Non-isothermal thermogravimetric experiments were carried out at four different heating rates to investigate thermal decomposition of *Polyalthia longifolia* leaves, with primary goals of determining kinetic triplets (activation energy, frequency factor, and reaction mechanism) and thermodynamic parameters. Kinetics investigation was conducted by utilizing five iso-conversional approaches, viz., Starink (STK), Ozawa-Flynn-Wall (OFW), Kissinger-Akahira-Sunose (KAS), differential Friedman method (DFM), and distributed activation energy model (DAEM). Results indicated that average activation energy (E_{α}) ranged between 211.57 and 231 kJ/mol. Average values of activation energy obtained by KAS (211.57 kJ/mol) were found to be in the neighborhood of that obtained by other three integral methods, i.e., OFW (210.80 kJ/mol), STK (211.80 kJ/mol), and DAEM (211.57 kJ/mol). Criado's master plots approach revealed that experimental data matches with none of the reaction model until conversion of 0.4 and thereafter follows D3 for conversion of 0.5–0.7, whereas master plots based on the integral form of data disclosed that this method is not appropriate for pyrolysis of the present biomass sample. Finally, pyrolysis of *P. longifolia* biomass to produce bioenergy is found to be feasible (E_{α} − ΔH = ∼5–6 kJ/mol).

## I. INTRODUCTION

The majority of the energy comes from fossil fuels. Fossil fuel supplies are being depleted at an alarming rate due to exponentially rising energy demand.^{1,2} Furthermore, the release of greenhouse gases (GHGs) during the burning of fossil fuels raises the temperature of the atmosphere and pollutes the air we breathe.^{3,4} As a result, it is crucial that energy derived from renewable sources should be both sustainable and clean. Biomass has gotten more attention than other renewable energy options because of its inherent benefits over other sources and also they are carbon-neutral; and biofuels can be used in a way that is both environmentally friendly and less harmful to the environment.^{5,6} It has been predicted that biofuel production will play a significant role in sustaining and correcting environmental harm caused by fossil fuel consumption.^{7} There are two primary types of biomass: lignocellulosic and non-lignocellulosic.^{8} Lignin, cellulose, and hemicellulose make up the majority of the biomass in lignocellulosic waste.^{9} Composition is highly dependent on the type of biomass, its age, the environment, and the locations where it was harvested.^{10} Manufacturing a variety of biofuels from lignocellulosic biomass is often regarded as the world's most widely available renewable source.^{11,12} It is challenging for bio-refineries to economically compete with petroleum refineries due to the low cost of crude.^{13} However, because of their low cost, lignocellulosic residues might be particularly useful raw materials for the production of gasoline additives and platform chemicals. Amongst the available biomass conversion processes, pyrolysis has achieved upper hand.^{14}

The pyrolysis process is quickly expanding and gaining popularity as a potential technology for transforming biomass into useful products such as biofuels, charcoal, and bio-based compounds. One of the important techniques within the broader area of pyrolysis processes is biomass fast pyrolysis. Fast pyrolysis involves rapidly heating biomass to high temperatures (usually between 400 °C and 600 °C) in a lack of oxygen environment, resulting in the production of bio-oil, char, and py-gas from waste biomass. In biomass fast pyrolysis, several methods and reactor designs are employed. Some of the most common reactors are fluidized bed reactors, circulating fluidized bed reactors, and entrained flow reactors, whereas some of the recent developments include auger reactors, revolving cone reactors, vacuum pyrolysis reactors, etc.

Thermogravimetric analysis (TGA) is a very simple, reliable, and fast analytical approach for examining the kinetics of the pyrolysis process, which provides data on mass loss of biomass samples as a function of temperature and time.^{15} TGA has been used extensively to characterize biomass, not only to validate biomass proximate analysis, but to also analyze pyrolysis kinetics in order to calculate E_{α} and other kinetic parameters using TGA data.^{16–18} To describe the kinetics of the TGA pyrolysis reaction, isothermal and non-isothermal approaches are used. In comparison to the isothermal approach, the non-isothermal method is believed to be simpler because it avoids changing physical and chemical properties of samples and provides useful information through a fewer experiments.^{19} Non-isothermal techniques are also divided into two groups: model-free and model fitting methods. In model-fitting methods, various models were fitted to the experimental data during the model-fitting method, and the model that provides the best statistical fit was chosen as the model from which E_{α} and pre-exponential factor were calculated. However, these techniques have a number of limitations, the most significant of which is their inability to select the most suitable reaction model. This resulted in the decline of these approaches in favor of iso- conversional approaches capable of estimating E_{α} without analyzing the reaction mechanism. The primary advantages of this approach are its flexibility and the elimination of inaccuracies associated with the selection of specific reaction models. The iso-conversional approach is referred to as the model-free approach due to its capacity to calculate E_{α} without taking into account any specific type of the reaction mechanism. These approaches, which require many kinetic curves for analysis, are frequently referred to as the multi-curve methods.^{20}

*Polyalthia longifolia* (PL), often known as the false Ashoka or *Monoon longifolium*, is an Asian tree of *Annonaceae* family. This evergreen tree may reach a height of over 20 m and is widely planted for its ability to reduce noise pollution. With long narrow lanceolate leaves, undulate borders, and willowy weeping pendulous branches, it grows in a symmetrical pyramidal shape. Because of their striking likeness, *P. longifolia* is occasionally mistaken for Ashoka tree (*Saraca indica*). Although it appears to have no branches, *P. longifolia* left to grow naturally, matures into a long tree that provides plenty of shade. The published experimental research and theoretical papers that are relevant to the pyrolysis kinetics of waste biomass are summarized in Table I. The goal of this study is to use thermogravimetric analysis (TGA) to investigate the pyrolysis kinetics of *P. longifolia* leaves at varied heating rates under nitrogen environment in the temperature range of 30 $\xb0C\u2013$ 900 $\xb0C$. Different model free approaches are used and compared in this study to evaluate the non-isothermal kinetic data and explore the thermal behavior of PL leaves by utilizing iso-conversional methods of distributed activation energy model (DAEM), Ozawa Flynn Wall (OFW), Starink (STK), Kissinger-Akahira-Sunose (KAS), and differential Friedman method (DFM). In addition to this, master plots based on the integral approach and Criado's master plots were used to find the reaction mechanism of the pyrolysis of the PL leaves. These findings should help pyrolysis researchers in predicting a reaction mechanism of pyrolysis of PL leaves and optimize process parameters.

Biomass used . | Heating rate, β (K/min) . | Methods used . | Obtained values of mean activation energy . | Thermodynamic properties . | References . |
---|---|---|---|---|---|

Wucaiwan lignite | 10, 20, and 30 | KAS and OFW methods | E_{α}: Average value was between 235.4 and 235.7 kJ/mol for all methods. | Average values of ΔH: 231.6–233.3 kJ/mol | 21 |

Average values of ΔG:200.5–201.8 kJ/mol | |||||

Average values of ΔS 1) KAS: -0.24 to 0.284 kJ/mol K 2) OFW: 0.0183 to 0.241 kJ/mol K | |||||

Wheat straw | 10, 20, and 30 | KAS, OFW, and Starink methods | E_{α}: Average value was between 340.84 and 345.66 kJ/mol for all methods. | Average values of ΔH: 169.85–334.75 kJ/mol | 22 |

Average values of ΔG: 151.93–187.64 kJ/mol | |||||

Average values of ΔS: −62.07 to 651.42 J/mol K | |||||

Chili straw | 5, 10, 20, and 30 | KAS, OFW, DFM, and Starink methods | E_{α}: Average value was between 195.48 and 227.15 kJ/mol for all methods. | Average values of ΔH: 190.67–231.55 kJ/mol | 23 |

Average values of ΔG: 154.12–155.04 kJ/mol | |||||

Banana leaves | 10, 20, and 30 | KAS and OFW methods | 31.6–105.5 kJ/mol for OFW and 27.8–105 kJ/mol for KAS method. | Average values of ΔH | 24 |

1) OFW: 29.8–101.9 kJ/mol | |||||

2) KAS: 26.8–102.3 kJ/mol | |||||

Average values of ΔG | |||||

1) OFW: 64.1–58.8 kJ/mol | |||||

2) KAS: 64.4–58.2 kJ/mol | |||||

Average values of ΔS | |||||

1) OFW: −148 to 101 J/ mol K | |||||

2) KAS: −163 t o 99 J/mol K | |||||

Dry cattle manure | 10, 20, 30, 40, 60, and 80 | OFW, KAS, and DFM methods | 121.7–327.2 kJ/mol for OFW, 119.4–332.4 kJ/mol for KAS method and 129.7–348.3 kJ/mol for DFM method. | Average values of ΔH: 161.5–166.2 kJ/mol | 25 |

Average values of ΔG: 125.5–342.5 kJ/mol | |||||

Average values of ΔS: 71.3 to −316.2 J/mol K | |||||

Rice husk | 10, 20, 50, and 100 | KAS and OFW methods | 156.4–267 kJ/mol for OFW and 153.8–269.4 kJ/mol for KAS method. | Average values of ΔH: 141.2–263.7 kJ/mol | 26 |

Average values of ΔG: 174.8–177.9 kJ/mol | |||||

Average values of ΔS: 7–142 J/mol K | |||||

Sugar cane leaves | 5, 10, 15, 20, 30, and 40 | OFW, KAS, Tang, Starink, DFM, and Vyazovkin methods | E_{α}: Average value was between 214.9 and 239.6 kJ/mol for all methods. | ⋯ | 27 |

Peanut shells | 2, 10, and 15 | Boswell, OFW , Starink, and Tang methods | E_{α}: Average value was between 169 and 268 kJ/mol for all methods. | Average values of ΔH: 164–259 kJ/mol | 28 |

Average values of ΔG: 173–188 kJ/mol | |||||

Average values of ΔS: −37 to 141 J/mol K | |||||

Sugar cane bagasse | 10, 30, and 40 | KAS, DFM , OFW, and advanced Vyazovkin methods | E_{α}: Average value was between 193.45 and 293.49 kJ/mol for all methods. | ⋯ | 29 |

Ficus nitida wood | 5, 10, 20, and 50 | DFM, OFW, and Vyazovkin methods | E_{α}: Average value was between 206.48 and 214.42 kJ/mol for all methods. | Average values of ΔH: 205 kJ/mol | 30 |

Average values of ΔG: 186.48 kJ/mol | |||||

Average values of ΔS: 30.68 J/mol K | |||||

Pigeon pea stalk | 10, 20, and 30 | KAS, DFM, OFW, and Starink methods | E_{α}: Average value was between 95.97 and 100.74 kJ/mol for all methods. | Average values of ΔH: 91.11–95.88 kJ/mol | 31 |

Average values of ΔG: 171–172 kJ/mol | |||||

Average values of ΔS:127.392 to −135.865 J/mol K | |||||

Buriti seeds | 5, 10, 15, and 20 | OFW, KAS, Starink, Tang and Vyazovkin methods | E_{α}: Average value was between 144 and 146 kJ/mol for all methods. | Average values of ΔH: 140–142 kJ/mol | 32 |

Average values of ΔS:144–151 kJ/mol | |||||

Average values of ΔS: 70 to −78 J/mol K | |||||

Mustard oil residue | 10, 20, and 30 | OFW, KAS, Starink, Tang, Vyazovkin, and DFM methods | E_{α}: Average value was 155 kJ/mol for all methods. | Average values of ΔH: 153 kJ/mol | 33 |

Average values of ΔG: 146 kJ/mol | |||||

Average values of ΔS: −70 to −78 J/mol K | |||||

Hybrid poplar sawdust | 5, 10, 15, and 20 | OFW method | E_{α}: Average value was between 38 and 141 kJ/mol for all methods. | Average values of ΔH: 33–136 kJ/mol | 34 |

Average values of ΔG: 102.76–184.82 kJ/mol | |||||

Average values of ΔS: −2.89 to −265.84 J/mol K | |||||

Cupuassu shell | 5, 10, 20, 30, and 40 | DFM, OFW, KAS, and Starink methods | E_{α}: Average value was between 177 and 243 kJ/mol for all methods. | Average values of ΔH: 125.27 kJ/mol | 35 |

Average values of ΔG: 196.69 kJ/mol | |||||

Average values of ΔS: −93.94 J/mol K | |||||

Butia seed | 5, 10, 20, 30, and 40 | OFW, KAS, Starink, and DFM methods | E_{α}: Average value was between 111.6 and 189.8 kJ/mol for all methods. | Average values of ΔH: 125.55 kJ/mol | 36 |

Average values of ΔG: 189.47 kJ/mol | |||||

Average values of ΔS: −101.06 J/mol K | |||||

Corn stover | 10, 20, 30, and 40 | Coats–Redfern, OFW, and KAS methods | E_{α}: Average value was between 181.66 and 191.57 kJ/mol for all methods. | Average values of ΔH: 153–210 kJ/mol | 37 |

Average values of ΔG: 171–172 kJ/mol | |||||

Average values of ΔS: −16 to 82 J/mol K | |||||

Horse manure | 1, 2, 5, and 10 | OFW, KAS, and DFM methods | E_{α}: Average value was between 149 and 200 kJ/mol for all methods | Average values of ΔH: 186–218 kJ/mol | 38 |

Average values of ΔG: 153–154 kJ/mol | |||||

Average values of ΔS: 58–60 J/mol K | |||||

Musa balbisiana flower petal | 5, 10, and 20 | KAS, OFW, and DFM methods | E_{α}: Average value was between 141.9 and 152.46 kJ/mol for all methods. | Average values of ΔH:147–150 kJ/mol | 39 |

Average values of ΔG:152–155 kJ/mol | |||||

Average values of ΔS: −70 to −75 J/mol K | |||||

T. latifolia | 10, 30, and 50 | KAS, OFW and Coats–Redfern methods | E_{α}: Average value was between 171.9 and 184.58 kJ/mol for all methods. | Average values of ΔH: 165–179 kJ/mol | 40 |

Average values of ΔG: 173–175 kJ/mol | |||||

Terminalia chebula | 10, 20, 35, and 55 | DFM, KAS, STK, OFW, and DAEM methods | E_{α}: Average value was between 227.11 and 229.21 kJ/mol for all methods. | Average values of ΔH: 236.40–221.8 kJ/mol | 41 |

Average values of ΔG: 179 kJ/mol | |||||

Average values of ΔS: 0.063–0.089 J/mol K |

Biomass used . | Heating rate, β (K/min) . | Methods used . | Obtained values of mean activation energy . | Thermodynamic properties . | References . |
---|---|---|---|---|---|

Wucaiwan lignite | 10, 20, and 30 | KAS and OFW methods | E_{α}: Average value was between 235.4 and 235.7 kJ/mol for all methods. | Average values of ΔH: 231.6–233.3 kJ/mol | 21 |

Average values of ΔG:200.5–201.8 kJ/mol | |||||

Average values of ΔS 1) KAS: -0.24 to 0.284 kJ/mol K 2) OFW: 0.0183 to 0.241 kJ/mol K | |||||

Wheat straw | 10, 20, and 30 | KAS, OFW, and Starink methods | E_{α}: Average value was between 340.84 and 345.66 kJ/mol for all methods. | Average values of ΔH: 169.85–334.75 kJ/mol | 22 |

Average values of ΔG: 151.93–187.64 kJ/mol | |||||

Average values of ΔS: −62.07 to 651.42 J/mol K | |||||

Chili straw | 5, 10, 20, and 30 | KAS, OFW, DFM, and Starink methods | E_{α}: Average value was between 195.48 and 227.15 kJ/mol for all methods. | Average values of ΔH: 190.67–231.55 kJ/mol | 23 |

Average values of ΔG: 154.12–155.04 kJ/mol | |||||

Banana leaves | 10, 20, and 30 | KAS and OFW methods | 31.6–105.5 kJ/mol for OFW and 27.8–105 kJ/mol for KAS method. | Average values of ΔH | 24 |

1) OFW: 29.8–101.9 kJ/mol | |||||

2) KAS: 26.8–102.3 kJ/mol | |||||

Average values of ΔG | |||||

1) OFW: 64.1–58.8 kJ/mol | |||||

2) KAS: 64.4–58.2 kJ/mol | |||||

Average values of ΔS | |||||

1) OFW: −148 to 101 J/ mol K | |||||

2) KAS: −163 t o 99 J/mol K | |||||

Dry cattle manure | 10, 20, 30, 40, 60, and 80 | OFW, KAS, and DFM methods | 121.7–327.2 kJ/mol for OFW, 119.4–332.4 kJ/mol for KAS method and 129.7–348.3 kJ/mol for DFM method. | Average values of ΔH: 161.5–166.2 kJ/mol | 25 |

Average values of ΔG: 125.5–342.5 kJ/mol | |||||

Average values of ΔS: 71.3 to −316.2 J/mol K | |||||

Rice husk | 10, 20, 50, and 100 | KAS and OFW methods | 156.4–267 kJ/mol for OFW and 153.8–269.4 kJ/mol for KAS method. | Average values of ΔH: 141.2–263.7 kJ/mol | 26 |

Average values of ΔG: 174.8–177.9 kJ/mol | |||||

Average values of ΔS: 7–142 J/mol K | |||||

Sugar cane leaves | 5, 10, 15, 20, 30, and 40 | OFW, KAS, Tang, Starink, DFM, and Vyazovkin methods | E_{α}: Average value was between 214.9 and 239.6 kJ/mol for all methods. | ⋯ | 27 |

Peanut shells | 2, 10, and 15 | Boswell, OFW , Starink, and Tang methods | E_{α}: Average value was between 169 and 268 kJ/mol for all methods. | Average values of ΔH: 164–259 kJ/mol | 28 |

Average values of ΔG: 173–188 kJ/mol | |||||

Average values of ΔS: −37 to 141 J/mol K | |||||

Sugar cane bagasse | 10, 30, and 40 | KAS, DFM , OFW, and advanced Vyazovkin methods | E_{α}: Average value was between 193.45 and 293.49 kJ/mol for all methods. | ⋯ | 29 |

Ficus nitida wood | 5, 10, 20, and 50 | DFM, OFW, and Vyazovkin methods | E_{α}: Average value was between 206.48 and 214.42 kJ/mol for all methods. | Average values of ΔH: 205 kJ/mol | 30 |

Average values of ΔG: 186.48 kJ/mol | |||||

Average values of ΔS: 30.68 J/mol K | |||||

Pigeon pea stalk | 10, 20, and 30 | KAS, DFM, OFW, and Starink methods | E_{α}: Average value was between 95.97 and 100.74 kJ/mol for all methods. | Average values of ΔH: 91.11–95.88 kJ/mol | 31 |

Average values of ΔG: 171–172 kJ/mol | |||||

Average values of ΔS:127.392 to −135.865 J/mol K | |||||

Buriti seeds | 5, 10, 15, and 20 | OFW, KAS, Starink, Tang and Vyazovkin methods | E_{α}: Average value was between 144 and 146 kJ/mol for all methods. | Average values of ΔH: 140–142 kJ/mol | 32 |

Average values of ΔS:144–151 kJ/mol | |||||

Average values of ΔS: 70 to −78 J/mol K | |||||

Mustard oil residue | 10, 20, and 30 | OFW, KAS, Starink, Tang, Vyazovkin, and DFM methods | E_{α}: Average value was 155 kJ/mol for all methods. | Average values of ΔH: 153 kJ/mol | 33 |

Average values of ΔG: 146 kJ/mol | |||||

Average values of ΔS: −70 to −78 J/mol K | |||||

Hybrid poplar sawdust | 5, 10, 15, and 20 | OFW method | E_{α}: Average value was between 38 and 141 kJ/mol for all methods. | Average values of ΔH: 33–136 kJ/mol | 34 |

Average values of ΔG: 102.76–184.82 kJ/mol | |||||

Average values of ΔS: −2.89 to −265.84 J/mol K | |||||

Cupuassu shell | 5, 10, 20, 30, and 40 | DFM, OFW, KAS, and Starink methods | E_{α}: Average value was between 177 and 243 kJ/mol for all methods. | Average values of ΔH: 125.27 kJ/mol | 35 |

Average values of ΔG: 196.69 kJ/mol | |||||

Average values of ΔS: −93.94 J/mol K | |||||

Butia seed | 5, 10, 20, 30, and 40 | OFW, KAS, Starink, and DFM methods | E_{α}: Average value was between 111.6 and 189.8 kJ/mol for all methods. | Average values of ΔH: 125.55 kJ/mol | 36 |

Average values of ΔG: 189.47 kJ/mol | |||||

Average values of ΔS: −101.06 J/mol K | |||||

Corn stover | 10, 20, 30, and 40 | Coats–Redfern, OFW, and KAS methods | E_{α}: Average value was between 181.66 and 191.57 kJ/mol for all methods. | Average values of ΔH: 153–210 kJ/mol | 37 |

Average values of ΔG: 171–172 kJ/mol | |||||

Average values of ΔS: −16 to 82 J/mol K | |||||

Horse manure | 1, 2, 5, and 10 | OFW, KAS, and DFM methods | E_{α}: Average value was between 149 and 200 kJ/mol for all methods | Average values of ΔH: 186–218 kJ/mol | 38 |

Average values of ΔG: 153–154 kJ/mol | |||||

Average values of ΔS: 58–60 J/mol K | |||||

Musa balbisiana flower petal | 5, 10, and 20 | KAS, OFW, and DFM methods | E_{α}: Average value was between 141.9 and 152.46 kJ/mol for all methods. | Average values of ΔH:147–150 kJ/mol | 39 |

Average values of ΔG:152–155 kJ/mol | |||||

Average values of ΔS: −70 to −75 J/mol K | |||||

T. latifolia | 10, 30, and 50 | KAS, OFW and Coats–Redfern methods | E_{α}: Average value was between 171.9 and 184.58 kJ/mol for all methods. | Average values of ΔH: 165–179 kJ/mol | 40 |

Average values of ΔG: 173–175 kJ/mol | |||||

Terminalia chebula | 10, 20, 35, and 55 | DFM, KAS, STK, OFW, and DAEM methods | E_{α}: Average value was between 227.11 and 229.21 kJ/mol for all methods. | Average values of ΔH: 236.40–221.8 kJ/mol | 41 |

Average values of ΔG: 179 kJ/mol | |||||

Average values of ΔS: 0.063–0.089 J/mol K |

## II. MATERIALS AND METHODS

### A. Materials

*P. longifolia* (PL) leaves were collected on the campus of the Indian Institute of Technology, Guwahati (India). Three days were spent drying the collected PL samples at ambient temperature. To create a sample of uniform size, the leaves were sliced into tiny pieces, powdered in a mixer grinder, and then sieved to obtain a sample of uniform size. The powdered biomass sample was maintained at room temperature in an airtight plastic bag to minimize moisture absorption and to facilitate subsequent characterization and testing.

### B. Thermogravimetric analysis

Pyrolysis of PL leaves was performed using a TG 209 F1 (Netsch, Germany) thermogravimetric analyzer, in order to obtain data on weight loss as a function of time and temperature during the reaction. Around 6 mg of powdered PL leaves was placed in a crucible and held at room temperature. Thermal investigation from $25\u2009\xb0C\u2009to\u2009900\u2009\xb0C$ was performed using four distinct non-isothermal heating rates of β = 10, 20, 35, and 55 K min^{−1} to determine the kinetic triplets, and the purpose for selecting these heating rates was to investigate the kinetics of pyrolysis behavior of PL leaves biomass in the slow, intermediate, and fast pyrolysis regimes. To avoid undesirable secondary reactions and oxidation of the material, inert gas was introduced into the pyrolysis reaction chamber at a flow rate of 20 ml/min.

## III. THEORY

### A. Kinetic analysis

The kinetics model is extremely useful for designing and optimizing pyrolysis equipment because it anticipates the distribution of products, thermal transfer, chemistry of solid decomposition, and mass loss behavior across equipment.^{42,43}

*k(T)*is commonly expressed by the Arrhenius equation:

*A,*$ E \alpha $, and

*R*represent the pre-exponential factor (s

^{−1}), apparent activation energy (kJ/mol), and universal gas constant, respectively. For a thermogravimetric degradation process, the fractional conversion (α) is defined as

*t*,” and at the end of the process. Non-isothermal pyrolysis experiments measured the sample weight as a function of temperature changes over time [

*T = T(t)*]. Thus, the heating rate is given as follows:

*x*is defined as $x= \u2212 E \alpha R T$. The

*p(x)*in the right-hand side of Eq. (7) is known as the temperature integral, and it lacks an analytical solution. To solve the temperature integral, numerous approximation approaches were developed, resulting in the development of several integral equations.

The numerous available methodologies for kinetic analysis can be divided into two categories: model fitting and model-free approaches. The model fitting approaches entail forcing kinetic parameters into the equation, resulting in unclear kinetic interpretations in which more than one reaction mechanism fits the data satisfactorily at the expense of extreme changes in the kinetic parameters.^{44} The model-free technique eliminates the need to assume specific reaction models and produces unique kinetic parameters as a function of either conversion or temperature.^{45} The iso-conversional approach is the more extensively used of the two basic methodologies, and it is rapidly being used in research on biomass thermal conversion.^{46}

#### 1. Calculation of activation energy and frequency factor

^{44,47}implying that

^{48}The differential Friedman method (DFM), Kissinger-Akahira-Sunose (KAS), Starink (STK), Flynn-Wall-Ozawa (OFW), and distributed activation energy model (DAEM) are the most commonly used iso-conversional methods. The reason behind selecting these models is to use the both integral and differential iso-conversional methods; and out of these methods, the differential Friedman method is a differential iso-conversional method, whereas the remaining four methods are integral iso-conversional methods. Among these methods, the DFM method is a better model compared to others because it does not require any assumptions to derive the equation to find the activation energy, whereas the remaining methods require assumptions to derive the equations to find the corresponding activation energy. However, the problem with the DFM is that it is intimately connected to some degree of error and imprecision, which introduces noise into the kinetic analysis and can lead to mistakes while smoothing the noisy data. The equations and their approximations were listed in Table II and those equations are of the linear form. By using linear fitting approach of these equations, activation energy and frequency factor can be estimated from the slope and intercept.

Model name . | Mathematical formula . | Temperature integral/exponential integral, p(x) . |
---|---|---|

Ozawa, Flynn, and Wall methods^{49} | $ log \beta = log A E \alpha g \alpha R \u2212 2.315 \u2212 0.4567 E \alpha R T$ | $ e \u2212 2.315 \u2212 0.4567 x$ |

Kissinger-Akahira-Sunose^{50} | $ ln \beta T 2= ln A R E \alpha \u2212 E \alpha R T$ | $ e \u2212 x x 2$ |

Distributed activation energy model^{51} | $ ln \beta T 2= ln A R E \alpha \u2212 E \alpha R T+0.6075$ | $\u2212$ |

Differential Friedman method^{52} | $ ln \beta d \alpha d t = ln f \alpha . A \u2212 E \alpha R T$ | $\u2212$ |

Starink method^{53} | $ ln \beta T 1.92 = \u2212 A E \alpha R T + C$ | $ e \u2212 1.0008 x \u2212 0.312 x \u2212 1.92$ |

Model name . | Mathematical formula . | Temperature integral/exponential integral, p(x) . |
---|---|---|

Ozawa, Flynn, and Wall methods^{49} | $ log \beta = log A E \alpha g \alpha R \u2212 2.315 \u2212 0.4567 E \alpha R T$ | $ e \u2212 2.315 \u2212 0.4567 x$ |

Kissinger-Akahira-Sunose^{50} | $ ln \beta T 2= ln A R E \alpha \u2212 E \alpha R T$ | $ e \u2212 x x 2$ |

Distributed activation energy model^{51} | $ ln \beta T 2= ln A R E \alpha \u2212 E \alpha R T+0.6075$ | $\u2212$ |

Differential Friedman method^{52} | $ ln \beta d \alpha d t = ln f \alpha . A \u2212 E \alpha R T$ | $\u2212$ |

Starink method^{53} | $ ln \beta T 1.92 = \u2212 A E \alpha R T + C$ | $ e \u2212 1.0008 x \u2212 0.312 x \u2212 1.92$ |

### B. Thermodynamic analysis

^{54}Calculating the change in enthalpy (ΔH) is critical for determining the total energy consumed during the conversion of raw biomass to products,

^{55}ΔG represents the total amount of energy that the reaction gains during the formation of the activated complex,

^{25}and ΔS indicates the system's proximity to thermodynamic equilibrium. Thermodynamic parameters

^{56}can be predicted from kinetic data as a function of conversion. The following formulae can be used to calculate the thermodynamic properties (ΔH, ΔG, and ΔS):

*A*is the pre-exponential factor (s

^{−1}) estimated from Eq. (9),

*T*was the peak temperature at various heating rates of 10, 20, 35, and 55 K min

_{m}(K)^{−1}, and $ E \alpha $ is the apparent activation energy (kJ mol

^{−1}).

### C. Reaction mechanism

#### 1. Criado's master plots method

^{57}Criado

*et al.*

^{58}describe a conversion function,

^{59}Eq. (14) is used to construct the theoretical curves, while Eq. (13) was utilized to define the experimental curves. The theoretically plotted curves were compared to the experimentally plotted curves to determine the exact response mechanism that fits the experimental plot satisfactorily.

#### 2. Master plots based on the integral form of kinetic data

In this study, master plots based on the integral form of kinetic data^{57,60} was also used to determine the reaction model.

*p(x)*$= \u222b \u221e x \u2212 e \u2212 x x 2 d x$, does not have an analytical solution but can be approximated. Secondary Senum–Yang's rational approximation produces precise findings: $p x= e \u2212 x x x + 4 x 2 + 6 x + 6$, $here\u2009x=\u2212 E \alpha R T$, and the final formula for calculating the kinetic model using integral master plots is as follows:

_{α}obtained from the DFM method was used. Equation (16) reveals that when a perfect kinetic model is utilized, the experimental value of $p(x)/p(0.5)$ and the theoretically computed values of $g(\alpha )/g(0.5)$ are comparable. This integral master-plots method can be used to calculate the kinetics of decomposition reactions.

## IV. RESULTS AND DISCUSSION

The proximate and ultimate analysis along with fuel potential of selected *P. longifolia* leaves biomass has already been reported in our previous works.^{61,62} Thus, in order to avoid repetitions, these are not shown here again. However, a summary of such results indicate that under the proximate analysis, the sample had 8.62%, 60.58%, 7.53%, and 23.27% of moisture content, volatile matter, ash content, and fixed carbon, respectively. On the other hand, the ultimate analysis of the sample had 44.31%, 6.09%, 0.59%, and 49.01% of carbon, hydrogen, sulfur, and oxygen, respectively. Furthermore, the higher heating value (HHV) of the sample was found to be 20.23 MJ/kg. In addition, the H/C ratio (determined on a molar basis from the ultimate analysis of PL leaves) yields a value of 1.64, indicating the suitability of this biomass waste to generate energy from it by thermochemical conversion processes. Thus, these analyses revealed that PL leaves are abundantly available and have a higher potential as a biomass feedstock for the manufacture of biofuels.

### A. Thermal analysis

The thermal decomposition behavior of PL leaves in non-isothermal conditions was investigated using TGA in the temperature range of 20 °C–900 $\xb0C$ for four heating rates (β = 10, 20, 35, and 55 K/min) in a N_{2} atmosphere. The TGA profile [Fig. 1(a)] revealed that biomass degraded in three stages: drying (up to 200 °C), active pyrolysis stage (200 °C–600 $\xb0C$), and char formation (>600 $\xb0C$). There is also a possibility of the removal of smaller molecular weight substances and water molecules up to 150 °C [Fig. 1(a)]. The lignocellulosic portion of the PL leaves remained stable at temperatures up to 200 °C, with negligible losses of moisture and low molecular weight volatile substances. Maximum breakdown was detected in the second temperature zone of 200 °C–600 °C, which appeared due to cellulose and hemicellulose degradation. This is referred to as the active pyrolytic stage and the kinetic evaluation was done in this stage. Higher molecular weight molecules were divided into smaller molecular weight molecules in this zone by continuously applying heat. The second zone consists of two exothermic simultaneous processes in which cellulose, hemicellulose, and lignin breakdown, resulting in the generation of more volatile compounds. At 20 K min^{−1} heating rate, conversion of PL leaves was found to be highest (73.82%) in the temperature range of 200 °C–600 °C (second zone) followed by at 10 K min^{−1} (63.83%), 55 K min^{-1} (63.32%), and 35 K min^{−1} (62.93%). Hemicellulose decomposes at a lower temperature ( $200\u2009\xb0C\u2013340\u2009\xb0C$) than cellulose ( $230\u2009\xb0C\u2013600\u2009\xb0C$) and lignin (more than 600 °C). According to White *et al.*,^{63} cellulose decomposition happened in two ways. At a lower temperature, the linkages first separated into monomers and generated carbonaceous gases, CO_{2}, and CO. Following that, at higher temperatures, bond disintegration results in the creation of liquid. The third zone is known as endothermic lignin decomposition, in which lignin decomposes at high temperature (>600 $\xb0C$) and at a delayed rate due to its association with the phenolic hydroxyl group.

The derivative of thermogravimetric curve [Fig. 1(b)] revealed that the first peak occurred as a result of the loss of light volatile materials and water when increased to 200 $\xb0C$. Decomposition of hemicellulose and cellulose components occurred in the second peak. The tailing region of the DTG curve, stage III, is characterized by lignin decomposition and additional char residue degradation. However, lignin breakdown proceeds slowly over an ever-expanding temperature range, including the active pyrolysis stage from around 200 $\xb0C$ to the end of the DTG curve, despite the fact its decomposition was not considered as rate-limiting. Figure 1(b) depicted the DTG profiles of *P. longifolia* leaves degradation at various heating rates (=10, 20, 35, and 55 K/min). From this figure, it was discovered that increasing the heating rate causes the peak temperature to rise. Poor heat transport and a shift in the response mechanism are to blame for the change in behavior. Lower heating rates were favored because heating of biomass happens continuously and allows for improved heat transfer to the interior of biomass.^{64} By increasing the rate of heating, more volatile components are released and less residues are left post pyrolysis.

### B. Kinetic analysis

Kinetic analysis is a crucial component in the effective design of thermochemical systems for biomass conversion. Iso-conversional approaches were used to compute kinetic parameters such as apparent activation energy (*E _{α}*) and pre-exponential factor (

*A*) of pyrolysis of PL leaves. Based on the DTG analysis, the temperature range studied for kinetic analysis in this study was 200 °C–600 °C. The kinetic analysis of pyrolysis of PL leaves was accomplished using five various iso-conversional approaches such as KAS, DFM, OFW, DAEM, and STK to the extent of conversion (0.1–0.8).

#### 1. Calculation of activation energy (E_{α})

The kinetic graphs of pyrolysis of PL leaves are depicted in Figs. 2(a)–2(e). The gradients of the kinetic plots were used to calculate the apparent activation energy for the various iso-conversional approaches. The E_{α} values are obtained using various iso-conversional methods, and the results were displayed in Fig. 2(f) and Table III. Because of variations in their mathematical formulations and approximations, different iso-conversional approaches exhibit marginal variation. The mean activation energy (in kJ/mol) obtained from five iso-conversional methods were as follows: DFM: 231.067; KAS: 211.57; OFW: 210.80; STK: 211.8, and DAEM: 211.57. A wide range of E_{α} values has been observed, which may be due to variations in the heating rate and feedstock composition,^{65} in addition to aforementioned reasons. The activation energy values of pyrolysis of PL leaves obtained through different iso-conversional procedures are comparable to data reported for other types of biomasses and are shown in Table IV. Damartzis *et al.*^{15} examined the pyrolysis kinetics of cardoon and determined E_{α}: 223.2 kJ/mol for cardoon stems and 351.06 kJ/mol for cardoon leaves. According to Lopez-Velazquez *et al.*,^{67} the average E_{α} values for orange waste pyrolysis vary between 121 and 251 kJ/mol. Amutio *et al.*^{68} examined the pyrolysis kinetics of pinewood waste and observed that E_{α} varies between 63 and 207 kJ/mol. Nadiene *et al.*^{69} reported the values of E_{α} for the pyrolysis of castor beans press cake by using various iso-conversional approaches and the values vary between 193 and 270 kJ/mol. The invasive reed canary was studied by Alhumade *et al.*^{70} for its pyrolysis kinetics and heat degradation behavior. When using the OFW and KAS methods, E_{α} ranges from 84.5 kJ/mol for the OFW to 366.53 kJ/mol for the KAS approach in conversion range of α = 0.1–0.9, respectively. The values of mean E_{α} were almost similar for all the methods except DFM, because it has been reported^{71} that there is no way to avoid inaccuracy and imprecision when using differential methods. However, it is also true that the DFM method cannot be very accurate because numerical differentiation was applied to the thermogravimetric data, which adds noise to the output.

α . | DFM . | KAS . | OFW . | STK . | DAEM . | |||||
---|---|---|---|---|---|---|---|---|---|---|

E_{α}
. | A . | E_{α}
. | A . | E_{α}
. | A . | E_{α}
. | A . | E_{α}
. | A . | |

0.1 | 217.85 | 1.35 × 10^{20} | 199.10 | 5.33 × 10^{18} | 197.83 | 2.00 × 10^{16} | 199.30 | 4.27 × 10^{18} | 199.10 | 5.06 × 10^{19} |

0.2 | 207.52 | 2.66 × 10^{18} | 199.17 | 1.30 × 10^{18} | 198.30 | 5.33 × 10^{15} | 199.39 | 1.04 × 10^{18} | 199.17 | 5.82 × 10^{18} |

0.3 | 209.25 | 1.00 × 10^{18} | 205.98 | 1.79 × 10^{18} | 205.10 | 7.37 × 10^{15} | 206.20 | 1.44 × 10^{18} | 205.98 | 5.02 × 10^{18} |

0.4 | 195.43 | 2.19 × 10^{16} | 194.31 | 5.90 × 10^{16} | 194.30 | 2.89 × 10^{14} | 194.56 | 4.77 × 10^{16} | 194.31 | 1.15 × 10^{17} |

0.5 | 213.32 | 3.24 × 10^{17} | 195.71 | 3.68 × 10^{16} | 195.87 | 1.87 × 10^{14} | 195.97 | 2.98 × 10^{16} | 195.71 | 5.31 × 10^{16} |

0.6 | 251.41 | 2.13 × 10^{20} | 197.48 | 2.70 × 10^{16} | 197.78 | 1.41 × 10^{14} | 197.74 | 2.19 × 10^{16} | 197.48 | 2.94 × 10^{16} |

0.7 | 236.03 | 3.05 × 10^{18} | 217.78 | 5.48 × 10^{17} | 217.37 | 2.50 × 10^{15} | 218.04 | 4.42 × 10^{17} | 217.78 | 4.55 × 10^{17} |

0.8 | 317.74 | 7.08 × 10^{23} | 283.04 | 1.43 × 10^{22} | 279.90 | 4.28 × 10^{19} | 283.26 | 1.14 × 10^{22} | 283.04 | 8.91 × 10^{21} |

Avg. | 231.07 | 8.86 × 10^{22} | 211.57 | 1.79 × 10^{21} | 210.81 | 5.35 × 10^{18} | 211.81 | 1.42 × 10^{21} | 211.57 | 1.12 × 10^{21} |

α . | DFM . | KAS . | OFW . | STK . | DAEM . | |||||
---|---|---|---|---|---|---|---|---|---|---|

E_{α}
. | A . | E_{α}
. | A . | E_{α}
. | A . | E_{α}
. | A . | E_{α}
. | A . | |

0.1 | 217.85 | 1.35 × 10^{20} | 199.10 | 5.33 × 10^{18} | 197.83 | 2.00 × 10^{16} | 199.30 | 4.27 × 10^{18} | 199.10 | 5.06 × 10^{19} |

0.2 | 207.52 | 2.66 × 10^{18} | 199.17 | 1.30 × 10^{18} | 198.30 | 5.33 × 10^{15} | 199.39 | 1.04 × 10^{18} | 199.17 | 5.82 × 10^{18} |

0.3 | 209.25 | 1.00 × 10^{18} | 205.98 | 1.79 × 10^{18} | 205.10 | 7.37 × 10^{15} | 206.20 | 1.44 × 10^{18} | 205.98 | 5.02 × 10^{18} |

0.4 | 195.43 | 2.19 × 10^{16} | 194.31 | 5.90 × 10^{16} | 194.30 | 2.89 × 10^{14} | 194.56 | 4.77 × 10^{16} | 194.31 | 1.15 × 10^{17} |

0.5 | 213.32 | 3.24 × 10^{17} | 195.71 | 3.68 × 10^{16} | 195.87 | 1.87 × 10^{14} | 195.97 | 2.98 × 10^{16} | 195.71 | 5.31 × 10^{16} |

0.6 | 251.41 | 2.13 × 10^{20} | 197.48 | 2.70 × 10^{16} | 197.78 | 1.41 × 10^{14} | 197.74 | 2.19 × 10^{16} | 197.48 | 2.94 × 10^{16} |

0.7 | 236.03 | 3.05 × 10^{18} | 217.78 | 5.48 × 10^{17} | 217.37 | 2.50 × 10^{15} | 218.04 | 4.42 × 10^{17} | 217.78 | 4.55 × 10^{17} |

0.8 | 317.74 | 7.08 × 10^{23} | 283.04 | 1.43 × 10^{22} | 279.90 | 4.28 × 10^{19} | 283.26 | 1.14 × 10^{22} | 283.04 | 8.91 × 10^{21} |

Avg. | 231.07 | 8.86 × 10^{22} | 211.57 | 1.79 × 10^{21} | 210.81 | 5.35 × 10^{18} | 211.81 | 1.42 × 10^{21} | 211.57 | 1.12 × 10^{21} |

Feedstock . | Heating rate, β (K min^{−1})
. | Average values of E_{α} (kJ mol^{−1})
. | |||||
---|---|---|---|---|---|---|---|

KAS . | DFM . | DAEM . | STK . | OFW . | References . | ||

P. longifolia leaves | 10, 20, 35 and 55 | 211.57 | 231.07 | 211.57 | 211.81 | 210.81 | Current study |

Cattle manure | 10, 20, 30, 40, 60, and 80 | 181.456 | 195.52 | ⋯ | 181.224 | 182.09 | 25 |

Peanut shells | 2, 10, and 15 | 213.94 | ⋯ | ⋯ | 209.35 | 207.93 | 28 |

Sugarcane bagasse | 10, 30, and 40 | 219.9 | 211.184 | ⋯ | ⋯ | 214.34 | 29 |

Yellow oleander | 10, 30, and 40 | 212.25 | 200.075 | ⋯ | ⋯ | 202.68 | 29 |

F. nitida wood | 5, 10, 20, and 50 | ⋯ | 248.23 | ⋯ | ⋯ | 237.85 | 30 |

Buriti seeds | 5, 10, 15, and 20 | 144.99 | ⋯ | ⋯ | 144.21 | 146.84 | 32 |

Inaja seeds | 5, 10, 15, and 20 | 112.01 | ⋯ | ⋯ | 111.52 | 115.88 | 32 |

Sugarcane leaves | 5, 10, 15, 20, 30, and 40 | 226.75 | 239.58 | ⋯ | 226.91 | 226.97 | 27 |

Cupuassu shell | 5, 10, 20, 30, and 40 | 176.72 | 243.01 | ⋯ | 177.37 | 180.03 | 35 |

Horse manure | 1, 2, 5, and 10 | 200.2 | 194.6 | ⋯ | ⋯ | 199.03 | 38 |

Butia seed | 5, 10, 20, 30, and 40 | 132.7 | 143.33 | ⋯ | 133.23 | 136.24 | 36 |

Banana leaves | 10, 20, and 30 | 79.36 | 73.89 | - | 92.12 | 84.02 | 24 |

Delonix regia | 5, 10, 20, 35, and 55 | 205.67 | 202.34 | 205.67 | 205.89 | 204.87 | 66 |

T. chebula | 10, 20, 35, and 55 | 227.116 | 241.719 | 227.116 | 229.573 | 225.543 | 41 |

Feedstock . | Heating rate, β (K min^{−1})
. | Average values of E_{α} (kJ mol^{−1})
. | |||||
---|---|---|---|---|---|---|---|

KAS . | DFM . | DAEM . | STK . | OFW . | References . | ||

P. longifolia leaves | 10, 20, 35 and 55 | 211.57 | 231.07 | 211.57 | 211.81 | 210.81 | Current study |

Cattle manure | 10, 20, 30, 40, 60, and 80 | 181.456 | 195.52 | ⋯ | 181.224 | 182.09 | 25 |

Peanut shells | 2, 10, and 15 | 213.94 | ⋯ | ⋯ | 209.35 | 207.93 | 28 |

Sugarcane bagasse | 10, 30, and 40 | 219.9 | 211.184 | ⋯ | ⋯ | 214.34 | 29 |

Yellow oleander | 10, 30, and 40 | 212.25 | 200.075 | ⋯ | ⋯ | 202.68 | 29 |

F. nitida wood | 5, 10, 20, and 50 | ⋯ | 248.23 | ⋯ | ⋯ | 237.85 | 30 |

Buriti seeds | 5, 10, 15, and 20 | 144.99 | ⋯ | ⋯ | 144.21 | 146.84 | 32 |

Inaja seeds | 5, 10, 15, and 20 | 112.01 | ⋯ | ⋯ | 111.52 | 115.88 | 32 |

Sugarcane leaves | 5, 10, 15, 20, 30, and 40 | 226.75 | 239.58 | ⋯ | 226.91 | 226.97 | 27 |

Cupuassu shell | 5, 10, 20, 30, and 40 | 176.72 | 243.01 | ⋯ | 177.37 | 180.03 | 35 |

Horse manure | 1, 2, 5, and 10 | 200.2 | 194.6 | ⋯ | ⋯ | 199.03 | 38 |

Butia seed | 5, 10, 20, 30, and 40 | 132.7 | 143.33 | ⋯ | 133.23 | 136.24 | 36 |

Banana leaves | 10, 20, and 30 | 79.36 | 73.89 | - | 92.12 | 84.02 | 24 |

Delonix regia | 5, 10, 20, 35, and 55 | 205.67 | 202.34 | 205.67 | 205.89 | 204.87 | 66 |

T. chebula | 10, 20, 35, and 55 | 227.116 | 241.719 | 227.116 | 229.573 | 225.543 | 41 |

The apparent activation energy is the minimal necessary amount of energy to initiate a chemical reaction. Apparent activation energy was also utilized to determine a fuel's reactivity.^{72} During the early phases of pyrolysis, a rise in E_{α} was detected. Figure 2(f) depicts the variation in activation energy in relation to conversion. The existence of endothermic reactions is indicated by an increase in E_{α} for conversion α = 0.1–0.3 and also for α = 0.4–0.7, whereas the presence of exothermic reactions is shown by a drop in the values of E_{α} for the conversion from α = 0.3 to 0.4 and for α = 0.7 to 0.8. Such a sudden change in the value of *E _{α}* existed for all the methods. This indicates that the reaction mechanism happening during the pyrolysis of PL leaves varies across the conversion range, indicating that it is a complicated mechanism. From the aforementioned findings, one can conclude that apparent activation energy is a robust function of conversion.

^{73}In other words, the decomposition ranges of lignin, hemicellulose and cellulose found in biomass are dissimilar; hence, the pyrolysis of lignocellulosic biomass involves a complicated reaction mechanism that takes place across several steps.

^{74}The E

_{α}of the pyrolysis reaction was obtained using the reaction mechanism. Consequently, a reaction with a low activation energy is more likely to occur rapidly; and out of all the methods utilized in this investigation, only the DFM method has the highest apparent activation energy. Due to the differential nature of the rate equation, this method is more effective for pyrolysis kinetic studies because no assumptions are necessary to calculate the activation energy (E

_{α}) from TGA analysis data. However, these data are numerically differentiated, which introduces noise into the result of this approach, and this is the big disadvantage of the DFM method. From the iso-conversional plots, it was found that the values of R

^{2}for all methods shown in Figs. 2(a)–2(e) are greater than 0.98 which shows that the TGA data on pyrolysis of PL leaves had a good fit for all the methods. The average R

^{2}values derived by the STK, KAS, OFW, DAEM, and DFM techniques were 0.9821, 0.982, 0.9835, 0.982, and 0.98, respectively. Based on the values of R

^{2}, one can conclude that all methods are reliable for pyrolysis of PL leaves.

#### 2. Calculation of pre-exponential factor (A)

The intercept of all the models was used to calculate pre-exponential values which were ranging from 10^{16} to 10^{23} min^{-1} and the average values of *A* (in min^{-1}) were as follows: DFM: 8.85 × 10^{22}; KAS: 1.79 × 10^{21}; OFW: 5.34 × 10^{18}; STK: 1.42 × 10^{21}; and DAEM: 1.21 × 10^{21}. The surface reaction is characterized by low values of frequency factors (less than $ 10 9\u2009 s \u2212 1$). When the reaction is not surface area dependent, the low values of frequency factor indicates a closed complex. A higher value of frequency factor suggests a simple complex. The frequency factor can range between $ 10 4$ and $ 10 18\u2009 s \u2212 1$ according to Turmonova *et al.*^{75} The complicated structure of the biomass sample explains the variance in frequency factor values throughout the conversion range, as well as the complicated processes that occur during thermal decomposition. It was discovered that the value of the frequency factor grows as the heating rate increases, which could be attributed to an intensification of collisions at high heating rates.^{76} PL leaves residue had frequency factor values that were nearly equivalent to Castor^{77} and higher than chicken manure, rice straw, and rice bran.^{55,78}

### C. Thermodynamic analysis

In addition to kinetic parameters, thermodynamic properties are critical for the optimization, scaling, and design of pyrolysis reactor.^{79} As a result, thermodynamic properties (ΔH, ΔG, and ΔS) were approximated using the kinetic parameters obtained from the five iso-conversional approaches, whose models best fit the data. The thermodynamic parameters were computed using Eqs. (10)–(12), and the results are reported in Figs. 3–5. Change in enthalpy (ΔH) is a thermodynamic property that represents a system's entire heat content. Change in enthalpy in pyrolysis refers to the total energy spent on biomass during its conversion to various products such as gas, char, and oil.^{80}^{,} Figures 3(a)–3(e) depict the ΔH with regard to the conversion, and the average values of ΔH at four heating rates (β = 10, 20, 35, and 55 K min^{−1}) were as follows: STK: 206.79, 206.74, 206.65, and 206.57 kJ mol^{−1}; OFW: 205.79, 205.74, 205.65, and 205.577 kJ mol^{−1}; KAS: 206.5561, 206.506, 206.4228, and 206.342 kJ mol^{−1}; DFM: 226.051, 226.0015, 225.9183, and 225.9183 kJ mol^{−1}; and DAEM: 206.5561, 206.506, 206.4228, and 206.342 kJ mol^{−1}, respectively. Figures 3(a)–3(e) show almost increase in ΔH with increasing conversion degree (from 0.4–0.8 conversion range), as well as the positive sign of ΔH for the whole conversion range by all methods. Furthermore, the heating rate has a negligible effect on ΔH. This means that the active pyrolysis stage was endothermic but that endo-thermicity increased as the reaction progressed. In other words, as the pyrolysis reactions advanced, the amount of heat energy consumed increased. All the values of ΔH were almost similar for the four iso-conversional methods expect DFM method. The little change in ΔH and E_{α} (∼5–6 kJ mol^{-1}) at each conversion point was shown to be owing to the difference in energy between the reagent and activated complex. A smaller energy gap promotes the production of activated complexes.^{81} The proximity of ΔH and E_{α} values indicates that product production is possible by providing an additional energy of 5 kJ/mol.^{70} The average enthalpy variation for pyrolysis of PL leaves was varied in the range of 206–226 kJ mol^{-1} using five iso-conversional methods at four heating rates, while the enthalpy variation for RPW (red pepper waste),^{78} dairy manure, rice straw, rice bran, chicken manure,^{55} and para grass^{40} was 24.48–143.12, 112.14, 161.34, 171.3, 152.2, and 172.55 kJ mol^{−1}, respectively, which were less than those for pyrolysis of PL leaves. On the other hand, for chili straw,^{23} wheat straw,^{22} and Wucaiwan lignite,^{21} the change in enthalpy values were similar or higher compared to those of pyrolysis of PL leaves.

Another thermodynamic property that can be utilized to determine equilibrium and the likelihood of a reaction moving in a specific direction is change in Gibbs free energy (ΔG). Figures 4(a)–4(e) display the ΔG based on the conversion, and the average values of ΔG at all heating rates (β = 10, 20, 35, and 55 K min^{−1}) were as follows: STK: 173.66, 172.04, 172.2378, and 172.8109 kJ mol^{−1}; OFW: 173.7, 172.06, 172.26, and 172.83 kJ mol^{−1}; KAS: 173.67,172.04,172.24, and 172.81 kJ mol^{−1}; DFM: 173.25, 171.62, 171.8, and 172.37 kJ mol^{−1}; and DAEM: 173.67,172.04,172.24, and 172.81 kJ mol^{−1}, respectively. All calculated ΔG values [Figs. 4(a)–4(e)] were positive, showing that pyrolysis reactions of PL leaves in active pyrolysis zone do not happen suddenly and requires an external energy. Higher ΔG values were reported to suggest a less favorable pyrolysis process and a high energy need for breakdown.^{82} Examining the minor increase in values of ΔG with α, a slight increase in the energy demand for the progression of pyrolysis reactions should be noted, particularly between conversions of α = 0.1–0.5. The value of ΔG remained almost unaffected by further increase in the conversion degree, which suggests that there was little chance of a change in the amount of energy required for conversions greater than 0.5.

Figures 5(a)–5(e) depict the change in entropy, ΔS (kJ mol^{−1} K^{−1}) corresponding to α at β = 10, 20, 35, and 55 K min^{-1} for all five iso-conversional procedures. As per Figs. 5(a)–5(e), the obtained ΔS values contain only positive values. The average ΔS values (kJ mol^{−1} K^{−1}) were as follows: STK: 0.0548, 0.0569, 0.0555, and 0.0536; STK: 0.1701, 0.171, 0.1678, and 0.1643; KAS: 0.1754, 0.1763, 0.1730, and 0.1693; DFM: 0.2339, 0.2342, 0.2300, and 0.2255; and DAEM: 0.1754,0.1763,0.1730, and 0.1693. The negative ΔS indicates that the products are more ordered than the reactants, while the positive ΔS indicates the opposite.^{83} The negative ΔS value indicates the proximity of thermodynamic equilibrium, showing a greater degree of order of products than initial reactants, which means that the time necessary to reach thermodynamic equilibrium is greater due to the slower reaction rate for achieving the activated complex (high thermodynamic stability). Conversely, the positive ΔS values of the PL pyrolysis showed a greater degree of disorder in the final product than in the biomass. The greater the value of ΔS, the greater the substance's reactivity and the shorter the time necessary to generate an activated complex.^{84} Positive entropy change indicates that the activated compound becomes loosely bound as its stability decreases, and biomass conversion follows a dissociation pathway.

### D. Reaction mechanism

#### 1. Criado's master plots method

The method by which a chemical reaction moves from the reactant to the product as it advances through the progressive sequence of fundamental reactions is referred to as the reaction mechanism. Understanding the reaction mechanism of biomass pyrolysis is also critical for optimizing processes and designing reactors. The biomass pyrolysis reaction comprises of numerous simultaneous multistage series reactions. Analyzing a single mechanism of reaction for the whole process is hard, especially for heterogeneous reactions, due to the fact that the complete reaction follows different kinetics and processes, with the conversion changing as the reaction progresses. In this present study, the Criado's master plot approach was used to estimate the reaction mechanism of solid-state pyrolysis of PL leaves at β = 10, 20, 35, and 55 K min^{-1}. The kinetic mechanism of the biomass pyrolysis reaction can be identified with the help of a master plot and activation energy data collected from iso-conversional methods.^{85,86} The master plots are independent of the heating rate and were reliant on the kinetic model used by the process. The theoretical curves were generated by utilizing the equations corresponding to the various reaction models presented elsewhere.^{59,66} The value of $g(\alpha )$ is based on the kinetic model and was used to depict the reaction mechanism of PL biomass. In this study, the reaction mechanism of the process was interpreted based on the value of E_{α} computed through the DFM method. Master plots were drawn for both experimental and theoretical values against α for pyrolysis of PL leaves, and the plots produced were shown in Figs. 6(a)–6(d) for different heating rates. Figure 6(a) illustrates the relationship between theoretical and experimental curves in order to estimate the reaction model for a heating rate of 10 K min^{−1}. Comparison of theoretical and experimental curves reveals that as the conversion changes from 0.1 to 0.5, it initially followed the F0, D1 and power-law models, while the conversions (0.6–0.7) followed F1 mechanism. At 20 K min^{−1}, the experimental curve proceeded through F0, D1 and power-law models for the conversion from 0.1 to 0.6, and for the remaining conversion 0.7, none of the reaction mechanism followed. At 35 K min^{−1}, for conversion values varied between 0.1 and 0.5, it was discovered that F0, D1, and power-law models were closely followed, but for the conversions (0.6 and 0.7), it followed R2 and F1 models. At 55 K min^{−1}, the experimental curve closely followed with the F0, D1 and power-law models until 0.5 conversion, after which it does not passed through any of the reaction mechanism. In a nutshell, master plots demonstrated that F0, D1, and power-law models reaction mechanisms drive the pyrolysis of PL biomass.

#### 2. Master plots based on the integral form of the kinetic data

Another crucial kinetic parameter is obtaining the reaction mechanism, which can be discovered by comparing theoretically plotted master plots to experimentally plotted ones. The $p(x)/p(0.5)$ values can be directly approximated by utilizing the predefined E_{α}, and the E_{α} values utilized in this work are those obtained via the linear iso-conversional DFM approach. The $g(\alpha )/g(0.5)$ graphs are calculated using the various kinetic models listed elsewhere.^{59,66} Figures 7(a)–7(d) depict theoretical master plots of several reaction processes as well as experimental curves for pyrolysis of PL leaves. It is worth noting from these figures that the $p(x)/p(0.5)$ values for four heating rates of β = 10, 20, 35, and 55 K min^{−1} are almost the same, implying that the degrading response mechanism can be decided regardless of the heating rate utilized. The biomass pyrolysis mechanism is a complicated one in which each of the three principal components (hemicellulose, lignin, and cellulose) plays different functions. Therefore, the behavior of these components must be addressed while evaluating the mechanism of biomass degradation. Wang *et al.*^{87} proposed that the primary degradation mechanisms of the hemicellulose component of biomass were diffusion and nucleation. Similarly, it was well understood that the cellulose component of biomass decomposes via a nucleation mechanism.^{71} On the other hand, the mechanism that determines the lignin decomposition of biomass may be quite complicated involving the combined impacts of diffusion, power law, nucleation, diffusion, geometrical contraction,^{26} etc. In the conversion range of α = 0.1–0.6, the principal thermal breakdown mechanisms of biomass waste were observed to be power and nucleation law. In this conversion zone, the highest amount of biomass was also converted into char and volatiles. During biomass pyrolysis, volatiles and gases can spread through the porous char.

On comparing both these methods, Criado's master plot approach produced better results for this work because differential techniques do not rely on approximations. However, the actual application of these methods is connected to some degree of error and imprecision. Thus, inaccuracies shall emerge when the reaction temperature is greatly dependent on the heating rate. Differential methods used on integral data include numerical differentiation, which introduces noise into the kinetic analysis and can lead to mistakes while smoothing the noisy data. Given these considerations, differential methods should have expected to be more accurate and precise than integral procedures.

## V. CONCLUSIONS

The thermogravimetric and derivative thermogravimetric curves of *P. longifolia* leaves migrated toward the higher temperature zone as the heating rate increased. Five iso-conversional approaches were used to derive kinetic parameters and thermodynamic properties (ΔH, ΔG, and ΔS). The mean values of E_{α} ranged from 211.57 to 231 kJ mol^{−1}, and the values were almost similar for all the methods except for DFM because of its differential nature. The R^{2} values (>0.98) of the kinetic plots obtained by all methods were nearly identical, indicating an excellent correlation. Because of the complicated nature of pyrolysis kinetics, the values of E_{α} fluctuate with the increase in conversion. The reaction mechanism was determined utilizing Criado's master plots approach and integral approach for pyrolysis of PL leaves and found that there was no exact single response mechanism for all heating rates especially for conversion range above 0.5. In other words, the experimental curves were found to going through many theoretical curves for both approaches, suggesting the complexity of the pyrolysis process of PL leaves.

## ACKNOWLEDGMENTS

P.K.R. Annapureddy is grateful to Mr. D. Rammohan and Ms. N. Thejaswini for their assistance at the initial stages of this work.

## AUTHOR DECLARATIONS

### Conflict of Interest

The authors have no conflicts to disclose.

### Author Contributions

**PKR Annapureddy:** Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Validation (lead); Writing – original draft (lead). **Nanda Kishore:** Conceptualization (lead); Funding acquisition (lead); Project administration (lead); Resources (lead); Supervision (lead); Writing – review & editing (equal).

## DATA AVAILABILITY

The data that support the findings of this study are available within the article.

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