# The Status of Pyrolysis Kinetics Studies by Thermal Analysis: Quality Is Not as Good as It Should and Can Readily Be

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## Abstract

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## 1. Introduction

## 2. Results and Discussion

#### 2.1. Overview of Thermokinetic Research Development

#### 2.2. Typical Problems of Kinetic Computations

_{p}with the heating rate β, to yield the activation energy E

_{a}and preexponential factor A. Strictly speaking, the Kissinger equation is valid for single-step first-order reactions, but often the resulting activation energy can be linked to the rate-limiting step of more complex processes [38]. The variation of the conversion degree at the DSC peak temperature can be considered as a measure of the reaction complexity and accuracy of the Kissinger method results [34]. Modifications of the Kissinger method allowing one to obtain the information relevant to the reaction model have been suggested by Burnham [39] and Farjas et al. [11,40]. A recent review [41] surveys the application of the Kissinger method to various processes and highlights associated problems, including the inability of the method to detect the multi-step kinetics and its inapplicability to the processes during cooling, such as melt crystallization. Overall, the Kissinger method is rarely a good choice for proper kinetic analysis.

_{a}) versus conversion degree α. For an ideal single-step reaction E

_{a}should be practically constant with the reaction progress. In practice, E

_{a}can be considered constant if within the range α = 0.1–0.9 the difference between the maximum and minimum value of E

_{a}is less than 10–20% of the average E

_{a}value [14]. Only in this situation one can be justified by replacing the observed weak dependence of E

_{a}on α with the average E

_{a}value. However, a larger variation of E

_{a}with α is frequently found that is usually associated with the multi-step character of the process. It should be stressed, that in the majority of analyzed papers the detected significant variation is neglected by averaging E

_{a}over the α range and reporting the mean activation energy. Note that such procedure cannot be justified statistically because by its meaning the mean value is the most probable value of the dataset. That is, the mean E

_{a}makes sense only when the E

_{a}values are scattered randomly over the α range, but no sense when E

_{a}shows significant systematic variation with α. Needless to say that the mean value also has no physical meaning in the case of a multi-step process because such a process is governed by more than one energy barrier, i.e., more than a single E

_{a}value. Furthermore, exploring a systematic dependence of E

_{a}on α can furnish the mechanistic information on the analyzed process [43]. Averaging obviously eliminates this information.

_{a}” [12]. Contrary to this recommendation, one can see from Figure 5 that this method is the most popular among the kinetic methods used in 2021 within the selected set of publications.

_{a}varies significantly with α [49]. Note that all the methods represented by Equation (4) are based on the integration over 0–α region and, thus, prone to the aforementioned systematic error in E

_{a}. This error is eliminated only if integration is performed over small Δα segments, i.e., in the piecewise manner. For instance, the Vyazovkin method uses a set of n experiments performed under arbitrary thermal programs T(t) and obtains the activation energy E

_{a}at a particular conversion degree α by minimizing function [49]:

_{a}when E

_{a}varies significantly with α, and, thus, delivers better accuracy than any of the methods based on Equation (4).

_{a}does not vary with α) and multi- (E

_{a}varies with α) processes [54]. The high accuracy of this method in the case of multistep processes has recently been demonstrated [55]. It is worthy of note that this method is only one of many important applications of the so-called isokinetic or entropy-enthalpy compensation relationships [56].

_{a}values computed by the methods of different accuracy” [12]. As our analysis of the selected publications shows, the majority of them, in turn, report the results of two or more isoconversional methods (e.g., [57,58,59]). This practice provides no kinetic insights, and the application of only one accurate method (e.g., the differential one of Friedman or integral of Ortega or Vyazovkin) is recommended.

_{a}, A, reaction model). In its core, the procedure boils down to fitting single heating rate data, and, all such procedures do not permit obtaining reliable kinetic parameters [64]. Thus, the ICTAC Kinetics Committee has recommended to avoid altogether the methods that are designed to evaluate kinetic parameters from single heating rate measurements [12].

_{α}is time to reach the extent of decomposition α at temperature T. The results obtained are both striking and illuminating. First, if the reported kinetic parameters are correct, the two natural wood species, Jasminum nudiflorum Lindl. bark [75] and tea oil camellia shells [72], should be very thermally unstable at 27 °C (Figure 6). The bark would decompose nearly completely in two days, whereas the shells would lose approximately 50% of their mass for a little over than 1 week. This obviously contradicts the well-known thermal stability of wooden species and, if was true, would be impossible to miss in practical handling of these materials. Similarly, if one uses the reported [73] kinetic triplet, lignin should almost entirely decompose at an ambient temperature for less than 3 weeks. If this was true, its major application as a fuel would be impossible. In reality, lignin does not undergo any significant decomposition on continuous heating below 200 °C [83]. Lastly, the kinetic parameters reported [80] for raw sample of the Shengdong coal predict that at an ambient temperature it would decompose by ~70% in one year. This result is clearly at odds with the common knowledge about coal stability.

_{a}value, whereas the latter (CR) relies on the single heating rate data analysis and can introduce an error in E

_{a}in excess of 100%. In spite of the clear ICTAC recommendations, the applications of poor kinetic methods continue to grow as can be visualized by observing the citation dynamics of original publications of the Flynn–Ozawa–Wall and Coats–Redfern methods (Figure 7). Such dynamics looks especially shocking when compared to the citation dynamics of the ICTAC recommendations for performing kinetic computations [12] (Figure 7). The document is one of the most cited in the field so that disregarding its advices appears more like intentional neglect than accidental unawareness of its existence.

#### 2.3. Typical Problems of Data Collecting and Reporting

^{−1}. On the whole, smaller sample sizes allow one to use faster heating rates and vice versa. As a rule of a thumb, the product of the sample mass and heating rate (m

_{s}·β) should be kept under 100 mg K min

^{−1}[13]. This rule is upheld by simulation work for degradation of polymers [95]. The value of the product is, of course, enthalpy dependent. The 100 mg K min

^{−1}is a reasonable value for processes whose enthalpy change is in the range of hundreds J g

^{−1}. In the case of energetic materials, which decompose releasing thousands J g

^{−1}the recommended sample masses are less than 1 mg and heating rates slower than 5 K min

^{−1}so that m

_{s}·β ≤ 5 mg K min

^{−1}.

_{s}·β [mg K min

^{−1}]). Figure 8b gives the distribution of the sample masses selected by the authors to obtain the thermal analysis data. The distribution shows two maxima, at 5 and 10 mg. Clearly, the majority of the authors select excessively large sample masses. Even more instructive is the distribution of the mass heating rate products (Figure 8c). It is seen that the majority of studies have been conducted at m

_{s}·β ≥ 100 mg K min

^{−1}, i.e., under the conditions when the heat and mass transfer phenomena are likely to have a non-negligible contribution to the chemical kinetics. In such a situation, the regular kinetic computations, which do not account for the aforementioned phenomena, yield erroneous values of the Arrhenius parameters. In particular, the error in the activation energy can readily reach tens of % [13].

^{2}≥ 0.9938), which is rarely accomplishable in routine measurements. Thus, careful studies tend to employ four, five or even more different heating rates (or temperatures for isothermal measurements), so that the corresponding critical values of r are significantly smaller. It is also a good idea to use a broad range of the heating rates by selecting the fastest so that it is approximately 10 times larger than the slowest. This secures a sufficiently broad temperature range required for proper kinetic analysis [13,98].

## 3. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Number of thermokinetic papers by year: Scopus and Dimensions databases. Citations number is shown in the right axis (gray curve, Dimensions database data).

**Figure 2.**Countries collaboration network visualization: (

**a**) 45 counties having at least 2 publications from 2000; (

**b**) 54 countries having at least 5 publications from 2021.

**Figure 3.**Co-occurrence of keywords extracted from thermokinetic papers published at 2000 (78 keywords occurred at least 10 times in the title and abstract).

**Figure 4.**Co-occurrence of keywords extracted from thermokinetic papers published at 2021 (89 keywords occurred at least 30 times in the title and abstract).

**Figure 5.**Occurrence of kinetic methods in top 100 most cited thermokinetic studies from 2021. Bars for isoconversional methods are filled as orange. Only methods appeared in more than 4% of analyzed papers are shown.

**Figure 8.**Summary of the experimental details extracted from the top 100 by citations thermokinetic papers from 2021: (

**a**) number of experiments used in kinetic analysis, (

**b**) distribution of the sample masses used to measure thermal analysis data, (

**c**) the product of sample mass and heating rate for nonisothermal data from the dataset.

**Table 1.**Number of documents and citations by journal title, for thermokinetic papers published at 2000 and 2021 (only top ten journals by publications number are shown).

2000 | 2021 | ||||
---|---|---|---|---|---|

Source Title | Documents | Citations | Source Title | Documents | Citations |

Journal of Thermal Analysis and Calorimetry | 114 | 2072 | Journal of Thermal Analysis and Calorimetry | 94 | 182 |

Thermochimica Acta | 68 | 3957 | Thermochimica Acta | 66 | 213 |

Journal of Applied Polymer Science | 31 | 818 | Polymers | 44 | 147 |

Polymer | 26 | 1307 | Fuel | 41 | 367 |

Polymer Degradation and Stability | 10 | 668 | Materials | 31 | 62 |

Journal of Polymer Science Part B Polymer Physics | 10 | 349 | ACS Omega | 28 | 52 |

European Polymer Journal | 8 | 189 | Biomass Conversion and Biorefinery | 26 | 98 |

Polymer Engineering & Science | 8 | 158 | Bioresource Technology | 21 | 185 |

Macromolecules | 7 | 473 | Journal of Analytical and Applied Pyrolysis | 19 | 125 |

Materials Science and Engineering A | 7 | 301 | Journal of Applied Polymer Science | 19 | 35 |

Total (2000) | 597 | 20163 | Total (2021) | 1630 | 5509 |

**Table 2.**Analysis of experimental section of top 100 by citations thermokinetic papers, published in 2021: thermal analysis and kinetic details.

Specific Aspect of Thermal Analysis Measurement | Percent of Studies Where It Is Reported |
---|---|

Sample mass | 79 |

Crucible type | 8 |

Software used for kinetic analysis | 12 |

Gaseous atmosphere (gas type) | 95 |

Calibration info | 8 |

Purge gas flow rate | 86 |

Repeatability of measurements | 37 |

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## Share and Cite

**MDPI and ACS Style**

Muravyev, N.V.; Vyazovkin, S.
The Status of Pyrolysis Kinetics Studies by Thermal Analysis: Quality Is Not as Good as It Should and Can Readily Be. *Thermo* **2022**, *2*, 435-452.
https://doi.org/10.3390/thermo2040029

**AMA Style**

Muravyev NV, Vyazovkin S.
The Status of Pyrolysis Kinetics Studies by Thermal Analysis: Quality Is Not as Good as It Should and Can Readily Be. *Thermo*. 2022; 2(4):435-452.
https://doi.org/10.3390/thermo2040029

**Chicago/Turabian Style**

Muravyev, Nikita V., and Sergey Vyazovkin.
2022. "The Status of Pyrolysis Kinetics Studies by Thermal Analysis: Quality Is Not as Good as It Should and Can Readily Be" *Thermo* 2, no. 4: 435-452.
https://doi.org/10.3390/thermo2040029