Thermal oxidation process of in-situ silicon carbide incorporated carbon aerogel, experimental and kinetic study

Accepted Manuscript Title: Thermal oxidation process of in-situ silicon carbide incorporated carbon aerogel, experimental and kinetic study Authors: Azadeh Seifi, Ahmad Reza Bahramian, Alireza Sharif PII: DOI: Reference:

S0010-938X(18)30774-1 https://doi.org/10.1016/j.corsci.2018.07.022 CS 7621

To appear in: Received date: Revised date: Accepted date:

29-4-2018 6-7-2018 16-7-2018

Please cite this article as: Seifi A, Bahramian AR, Sharif A, Thermal oxidation process of in-situ silicon carbide incorporated carbon aerogel, experimental and kinetic study, Corrosion Science (2018), https://doi.org/10.1016/j.corsci.2018.07.022 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Thermal oxidation process of in-situ silicon carbide incorporated carbon

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aerogel, experimental and kinetic study

Azadeh Seifi, Ahmad Reza Bahramian*, Alireza Sharif

Polymer Engineering Department, Faculty of Chemical Engineering, Tarbiat Modares

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University, P. O. Box 14115-114 Tehran, Iran

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Corresponding Author. Tel.:+98-21-8288-4938; Fax: +98-21-8288-4931

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E-mail address: [email protected]

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The silicon carbide phase was incorporated in carbon aerogel using the sol-gel polymerization. A 40 % decline was observed in the overall rate of oxidation of the resultant hybrid aerogel in comparison with the neat carbon aerogel. The global oxidation kinetics of the hybrid aerogel was found to be strongly dependent on the reaction condition due to the highly porous nature of the aerogel samples. A gradual shift was observed from the reaction-control to diffusion- control regimes in the kinetic scheme of the oxidation reaction by increasing the heating rate. Applying the NPK method on the non-isothermal thermo-gravimetric data enables one to differentiate between the rates constant values of the reaction-control and diffusioncontrol regimes of the oxidation reaction.

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Highlights

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Abstract

Si-based phase component was incorporated in carbon aerogel using the sol-gel polymerization.

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The results of non-isothermal kinetic study in the temperature range of 500-1200 ºC confirm the determinant role of the diffusion process in the global oxidation kinetic due to the highly porous character of the hybrid aerogel. This leads to the effect of the reaction condition on the reaction pathway; so that, a shift is observable from the reaction-control to diffusion-control regimes of the oxidation process by increasing the heating rate. The rate constants corresponding to these

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two different regimes were differentiated by applying the non-parametric kinetic analysis.

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Keywords: Reinforced Carbon Aerogel, Silicon Carbide, Kinetic of Oxidation, NPK method

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1. Introduction Organic polymer-derived carbon aerogels on account of such excellent functional properties as

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low density, high specific strength and low thermal conductivity are a good choice for using in thermal management applications such as heat shields and thermal insulation[1-3]. However, these materials suffer from a main drawback, which is structural destruction caused by the thermal oxidation at temperatures above 450oC under the air atmosphere that restricts the wide spread use of these materials. An acceptable efficient way for increasing the oxidation resistance

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is the incorporation of Si-based refractory materials such as silicon carbide into the colloidal

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network structure of the carbon aerogels. Despite the many research works in this field[4-8], no

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attempt, according to our knowledge, has been made to evaluate comprehensively the oxidation

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kinetics of these materials with a highly porous character. However, many researchers perform a

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mechanistic study on the thermal oxidation of C/SiC composites[9-12] by applying the model-

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fitting or isoconversional model-free approaches in kinetic analysis to get some insights about the oxidation mechanism of these composites. But, in both of these approaches an assumption is

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made either on the functionality of the kinetic model or the rate constant before estimation of the activation energy. For example, the use of the oversimplified Arrhenius relation, that is specific

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to single step homogeneous reactions, in these approaches leads to the apparent and not true

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quantities for the activation energies[13-15].So, an indubitable mechanistic interpretation of the complex processes with heterogeneous nature cannot be made by the sole use of these methods, and there is a need for complementary methods. In a recently published paper[16], the different pore structure of the carbon aerogels was used as a mean, beside the results of the isoconversional methods, for getting more mechanistic clues on the thermal oxidation reaction. 3

This was achieved by comparing the reaction rates of the carbon aerogels with different microstructural parameters at various heating rates. The NPK (Non-Parametric Kinetics) method proposed by Serra et.al [17, 18]is an efficient

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method which can be used as a less speculative complementary method for the kinetic study of the solid-state reactions. The most significant feature of this method, in comparison with the other kinetic methods, is its ability to obtain the more confident kinetic model and the accurate rate constant without any previous assumption on their functionality[17-20].

The objective of this paper is, therefore, to perform a detailed theoretical and experimental study

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on the thermal oxidation reaction of SiC-incorporated carbon aerogels via the method of NPK.

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As far as the authors know, this is the first report for the use of the powerful method of NPK for

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the analysis of the thermal oxidation kinetics of SiC-reinforced carbon aerogels as a highly

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porous nanostructure. Four isoconversional methods (Friedman’s differential method along with

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two integral ones: Kissiner-Akahira-Sunose (KAS) and Flynn-Wall-Ozawa (FWO) and the

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Vyazovkin method) were also used for the model-free kinetic analysis of the thermal oxidation of reinforced carbon aerogels and their results were compared with the NPK method. An attempt

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was also made to investigate the kinetic scheme of the oxidation reaction by using the results of the performed kinetic analysis.

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The “Sol-gel under the solvent-saturated vapor atmosphere” (SSVA) method[21, 22] was

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initially employed in the present work for in-situ incorporation of silica into the colloidal network of novolac aerogel. The resultant novolac-silica hybrid aerogel was then exposed to high temperature under an inert atmosphere for interaction of carbon and silica and the formation of silicon carbide in the nanostructure of carbon aerogel.

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2. Experimental section 2.1 Materials

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Novolac resin powder (IP 502 Resitan Co. Iran) containing 9 wt. % hexamethylenetetramine (HMTA) was used as the organic monomer. Tetraethoxysilane (TEOS; Merck, Germany) was used as the inorganic component of precursors. 2-propanol (Dr. Mojallali Co. Iran) was used as

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solvent and hydrochloric acid (Merck, Germany) was used as catalyst of the hydrolysis reaction.

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2.2 Preparation of reinforced carbon aerogel

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In order to synthesize novolac-silica hybrid aerogel, two solutions of novolac (solution A) and

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TEOS (solution B) were first prepared separately in 2-propanol solvent with the final mass concentration of 30wt.%. Since the final solid content of 30wt.% is required for the hybrid

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aerogels, the weight loss of TEOS caused by the hydrolysis reaction were also intended for

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preparation of the solution B. The appropriate amount of HCl (as a catalyst) and distilled water according to TEOS:H2O:HCl molar ratios of 1:2:1.8×10-3 were added to solution B for

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completing the hydrolysis reaction. After stirring the solution B for 30 min, two solutions were

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equally mixed together and stirred for another 30 min. The sol-gel polymerization was performed in an autoclave at 120 oC for 5 h under the pressure of about 1.5 MPa. In order to develop this

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pressure, a small amount of the sol-gel solvent (2-propanol) was poured into the autoclave before sealing. The obtained gel was subsequently dried at ambient conditions for 48 h, followed by three high temperature drying steps at 90 oC and 120°C for 24 h and 140 oC for 4 h. The resultant hybrid aerogel (silica-novolac aerogel) was then heat treated at 1500oC for 5h with the heating rate of 5oC/min under the inert atmosphere of argon (100 ml/min) for the effective interaction of 5

carbon and silica and preparation of the reinforced carbon aerogel (RCA).The silicon carbide component is believed to be formed at this stage as a result of the carbo-thermal reduction process according to the following reaction[5, 23, 24]: 𝑆𝑖𝑂2 (𝑠) + 3𝐶(𝑠) → 𝑆𝑖𝐶(𝑠) + 2𝐶𝑂(𝑔)

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(1)

In order to determine the mass ratio of carbon to silica that is available for this reaction, the same heat treatment was also performed on novolac-silica aerogel at 800 oC for 2 h. Since no interaction is possible between silica and carbon at this temperature, the silica content can be determined after the oxidative removal of carbon phase. The resultant samples are named as

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carbon-silica aerogel. The neat carbon aerogel (CA) was also prepared with the initial

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concentration of 30 wt.% of the novolac solution and exposed to the same heat treatment at 1500 o

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C for comparison purposes.

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3. Characterization

Bulk density (𝜌𝑎 ) of the aerogel were calculated from the weight and geometrical sizes of the

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cylinder-shape samples. The true density (skeletal density, 𝜌𝑠 ) was determined by helium

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pycnometry (AccuPyc 1330, Micromeritics, USA). Porosity (𝜀)of the aerogel samples was calculated using the bulk and true density values (𝜀 = 1 − 𝜌𝑎 /𝜌𝑠 ). Linear shrinkage of the hybrid

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aerogel samples was determined from the diameters of the samples (D) before and after ambient pressure drying. The morphology and microstructure of the aerogels was investigated by Field

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Emission Scanning Electron Microscopy, FE-SEM, (TE-SCAN model MIRA3, USA). X-ray diffraction patterns were recorded in the range of 2𝜃 from 5° to 70°using a Philips XPert MPD diffractometer (made in USA) with CuKα radiation source. Fourier transform infrared spectroscopy (FTIR; PerkinElmer Spectrum 10.03.06, Germany) was used for getting

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information about the present bonds in the chemical structure of the prepared aerogels. Thermal oxidation of the aerogel samples were investigated by non-isothermal thermo-gravimetric analysis (TGA) up to 1200 ºC using a TGA 1Star System analyzer (Co. Mettler Toledo,

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Switzerland). Initially, about 8 mg of the sample powder was placed in alumina pans. The temperature was then increased at a constant rate under the air flow of 50 ml/min. The measurements were repeated at several heating rates (6, 10, 12, 15oC.min-1) for doing the subsequent kinetic analysis.

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4. Results

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4.1. Structural analysis

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Table 1 summarizes the physical characteristics of the novolac, novolac-silica and the

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corresponding heat-treated carbon-based aerogels. Generally, the samples containing the Sibased component shrink more in comparison with the same sample without this component

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because of the more shrinkable character of the silica network. The significant value of the

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skeletal density reported for the reinforced carbon aerogel can be a sign of formation of a denser

(Table 1)

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component rather than silica and carbon phase in the structure of this sample.

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In order to determine the carbon to inorganic phase ratio, the RCA sample was weighted and exposed to oxidation reaction at 600 oC for 2 h to burn off the free carbon phase. The carbon and inorganic phase content were then determined from the amount of loss and residual weight, respectively. The resultant ash was then treated with 2M NaOH solution at 60 oC for 2 h in order to remove the free silica phase. After this stage, the white silica particles were disappeared and a 7

dark suspension was obtained. The resultant suspension was then diluted and centrifuged at 5000 rpm for 20 min in order to separate the particles of silicon carbide. The obtained clear liquid on top was delicately poured off and replaced with fresh distilled water. After repeating the

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centrifuge process, the precipitated dark solid was dried and weighted in order to determine the silicon carbide content of the RCA sample. The result of the quantitative phase analysis was reported in table 2.

(Table 2)

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The uniform distribution of silica in cross-sectional area of the hybrid aerogels was evaluated by

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doing the Si-mapping from the fracture surface of the novolac-silica aerogel (not shown here).

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The silica distribution in longitudinal direction was also examined by cutting several small

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samples from the prepared silica-carbon aerogel and exposing them to oxidation reaction for

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removing the carbon phase. The standard deviation of 0.0074 was calculated for the silica

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content of the cut samples that confirms the uniform distribution of silica in longitudinal direction.

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Fig. 1 represents the XRD data for the neat (CA) and reinforced carbon aerogel (RCA) in addition to the RCA residue after oxidative removal of the free carbon (RCA-ash) and after

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treatment of the resultant ash with 2M NaOH solution for removing the unreacted silica phase (RCA-ash-OH treated). Two nearly broad peaks centered at 2θ values of 23 and 43° (pointed at

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by arrows) in the diffraction pattern of the CA sample are characteristics of the turbostratic carbon that is generally regarded as a variant of hexagonal graphite. Despite the ordered stacking structure of graphite, the graphene layers of the turbostratic carbon may randomly translate to each other and rotate about the normal of the graphene layers [25]. There are three hardly

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detectable peaks located at 2θ values of 43, 58 and 66° in the X-ray diffraction pattern of RCA sample that may be assigned to silicon carbide and/or to graphite crystals that.

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(Fig. 1)

No sharp diffraction lines with significant strength are visible in the X-ray diffraction pattern of this sample; the structure is therefore mainly amorphous with trace amount of very fine crystals. After removal of carbon from RCA sample, these peaks are disappeared and only one broad peak centered at 2θ value of 22° remains in the diffraction pattern of the RCA-ash sample which is

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characteristic of the vitreous silica. In order to remove the probable disturbing effect of silica in

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detecting the silicon carbide by the XRD analysis, the RCA-ash sample was treated with 2M

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solution of NaOH in order to remove the silica phase. The X-ray diffraction pattern of the

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separated particles (RCA-ash-NaOH treated) was shown in Fig. 1. The broad shape of the pattern at low angles beside the appearance of four new peaks with low intensity at 2θ values of 26, 30,

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32 and 39° indicate an amorphous form of SiC with tiny regions of crystalline phase. These

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visible diffraction lines are close to that reported by other researchers [26]. As seen from the X-

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ray pattern of "RCA-ash-NaOH treated" sample, the broad peak near to 22ᵒ has been disappeared that confirms the successful removal of the silica phase after treating the RCA-ash sample with

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NaOH solution.

Fig. 2 represents the FTIR spectra of the neat carbon aerogel (CA) and the reinforced one (RCA)

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in addition to the RCA residue after removal of the free carbon (RCA-ash) and free silica phase (RCA-ash-NaOH treated).

(Fig. 2)

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As seen from Fig. 2, three characteristic group peaks near 1100, 800 and 480 cm-1 are visible in the spectra of the silica, RCA and RCA-ash samples that are common to all polymorphs of SiO2 and correspond to the stretching and bending vibration modes of Si-O bonds. When the RCA

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sample cleaned from the unreacted silica and carbon phase, no peak with obvious strength was observed in these frequencies in the FTIR spectra of the residue. Instead, a broad bond was appeared near the 1007 cm-1 in the FTIR spectra of the ‘RCA-ash-NaOH treated’ sample and can be assigned to silicon carbide that was reported recently by other researches for the rhombohedral form of the silicon carbide [26]. According to a systematic study performed by

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Karbovnyk and et.al [18], the nanostructure morphology of silicon carbide has a clear influence

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on theIR absorbance spectra[27]. In order to get more information about the morphology of the

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aerogel samples, the FESEM analysis was performed on the CA and RCA and RCA-ash samples

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and the results were shown in Fig. 3. The morphology of the RCA sample is superficially similar to carbon aerogel with the difference that the colloidal particles become smaller in size in the

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structure of the RCA sample. Some larger particles with the plate like morphology is also

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observable in the FESEM image of RCA sample upon closer examination. Since, the similar

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plate like morphology is also present in the FESEM image of the neat carbon aerogel, these particles can be assigned to partial formation of graphite crystals formed during the high heat

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treatment at 1500 oC. Moreover, in accordance with this idea, these particles are disappeared

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from the structure of the RCA sample after oxidation at 600 oC as shown in Fig.3c.

(Fig. 3)

The pore structure of the CA, RCA and RCA-ash samples were evaluated by doing the nitrogen adsorption-desorption analysis and the resultant isotherms were shown in Fig. 4.Table 3

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summarizes some characteristics of the porous structures derived from theses isotherms using standard analysis methods. According to the IUPAC classification[28], all the isotherms are type IV

with the obvious character of presenting the hysteresis loopwhich is specific to mesoporous

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materials. The pore size distribution (PSD) curves, obtained by using the BJH method, were 𝑑𝑉𝑝

plotted as pore volume density ( 𝑑𝑟 ) versus the pore radius (𝑟𝑝 ) as shown in Fig. 4. In this way, 𝑝

the interference of the pore size inthe evaluation of the adsorbed gas volume is eliminated, so that the volume frequency of the pores will become comparable within the whole range of the pore size. The presence of the pores in the upper and lower limits of the pore size is predominant

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in the structure of the CA sample as evidenced by thehigh regions in the PSD curve.

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Incorporation of the Si-based refractory components in this sample yields an even PSD curvefor

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the RCA sample. This further leads to a 50% decline in both, the surface area and the total pore

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volume as reported in table 3. A considerable increase was observed in the surface area of the

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RCA sample after the removal of the free carbon phase. This can be assigned to the significant

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increase inthe pores with dimensions smaller than 5 nm in the structure of the RCA-ash sample

Fig. 4 Table 3

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in comparison with the RCA sample as confirmed by the PSD curves in Fig. 4.

4.2. Thermal analysis Thermal oxidation performance of the SiC reinforced carbon aerogel (RCA) was compared with the unreinforced one (CA) by doing the TG-DTG analysis and the results were shown in Fig. 5. The rate of weight loss (dµ/dT), as a sign of the oxidation rate, decreased in the presence of the 11

Si-based reinforcing agents, i.e. silica and silicon carbide, as evidenced by a nearly 40 % decline in the absolute maximum values of the DTG curves. In fact, the presence of the reinforcing agent not only delays the oxidation reaction but also reduces its overall rate. About 47% of the initial

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weight of the RCA sample remains after the thermal oxidation reaction at temperature up to 1200 o

C. This results overall confirm the effective role of the Si-based reinforcing agent in thermal

performance improvement of the carbon aerogels.

The conversion-temperature (α-T) curves were obtained using the TGA results of the RAC sample according to the following equation. 𝑚 −𝑚

𝛼(𝑇) = 𝑚0−𝑚𝑇

(2)

∞

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0

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Where m0, 𝑚∞ and mT represent the sample mass at the beginning, at the end and during the

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oxidation reaction, respectively.

(Fig.5)

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The apparent reaction rate, dα/dt, was calculated as a differential of the conversion degree versus time. The results at different heating rates were depicted in Fig.6. A bimodal shape with two

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different modes was appeared in the reaction rate curve versus temperature by increasing the heating rate from 12 to 15 oC/min. A similar behavior was also observed for the neat carbon

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aerogel, but at lower heating rate, i.e. 10 oC/min as shown in Fig.5. The appearance of the second mode in reaction rate curve suggests the multistep character of the oxidation reaction. This

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means that several processes with different kinetics are involved in the overall reaction that can be separated on a temperature scale only when the heating rate increases and reaches a special value. At low heating rates; these processes overlap that create only one mode in the reaction rate curve.

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(Fig.6)

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4.3. Kinetic analysis Kinetic study of solid state reactions is usually based on a general equation in which the reaction 𝑑𝛼

rate ( 𝑑𝑡 ) is expressed as the product of two independent functions: 𝑑𝛼 𝑑𝑡

= 𝑓(𝛼)𝑔(𝑇)

(3)

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The first function,𝑓(𝛼), denotes the kinetic model and the second represents the rate constant of

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the reaction that is not necessarily an Arrhenius-type equation. By using the Arrhenius

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temperature dependency for the rate constant in equation 3 and applying logarithms to it, the

𝑑𝛼

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differential isoconversional method suggested by Friedman is obtained[29]: 𝐸

ln (𝛽 𝑑𝑇 ) = ln(𝐴𝑓(𝛼)) − 𝑅𝑇𝑎

(4)

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Here β represents the heating rate, f(α) is the differential conversion function and A and Ea are

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the kinetic parameters of the Arrhenius relation which denotes the pre-exponential factor and the

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apparent activation energy, respectively. By integrating from equation 2 after replacing the Arrhenius relation, the general form of integral isoconversional methods is obtained. Depending

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on the approximation used for the temperature integral, the FWO or KAS methods are obtained. The FWO method uses the Doyle approximation of the temperature integral which results in the

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following final equation[30, 31]: 𝐴𝐸

𝐸

𝑎 𝑙𝑛𝛽 = 𝑙𝑛 𝑅ℎ(𝛼) − 5.331 − 1.052 𝑅𝑇𝑎

(5)

Where ℎ(𝛼) denotes the integral conversion function. The integral method of KAS uses the Coats-Redfern approximation of the temperature integral which leads to equation 6[32, 33]:

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𝛽

𝑙𝑛 𝑇 2 = 𝑙𝑛 𝐸

𝐴𝑅

𝑎

𝐸

− 𝑅𝑇𝑎 ℎ(𝛼)

(6)

The plot of the left side of the aforementioned equations (eq. 4-6) versus 1/𝑇, obtained from TG curves recorded at several heating rates, is expected to result in an straight line which from its

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slope the apparent activation energy can be calculated for every value of 𝛼. The kinetic study of the thermal oxidation reaction of RCA sample was performed using the TG data obtained in air atmosphere at four heating rates: 6, 10, 12 and 15 oC/min. Three isoconversional methods, a differential (Friedman) and two integral ones (FWO and KAS), were applied in order to determine the change in apparent activation energy with progress of the oxidation reaction. An

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alternative isoconversional method proposed by Vyazovkin was also applied for the more

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minimization of the following non-linear equation:

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accurate determination of the apparent activation energy. This method is based on the

∑𝑛𝑖 ∑𝑛𝑗≠𝑖[𝐼(𝐸𝛼 , 𝑇𝛼,𝑖 )𝛽𝑗 ]/[𝐼(𝐸𝛼 , 𝑇𝛼,𝑗 )𝛽𝑖 ] = 𝑚𝑖𝑛

(7)

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Where n denotes the number of heating rates, 𝑇𝛼,𝑖 is the temperature corresponding to the α value

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at heating rate equal to 𝛽𝑖 and 𝐼(𝐸𝛼 , 𝑇𝛼,𝑖 ) is the temperature integral that can be found with the

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help of the accurate Senum-Yang approximation. The 𝐸𝛼 values that minimizes the equation 6 gives the apparent activation energy at a certain conversion degree[15].

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The validity of the isoconversional methods in the applied range of heating rates was evaluated by checking the linearity of thee quations 4 to 6. The results were shown in Fig.7 for two

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different ranges of heating rates, the first that contains only the heating rates with the corresponding unimodal reaction rate as shown in Fig.6 and the second that covers all of them. The plotted curves were obtained for α range between 0.04 and 0.96 with a α variation step of 0.06. The contribution of the data related to the highest heating rate for which the bimodal shape

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of the reaction rate is appeared, leads to the significant deviation from the linear behavior in isoconversional methods as shown in Fig.7b. It has been confirmed that in multistep processes with competitive reactions, the obtained activation energy from isoconversional methods are

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strongly dependent on the range of heating rates used for doing the thermo-analytical experiments [13]. The isoconversional methods are based on the reality that for a given degree of conversion, the kinetic function, 𝑓(𝛼), and so the reaction mechanism doesn’t depend on the heating rate. Thus, the observed deviation from the straight line is likely because of the change

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(Fig.7)

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indominant mechanism of oxidation reaction with increasing the heating rate.

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The results of applying the above-mentioned isoconversional techniques for calculation of the

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activation energy are shown in Fig. 8. The substantial change of the apparent activation energy,

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obtained from these methods, discloses the complexities in the oxidation reaction kinetic of the

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RCA sample. In other words, the thermal oxidation of the RCA sample is a multistep process in which the contribution of the processes involved in the global kinetic is varying with progress of

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reaction. The average values of the apparent activation energy related to each method is reported in Table 4 in order to compare these results later with the ones obtained from the NPK analysis.

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The method of KAS and FWO yield nearly the same results that are also in accordance with the

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Vyazovkin method at α value higher than 0.2. The Friedman method yields an average activation energy that is much smaller than that from the other isoconversional methods. The high values (up to 50 % for Friedman method) reported for the standard deviation confirms the considerable change in activation energy with progress of the oxidation reaction.

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(Fig.8)

(Table 4)

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The kinetics of the thermal oxidation of the RCA sample was also analyzed by the NPK method. This method allows the separation of the degree of conversion,𝑓(𝛼), andtemperature, 𝑔(𝑇), functions by the direct use of TG data and without any previous assumption about their functionality. This method starts with construction of some overlapping sub-matrixes using the thermo-analytical data. The singular value decomposition (SVD) algorithm is then applied on

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each sub-matrix which results in two orthonormal matrixes, named as 𝑈𝑖 and 𝑉𝑖 , and a diagonal

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matrix with singular values elements, named as 𝑊𝑖 , for each sub-matrix. If the first singular

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value is much bigger than the rest, then only the first column of the 𝑈𝑖 and 𝑉𝑖 , respectively called

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𝑢𝑖 and 𝑣𝑖 , and the first singular value, called 𝑤𝑖 , are chosen. To ensure continuity of the resultant vectors 𝑢𝑖 and 𝑣𝑖 , the first vector has to multiplied by a suitable factor 𝜑𝑖 and the corresponding

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vector 𝑣𝑖 has to be divided by the same factor. This is why the overlapping sub-matrixes were

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chosen at first. By doing this procedure, the final 𝑢𝑓 and 𝑣𝑓 vectors, that are respectively

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proportional to 𝑓(𝛼) and 𝑔(𝑇) functions, can be expressed according to the following equations:

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𝒖𝒇 = (𝒖𝟏 𝜑2 𝒖𝟐 . . . 𝜑𝑞 𝒖𝒒 ) 𝒗𝒇 = (𝑤1 𝒗𝟏

𝑤2 𝜑2

𝒗𝟐 . . .

𝑤𝑞 𝜑𝑞

(8)

𝒗𝒒 )

(9)

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Where 𝜑1 has been fixed equal to one. In the present work, the NPK algorithm was written in Matlab software in order to determine the kinetic parameters of the oxidation reaction of the RCA samples. The values of the 𝑢𝑓 and 𝑣𝑓 vectors, derived from NPK analysis, are then used respectively for calculation of the kinetic

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model and the rate constant values of the oxidation reaction by fitting the conventional models to the data points using SAS (JMP) software. Following the principles of the NPK method, the data obtained from the TG analysis was

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organized in overlapping sub-matrixes using two different ranges of heating rate as indicated in Fig. 9. Because of the change in reaction control mechanism by increasing the heating rate from 12 to 15 oC/min, as evidenced by the isoconversional analysis, the selective method of arranging

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(Fig.9)

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the sub-matrixes is believed to influence the result of the NPK algorithm.

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The method for setting the sub-matrix members has also been shown in Fig.9c. The sub-matrixes

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were selected in such a way that two successive sub-matrixes overlap each other by two and three lines with a conversion variation step of 0.025.

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Applying the SVD algorithm on each 35 selected sub-matrixes from the first range of heating

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rate (Fig.9a) results in 35ui and wivi vectors that are shown in Fig.10 (parts a and c). It should be noted that, for each sub-matrix, the first singular value, wi, accounts for more than 96% of the

EP

sum of the non-zero singular values of the 𝑊𝑖 vector. So, just the first singular values of the 𝑊𝑖

CC

vectors were selected in the NPK algorithm. The overlapping members of the two successive sub-matrixes were used for finding the average values of the vertical transformation factor, i.e.

A

𝜑𝑖 , for each 𝒖𝒊 vector. Fig.10b. shows the final continuous 𝒖𝒇 vector that is proportional to the conversion function, f(α). Forcing the 𝒖𝒊 vectors to become continuous by using the appropriate factor (𝜑𝑖 ), results in the branched shape of the 𝒗𝒇 vector, even after using the suitable factor (1/𝜑𝑖 ) defined in the NPK algorithm for each 𝑤𝑖 𝒗𝒊 vector, as shown in Fig.10d.

17

(Fig.10)

A set of kinetic models that are conventionally used in studying the solid-state reactions[34] were constructed in JMP software for finding the best fitted model to 𝒖𝒇 data. Fig.11 shows the result

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of the best fitted line for three kinetic models of Nomen-Sempere, Sestak-Berggren and JohnsonMehl-Avrami-Erofeyev-Kolmogorov (JMAEK) that gives the lowest RMSE values among the other kinetic models. Since the 𝒖𝒇 vector is proportional to the conversion function, a constant coefficient, c, was applied in all kinetic models in fitting procedure that is subsequently used to

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obtain the corrected g(T) function.

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Table 5 reports the results of the fitting of three kinetic models to NPK-derived conversion

A

function. Although the Sestak-Berggren model showed the best fit (according to RMSE value),

M

but the physical significance of its parameters and the underlying mechanism has not yet been proposed for this model. So, the Nomen-Sempere model seems to be the most suitable model for

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TE

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describing the kinetic of the thermal oxidation reaction of the RCA sample.

(Fig.11)

(Table 5)

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The m and n parameters in this model are reaction orders suggesting the contribution of physical and chemical phenomena to the overall reaction kinetic, respectively [35]. Because of the highly

A

porous character of the RCA structure, the physical phenomena, such as diffusion, seem to play a determinant role in the reaction kinetic. This is evidenced by the significant value of the m parameter which is also larger than the n parameter value in the Nomen-Semper kinetic model. Fig.12 shows the NPK-derived g(T) function and the two best-fit lines of Arrhenius to the first and second branch of this function. Table 6 lists separately the values of the fitted parameters 18

and their approximate standard errors in addition to RMSE for these fittings. Upon closer examination, the present points in the first branch of the g(T) function was realized in relation to the heating rate of 6 oC/min. Actually, at heating rate as low as 6 oC/min, where the diffusional

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limitations are less important, a monotonous increase was observed in the first branch of the g(T) function with increasing the temperature until the complete removal of the free carbon phase from the RCA sample. At higher heating rates, the diffusional limitations become significant especially at higher temperatures which causes the g(T) function to goes through a nearly constant value after the initial increase. According to the reported RMSE value in table 6, the

U

rate constant values in the first branch of g(T) function can be very well approximated with an

N

Arrhenius relation as shown in Fig.12. The reported value of the activation energy for the first

A

branch of g(T) is in accordance with the average values estimated by the isoconversional

M

methods, except Fridman method, as reported in Table 4. Although the Arrhenius relation again show an appropriate fitting to the second branch of the g(T) function (according to RMSE value

TE

(Fig.12)

(Table6)

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depicted in Fig.12.

D

in Table 6), but it can’t predict the tendency of the rate constant to reach a constant value as

The NPK algorithm was also applied on the sub-matrixes arranged using the whole range of

A

heating rate (see Fig.9b) in order to check the influence of incorporating the data related to heating rate of 15 oC/min, with the corresponding bimodal reaction rate, on the kinetic analysis results. The resultant 𝒖𝒇 and 𝒗𝒇 vectors are shown in Fig.13 parts a and b, respectively. The same as before, applying the appropriate factor (𝜑𝑖 ) to make the ui vectors continuous, results in

19

some discontinuity in vi vectors even after using the defined factor (𝑤𝑖 /𝜑𝑖 ) in the NPK algorithm. In fact, at different values of the heating rate the overall rate of oxidation seems to be affected by the diffusional limitations in a different manner. This results in branching the g(T)

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function by separating the points corresponding to each specified column from the initial selected sub-matrixes for the NPK analysis as shown in Fig. 9c. (Fig.13) 5. Discussion

During the thermal oxidation reaction of the RCA sample, an excess layer composed of the Si-

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based refractory phase components (silica and silicon carbide) is formed on top of the surface as

N

shown in Fig. 14. In this situation, the continuance of the oxidation reaction requires the

A

diffusion of oxygen molecules in this layer before reaching the reaction zone. In fact, at any

M

temperature above the onset of the oxidation reaction (𝑇 > 𝑇0 ) there is a top-oxidized and an

D

intact layer that are exposed to the oxidation process. The weight loss of the RCA sample during

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the non-isothermal oxidation occurs at two different temperature intervals as shown in Fig. 15.

Fig. 14 Fig. 15

A

The major weight loss happens in the first temperature interval (500-700 ºC) which is mainly due to the carbon phase oxidation. Although the oxidation of the SiC phase is also possible at this temperature interval[36, 37], the resulting weight loss is very small compared to that due to the carbon phase oxidation. This is confirmed by the considerable decline in the slope of the weight

20

loss curve versus temperature in the second temperature interval (700-1200 ºC). Actually, the active oxidation of the silicon carbide phase in this temperature range results in only two percent of the total weight loss. So, it seems reasonable to approximate the diffusive properties of the

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top-oxidized and the intact layers by doing the adsorption-desorption test on the RCA-ash and RCA samples, respectively. The evolution of the top-oxidized layer during the oxidation reaction of the RCA sample beside the less total pore volume of this sample compared to the CA one (see table 3) impose more diffusional limitations on the global reaction kinetics. This leads one to expect the bimodal nature of the reaction rate of the RCA sample to occur at the lower heating

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rate than that for the CA sample. But, this is not the case according to the Fig. 6 where the

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second mode appears at the heating rate of 15 ºC/min which is higher than that for the CA

A

sample (see Fig. 5). So, this behavior is more attributable to the considerable decrease in the

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reaction rate of the RCA sample compared to the CA one, rather than to their pore structure, which results in the production of the lower amounts of the generated gases in the same

D

temperature interval.

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The decreasing trend of Eα with α, obtained by isoconversional methods (see Fig. 8), is a sign of

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the occurrence of the simultaneous processes with varying contribution during the thermal oxidation reaction of the RCA sample. These processes can be separated kinetically by

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increasing the heating rate up to 15 ºC/min, which results in the appearance of the second mode in the reaction rate curve (see Fig. 6) and the strong deviation from the linear behavior in

A

isoconversional methods as seen in Fig. 7b. The shape of the Eα dependency to α, suggests the possible kinetic scheme involving the reactions complicated by diffusion [38]. Thus, the diffusion process beside the intrinsic chemical reaction (oxidation of C and SiC components) are considered as the important processes included in the overall reaction kinetic. This was

21

confirmed by the result of the NPK method where the two parameter model of Nomen-Sempere provided the best fit to the resulting f(α) function. The estimated parameters (see table 5) denote the relative contribution of the processes with physical and chemical nature in the overall

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reaction kinetic, respectively. The highly porous character of the RCA sample makes the effect of the diffusion phenomena more significant which causes the rate constant values of the oxidation reaction to be more influenced by the reaction conditions such as the heating rate. This seems to be responsible for the branched shape of the g(T) function derived by the NPK method which makes it possible to

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differentiate between the rate constant values of the reaction-control and diffusion-control

N

regimes of the oxidation reaction. At low heating rate, such as 6 oC/min, where there is more

A

time for the reactant and generated gases to diffuse into and outside of the porous structure of the

M

aerogel, a continuous increase is observed in the rate constant values without any plateau state as shown with triangle marker in Fig.13b. In this case, the oxidation reaction seems to be controlled

D

by the intrinsic chemical reaction (mainly between carbon and oxygen) and the overall rate of

TE

oxidation is not seriously influenced by the diffusional limitations. The temperature functionality

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of the rate constant, at this condition, is best approximated by an Arrhenius relation. By increasing the heating rate (such as 10 and 12 oC/min), the global oxidation kinetic seems to be

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more influenced by the diffusional limitations which causes the rate constant to reach a plateau at higher temperatures which cannot be predicted by an Arrhenius relation. At higher heating rate

A

such as 15 oC/min, the rate constant decreases after the initial increase and after reaching the plateau state as shown with square marker in Fig.13.b. In this case, the chemical reaction control and the diffusion control regimes are separated on the temperature scale. The matching of the

22

rate constant values corresponding to heating rates of 6 and 15 oC/min at low temperature range is a confirmation for the proposed mechanism.

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6. Conclusion

The thermal stability especially the oxidation resistance of the carbon aerogels was improved by silicon carbide incorporation using the sol-gel polymerization under the solvent-saturated vapor atmosphere. A 40 % decline in the overall rate of oxidation was observed for the reinforced

U

carbon aerogel (RCA) in comparison with the unreinforced one. The results of the NPK analysis

N

and isoconversional methods confirm the determinant role of the diffusion process in the overall

A

oxidation reaction kinetic of the RCA sample because of its highly porous structure. This

M

structural feature further results in the strong effect of the reaction condition such as the heating rate on the reaction pathway. Applying the NPK analysis enables one to differentiate between the

D

rates constant values of the reaction-control and diffusion-control regimes of the oxidation

TE

reaction. According to the obtained results, it is finally recommended that the range of heating

EP

rates for performing the multi-curve methods of kinetic analysis for highly porous solids are selected so that the corresponding reaction rate curves show only one mode. This is due to the

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unusual results obtained from the isoconversional methods if both of heating rates related to

A

single and binary modes in reaction rate curves are selected. Acknowledgement The authors would like to thank Tarbiat Modares University and Iran Nanotechnology Initiative Council (INIC) for supporting this research work.

23

Refrences

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[1] A. Allahbakhsh, A.R. Bahramian, Self-assembled and pyrolyzed carbon aerogels: an overview of their preparation mechanisms, properties and applications, Nanoscale, 7 (2015) 14139-14158. [2] J. Biener, M. Stadermann, M. Suss, M.A. Worsley, M.M. Biener, K.A. Rose, T.F. Baumann, Advanced carbon aerogels for energy applications, Energy & Environmental Science, 4 (2011) 656-667. [3] M. Wiener, G. Reichenauer, S. Braxmeier, F. Hemberger, H.P. Ebert, Carbon Aerogel-Based High-Temperature Thermal Insulation, International Journal of Thermophysics, 30 (2009) 13721385. [4] M.M. Seraji, S. Kianersi, S.H. Hosseini, J. Davarpanah, S. Elahi, Performance evaluation of glass and rock wool fibers to improve thermal stability and mechanical strength of monolithic phenol-formaldehyde based carbon aerogels, Journal of Non-Crystalline Solids, 491 (2018) 8997. [5] N.S. Ghafoorian, A.R. Bahramian, M.M. Seraji, Investigation of the effect of rice husk derived Si/SiC on the morphology and thermal stability of carbon composite aerogels, Materials & Design, 86 (2015) 279-288. [6] M.M. Seraji, N.S. Ghafoorian, A.R. Bahramian, A. Alahbakhsh, Preparation and characterization of C/SiO 2/SiC aerogels based on novolac/silica hybrid hyperporous materials, Journal of Non-Crystalline Solids, 425 (2015) 146-152. [7] H. Mei, S. Farhan, D. Han, G. Liu, Z. Wang, G. Zhao, Mechanical, structural and oxidation resistance enhancement of carbon foam by in situ grown SiC nanowires, Ceramics International, 42 (2016) 4723-4733. [8] X. Wu, G. Shao, X. Shen, S. Cui, X. Chen, Evolution of the novel C/SiO2/SiC ternary aerogel with high specific surface area and improved oxidation resistance, Chemical Engineering Journal, 330 (2017) 1022-1034. [9] J. Prakash, P. Sarkar, J. Bahadur, K. Dasgupta, Effect of in-situ grown SiC nanowire and dense SiC on oxidation resistance of carbon fiber/SiC nanowire/SiC matrix composite in high temperature atmospheric environment, Corrosion Science, 135 (2018) 46-56. [10] J. Dai, J. Sha, J. Shao, Y. Zu, M. Lei, S. Flauder, N. Langhof, W. Krenkel, In-situ growth of SiC nanostructures and their influence on anti-oxidation capability of C/SiC composites, Corrosion Science, 124 (2017) 71-79. [11] R. Naslain, A. Guette, F. Rebillat, S. Le Gallet, F. Lamouroux, L. Filipuzzi, C. Louchet, Oxidation mechanisms and kinetics of SiC-matrix composites and their constituents, Journal of Materials Science, 39 (2004) 7303-7316. [12] Y. Shi, K. Tushtev, J.M. Hausherr, D. Koch, K. Rezwan, Oxidation kinetics and its impact on the strength of carbon short fiber reinforced C/SiC ceramics, Advanced Engineering Materials, 15 (2013) 19-26. [13] J. Criado, P. Sánchez-Jiménez, L. Pérez-Maqueda, Critical study of the isoconversional methods of kinetic analysis, Journal of Thermal Analysis and Calorimetry, 92 (2008) 199-203. [14] P. Simon, Isoconversional methods, Journal of thermal analysis and calorimetry, 76 (2004) 123-132. [15] S. Vyazovkin, Advanced isoconversional method, Journal of thermal analysis, 49 (1997) 1493-1499.

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[16] A. Seifi, A.R. Bahramian, A. Sharif, Correlation between structure and oxidation behavior of carbon aerogels, Journal of Energy Storage, 7 (2016) 195-203. [17] R. Serra, R. Nomen, J. Sempere, The non-parametric kinetics a new method for the kinetic study of thermoanalytical data, Journal of thermal analysis and calorimetry, 52 (1998) 933-943. [18] R. Serra, J. Sempere, R. Nomen, A new method for the kinetic study of thermoanalytical data:: The non-parametric kinetics method, Thermochimica acta, 316 (1998) 37-45. [19] J. Sempere, R. Nomen, R. Serra, Progress in non-parametric kinetics, Journal of thermal analysis and calorimetry, 56 (1999) 843-849. [20] J. Sempere, R. Nomen, R. Serra, J. Soravilla, The NPK method: an innovative approach for kinetic analysis of data from thermal analysis and calorimetry, Thermochimica acta, 388 (2002) 407-414. [21] I. Naseri, A. Kazemi, A.R. Bahramian, M. Razzaghi Kashani, Preparation of organic and carbon xerogels using high-temperature-pressure sol-gel polymerization, Materials & Design, 61 (2014) 35-40. [22] M.M. Seraji, A. Seifi, A.R. Bahramian, Morphology and properties of silica/novolac hybrid xerogels synthesized using sol-gel polymerization at solvent vapor-saturated atmosphere, Materials & Design, 69 (2015) 190-196. [23] N. Leventis, A. Sadekar, N. Chandrasekaran, C. Sotiriou-Leventis, Click synthesis of monolithic silicon carbide aerogels from polyacrylonitrile-coated 3D silica networks, Chemistry of Materials, 22 (2010) 2790-2803. [24] Y. Kong, Y. Zhong, X. Shen, L. Gu, S. Cui, M. Yang, Synthesis of monolithic mesoporous silicon carbide from resorcinol-formaldehyde/silica composites, Materials Letters, (2013). [25] Z. Li, C. Lu, Z. Xia, Y. Zhou, Z. Luo, X-ray diffraction patterns of graphite and turbostratic carbon, Carbon, 45 (2007) 1686-1695. [26] İ.A. Kari̇ per, The Synthesis of Silicon Carbide in Rhombohedral Form with Different Chemicals, Metallurgical and Materials Transactions A, 48 (2017) 3108-3112. [27] P.S. I. Karbovnyk, A. Huczko, M.C. Guidi, C. Mirri, and, A.I. Popov, FTIR studies of silicon carbide 1D-nanostructures, Mater. Sci. Forum, 821-823 (2015) 261-264. [28] K.S. Sing, R.T. Williams, Physisorption hysteresis loops and the characterization of nanoporous materials, Adsorption Science & Technology, 22 (2004) 773-782. [29] H.L. Friedman, New methods for evaluating kinetic parameters from thermal analysis data, Journal of Polymer Science Part C: Polymer Letters, 7 (1969) 41-46. [30] J. Flynn, L. Wall, Thermal analysis of polymer by thermogravemetric analysis, J. Res. Natl. Bur. Stand. Sect. A, 70 (1966) 487. [31] T. Ozawa, A new method of analyzing thermogravimetric data, Bulletin of the chemical society of Japan, 38 (1965) 1881-1886. [32] T. Akahira, Trans. Joint convention of four electrical institutes, Res. Rep. Chiba Inst. Technol., 16 (1971) 22-31. [33] H.E. Kissinger, Reaction kinetics in differential thermal analysis, Analytical chemistry, 29 (1957) 1702-1706. [34] A. Khawam, D.R. Flanagan, Solid-state kinetic models: basics and mathematical fundamentals, The journal of physical chemistry B, 110 (2006) 17315-17328. [35] J. Šesták, G. Berggren, Study of the kinetics of the mechanism of solid-state reactions at increasing temperatures, Thermochimica Acta, 3 (1971) 1-12. [36] J. Quanli, Z. Haijun, L. Suping, J. Xiaolin, Effect of particle size on oxidation of silicon carbide powders, Ceramics international, 33 (2007) 309-313. 25

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[37] R. Vaben, D. Stöver, Oxidation of ultrafine (Si-) SiC powders, Journal of materials science, 29 (1994) 3791-3796. [38] S. Vyazovkin, A unified approach to kinetic processing of nonisothermal data, International Journal of Chemical Kinetics, 28 (1996) 95-101.

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Fig. 1: X-ray diffraction pattern of the neat carbon aerogel and the reinforced one processed at

A

1500 oC. Data are also depicted separately for the RCA sample after removal of the free carbon

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(at 600 oC in air) and after treating the resulting ash with 2M NaOH solution

27

Fig. 2: FTIR spectra of the reinforced carbon aerogel before and after removal of free carbon at 600 oC in air and the following treatment of the resulting ash with 2M NaOH solution. The spectra for silica sample relates to the silica xerogel exposed at the same heat treatment at 1500 o

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C.

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Fig. 3: FESEM images of the a) CA, b) RCA sample and c) the resulting ash after removal of the

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A

free carbon phase at 600 oC

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Fig. 4: Nitrogen adsorption-desorption isotherms for the CA, RCA and RCA-ash samples and the corresponding pore size distribution curves derived from these isotherms using BJH method

28

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Fig.5: TG-DTG results at heating rate of 10 oC/min for the thermal oxidation reaction of neat

M

A

N

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(CA) and reinforced (RCA) carbon aerogels (𝜇 = 𝑚/𝑚0 × 100)

D

Fig.6: Rate of oxidation and conversion versus temperature curves for RCA sample at several

A

CC

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heating rates

29

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Fig.7: The validity of the linearized form of three isoconversional methods using the TG data at

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heating rates corresponding to a) unimodal (6, 10 and 12 oC/min) and b) unimodal and bimodal

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shape of the reaction rate (6,10,12 and 15 oC/min)

30

Fig.8: Change of the apparent activation energy with degree of oxidation conversion calculated by several isoconversional methods (only the heating rates related to unimodal shape of reaction

A

N

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rates were selected)

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Fig.9: Two method of arranging the sub-matrices from α - T curves of the RCA sample by using

D

a) first range (6,10 and 12oC/min) and b) second range of heating rates (6, 10, 12 and 15oC/min)

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for doing the NPK analysis. A typical sub-matrix with its members was depicted in part c. The

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red circles show the experimental data and the blue ones show the interpolated points

31

Fig.10: The 𝒖𝒊 and 𝑤𝑖 𝒗𝒊 vectors derived from applying the SVD algorithm on each sub-matrices showed in Fig. 8 (parts a) and the corresponding uf and vf vectors after applying the suitable

U

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factor for continuity purpose (parts c and d, respectively)

N

Fig.11: The uf vector determined from the NPK method (circles) and the best-fitted kinetic

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D

M

A

models of the oxidation reaction

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Fig.12: The best fitted Arrhenius lines to the first and second branch of the g(T) function derived

A

from the NPK analysis for thermal oxidation reaction of the RCA sample

32

Fig.13: The resultant 𝒖𝒇 and 𝒗𝒇 vectors from applying the NPK analysis on the sub-matrixes

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arranged using the whole range of heating rates

D

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A

N

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Fig. 14: The oxidation scheme of the RCA sample during the non-isothermal oxidation reaction

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Fig. 15: Two stages of the weight loss during the non-isothermal thermal oxidation of the RCA sample

33

Table 1: characteristics of the silica-novolac and carbon-based aerogels Shrinkage1 (%)

Apparent density (g cm-3)

Skeletal density (g cm-3)

Porosity (%)

Novolac aerogel

No shrinkage

0.309

1.180

73.81±0.01

Novolac-silica aerogel

24.57±0.02

0.420

1.637

75.15±0.01

SiC reinforced carbon aerogel, RCA

38.91±0.02

0.530

2.703

80.39±0.01

Relative to diameter of the mold (1.465 cm)

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A

N

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1.

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Sample

34

Table 2: The phase analysis of the RCA sample Free carbon phase (%)

SiC phase (%)

RCA

50

35.62

Unreacted silica content (%) 14.38

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Sample

Table 3: Characteristics of the porous structure of the CA, RCA and RCA-ash samples derived from nitrogen adsorption-desorption analysis

35

RCA

RCA-ash

CA

BET surface area (m2 g -1)

35.95

93.20

70.39

Total pore volume (cm3g -1)

0.43

0.68

0.83

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Sample

Table 4: The average values of the apparent activation energy calculated by isoconversional methods Method

Average Ea (kJ mol-1)

Standard deviation

FWO KAS

94.25 83.68

22.69 24.58 36

76.62 48.74

12.67 24.00

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Vyazovkin Freidman

Table 5 Values of the fitted parameters and RMSE for three best-fit kinetic models

Model

𝒇(𝜶)

Parameter

Estimate of the best fit

NomenSempere

𝜶𝒎 (𝟏 − 𝜶)𝒏

m n

0.3903 0.1521

37

Approximate standard error 0.0087 0.0072

RMSE 0.0154

(

𝒏(𝟏 − 𝜶)[− 𝐥𝐧(𝟏 − 𝜶)]

𝒏−𝟏 ) 𝒏

m n

2.1427 -0.3390

0.0119 0.2341 0.0857

p

-1.9216

0.2257

c

1.0896

0.0244

n

1.8041

0.0509

c

0.8879

0.0185

0.0118

0.0695

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A

N

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JMAEK

𝜶𝒎 (𝟏 − 𝜶)𝒏 (− 𝐥𝐧(𝟏 − 𝜶))𝒑

0.9202

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SestakBerggren

c

A

Table 6: Values of the fitted parameter and RMSE for the best fitted Arrhenius model to g(T) function after applying the correction factor on vf vector Approximate standard Model Parameter Estimate of the best fit RMSE error Ea (kJ/mol) 58.0080 0.7434 Arrhenius 0.0000727 (second branch) A (1/s) 2.6103 0.2418 Arrhenius (first branch)

Ea (kJ/mol)

88.650

0.7603

A (1/s)

170

16.8694

0.0000221

38

39

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M