# #

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increasing nucleation rate.

The kinetics triplet, i.e. apparent activation energy (*E*a), frequency factor (*A*) and mechanism of the process and thermodynamics of these processes are the objective of numerous works [64-66]. The processes, especially dehydroxylation, are affected by the structural changes in kaolinite. In order to estimate the influence of potential treatment or activation of clay by the termites, the kinetics of the dehydroxylation and formation of spinel phase was investigated via Kissinger kinetic equation [67]:

$$\ln\left[\frac{T\_m^2}{\Theta}\right] = \ln\left[\frac{AR}{E\_a}n(1-\alpha)^{n-1}\right] - \frac{E\_a}{RT\_m} = const. - \frac{E\_a}{RT\_m} \tag{8}$$

The *T*m denotes the peak temperature of thermal analysis (DTA, DTG, DSC EGA...), Θ is the heating rate, *n* is the empirical reaction order (kinetic exponent), *α* is conversion degree (fractional conversion) and *R* is the universal gas constant. The constant term is equal to ln(*AR*/ *E*a) for the pseudo first-order type of reaction. The plot of *ln*[Θ/*T*<sup>m</sup> 2 ] on reciprocal temperature 1/*T*m (Kissinger plot) provides the straight line with slope of *E*a/*R*.

The mechanism of the investigated process can be estimated from the shape of TDA peak. The peak parameters of TA curves enable to determine the value of kinetic exponent (*n*) as follows [68-70]:

$$m = \frac{2.5 \text{ R } T\_m^2}{w\_{1/2} E\_a} \tag{9}$$

<sup>19</sup> The course of dehydroxylation is affected by the burning of organic matter (actually there is feedback between both processes) hence The formation of water during pyrolysis of SOM decreases equilibrium constant of the process [71].

Investigation of Subterranean Termites Nest Material Composition, Structure and Properties http://dx.doi.org/10.5772/55145 539

**Figure 17.** The shift of DTA effect with heating rate (a) and Kissinger plot (b).

400 700

1200 2 2 () () *<sup>C</sup> SiO amorphous SiO cristobalite* ³

<sup>1</sup> ln ln (1 ) . *<sup>m</sup> <sup>n</sup> a a*

a- é ù é ù ê ú = - -= - ê ú ê ú ë û <sup>Q</sup> ë û

*E*a) for the pseudo first-order type of reaction. The plot of *ln*[Θ/*T*<sup>m</sup>

1/*T*m (Kissinger plot) provides the straight line with slope of *E*a/*R*.

*T AR E E n const E RT RT*

*a mm*

The *T*m denotes the peak temperature of thermal analysis (DTA, DTG, DSC EGA...), Θ is the heating rate, *n* is the empirical reaction order (kinetic exponent), *α* is conversion degree (fractional conversion) and *R* is the universal gas constant. The constant term is equal to ln(*AR*/

The mechanism of the investigated process can be estimated from the shape of TDA peak. The peak parameters of TA curves enable to determine the value of kinetic exponent (*n*) as follows

2

*R T*

*a*

19 The course of dehydroxylation is affected by the burning of organic matter (actually there is feedback between both processes) hence The formation of water during pyrolysis of SOM decreases equilibrium constant of the process [71].

1/2 2.5 *<sup>m</sup>*

*n*

The kinetics triplet, i.e. apparent activation energy (*E*a), frequency factor (*A*) and mechanism of the process and thermodynamics of these processes are the objective of numerous works [64-66]. The processes, especially dehydroxylation, are affected by the structural changes in kaolinite. In order to estimate the influence of potential treatment or activation of clay by the termites, the kinetics of the dehydroxylation and formation of spinel phase was investigated

925 1050

1050

**•** Formation of the Al-Si spinel phase 20;

**•** Formation of the mullite;

538 Materials Science - Advanced Topics

**•** Formation of the cristobalite.

via Kissinger kinetic equation [67]:

[68-70]:

2

23 2 2 23 2 2 2 2 2 2 () *<sup>C</sup> Al O SiO H O Al O SiO H O g* - × × ¾¾¾¾¾® × + (4)

23 2 23 2 2 2( 2 ) 23 ( ) *<sup>C</sup> Al O SiO Al O SiO SiO amorphous* - × ¾¾¾¾¾® × + (5)

23 2 23 2 2 3 (2 3 ) 2 (3 2 ) 5 ( ) *<sup>C</sup> Al O SiO Al O SiO SiO amorphous* ³ × ¾¾¾¾® × + (6)

¾¾¾¾® (7)

2

*w E* <sup>=</sup> (9)

] on reciprocal temperature

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The DTA results of sample D and Kissinger plot are shown in Fig. 17 (a) and (b), respectively. The formations of mullite (Eq.4) and cristobalite (Eq.5) show compound inexpressive effect on DTA hence the determined value is related to both processes. The overview of kinetic results including activation energy, frequency factor and the most probable mechanism are listed in Table 5.


**Table 5.** The kinetics of thermal transformations of kaolin from termite nest.

The most frequently published value of the activation energy for dehydroxylation process of kaolinite ranges from 140 to 250 kJ∙mol-1 and formation of Al-Si spinel shows *E*a of 856 kJ∙mol-1 [72]. The results indicate that the mechanism and kinetics of investigated process are not changed hence there is no supporting evidence for an activation process that would have a significant effect of termites on the structure of clay minerals.

The correlation between kinetic and thermodynamic parameters of the investigated process results from the combination of Arrhenius with Eyring or Wertera and Zenera laws related to the temperature dependence of rate constant (*k*(*T*)) [73]:

$$k(T) = A \exp\left[-\frac{E\_a}{RT}\right] = \frac{k\_B T}{h} \exp\left[\frac{\Delta S^\ddagger}{R}\right] \exp\left[-\frac{\Delta H^\ddagger}{RT}\right] = \nu \exp\left[-\frac{\Delta G^\ddagger}{RT}\right] = \nu \,\,\mathrm{K}^\ddagger\tag{10}$$

where *k*B, *h*, *ν* = *k*B*T*/*h* and *K*# are Boltzmann, Plank constant, vibration frequency and equili‐ brium constant of formation of activated complex, respectively.

The thermodynamic parameters of activated complex, including free energy (Δ*G*# ), enthalpy (Δ*H*# ) and entropy (Δ*S*# ) of process were calculated using Eyring equations:

$$
\Delta H^\ddagger = E\_a - RT\tag{11}
$$

of water vapour slows down the rate of decomposition of activated complex into product and

Investigation of Subterranean Termites Nest Material Composition, Structure and Properties

**Figure 18.** Temperature dependence of Δ*G*# for burning of SOM and dehydroxylation (a) and temperature depend‐
