Introduction

Since the pioneering study of Yajima et al. [1] extensive efforts have been devoted to the development of novel polymeric precursors that can be used to generate various ceramic materials [2–6]. The complete process from polymer precursors to the final ceramic materials includes several subprocesses, namely curing, pyrolysis, and annealing [7]. The pyrolytic process of precursors, characterized by gas release, composition change, and structural rearrangement, actually plays a critical role in determining the mechanical properties of the resulting ceramics. In order to investigate the pyrolytic process, kinetic analysis based on experimental TG data recorded under nonisothermal conditions is necessary. In this way, insight can be gained into the conversion of precursors into ceramics.

The decomposition of precursors involves several overlapping solid-state reactions. For a kinetic description of the overall pyrolytic process, a peak-fitting method has recently been introduced to analyze the experimental derivative thermogravimetric (DTG) curves [8–10]. Although this method provides a new way of understanding pyrolytic process in detail, examples of precursor-to-ceramic processes that have been analyzed in this way are still limited. To the best of our knowledge, poly[B-(methylamino)borazine] [9] and polysiloxane prepared by the hydrolysis–condensation reaction of methyltriethoxysilane [10] are the only precursors that have been subjected to this analysis.

Kinetic parameters and the pyrolytic pathway are highly dependent on the composition and structure of the precursors. We have reported a new polysiloxane, poly[hydridomethylsiloxane-co-vinylmethylsiloxane] (PSO), which has been used as a key precursor to fabricate micro/nanoporous materials [4] and fiber-reinforced ceramic matrix composites. To get a clear insight into the conversion of the new precursor to SiOC ceramic, in this study, kinetic analysis of its pyrolytic process has been conducted by means of a peak-fitting method, on the basis of thermogravimetric (TG) and mass spectrometric (MS) data.

Theory

Kinetic equation

The rate law for a single solid-state process can be expressed by a simple differential kinetic equation:

$$ {\text{d}}\alpha /{\text{d}}t = A\,{ \exp }( - E/RT)\,f(\alpha ) $$
(1)

where α is the conversion fraction, defined as the ratio of the actual mass loss to the total mass loss corresponding to a given step of the decomposition, Α is the preexponential factor, E is the activation energy, R is the gas constant, T is the absolute temperature in Kelvin, and f(α) is a function of α, depending on the particular reaction mechanism.

When the temperature function φ (φ = dT/dt) is introduced, Eq. (1) can be transformed into:

$$ {\text{d}}\alpha /{\text{d}}T = A/\varphi \, { \exp }( - E/RT) \,f(\alpha ) $$
(2)

The above two equations are the differential forms of the isothermal and nonisothermal rate laws, respectively. By separating the variables and integrating of Eq. (2), the integral function of conversion, g(α), can be obtained [11]:

$$ g\left( \alpha \right) = \mathop \int \limits_{{\alpha_{ 0}}}^{{\alpha_{\text{p}} }} {\raise0.7ex\hbox{${{\text{d}}\alpha }$} \!\mathord {\left/ {\vphantom {{d\alpha } {f\left( \alpha \right)}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${f\left( \alpha \right)}$}} = A/\varphi \mathop \int \limits_{{T_{0}}}^{{T_{\text{p}} }}{\text{e}}^{-{\text{E}}/{\text{RT}}}{\text{d}}T $$
(3)

The widely used kinetic expressions (f(α) and g(α)) are included in Table 1 [12] and have been systematically reviewed [13, 14].

Table 1 Algebraic expressions for the most widely used kinetic models in solid-state processes
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Peak fitting

For a complicated decomposition process with chemical reactions taking place simultaneously and/or successively, peak fitting of the experimental DTG curves is required before using Eq. (2) for data analysis. The principle of peak fitting is to represent the overlapped peaks by certain analytical functions. Different fitting functions that have been used for the peak-fitting process include the Gaussian, Lorentzian, and Weibull functions [8]. PeakFit® software, as has been used for nonlinear least-squares curve fitting, involves an interactive peak-fitting process. The fitting process proceeds until a maximum r 2 (coefficient of determination) and a minimum residual are reached for a given number of component bands.

Determination of the activation energy

After peak fitting, the activation energy for each peak can be determined by a model-free approach without any previous assumption on the kinetic model [15–24].

One of the most extensively used model-free approaches is the Kissinger method [15–17]. According to this method, the activation energy can be determined from a plot of the logarithm of the heating rate over the squared temperature at the maximum reaction rate versus 1/T m for a series of runs at different heating rates, as shown by the following equation:

$$ { \ln }\left( {\varphi /T_{\text{m}}^{ 2} } \right) = {\text{const}}. \, - E/RT_{\text{m}} $$
(4)

where T m is the temperature corresponding to the inflection point of each thermo-degradation stage, which corresponds to the maximum reaction rate.

In comparison, the isoconversional approach allows complex processes to be detected through the variation of E with α [18–24]. Taking the logarithm form of Eq. (3) after rearranging, we obtain:

$$ { \log }\;g\left( \alpha \right)\; = \;{ \log }\left[ {AE/\left( {\varphi R} \right)} \right]\; + \;{ \log }\;p\left( x \right) $$
(5)

where p(x) is the function known as the Arrhenius integral that has no analytic solution but can be resolved either by numerical methods or by different approximations. If we use Doyle’s approximation [25] for p(x), then we obtain from Eq. (5) the popular equation proposed by Ozawa for determining activation energy by isoconversional methods [24]:

$$ { \log }\varphi_{\alpha } = { \log }\left[ {A_{\alpha } E_{\alpha } /\left( {g\left( \alpha \right)R} \right)} \right] - 2. 3 1 5- 0. 4 5 7E_{\alpha } /RT_{\alpha } $$
(6)

A plot of log φ versus 1/RT at each α yields E from the slope for that α, regardless of the model.

Solid-state reaction mechanisms

Once the activation energy is determined and is independent of the degree of conversion, it is possible to delineate a kinetic model according to the Master plot method introduced by Málek et al. [12, 26, 27].

The Master plot method involves the introduction of an empirical function z(α) defined by Eq. (7):

$$ z\left( \alpha \right) \, = f\left( \alpha \right)g\left( \alpha \right) \, = {\text{ d}}\alpha\, \pi \left( x \right) \, T/\varphi \,{\text{d}}t $$
(7)

where π(x) (x = E/RT) is the temperature integral approximation, which is sufficiently precise according to Senum and Yang [28].

According to Eq. (7), reference curves (Fig. 1) can be plotted using the definitions of f(α) and g(α) for each model listed in Table 1. Comparison between Master plots and experimental curves obtained by plotting \( {\text{d}}\alpha \, \pi \left( x \right) \,T/\varphi {\text{ d}}t \) as a function of α allows the most appropriate kinetic models included in Table 1 to be determined for each individual decomposition stage. It should be mentioned that α first needs to be normalized within the [0,1] conversion range.

Fig. 1
figure 1

Master plots of z(α) function versus α for the most widely used kinetic models in solid-state process

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Experimental

Materials

The polysiloxane (PSO) used in this experiment was synthesized by cationic ring-opening polymerization reaction of tetramethyltetravinylcyclotetrasiloxane (TMTVS), tetramethylcyclotetrasiloxane (TMS) and the end-capping reagent, tetramethyldivinyldisiloxane (TMDVS) according to Scheme 1 [4].

Scheme 1
scheme 1

Synthesis scheme of PSO

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The 1H NMR (Fig. 2) of PSO shows the molar ratio (m/n) of Si–H and Si–Vi was 0.97. This liquid precursor was cured by hydrosilylation to form a crosslinked solid which was then ground and sieved. The fractions with particle size below 125 μm were used for the following analyses.

Fig. 2
figure 2

1H NMR spectrum of PSO

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TG-MS experiments

Nonisothermal decomposition analyses at various heating rates (5, 7, 10, 15, and 20 K min−1) were performed on a TG analyzer from 303 to 1,273 K in a controlled N2 flow of 200 mL min−1. Gaseous by-products generated during pyrolysis were identified by means of a quadrupole mass spectrometer (MS, Quadrex 200, Leybold Heraeus, 70 eV, electron impact).

FTIR spectroscopy

FTIR spectroscopy was used to characterize the evolution of the sieved powder during the ceramization process. Powder samples were heated to 873, 923, 973, or 1,023 K at a heating rate of 5 K min−1 under Ar gas flow and were then allowed to cool. IR spectra were recorded in the wavenumber range ν = 4,000–400 cm−1 using a Nicolet Magna 550 Fourier-transform infrared (FTIR) spectrometer.

Results and discussion

The obtained TG curves are presented in Fig. 3, which show the mass loss as a function of temperature at different heating rates. According to the TG curves, the main mass loss occurs between 700 and 1,100 K, which corresponds to the stage of organic-to-inorganic transformation. The total mass loss by 1,273 K is ca. 20 %.

Fig. 3
figure 3

Decomposition curves of PSO at five heating rates in nitrogen atmosphere

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Figure 4 shows the first-derivative curves of the mass loss with respect to temperature. Three clear peaks and a shoulder peak can be discerned, which shift to higher temperatures as the heating rates are increased from 5 to 20 K min−1. The existence of a shoulder peak indicates a complicated decomposition process.

Fig. 4
figure 4

Decomposition rate of PSO as a function of temperature for five heating rates

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Figure 5 shows a MS analysis chart of the decomposition stream during pyrolysis. The detected species were exclusively carbon-containing moieties and hydrogen, and no measurable signals of oxygen- or silicon-containing gaseous species were observed. In addition, hydrogen and methane/methyl were released in a multistep process, as befits a complex decomposition.

Fig. 5
figure 5

MS charts of PSO obtained at the heating rate of 10 K min−1

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Peak fitting

The above results suggest that the thermal decomposition of PSO involves overlapping solid-state chemical reactions that cannot be directly analyzed. It is necessary to use a peak-fitting method to separate the experimental curves shown in Fig. 4. For any original signal, curve fitting is nonunique, and the more component peaks that are used in the fitting, the higher the r 2 value obtained. Nevertheless, high r 2 values do not necessarily lead to valid peak identification, and too many component peaks make analysis meaningless and impossible [29]. In order to determine the number of component peaks, the following procedure for peak fitting is proposed and performed:

  1. 1.

    Estimation of the number range of component bands. The number of component peaks should be no less than four, since a hidden peak and three clear peaks are evident in Fig. 4, but no more than five on the basis of the MS data. Clearly, the mass loss during pyrolysis is mainly caused by gas release, which can be detected by MS. From the MS data, it can be seen that hydrogen shows two releasing peaks, methane and methyl have two overlapped releasing peaks, ethylene and ethyne have one overlapped peak. Hence, according to the MS data, there are five peaks in all.

  2. 2.

    The same number of component peaks should be used to fit experimental curves for various heating rates, on the reasonable assumption that the transformation process does not change with the heating schedule.

After a computational procedure based on PeakFit® software, each of the DTG curves obtained at various heating rates was finally resolved into four Gaussian peaks, as shown in Fig. 6.

Fig. 6
figure 6

Simulation of the DTG curves using four Gauss peaks

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Determination of activation energy

Ozawa’s method allows delineation of the variation of E as a function of the conversion [23, 24]. An Ozawa’s plot of log φ versus 1/T at each α yields E for the four peaks at different heating rates. It should be mentioned that α first needs to be normalized within the [0,1] conversion range for each individual peak after peak fitting. The values of E obtained for each peak as a function of α by Ozawa’s method are plotted in Fig. 7. It can be seen that the activation energies for Peaks 1 and 2 are independent of the degree of conversion, while the activation energies for Peaks 3 and 4 display significant changes.

Fig. 7
figure 7

Variation of the activation energy with α, evaluated by OFW

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The activation energy for each peak was also calculated by the Kissinger method, and the results are summarized in Table 2. The activation energies of Peaks 1 and 2 were determined as 170 and 185 kJ mol−1, respectively, which are in good agreement with those calculated by the isoconversional method. However, the error associated with the activation energies of Peaks 3 and 4 is significant.

Table 2 Determination of the activation energy for each peak using the Kissinger method
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Estimation of solid-state reaction mechanisms and pyrolysis pathway

Owing to the independence of the activation energies for Peaks 1 and 2 on the degree of conversion, Eq. 7 introduced by Málek was used to delineate a kinetic model for these peaks. The experimental curves of z(α) versus α for Peaks 1 and 2 at a heating rate of 5 K min−1 (Fig. 8) show that Peak 1 is similar to the reference curves of R2-type mechanisms, while Peak 2 is best fitted with reference curves based on D2-type kinetic models. These findings suggest that Peaks 1 and 2 may be reaction controlled or diffusion controlled. Under reaction control, the escaping flux of molecules is limited by the rate of the intrinsic molecular reaction that occurs on the surface. Under diffusion control, the flux is limited by the mass transport of the evolved species through the gas pressure bearing down on the surface [10].

Fig. 8
figure 8

Experimental curves for the plot of the z(α) versus α for Peaks 1 and 2 at 5 K min−1

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Plausible chemical pathways for generating the evolved gases within these peaks are discussed below. During heating from room temperature to 780 K (Peak 1), PSO exhibited a mass loss of ~2 %. However, no gaseous species were detected by MS. This suggests that the first mass loss may be associated with the escape of some volatile species from the polysiloxane network.

A previous study suggested that the transformation of organosilicon polymers into ceramics under an inert atmosphere proceeds through a free radical reaction mechanism [30]. Considering the energies of the various bonds present in the polymer and the MS data, it is reasonable to assume that only Si–C, C–C, Si–H, and C–H bonds were broken to form radicals during the pyrolysis process, and that cleavage of Si–C would occur first as it has the lowest bond energy among the four bonds (Table 3). Therefore, the evolution of carbon-containing species in the region 750–950 K (Peak 2) may be due to the cleavage of Si–CH3 and unreacted residual vinyl groups according to the following mechanism:

$$ \begin{gathered} - {\text{CH}}{=}{\text{CH}}_{ 2} + {\text{ Si}}{-}{\text{H}} \to {{\text{CH}}_{ 2}{=}} {\text{CH}}_{ 2} \uparrow \hfill \\ {\text{Si}}{-}{\text{CH}}{=}{\text{CH}}_{ 2} \to {\text{CH}{\equiv}}{\text{CH}} \uparrow + {\text{ Si}}{-}{\text{H}} \hfill \\ {\text{Si}}{-}{\text{CH}}_{ 3} + {\text{ Si}}{-}{\text{H}} \to {\text{Si}}{-}{\text{Si }} + {\text{ CH}}_{ 4} \uparrow \hfill \\ \end{gathered} $$
Table 3 Bond energies of various bonds present in polymeric precursors
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Although slow release of H2 started in the temperature range of Peak 2, and increased slightly, its contribution to the mass loss can be neglected due to its relatively low concentration and low relative molecular mass. Therefore, the activation energy (185 kJ mol−1) is mainly associated with Si–C and is stable in the temperature range of Peak 2.

The Málek procedure, which was derived by assuming independence of the activation parameters on the degree of conversion, cannot be used to analyze Peaks 3 and 4. Therefore, it is difficult to delineate a single reaction mechanism or a formal physical description for Peaks 3 and 4 by a peak-fitting method. Although kinetic activation energies for these two peaks have no physical–geometrical meaning, the complexity of reaction can be revealed and can be analyzed on the basis of MS data.

Peak 3 (820–970 K) was strongly overlapped with Peaks 2 and 4. The formation of CH4/CH3 and H2, in this temperature range, can be explained in terms of homolytic cleavage of the Si–C and Si–H bonds with the formation of CH ·3 and H· radicals, which then abstract H from the C–H bonds, leading to the final volatile products. The major reactions can be envisaged as [31]:

$$ \begin{gathered} {\text{Si}} {-} {\text{H}} \to {\text{Si}}^{\cdot} + { 1}/ 2 {\text{H}}_{ 2} \uparrow \hfill \\ {\text{Si}}^{\cdot} \, + {\text{ Si}} {-} {\text{CH}}_{ 3} \to {\text{Si}} {-} {\text{CH}}_{ 2} {-} {\text{Si }} + { 1}/ 2 {\text{H}}_{ 2} \uparrow \hfill \\ {\text{Si}} {-} {\text{CH}}_{ 3} \to {\text{CH}}_{ 3}^{\cdot} \hfill \\ {-} {\text{CH}}_{ 3}^{\cdot} \, + {\text{ Si}} {-} {\text{H}} \to {\text{CH}}_{ 4} \uparrow \hfill \\ \end{gathered} $$

These reactions gradually consume the C–H bonds and produce Si–C bonds, which are generally observed in the pyrolysis of a polysiloxane in this temperature range.

The principal reaction in Peak 4 is the evolution of CH4/CH3 and H2 (Fig. 5). FTIR spectra of the solid intermediates obtained at various temperatures show a new peak at around v = 1,630 cm−1 (indicated by an arrow in Fig. 9). This peak is assigned to the C=C (sp2-bonded) stretching mode of Cx, which suggests that aliphatic and aromatic carbon, so-called free carbon, is produced during the ceramization process. The proposed mechanism can be described as follows:

$$ \begin{gathered} {\text{Si}}{-}{\text{CH}}_{ 2}{-}{\text{Si }} + {\text{ Si}}{-}{\text{CH}}_{ 3} \to {\text{Si}}{-}{\text{C}}\left( {\text{Si}} \right){\text{H}}{-}{\text{Si }} + {\text{ CH}}_{ 4} \uparrow \hfill \\ {\text{Si}}{-}{\text{CH}}_{ 2}{-}{\text{CH}}_{ 2}{-}{\text{Si }} \to {\text{ Si}}{-}{\text{CH}}_{ 2}{-}{\text{Si}} + {\text{ C}}_{x} + {\text{ H}}_{ 2} \uparrow \hfill \\ {\text{Si}}{-}{\text{CH}}_{ 2}{-}{\text{CH}}_{ 2}{-}{\text{Si }} \to {\text{ Si}}{-}{\text{CH}}_{ 2}{-}{\text{Si}} + {\text{ C}}_{x} + {\text{ CH}}_{ 4} \uparrow \hfill \\ {\text{Si}}{-}{\text{CH}}_{ 2}{-}{\text{CH}}_{ 2}{-}{\text{Si }} + {\text{ Si}}{-}{\text{H}} \to {\text{Si}}{-}{\text{C }}\left( {\text{Si}} \right){\text{ H}}{-}{\text{Si }} + {\text{ CH}}_{ 4} \uparrow \hfill \\ {\text{Si}}{-}{\text{C}}\left( {\text{Si}} \right){\text{H}}{-}{\text{Si }} + {\text{ Si}}{-}{\text{CH}}_{ 3} \to {\text{ Si}}{-}{\text{C}}\left( {\text{Si}} \right)_{ 2}{-}{\text{Si }} + {\text{ CH}}_{ 4} \uparrow \hfill \\ \end{gathered} $$
Fig. 9
figure 9

Infrared spectra of intermediates of PSO heated to various temperatures at the heating rate of 5 K min−1

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Based on the above analysis, it is clear that two kinds of elementary and parallel steps, associated with Si–H and Si–CH3, are involved in the temperature range of Peak 3, while two kinds of elementary and parallel steps associated with C–H and Si–Cx–Si are involved in the temperature range of Peak 4. Considering the different bond energies, it is rational to assume that each elementary step has unique activation energy, and thus affects the rate of product formation. In such a reaction, a change in the activation energy as the reactions progress would be observed. This change will depend on the contribution of each elementary step, which gives an apparent activation energy that varies with reactions progress. The apparent activation energy can be mathematically derived from the nonisothermal degradation rate law (Eq. 8) [14].

$$ E_{{\alpha\;{\text{ apparent}}}} = \Upsigma A_{{\alpha {\text{i}}}} E_{{\alpha {\text{i}}}} \, { \exp }( - E_{{\alpha {\text{i}}}} /RT) \,_{{}} f_{{\alpha {\text{i}}}} (\alpha )/\Upsigma A_{{\alpha {\text{i}}}} { \exp }( - E_{{\alpha {\text{i}}}} /RT) \, f_{{\alpha {\text{i}}}} (\alpha ) $$
(8)

Previous studies have demonstrated that thermolysis steps of precursors include the mineralization and ceramization processes [9]. For the pyrolysis of PSO, Peak 2 is associated with the mineralization process, corresponding to the major mass loss (12 % mass loss indicated by Fig. 2), while Peak 4 represents the ceramization process which leads to the SiOC ceramic. In comparison, the mass losses associated with Peaks 1 and 3 are minor, and Peak 3 can be considered as a transition stage between the mineralization and ceramization processes.

Conclusions

The thermal decomposition of PSO to silicon oxycarbide ceramic has been studied by TG-MS. To provide an insight into the overall reaction, a peak-fitting method has been used to deconvolute the DTG curves. It is shown that the pyrolytic process can be fitted by four peaks, and that the heating rate has no effect on the mechanism. The activation energy for each stage and kinetic models for Peak 1 and 2 have been determined by an isoconversional method and Master plots, respectively. The results show that the activation energies for Peaks 1 and 2 are independent of the degree of conversion, and follow R2- and D2-type kinetic models, respectively. In contrast, the activation energies for Peaks 3 and 4 show significant changes. Therefore, the processes in the temperature range of Peaks 3 and 4 cannot be described by a kinetic model. Nevertheless, plausible chemical pathways accounting for the generation of the evolved gases are proposed.