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Ind. Eng. Chem. Res. 2004, 43, 2054-2059
Kinetic Studies of the Calcination of Ammonium Metavanadate by Thermal Methods Tang Wanjun, Liu Yuwen, Yang Xi, and Wang Cunxin* College of Chemistry and Molecular Science, Wuhan University, Wuhan 430072, People’s Republic of China
The calcination of ammonium metavanadate was investigated using simultaneous thermogravimetric analysis (TGA) and differential scanning calorimetry techniques. The decomposition of ammonium metavanadate proceeded in three steps, and kinetic analysis was performed under nonisothermal conditions using an integral composite method. The integral “model-free” method of TGA data at various heating rates suggested that each step be subjected to a single kinetic process. The integral master plot method showed that the calcination reaction for the three steps was best described by accommodated nucleation and nuclei growth kinetic models. Also, the preexponential factors and exact kinetic exponents for these three steps were finally evaluated on the basis of predetermined activation energies and kinetic models. The results of nonisothermal kinetic analysis of the calcination of ammonium metavanadate suggested that this integral composite method was very successful in evaluating kinetic parameters and describing the kinetic model. Introduction Ammonium metavanadate (NH4VO3) is usually used as the basic source for the preparation of vanadium pentoxide (V2O5) based catalysts.1,2 Calcination of NH4VO3 is the most popular method to prepare V2O5,3 which has attracted serious attention because of its wide application in selective oxidation of hydrocarbon, selective catalytic reduction of nitrogen oxides, and oxidation of sulfur dioxide.4 The industrial importance of V2O5 as a key catalyst has promoted a large number of characterizations to better understand the thermal decomposition of NH4VO3, which has been studied with thermogravimetric analysis (TGA), differential thermal analysis (DTA), X-ray diffraction, and thermo-Raman spectroscopy. Sacken and Dahn have studied the effects of different atmospheres on these reactions by thermogravimetry (TG) and evolved gas analysis and concluded that the stoichiometry of the final products obtained from the thermal decomposition of NH4VO3 is governed by atmospheres above 250 °C.5 Twu et al. have studied these reactions under N2 and NH3 + H2O on a molecular level by in situ Raman spectroscopy in the temperature range of 150-400 °C.6 They observed that the decomposition mechanism leading to the formation of V2O5 proceeds via two intermediates: amorphous, transitional (NH4)2V4O11 and NH4V3O8, under a N2 atmosphere. The kinetic parameters of thermal decomposition of solid materials have been obtained through various theoretical methods using TG, DTA, and differential scanning calorimetery (DSC). As far as NH4VO3 is concerned, most previous studies were mainly focused on the synthesis of new catalysts containing V2O5 from precursor NH4VO37 and their static descriptions, i.e., geometrical and catalysis properties, and the overall thermal decomposition behavior of this precursor.8 However, the kinetics of the preparation process of V2O5 has not yet been studied in detail because of the complexity of this decomposition process. A kinetic * To whom correspondence should be addressed. Fax: +86 27 87647617. E-mail:
[email protected].
interpretation is always required for an understanding of the process of solid-state reactions. Therefore, the main aim of this work is to determine the kinetic parameters of calcination of NH4VO3 under an inert atmosphere. Various procedures have been advanced in the literature for evaluation of kinetic parameters and for discrimination of the kinetic model obeyed by the reaction from nonisothermal data from TG and DSC curves,9-15 some of which have been reviewed in recent papers.16,17 More and more evidences show that kinetic methods that use single heating rate data are very limited in their applicability. Estimating the kinetic parameters by forcing various reaction models to fit single heating rate data results in a large uncertainty because several kinetic models might relatively correctly describe the same thermal analysis curve.18-22 To obtain a reliable kinetic description, one should use model-free isoconversional methods, which allow the model-fitting step to be avoided by using multiple heating rate experiments, to eliminate the uncertainty arising from a single-rate “model-fitting” method. However, only one parameter, usually the activation energies calculated by model-free isoconversional methods, does not permit adequate interpretation of kinetic data. An evaluation of full kinetic triplets, i.e., the kinetic model, preexponential factor, and activation energy, is very important for the characterization of any solid-state reactions.23 In this paper, a composite kinetic analysis procedure is applied to evaluate full kinetic triplets of nonisothermal kinetic data. The kinetic triplets of each step of the calcination of NH4VO3 were proposed for the first time from the simultaneous TGA-DSC measurements in flow N2 at different heating rates. The conditions that affect this calcination process and the accuracy of the kinetic parameters obtained were also discussed. Also, the results verified the reasonability of this procedure in nonisothermal kinetic analysis. Experimental Section Analytical-grade NH4VO3 powder (about 100 mesh) was used without further treatment. The thermal
10.1021/ie030418g CCC: $27.50 © 2004 American Chemical Society Published on Web 04/01/2004
Ind. Eng. Chem. Res., Vol. 43, No. 9, 2004 2055
analysis experiments were performed using a Setaram TG/DTA/DSC-16 instrument. The sample was loaded in an open alumina crucible, and γ-alumina was used as the reference. The furnace temperature, which was controlled by a thermocouple, rose linearly according to the preset linear temperature schedules. Also, the sample temperature was measured using another thermocouple located between the sample crucible and the reference crucible. The sample temperature had been calibrated using standard metals including indium, lead, aluminum, silver, and gold. Samples of NH4VO3 in alumina crucibles were heated in a low-flowing atmosphere of nitrogen (20 mL‚min-1). The temperature of the furnace was programmed to rise from room temperature (20 °C) to 350 °C at various heating rates. After an initial period of nonlinear heating, the programmed linear rates were achieved. The actual heating rates for the temperature region of NH4VO3 calcination were evaluated by using the sample temperature vs time curve. Different sample masses and various heating rates were used to test their effects on the calcination process. Theoretical Background In this work, the calcination reaction of NH4VO3 can be described as the thermal decomposition of a solid:
Asolid f Bsolid + Cgas Kinetic analysis of solid-state decomposition is usually based on a single-step kinetic equation. The rate of nonisothermal decomposition of this type of reaction is expressed as
dR/dT ) (A/β) exp(-E/RT)f(R)
(1)
where T is the temperature, R is the extent of conversion, β is the linear heating rate, f(R) is the reaction model depending on the reaction mechanism, A is the preexponential factor, R is the gas constant, and E is the activation energy. The reaction models, which are derived by assuming simply idealized models, may take various forms, and some widely used mechanisms in solid-state reactions are listed in Table 1.24 Rearranging eq 1 and integrating both sides of the equation leads to the following expression:
∫T exp(-E/RT) dT ≈ T (A/β)∫0 exp(-E/RT) dT ) (AE/βR)P(u)
g(R) ) (A/β)
T
0
(2)
where P(u) ) ∫u∞-(e-u/u2) du and u ) E/RT. Generally, decomposition reactions are very slow at subambient temperatures so that the lower limit of the integral on the right-hand side of eq 2, T0, can be approximated to be zero. Unfortunately, P(u), also called the “temperature integral”, cannot be analytically integrated. In this paper, to solve this problem, an approximate formula25 is introduced into eq 2, and taking the logarithms of both sides, eq 3 is obtained as
Table 1. Kinetic Model Function g(r) Usually Employed for the Solid-State Reaction no.
reaction model
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Avrami-Erofeyev, m ) 4 Avrami-Erofeyev, m ) 3 Avrami-Erofeyev, m ) 2 Avrami-Erofeyev, m ) 1.5 phase boundary reaction, n ) 1 phase boundary reaction, n ) 2 phase boundary reaction, n ) 3 one-dimensional diffusion two-dimensional diffusion three-dimensional diffusion Jander’s type diffusion power law, n ) 1/4 power law, n ) 1/3 power law, n ) 1/2 power law, n ) 3/2 first order second order third order
symbol A4 A3 A2 A1.5 R1 R2 R3 D1 D2 D4 D3
A 1, F 1 F2 F3
g(R) [-ln(1 - R)]1/4 [-ln(1 - R)]1/3 [-ln(1 - R)]1/2 [-ln(1 - R)]2/3 R 1 - (1 - R)1/2 1 - (1 - R)1/3 1/2R2 1/2[1 - (1 - R)1/2]1/2 1 - 2R/3 - (1 - R)2/3 [1 - (1 - R)1/3]2 R1/4 R1/3 R1/2 R3/2 -ln(1 - R) (1 - R)-1 - 1 1/2[(1 - R)-2 - 1]}
considered runs, analysis of the measurements related to a given extent of conversion R at different heating rates allows us to evaluate the activation energy without knowledge of the true g(R) function. If this basic assumption is not fulfilled, an apparent E value would be calculated, which differs from the actual value. It is preferable to perform the isoconversional analysis at different R values in order to prove the invariance of the apparent E value. Analysis of the invariance of the apparent E value will provide important clues about the reaction mechanism.26,27 Normally, a constant E value is assumed in the case of single-step reactions. For a single-step process with an invariant g(R) expression, an analysis using the master plots delivers an unambiguous choice of the appropriate kinetic model. Taking account into a single-step process, the kinetic triplets, i.e., g(R), A, and E, are invariable. Using a reference at point R ) 0.5 and according to eq 2, one gets
g(0.5) ) (AE/βR)P(u0.5)
(4)
where u0.5 ) E/RT0.5. When eq 2 is divided by eq 4, the following equation is obtained:
g(R)/g(0.5) ) P(u)/P(u0.5)
(5)
Plotting g(R)/g(0.5) against R corresponds to theoretical master plots of various g(R) functions.28,29 To draw the experimental master plots of P(u)/P(u0.5) against R from experimental data obtained under any heating rates, the knowledge of temperature as a function of R and the value of E for the process should be known in advance, and P(u) can be calculated directly using a numerical Simpson’s procedure or some approximate formulas. In this paper, an approximate formula30 of P(u) with high accuracy was used.
P(u) ) exp(-u)/[u(1.00198882u + 1.87391198)] (6)
ln(β/T1.894661) ) ln[AE/Rg(R)] + 3.635041 1.894661 ln E - 1.001450E/RT (3)
The experimental master plot is independent of the heating schedule. Equation 5 indicates that, for a given R, the experimental value of P(u)/P(u0.5) and theoretically calculated values of g(R)/g(0.5) are equivalent when an appropriate kinetic model is used. This integral master plot method can be used to determine the reaction kinetic models of solid-state reactions.
Equation 3 is the basis of the model-free isoconversional method for nonisothermal data. Assuming that the reaction model, g(R), must be invariant for all
Results and Discussion TG-DTG and DSC Curves for the Calcination Process of NH4VO3. Both heating rates and sample
2056 Ind. Eng. Chem. Res., Vol. 43, No. 9, 2004
Figure 1. TG-DTG curves at a heating rate of 2 K‚min-1 under a sample weight of 2.232 mg.
mass affect the resolving power of thermal analysis curves greatly for separating the first and second steps of the calcination of NH4VO3 because these two steps may become partially overlapped under increasing heating rates or sample amounts. In practical kinetic analysis, heating rates of 2, 3, 4, and 5 K‚min-1 and a sample mass of 2.0 ( 0.2 mg were used to acquire highquality measurements. TG-DTG curves at a heating rate of 2 K‚min-1 are shown in Figure 1. DSC curves at various heating rates are shown in Figure 2. Calcination Mechanism of NH4VO3. Figures 1 and 2 show that the calcination of NH4VO3 can be divided into three distinguished steps in the temperature range of 50-350 °C. Also, three endothermic peaks are observed in this temperature range. The average weight loss is about 11.45% for the first step, 3.84% for the second step, and 6.81% for the third step. Upon comparison with Sacken and Twu’s studies,5,6 the observed NH4VO3 mass loss pattern is -
1 1 H O, - NH3 4 2 2
NH4VO3 98 -
1
H O, -
1
Figure 2. DSC curves for NH4VO3 at heating rates of 2, 3, 4, and 5 K‚min-1 under a sample weight of 2.0 ( 0.2 mg.
Figure 3. Plots for determination of the activation energy of the first step of the calcination of NH4VO3 at different R values: 0.2 (9), 0.3 (0), 0.4 (2), 0.5 (4), 0.6 (1), 0.7 (3), and 0.8 (b). Solid lines are linear fits corresponding to different R values.
NH
3 12 2 6 1 (NH4)2V4O11 98 4
-
1
H O, -
1
NH
3 6 2 3 1 1 NH4V3O8 98 V2O5 3 2
The theoretical weight loss is 11.1% for the first step, 3.7% for the second step, and 6.4% for the third step. Nonisothermal Kinetics for the First Step of Calcination of NH4VO3. (a) Integral Model-Free Method for Estimating the Activation Energy Dependence. When R ) 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, and 0.8 are used and ln[β/T1.894661] vs 1/T is plotted, a group of parallel lines (shown in Figure 3) were obtained. The activation energy can be obtained from the slope of the regression line. The activation energy on the dependence of the extent of conversion is shown in Figure 4. This dependence shows that the activation energy hardly varies with the extent of conversion and the mean activation energy is 150.69 ( 1.86 kJ‚mol-1. Little dependence of the activation energy on the extent of conversion indicates that there is a high probability for the presence of a single-step reaction.
Figure 4. Dependence of the apparent value of E on R for steps I (9), II (b), and III (2).
(b) Master Plot Method for Determining the Kinetic Model. Using the predetermined value of E, 150.69 ( 1.86 kJ‚mol-1, along with the temperature measured as a function of R under various heating rates,
Ind. Eng. Chem. Res., Vol. 43, No. 9, 2004 2057
Figure 5. Master plots of theoretical g(R)/g(0.5) against R for various reaction models (solid curves, as enumerated in Table 1, and curve 19 represents function g(R) ) [-ln(1 - R)]0.57) and experimental data for the first step of the calcination of NH4VO3 at heating rates of 2 (9), 3 (b), 4 (2), and 5 (1) K‚min-1.
the experimental master plots for TGA data were constructed according to eqs 5 and 6. The experimental master plots of P(u)/P(u0.5) against R constructed from experimental data under different heating rates are shown in Figure 5. Also, the theoretical master plots of various kinetic functions are also shown in Figure 5. It is shown that all of these experimental master plots closely match each other irrespective of temperature schedules. The comparison of the experimental master plots with theoretical ones indicates that the kinetic process for the first step of the calcination of NH4VO3 is most probably described by the Am model, g(R) ) [-ln(1 - R)]1/m, because the experimental master plots lie between the theoretical masters plots A1.5 and A2. It is likely that the reaction geometry of the overall reaction cannot be expressed in terms of an integral value of m. A nonintegral exponent was introduced because it was thought that the idealized conditions for nucleation and nuclei growth could not be met in this process.31 (c) Estimating the Preexponential Factor and Kinetic Exponent. The most appropriate kinetic model was estimated as the Am function with nonintegral kinetic exponent m, which was used to accommodate the distortion of the actual reaction models from the idealized nucleation and nuclei growth ones. By assuming the Am law, experimental data, the expression of the Am model, and the average reaction energy predetermined were introduced into eq 2, the following expression was obtained.
Figure 6. Plotting ln[βR/E] - ln[P(u)] against -ln[-ln(1 - R)] for the first step of the calcination of NH4VO3 at heating rates of 2 (9), 3 (b), 4 (2), and 5 (1) K‚min-1 and their linear-fit drawing (solid lines), respectively. Table 2. Preexponential and Kinetic Exponents for Each Step of the Calcination of NH4VO3 under Various Heating Rates E (kJ‚mol-1)
β (K‚min-1)
ln A (s-1)
m
r
I
150.69 ( 1.86
168.17 ( 2.83
34.66 34.65 34.61 34.68 34.65 ( 0.03 36.75 36.73 36.76 36.74 36.74 ( 0.01 30.91 30.83 30.84 30.91 30.87 ( 0.04
1.77 1.75 1.71 1.75 1.75 ( 0.02 3.47 2.92 3.28 3.13 3.20 ( 0.24 1.89 1.85 1.77 1.79 1.83 ( 0.06
0.9999 0.9999 0.9997 0.9997
II
2.11 3.17 4.27 5.38 mean 2.09 3.16 4.24 5.36 mean 2.06 3.09 4.13 5.18 mean
step
III 169.37 ( 4.65
0.9865 0.9877 0.9911 0.9902 0.9988 0.9990 0.9987 0.9990
ln[βR/E] - ln[P(u)] ) ln A - (1/m) ln[-ln(1 - R)] (7) A group of lines were obtained by plotting ln[βR/E] - ln[P(u)] against -ln[-ln(1 - R)]. As shown in Figure 6, the lines corresponding to various heating rates superpose each other nearly completely. The resulting logarithmic values of the preexponential factor, kinetic exponent m, and actual values of the heating rates for the temperature region of NH4VO3 calcination are presented in Table 2. Kinetic Triplets for Three Steps of the Calcination of NH4VO3. The same procedures were followed for the second and third steps of the calcination of NH4-
Figure 7. Master plots of theoretical g(R)/g(0.5) against R for various reaction models (solid curves, as enumerated in Table 1, and curve 19 represents function g(R) ) [-ln(1 - R)]0.31) and experimental data for the second step of the calcination of NH4VO3 at heating rates of 2 (9), 3 (b), 4 (2), and 5 (1) K‚min-1.
VO3. The activation energy dependences for the second and third steps are shown in Figure 4. It is shown that the activation energies are nearly independent of conversion and the mean activation energies are
2058 Ind. Eng. Chem. Res., Vol. 43, No. 9, 2004
through a single-rate process. The master plot method indicated that the most possible kinetic models for each decomposition process be described by using an accommodated Avrami-Erofeyev equation, g(R) ) [-ln(1 R)]1/m. The preexponential factors and exact kinetic exponents for these three steps were finally determined, respectively. Using the integral composite procedure above, it is possible to describe the kinetic aspects of nonisothermal decomposition of a solid material. By this method, it seems to be easy to estimate the kinetic triplets of nonisothermal solid decomposition kinetics satisfactorily. Acknowledgment This project was supported by National Nature Sciences Foundation of China (Project 30070200). Figure 8. Master plots of theoretical g(R)/g(0.5) against R for various reaction models (solid curves, as enumerated in Table 1, and curve 19 represents function g(R) ) [-ln(1 - R)]0.55) and experimental data for the third step of the calcination of NH4VO3 at heating rates of 2 (9), 3 (b), 4 (2), and 5 (1) K‚min-1.
168.17 ( 2.83 and 169.37 ( 4.65 kJ‚mol-1, respectively. These facts indicate that there exists a high probability for the presence of a single-step reaction for the second and third steps, respectively. Their experimental master plots of P(u)/P(u0.5) against R constructed from experimental data and theoretical master plots are shown in Figures 7 and 8, respectively. Figures 7 and 8 indicate that the most probable kinetic models for the second and third steps of the calcination of NH4VO3 are best described with accommodated nucleation and growth model also. Their logarithmic values of preexponential factors, kinetic exponents, and corresponding local heating rates are also presented in Table 2. It can be concluded from Table 2 that the possible mechanisms for decompositions of NH4VO3 and two intermediates, (NH4)2V4O11 and NH4V3O8, are random nucleation and subsequently growth under a N2 atmosphere. The measurements suggest that the possible forms of g(R) for decomposition of NH4VO3 are
g(R) ) [-ln(1 - R)]0.57
(8)
for the first step,
g(R) ) [-ln(1 - R)]0.31
(9)
for the second step, and
g(R) ) [-ln(1 - R)]0.55
(10)
for the third step. Compared with an idealized AvramiErofeyev equation, a nonintegral value of kinetic exponent m is more appropriate to describe the actual decomposition process. Conclusion The calcination of NH4VO3 proceeded in a very complicated way because the decomposition rates changed with the heating rates or sample masses. Kinetic analysis was applicable under this experimental condition with low heating rates and small sample weights. Considering little dependence of the activation energy on the extent of conversion, it could be postulated that each step of the calcination of NH4VO3 is carried
Nomenclature R ) extent of conversion β ) heating rate, K‚min-1 T ) temperature at a special point in time, K m ) kinetic exponent of the Avrami-Erofeev equation A ) pre-exponential factor, s-1 E ) Arrhenius activation energy, kJ‚mol-1 R ) gas constant, 8.314 J‚K-1‚mol-1
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Received for review May 14, 2003 Revised manuscript received September 28, 2003 Accepted September 28, 2003 IE030418G
