evaluation with other sugarcane residues. Sci Rep 14, 2076 (2024). https://doi.org/10.1038/s41598-024-52500-x
DOI: https://doi.org/10.1038/s41598-024-52500-x
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