Nonisothermal Kinetic Study: IV. Comparative Methods To Evaluate

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Nonisothermal Kinetic Study: IV. Comparative Methods To Evaluate Ea for Thermal Decomposition of KZn2(PO4)(HPO4) Synthesized by a Simple Route Zhipeng Chen, Qian Chai, Sen Liao,* Xia Chen, Yu He, Yu Li, Wenwei Wu, and Bin Li College of Chemistry and Chemical Engineering, Guangxi University, Nanning 530004, Guangxi, China ABSTRACT: The single-phase KZn2(PO4)(HPO4) was synthesized via solid-state reaction at 80 °C using K3PO4·3H2O, K2HPO4·3H2O, and ZnSO4·7H2O as raw materials. The thermal decomposition of KZn2(PO4)(HPO4) experienced one step, which was the intramolecular dehydration of the protonated phosphate groups to form Zn2P2O7. The apparent activation energy Ea was estimated with six comparative isoconversional procedures. The average value of the apparent activation energy Ea associated with the thermal decomposition of KZn2(PO4)(HPO4) was determined to be 411.49 ± 14.37 kJ mol−1, which demonstrates that the thermal decomposition of KZn2(PO4)(HPO4) is a single-step kinetic process and can be described by a unique kinetic triplet [Ea, A, g(α)]. A new modified method for multiple rate isotemperature was used to define the most probable reaction mechanism g(α), and reliability of the used method for the determination of the kinetic mechanism was tested by the comparison between experimental plots and modeled results for every heating rate. The results show that the mechanism function is reliable. The value of pre-exponential factor A was obtained on the basis of Ea and g(α). Some thermodynamic functions (ΔS⧧, ΔH⧧, and ΔG⧧) of the transition state complex were also calculated. isotemperature method.25 Experimental and modeled results were compared to test the reliability of the established kinetic mechanism. The pre-exponential factor A was calculated using Ea and g(α). The kinetic triplet (Ea, A, and mechanism of the reaction) and some thermodynamic functions (ΔS⧧, ΔH⧧, and ΔG⧧) of the decomposition reaction of KZn2(PO4)(HPO4) are discussed for the first time.

1. INTRODUCTION Layered zinc phosphates have received considerable interest during the past two decades owing to their potential applications as new materials that may have ion exchange, absorption, separation, ionic conductivity, and heterogeneous catalytic and second-order nonlinear optical properties.1−10 In the family of microporous metal phosphate materials, zinc phosphates have the most abundant topological structures. So, during the recent decades, about 100 chain-, layered- and threedimensional framework zinc phosphates (ZnPOs) have been synthesized under hydrothermal or solvothermal conditions.3 For example, a layered potassium zinc phosphate compound with composition KZn2(PO4)(HPO4) was prepared by the hydrothermal reaction of zinc chloride and phosphoric acid in the presence of KOH and triethanolamine.7 But only a few preparations of metal phosphates were carried out via solidstate reaction at room temperature or near room temperature.11−22 Solid-state reaction at room temperature or near room temperature is a novel synthetic technique that has been developed in recent decades.11−22 Recently, we successfully used this novel technique to synthesize several transition metal phosphates.11−22 So, as a part of the systematic kinetics researches,20−22 the aim of this work is to study the kinetics and thermodynamics of the thermal decomposition of single-phase KZn2(PO4)(HPO4) prepared using the above novel synthetic technique. Kinetic data were collected using TG-DTG technique. Nonisothermal kinetics of the decomposition process of KZn2(PO4)(HPO4) was analyzed using a new modified method.23−28 The values of apparent activation energy Ea were obtained from six comparative isoconversional procedures.23−41 The most probable mechanism function g(α) of the thermal decomposition reaction was deduced from a multiple rate © 2012 American Chemical Society

2. EXPERIMENTAL AND METHODOLOGY 2.1. Reagent and Apparatus. All chemicals were of reagent grade purity. TG-DTG measurements were made using a Netsch 40PC thermogravimetric analyzer. High purity nitrogen gas (99.999%) was used as protective atmosphere, flowing at 20 mL min−1. The results presented in this paper were calculated by the programs compiled by ourselves. Powder X-ray diffraction (XRD) was performed at room temperature using a Rigaku D/max 2500 V diffractometer equipped with a graphite monochromator and a Cu target, and the XRD data were collected from 5° to 70° of 2θ with a step size of 0.02° and step time of 0.24 s. Fourier transform infrared (FT-IR) spectra was recorded on a Nicolet NEXUS-470 spectrometer in the wavenumber range of 400−4000 cm−1, and the samples were prepared as the KBr pellets. 2.2. Preparation of KZn2(PO4)(HPO4). The potassium zinc hydrogen phosphate KZn2(PO4)(HPO4) was prepared via solid-state reaction at 80 °C using K 3 PO 4 ·3H 2 O, K2HPO4·3H2O, and ZnSO4·7H2O as starting materials. In a typical synthesis: K3PO4·3H2O (26.25 mmol, 6.99 g), K2HPO4·3H2O (26.25 mmol, 5.99 g), ZnSO4·7H2O (50.0 Received: Revised: Accepted: Published: 8985

March 27, 2012 June 13, 2012 June 14, 2012 June 14, 2012 dx.doi.org/10.1021/ie300774x | Ind. Eng. Chem. Res. 2012, 51, 8985−8991

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values obtained by this method are usually regarded as more reliable than those obtained by a single TG curve. 2.3.2. Determination of the Most Probable Mechanism Function. The following equation is used to estimate the most correct reaction mechanism, i.e., g(α) function25

mmol, 14.38 g), and surfactant polyethylene glycol-400 (PEG400) (2.0 mL) were put in a mortar, and the mixture was fully ground for 30 min. The reaction mixture gradually became damp, and then a paste formed quickly. The reaction mixture was kept at 80 °C for 6 h, then washed with deionized water to remove soluble inorganic salts until SO42‑ ion could not be visually detected with a 0.5 mol L−1 BaCl2 solution. The solid was then washed with a small amount of anhydrous ethanol and dried at 110 °C for 3 h to give the single-hase KZn2(PO4)(HPO4). 2.3. Kinetic and Thermodynamic Studies. According to nonisothermal kinetic theory, kinetic equation of thermal decomposition of solid-state material23 is ⎛ E ⎞ dα A exp⎜ − a ⎟f (α) = ⎝ RT ⎠ dT β

⎤ ⎡ AEa e −x ln g (α) = ⎢ln + ln 2 + ln h(x)⎥ − ln β ⎦ ⎣ R x

The degrees of conversion α corresponding to multiple rates at the same temperature are put into the left side of eq 8; combined with 31 types of mechanism functions,25 the slope km of the straight line and the linear correlation coefficient r are obtained from the plot of ln[g(α)] vs ln β. The probable mechanism function is the one for which the value of the slope km is near −1.00000, and the correlation coefficient r is better. If several g(α) functions meet this requirement, the degrees of conversion corresponding to multiple heating rates at several temperatures are applied to calculate the probable mechanism by the same method. The function, whose km value is the closest to −1.00000 and the correlation coefficient r that is also high at all these temperatures, is considered to be the most probable mechanism function. 2.3.3. Calculation of Pre-Exponential Factor A. The preexponential factor A can be estimated from the intercept of the plots of eq 6 or 7 by inserting the g(α) function determined to be the most probable. 2.3.4. Calculation of Some Thermodynamic Functions (ΔS⧧, ΔH⧧, and ΔG⧧) of the Transition State Complex of Thermal Decomposition Reaction. Some thermodynamic functions (ΔS⧧, ΔH⧧, and ΔG⧧) may be calculated according to the following eqs44−46

(1)

where α is the degrees of conversion, β is the heating rate (°C min−1), Ea is the apparent activation energy, A is the preexponential factor, and R is the gas constant (8.314 J mol−1 K−1). 2.3.1. Calculation of Activation Energy by Isoconversional Procedures. From eq 1, the OFW equation,35−38 KAS equation,39−41 Tang equation,33,34 and Starink equation32 are deduced by a series of transforms OFW equation: ln β = ln

KAS equation: ln

Tang equation: ln

0.0048AEa E − 1.0516 a g (α )R RT

E β AR = ln − a 2 g (α)Ea RT T β T

Starink equation: ln

1.894661

β T1.92

= C1 − 1.001450

E = C2 − 1.0008 a RT

(2)

(3)

Ea RT

⎛ Ah ⎞ ΔS ⧧ = R ln⎜ ⎟ ⎝ eχkBTP ⎠

(4)

(5)

The iterative procedure24−27,42 is used to calculate the approximate value of Ea approaching to the exact value; the eqs are expressed ln

E 0.0048AEa β = ln − 1.0516 a H (x ) g (α )R RT

(6)

E β AR = ln − a 2 g (α)Ea RT h(x)T

(7)

(9)

ΔH ⧧ = E ⧧ − RTP

(10)

ΔG⧧ = ΔH ⧧ − TpΔS ⧧

(11)

where A is the pre-exponential factor, e = 2.7183 is the Neper number, χ is the transition factor, which is unity for monomolecular reactions, kB is the Boltzmann constant (1.381 × 10−23 J K−1), h is the Plank constant (6.626 × 10−34 J s), TP is the peak temperature in DTG curve, and R is the gas constant (8.314 J mol−1 K−1). E‡ is the activation energy, Ea, which is obtained from eq 7.

and ln

(8)

3. RESULTS AND DISCUSSION 3.1. XRD Analysis of the Product and Its Calcined Sample. The XRD characteristic result of the product dried at 110 °C is shown in Figure 1a. Figure 1b shows the XRD pattern of the sample resulted from calcination at 650 °C for 3 h. The strong intensity, smooth baseline, and a diffraction pattern characteristic of the product (Figure 1a) indicate that the product is well crystallized. All the diffraction peaks in the pattern are in agreement with that of KZn2(PO4)(HPO4) (PDF card 20-1445), and no diffraction peaks of impurities, such as Zn3(PO4)2·4H2O, are observed. Paillaud et al.7 reported that the triclinic KZn2(PO4)(HPO4) could be synthesized with hydrothermal method in an aqueous solution at 100 °C for 24 h. So, it is obvious that the single-phase KZn2(PO4)(HPO4) also can be successfully prepared via solid-state reaction at 80

where x = Ea/RT, h(x) is expressed by the fourth Senum and Yang approximation formulas,24,43and H(x) is also calculated from x.24 The iterative procedure performed involve the following steps:24 (i) Assume h(x) = 1 or H(x) = 1 to estimate the initial value of the activation energy Ea1. The conventional isoconversional methods stop the calculation at this step. (ii) Using Ea1, calculate a new value of Ea2 for the activation energy from the plot of ln[β/H(x)] vs 1/T or ln[β/(h(x)T2)] vs 1/T. (iii) Repeat step (ii), replacing Ea1 with Ea2. When |Eai − Ea(i−1)| < 0.01 kJ mol−1, the last value of Eai is considered to be the exact value of the activation energy of the reaction. These plots are model independent because the estimation of the apparent activation energy does not require selection of particular kinetic model (type of g(α) function). Therefore, the activation energy 8986

dx.doi.org/10.1021/ie300774x | Ind. Eng. Chem. Res. 2012, 51, 8985−8991


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Figure 2. TG/DTG curves of the KZn2(PO4)(HPO4) at different heating rates.

Figure 1. XRD patterns of the product (a) and its calcined sample at 650 °C for 3 h (b).

°C. From Figure 1b, the diffraction peaks in the XRD pattern can be indexed to that of hexagonal KZnPO4 (PDF card 340194), space group P63/*(176), and Zn2P2O7 (PDF card 501370). 3.2. TG-DTG Analysis of the Synthetic Product. Figure 2 shows the TG-DTG curves of the synthetic product at four different heating rates from ambient temperature to 800 °C, respectively. The DTG curve with the presence of only one decomposition step centered at about 470 °C that is about 10 °C lower than that of triclinic phase.7 So, the thermal stability of this prepared KZn2(PO4)(HPO4) is slightly lower than that of triclinic one. The TG-DTG curves show that thermal decomposition of KZn2(PO4)(HPO4) below 800 °C are clear. The mass loss starts at about 420 °C and ends at about 510 °C. The observed mass loss in the TG (β = 5 °C min−1) curve is 2.556%, which is in good agreement with the theoretic 2.496% mass loss of the decomposition of KZn2(PO4)(HPO4). 3.3. FT-IR Spectroscopic Analysis of the Product and Its Calcined Sample. FT-IR spectra of the product and its calcined sample are shown in Figure 3a and b, respectively. From Figure 3a, the bands observed at 750−810, 840−930, 940−1230, 2300−2440, and 2800−3120 cm−1 are vibrational bands of the HPO42‑ ion, and can be assigned to γ(POH), ν(PO2(OH)), δ(POH), B band (νOH, HPO42‑), and A band (νOH, HPO42‑), respectively.47 The bands appeared at 550−600 cm−1 are attributed to PO2 bending modes.48 From Figure 3b, the bands in the 920−1130 cm−1 region can be ascribed to the P−O stretching modes of the [P2O7]4− anion. There are two strong bands located at 932 and 1035 cm−1, where the symmetric PO2 stretching vibration (νsym, PO2) and the asymmetric stretching vibration (νasym, PO2) are known to appear, respectively.47 The asymmetric (νasym, POP) and symmetric stretch (νsym, POP) bridge vibrations are observed at 730 cm−1, while the bands observed at 510−580 cm−1 region

Figure 3. Infrared spectroscopy of the product (a) and its calcined sample at 650 °C for 3 h (b).

are assigned to PO3 deformation and rocking modes, the POP deformations, and the torsional and external modes.47 3.4. Kinetic Parameters and Thermodynamic Functions of Thermal Decomposition. The results from TGDTG and XRD analyses of the product and its calcined product suggest that the thermal decomposition process of KZn2(PO4)(HPO4) below 800 °C consists of one step KZn2(PO4 )(HPO4 ) → KZnPO4 + 0.5Zn2P2O7 + 0.5H 2O (12)

3.4.1. Calculation of Activation Energy Ea by Iterative Procedure. According to eqs 2−7, the isoconversional calculation procedures are used. The values of Ea of the thermal decomposition of KZn2(PO4)(HPO4) corresponding to different degrees of conversion α for β = 5, 10, 15, and 20 °C min−1 are obtained from the isoconversional calculation procedures and are listed in Table 1. The relative errors of 8987



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Table 1. Activation Energies for Thermal Decomposition of KZn2(PO4)(HPO4), Ea (kJ mol−1), and the Intercept, B, at Different Degrees of Conversion α and Calculation Procedures Ea/kJ mol−1 α

E1a

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 average

E2b 415.18 411.43 408.52 405.53 402.91 400.42 397.70 394.50 389.38 402.84

E3c 424.52 420.49 417.37 414.19 411.38 408.73 405.82 402.40 396.93 411.31

E4d 424.55 420.52 417.41 414.23 411.44 408.79 405.88 402.47 397.01 411.37

E5e 424.67 420.64 417.53 414.35 411.55 408.90 405.99 402.57 397.11 411.48

E6f 424.69 420.66 417.54 414.36 411.56 408.90 406.00 402.58 397.12 411.49

Bg 424.69 420.66 417.54 414.36 411.56 408.90 406.00 402.58 397.12 411.49

59.44029 58.26994 57.43132 56.64798 55.95304 55.28621 54.56119 53.70345 52.36503

a

E1 is the result of the OFW method. bE2 is the result of the KAS method. cE3 is the result of the Tang method. dE4 is the result of the Starink method. eE5 is the iterative result of the OFW method. fE6 is the iterative result of the KAS method. gB is the intercept of the plot of eq 7.

KAS, Tang, and Starink methods, the Ea values obtained by OFW method is lower; however, the results obtained from the iterative method and the KAS or Tang or Starink methods are very close to each other. Meanwhile, it can be discovered that the values obtained from the plot of ln[β/H(x)] vs 1/T are the same as that obtained from the plot of ln[β/(h(x)T2)] vs 1/T. Besides the iterative procedures from Table 2, the analysis of relative errors of the values of activation energy for comparative methods shows that accuracy increases in the order of eqs 2, 3, 4, and 5. So, it is obvious that the values of Ea obtained from the iterative method or the Starink or Tang methods are more reliable.23 The activation energy values of the thermal decomposition of KZn2(PO4)(HPO4) is determined to be 411.49 ± 14.37 kJ mol−1 (3.5%) in the range of 0.10 ≤ α ≤ 0.90 and listed in Table 1. If Ea values are independent of α, the decomposition process is dominated by a single reaction step;41,49 on the contrary, a significant variation of Ea with α should be interpreted in terms of multi-step reaction mechanisms.28,41,50 It is considered that the Ea values are independent of α if the relative error of the slope of straight lines of iterative equation is lower than 10%.23,51 So, from Table 1, it is obvious that activation energies at different degrees of conversion vary here by about 3.5% (less than 10%), which indicates that the thermal decomposition process of KZn2(PO4)(HPO4) could be considered as single-step reaction mechanism. Furthermore, the obtained results of activation energy reveal that the

activation energy values obtained from different calculation procedures for the thermal decomposition of KZn2(PO4)(HPO4) at different degrees of conversion are showed in Table 2. Table 2. Relative Errors of Activation Energy for Thermal Decomposition of KZn2(PO4)(HPO4), RE (%), with Different Calculation Procedures at Different Degrees of Conversion REa (%)

a

RE1

RE2

RE3

RE4

RE5

RE6

−2.239 −2.194 −2.160 −2.131 −2.102 −2.074 −2.044 −2.007 −1.949

−0.040 −0.040 −0.041 −0.041 −0.044 −0.042 −0.044 −0.045 −0.048

−0.033 −0.033 −0.031 −0.031 −0.029 −0.027 −0.030 −0.027 −0.028

−0.005 −0.005 −0.002 −0.002 −0.002 0.000 −0.002 −0.002 −0.003

0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0

REi = 100*(Ei − E6)/E6.

The iterative procedure (eqs 6 and 7) is used to calculate the approximate value of Ea approaching to the exact value. As listed in Tables 1 and 2, compared with the relative errors of the values of Ea obtained by the iterative method and the OFW,

Table 3. Relation of Temperature and Degrees of Conversion α at Different Heating Rates β (°C min−1) and Results of lng(α) vs ln β Curves of Three Types of Probable Mechanism Functions α T/K

β=5

β = 10

β = 15

β = 20

function no.

B

−km

−r

741

0.77977

0.51969

0.34732

0.24836

12 13 14

0.641062 0.817075 1.007232

1.089088 1.054806 0.989032

0.995568 0.994845 0.993198

742

0.80641

0.55880

0.38284

0.27829

12 13 14

0.637056 0.805042 0.980549

1.044735 1.008331 0.938787

0.995042 0.994214 0.99232

743

0.83043

0.59715

0.41965

0.31034

12 13 14

0.626763 0.786803 0.947961

0.999502 0.961076 0.888007

0.994509 0.99357 0.991414

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dependence of the activation energy (Ea) on the degrees of conversion (α) helps to identify kinetic scheme of the thermal decomposition process. The data presented in Table 1 show a clear and slight tendency of decreasing values of Ea with respect to increasing values of α. It is obvious that the Ea values shown in Table 1 demonstrate a typical dependence of Ea on α according to Vyazovkin et al.23,52 Vyazovkin and Linert52 have shown that the decreasing dependence of Ea on α corresponds to the kinetic scheme of an endothermic reversible reaction followed by an irreversible one. So, the result of Table 1 indicates that the thermal decomposition process of KZn2(PO4)(HPO4) is a process involving a reversible step and reflects a departure from the initial equilibrium.23,52 3.4.2. Determination of the Most Probable Mechanism Function. Equation 8 is used to find the most probable reaction mechanism. The degrees of conversion for β = 5, 10, 15, and 20 °C min−1 at the same temperature are listed in Table 3. The appropriate temperatures are randomly selected, and the range of the degrees of conversion corresponding to the temperature should be within 0.1−0.9. The corresponding degrees of conversion of three temperatures are chosen as examples to put into 31 types of mechanism functions.25 The slope km, correlation coefficient r, and intercept B of linear regression of ln[g(α)] vs lnβ are obtained. The results of the linear regression show that the slopes of No. 12 (g(α) = 1 − (1 − α)1/4), No. 13 (g(α) = 1 − (1 − α)1/3), and No. 14 (g(α) = 1 − (1 − α)1/2) mechanism functions are the most adjacent to −1.00000, and the correlation coefficients r are better, which are listed in Table 3. Therefore, No. 13 (g(α) = 1 − (1 − α)1/3), which belongs to the mechanism of the contracting sphere, is determined to be the most probable mechanism function of the thermal decomposition of KZn2(PO4)(HPO4). 3.4.3. Calculation of Pre-Exponential Factor A. The preexponential factors A for the thermal decomposition of KZn2(PO4)(HPO4) are estimated from the intercept of the plots of eq 7 (the intercept, B, is listed in Table 1), inserting the determined most probable g(α) function (No.13). The results show that the range of pre-exponential factor A is 2.35 × 10251.92 × 1027 s−1, and the average value of A is 5.86 × 1026 s−1. The high values of Ea and A observed for the thermal decomposition of KZn2(PO4)(HPO4) show that the bond strength between Zn2+ and HPO42‑ ions is very high. The preexponential factor (A) values in the Arrhenius equation for solid state reactions are expected to be over a wide range (6 or 7 orders of magnitude), even after the effect of surface area is taken into account.53−56 Low pre-exponential factors will often indicate a surface reaction, but if the reactions are not dependent on surface area, the low factor may demonstrate a “tight” complex. High factors will usually indicate a “loose” complex.54 Even higher factors (after correction for surface area) can be obtained for complexes having free translation on the surface. On the basis of these reasons, the high values of pre-exponential factor A of the thermal decomposition of KZn2(PO4)(HPO4) reveal a “loose” complex, which is consistent with the reaction mechanism of contracting sphere. 3.4.4. Test of Reliability of the Determined Mechanism Function. In order to prove the validity of the kinetic mechanism of the thermal decomposition of KZn2(PO4)(HPO4), the comparisons were drawn between experimental data and results calculated using the kinetic functions for every heating rate. The results are shown in Figure 4. It can be found that the model predicted plots agree with the experimental

Figure 4. Nonisothermal TG curves (solid lines) and modeled curves (broken lines) of the thermal decomposition of KZn2(PO4)(HPO4) for different heating rates.

plots, indicating that the mechanism function of thermal decomposition of KZn2(PO4)(HPO4) is reliable. 3.5. Determination of Some Thermodynamic Functions of Thermal Decomposition Reaction. Equations 9−11 are used to calculate some thermodynamic functions (ΔS‡, ΔH‡, and ΔG‡) of the transition state complex. The average values of the functions are as follow: ΔS‡ = 251.6 J mol−1 K−1, ΔH‡ = 405.3 kJ mol−1, and ΔG‡ = 218.6 kJ mol−1. As seen from the results, the value of ΔS‡ for the thermal decomposition is positive. The positive value of ΔG‡ is due to the fact that the thermal decomposition process of KZn2(PO4)(HPO4) is not spontaneous at room temperature.

4. CONCLUSIONS This work has successfully achieved a simple synthesis of singlephase KZn2(PO4)(HPO4) via solid-state reaction at 80 °C. The thermal decomposition process of KZn2(PO4)(HPO4) involved one stage, which was the intramolecular dehydration of the protonated phosphate groups to form Zn2P2O7. The values of activation energies estimated with six comparative isoconversional procedures of the thermal decomposition stage indicate that the stage is a single-step kinetic process and can be adequately described by a unique kinetic triplet [Ea, A, g(α)]. The most probable mechanism for the thermal decomposition stage is a contracting sphere. The results predicted by the models agree well with the experimental values. The calculated thermodynamic functions (ΔS‡, ΔH‡, and ΔG‡) of the transition state complex are consistent with the experimental observation.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +86 771 3233718. Fax: +86 771 3233718. E-mail: [email protected]; [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was financially supported by the National Natural Science Foundation of China (No. 21161002), the Key Laboratory of New Processing Technology for Nonferrous Metals and Materials, Ministry of Education, Guangxi University (No. GXKFZ-02), the Guangxi Natural Scientific Foundation of China (Grant Nos. 0991108 and 0832111), and 8989



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non-isothermal kinetics and thermodynamics of thermal decomposition. J. Therm. Anal. Calorim. 2012, 108, 1235. (21) He, Y.; Liao, S.; Chen, Z. P.; Chai, Q.; Li, Y.; Su, Y. Y.; Wu, W. W.; Li, B. Application of isoconversional calculation procedure to nonisothermal kinetics study: Part II. Thermal decomposition of NH4CuPO4·H2O. J. Therm. Anal. Calorim. 2012, http://dx.doi.org/ 10.1007/s10973-012-2306-6. (22) Chen, Z. P.; Chai, Q.; Liao, S.; He, Y.; Li, Y.; Bo, X. H.; Wu, W. W.; Li, B. Application of isoconversional calculation procedure to nonisothermal kinetic Study: III. Thermal decomposition of ammonium cobalt phosphate hydrate. Thermochim. Acta 2012, http://dx.doi.org/ 10.1016/j.tca.2012.05.027. (23) Vyazovkin, S.; Burnham, A. K.; Criado, J. M.; Pérez-Maqueda, L. A.; Popescu, C.; Sbirrazzuoli, N. ICTAC Kinetics Committee recommendations for performing kinetic computations on thermal analysis data. Thermochim. Acta 2011, 520, 1. (24) Genieva, S. D.; Vlaev, L. T.; Atanassov, A. N. Study of the thermooxidative degradation kinetics of poly(tetrafluoroethene) using iso-conversional calculation procedure. J. Therm. Anal. Calorim. 2010, 99, 551. (25) Li, L. Q.; Chen, D. H. Application of iso-temperature method of multiple rate to kinetic analysis. Dehydration for calcium oxalate monohydrate. J. Therm. Anal. Calorim. 2004, 78, 283. (26) Guan, C. X.; Shen, Y. F.; Chen, D. H. Comparative method to evaluate reliable kinetic triplets of thermal decomposition reactions. J. Therm. Anal. Calorim. 2004, 76, 203. (27) Gao, Z.; Amasaki, I.; Nakada, M. A description of kinetics of thermal decomposition of calcium oxalate monohydrate by means of the accommodated Rn model. Thermochim. Acta 2002, 385, 95. (28) Gao, X.; Dollimore, D. The Thermal decomposition of oxalates: Part 26. A kinetic study of the thermal decomposition of manganese(II) oxalate dehydrate. Thermochim. Acta 1993, 215, 47. (29) Nong, W. J.; Chen, X. P.; Wang, L. L.; Liang, J. Z.; Zhong, L. P.; Tong, Z. F. Nonisothermal decomposition kinetics of abietic acid in argon atmosphere. Ind. Eng. Chem. Res. 2011, 50, 13727. (30) Boonchom, B.; Baitahe, R.; Kongtaweelert, S.; Vittayakorn, N. Kinetics and thermodynamics of zinc phosphate hydrate synthesized by a simple route in aqueous and acetone media. Ind. Eng. Chem. Res. 2010, 49, 3571. (31) Janković, B. Nonisothermal degradation of zetaplus impression material: Kinetic aspects. Ind. Eng. Chem. Res. 2009, 48, 7044. (32) Starink, M. J. The determination of activation energy from linear heating rate experiments: A comparison of the accuracy of isoconversion methods. Thermochim. Acta 2003, 404, 163. (33) Tang, W. J.; Liu, Y. W.; Zhang, H.; Wang, C. X. New approximate formula for arrhenius temperature integral. Thermochim. Acta 2003, 408, 39. (34) Janković, B.; Adnadević, B.; Jovanović, J. Application of modelfitting and model-free kinetics to the study of non-isothermal dehydration of equilibrium swollen poly(acrylic acid) hydrogel: Thermogravimetric analysis. Thermochim. Acta 2007, 452, 106. (35) Ozawa, T. A new method of analyzing thermogravimetric data. Bull. Chem. Soc. Jpn. 1965, 38, 1881. (36) Flynn, J. H. The “Temperature Integral”: Its use and abuse. Thermochim. Acta 1997, 300, 83. (37) Seo, D. K.; Park, S. S.; Kim, Y. T.; Hwang, J.; Yu, T. U. Study of coal pyrolysis by thermo-gravimetric analysis (TGA) and concentration measurements of the evolved species. J. Anal. Appl. Pyrolysis 2011, 92, 209. (38) Seo, D. K.; Park, S. S.; Hwang, J.; Yu, T. U. Study of the pyrolysis of biomass using thermo-gravimetric analysis (TGA) and Concentration measurements of the evolved species. J. Anal. Appl. Pyrolysis 2010, 89, 66. (39) Akahira, T.; Sunose, T. Method of determining activation deterioration constant of electrical insulating materials. Res. Rep. Chiba Inst. Technol. (Sci. Technol.) 1971, 16, 22. (40) Soltan, A. S. A study of DSC non-isothermal pre-crystallization kinetics of Pb10Se90 glass using isoconversional kinetic analysis. Phys. B 2010, 405, 965.

the Guangxi Science and Technology Agency Research Item of China (Grant No. 0895002-9).

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Nonisothermal Kinetic Study: IV. Comparative Methods To Evaluate

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