Potentialities of mass spectrometry on activation energy and secondary reactions determination of calcium oxalate thermal decomposition

Correspondence M.Grigiante,Department ofCivil and Environmental Engineering,University of Trento,ViaMesiano 77, 38123, Trento, Italy Email:maurizio.grigiante@unitn.it Abstract This work investigates the potentialities of the thermal analysis (TA) coupled with the mass spectrometry (MS) technique by studying the thermal decomposition of calcium oxalate monohydrate (CaC2O4⋅H2O). The aim of this work is twofold: to demonstrate, at first, the efficacy of coupling the thermal gravimetric (TG)-MS experimental approach to check the presence of intermediate reactions beyond the conventional three-step decomposition: dehydration, decarbonylation, and decarbonation; second, to test the reliability of different modeling approaches in determining the activation energy (E) including, as innovative alternative, the use of theMS signals. The TA is carried out at selected constant heating rates by recording both the thermal gravimetric analysis, differential thermal analysis) profiles, and, simultaneously from the MS data, the signals of the total ion current and the ion currents selected to monitor the release of the H2O, CO, and CO2 species. These experimental results are effective in determining the E through different modeling approaches based on the maximum reaction rate method and isoconversional procedures including both TG and MS signals. Coupling the TA-MS technique has allowed us to check the concurrent presence of the dismutation reaction of carbon monoxide, occurring during the decarbonylation event, and to determine the corresponding E value (E = 169.7 kJ/mol). These results present a surprising correlation between the global enthalpy of the two reactions involved in this second step and their activation energy values. On the whole, the results satisfy the conventional constraints usually adopted to test the reliability of the E results and are consistent with the majority of the datasets published in the literature on this subject.


INTRODUCTION
Studies on reactions involving solid materials represent a difficult task due to the great variety of factors having different impacts on solid-state reconstruction, diffusion of reaction products and reagents, materials properties, and physical state of the evolving solid-state surface. The experimental techniques involving thermal analysis (TA), including thermogravimetric analysis (TGA), differential thermal analysis (DTA), represent a universal and effective approach for investigating the kinetics of the thermal degradation of solids. Nevertheless, isothermal TGA measurements cannot rigorously be carried out due to the unavoidable presence of finite nonisothermal heat-up time associated with this constraint. At higher temperatures, before reaching the isothermal regime, significant degradations can be observed while, at lower temperatures, a complete conversion can be achieved only by accepting a long reaction time. In addition, at slow heating rates, the weight loss during heat-up time can affect significantly the results of kinetics elaboration. 1,2 Therefore, at an isothermal regime, the nonzero extent of conversion appears particularly critical and the investigations have to be carried out carefully. In constant heating rate analysis, these problems can be avoided by starting at a temperature reasonably below that at which the thermal decomposition starts. 3 The authors are aware that in kinetics it is a good practice to propose a combination of nonisothermal and isothermal analysis. Nevertheless, considering the focus of this work, TA has been limited to a constant heating rate in view of proposing an extended elaboration on further planned investigations. Under the nonisothermal TGA constraint, quantitative methods can be used to determine kinetic parameters from the TGA curves of which the achievement of the activation energy (E) and the preexponential factor (A) represents the main pursued task. Numerous approaches, including the model-fitting method, 4,5 model-free method, 6,7 and distributed activation energy model method 8,9 have been applied to various kinetic studies.
Coupling the TA with the gas analysis evolving during thermal degradation provides relevant advantages since mass changes can be correlated with the identity of a gaseous volatile compound released during a specific thermal event. [10][11][12] Among these techniques, TGA coupled with mass spectrometry (TG-MS) can achieve real-time and sensitive detection of evolved gases [13][14][15][16][17] including quantitative information regarding gas product compositions 13,14 as a result of integration elaboration of the evolution profiles for all the detected species. Thus, TG-MS has revealed a precise and sensitive method to investigate the release patterns and identities of volatile components evolving from a multitude of thermal degradation processes as recently proved for coal, 13,15,18 biomass, 17 municipal solid waste, 9 and other materials. [18][19][20][21] The TG-MS techniques have been utilized in some of the cited works to detail specific thermal trends: Han et al. 15 discovered that the most prominent peaks of gaseous products evolving during thermal decomposition of lignite samples range from 400 to 700 • C; Wang et al. 16 reported the characteristics of gas production by hydrocarbons (HCs) and nonhydrocarbons (nonHCs) during coal pyrolysis and determined its late gas generation potential through TG-MS. To the knowledge of the authors, the use of the TG-MS technique to calculate the kinetic parameters of the solid decomposition is not usually performed since it is mainly utilized to analyze the thermal decomposition data pertaining to the evolved gas phase. Only in a limited number of cases, it is applied to investigate the kinetic parameters of the gaseous species as done by Seo et al. 11 and Nelson et al. 22 for volatiles compounds evolving during coal pyrolysis using single and parallel models.
This work is determined to enhance the potentialities of the TG-MS technique by investigating, as a case test, the thermal decomposition of the calcium oxalate monohydrate (CaC 2 O 4 ⋅H 2 O) and, specifically, it aims to 1. exploit the MS signals to set up an alternative procedure to calculate the E for each single reactions involved in the thermal decomposition of the selected solid besides the apparent E related to the whole event; 2. to make evident the fundamental role of the MS analysis in providing a more correct interpretation of the chemical events occurring during the thermal decomposition of the solids that cannot be completely described by limiting the elaborations only to the signals coming out from the TA.
Regarding the selected compound, two calcium oxalate hydrate forms, referred to as whewellite and weddellite, are the most common. The whewellite, also known as calcium oxalate monohydrate (COM) and here utilized, is the most thermodynamically stable phase. Weddellite, known as calcium oxalate dihydrate (COD), is the metastable form at room temperature while the third hydrate form, indicated as calcium oxalate trihydrate (COT), is rarely observed due to its thermodynamic instability. In addition to their multiple industrial usage, these minerals are heavily studied since calcium oxalate makes up approximately 70% of kidney stones whose formation causes dietary, environmental, genetic diseases, 23 and urolithiasis, the urinary stone disease that affects ∼10% of the world's population per generation. 24 Besides these reasons, which make the COM a fully investigated compound, 25 chosen this material since it is conventionally selected as reference substance for thermal calibration. Therefore, it has been possible to compare and discuss the elaborations highlighted in the indicated items (1) and (2) against a large number of published results dealing with the thermal behavior of this compound. Focusing on proposals of item (1), it is well known that the thermal decomposition of COM, which occurs under an inert atmosphere following the three successive decomposition steps (Table 1), has been widely investigated in view of determining the values of E, preexponential factor, and kinetic model exponent. In these studies, this is achieved by elaborating the TA information carried out, in particular, under constant heating rate constraint. 25,[31][32][33][34] Some of these works exploit the TA and MS techniques to identify the reaction mechanisms involved in the indicated steps. [35][36][37][38] As alternative approach, in this work, the E is determined, for each of the three reaction steps, by elaborating the MS signals through consolidated kinetic models as those of Kissinger, Ozawa, and Starink. In addition, the MS signals have been further processed to calculate this parameter through suitable isoconversional procedures involving the known models of Friedman and Starink.
Regarding item (2), as the main novelty, this study makes evident the fundamental role of the MS analysis in providing a correct interpretation of the chemical events occurring, in particular, during the II • step. Through a detailed analysis of the MS signals, it is possible to identify unambiguously the contemporary presence of the exothermic reaction of dismutation of CO into CO 2 and C-graphite. The relevance of this investigation lies in the fact that the presence of this reaction cannot be inferred by the elaboration of the mass loss measurements but only through a specific analysis of the MS signals. This enables to identify and quantify the volatile compounds CO and CO 2 evolving during this step, and, consequently, the contribution of the thermal effects of the indicated reaction within the global thermal balance of this II • event. These outcomes agree with the conclusions pointed out in an indepth analysis of the thermal behavior of the COM recently published. 34

Chemical reagents and sample synthesis
Sodium oxalate (RS-grade, cod. 482101, CAS 62-76-0) and calcium chloride anhydrous (RS-grade, cod. 433535, CAS 10043-52-4) were purchased from Carlo Erba Reagents and used as received. Fresh bi-distilled water was used, stored in a plastic wash-bottle open to air atmosphere.
Calcium oxalate powder was prepared to exploit the different salt's solubility and avoiding acid-base reaction, following the precipitation reaction at room temperature by using the minimum water volume: Na 2 C 2 O 4(aq) + CaCl 2(aq) → CaC 2 O 4(s) + 2 NaCl (aq) .
4.585 g of pure sodium oxalate (34.2 mmol) was slowly dissolved by adding the minimum volume of distilled water (200 mL) under stirring at room temperature. Analogously, a second solution was easily prepared by dissolving 3.798 g of anhydrous calcium chloride (34.2 mmol) into 20 mL of distilled water. Then the CaCl 2 solution was added dropwise to the NaC 2 O 4 solution under vigorous stirring. Immediately, a white precipitate was formed, the suspension was aged at room temperature for some hours, and, after stopping the stirring, the precipitate was left to spontaneously settle for several hours. The overlying transparent liquid phase, presenting a pH 6.8, was carefully removed by suction, while the remaining wet solid fraction was washed by adding 50 mL of distilled water. The resulting suspension was stirred for 15 min and left again to settle. The washing process was repeated three times. After the calcium oxalate powder was settled, the pH of each overlying washing was measured, finding the constant value of pH 6.8 (i.e., the value of the distilled water, used for washing). The suspension was then carefully filtered on a filter paper (retention grade < 2 μm); the powder was dried in an oven at 80 • C for 12 h and stored in a closed vessel. Finally, 4.728 g of powder was recovered (i.e., 32.3 mmol of CaC 2 O 4 ⋅H 2 O; yield of 94.6%).

Infrared spectroscopy analysis
The Fourier-transform infrared spectroscopy (FTIR) spectra of the obtained dried powder were recorded on a Varian Excalibur 4100 spectrophotometer working in ATR (attenuated total reflection) mode in the 4000-550 cm −1 range. The pure sample powder was laid on the diamond F I G U R E 1 FTIR-ATR spectrum of the obtained calcium oxalate monohydrate crystal (Golden Gate Specac Graseby) collecting 64 scans with a 4 cm −1 resolution. The ATR spectrum is reported in Figure 1.

X-ray diffraction analysis
The crystal structure of the synthesized powder has been investigated through the x-ray diffraction (XRD) analysis carried out by an IPD3000 diffractometer equipped with a Co anode source (line focus) and a multilayer monochromator to suppress kβ radiation. The sample was measured in reflection geometry with a fixed incident angle of 5 • . Diffraction data were collected by means of an Inel CPS120 detector over 5-120 • 2θ range, 0.03 • per channel, and an acquisition time of 60 min. The diffraction spectrum is reported in Figure 2.

FTIR characterization data
The FTIR-ATR spectrum of the synthesized powder, reported in Figure 1, shows a frequency pattern that well corresponds to the pure calcium oxalate monohydrate form: CaC 2 O 4 ⋅H 2 O, COM. In particular, the presence of one single water molecule in the calcium oxalate solid structure gives rise, at room temperature, to the formation of the typical frequencies pattern in the 3500-2800 cm −1 range. As indicated in the work of Conti et al., 39  fifth band at 3257 cm −1 could be assigned to the first overtone of the H-O-H bending, which fundamentally (at ca. 1628 cm −1 ) could be lost in the overlap with the more intense band of the C=O stretching, justifying its asymmetric form. So that, following the frequencies labeling described in Conti et al., 40 the C=O stretching vibration, ν 11 , originates the intense band at 1602 cm −1 while the second stretching ν 9 is revealed by the sharp peak at 1313 cm −1 . The less intense sharp peak at 778 cm −1 could be attributed to the in-plane OCO group bending ν 12 , whereas the OCO out-of-phase rocking ν 10 is detected by the small band at 1380 cm −1 . Finally, in this lower frequency region, the weak bands detected at 948 and 885 cm −1 are assigned to the vibrations of the water molecule in the COM solid structure.

XRD characterization data
The XRD spectrum shows that the only crystal structure present in our synthesized powder samples is the calcium oxalate whewellite being its experimental diffraction pattern coincident with the whewellite ideal crystal structure COD (Crystallography Open Database) entry 9000763. [40][41][42] The calculation was made by the Rietveld program MAUD. 43 In particular, Figure 2 shows the pattern of our prepared sample (green line), in comparison with the one recorded for the pure standard-reagent counterpart, CaC 2 O 4 ⋅H 2 O (Sigma-Aldrich, cod C0350000, CAS 5794-28-5) (red line).

Thermal analysis
TGA and DTA were performed on a LabSys Setaram thermobalance, operating in the range 20-1000 • C. Measurements were carried out fluxing the thermobalance furnace with He (99.999% purity) at a constant flow of 120 cm 3 ⋅min −1 (measured at 20 • C and 0.1 MPa). Thermal analyses were recorded using similar amounts of powder (5.5-5.9 mg) and carried out by selecting, progressively, the following constant heating rates (β): 7, 10, 13, 16, 19, 22, and 25 • C⋅min −1 . The sample powders were quickly weighed and loaded into alumina crucibles (volume 0.1 cm 3 ) then the thermobalance was immediately closed and purged with He flux adjusted and controlled by means of a Matheson mass flow controller. The thermobalance, previously kept under constant He flux and precharged with a standard amount of α-Al 2 O 3 (8.7 mg) as reference compound, was quickly opened to insert the crucible sample and immediately closed. During this preliminary procedure, the He flux was increased up to 300 cm 3 · min −1 by adding a supplementary flow from a second inlet port located at the bottom of the balance body. This condition has been maintained for ca. 30 min to promote the rapid removal of air from the apparatus, which achieves the inert atmosphere in a few minutes as proved by the exponential decay of the N 2 and O 2 IC signals detected by the mass spectrometer. The He was then restored to the operative (120 cm 3 · min −1 ) flux to start the analysis.

Mass spectrometry analysis
Mass spectrometric analysis was carried out using a TRIO-1 VG quadrupole mass spectrometer detector. The furnace of the thermobalance was connected with the ion-ization chamber of the mass spectrometer through a homebuilt transfer line 19 made with an empty and deactivatedsilica capillary-column (0.32 mm internal diameter, 13.5 m length) enveloped in a thermostatic jacket heated at 238 ± 1 • C. (This column length is required for maintaining the vacuum inside the mass spectrometer). During the thermal analyses, an appropriate fraction of the purging He flux sampled a few millimeters above the sample crucible, was continuously withdrawn and analyzed. Electron impact mass spectra (70 eV) were continuously recorded in the scan mode in the 1-400 amu range with the frequency of 1 scan s −1 (ionization chamber temperature 180 • C). The quadrupole mass spectrometer was calibrated weekly by using perfluorotributylamine (C 12 F 27 N, CAS: 311-89-7) as reference, while operative parameters were tuned daily with particular attention to the improvement of the He signal. Operative experiments showed that gaseous species usually required less than 40 s to travel the whole transfer line before being detected. MS data are recorded as a continuous sequence of mass spectra so that any gas species released from the solid sample can be easily monitored by the detection of its fragmentation ion patterns in the recorded spectra. From these MS data, it is also possible to obtain both the total ion current curve (TIC graph) and the single contributions of any m/z ion current curve (IC graphs) versus time, that is, the linear increase of temperature recorded during the entire TA. The trend of the TIC curve reveals therefore the global release of the compounds, while each IC curve allows to monitor the presence of individual chemical species presenting appropriate m/z values belonging to particular ions not present in the fragmentation ion pattern of the other released compounds. In our experience, we usually observed that in TG-MS analyses repeated on the same sample under the same operative conditions when the temperature peaks differ for values minor of 1 • . For this reason, the temperature values will be reported in the text without their decimal points.

KINETICS MODELING
The use of dynamic TA represents a recognized experimental tool to study the kinetics of complex processes as those occurring during the thermal decomposition of solids. As well known, the obtained experimental results can be elaborated to set up a variety of kinetic models, the majority of which lead to the degradation rate to two functions: the k(T) term to account for the temperature dependency and the f(α) function, depending only on the extent of conversion α, to express the reaction model scheme: The parameter α is conventionally defined as where m 0 and m ∞ are the initial and the final mass of the sample, respectively, while the term m t,T indicates the mass of the sample referred to time t and temperature T.
The k(T) function can be successfully modeled by assuming the Arrhenius equation form: where A is the preexponential factor, E the apparent activation energy, and R the universal gas constant. Combining Equation (3) with Equation (1), the basic form of the kinetic equation is achieved: In this study, all the runs of the TA have been carried out under constant heating constraint by selecting suitable values for the parameter = ( ∕ ) = const. By including it into Equation (4), the following differential form of the kinetic equation is derived: The determination of the kinetic parameters of Equation (5) can be pursued following different approaches. Since the kinetic study proposed in this work limits only to E estimation, the so-called "model-free" methods have been adopted avoiding, therefore, the choice of suitable selections for the f(α) function. The models included in this work do not cover all the existing model-free methods but, from the knowledge of the authors, those considered here are widely utilized to describe the thermal degradation of solids. In the following subsections, a synthetic description of the selected models is proposed.

Maximum reaction rate method
The method of Kissinger can be derived from Equation (5) when it is referred to the maximum reaction rate by imposing the constraint: 2 ∕ 2 = 0. After simple elaboration, 44,45 the indicated equation can be rearranged to provide the conventional Kissinger equation form: where the term f′(α m ) represents the f(α) derivative evaluated at the maximum reaction rate (α m ). The E can be determined from the slope of the straight line resulting from the plot of the left-hand side of Equation (6)versus 1/T m . This procedure requires, for each β, the value of the temperature T m detected in correspondence to the maximum conversion rate that, rigorously, corresponds to the temperature of the flex point of the TG profile curve inside a specific mass loss event here indicated as T f (flex point temperature). Since, at this condition, the corresponding α m value can vary significantly with β, this procedure cannot rigorously be classified as "isoconversional" even if, due to this misunderstanding, it is usually confused with the isoconversional Kissinger-Akahira-Sunose (KAS) model. As evidenced in Starink's paper, 46 this condition can be approximated as a specific stage of the thermal reaction referred to as the maximum transformation rate (or reaction rate). Since the peak temperature points T p of both the DTG and DTA profiles are achieved in correspondence to this condition, they can as well be utilized as substitutes of T m in Equation (6). For sake of clearness, a representation of the T f and T p points, here introduced, is shown in Figure 5. Moving from this observation, two further equations, presenting a similar structure of Equation (6), have been considered in this work: the first is the Ozawa equation 47,48 : the second is the Starink equation 46 : From Equations (7) and (8), the E can be as well determined following the procedure indicated for Equation (6). In this work, this approach has been extended by substituting the T f (flex point temperature of the TG profile) or, alternatively, the T p values (peak point temperature of the DTG or DTA profiles) for T m. This procedure, requiring only the knowledge of these remarkable points, is here indicated as the maximum reaction rate (MRR) method.

Isoconversional methods
As reported in reference papers including also the recommendations indicated by the Kinetics Committee of the International Confederation for Thermal Analysis and Calorimetry (ICTAC), 45,49 to which reference is made for the fundamentals of these methods, the isoconversional principle states that the reaction rate at the constant extent of conversion is only a function of temperature. To obtain experimentally the temperature dependence of the isoconversional rate, a series of runs have to be performed. In this work, seven constant heating rates (β values) were chosen as indicated in Section 3.1. Two computational schemes can be elaborated to exploit the experimental results to derive the kinetic parameters of the studied processes: differential and integral methods. The most consolidated models representative of the differential methods are those of Friedman 50,51 and Flynn and Wall 52 expressed by Equations (9) and (10), respectively: The integral methods can be derived from the following generalized equation representative of the so-called "direct isoconversional methods": By assigning the value n = 0 and ω = −1,052 to the parameters, Equation (11) turns to the Ozawa equation (previous Equation (7)) known, in this contest, as the Flynn-Wall-Ozawa (FWO) isoconversional method, while, assigning to the parameters the values n = 1,92 and ω = −1,0008, the Starink equation indicated in Equation (8) is obtained. When utilized within the isoconversional procedure it turns to the Starink isoconversional method. Assigning the values n = 2 and ω = 1 to the coefficients, Equation (11)

MS applied to the isoconversional procedure
This section presents the procedure identified in this work to determine the E by applying the results of the MS signals to the isoconversional approach. Since the mass spectrometer apparatus utilized for the experimental campaign does not allow to export of the recorded data, the elaboration of the data has been limited by the operative procedures implemented in the instrument software. In particular, the procedure to determine the temperatures for each of the selected isoconversion points (T α = α ) for the three IC signals (m/z 18, 28, and 44) has required a complex sequence of elaborations here described. It must be pointed out that this operative program allows to directly calculate the area value below a band of an IC only when the initial and final points are chosen before and after the maximum of the obtained curve. For each released species (H 2 O, CO, and CO 2 ), the area value (A) below the whole band of each IC molecular ion curve (A tot ) was measured in order to quantify its total released amount during that specific thermogravimetric event. Then the progressive nominal values of the areas corresponding to the conversion degrees from α = 0.1 to α = 0.9 were calculated (A (α = α)nominal ). Taking into account all these nominal values in correspondence to each chemical species, for each conversion degree value (α = α) and each heating rates, the integrations of the IC band were made, starting from the same constant initial point (initial time "t initial ") to a final one (t j ) in order to get an area value (A (α = α)tj ) more close to the nominal value of the selected area (A (α = α)nominal ). For example, for sake of clarity these steps are summarized in Figure 3 where in part (A) the shift on the temperature scale of the IC m/z 28 band is reported by increasing β while, in part (B), this procedure referred to α = 0.7 is outlined. After the determination of an appropriate number (n) of these experimental points (usually n from 3-7), a graph of the area values versus their respective final time values is plotted. These points have been interpolated with a second-degree polynomial function to determine the nominal time value for the selected conversion degree value, t α = α , as shown in Figure 4A. Then the t α value has been converted to the corresponding temperature value T α = α by considering the respective heating rate β. Finally, for each released species and all the conversion degree values, the set of the T α = α temperature values was used to plot the "Arrhenius graph" by using the three KAS, FWO, and Starink(T 1.92 ) equations  Figure 4B for the case of the Starink equation.

Experimental results
Keeping in mind the parameters of the proposed MRR models, the thermal decomposition of COM has been characterized by identifying the remarkable points introduced in Sections 4.1 and 4.3.1: the flex temperature T f of the TGband curve, the peak temperature T p of both the DTG and DTA-band curves, the peak temperature T p , MS of the TIC and the selected IC curves derived from the MS analysis. All these points have been detected for each of the three reactions reported in Table 1 and for each heating rate (β values). Figure 5 depicts the TG, DTG, and DTA curves and, in the upper part, the corresponding peak points (T p,MS ) of the TIC curve for the thermal run at β = 7 • C min −1 . Table 2

TA B L E 2
Flex temperature T f of the TG-band curve, peak temperatures T p of the DTG and DTA band curves, peak temperatures, T p,TIC and T p,IC from the TIC and IC curves of the MS analysis

TG, DTG, and DTA analysis T f of the TG curve ( • C) T p of the DTG curve ( • C) T p of the DTA curve ( • C) β ( • C⋅min −1 ) StepI •
Step II  Figure 6 depicts, for all the selected β, the profiles of the IC curves within the temperature range of interest and highlights the peak temperature T p,IC whose values are included in Table 2. Figure 6 has been expressly included to highlight the shift of the T p,IC values as β increases.
To complete the overall view of the experimental section, the results of the temperature of the isoconversion points (T α = α ) in correspondence to the selected α value (α range: 0.1-0.9, step 0.1), for the three IC signals (m/z 18, 28, and 44) and each β, are included in Table 3. For sake of clearness, these values are obtained following the procedure described in Section 4.3.2. Figure 7 provides an overall overview of the E trends obtained from the application of the MRR models. For summary issues, the numerical values comprehensive of the uncertainties are summarized in Table A Figure 8 shows the E results of the isoconversion models introduced in Section 4.3.2. (See Table B of the SI for the numerical values.) Due to the feature of these methods, the E trend is depicted versus the extent of conversion α in the range 0.1 < α < 0.9 and, henceforth, when referred to the isoconversional option E will be indicated as E α . In Figure 8,  Figure 7, the data arising from the three thermal events are represented with different colors.

MRR models
A general overview shows that the E results are the same independently from the adopted MRR method (Figure 7). The Ozawa model provides results slightly higher if compared with those of Kissinger and Starink, practically equal within the uncertainty of the experimental error bands (see SI, Table A). Narrowing the view to the TA (Figure 7), the results of the DTG elaboration are always the highest for the three thermogravimetric events while those of the I • and III • events are quite similar both for the TG and the DTA analysis.
Looking specifically at the II • event, the E derived from DTA is always significantly lower compared to that from TG and DTG. This achievement is almost independent of the models as can be seen by calculating the ΔE % [100⋅(E Tp-DTA − E Tf-TG )/E Tf-TG ] quantity that, selecting the TG curve as reference, provides −33.11%, −31.31, and −33.05% for the Kissinger, Ozawa, and Starink models, respectively (data from SI, Table A). As it will be deeply discussed in Section 6, it is precisely this behavior that has suggested for the second step to hypothesize the occurring of a further parallel reaction in addition to conventional reaction 2. Regarding the impact of the different signals, Figure 7 evidences that the E obtained from the MS are usually lower than those derived from the TA without significant differences from the adopted models.
Considering the results of the Starink model as case test and assuming the TG data as reference, the differences of the E calculated from the T p of the TIC curve to the E derived from the T f of the TG curve provides: −62.16%, −25.66%, and −16.69% moving from the I • to the III • step, respectively. This difference is particularly drastic for the dehydration of the calcium oxalate (I • step). Considering these discrepancies, one wonders about the reliability of these results that, ultimately, can be led back to the approximations adopted for the temperature integral. In the literature, 53 this condition is expressed in terms of the parameter Y = E/RT whose variability must be verified and to be within 15 < Y < 60. For the TIC and the IC analysis referred to the I • event (m/z 18), this constraint is never satisfied since the resulting values for the Y set, in any case, are below 10. When reference is made to the temperatures T f of the TG curve or T p of the DTA curve, the Y values are set around 20. Consequently, the E values of the dehydration step obtained from the MS analysis have to be considered unreliable while, for the II • and III • TA B L E 3 Experimental temperature T (α = α) for the three species: H 2 O, CO, and CO 2 determined for each α values following the isoconversional procedure introduced in Section 4.3.2

Isoconversional models
Comparing the performances of the isoconversional methods applied to TA and reported in the left sides of plots A and B of Figure Table B of the SI. Regarding the reliability of these results, the constraints of the Y parameter introduced in the previous section are in this case as well satisfied with the exception of the E α results of the I • event obtained from the TIC and IC elaborations. This confirms, therefore, the criticalities pointed out for the MRR models. Looking at the sequence of the events and at the impact of the two signals (TG and MS), the results of the MS signals are always lower than those derived from the TA with a decreasing trend moving from the I • to the III • events. For the I • event (dehydration), the E α decreases as α increases. This is in accordance with the results of recent study 42 dealing with the characterization of the crystal structure of the calcium oxalate. This study demonstrates that the progressive release of water entails a progressive modification of the interactions of the residual water molecules with the solid structure that, consequently, affects the E α evolution as dehydration occurs. From the point of view of the authors, the cited study is considered particularly relevant since the sample powder preparation has followed a very close procedures adopted for the investigation here proposed. These factors, probably, play a more limited role in the release of CO and CO 2 molecules involved in the II • and III • events. To this concern, it must be noted that in reaction 2 and 3 the energy demand to break the covalent chemical bonds inside the oxalate and carbonate molecular structure accounts for a higher contribution to form and release the CO and CO 2 species with respect to that required to break the only physical interaction required for the water molecule release from the solid crystal network; all that in agreement with the E values of the first event which are at least halved or less compared to those of the II • and III • event.
For the II • event, the plots evidence that the E α value referred to TG signal and for α = 0.1 (Figure 8, left side) is significantly smaller than the others. Only in correspondence to the central α range, the E α reaches roughly constant values as can be observed for the trends derived from the MS signal with the exception of the extreme cases, α = 0.1 and 0.9 in Figure 8 (right side). From the point of view of the authors, these discrepancies are probably due to a higher error in calculating the relative area values from the partial integration of the IC signal (see Section 4.3.2).
As final observation, the E α trends obtained from the TG analysis (Figure 8, left side) present a significant scattering, while those referred to the MS signals (Figure 8, right side) present a reduced background noise so that, the use of MS signals, allows to obtain for E α a better defined trend.

Comparison with literature data
The reliability of the obtained E results has been tested versus literature sources. Despite the relevant number of studies dedicated to COM decomposition, the comparison is proposed with respect to the outcomes reported in Anderson et al.'s paper. 54 This publication ranks significantly since the reported results have been obtained by the kinetic working group of the German Society of Thermal Analysis by processing 144 experimental TG datasets conforming to the Round Robin Test protocol.
The results of the investigations carried out in our work, subdivided for each reaction, have been compared with those of the cited work 54 gathered, for each step, within their ranges with the E values expressed in kJ kmol −1 : • First event 54 : 78.4 ≤ E ≤ 104. 35. These values are consistent with the results of Tables 6 and 7 of the SI. Excluding the problems evidenced for the MS analysis referred to the first step, the E values set within the lower value: E = 74.9 (Kissinger) (not too far from the lower indicated limit) and the higher E = 103.5 (Ozawa, DTG). Similarly, the average value of the isoconversional method sets at E α = 91.2 and E α = 83.8 for Friedman and Starink, respectively. • Second step 54 : 213.6 ≤ E ≤ 261.56. The results of the MRR methods, obtained from the TG signals, are set within this range for the three selected models (Kissinger, Ozawa, Starink; see Table A in the SI). For all the other models, including the isoconversional methods, the achieved E values are lower than those reported in the cited publication. The E values derived from the DTA signals are set below the lower limit while those from the DTG are set above the upper. This behavior will be better analyzed in Section 6. • Third step 54 : 192.9 ≤ E ≤ 225.9. The results of the MRR method, referred to as the TG and the DTA signals, set within the indicated range for the three examined models. Furthermore, they are above the indicated upper limit (225.9) for the DTG signal elaborations (see Table A in SI). The values derived from the three models applied to the MS signals are close to the lower indicated limit. This can be seen in particular for the TIC signal including the error band ranges (Table 4, second section). This trend is also confirmed for the isoconversional models limiting the results to 0.3 ≤ α ≤ 0.8 in particular for the Friedman model. (See Table B in SI.)

Experimental results
In all the TG-MS analysis recorded at the selected β the trend of the IC m/z 44 ion current (used to monitor the CO 2 evolution) presents the formation of a smaller band in the range 365-600 • C in correspondence to the oxalate decarbonylation reaction (second event), besides the CO 2 development occurring during the carbonate decomposition (third event in the temperature range: 600-850 • C). Indeed, the mass spectra recorded inside this small band disclose, although with a modest intensity, the presence of the m/z 44 ion confirming the presence of CO 2 . These events are shown in Figure 9, which includes also the mass spectra detected at the T p of the two bands for the analysis carried out at β = 25 • C/min for example.
F I G U R E 9 IC m/z 44 trends to monitor CO 2 evolution during the second and third thermal events. In the insets, the mass spectra recorded at the T p of the two bands in the β = 25 • C⋅min −1 TG-MS analysis The peak temperatures of these IC m/z 44 smaller bands inside the second thermal event, T p(ICm/z44-II • event) , are reported in Table 4.

Modeling
The detection of CO 2 during the thermal decomposition of calcium oxalate unequivocally indicates the occurrence of a further secondary reaction during the second step. To the authors knowledge, this CO 2 formation, mentioned in some papers 30,34,55,56 is always led back to a partial (or total) oxidation of CO, yielded from reaction 2, following the stoichiometry: CO + 1∕2 ⋅ O 2 → CO 2 even though the thermal process is claimed to be carried out under an inert atmosphere neglecting, therefore, any justification pertaining to the oxygen source. The presence of CO 2 is also supported by the exothermic effect measured from the DTA or DSC signals during this decomposition process. Considering the following observations emerging during our TG-MS experiments campaign: • the powder recovered at the end of the entire TG-MS analysis (or when the measure is arbitrary stopped after the II • event) presents a gray color instead of white as expected for the formation of pure calcium oxide (or calcium carbonate); • the different and irregular shape of the DTA profile observed for the II • event with respect to those pertaining to the I • and III • steps ( Figure 5), where the contribution of a more modest exothermic band seems to overlap on the original development of the expected endothermic band of reaction 2; • the different (lower) mass-loss percentage-value of this II • event that always we detected with respect to the nominal one associated with pure oxalate into carbonate decomposition.
This makes it right to consider the thermal dismutation of CO into CO 2 and carbon graphite as a second consecutive reaction. This reaction, occurring during the II • step (also known as the Boudouard reaction), take places in the gas-phase and leads to the CO 2 formation without requiring an oxidizing counterpart: secondary reaction-step II 2 ⋅ CO ( ) = CO 2( ) + C ( ) (R4) Moreover, at these temperatures, the yielded carbon graphite immediately sublimated to the solid-state covering both the residual solid sample, the sample holder, and the internal chamber of the thermobalance modifying, therefore, the measured mass-loss of this second event.
The E of this reaction has been determined by applying the Kissinger, Ozawa, and Starink MRR method (see Section 5.2.1) to the peak temperatures (T p(ICm/z44-II • event) ) reported in Table 4. The results are summarized in Table 5 together with the values of the uncertainty, the R 2 , and the Y parameter introduced in Section 5.3.1. Figure 10 depicts the "Arrhenius graph" as a result of the data-processing procedure applied to the Starink equation. It is important to highlight that it has been possible to determine the E of this secondary reaction only by monitoring the IC m/z 44 signal within this second event where only the CO should be the expected species.

Discussion
In order to study the effective course of the CO dismutation reaction, the relative percentage of the CO 2 yielded during the entire course of the II • thermogravimetric event has been estimated. Figure 11 presents for β = 7 • C/min, the trends of the TIC profile and those of the IC curves of the H 2 O, CO e CO 2 species including the area of each of the detected IC bands that are proportional to the amount of the species released during the thermal event. In the insets above the curves, the mass spectra recorded at the T p of the TIC bands are also included. During the I • and III • CaC 2 O 4(s) → CaCO 3(s) + (1-α) CO (g) + (α/2) C (s) + (α/2) CO 2(g) R6 event, the mass spectra highlight, as expected, the exclusive presence of H 2 O and CO 2 while, during the II • event, the recorded mass spectra show, besides the expected CO yielded from reaction 2, the minor presence of CO 2 yielded from the partial occurrence of the CO dismutation reaction.
Considering the areas of the two bands referred to the IC m/z 44 and 28 curves of the II • and III • event, an amount of 4.3 mol% of CO 2 has been calculated as specific contribution of the II • event (details of this elaboration are reported in Section A of SI). Considering the equations scheme of Table 6, this event can be entirely described as the sum of the quantitative course of reaction 2 by adding reaction 4 which does not occur quantitatively (in this scheme included as reaction 5 with a ½ stoichiometry), leading to the indicated global reaction 6.
Considering the presence of the CO 2 in the evolved gas-phase ( mol %(CO 2 ) = 4.3), a stoichiometric elaboration allows to quantify the course of reaction 5 (α R5 = α) with respect to the quantitative course of the reaction 2(α R2 = 1), yielding the following conversion degree whose details are reported in Section B of the SI: R5 = 2∕(1 + 100∕ mol %(CO 2 )) = 0.0825 F I G U R E 1 0 Arrhenius graph elaboration of the CO dismutation reaction obtained by applying the Starink MRR method to the T p(ICm/z44-II • event) values F I G U R E 1 1 TG-MS analysis carried out at β = 7 • C⋅min −1 . TIC and IC curves of the released H 2 O, CO, and CO 2 species. In the inset, mass spectra recorded at the T p of the TIC curve The standard enthalpy of reaction 4, ΔH • R4 , at 496 • C has been carefully calculated by considering the enthalpy data of the involved species available in the literature. 57,58 Unlikely, the standard enthalpy of reaction 2 has been only roughly estimated since the temperature dependency of the specific molar heat (c p ) of calcium oxalate anhydrous and monohydrate was not found so that they have been kept constant at the reference temperature (25 • C). Detailed elaborations are reported in Section C of the SI.
With this assumption the standard enthalpy of reactions 2 and 4 becomes, respectively: In conclusion, during this II • thermal event a percentage decrease of the global enthalpy effect, due to the partial course of the CO dismutation reaction, can be quantified: In this regard, it is to remember that the two signals provide the following information: • The latter (TG-curve) is unable to detect the course of reaction 4 since it only monitors the effects of the mass variation due to the oxalate decomposition into the carbonate in a quantitative transformation (α R2 = 1); • the former (IC m/z 28) is able to specifically detect the effective presence of the CO species; therefore, the effect of reaction 2 (which quantify its production) together with those of reaction 4 (which quantifies its partial course) provides the real global course of this II • event occurring in the gas phase.
Concerning the E, a second remarkable correlation can be found among the values resulting from the MS analysis. The first pertains to the E obtained by processing the T p of the II • -TIC-bands whose signal monitors all the events occurring in this temperature range (i.e., the course of reaction 6). The second concerns the E referred to the course of each one of the single reactions 2 and 4 (characterized by opposite endo-exo-thermally effects) obtained by evaluating the T p of the bands of the IC m/z 28 and 44 signals detected inside the II • thermal event.
When these two last E values are weighted with the molar percentage of the corresponding CO and CO 2 species evolved in the gas phase, the weighted E value results very close to that obtained from the TIC curve.
In fact, in the hypothesis of considering that the endoexo-thermally effects of these two reactions act in contrast with each other and also taking into account the uncertainty of these E values, obtained from the Starink equations, the so obtained values can be considered almost coincident: This fact confirms general feedback often observed in our experimental TG-MS measurements. In the course of a complex endothermic thermal decomposition event, characterized by the contemporaneous occurrence of different chemical reactions, the apparent activation energy value obtained elaborating the TIC signal results equal to that obtained from the average of the E values calculated for each of the single reaction and weighted by the molar composition of the corresponding product of these reactions. 59,60 This obviously occurs only if the complex decomposition event is previously correctly described by the complete identification of all the involved reactions pattern.

CONCLUSIONS
The E involved in the three steps decomposition of calcium oxalate monohydrate has been determined by adopting both the MRR and the isoconversional procedures. An innovative approach has been proposed by coupling the conventional TA with MS signals elaborations.
Examining the results of the MRR method, the E trends are practically independent of the adopted models (Kissinger, Ozawa, Starink). Referring to the elaborated signals (TG, DTG, DTA, TIC, and IC for m/z 18, 28, and 44), the higher values of E are achieved indifferently from the TG and DTA signals elaborations while, for the II • reaction, the E calculated from the DTA signals is significantly lower than those derived from the TG elaborations. This discrepancy, thoroughly investigated by exploiting the potentiality of the coupled TG-MS technique, has allowed us to identify the occurrence of the CO dismutation (Boudouard reaction). The extended elaborations of the MS signals to the isoconversional methods have evidenced that the E α trends are independent of the adopted equation models (Friedman, FWO, and Starink). Within the limits of these preliminary outcomes, the MS signals approach introduced in this study looks promising as reliable alternative for the E calculation. The consistency of the achieved results has been checked by the consolidated criterion expressed in terms of the parameter Y = E/RT. Some questions are still open as the unreliable E values obtained for the I • reaction and derived from the IC and TIC signals elaborations. Nevertheless, this study extensively confirms most of the results available in the literature. The proposed approaches look particularly suitable to encourage the application of the TG-MS techniques to the kinetic analysis.

D ATA AVA I L A B I L I T Y S TAT E M E N T
Data are available on request from the authors.