Kinetics and thermodynamics of beech wood pyrolysis mechanism

ABSTRACT Beech wood pyrolysis is capable of providing fuel as well as invaluable materials of industrial importance besides being CO2-neutral. Mechanistic insights revealed by the kinetics and thermodynamics of beech wood pyrolysis may not only lead to controlling the process but also to optimize its efficiency. However, the literature lacks in some reliable and physically meaningful mechanistic insights into beech wood pyrolysis process. Moreover, beech wood pyrolysis thermodynamics has not yet been reported. Therefore, the present paper puts forward a detailed kinetic and thermodynamic study on the beech wood pyrolysis. The beech wood pyrolysis is firstly deconvoluted into three isolated pseudo-hemicellulose, pseudo-cellulose and pseudo-lignin thermal degradation processes by an effective deconvolution function. Afterwards, generalized integral isoconversional method is applied. It suggests that the three processes follow single-step kinetics. Advanced reaction model determination methodology reveals that the thermal degradation processes of pseudo-hemicellulose, pseudo-cellulose and pseudo-lignin go to completion by respectively following, second order (RO), two-dimensional (2D) nucleation/growth and complicated diffusion mechanisms. The thermodynamics of beech wood pyrolysis puts forth interesting and important information regarding the endothermicity of the processes involved and arrangement/orientation of the activated complexes in transition state. The practical valuation of the present research is also pointed out and discussed. GRAPHICAL ABSTRACT


Introduction
Over the decades, energy has evolved into a crucial issue.The diminution of fossil fuel reservoirs and their adverse climatic influence along with an abrupt rise in population have made energy a global concern (Muhammad 2019, Liu et al. 2020, Bu et al. 2022).To address the aforementioned issue, the energy policies alongside energy management put a special emphasis on harnessing renewable energy resources.This approach on the one hand is capable of satisfying the foreseen substantial energy demand and on the other hand, it may effectively contribute to minimizing the CO 2 emissions (a widely advocated rationale/contributor behind/in the worldwide climate change) (Arshad et al. 2018a, Matthews et al. 2022, UN 2023).Biomass, a material derived from living organisms (such as animals and mainly plants), is recognized as one of the important renewable energy resources which is ubiquitous around the world.It is, in fact, the fourth largest energy resource today (following natural gas, coal and petroleum) and is of particular interest/use to developing countries (Jahirul et al. 2012, Shah et al. 2019).Despite the structural and compositional complexities, plant-based biomass contains minute quantities of nitrogen, sulfur and ash.For that reason, the thermochemical treatment of biomass leads to less hazardous gas emissions such as NO x (nitrogen oxides), SO 2 (sulfur dioxide) and soot than the common fossil fuels.Moreover, biomass is considered CO 2 -neutral as the amount of CO 2 emitted during biomass combustion is recycled into plants by photosynthesis (Tsai et al. 2007).Some well-known thermochemical conversion processes of biomass include combustion, gasification and pyrolysis which have attracted the attention of academia and industry equally owing to the obtention of biofuels, biohydrogen and biochar during those processes (Ryu et al. 2020, Lee et al. 2022, Qiu et al. 2022, Seo et al. 2022, Valizadeh et al. 2022a, Valizadeh et al. 2022b, Lee et al. 2023).Combustion refers to the exothermic thermal oxidation of materials at elevated temperatures, producing a mixture of gases and energy.Biomass combustion straightforwardly implies burning organic matter at high temperatures for heat and power (Hupa et al. 2017).It is noteworthy that wood is a commonly employed combustion feedstock.Gasification is a technological process capable of converting a carbonaceous material into syngas (a mixture of carbon monoxide and hydrogen).
Biomass gasification technology consists of a controlled process involving heat, steam, and oxygen to convert biomass mainly into biohydrogen, without combustion (Mishra et al. 2021, Valizadeh et al. 2022a, Valizadeh et al. 2022b).Pyrolysis, in general, and biomass pyrolysis, particularly, is defined as the thermal decomposition of a material in an inert environment (Sandberg et al. 2013).Biomass pyrolysis is carried out to produce biofuels and biochar (Qiu et al. 2022).Biofuels are solid, liquid and gaseous fuels obtained by pyrolyzing biomass to generate heat and electricity (Yang et al. 2022).Biochar is the end-product of biomass pyrolysis comprising a porous carbonaceous material with a large specific surface area and rich in surface charges and surface-free radicals.Biochar finds applications in electrochemical energy storage, energy catalysis, counteracting/minimizing damage to environment, etc. (Weber et al. 2018, Gao et al. 2020, Li et al. 2020, Sun et al. 2020, Xiang et al. 2020, Gautam et al. 2021, Shukla et al. 2021, Wang et al. 2021, Chen et al. 2022).
Beech wood belongs to plant-based biomass and is native to clement Asia, Europe and Northern America.Owing to its intriguing physical and mechanical properties, it is among the mostly employed wood species in various industries and also finds applications in furniture and household appliances (Ding et al. 2016a, Ding et al. 2016b).It is worth mentioning here that wood is, in fact, a major component of agricultural biomass waste.Beech wood pyrolysis is carried out aiming at obtaining bioenergy (wood is hitherto the largest bioenergy resource) and deriving indispensable materials from this type of biomass.The wood pyrolysis mechanism enables one to probe the pathway of pyrolysis processes taking place in the wood biomass.Mechanistic insights thus revealed are absolutely necessary to control the wood pyrolysis process and/or optimize its efficiency.Pyrolysis kinetics and thermodynamics in this regard play a pivotal role.Specifically, pyrolysis kinetics parameters are advantageous in designing efficacious pyrolysis reactors for large-scale (engineering) applications and technology commercialization.In addition, they may aid in computational fluid dynamics (CFD) simulation (Papadikis et al. 2009, Cho et al. 2012, Zhou et al. 2015).Although several studies have been attributed to beech wood pyrolysis kinetics (Gašparovič et al. 2010, Peters et al. 2011, Ding et al. 2016b, Abdelouahed et al. 2017, Ding et al. 2017, Gogoi et al. 2018, Soria-Verdugo et al. 2020), the literature substantially lacks some plausible and physically meaningful mechanistic insights into beech wood pyrolysis process.Furthermore, the thermodynamics of the beech wood pyrolysis process is yet to be determined.
Kinetics and thermodynamics of wood pyrolysis may predict the process mechanism of wood pyrolysis and shed light on its transition state.It is worth pointing out that biomass, in general, and beech wood, in particular, constitute principally hemicellulose, cellulose and lignin in various compositions and pseudo-forms.Biomass is known to pyrolyze in no less than three parallel processes (Schröder et al. 2004, Chen et al. 2022).Due to the differences in relative compositions of hemicellulose, cellulose and lignin and their possible interactions, devising a generalized kinetic expression to plausibly describe the overall biomass pyrolysis kinetics is less likely.In this context, systematic and advanced kinetic approaches to pyrolysis deserve prominence.Hitherto, researchers have questionably been employing the model-fitting approaches to kinetically describe the pyrolysis processes in biomass (Wang et al. 2017, Hameed et al. 2019).It must be mentioned here that the assumption of a particular form of process model is strongly discouraged in condensed phase kinetics as it remains ambiguous whether the process under consideration really follows the same mechanism being supposed (Vyazovkin et al. 2011).Thus, isoconversional kinetics and the kinetic frameworks based on it, like the one suggested by Arshad & Maaroufi, may illuminate credible mechanistic information regarding the pyrolysis process (Arshad et al. 2014).As the number/ nature of processes occurring during the beech wood pyrolysis is perceivable, peak deconvolution might adequately simulate the pyrolysis process of beech wood (Arshad et al. 2017).The present work puts forward the very first thorough study on the combined peak deconvolution-advanced reaction model determination methodology approach to model the beech wood pyrolysis process and predict its mechanism.Based on the pyrolysis kinetic study, thermodynamic parameters associated with the transition state(s) of beech wood pyrolysis will be evaluated and discussed.

Kinetics and thermodynamics of biomass pyrolysis
The kinetics of biomass pyrolysis is primarily carried out by a familiar thermal analysis technique, thermogravimetric analysis (TGA).The advancement of the biomass pyrolysis process is monitored by a term degree of conversion "α" which is defined as follows: where "m 0 " is the initial mass of the reactant, "m t " is its mass at a certain time (isothermal analysis) or temperature (non-isothermal analysis) during the pyrolysis process and "m ⍰ " is its mass at the end of the process.In a pyrolysis process, the process rate dα/dt (being a function of α) can be expressed as follows: Equation ( 2) is the fundamental kinetic equation of biomass pyrolysis.As pyrolysis is a thermally activated process, the value of rate constant "k" is usually substituted into Equation (2) by the Arrhenius equation which can be transformed into the following form: where E α is the energy of activation, f(α) is the function of the degree of conversion, called reaction model, "A" is the preexponential factor, and R is the gas constant.In a physical sense, Eα is the activation energy barrier(s) of the reaction f (α) is an expression for the mechanism of the reaction, and "A" interprets the collision frequency of the particles involved in the formation of the activated complex (Vyazovkin et al. 2011, Arshad et al. 2014).A set of {A, E α , f(α)} is called the kinetic triplet.Table 1/Figure 1 presents some familiar solidstate process models.To systematically carry out the biomass pyrolysis kinetics, activation energy is determined in the first step followed by the reaction model and finally the pre-exponential factor.Activation energies of pyrolysis processes are determined by isoconversional kinetic analysis.Isoconversional methods may generate/examine the variation in activation energy with the degree of conversion, and, therefore, the nature/complexity of the pyrolysis process.A pyrolysis process can be fairly described as a single-step process if the variation in its activation energy with the degree of conversion is insubstantial.Or else, the reaction is recognized as the one pursuing a complex process mechanism.Isoconversional methods can be linear/nonlinear, differential/integral and isothermal/nonisothermal (Vyazovkin et al. 2011, Arshad et al. 2014).
Taking the logarithm of Equation ( 3) gives the following linear differential isoconversional method, known as Friedman's method (Friedman 1965).
where b = dT dt is the heating rate.E α values over a range of α values can be determined by the slope of the plot ln(dα/dt) versus 1/T α at constant values of α which appears as a straight line.The E α values thus obtained might be irregular/scattered due to the involvement of numerical differentiation in Equation ( 4).The numerical differentiation may, therefore, be avoided by employing integral isoconversional methods.
Aiming at determining kinetically the process models of solid-state processes and predicting their trustworthy mechanisms, Arshad and Maaroufi put forth an advanced reaction model determination methodology (Arshad et al. 2014).The suggested methodology is more efficacious than the pre-existing kinetic modeling methodologies as it is equally useful in isothermal and non-isothermal kinetics and may not only kinetically interpret single-step but also multi-step condensed phase processes.The authors utilized a modified Arrhenius equation in their approach, which includes variable activation energy and pre-exponential factor as expressed in Equation ( 6): where "A 0 " is the value of pre-exponential factor at ambient temperature "T 0 " and "n" are numerical constants which usually attain the values, n [ [0, 1].However, it may take certain positive values other than those mentioned in the interval and it may be negative numbers (Arshad et al. 2016).
Based on Equation ( 6), Arshad and Maaroufi (Arshad et al. 2014) derived a new generalized function of the degree of conversion h(α) to predict the reaction mechanisms of complex solid-state processes under isothermal conditions: Now, if the variation in activation energy with the degree of conversion is insignificant (dE/dα = 0), the process presumably pursues a single-step mechanism.Therefore, Equation ( 7) can be rearranged as follows: Details on determining the parameter "n" in isothermal/nonisothermal kinetics have been given in previous work (Arshad 2020).It is noteworthy that the reaction model accuracy of a solid-state process becomes sensitive to parameter "n" when its activation energy attains a relatively lower value (Arshad et al. 2016, Arshad 2020).However, when E α /RT factor in Equations ( 7)-( 8) acquires a value greater than 30, the influence of parameter "n" on the reaction model might be inconsequential.Thus To find the most probable reaction model for a solid-state process over the entire "α" domain in single-step kinetics, the curves obtained from the biomass pyrolysis data in the righthand sides of Equations ( 8)-( 9) are correlated with the lefthand sides of the same equations which are by definition, theoretical h(α) functions.A good correlation between the experimental curve and mechanistic h(α) curve can lead to an appropriate process model of biomass pyrolysis.Some wellknown reaction models and their respective h(α) expressions are represented in Table 1/Figure 1.Following Table 1/Figure 1, the diffusion models are determined by the distinguishable shapes of their h(α) curves and their associated maxima (α max ).Notwithstanding, in the case of diffusion behavior described by the h(α) curve of the JMA model (0 < P < 1), its α max.value does not match with any of the aforementioned diffusion models.The α max. of the JMA model (when the JMA model parameter ranges in 0 < P < 1) shows dependence on the JMA parameter "P".The reaction model, in that case, is determined by fitting the experimental h(α) curve by the theoretical h(α) JMA model within P[(0, 1).Similarly, generalized shapes of h(α) function curves remain the same in the case of RO, JMA (P > 1), SB (m, n) and Pr models, though these curves exhibit a shift depending on the values of the reaction model parameters.Thus, these generalized shapes of the h(α) function (Figure 1) can be taken as criteria to determine the appropriate process models for biomass pyrolysis.
Once the activation energy and reaction model of singlestep biomass pyrolysis are known and the temperature-dependence of pre-exponential is negligible, Equation (3) can be rearranged as follows to evaluate the pre-exponential factor: In point of fact, the preceding methodology may adequately model the single-step kinetics in solids.It is worth reminding though that the majority of solid-state processes go to completion in multiple steps.Generally besides DTG, a straightforward indicator of multi-step kinetics in a solid is its substantial variation in activation energy with respect to its degree of conversion.If a pyrolysis process follows multi-step kinetics, one needs to see whether the number/nature of reactions (parallel, successive or both simultaneously) taking place during pyrolysis is certain.If it is so, peak deconvolution of DTG or dα/dt curves of a solid might help in appropriately modeling the multi-step kinetics in that solid (as is the case with the Table 1.f(α) and h(α) functions of well-known condensed phase process models with the respective maxima α max. of h(α) functions (where applicable) (Vyazovkin et al. 2011, Arshad et al. 2014).

Reaction model Notation
Johnson Mehl Avrami Equation (Probable Diffusion in Amorphous Materials) expressions of some well-known solid-state reaction models (Table 1); (B) Graphical representation of the h(α) expressions of the respective reaction models shown in Figure 1(A).
beech wood pyrolysis).As the kinetic curves are in principle asymmetric, typical peak deconvolution functions (Gaussian, Lorentzian, Voigt, etc.) may not adequately deconvolute the thermoanalytical data and advanced functions (Weibull, Bigaussian, Fraser-Suzuki, etc.) are recommended (Perejón et al. 2011) where the five arguments in Equation ( 11) are T m,i representing the peak temperature, w 1,i is the width of the curve (greater than zero), w 2,i and w 3,i are the shape parameters (greater than zero) and θ i is the maximum amplitude (Chen et al. 2017, Mumbach et al. 2019, Mumbach et al. 2022b).The subscript "i" is related to an individual Asym2sig function associated with the kinetic curve.
As mentioned earlier, anoxic/anaerobic thermal degradation of hemicellulose, cellulose and lignin (in pseudo forms) contributes to the overall biomass pyrolysis.Therefore, the biomass pyrolysis rate curve can be accumulatively expressed as follows: where r i is the weighted factor and is attributed to the area under each deconvoluted curve (Ma et al. 2022).It provides information about the fraction of each involved process in the overall biomass pyrolysis.Once the experimental kinetic curves are deconvoluted at different heating rates, kinetic modeling can be performed on the deconvoluted data by employing the single-step kinetics methodology detailed above.By gaining knowledge of biomass pyrolysis kinetic triplets, evaluation of its thermodynamic parameters can be carried out.Thermodynamics of biomass pyrolysis may not only help in determining the spontaneity/non-spontaneity of the process but also (and especially) help in revealing some invaluable information regarding the transition state.According to the transition state theory of reactions, the pre-exponential factor "A" can be mathematically expressed as follows (Vlaev et al. 2003, Arshad 2020): where T p is the temperature at maximum reaction rate (experimentally determined from DSC, DTA, DTG or dα/dt peak), k B is the Boltzmann constant, "h" is the Plank constant, χ denotes the transition factor (which is one in the case of uni-molecular reactions) and e = 2.7183 is the Neper number.The rearrangement of Equation ( 13) leads to the following expression of transition state entropy: Moreover, transition state enthalpy can be expressed: A well-known thermodynamic equation (as given below) can be employed to determine the Gibbs free energy associated with the activated complex formation (ΔG ≠ ): It should be noted here that the thermodynamic parameters associated with the transition state of biomass pyrolysis {ΔS*, ΔH* and ΔG*) are determined in an isolated way for the involving (deconvoluted) processes.

Experimental
For kinetic modeling of the beech wood pyrolysis mechanism, the author availed the experimental data published in the scholarly literature.The pyrolysis data reported by Soria-Verdugo et al. under the non-isothermal conditions in this regard were taken into account (Soria-Verdugo et al. 2020).The aforestated experimental data are worth relying on as they were gathered by following the ICTAC Kinetics Committee recommendations for collecting the experimental thermoanalytical data for kinetic computations (Vyazovkin et al. 2011, Vyazovkin et al. 2014).The digitized data were obtained by an efficient digitizing tool WebPlotDigitize (available online) developed by A. Rohatgi, and the noise in the data was manipulated by Savitzky-Golay's smoothing filter available in the Originlab.The trustworthiness and efficacy of this procedure have been evidenced in the previous research studies (Arshad et al. 2020, 2018b, Arshad 2023, 2021a, 2021b, 2020).

Results and discussion
The beech wood pyrolysis profile obtained by TGA is, in fact, an accumulated process profile of the parallel thermal degradation of pseudo-hemicellulose, pseudo-cellulose and pseudo-lignin (in the absence of oxygen) over long temperature ranges.Overall, plant-based biomass comprises nearly 16-23% hemicelluloses, 42-49% cellulose and 21-39% lignin (Zhou et al. 2015).In the case of beech wood, precise values of 33.9%, 44.9% and 21.2% for hemicelluloses, cellulose and lignin, respectively were reported by Soria-Verdugo et al. (Soria-Verdugo et al. 2020).Among these three components, cellulose is crystalline while hemicellulose and lignin are amorphous materials (Hill 2007).Hemicellulose belongs to the polysaccharides class of polymers with several branched chains, consisting of xylose, arabinose, mannose and glucose.It possesses a degree of polymerization ranging from 50 to 200 monomers (substantially lower than cellulose).Hemicellulose shows relatively poor thermal stability and starts decomposing first at low temperatures.The largest constituent of biomass is cellulose which is a straight-chain polymer linked by glycosidic bonds.Intermolecular/intermolecular hydrogen bonds in cellulose interact with one another by three hydroxyl groups in each glucose monomer, giving rise to a stable crystalline structure and particular mechanical properties.Although cellulose exhibits more thermal resistance than hemicellulose, its degradation range is sharp.Lignin among them has the most complicated structure, consisting of a random three-dimensional (3D) polymer network which is difficult to degrade due to the presence of connected phenylpropane units in its structure (Zhu et al. 2020).It has been reported that the decomposition regions of hemicellulose and cellulose range around 220-315°C and 315-400°C, respectively, while lignin decomposition ranges between 180°C and 900°C (Yang et al. 2007).It should be mentioned that biomass pyrolysis depends on several factors including mainly, the temperature, heating rate, and possible interactions among the biomass constituents and its inorganic  (B) Plots of beech wood pyrolysis rate versus temperature at different heating rates (redrawn from its source i.e. Figure 3A) along with the variation of degree of conversion with temperature at different heating rates.
components (Hameed et al. 2019).Depending on the relative composition of the principal biomass constituents, it might be suggested for biofuel or biochar, as shown in Figure 2.For instance, biomass rich in cellulose, as is the case with beech wood (Soria-Verdugo et al. 2020), is appropriate for biofuel and rich in lignin is suitable for biochar (Venderbosch et al. 2010)..min − , β 3 = 50°C.min − are represented versus temperature in Figure 3B.The degree of conversion curves of the beech wood pyrolysis derived from their respective pyrolysis rates as functions of temperature is also represented in Figure 3B.To isolate the thermal degradation processes contributing toward the overall beech wood pyrolysis, Asymmetric Double Sigmoidal (Asym2sig) function as mathematically expressed in Equation ( 11), is applied to the experimental data associated with Figure 3B and the obtained results are depicted in Figure 4. Obtention of desirable agreements between the experimental and cuulative peak fit, and residual analysis in Figure 4A-C elucidates the capability and effectiveness of the Asymmetric Double Sigmoidal (Asym2sig) function in plausibly deconvoluting the beech wood pyrolysis processes.The processes thus deconvoluted are shown in Figure 5 at different heating rates.Elaborately, Process 1 in Figure 5A deals with the pyrolysis of pseudo-hemicellulose (P-HC l ), process 2 in Figure 5B with pseudo-cellulose (P-C l ), and process 3 in Figure 5C with pseudo-lignin (P-L g ).Deconvolution analysis by the Asym2sig function suggests that the weighted factor (r) in the case of beech wood pyrolysis attains a value of more or less 40% for both the P-HC l and P-C l , while it attains a value of 20% for P-L g .
As a preliminary condition of moeling beech wood pyrolysis kinetics, activation energies of the participating processes at different degrees of conversion values are determined.As pointed out earlier, this is done in view of estimating the nature and complexity of the processes involved in biomass pyrolysis.The generalized linear integral isoconversional method (GLIM), expressed mathematically in Equation ( 5), is applied to assess the trend of activation energies of the three processes over the defined domain of degree of conversion, a [ [0.05, 0.95].The results thus obtained are shown in Figure 6.Evidently, the straight lines in all three cases (Figure 6A-C) fit well the experimental data which justifies the reliability of the activation energies values obtained.The plot of activation energies versus the degree of conversion of all three processes is shown in Figure 7.The figure reveals that the thermal degradation of P-HC l , P-C l and P-L g goes to  completion in fairly single steps with effective (average) activation energies (E) P−HC l = 136 kJ.mol −1 , (E) P−C l = 162 kJ.mol −1 and (E) P−Lg = 109 kJ.mol −1 .In addition, the E/RT factor remains either around 30 or greater than 30 in all three cases studied which points out insignificant temperature dependence of pre-exponential factors.
In the next step, process models of the three deconvoluted processes need determination.For this purpose, Equation ( 9) is applied to the experimental data associated with the deconvoluted processes at β 2 = 25°C.min−1 and the h(α) results obtained are shown in Figure 8A-C.It is evident in Figure 8A that the process model followed by Process 1 is predominantly the reaction order (RO) model.Similarly, Figure 8B elucidates that the mechanism pursued by Process 2 is probably the nucleation-growth mechanism which could be best described by the two-parameter Sestak-Berggren SB (M, N) model.Nevertheless in the third case (Figure 8C), indeed the experimental h (α) curve is analogous to those of diffusion models, α max. of h(α) curve does not match with any of the known diffusion models.While addressing the aforementioned issue, Arshad and Maaroufi stated that the diffusion phenomena in amorphous materials which could not be described by the known diffusion models, might plausibly (and perhaps only) be simulated by the Johnson-Mehl-Avrami (JMA) model (with, 0 < P < 1) (Arshad et al. 2015).The theoretical h(α) functions, h(α) RO , h (α) SB and h(α) JMA show good agreements with the experimental h(α) curves related to Process 1, Process 2 and Process 3, respectively, as can be seen in Figure 8A-C, and the entire results regarding the model parameters at different heating rates are displayed in Table 2. Once the activation energies and the reaction models of the processes involved in beech wood pyrolysis are known, their pre-exponential factors can be calculated by applying Equation (10) on the data of deconvoluted processes and the obtained results are shown in Table 2.
As the kinetic triplets of the three processes are now known, they can be substituted into Equation (3) to construct the following kinetic expressions:   As a matter of fact, Equations ( 17)-( 19) give individual though generalized kinetic descriptions of the thermal degradation processes taking place in pseudo-hemicellulose, pseudo-cellulose and pseudo-lignin during the beech wood pyrolysis.Figure 9A-C evidences that Equations ( 17)-( 19) are capable of adequately reproducing the process rate curves of P-HC l , P-C l and P-L g at different heating rates.Physically, Equations ( 17)-( 19) interpret that the thermal degradation of P-HC l more likely follows a second-order kinetics (analogous to homogeneous kinetics).Although thermal degradation of P-C l pursues SB (M, N) model, it may rationally be described in terms of the JMA model parameter (P).This is because the condition for the SB (M, N) model parameters to correlate with the JMA model parameter i.e.M [0, 3/4], N [0.8, 1] and M < N (Arshad 2021b, Arshad et al. 2015) is valid.The SB (M, N) model parameters correlate in this case with the JMA parameter "2" which, in fact, has more than one rational interpretation (Blazquez et al. 2022).Predominantly, the thermal degradation of P-C l follows a diffusion-controlled two-dimensional (2D) nucleation/growth mechanism though by following a constant nucleation rate.In the third case of P-L g , the JMA model parameter does not fall in [1,4] rather it attains a value between zero and unity, which means that the thermal degradation of pseudo-lignin can be satisfactorily described by a probable diffusion mechanism, as detailed previously (Arshad et al. 2015).A slight disagreement between the JMA model (0 < P < 1) with the experimental rate at relatively low heating rates is due possibly to the complex nature of the diffusion mechanism in amorphous materials as pointed out previously (Arshad et al. 2015).
Taking into account the kinetic parameters of the three degradation processes, thermodynamic parameters associated with the transition states of the three processes are calculated by employing Equations ( 14)-( 16) and the results are displayed in Table 3.This table explicates that P-L g attains the highest transition state free energy (ΔG*) value also through the lowest transition state entropy (ΔS*) value.It means that P-L g demonstrates the highest endothermicity, while its activated complex is the most systematically arranged one among all three cases.On the other hand, the least systematically arranged activated complex may be attributed to P-C l .Based on Table 3, the descending order of non-spontaneity at room temperature and endothermicity of the three beech wood components is P − L g .P − C l .P − HC l While the descending order of the relative arrangement of the activated complex is P − L g .P − HC l .P − C l Moreover, the transition state enthalpies of all three processes are found comparable with their effective activation energies obtained by the generalized linear integral isoconversional method.

Conclusion
In this paper, a thorough kinetic and thermodynamic study on the pyrolysis process of beech wood has been carried out and reported.The overall beech wood pyrolysis is deconvoluted into three isolated p-hemicellulose (P-HC l ), p-cellulose (P-C l ) and p-lignin (P-L g ) degradation processes by an efficacious Asymmetric Double Sigmoidal (Asym2sig) function.Isoconversional analysis suggests that the thermal degradation processes of P-HC l , P-C l and P-L g go to completion in fairly single steps.Reaction models determined by the advanced reaction model determination methodology reveal that the thermal degradation of P-HC l , P-C l and P-L g pursues Reaction Order (RO), nucleation/growth and complex diffusion mechanisms, respectively.In addition, the thermodynamic parameters of the three processes unfold that the highest endothermicity and arrangement of the activated complex in transition state are attributable to P-L g .While the least structurally oriented activated complex is obtained in the case of P-HC l .These findings advocate the efficacy/soundness of the advanced reaction model determination methodology in plausibly modeling the biomass pyrolysis processes.Moreover, these results are of great importance in controlling the beech wood pyrolysis and optimizing the process efficiency for engineering applications.
ln da dt exp (E/RT) = ln f (a) + ln A (10) Equation (10) is, in fact, an equation of a straight line in the form y = mx + c of E as the energy of activation for the single-step process (usually taken as an average value over the αdomain).The value of the pre-exponential factor can be calculated by the intercept of the straight line (c = lnA).

Figure 2 .
Figure 2. Representation of the reaction paths for wood pyrolysis (Venderbosch et al. 2010) (reused with kind permission from Wiley).

Figure 3 .
Figure 3. (A) Plots of beech wood pyrolysis rate versus temperature at different heating rates (Soria-Verdugo et al. 2020) (reused with kind permission from Elsevier).(B)Plots of beech wood pyrolysis rate versus temperature at different heating rates (redrawn from its source i.e.Figure3A) along with the variation of degree of conversion with temperature at different heating rates.

Figure 7 .
Figure 7.The plot of activation energies of the process (Process 1, Process 2 and Process 3) contributing toward the overall beech wood pyrolysis versus degree of conversion 'α'.

Figure 9 .
Figure 9. Agreement between experimental and theoretical pyrolysis rates of the contributing processes (A) Process 1, (B) Process 2 and (C) Process 3 toward the overall beech wood pyrolysis at different heating rates.

Table 2 .
Process model parameters and pre-exponential factors associated with the three contributing processes toward beech wood pyrolysis.