Results and Discussion
Kinetic Characterization of the Pyrolysis of the Yerba Mate Twigs
Typical nonisothermal TGDTG curves for the pyrolysis of the yerba mate twigs are shown in Figure 1. Instantaneous weight fractions (w), namely instantaneous weight losses normalized by the initial mass of the sample, represented as a function of the temperature (T) are illustrated in the figure. Likewise, the reaction rates, obtained by differentiation of the normalized weight lossestime curve, versus T can also be appreciated in the same figure.
Figure 1. TG  DTG curves for the pyrolysis of yerba mate twigs. Comparison between experimental data (symbols) and predictions of the deactivation model (Model II, lines).
As seen, a noticeable decrease in weight fractions, associated with the release of volatiles present in the twigs (Table 1), takes place between 150  350 °C. At higher temperatures, only slight variations occur accompanied by a pronounced decrease in reaction rates. The latter attained a sharp maximum at 300 °C. It is generally accepted that biomass pyrolysis proceeds through a sequence of primary transformations. Initially release of free moisture from the biomass takes place, followed by degradation of the more unstable biopolymers, namely cellulose and hemicellulose possessing a polysaccharide structure relatively easy to breakdown, predominantly at the lower temperatures. With increasing temperature the more refractory components, basically lignin, which is more resistant to degrade due to its cross linked aromatic structure, begin to decompose and volatiles are released from the substrate matrix. Solid char residue that is formed during the primary decomposition phase, taking place in the range 200  400 °C, apparently undergoes slow aromatization in a secondary pyrolysis stage that occurs at temperatures higher than 400 °C (White et al., 2011; Bonelli and Cukierman, 2012).
To evaluate the kinetic parameters, modeling of the TG curves was carried out. Kinetic modeling of pyrolysis of carbonaceous materials, such as coal and biomass, is complex because of numerous chemical reactions taking place simultaneously. To describe kinetic data, the process was assumed as a single firstorder overall decomposition reaction. The reaction rate is given by the following equation:
w and w_{r} in Eq.(1) are the instantaneous and residual weight fractions, respectively, and k_{app}, the apparent reaction rate constant. Two different models were adopted to account for the dependence of k_{app} on the temperature. On one side, the conventional Arrheniustype expression (Model I) was considered:
where k_{0I} is the preexponential factor, E_{A}, the activation energy, R, the universal gas constant, and T, the absolute temperature.
On the other hand, the second model applied supposes that the significant physicochemical changes which take place within the YMT as pyrolysis proceeds cause their deactivation (Model II). This fact may affect the reaction rate constant (kapp) and is taken into account through an increase of the activation energy with the temperature and the solid conversion according to the following expression (Balci et al., 1993; Della Rocca et al., 1999; Bonelli et al., 2003):
X in Eq. (3) is the normalized fractional conversion of the solid defined as:
whereas E_{Ai} is the initial activation energy for X=0; ft and у are fitting parameters (ft, the deactivation rate, and у, the order with respect to X).
Characteristic parameters of both models are reported in Table 3 along with standard deviations (5) and the range of temperatures for which each model enabled to properly describe the experimental data. They were evaluated by nonlinear regression analysis, by minimizing the sum of squares of the differences between the experimental and predicted model values for weight losses curves (w vs T) and considering the measured linear relationship between temperature and time. Thus, both models were adjusted to the data minimizing the following objective function (O.F.):
where w_{exp} and w_{mod} represent, respectively, the experimental data and the value predicted by the model.
The capability of each applied model to represent the experimental data was compared by estimating the standard deviation (5) as:
being N, the number of data, andp, the number of fitted parameters.
Table 3. Model characteristic parameters estimated for the pyrolysis of yerba mate
twigs and range of temperature
Model I 

kcI [min^{1}] 
2.8 x 10^{4} 
E_{a} [kJ mol^{1}] 
46 
wr 
0.37 
s [%] 
1.5 
Temperature range [°C] 
25  450 
Model II 

ken [min^{1}] 
3.5 x 10^{4} 
E_{a} [kJ mol^{1}] 
49 
P [K^{1}] 
1.5 x 10^{3} 
Y 
5.5 
s [%] 
1.3 
Temperature range [°C] 
25  900 
Although both models led to acceptable s values (Table 3), Model I only provided a proper fit up to 450 °C. Instead, Model II succeeded in representing the experimental curves over the whole temperature range up to 900 °C, as shown in Figure 1. As seen in Table 3, the estimated values for the preexponential factor and the initial activation energy of Model II were quite similar to those of Model I.
The initial activation energy is within values obtained for the pyrolysis of other biomasses under similar conditions (Bonelli et al., 2001b). Estimated values of the activation energy varied from 49 to 137 kJ mol^{1} for the temperature range 25  900 °C.