An improved model for the kinetic description of the thermal degradation of cellulose
PedroE.Sánchez-Jiménez1, LuisA.Pérez-Maqueda1, AntonioPerejón1, JoséPascual-Cosp2, MónicaBenítez-Guerrero2 and JoséM.Criado1
(1) / Instituto de Ciencia de Materiales de Sevilla, C.S.I.C.-Universidad de Sevilla, C. Américo Vespucio no 49, 41092Sevilla, Spain(2) / Departamento de Ingeniería Civil, Materiales y Fabricación, Universidad de Málaga, ETSII, 29071Málaga, Spain
Abstract
In spite of the large amount of work performed by many investigators during last decade, the actual understanding of the kinetics of thermal degradation of cellulose is still largely unexplained. In this paper, recent findings suggesting a nucleation and growth of nuclei mechanism as the main step of cellulose degradation have been reassessed and a more appropriate model involving chain scission and volatilization of fragments has been proposed instead. The kinetics of cellulose pyrolysis have been revisited by making use of a novel kinetic method that, without any previous assumptions regarding the kinetic model, allows performing the kinetic analysis of a set of experimental curves recorded under different heating schedules. The kinetic parameters and kinetic model obtained allows for the reconstruction of the whole set of experimental TG curves.
Keywords
Kinetics–Cellulose–Thermal degradation–Chain scission
Introduction
Cellulose is the most abundant biopolymer on earth and, together with hemicellulose and lignin, is one of the main three constituents of biomass, which is being increasingly considered as fuel or source for renewable energy (Saddawi et al. 2010; Emsley 2008) Thermal decomposition of biomass can also be used for the production of chemicals and bio-oils (Mohan et al. 2006). Moreover, due to its availability, low cost and biodegradability, cellulose is more and more used to reinforce polymeric materials and to design a huge array of novel biopolymers and biocomposites (Liu et al. 2010; Ganster and Fink 2006). The accurate modeling of the thermal degradation kinetics is vital for the control of combustion processes, for the thermal characterization of newly designed biocomposites and for the assessment of possible damage during processing.
The degradation of cellulose has attracted a great deal of attention during the last decade (Bigger et al. 1998; Volker and Rieckmann 2002; Mamleev et al. 2006; Capart et al. 2004; Shen and Gu 2009; Mamleev et al. 2007a, b; Lin et al. 2009; Ding and Wang 2008b; Calvini et al. 2008). Cellulose can be degraded under thermal, oxidative, hydrolytic or enzymatic conditions; in every case yielding sugar fragments of varying length due to the scission of polymeric chains. Thus, the degradation process can be characterized by following the evolution of the chain scissions and the degree of polymerization with time, usually utilizing kinetic equations derived from the first or pseudo-zero order Ekenstam’s relationship (Emsley 2008; Calvini et al. 2008; Ding and Wang 2008b; Calvini 2005, 2008; Ding and Wang 2008a). These studies are usually supported by experimental data obtained from cellulose degradation by hydrolysis or thermal ageing at low temperatures. However, since the scission of bonds is not a variable easy to measure directly, the thermal degradation of cellulose is instead often studied by monitoring the weight loss endured during thermogravimetric experiments at high temperatures (250–400°C), where the evolution of the degradation process can be followed in situ. This approach has produced an important body of work and it is generally acknowledged now that cellulose decomposes through parallel or competitive reactions, producing tar, gases and residual char (Shen and Gu 2009; Capart et al. 2004; Mamleev et al. 2009; Mamleev et al. 2007a, b). Many authors have proposed single step first order models to describe the kinetics of cellulose decomposition, (Varhegyi et al. 1994; Antal et al. 1998) while others like Agrawal or Bradbury (Bradbury et al. 1979; Agrawal 1988a, b) have resorted to multistep kinetic pathways. These multistep models assume several consecutive or competitive pathways, as suggested by the fact that the amount and type of volatiles and the residual char distinctly depend on the heating rate used in the experiments (Mamleev et al. 2007a; Kilzer and Broido 1965). However, the formation of “active cellulose” and other intermediates assumed in several multistep models remains controversial because such products are difficult to identify and quantify (Shen and Gu 2009; Capart et al. 2004; Lin et al. 2009). Also, the use of sophisticated multistep kinetic models involves a high number of fitting parameters that will inevitably lead to an acceptable fit of the experimental data, regardless the validity of such model. Furthermore, for the sake of simplicity the individual steps are all usually assumed to obey first order kinetic laws, what might easily constitute an oversimplification. Nevertheless, most authors still consider that complex multistep models are not needed to simulate the weight loss behavior during the pyrolysis of cellulose, and that single step models are sufficient to describe the system adequately since “depolymerization by transglycosylation”, namely the scission of the internal glycosidic bonds, has been reported to be the limiting step (Varhegyi et al. 1994; Mamleev et al. 2006). Within the single step models, first order (Varhegyi et al. 1994; Antal et al. 1998; Shen and Gu 2009) or nth order kinetics (Barneto et al. 2009) are still assumed in the majority of the situations. However, some authors have recently found autoaccelerated models such as Avrami-Erofeev or Prout-Tompkins, which are commonly related to nucleation and growth mechanisms, to be a better depiction (Dollimor and Holt 1973; Reynolds and Burnham 1997). More recently, Mamleev (Mamleev et al. 2007a) and Capart (Capart et al. 2004) confirmed that nucleation models are far more suited than the so often used first order models. In his work, Capart (Capart et al. 2004) assumed two independent reactions; one related to the bulk decomposition of cellulose and a second one related to a much slower residual decomposition. Alternatively, Mamleev (Mamleev et al. 2006) proposed a two step kinetic model that described the mass loss by two competing pathways; a dominant “depolymerisation by transglycosilation” reaction producing tar, and an elimination reaction that produces char and light gases.
Thus, despite the huge amount of work published, the kinetics of cellulose pyrolysis constitutes a topic still profusely under debate. It is a complex process involving complicated chemical pathways, mass and heat transfer phenomena and possible intermediates. As a consequence, there is a large variation in the magnitude of activations energies published for describing the reaction (Antal et al. 1998; Capart et al. 2004; Lin et al. 2009). This dispersion has been attributed mainly to thermal lag and uncontrolled heat transfer issues, (Antal et al. 1998; Lin et al. 2009) and to the different morphologies and crystallinities of the studied samples (Capart et al. 2004; Antal et al. 1998). The influence of different initial sample sizes on the products yielded by experiments carried out under similar thermal treatments has shown the importance of heat transfer in this process (Volker and Rieckmann 2002; Shen and Gu 2009). An alternative explanation for the dispersion of results could lie in the fact that most kinetic studies are performed using model-fitting methods, consisting on fitting the experimental curves to different mathematical models, described based on certain physico-geometrical assumptions. This approach entails an often overlooked limitation: the kinetic parameters thus obtained are highly dependent on the kinetic model assumed. Thus, since any list of kinetic models is inevitably incomplete, the best fit in a set does not necessarily imply that the selected model is the right one. Additionally, in many cases the kinetic models are used merely as fitting equations and hence they grant no further understanding of the degradation mechanism (Capart et al. 2004; Barneto et al. 2009).
In this work, a non conventional kinetic analysis procedure (Perez-Maqueda et al. 2006; Criado et al. 2003; Perez-Maqueda et al. 2003) has been applied to cellulose decomposition in order to shed new light to the process. The recently proposed combined kinetic analysis is a method that allows for the simultaneous analysis of a set of experimental curves recorded under any thermal schedule, and more importantly, without any previous assumption about the kinetic model followed by the reaction. This constitutes an important improvement over the most commonly used model fitting methods because, unlike them, combined kinetic analysis does not constrain the experimental data into a predefined kinetic model. The results, obtained from the combined analysis of experimental data recorded under isothermal, linear heating and Constant Rate Thermal Analysis (CRTA) conditions, are compared with the most widely used kinetic models in literature, including a recently proposed one for chain scission mechanisms, which seems especially well suited to the case of cellulose degradation.
Experimental
Commercial microcrystalline cellulose from Aldrich, (product number 435236) was used for performing the study. Thermogravimetric measurements were carried out with a TA instruments Q5000 IR electrobalance (TA Instruments, Crawley, UK) connected to a gas flow system to work in inert atmosphere (150mLmin−1 N2). The experiments were performed with the utmost care in order to minimize heat and mass transfer phenomena so that kinetic parameters more representative of the forward reaction are obtained. Small initial mass samples (8–10mg) were placed over a 1cm diameter platinum pan. The sample was well dispersed and with negligible depth in order to minimize heat and mass transfer phenomena, along with possible secondary carbon yielding reactions, by reducing the residence time of the volatiles within the solid (Capart et al. 2004). Experimental data were obtained from experiments run under three different heating schedules: isothermal conditions, linear heating rate and Constant Rate Thermal Analysis (CRTA). This method implies controlling the temperature in such a way that the reaction rate is maintained constant all over the process at a value previously selected by the user. Isothermal experiments were carried out at 533 and 548K. Four different heating rates, 1, 2, 5 and 10Kmin−1 were used for experiments run under linear rise in temperature. The α-T (or time) plots obtained from these two methods were differentiated by means of the Origin software (OriginLab) to get the differential curves employed in the kinetic analysis. Finally, CRTA experiments were performed at constant reactions rates of 0.006 and 0.009min−1, respectively.
Theory
Theoretical background
The reaction rate, dα/dt, of a solid state reaction can be described by the following general equation:
/ (1)where A is the Arrhenius pre-exponential factor, R is the gas constant, E the activation energy, α the reacted fraction, T is the process temperature and f(α) accounts for the reaction rate dependence on α. The kinetic model f(α) is an algebraic expression which is usually associated with a physical model that describes the kinetics of the solid state reaction. Table1 lists the functions corresponding to the most commonly used mechanisms found in literature. In this work, the reacted fraction, α, has been expressed with respect to the degradable part of the cellulose, as defined below:
/ (2)where w o is the initial mass of cellulose, w f the mass of residual char and w the sample mass at an instant t.
Equation1 is a general expression that describes the relationship among the reaction rate, reacted fraction and temperature independently of the thermal pathway used for recording the experimental data. For experiments performed under isothermal conditions, the sample temperature is rapidly increased up to a certain temperature and maintained at this temperature while the reaction evolution is recorded as a function of the time. Under these experimental conditions, at a given temperature T, the term A exp(−E/RT) remains constant at a value k T , and therefore, Eq.1 can be written as follows:
/ (3)Sample Controlled Thermal Analysis (SCTA) constitutes an alternative approach that, while amply used in solid state kinetic studies and preparation of materials (Rouquerol 2003; Perez-Maqueda et al. 1999), it has only recently extended to polymer decomposition reactions (Sanchez-Jimenez et al. 2009, 2010c; Sanchez-Jimenez et al. 2010a; Arii et al. 1998). In SCTA experiments, the evolution of the reaction rate with time is predefined by the user and, most usually, it is maintained at a constant value along the entire process. In this case, the technique is named Constant Rate Controlled Analysis (CRTA). This way, by selecting a low enough decomposition rate, the mass and heat transfer phenomena occurring during the reaction are minimized. This is a very useful asset when dealing with complex reactions such as cellulose pyrolysis, which has proven to be very susceptible to mass and heat transfer phenomena (Volker and Rieckmann 2002; Lin et al. 2009). As a consequence, the results obtained by CRTA are more representative of the forward reaction than those obtained from conventional methods such as linear heating programs or isotherms (Koga and Criado 1998; Rouquerol 2003; PerezMaqueda et al. 1996). Under constant rate thermal analysis (CRTA) conditions, the reaction rate is maintained at a constant value C=dα/dt selected by the user and Eq.1 becomes:
/ (4)Isoconversional analysis
Isoconversional methods, also known as “model-free”, are used for determining the activation energy as a function of the reacted fraction without any previous assumption on the kinetic model fitted by the reaction. The Friedman isoconversional method is a widely used differential method that, unlike conventional integral isoconversional methods, provides accurate values of the activation energies even if they were a function of the reacted fraction (Criado et al. 2008). Equation1 can be written in logarithmic form: