A New Method for Evaluation of the Isothermal Conversion Curves

Dec 29, 2008 - Faculty of Physical Chemistry, UniVersity of Belgrade, Strudentski trg ... A new method for evaluation of isothermal conversion curves ...
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Ind. Eng. Chem. Res. 2009, 48, 1420–1427

A New Method for Evaluation of the Isothermal Conversion Curves from the Nonisothermal Measurements. Application in Nickel Oxide Reduction Kinetics Borivoj Adnadevic´* and Bojan Jankovic´ Faculty of Physical Chemistry, UniVersity of Belgrade, Strudentski trg 12-16, P.O. Box 137, 11001 Belgrade, Serbia

A new method for evaluation of isothermal conversion curves from the experimentally determined nonisothermal conversion curves for the nickel oxide reduction process in hydrogen atmosphere was established. It was concluded that by applying the conventional and proposed prediction methods it was not possible (at Tiso e 300 °C) to calculate the isothermal conversion curves using the experimentally obtained nonisothermal conversion curves for this reduction process. The dependence of the apparent activation energy on the degree of conversion shows that the investigated reduction process is complex under isothermal or nonisothermal conditions. By applying Miura’s procedure, the shape of density distribution functions of the apparent activation energies was determined for the isothermal and nonisothermal reduction processes. It was concluded that the existence of different distributions of internal energy of the NiO reduction centers is a consequence of different reduction kinetics under isothermal and nonisothermal experimental conditions. 1. Introduction Metal oxides are widely used in many technological applications, such as coating, catalysis, electrochemistry, optical fibers, sensors, etc.1,2 For the preparation of active oxide catalysts, the partial reduction of nickel oxide under hydrogen at elevated temperatures is the effective method.3-5 Reduction of nickel oxide by hydrogen was the object of numerous studies, because nickel oxide is a component of many industrial catalysts and electromagnetic devices. Kinetic studies of nickel oxide reduction by hydrogen usually can be carried out under isothermal or nonisothermal experimental conditions. In the field of thermal analysis, much attention has been directed toward the problem of obtaining the kinetic information from programmed temperature, dynamic, or nonisothermal experiments. Richardson et al.6 have given a detailed inspection of results in the kinetic parameters and reaction models determination, for hydrogen reduction of different prepared samples of NiO under isothermal and nonisothermal conditions. Many studies have been published in this area,7-23 including those of Jankovic´ et al.21,22 who performed the temperatureprogrammed reduction of NiO under hydrogen atmosphere. It was concluded that the reduction of NiO using hydrogen is a multistep mechanism and can be described by the two-parameter autocatalytic Sesta´k-Berggren (SB) reaction model. The following kinetic parameters were obtained for the temperatureprogrammed reduction of nickel oxide in hydrogen atmosphere: Ea ) 96.4 kJ mol-1 and A ) 1.04 × 108 min-1. Thermoanalytical methods for determination of kinetic parameters in both isothermal and nonisothermal regimes are wellknown in the scientific literature. The results depend on the precision of the experimental data and on the mathematical modeling of the investigated process. Gonzales and Havel24 have developed the computation method for evaluation of Arrhenius equation parameters from the nonisothermal kinetic data. A graphical and analytical method for generating reaction isotherms from a set of nonisotherms, and vice versa, have been presented by Telea and co-workers.25 The method was tested using the computer-generated isotherms and nonisotherms, and * To whom correspondence should be addressed. E-mail: bora@ ffh.bg.ac.yu. Tel./Fax: +381-11-2187-133.

experimentally for dehydration of calcium oxalate. Kinetic parametrization of transitions and reactions in food systems from isothermal and nonisothermal DSC trace data was presented in a paper by Riva and Schiraldi.26 Rios27 established a mathematical method for conversion of a continuous cooling transformation curve into an isothermal transformation curve. Liu et al.28 combined an analytical method with numerical calculations for conversion of continuous heating data (CHD) or cooling transformation data (CTD) into isothermal transformation data (ITD), and also conversion of ITD into CHD or CTD data. In the present paper a possibility of applying a new computational procedure for evaluation of isothermal conversion curves from experimentally obtained nonisothermal conversion curves is investigated. The new computational method is applied on the reduction process of nickel oxide under hydrogen atmosphere in order to understand the mechanism of that process. 2. Isoconversional (Model-Free) Analysis The differential isoconversional method by Friedman29 is based on the following equation:

[ ( dRdT )]

ln Vh

R,i

) ln[AR f (R)] -

Ea,R RTR,i

(1)

where Vh is the heating rate, Ea,R is the value of apparent activation energy at a given conversion (R), AR represents the value of the pre-exponential factor at a specific degree of conversion (R), f (R) is the reaction model, and R is the gas constant. The subscript i denotes the ordinal number of a nonisothermal experiment conducted at heating rate Vh,i and the subscript R denotes the quantities evaluated at a specific degree of conversion. At a certain conversion, the slope and the intercept of the straight line of ln[Vh(dR/dT)]R,i versus 1/TR,i give the apparent activation energy and the product AR f(R), respectively. In a simple single-step process, the obtained values of Ea,R are invariant with respect to R. If the value of Ea,R varies with the degree of conversion, the results should be interpreted in the terms of a multistep reaction mechanism.

10.1021/ie801074j CCC: $40.75  2009 American Chemical Society Published on Web 12/29/2008

Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009 1421 30,31

The integral isoconversional method is an isothermal method which is based on taking the natural logarithm of

( )

g(R) ) A exp -

Ea t RT

(2)

which gives

[ ]

-ln tR ) ln

AR Ea,R g(R) RTR

(3)

where g(R) is the integral function of reaction model, t is the time, tR is the time at a given conversion (R), AR is the preexponential factor at a given R, Ea,R is the apparent activation energy for each given value of R, TR is the absolute temperature value at a given R, and R is the gas constant. For a constant value of R, the first term in eq 3 is a constant, and Ea,R can be determined from the slope of -ln tR versus 1/TR, regardless of the form of the reaction model. 3. Conventional Isothermal “Predictions” Kinetic computations can be used for drawing mechanistic conclusions or for making simulations of the process. One of the most used simulations is called “isothermal predictions”, which means that the nonisothermal kinetic parameters can be used to simulate the variation of the degree of conversion (R) versus time (t) for a given (constant) temperature (Tiso). These simulations can be obtained using the following equation:32,33

[ ( )] ∑ ∫

tR ) Vh exp -

Ea,R RTiso

-1 R 0

TR

TR-∆R

( )

exp -

Ea,R dT RT

(4)

where tR is the time to reach a given conversion (R), Vh is the heating rate of the nonisothermal experiment used for the computation, Tiso is the isothermal temperature of the isothermal simulation, Ea,R is the value of apparent activation energy obtained from isoconversional analysis at a given conversion (R), and R is the gas constant. In eq 4, the integral was evaluated by numerical integration of the data using the trapezoid rule, and R was varied between 0.00 and 0.95 in steps of 0.02. As can be seen from eq 4, these simulations can be done using sole Ea,R-dependence computed with the Friedman (FR) isoconversional method. 4. Experimental Section 4.1. Materials and Methods. The NiO samples were obtained by a gel-combustion method described elsewhere.34 A green-colored transparent gel was obtained by drying an aqueous solution of nickel nitrate hexahydrate (Fluka, 99.5%) and citric acid (Fluka, 99.5%), dissolved in a mole ratio of 1.8: 1. This gel further underwent self-ignition by being heated in air up to 300 °C, and then by an additional heating up to 500 °C which produced very fine nickel oxide powder. The mean size of nickel oxide particles, determined from XRD data was dm ) 30 nm, and this value agrees very well with the data published by Wu and co-workers.35 4.2. Nonisothermal Thermogravimetric Measurements. The experiments were carried out in a TA SDT 2960 device, capable of simultaneous TGA-DTA analysis in a temperature range from 25 to 1500 °C. The nickel oxide samples were reduced directly within the thermo-balance, in silicon carbide pans, in (99.9995 vol%) hydrogen flowing at a rate of 100 mL min-1, using various heating rates: Vh ) 2.5, 5, 10, and 20 °C min-1, in the temperature range from ambient to 500 °C. The

Figure 1. Experimental nonisothermal conversion (R-T) curves for the reduction process of nickel oxide by hydrogen at four different heating rates (2.5, 5, 10, and 20 °C min-1). Table 1. The Influence of Heating Rate on Characteristic Temperatures of the Reduction Process of NiO Using Hydrogen Vh (°C min-1)

Ti (°C)

Tp (°C)

Tf (°C)

∆T (°C)

2.5 5 10 20

260 275 285 300

285 300 315 340

395 455 465 485

135 180 180 185

mass of the samples used for thermogravimetric investigations was about 25 ( 0.5 mg. 4.3. Isothermal Thermogravimetric Measurements. The reduction experiments were carried out in a TA SDT 2960 device, capable of simultaneous TGA-DTA analysis in the temperature range from ambient to 1500 °C. The nickel oxide samples were reduced directly within the thermo-balance, in silicon carbide pans, in (99.9995 vol%) hydrogen flowing at a rate of 100 mL min-1. The mass loss experiments were carried out at five different operating (isothermal) temperatures: Tiso ) 245, 255, 265, 275, and 300 °C. The sample mass used for thermogravimetric investigations was about 25 ( 0.5 mg, as in the case of nonisothermal experiments. The isothermal conversion curve represents the dependence of the degree of conversion (R) on the reaction time (t), R ) f(t), at a constant value of experimental isothermal temperature (Tiso). The experimentally determined degree of conversion (R) for the reduction process under isothermal conditions can be expressed as R)

m0 - mt m0 - mf

(5)

where m0, mt, and mf refer to the initial, actual (at time t), and final mass of the investigated sample. Nonisothermally, the degree of conversion at any temperature is: R)

m0 - mT m0 - mf

(6)

where, mT is the sample mass at temperature T. 5. Results and Discussion Considering the conversion grade as defined in eq 6, it is possible to use the corresponding mass values determined by TG to obtain the evolution of conversion with temperature. Figure 1 shows experimentally obtained conversion curves under nonisothermal conditions for the investigated reduction process.21,22

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Figure 2. Dependences of the apparent activation energy (Ea,R) (a) and the apparent intercept (ln[ARf (R)]) (b) on the degree of conversion (R) evaluated by the Friedman’s isoconversional method for the nonisothermal reduction process of NiO by hydrogen.

Figure 3. Comparison between the experimental isothermal conversion curve at Tiso ) 245 °C and predicted isothermal curves (eq 4) using four different heating rates (Vh ) 2.5, 5, 10, and 20 °C min-1).

Table 1 shows the influence of heating rate on characteristic temperatures of the reduction process: the onset temperature (Ti), the inflection (peak) temperature (Tp), the final temperature (Tf) and temperature differences (∆T ) Tf - Ti). The increase of the heating rate leads to increases of Ti, Tp, Tf, and ∆T values, which indicates that the onset of reduction process occurs at progressively higher experimental temperatures. The results obtained by application of the Friedman (FR)29 method on the investigated reduction process are presented in Figure 2a,b. Solid and empty symbols in the figure represent the apparent activation energy values and the values of isoconversional intercepts, respectively (eq 1). Within the limits of the experimental error in the determination of Ea,R by the Friedman’s method (Ea,R exhibits values of a relative standard deviation lower than 10%) the apparent activation energy of the reduction process of nickel oxide by hydrogen in the 0.20 e R e 0.60 range is a constant value, independent of R values (Ea ) 90.8 kJ mol-1). Discrepancies can be observed for conversions lower than R ) 0.20 and higher than R ) 0.60, where the calculated errors of Ea,R are significantly higher, in comparison with the calculated errors of Ea,R for the intermediate R range. These results allow for a conclusion that the values of Ea for the 0.20 e R e 0.60 range were constant and independent of R. Alternatively, the ln[AR f (R)]-R plot demonstrates identical behavior (Figure 2b),

Figure 4. Comparison between the experimental isothermal conversion curve at Tiso ) 255 °C and the predicted isothermal curves (eq 4) using the four different heating rates (Vh ) 2.5, 5, 10, and 20 °C min-1).

Figure 5. Comparison between the experimental isothermal conversion curve at Tiso ) 265 °C and the predicted isothermal curves (eq 4) using the four different heating rates (Vh ) 2.5, 5, 10, and 20 °C min-1).

which may suggest that both the apparent activation energy (Ea) and the pre-exponential factor (A) are practically independent of the degree of conversion, in this R range. The existence of a plateau in Figure 2a,b, in a wide range of R values, is proof of a single-step reaction. Figures 3-7 show a comparison between the experimental (symbols) and predicted (lines) values of R versus t for the isothermal reduction process at five different operating temperatures (Tiso ) 245, 255, 265, 275, and 300 °C), using four different heating rates (Vh ) 2.5, 5, 10, and 20 °C min-1) in the nonisothermal experiments. The Ea,R values evaluated from the Friedman (FR) method (eq 1) were used for isothermal predictions. Deviations of the predicted results from the experimental data can be calculated by the following expression: N

S)

∑ [R

i,calcd - Ri,exp

]2

(7)

i)1

where Ri,calcd is the predicted data, Ri,exp is the experimental data, and N is the number of data items. The deviations (S) of the predicted results from the experimental ones at all operating temperatures are shown in Table 2. It can be seen from Table 2 that the least deviation of the predicted conversion curve from the experimental one can be observed at Vh ) 10 °C min-1, at all operating temperatures.

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problem, which is connected with the complexity of the investigated process in the solid phase. This phenomenon was especially manifested in nonisothermal conditions. 5.1. The New Prediction Method. Assuming that the reaction times of the reduction process are randomly distributed according to the Weibull distribution function, and assuming that the value of Weibull distribution function of reaction times is proportional to the degree of conversion (R), the following applies:37

[(

R(T) ) 1 - exp -

Figure 6. Comparison between the experimental isothermal conversion curve at Tiso ) 275 °C and the predicted isothermal curves (eq 4) using the four different heating rates (Vh ) 2.5, 5, 10, and 20 °C min-1).

(T - T0) Vhη

( )

heating rate, Vh (°C min-1) temperature, T (°C)

2.5 S

5 S

10 S

20 S

245 255 265 275 300

0.8661 1.6696 2.3389 2.4270 3.5123

0.7965 1.2844 1.6202 1.7901 2.3279

0.1774 0.6455 0.8365 1.2352 1.6230

0.3758 1.2822 1.7438 1.9914 2.3634

On the other hand, the value of S increases with increasing operating temperature, independently of the heating rate. However, it can be observed from Figures 3-7 that there are great discrepancies between the experimentally obtained and the predicted conversion curves, at each Tiso. The experimentally determined values of kinetic parameters for the reactions in the solid state, obtained under isothermal and nonisothermal conditions, can be significantly different.36 According to Vyazovkin et al.,36 there are two basic groups of causes that lead to different values of kinetic parameters of the investigated process under isothermal and nonisothermal conditions. These are (1) physical causes and (2) formal mathematical causes.36 The formal mathematical cause of disagreement of the kinetic parameter values under different experimental conditions is the nonuniform solving of the invariant kinetic

(8)

(9)

Vh (10) φ where A, B, C, D and φ are the corresponding numerical constants necessary to describe the relationships between the mentioned parameters and the heating rate. The constant A is dimensionless, as is the parameter β, whereas constant B has dimensions [min °C-1]; C and D have dimensions of the parameter η, whereas φ has dimensions of the heating rate ([°C min-1]). In the considered case, we have the following values of the numerical constants: A ) 2.440, B ) 0.038 min °C-1, C ) 2.541 min, D ) 18.764 min and φ ) 3.147 °C min-1. The above results enable us to calculate the nonisothermal conversion curves (R ) R(T)Vh) for a given system and an arbitrary set of Vh. We can thus say that by applying the analytical or graphical method we can obtain a satisfactory number of data for calculating the isothermal conversion curves (R ) R(t)T) at different isothermal operating temperatures (Ti). Subscript i is the ordinal number of an experiment performed at a given operating temperature (Ti). The above procedure allows the evaluation of isothermal conversion curves from the well-known nonisothermal conversion curves. The obtained results can be compared with the results of direct isothermal measurements. By applying the new computational procedure we can check the above results and draw appropriate conclusions about reaction mechanisms for the investigated reduction process under different experimental conditions. Figure 8 shows the calculated nonisothermal conversion curves (full lines) for the investigated reduction process of nickel oxide, determined at 45 values of heating rates (from left to right: 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 1.5, 2, 2.5 (exptl), 3, 3.5, 4, 4.5, 5 (exptl), 6, 7, 8, 9, 10 (exptl), 12, 14, 15, 16, 18, 20 (exptl), 22, 24, 26, 28, 29, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48 and 50 °C min-1). The nonisothermal conversion curves for the chosen set of heating rates including the experimental values of Vh (Figure 8) are calculated using eqs 8-10. η ) C + D exp -

Table 2. Deviations (S) (eq 7) of the Predicted Results (eq 4) from the Experimental Isothermal Data at Five Operating Temperatures (Tiso ) 245, 255, 265, 275, and 300 °C) Using Four Different Heating Rates (Wh ) 2.5, 5, 10, and 20 °C min-1)

β

where R(T) is the degree of conversion or the cumulative Weibull distribution function, (T - T0)/Vh ) t is the reaction time, T is the absolute temperature, T0 is the temperature of the system at the beginning of the process, Vh is the heating rate, β is the shape parameter (because it determines the shape of conversion curve), and η is the scale parameter (as it scales the T variable). The values of nonisothermal conversion (distribution) parameters (β,η) are in a functional relationship with the heating rate of the system. The functional relationships between the parameters β, η, and Vh for the investigated nonisothermal reduction process of nickel oxide can be expressed through the following numerical relations: β ) A + BVh

Figure 7. Comparison between the experimental isothermal conversion curve at Tiso ) 300 °C and the predicted isothermal curves (eq 4) using the four different heating rates (Vh ) 2.5, 5, 10, and 20 °C min-1).

)]

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Figure 8. Calculated nonisothermal conversion curves (full lines) for the investigated reduction process of nickel oxide determined at 45 values of heating rates (from left to right: Vh ) 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 22, 24, 26, 28, 29, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48 and 50 °C min-1); T1 (0), T2 (O), T3 ()), T4 (∆) and T5 (×) represent the isothermal operating temperatures 245, 255, 265, 275, and 300 °C, respectively.

Figure 9. Comparison between the experimental (full lines) and the calculated (dash-dot lines) isothermal (R-t) conversion curves at four different operating temperatures (Ti): T1 ) 245, T2 ) 255, T3 ) 265 and T4 ) 275 °C, for the reduction process of nickel oxide by hydrogen.

For the isothermal operating temperatures (T1 ) 245, T2 ) 255, T3 ) 265, T4 ) 275 and T5 ) 300 °C) the values of Rj,iso ) Rj,iso(t) were determined using the graphical and analytical procedures. Subscript j represents the number of R value obtained at every intersection point of the corresponding symbols (isothermal operating temperature Ti) and the corresponding nonisothermal conversion curve (line) (see Figure 8). The calculated isothermal conversion curves at the given operating temperatures are presented in Figures 9 and 10 (dash-dot curves). The experimentally determined isothermal conversion curves are presented in the same figures (Figures 9 and 10, full line curves). The deviations (S) of the calculated conversion curves from the experimentally obtained isothermal conversion curves

Figure 10. Comparison between the experimental (full line) and the calculated (dash-dot line) isothermal (R-t) conversion curve at the highest operating temperature, T5 ) 300 °C, for the reduction process of nickel oxide by hydrogen. Table 3. Deviations (S) (eq 7) of the Calculated Conversion Curves from the Experimentally Obtained Isothermal Conversion Curves at Tiso ) 245, 255, 265, 275, and 300 °C temperature, T (°C)

S

245 255 265 275 300

2.5075 1.3382 0.6413 0.3082 0.1124

(Figures 9 and 10), at five different operating temperatures are shown in Table 3. From the results presented in Table 3, it can be concluded that with the increasing of isothermal temperature, the value of S decreases. It can be pointed out that at T5 ) 300 °C (Figure 10) the agreement between the experimentally determined conversion curve and the calculated one is satisfactory, compared with the results obtained by the conventional prediction method (eq 4), at the same temperature for all considered heating rates (Table 2). The agreement between the experimental and the calculated isothermal conversion curves increases with increasing operating temperature from T1 to T5 (Table 3). On the basis of the above results, it can be concluded that by applying both prediction methods, the isothermal conversion curves at Tiso e 300 °C cannot be calculated with a satisfactory degree of deviation from nonisothermal conversion curves. Figure 11a,b shows the apparent activation energy Ea,R and ln[AR/g(R)] as functions of the degree of conversion (R) calculated by the integral isoconversional method, from the slope and intercept of the -ln tR versus 1/TR plots (eq 3). Any point in this figure is obtained from the above relationship within certain error limits, specified by error bars. In the case of an isothermal reduction process the values of the apparent activation energy show a decreasing behavior throughout the conversion range (see Figure 11a). However, the values of the apparent activation energy do not decrease sharply with conversion. From the established Ea,R-R dependence for the isothermal reduction process, the existence of low and high temperature steps can be observed. This type of Ea,R dependence corresponds to a sequential reaction mechanism.38 Alternatively, ln[AR/g(R)]-R plot demonstrates identical characteristics (Figure 11b), and this suggests that the apparent activation energy (Ea,R) and the pre-exponential factor (AR) both depend in the same way on the degree of conversion (R).38 This behavior is completely different from the dependence of the apparent

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Figure 11. Dependences of the apparent activation energy (Ea,R) (a) and the apparent intercept (ln[AR/g(R)]) (b) on the degree of conversion (R) evaluated by the integral isoconversional method for the isothermal reduction process of NiO in hydrogen atmosphere.

Figure 12. Isokinetic relationships (IKR, compensation effect) evaluated for the isothermal (O) and the nonisothermal (0) reduction process of nickel oxide in hydrogen atmosphere.

activation energy (Ea) on the degree of conversion (R) in the case of nonisothermal reduction process (Figure 2a,b). The changes of Ea and ln A values with degree of conversion (R), in the cases of isothermal and nonisothermal reduction conditions, are connected via the following relations (compensation effect (isokinetic relationships)):39-41

[ ]

ln

AR ) -6.79005 + 0.26653Ea,R g(R) a b

ln[AR f (R)] ) -1.35271 + 0.20839Ea,R a

(11) (12)

b

where a and b represent constants, the “compensation parameters”, while f (R) and g(R) represent the differential and the integral forms of reaction mechanism function. Figure 12 shows the isokinetic relationships (IKR) obtained for the isothermal and nonisothermal reduction process of nickel oxide in hydrogen atmosphere. It can be seen from Figure 12 that the obtained isokinetic lines have drastically different slopes. This causes differences in the compensation parameters a and b, in eqs 11-12. It can be observed in the same figure that the calculated apparent activation energy values, Ea,R, for the nonisothermal reduction, group in a very narrow range (Ea,R ) 90.5-107.3 kJ mol-1). On the other hand, in the case of the isothermal process, the values of the apparent activation energy, Ea,R, are spread across quite a wide range (Ea,R ) 70.4-155.2 kJ mol-1).

Figure 13. Density distribution functions (ddf) of the apparent activation energies (Ea) for (a) the isothermal reduction process and (b) the nonisothermal reduction process of nickel oxide in hydrogen atmosphere.

It should be mentioned that in many reports of kinetic and mechanistic studies of heterogeneous catalytic reactions one can find that the group of rate processes considered exhibits compensation behavior.42,43 The isokinetic temperature (Tisokin ) 1/Rb), corresponding to the most frequently observed values of parameter b, is in the range of 170-320 °C, a temperature range widely used in the experimental kinetic studies of catalysis,42 so that changes in rate attributable to variation of one kinetic parameter are completely (or largely) offset by changes in the other. In the case of nonisothermal reduction process of NiO by hydrogen we obtained the value of Tisokin ) 304 °C for the isokinetic temperature, close to the upper limit of the mentioned range of Tisokin values. The occurrence of isokinetic behavior of any group of related reactions may be indicative of participation of common surface intermediates, or a rate controlling step involving similar surface bond redistribution steps. In addition, the explanation for the kinetic compensation effect will probably not be the same for dissimilar rate controlling steps. The existence of different shapes of plots Ea,R versus R and compensation effects for isothermal and nonisothermal reduction processes, indicates the following: (a) presence of energy distribution of reduction centers across the boundary phase of the interaction and (b) difference in shapes of this distribution under isothermal or nonisothermal conditions. Using Miura’s procedure,44,45 density distribution functions of the apparent activation energies (ddfEa) for isothermal and nonisothermal nickel oxide reduction processes were established. Figure 13 traces a and b shows ddfEa evaluated for the isothermal and nonisothermal reduction process of NiO under hydrogen atmosphere, respectively. From Figure 13a,b it can be observed that the evaluated distributions are quite different between the isothermal and nonisothermal reduction processes. The density distribution function of Ea values for the isothermal reduction process is very wide and includes a broad range of the apparent activation energy values. On the other hand, the density distribution function of Ea values for the nonisothermal reduction process is narrow and asymmetric. The basic characteristics of the ddfEa, presented in Table 4, are as follows: Ea,max, the value of apparent activation energy at the maximum of the distribution function; g(Ea)max, the maximum of ddf; SF, the shape factor or factor of asymmetry; and HW, the half-width of the ddf.

1426 Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009 Table 4. Basic Characteristics of Density Distribution Functions (ddf) of the Apparent Activation Energies, g(Ea), for the Isothermal and Nonisothermal Reduction Process of Nickel Oxide in Hydrogen Atmosphere Ea,max g(Ea)max shape half-wide, HW (kJ mol-1) (mol kJ-1) factor, SF (kJmol-1) isothermal reduction process nonisothermal reduction process

95.2

0.0176

0.7349

43.2

91.1

0.2571

0.3333

2.0

From Table 4 it can be observed that the shape factor (SF) of ddf for the isothermal reduction process is higher than the shape factor of ddf for the nonisothermal reduction process (distribution function is more asymmetrical). On the other hand, half-width values of ddf are much higher than unity (HW . 1 kJ mol-1) in the case of the isothermal process, in contrast to the same values obtained for the nonisothermal reduction process (HW ) 2.0 kJ mol-1). The “activation” represents the process of increasing the internal energy of the reaction species (in our case, the reduction centers of NiO). It follows that the activation energy of a reaction species is inversely proportional to its internal energy. We can thus conclude that at the different experimental conditions of realization of the reduction process (isothermal or nonisothermal mode) different activation of NiO reduction centers occurs. In addition, a perfect NiO(100) surface, the most common face of nickel oxide, exhibits negligible reactivity toward hydrogen. The presence of oxygen (O) vacancies leads to an increase in the adsorption energy of H2 and substantially lowers the energy barrier associated with the cleavage of the H-H bond. At the same time, adsorbed hydrogen can induce the migration of O vacancies from the bulk to the surface of the oxide. In the isothermal conditions, the reduction centers with higher internal energy (i.e., with lower value of Ea (Ea ≈ 70.4 kJ mol-1; Figure 13a)) are activated first, while at nonisothermal conditions, the reduction centers with lower internal energy (i.e., with higher value of Ea (Ea ≈ 90.5 kJ mol-1)) are activated first. The final conclusion is that the established difference in the density distribution functions of Ea values under isothermal and nonisothermal conditions is a consequence of different kinetic mechanisms, indicating that it is impossible to evaluate isothermal conversion curves from nonisothermal conversion curves, for the investigated nickel oxide reduction process. 6. Concluding Remarks It is not possible to calculate the isothermal conversion curves using the experimentally obtained nonisothermal conversion curves, for the reduction process of NiO using hydrogen, by applying conventional and the proposed prediction methods, at Tiso e 300 °C. The existence of different distributions of the internal energy of NiO reduction centers is a consequence of different reduction kinetics under isothermal and nonisothermal experimental conditions. These facts represent the basic causes of the impossibility to evaluate isothermal conversion curves from the nonisothermal conversion curves for the reduction process of nickel oxide. Acknowledgment The investigation was partially supported by the Ministry of Science under the Project 142025.

Literature Cited (1) Heinrich, V. E.; Cox, P. A. The Surface Science of Metal Oxides; Cambridge University Press: Cambridge, U.K. 1994. (2) Pacchioni, G. Ab Initio Theory of Point Defects in Oxide Materials: Structure, Properties, Chemical Reactivity. Solid State Sci. 2000, 2, 161. (3) Furstenau, R. P.; McDougall, G.; Langell, M. A. Initial Stages of Hydrogen Reduction of NiO (100). Surf. Sci. 1985, 150, 55. (4) Delmon, B. In Handbook of Heterogeneous Catalysis; Ertl, G., Kno¨zinger, H., Weitkamp, J., Eds.; Wiley-VCH: New York, 1997; p 264. (5) Lescop, B.; Jay, J.-Ph.; Fanjoux, G. Reduction of Oxygen Pre-treated Ni (111) by H2 Exposure: UPS and MIES Studies Compared with Monte Carlo Simulations. Surf. Sci. 2004, 548, 83. (6) Richardson, J. T.; Scates, R.; Twigg, M. V. X-ray Diffraction Study of Nickel Oxide Reduction by Hydrogen. Appl. Catal., A 2003, 246, 137. (7) Brito, J. L.; Laine, J.; Pratt, K. C. Temperature-programmed Reduction of Ni-Mo Oxides. J. Mater. Sci. 1989, 24, 425. (8) Chen, J. G.; Fischer, D. A.; Hardenbergh, J. H.; Hall, R. B. A Fluorescence Yield Near-edge Spectroscopy (FYNES) Investigation of the Reaction Kinetics of NiO/Ni(100) with Hydrogen. Surf. Sci. 1992, 279, 13. (9) Houalla, M.; Delannay, F.; Matsuura, I.; Delmon, B. PhysicoChemical Characterization of Impregnated and Ion-Exchanged SilicaSupported Nickel Oxide. J. Chem. Soc., Faraday Trans. 1 1980, 76, 2128. (10) Campbell, C. T. Studies of Model Catalysts with Well-Defined Surfaces Combining Ultrahigh Vacuum Surface Characterization with Medium - and High-Pressure Kinetics. AdV. Catal. 1989, 36, 1. (11) Benton, A. F.; Emmett, P. H. The Reduction of Nickelous and Ferric Oxides by Hydrogen. J. Am. Chem. Soc. 1924, 46, 2728. (12) Parravano, G. The Reduction of Nickel Oxide by Hydrogen. J. Am. Chem. Soc. 1952, 74, 1194. (13) Charcosset, H.; Frety, R.; Soldat, A.; Trambouze, Y. Increase of Reducibility of NiO by H2 Due to Pretreatment with Salt Solutions. J. Catal. 1971, 22, 204. (14) Charcosset, H.; Frety, R.; Labbe, G.; Trambouze, Y. Increase of the Rate of Reduction of NiO by H2 Due to Pretreatment with CO or NH3. J. Catal. 1974, 35, 92. (15) Richardson, J. T.; Turk, B.; Lei, M.; Forster, K.; Twigg, M. V. Effects of Promoter Oxides on the Reduction of Nickel Oxide. Appl. Catal., A 1992, 83, 87. (16) Koga, Y.; Harrison, L. G. In ComprehensiVe Chemical Kinetics; Bamford, C. H., Tipper, C. F. H., Compton, R. G., Eds.;, Elsevier, Amsterdam, 1984; Vol. 21, p 120. (17) Szekely, J.; Evans, J. W. A Structural Model for Gas-Solid Reactions with a Moving Boundary. Chem. Eng. Sci. 1970, 25, 1091. (18) Szekely, J.; Evans, J. W. A Structural Model for Gas-Solid Reactions with a Moving Boundary II: The Effect of Grain Size, Porosity, and Temperature on the Reaction of Porous Pellets. Chem. Eng. Sci. 1971, 26, 1901. (19) Szekely, J.; Lin, C. I.; Sohn, H. Y. A Structural Model for GasSolid Reactions with a Moving Boundary-V: An Experimental Study of the Reduction of Porous Nickel-Oxide with Hydrogen. Chem. Eng. Sci. 1973, 28, 1975. (20) Rashed, A. H.; Rao, Y. K. Kinetics of Reduction of Nickel Oxide with Hydrogen Gas in the 230-452 0C Range. Chem. Eng. Commun. 1997, 156, 1. (21) Jankovic´, B.; Adnac, B.; Mentus, S. The Kinetic Analysis of Non-Isothermal Nickel Oxide Reduction in Hydrogen Atmosphere Using the Invariant Kinetic Parameters Method. Thermochim. Acta 2007, 456, 48. (22) Jankovic´, B.; Adnac, B.; Mentus, S. The Kinetic Study of Temperature-Programmed Reduction of Nickel Oxide in Hydrogen Atmosphere. Chem. Eng. Sci. 2008, 63, 567. (23) Utigard, T. A.; Wu, M.; Plascencia, G.; Marin, T. Reduction Kinetics of Goro Nickel Oxide Using Hydrogen. Chem. Eng. Sci. 2005, 60, 2061. (24) Gonzalez, J. L.; Havel, J. Computation in Kinetics, IV. Regression Estimation of Arrhenius Equation Parameters from Non-Isothermal Kinetic Data. React. Kinet. Catal. Lett. 1989, 39, 147. (25) Telea, C.; Chilom, O.; Geambas, G.; Popa, V. Comparative Study of Isothermal and Non Isothermal Thermokinetic Processes. J. Therm. Anal. Calorim. 1997, 50, 647. (26) Riva, M.; Schiraldi, A. Kinetic Parameterization of Transitions and Reactions in Food Systems from Isothermal and Non-Isothermal DSC Traces. Thermochim. Acta 1993, 220, 117.

Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009 1427 (27) Rios, P. R. Relationship Between Non-Isothermal Transformation Curves and Isothermal and Non-Isothermal Kinetics. Acta Mater. 2005, 53, 4893. (28) Liu, F.; Yang, C.; Yang, G.; Zhou, Y. Additivity rule, Isothermal and Non-Isothermal Transformations on the Basis of an Analytical Transformation Model. Acta Mater. 2007, 55, 5255. (29) Friedman, H. L. Kinetics of Thermal Degradation of Char-forming Plastics from Thermo gravimetry - Application to Phenolic Plastic. J. Polym. Sci. 1965, C6, 183. (30) Baitalow, F.; Schmidt, H.-G.; Wolf, G. Formal Kinetic Analysis of Processes in the Solid State. Thermochim. Acta 1999, 337, 111. (31) Vyazovkin, S. Computational Aspects of Kinetic Analysis: Part C. The ICTAC Kinetics ProjectsLight at the End of the Tunnel. Thermochim. Acta 2000, 355, 155. (32) Vyazovkin, S. A Unified Approach to Kinetic Processing of Nonisothermal Data. Int. J. Chem. Kinet. 1996, 28, 95. (33) Vyazovkin, S.; Wight, C. A. Model-Free and Model-Fitting Approaches to Kinetic Analysis of Isothermal and Nonisothermal data. Thermochim. Acta 1999, 340-341, 53. (34) Mentus, S.; Majstorovic´, D.; Tomic´, B.; Dimitrijevic´, R. Reduction of NiO-WO3 Oxide Mixtures Synthesized by Gel-Combustion Technique: A Route to Ni-W Alloys. Mater. Sci. Forum 2005, 494, 345. (35) Wu, Y.; He, Y.; Wu, T.; Chen, T.; Weng, W.; Wan, H. Influence of Some Parameters on the Synthesis of Nanosized NiO Material by Modified Sol-Gel Method. Mater. Lett. 2007, 61, 3174. (36) Vyazovkin, S.; Lesnikovich, A. I. Preobrazovanie kineticheskikh dannikh “stepen prevrasheniya ot temperatury” v “stepen prevrasheniya ot vremeni”. Zh. Fiz. Khim 1988, 11, 2949.

(37) Adnac, B.; Jankovic´, B.; Kolar-Anic´, Lj.; Minic´, D. Normalized Weibull Distribution Function for Modelling the Kinetics of Non-Isothermal Dehydration of Equilibrium Swollen Poly (Acrylic Acid) Hydrogel. Chem. Eng. J. 2007, 130, 11. (38) Jankovic´, B. Isothermal Reduction Kinetics of Nickel Oxide Using Hydrogen: Conventional and Weibull Kinetic Analysis. J. Phys. Chem. Solids 2007, 68, 2233. (39) Agrawal, R. K. On the Compensation Effect. J. Therm. Anal. Calorim. 1986, 31, 73. (40) Agrawal, R. K. The Compensation Effect: A Fact or a Fiction. J. Therm. Anal. Calorim. 1989, 35, 909. (41) Vyazovkin, S.; Linert, W. Evaluation and Application of Isokinetic Relationships: The Thermal Decomposition of Solids Under Nonisothermal Conditions. J. Chem. Inf. Comput. Sci. 1994, 34, 1273. (42) Galwey, A. K.; Brown, M. E. Compensation Parameters in Heterogeneous Catalysis. J. Catal. 1979, 60, 335. (43) Benson, S. W. Foundations of Chemical Kinetics; McGraw-Hill: New York, pp 86-94. (44) Miura, K. A New and Simple Method to Estimate f(E) and k0(E) in the Distributed Activation Energy Model from Three Sets of Experimental Data. Energy Fuels 1995, 9, 302. (45) Miura, K.; Maki, T. A Simple Method for Estimating f(E) and k0(E) in the Distributed Activation Energy Model. Energy Fuels 1998, 12, 864.

ReceiVed for reView July 14, 2008 ReVised manuscript receiVed September 28, 2008 Accepted October 16, 2008 IE801074J