Isoconversional kinetics of thermal oxidation of

Thermochimica Acta 623 (2016) 65–71

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Isoconversional kinetics of thermal oxidation of mesoporous silicon Ali Ghafarinazari a,b,∗ , Emanuele Zera c , Anna Lion d , Marina Scarpa d , Gian Domenico Sorarù c , Gino Mariotto a,b , Nicola Daldosso a,b a

School of Natural and Engineering Sciences, Nanoscience and Advanced Technologies, University of Verona, Strada le Grazie 15, 37134 Verona, Italy Department of Computer Science, University of Verona, Strada le Grazie 15, 37134 Verona, Italy Department of Industrial Engineering, University of Trento, Via Mesiano 77, 38123 Trento, Italy d Laboratory of Nanoscience, Department of Physics, University of Trento, Via Sommarive 13, 38123 Trento, Italy b c

a r t i c l e

i n f o

Article history: Received 7 August 2015 Received in revised form 15 October 2015 Accepted 23 November 2015 Available online 2 December 2015 Keywords: Mesoporous silicon Model-free kinetics Model fitting kinetics Thermal oxidation Thermogravimetry Crystallography

a b s t r a c t Mesoporous silicon (pSi) has several interesting features that makes it suitable for various biomedical applications. In particular, the large surface area make it very sensitive to environment changes. Among other approaches, thermal oxidation is an effective way to passivate its surface. Herein, we present experimental and analytical results concerning kinetics of thermal oxidation reaction of pSi. The experiments were conducted on pSi powders produced from silicon wafer by anodization and converted to particles by sonication. Oxidation experiments were carried out at different heating rates. Structure and morphology of the samples have been investigated by XRD and SEM before and after thermal oxidation. The model-free kinetics proposed by Ozawa–Flynn–Wall (OFW) was used to determine the Arrhenius relationship for the pSi thermal oxidation. The obtained apparent activation energy by OFW was confirmed by Starink method. At low temperature, the oxidation of surface dangling bonds obeys the Avrami–Erofeev mechanism. At high temperature, oxidation is followed by classical bulk oxidation according to diffusion mechanism controlled by the diffusion of oxygen through the silicon dioxide layer on the surface of the pSi. The reaction mechanism was checked by the model fitting kinetics, which confirmed the reaction is a kind of sequential two-stage process, Avrami–Erofeev and 3D diffusion. Finally, differential thermal analysis suggests that the second oxidation step is also possibly affected by phase transformation of the silicon dioxide. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Mesoporous silicon (pSi) possesses some specific properties like biocompatibility, photoluminescence and non-immune response, which makes it a promising material for biomedical applications [1]. Due to its large surface area and highly reactive surface functional groups, pSi is particularly susceptible to air, water, or chemical oxidation [2]. This oxidation has side effects of redox in the biological systems such as tissues [3], proteins [4], and drugs [5]. Nowadays, partial thermal oxidation of pSi has been suggested to solve this issue [6]. Thermal oxidation has been extensively employed by the microelectronic industry to produce high-quality oxides on silicon, and this approach also works with pSi [7]. Noticeably, the rate of oxidation of pSi is greater than that of flat bulk silicon due to the porous structure. The oxidation conditions can be tuned to obtain

∗ Corresponding author. Tel.: +39 388 6598606. E-mail address: [email protected] (A. Ghafarinazari). http://dx.doi.org/10.1016/j.tca.2015.11.017 0040-6031/© 2015 Elsevier B.V. All rights reserved.

materials with different properties. Up to now, a variety of effects of oxidation on properties of pSi has been investigated, such as photoluminescence [8,9], biodegradability [10], phonon thermal conductivity [11], and surface reactivity [12]. However, there are only few preliminary reports about thermal oxidation mechanism of pSi [13–15]. For instance, Pep et al. [13] reported that thermal oxidation of pSi consists in two separated steps as a function of the temperature but without any further information and discussion about the kinetic mechanism and the modeling. In this work, we performed a comprehensive study, both experimental and theoretical, on thermal oxidation of pSi by model-free kinetic (MFK) and model fitting to determine oxidation mechanism. In the case of MFK, OFW (Ozawa–Flynn–Wall) methodology has been used to estimate the kinetic triplet (E, A, and f(˛)); the obtained E values were confirmed by Starink method. Moreover, model fitting has been applied to find the best kinetic model to disclose the mechanism of thermal oxidation in pSi. The understanding of the oxidation process and the relative mechanism is an important result for basic research on porous materials and also for applicative purposes, mainly in microelectronic and biomaterials fields.

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A. Ghafarinazari et al. / Thermochimica Acta 623 (2016) 65–71 Table 1 Reaction types and corresponding type of f(˛) [17].

2. Experimental procedure The porous silicon samples have been prepared by anodizing ntype Si (1 0 0) wafers with a resistivity of 0.01–0.02 cm, Sb doped, in a HF (48%), water and Triton X-100 solution (25:200:1). The current density was kept constant at 15 mA cm−2 and the etching time was 10 min. The porosity of the samples obtained under these experimental conditions was determined by gravimetric analysis [16] and was found 74 ± 8%. The porous layer was detached from the bulk silicon and fragmented into micro particles by 20 min sonication at 400 W delivered in 80 mL hexane sample volume. Then, the micro particle suspension was centrifuged at 500 × g for 5 min, the surnatant was discarded, the micro particles were dried under gentle nitrogen flow and used within few hours. X-ray diffraction (XRD) patterns were measured with a D8 Advance Bruker diffractometer, equipped with a Göbel mirror using ˚ The patterns were collected with a Cu-K␣1 radiation at 1.5406 A. scan rate of 0.04◦ /s in the 8◦ –90◦ 2 range. In order to enhance both background and small peak signals, square root of intensity has been illustrated. The crystallite phases were then identified using the Joint Compounds Powder Diffraction Standards (JCPDS) database. Morphological characteristics have been investigated by scanning electron microscopy with a FE-SEM Zeiss supra 60. The accelerating voltage was 2 kV. The samples were sputtered with gold to assure sufficient conductance. The simultaneous thermal analyses (STA; i.e. differential thermal analysis (DTA) and thermogravimetry (TG) analysis) were done in synthetic air atmosphere from room temperature to 1273 K with STA 409 (Netzsch–Gerätebau GmbH, Selb, Germany). The STA were conducted at three different heating rate values: 3, 6, and 10 K/min with a flow of 50 mL/min, under ambient atmospheric pressure up to 1273 K. Then, the sample was cooled to room temperature by the rate of 10 K/min. The powder samples, about 20 mg, were kept in alumina crucibles. A direct way to monitor oxidation phenomenon is TG measurement [13]. The mass variation from TG analysis is correlated to a conversion (˛) value by Eq. (1): ˛i =

ms − mi ms − mf

(1)

where ms is the starting mass and mf is the mass after the oxidation. Reaction kinetic can be evaluated by the kinetic triplet (A, E, and f(˛)) in the kinetic equation expressed in the form of the Arrhenius relationship: d˛ = A · e−E/RT · f (˛) dt

(2)

Values of the Arrhenius parameters (E and A) are accepted as providing the height of the energy barrier for reaction to occur (the activation energy, E) and the frequency of occurrence of reaction configuration that may lead to product formation (the frequency factor, A). Hence, the reaction model, f(˛), represents the dependence on the conversion extent. The best methodology to evaluate the kinetic triplet (E, A and f(˛)) is the MFK approach for all kind of reactions [17,18]. Ozawa, Flynn and Wall (OFW) adapted this method to the TG analysis [19,20] and the obtained procedure was validated by the American Society for Testing and Materials (ASTM) for differential scanning calorimetry (DSC) analysis [21]. In summary, integration of Eq. (2) and Doyle approximation [19] leads to: Ln(ˇ) = Ln

A · E R

= Ln 0

˛

d˛ f (˛)

− 5.330 − 1.052

E RT

(3)

where ˇ is the heating rate. According to Eq. (3), plotting of Ln(ˇ) as function of 1/T at different ˛ led to straight lines with slope equal to

Model notation Fn Cn An D1 D2 D3 D4 Rn Bna

Reaction type nth order (n = 1–3) nth order autocatalysis (n = 1–3) Avrami–Erofeev (n-D nucleation; n = 1–3) 1D diffusion 2D diffusion Jander 3D diffusion Ginstling–Brounshtein 3D diffusion Reaction on the n-D interface (n = 2, 3) Prout–Tompkins nth order autocatalysis

f(˛) (1 − ˛)n (1 + Kcat ˛) × (1 − ˛)n n × (1 − ˛) × [−ln(1 - ˛)](1−1/n) 0.5˛ [−ln(1 − ˛)]−1 1.5(1 − ˛)2/3 × [1 - (1 - ˛)1/3 ]−1 1.5[(1 − ˛)−1/3 - 1]−1 n × (1 − ˛)(1−1/n) (1 − ˛)n × ˛a

−1.052E/R. The apparent activation energy at the different conversion degree can be calculated from ˛these slopes. Moreover, under the condition of constant ␣ (Ln 0 fd˛ = 0), by introducing in (˛) Eq. (3) the calculated E value, and plotting Ln(ˇ) versus 1/T, we can estimate the value of Ln(A) [22]. Moreover, Starink [23] proposed another equation (Eq. (4)) to estimate the oxidation kinetic in a more accurate way.

Ln

ˇ T 1.92

= Ln

A · E R

= Ln 0

˛

d˛ f (˛)

− 1.0008

E RT

(4)

In this case, plotting Ln(ˇ/T1.92 ) versus 1/T leads to the apparent activation energy. We implemented this method and compared the results with those obtained by OFW method. Therefore, f(˛) can be estimated by inserting E and A values in Eq. (2). The kinetic triplet can be derived without any assumption or approximation. By these outcomes, mechanism and kinetics of the oxidation mechanism can be investigated. Beside to MFK, Model-fitting method is the conventional way to estimate the reaction model (f(˛)) [24]. In this method, initially, the conventional models (Table 1) were implemented to obtain the best fit model [17]. For each model, the goodness of the fit is customarily estimated by a coefficient of linear correlation (r). A single pair of E and A is then commonly chosen as that corresponding to a reaction model that gives rise to the maximum absolute value of the correlation coefficient [25]. However, this pair of E and A does not have physical meaning. At the end, the obtained model (f(˛)) has been compared with f(˛) estimated by OFW. Finally, differential thermal analysis (DTA) is performed with identical thermal cycles to obtain an indication of the enthalpy change associated to the reactions (exothermic or endothermic) [4]. This technique helps to define the critical temperatures of the oxidation steps. 3. Results and discussion The structure and the morphology of pSi samples were investigated by both XRD and SEM. XRD patterns of the as-anodized sample (pSi) and of the sample after heating at 3 K/min up to 1273 K (pSiO2 ) are shown in Fig. 1, top and bottom panel, respectively. Formation of single crystalline silicon nanostructure in pSi sample was confirmed (fit to the JCPDS file 27-1402). Indeed, the Bragg condition is only satisfied for 4 0 0 reflection peaked at 2 = 69.13◦ , according to Ogata et al. [26]. The broad peak at low angles (i.e. 15◦ –30◦ ) is associated to the amorphous silica [27], probably due to surface oxidation of the silicon crystallites during the sonication. The interface between the oxidized layer and the silicon core is amorphous silicon in the order of ppm, thus not appreciable [28,29]. Moreover, on the pSi surface there are functional groups such as

A. Ghafarinazari et al. / Thermochimica Acta 623 (2016) 65–71

Fig. 1. XRD diffraction of the freshly anodized pSi powder; and after oxidation by heating rate of 3 K/min up to 1273 K (pSiO2 ). The sharp peak at 69.1◦ (“*” at upper panel) is due to the 4 0 0 reflection of crystalline Si, while the sharps reflection peaks (#) at bottom panel suggest the occurrence of ␣-quartz phase.

SiHx and/or SiOH, formed during the fabrication [1], which make phase composition not quantitatively assessable [7]. Oxidized pSi (pSiO2 ) XRD pattern is shown in Fig. 1 (bottom panel). After heating treatment, the Si peak at 69.13◦ disappeared and a crystalline phase was detected, as shown by the sharp peaks

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at 2 = 20.76◦ and 36.60◦ . This new crystalline phase corresponds to ␣-quartz (JCPDS 02-0458). It is worth noting that the broad signal at low angle (15◦ –30◦ ) did not change by heating up to 1273 K, which confirms that the main part of oxidized pSi remains amorphous silicon oxide. Morphological characterization was carried out by SEM analysis (Fig. 2). Fig. 2a shows pSi particles in the micrometre scale. This uniform porous structure can be better appreciated in Fig. 2b with pore diameter about 50 nm, layer thickness about 6 ␮m. The thickness of pSi layers, pore walls, is around 20 nm, which is one of the most critical parameters for oxygen diffusion at the pSi to get efficient thermal oxidation [30]. Fig. 2c and d reports SEM images after thermal oxidation by heating the sample at 3 K/min. Particle size and morphology did not change significantly while the porous surface is rather changed (Fig. 2d), the silica formed upon oxidation led to a closure of the pores. The final value of the mass variation from TG analysis, according to Eq. (1), is 94.6% for heating to 1273 K with rate of 3 K/min. Taking into account the reaction stoichiometry, complete oxidation of pure silicon would cause 114.3% of mass increase [27]. Owing to the fact that oxidation was completed by heating the sample under the reported condition, based on XRD analyses, reaction conversion (˛) should be around 100%. Therefore, initial value of ˛ is estimated to be 17.2% (i.e. (114.3−94.6) × 100), which is related to the reactive sur114.3 face groups that can be oxidized during the sample preparation [1]. Taking into consideration this effect, ˛ value was calculated from TG analyses by Eq. (1) as reported in Fig. 3.

Fig. 2. SEM images of pSi samples before and after thermal oxidation. (a) pSi particles as anodized; (b) surface of pSi particles with higher magnification; (c) thermally oxidized pSi particles with rate of 3 K/min; and (d) surface of thermally oxidized pSi particles.

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Fig. 3. Conversion curves as a function of temperature at heating rates of 3, 6, and 10 K/min.

Note that during the cooling from 1273 K to room temperature, there is less than 4% weight reduction, which could be related to the oxygen absorption and desorption [27,31]. Since this value was lower than 4% of the total mass, it was neglected in our analysis, in which we considered the other correction methods as recommended by the International Kinetics Committee, such as baseline corrections, buoyancy effect, sample mass, heating rates [32]. According to Fig. 3, it is possible to infer that no plateau is reached in the case of oxidation with heating rate of 10 K/min. This rate is the maximum acceptable one for kinetic analysis [17] and it is also the most common rate for thermal analysis studies [26,33]. This sample after reaching the maximum temperature (1273 K) was isothermally heated for 10 min at the same temperature to be sure about saturation state. However, the TG value increased from 90% to 93.7% suggesting that oxidation was not complete. It is also worth noting that oxidation increased remarkably with a reduction of the heating rates to 6 and 3 K/min. At these lower rates, saturation state is reached and the onset temperature was dependent on the heating rate. Sigmoidal shape of the isoconversional curves is a common form for such reactions [17]. In the isothermal analysis, the type of reaction (f(˛)) can be pointed out by looking ˛–T curves. Furthermore, sudden increase of ˛ above 500 K is an evidence that the oxidation process is a multistep reaction, therefore being unsuitable to propose just one kinetics model [34]. Based on Eq. (3), Ln(ˇ) versus 1/T was plotted in Fig. 4a. According to OFW methodology, for a series of measurements with different heating rates (ˇ), the slope and linear coefficient of plotting Ln(ˇ) versus 1/T at different and constant ˛ gives the E and A values (Fig. 4b). In order to validate E values obtained by OFW method, also Starink method has been implemented as described in Section 2. In general, E is considered as the threshold or energy barrier that must be overcome to permit the bond redistribution steps that are essential for the transformation of reactants into products. The variation of E with ˛ indicates that this reaction is a complex (multistep) process [35]. At the beginning of the conversion, E value is just about 10 kJ/mol since pSi is easily oxidized in air [36]. This value is in line with published results [13]. In the initial stage, ˛ < 37%, there is a positive convexity of the E versus ˛ curve (Fig. 4b), which indicates that this process is irreversible [37]. This outcome is in agreement with enthalpy of Si–O that is higher than other Si bonds such as Si–Si, Si–H, and Si–C [7]. The second stage, at ˛ > 37%, accounts for a continuous linearly increment of E value; this stage seems to be driven by parallel processes [38,39]. The final value is in accordance with energy of oxygen diffusion into fused

Fig. 4. (a) Natural logarithm of heating rate versus 1000/T of the pSi thermal oxidation at different reaction degree. (b) Variation of E and Ln(A) by conversion obtained from Eq. (3), Est . (*) is the E value obtained by Starink method. (c) The dependence of Ln(A) with E.

silica, which has been reported to be 104.6 kJ/mol [40]. As it can be seen, E values estimated by Starink method (Est ) have no significant difference from those obtained by OFW method. This similarity has been also found by other experimental data sets [41,42]. The pre-exponential term, A, is a measure of the frequency of occurrence of the reaction and it is regarded to include the vibration frequency in the reaction coordinate. Ln(A) and E show a similar dependence on ˛ (Fig. 4b). Fig. 4c shows a linear dependence of A versus E for the two ranges considered (after and before ˛ = 37%):

Ln(A) = 0.27E − 9.7

˛ ≤ 37%

(I)

Ln(A) = 0.12E − 7.9

˛ > 37%

(II)

(4)

This linear behavior is described by the compensation equation [43]. Although many theoretical explanations for compensation


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Table 2 Arrhenius parameters for thermal oxidation of pSi using model fitting for stage 1 (˛ < 37%). Model

E (kJ mol−1 )

Ln A (s−1 )

R

F1 F2 Fn C1 Cn A2 A3 An D1 D2 D3 D4 R2 R3 Bna

93.65 7.50 21.17 7.12 21.17 7.91 8.08 17.56 19.46 19.69 19.86 19.73 10.72 10.83 21.17

13.79 −7.81 −2.85 −7.98 −2.85 −6.69 −6.45 −6.14 −6.80 −7.40 −8.82 −8.88 −7.48 −7.84 −2.84

0.651 0.841 0.939 0.936 0.939 0.932 0.961 0.985 0.922 0.922 0.921 0.932 0.945 0.946 0.929

Fig. 5. f(˛) derived from Eq. (2) for thermal oxidation of pSi.

behavior have been proposed, none of them has received general acceptance. Aspects of the compensation phenomena in thermoanalytical data are reviewed by Koga [44]. These two lines (lines I and II in Fig. 4c) are another evidence of having two consecutive reactions. Finally, the f(˛) shape can be matched to the theoretical models describing the oxidation mechanism [45]. In fact, once both E and A have been evaluated, it is possible to numerically reconstruct the reaction model, f(˛), derived from Eq. (2) as shown in Fig. 5 [46]. As described earlier, there are two separate stages: after and before ˛ = 37%. In the initial stage, the shape of f(˛) is compatible with the Avrami–Erofeev model. This model is generally used to describe nucleation and growth phenomena in random places [47]. On the other hand, the final step agrees with the diffusion mechanism. Clearly, the initial silicon dioxide layer acts as a barrier and oxygen must diffuse through this layer to react with silicon at the interface silicon/silicon dioxide [48,49]. Two different mechanisms depending on the conversion degree were already observed by Leppavuori et al. by isothermal measurements [13]. In order to get more information about the mechanism of pSi oxidation and also to check the values obtained by OFW method, model fitting has been used. We could not obtain acceptable correlation coefficient (r ≥ 0.95) of Arrhenius parameters by implementation of this method by assumption of having a single stage reaction. Then, experimental data was separated to two stages based on MFK method, and in this case, the model fitting was satisfied. The fitted values of Arrhenius parameters evaluated for the experimental data by the model-fitting method are presented in Tables 2 and 3 for comparison. As it can be seen in Table 2, the best fitted model for the first stage (˛ < 37%) is Avrami–Erofeev n-dimensional nucleation model. Recently, the Avrami–Erofeev kinetic model was applied for surface reactions at mesoporous chitosan [50]. This model was also applied to describe the adsorption of anionic dyes on a functionalized silica [51]. After this assumption, there are several articles for application of this model for surface reactions of mesoporous materials, mainly about absorption on silica/silicon [52,53]. Therefore, the Avrami–Erofeev kinetic model has high potential to describe the first step of pSi oxidation based on absorption and reaction of oxygen at the surface. As for the second stage of the oxidation (˛ > 37%), the best models to interpret the data are diffusion ones, particularly three dimensional (3D) models (Table 3). This model is in agreement with oxygen diffusion across silica, produced by the first step of oxidation, through the network of pSi as described before. In order to better identify and separate the oxidation steps, particularly at ˛ > 37%, derivative thermogravimetry curve (DTG) has been calculated (dashed line, Fig. 6). It turns out in good agreement

Table 3 Arrhenius parameters for thermal oxidation of pSi using model fitting for stage 2 (˛ > 37%). Model

E (kJ mol−1 )

Ln A (s−1 )

R

F1 F2 Fn C1 Cn A2 A3 An D1 D2 D3 D4 R2 R3 Bna

20.30 26.94 25.08 20.30 25.08 14.28 16.43 43.24 29.43 33.18 38.75 35.07 18.05 18.54 35.79

−5.59 −4.07 −4.48 −5.59 −4.48 −6.43 −6.06 −2.42 −5.33 −5.19 −5.57 −6.30 −6.89 −7.14 −2.89

0.911 0.924 0.924 0.911 0.924 0.714 0.508 0.948 0.955 0.955 0.964 0.966 0.873 0.890 0.912

Fig. 6. DTA, DTG, and E derived from heating rate of 10 K/min.

with DTA trace. To this aim, the reaction has been investigated as a function of temperature. Fig. 6 shows the results obtained at 10 K/min heating rate; similar results have been obtained with other heating rates with a small shift to the lower temperature. All of the reaction steps are exothermic (based on DTA) and bring to mass increment (based on TG). As it was mentioned [54,55], by heating of pSi rapidly surface functions decomposed and evaporated. But, these reactions have no significant effect on enthalpy and mass loss in comparison to oxidation as it can be seen. Also, due to the broadness of the DTA peaks, no information can be extracted regarding possible physical or morphological transformations. The plot resulting from the superimposition of the DTA and DTG traces

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is in line with Salonen results [56], with the difference that the second and third steps are more separated and evident. This is due to the lower aging of the pSi and mainly the use of lower heating rate; since these authors utilized 20 K/min heating rate. Owing to the fact that oxygen at around 350 K will begin to remove Si–H and Si–Si species present on the surface, generating Si–O [57], the first stage of oxidation started at about this temperature up to 600 K. As we mentioned before, this stage of oxidation is in accordance with the Avrami–Erofeev model. At this stage, the main enthalpy variation (DTA) is at 500 K [56]. As mentioned before, pSi leads to reduction in biological systems during protein or drug delivery and also bioimaging. Previous studies confirm that partial oxidation (up to 600 K) would be sufficient to avoid redox reaction with proteins (such as albumin) [4]. On the other hand, this degree of oxidation is not enough to avoid redox reactions in other biological systems (tissue and also drugs) so further oxidation of pSi is needed [3,5,6]. In the second oxidation step, which is controlled by diffusion mechanism, there are two peaks at about 850 and 1150 K on DTA curve that are in agreement with phase transition of silicon dioxide. In the bulk silicon dioxide, trigonal ␣-quartz (with density of 2.65 g/cm3 ) at 846 K transforms reversibly and easily into hexagonal ␤-quartz (2.53 g/cm3 ), and upon further temperature increase the ␤-quartz will transform into hexagonal ␤-tridymite (2.25 g/cm3 ) at 1143 K [58]. Differently from ␣ to ␤-quartz transition, transformation of ␤-quartz to ␤-tridymite is hard and irreversible for a bulk silica, but probably based on existence of Sb, as dopant n type silicon wafer, and nanostructural size effect this phase transition simplified [59]. It should be reminded that XRD results showed a small amount of crystalline SiO2 at the end of thermal oxidation under the minimum heating rate (Fig. 1). Then, by expansion of the crystalline structure of SiO2 , disordering in the interface of silicon dioxide, amorphous oxides, and silicon of core structure increased. This disordered layer by heating has been observed by XPS analysis [60]. Diffusion of oxygen from the atmosphere to core silicon across silica is completely controlled by silica morphology [61]. And finally, maximum value of E is in line with published data of oxygen diffusion in fused silica as discussed before [40]. Apparent activation energy is represented as a function of temperature in the range 20% ≤ ˛ ≤ 90% and each point represents 1% of conversion. For the sake of clarity, the value of ˛ is less than 4% until about 500 K; therefore, we cannot calculate E value at temperature lower than 500 K. As it can be seen, enthalpy of reaction (DTA) shows correlation with E value. Initially, E value is low because the reaction is exothermic and releases high energy based on peak of DTA. Indeed, this release of energy provides power for further oxidation till the maximum value of the first DTA peak. Next, apparent activation energy increased up to 600 K. Then, E decreased according to the Avrami–Erofeev model. At the second stage of oxidation based on oxygen diffusion in silicon dioxide layer more energy is needed, so the E increased dramatically. The slope of this increment was increased by phase transformation of silicon dioxide.

4. Conclusion Mechanism of thermal oxidation of mesoporous silicon (pSi) particles has been systemically investigated. For this purpose, pSi was synthesised by anodization of silicon wafer and then fractured to particles by sonication. XRD confirmed single crystallinity of pSi and also complete oxidation after thermal oxidation. SEM investigations disclosed morphological behavior of oxidation in details. The kinetic triplet for the pSi thermal oxidation was obtained by model-free kinetics. These results were validated by Starink method and model fitting kinetics for E and f(˛), respectively.

The results confirm that there are two separate oxidation steps. The first one is oxidation at low temperature of surface functional groups which can be modeled with the Avrami–Erofeev. The second appears to be oxidation according to 3-dimensional diffusion mechanism controlled by the diffusion of oxygen through the silica layer on the surface of the pSi. Phase transformation of silica influenced the second oxidation step according to differential thermal analysis.

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