A New Method for Evaluation of the Iso Thermal Conversion Curves From the Non Iso Thermal Measurements. Application in Nickel Oxide Reduction Kinetics

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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 determinednonisothermal 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 (atT iso e 300 °C) to calculate the isothermal conversion curves using the experimentally obtained nonisothermalconversion curves for this reduction process. The dependence of the apparent activation energy on the degreeof conversion shows that the investigated reduction process is complex under isothermal or nonisothermalconditions. By applying Miura’s procedure, the shape of density distribution functions of the apparent activationenergies was determined for the isothermal and nonisothermal reduction processes. It was concluded that theexistence of different distributions of internal energy of the NiO reduction centers is a consequence of differentreduction kinetics under isothermal and nonisothermal experimental conditions.

1. Introduction

Metal oxides are widely used in many technological applica-tions, such as coating, catalysis, electrochemistry, optical fibers,sensors, etc.1,2 For the preparation of active oxide catalysts, thepartial reduction of nickel oxide under hydrogen at elevatedtemperatures 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 manyindustrial catalysts and electromagnetic devices. Kinetic studiesof nickel oxide reduction by hydrogen usually can be carriedout under isothermal or nonisothermal experimental conditions.In the field of thermal analysis, much attention has been directedtoward the problem of obtaining the kinetic information fromprogrammed temperature, dynamic, or nonisothermal experi-

ments. Richardson et al.6 have given a detailed inspection of results in the kinetic parameters and reaction models determi-nation, for hydrogen reduction of different prepared samplesof NiO under isothermal and nonisothermal conditions.

Many studies have been published in this area,7-23 includingthose of Jankovic et al.21,22 who performed the temperature-programmed reduction of NiO under hydrogen atmosphere. Itwas concluded that the reduction of NiO using hydrogen is amultistep mechanism and can be described by the two-parameterautocatalytic Sestak -Berggren (SB) reaction model. The fol-lowing kinetic parameters were obtained for the temperature-programmed reduction of nickel oxide in hydrogen atmosphere:

E a ) 96.4 kJ mol-1 and A ) 1.04 × 108 min-1.

Thermoanalytical methods for determination of kinetic pa-rameters in both isothermal and nonisothermal regimes are well-known in the scientific literature. The results depend on theprecision of the experimental data and on the mathematicalmodeling of the investigated process. Gonzales and Havel24 havedeveloped the computation method for evaluation of Arrheniusequation parameters from the nonisothermal kinetic data. Agraphical and analytical method for generating reaction iso-therms from a set of nonisotherms, and vice versa, have beenpresented by Telea and co-workers.25 The method was testedusing the computer-generated isotherms and nonisotherms, and

experimentally for dehydration of calcium oxalate. Kinetic

parametrization of transitions and reactions in food systems fromisothermal and nonisothermal DSC trace data was presented ina paper by Riva and Schiraldi.26 Rios27 established a math-ematical method for conversion of a continuous coolingtransformation curve into an isothermal transformation curve.Liu et al.28 combined an analytical method with numericalcalculations for conversion of continuous heating data (CHD)or cooling transformation data (CTD) into isothermal transfor-mation data (ITD), and also conversion of ITD into CHD orCTD data.

In the present paper a possibility of applying a newcomputational procedure for evaluation of isothermal conversioncurves from experimentally obtained nonisothermal conversion

curves is investigated. The new computational method is appliedon the reduction process of nickel oxide under hydrogenatmosphere in order to understand the mechanism of thatprocess.

2. Isoconversional (Model-Free) Analysis

The differential isoconversional method by Friedman29 isbased on the following equation:

ln[Vh(dR

dT )]R,i) ln[ A

R f (R)] -

E a,R

RT R,i

(1)

where Vh is the heating rate, E a,R is the value of apparent

activation energy at a given conversion (R), AR represents thevalue of the pre-exponential factor at a specific degree of conversion (R), f (R) is the reaction model, and R is the gasconstant. The subscript i denotes the ordinal number of anonisothermal experiment conducted at heating rate Vh,i and thesubscript R denotes the quantities evaluated at a specific degreeof conversion. At a certain conversion, the slope and theintercept of the straight line of ln[Vh(dR /dT )]R,i versus 1/ T R,i givethe apparent activation energy and the product AR f (R), respec-tively. In a simple single-step process, the obtained values of

E a,R are invariant with respect to R. If the value of E a,R varieswith the degree of conversion, the results should be interpretedin the terms of a multistep reaction mechanism.

* To whom correspondence should be addressed. E-mail: [email protected]. Tel./Fax: +381-11-2187-133.

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The integral isoconversional method30,31 is an isothermalmethod which is based on taking the natural logarithm of

g(R) ) A exp(- E a

RT )t (2)

which gives

-ln t R

) ln[A

R

g(R)] - E a,R

RT R

(3)

where g(R) is the integral function of reaction model, t is thetime, t R is the time at a given conversion (R), AR is the pre-exponential factor at a given R, E a,R is the apparent activationenergy for each given value of R, T R is the absolute temperaturevalue at a given R, and R is the gas constant. For a constantvalue of R, the first term in eq 3 is a constant, and E a,R can bedetermined from the slope of -ln t R versus 1/ T R, 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 beused to simulate the variation of the degree of conversion (R)versus time (t ) for a given (constant) temperature (T iso). Thesesimulations can be obtained using the following equation:32,33

t R

) [Vh exp(- E a,R

RT iso)]

-1

∑0

R

∫T R-∆R

T Rexp(-

E a,R

RT ) dT (4)

where t R is the time to reach a given conversion (R), Vh is theheating rate of the nonisothermal experiment used for thecomputation, T iso is the isothermal temperature of the isothermalsimulation, E a,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 evaluatedby numerical integration of the data using the trapezoid rule,and R was varied between 0.00 and 0.95 in steps of 0.02. Ascan be seen from eq 4, these simulations can be done usingsole E a,R-dependence computed with the Friedman (FR) iso-conversional method.

4. Experimental Section

4.1. Materials and Methods. The NiO samples wereobtained 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 inair up to 300 °C, and then by an additional heating up to 500°C which produced very fine nickel oxide powder. The meansize of nickel oxide particles, determined from XRD data wasd m ) 30 nm, and this value agrees very well with the datapublished 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 temperaturerange from 25 to 1500 °C. The nickel oxide samples werereduced directly within the thermo-balance, in silicon carbidepans, 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 °Cmin-1, in the temperature range from ambient to 500 °C. The

mass of the samples used for thermogravimetric investigationswas about 25 ( 0.5 mg.

4.3. Isothermal Thermogravimetric Measurements. Thereduction experiments were carried out in a TA SDT 2960device, capable of simultaneous TGA-DTA analysis in thetemperature range from ambient to 1500 °C. The nickel oxidesamples were reduced directly within the thermo-balance, insilicon carbide pans, in (99.9995 vol%) hydrogen flowing at a

rate of 100 mL min-1

. The mass loss experiments were carriedout at five different operating (isothermal) temperatures: T iso )

245, 255, 265, 275, and 300 °C. The sample mass used forthermogravimetric investigations was about 25 ( 0.5 mg, as inthe case of nonisothermal experiments. The isothermal conver-sion 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 (T iso).

The experimentally determined degree of conversion (R) forthe reduction process under isothermal conditions can beexpressed as

R )m0 - mt

m0 - mf

(5)

where m0, mt , and mf refer to the initial, actual (at time t ), andfinal mass of the investigated sample. Nonisothermally, thedegree 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 ispossible to use the corresponding mass values determined byTG to obtain the evolution of conversion with temperature.

Figure 1 shows experimentally obtained conversion curves undernonisothermalconditionsfortheinvestigatedreductionprocess.21,22

Figure 1. Experimental nonisothermal conversion (R-T ) curves for thereduction 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 CharacteristicTemperatures of the Reduction Process of NiO Using Hydrogen

Vh (°C min-1) T i (°C) T p (°C) T f (°C) ∆T (°C)

2.5 260 285 395 1355 275 300 455 18010 285 315 465 18020 300 340 485 185

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Table 1 shows the influence of heating rate on characteristictemperatures of the reduction process: the onset temperature(T i), the inflection (peak) temperature (T p), the final temperature(T f ) and temperature differences (∆T ) T f - T i).

The increase of the heating rate leads to increases of T i, T p,T f , and ∆T values, which indicates that the onset of reductionprocess 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 representthe apparent activation energy values and the values of isocon-versional intercepts, respectively (eq 1).

Within the limits of the experimental error in the determi-nation of E a,R by the Friedman’s method ( E a,R exhibits valuesof a relative standard deviation lower than 10%) the apparentactivation energy of the reduction process of nickel oxide byhydrogen in the 0.20 e R e 0.60 range is a constant value,independent of R values ( E a ) 90.8 kJ mol-1). Discrepanciescan be observed for conversions lower than R ) 0.20 and higherthan R ) 0.60, where the calculated errors of E a,R aresignificantly higher, in comparison with the calculated errorsof E a,R for the intermediate R range. These results allow for aconclusion that the values of E a for the 0.20 e R e 0.60 range

were constant and independent of R. Alternatively, theln[ AR f (R)]-R plot demonstrates identical behavior (Figure 2b),

which may suggest that both the apparent activation energy ( E a)and the pre-exponential factor ( A) are practically independentof 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 theisothermal reduction process at five different operating temper-atures (T iso ) 245, 255, 265, 275, and 300 °C), using fourdifferent heating rates (Vh ) 2.5, 5, 10, and 20 °C min-1) in thenonisothermal experiments. The E

a,R values evaluated from the

Friedman (FR) method (eq 1) were used for isothermalpredictions.

Deviations of the predicted results from the experimental datacan be calculated by the following expression:

S )∑i)1

N

[Ri,calcd - Ri,exp]2 (7)

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 experimentalones 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 beobserved at Vh ) 10 °C min-1, at all operating temperatures.

Figure 2. Dependences of the apparent activation energy ( E a,R) (a) and theapparent intercept (ln[ AR f (R)]) (b) on the degree of conversion (R) evaluatedby the Friedman’s isoconversional method for the nonisothermal reductionprocess of NiO by hydrogen.

Figure 3. Comparison between the experimental isothermal conversioncurve at T iso ) 245 °C and predicted isothermal curves (eq 4) using fourdifferent heating rates (Vh ) 2.5, 5, 10, and 20 °C min-1).

Figure 4. Comparison between the experimental isothermal conversioncurve at T iso ) 255 °C and the predicted isothermal curves (eq 4) using thefour different heating rates (Vh ) 2.5, 5, 10, and 20 °C min-1).

Figure 5. Comparison between the experimental isothermal conversion

curve at T iso ) 265 °C and the predicted isothermal curves (eq 4) using thefour different heating rates (Vh ) 2.5, 5, 10, and 20 °C min-1).

1422 Ind. Eng. Chem. Res., Vol. 48, No. 3, 2009







On the other hand, the value of S increases with increasingoperating temperature, independently of the heating rate.However, it can be observed from Figures 3-7 that there aregreat discrepancies between the experimentally obtained andthe predicted conversion curves, at each T iso.

The experimentally determined values of kinetic parametersfor the reactions in the solid state, obtained under isothermaland 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 theinvestigated process under isothermal and nonisothermal condi-tions. These are (1) physical causes and (2) formal mathematicalcauses.36 The formal mathematical cause of disagreement of

the kinetic parameter values under different experimentalconditions is the nonuniform solving of the invariant kinetic

problem, which is connected with the complexity of theinvestigated process in the solid phase. This phenomenon wasespecially manifested in nonisothermal conditions.

5.1. The New Prediction Method. Assuming that thereaction times of the reduction process are randomly distributedaccording to the Weibull distribution function, and assumingthat the value of Weibull distribution function of reaction timesis proportional to the degree of conversion (R), the followingapplies:37

R(T ) ) 1 - exp[-((T - T 0)

Vhη) β

] (8)

where R(T ) is the degree of conversion or the cumulativeWeibull distribution function, (T - T 0)/ Vh ) t is the reactiontime, T is the absolute temperature, T 0 is the temperature of thesystem at the beginning of the process, Vh is the heating rate, βis the shape parameter (because it determines the shape of conversion curve), and η is the scale parameter (as it scales theT variable).

The values of nonisothermal conversion (distribution) pa-rameters ( β,η) are in a functional relationship with the heatingrate of the system. The functional relationships between the

parameters β, η, and Vh for the investigated nonisothermalreduction process of nickel oxide can be expressed through thefollowing numerical relations:

β ) A + BVh (9)

η ) C + D exp(-Vh

φ) (10)

where A, B, C , D and φ are the corresponding numericalconstants necessary to describe the relationships between thementioned parameters and the heating rate. The constant A isdimensionless, as is the parameter β, whereas constant B hasdimensions [min °C-1]; C and D have dimensions of theparameter η, whereas φ has dimensions of the heating rate ([°C

min-

1]). In the considered case, we have the following valuesof 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 anarbitrary set of Vh. We can thus say that by applying theanalytical or graphical method we can obtain a satisfactorynumber of data for calculating the isothermal conversion curves(R ) R(t )T ) at different isothermal operating temperatures (T i).Subscript i is the ordinal number of an experiment performedat a given operating temperature (T i).

The above procedure allows the evaluation of isothermalconversion curves from the well-known nonisothermal conver-

sion curves. The obtained results can be compared with theresults of direct isothermal measurements.By applying the new computational procedure we can check

the above results and draw appropriate conclusions aboutreaction mechanisms for the investigated reduction process underdifferent experimental conditions.

Figure 8 shows the calculated nonisothermal conversioncurves (full lines) for the investigated reduction process of nickeloxide, determined at 45 values of heating rates (from left toright: 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 (Figure8) are calculated using eqs 8-10.



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

heating rate, Vh (°C min-1) 2.5 5 10 20temperature, T (°C) S S S S

245 0.8661 0.7965 0.1774 0.3758255 1.6696 1.2844 0.6455 1.2822265 2.3389 1.6202 0.8365 1.7438275 2.4270 1.7901 1.2352 1.9914300 3.5123 2.3279 1.6230 2.3634






For the isothermal operating temperatures (T 1 ) 245, T 2 )

255, T 3 ) 265, T 4 ) 275 and T 5 ) 300 °C) the values of R j,iso

) R j,iso(t ) were determined using the graphical and analyticalprocedures. Subscript j represents the number of R valueobtained at every intersection point of the correspondingsymbols (isothermal operating temperature T i) and the corre-sponding nonisothermal conversion curve (line) (see Figure 8).

The calculated isothermal conversion curves at the givenoperating temperatures are presented in Figures 9 and 10(dash-dot curves). The experimentally determined isothermalconversion curves are presented in the same figures (Figures 9and 10, full line curves).

The deviations (S) of the calculated conversion curves fromthe experimentally obtained isothermal conversion curves

(Figures 9 and 10), at five different operating temperatures areshown in Table 3.

From the results presented in Table 3, it can be concludedthat with the increasing of isothermal temperature, the value of S decreases. It can be pointed out that at T 5 ) 300 °C (Figure10) the agreement between the experimentally determined

conversion curve and the calculated one is satisfactory, com-pared with the results obtained by the conventional predictionmethod (eq 4), at the same temperature for all considered heatingrates (Table 2). The agreement between the experimental andthe calculated isothermal conversion curves increases withincreasing operating temperature from T 1 to T 5 (Table 3).

On the basis of the above results, it can be concluded that byapplying both prediction methods, the isothermal conversioncurves at T iso e 300 °C cannot be calculated with a satisfactorydegree of deviation from nonisothermal conversion curves.

Figure 11a,b shows the apparent activation energy E a,R andln[ AR / g(R)] as functions of the degree of conversion (R)calculated by the integral isoconversional method, from the slopeand intercept of the -ln t R versus 1/ T R plots (eq 3).

Any point in this figure is obtained from the above relation-ship within certain error limits, specified by error bars. In thecase of an isothermal reduction process the values of theapparent activation energy show a decreasing behavior through-out the conversion range (see Figure 11a). However, the valuesof the apparent activation energy do not decrease sharply withconversion. From the established E a,R-R dependence for theisothermal reduction process, the existence of low and hightemperature steps can be observed. This type of E a,R dependencecorresponds to a sequential reaction mechanism.38 Alternatively,ln[ AR / g(R)]-R plot demonstrates identical characteristics (Figure11b), and this suggests that the apparent activation energy ( E a,R)and the pre-exponential factor ( AR) both depend in the same

way on the degree of conversion (R).38 This behavior iscompletely different from the dependence of the apparent

Figure 8. Calculated nonisothermal conversion curves (full lines) for theinvestigated 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); T 1(0), T 2 (O), T 3 ()), T 4 (∆) and T 5 (×) represent the isothermal operatingtemperatures 245, 255, 265, 275, and 300 °C, respectively.

Figure 9. Comparison between the experimental (full lines) and thecalculated (dash-dot lines) isothermal (R-t ) conversion curves at fourdifferent operating temperatures (T i): T 1 ) 245, T 2 ) 255, T 3 ) 265 and T 4)

275°

C, for the reduction process of nickel oxide by hydrogen.

Figure 10. Comparison between the experimental (full line) and thecalculated (dash-dot line) isothermal (R-t ) conversion curve at the highestoperating temperature, T 5 ) 300 °C, for the reduction process of nickeloxide by hydrogen.

Table 3. Deviations (S) (eq 7) of the Calculated Conversion Curvesfrom the Experimentally Obtained Isothermal Conversion Curves atTiso ) 245, 255, 265, 275, and 300 °C

temperature, T (°C) S

245 2.5075255 1.3382265 0.6413275 0.3082300 0.1124







activation energy ( E a) on the degree of conversion (R) in thecase of nonisothermal reduction process (Figure 2a,b).

The changes of E a and ln A values with degree of conversion(R), in the cases of isothermal and nonisothermal reductionconditions, are connected via the following relations (compensa-tion effect (isokinetic relationships)):39-41

ln[A

R

g(R)] ) -6.79005a

+ 0.26653b

E a,R(11)

ln[ AR

f (R)] ) -1.35271a

+ 0.20839b

E a,R(12)

where a and b represent constants, the “compensation param-eters”, while f (R) and g(R) represent the differential and theintegral forms of reaction mechanism function. Figure 12 showsthe isokinetic relationships (IKR) obtained for the isothermaland nonisothermal reduction process of nickel oxide in hydrogenatmosphere.

It can be seen from Figure 12 that the obtained isokineticlines have drastically different slopes. This causes differencesin the compensation parameters a and b, in eqs 11-12. It canbe observed in the same figure that the calculated apparentactivation energy values, E a,R, for the nonisothermal reduction,group in a very narrow range ( E a,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, E a,R, are spread acrossquite a wide range ( E a,R ) 70.4-155.2 kJ mol-1).

It should be mentioned that in many reports of kinetic andmechanistic studies of heterogeneous catalytic reactions one can

find that the group of rate processes considered exhibitscompensation behavior.42,43 The isokinetic temperature (T isokin

) 1/ Rb), corresponding to the most frequently observed valuesof parameter b, is in the range of 170-320 °C, a temperaturerange 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 bychanges in the other. In the case of nonisothermal reductionprocess of NiO by hydrogen we obtained the value of T isokin )

304 °C for the isokinetic temperature, close to the upper limitof the mentioned range of T isokin values. The occurrence of isokinetic behavior of any group of related reactions may beindicative of participation of common surface intermediates, ora rate controlling step involving similar surface bond redistribu-tion steps. In addition, the explanation for the kinetic compensa-tion effect will probably not be the same for dissimilar ratecontrolling steps.

The existence of different shapes of plots E a,R versus R andcompensation effects for isothermal and nonisothermal reductionprocesses, indicates the following: (a) presence of energydistribution of reduction centers across the boundary phase of the interaction and (b) difference in shapes of this distributionunder isothermal or nonisothermal conditions.

Using Miura’s procedure,44,45 density distribution functionsof the apparent activation energies (ddf E a) for isothermal andnonisothermal nickel oxide reduction processes were established.

Figure 13 traces a and b shows ddf E a evaluated for theisothermal and nonisothermal reduction process of NiO underhydrogen atmosphere, respectively.

From Figure 13a,b it can be observed that the evaluateddistributions are quite different between the isothermal andnonisothermal reduction processes. The density distributionfunction of E a values for the isothermal reduction process isvery wide and includes a broad range of the apparent activationenergy values. On the other hand, the density distributionfunction of E a values for the nonisothermal reduction processis narrow and asymmetric.

The basic characteristics of the ddf E a, presented in Table 4,are as follows: E a,max, the value of apparent activation energyat the maximum of the distribution function; g( E a)max, the

maximum of ddf; SF, the shape factor or factor of asymmetry;and HW, the half-width of the ddf.

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

Figure 12. Isokinetic relationships (IKR, compensation effect) evaluated

for the isothermal (O

) and the nonisothermal (0

) reduction process of nickeloxide in hydrogen atmosphere.

Figure 13. Density distribution functions (ddf) of the apparent activationenergies ( E a) for (a) the isothermal reduction process and (b) the noniso-thermal reduction process of nickel oxide in hydrogen atmosphere.







From Table 4 it can be observed that the shape factor (SF)of ddf for the isothermal reduction process is higher than theshape 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 . 1kJ mol-1) in the case of the isothermal process, in contrast tothe same values obtained for the nonisothermal reduction process(HW ) 2.0 kJ mol-1).

The “activation” represents the process of increasing theinternal energy of the reaction species (in our case, the reductioncenters of NiO). It follows that the activation energy of areaction species is inversely proportional to its internal energy.

We can thus conclude that at the different experimentalconditions of realization of the reduction process (isothermalor nonisothermal mode) different activation of NiO reductioncenters occurs.

In addition, a perfect NiO(100) surface, the most commonface of nickel oxide, exhibits negligible reactivity towardhydrogen. The presence of oxygen (O) vacancies leads to anincrease in the adsorption energy of H2 and substantially lowersthe energy barrier associated with the cleavage of the H-Hbond. At the same time, adsorbed hydrogen can induce themigration of O vacancies from the bulk to the surface of theoxide.

In the isothermal conditions, the reduction centers with higher

internal energy (i.e., with lower value of E a ( E a ≈ 70.4 kJ mol-1

;Figure 13a)) are activated first, while at nonisothermal condi-tions, the reduction centers with lower internal energy (i.e., withhigher value of E a ( E a ≈ 90.5 kJ mol-1)) are activated first.

The final conclusion is that the established difference in thedensity distribution functions of E a values under isothermal andnonisothermal conditions is a consequence of different kineticmechanisms, indicating that it is impossible to evaluate iso-thermal conversion curves from nonisothermal conversioncurves, for the investigated nickel oxide reduction process.

6. Concluding Remarks

It is not possible to calculate the isothermal conversion curvesusing the experimentally obtained nonisothermal conversioncurves, for the reduction process of NiO using hydrogen, byapplying conventional and the proposed prediction methods, atT iso e 300 °C. The existence of different distributions of theinternal energy of NiO reduction centers is a consequence of different reduction kinetics under isothermal and nonisothermalexperimental conditions. These facts represent the basic causesof the impossibility to evaluate isothermal conversion curvesfrom the nonisothermal conversion curves for the reductionprocess 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 OxideMaterials: 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.,Knozinger, H., Weitkamp, J., Eds.; Wiley-VCH: New York, 1997; p 264.

(5) Lescop, B.; Jay, J.-Ph.; Fanjoux, G. Reduction of Oxygen Pre-treatedNi (111) by H2 Exposure: UPS and MIES Studies Compared with MonteCarlo Simulations. Surf. Sci. 2004, 548, 83.

(6) Richardson, J. T.; Scates, R.; Twigg, M. V. X-ray DiffractionStudy of Nickel Oxide Reduction by Hydrogen. Appl. Catal., A 2003,246 , 137.

(7) Brito, J. L.; Laine, J.; Pratt, K. C. Temperature-programmedReduction of Ni-Mo Oxides. J. Mater. Sci. 1989, 24, 425.

(8) Chen, J. G.; Fischer, D. A.; Hardenbergh, J. H.; Hall, R. B. AFluorescence 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. Physico-Chemical Characterization of Impregnated and Ion-Exchanged Silica-Supported Nickel Oxide. J. Chem. Soc., Faraday Trans. 1 1980, 76 ,2128.

(10) Campbell, C. T. Studies of Model Catalysts with Well-DefinedSurfaces Combining Ultrahigh Vacuum Surface Characterization withMedium - and High-Pressure Kinetics. Ad V. Catal. 1989, 36 , 1.

(11) Benton, A. F.; Emmett, P. H. The Reduction of Nickelous andFerric 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 ComprehensiV

e 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-SolidReactions with a Moving Boundary. Chem. Eng. Sci. 1970, 25, 1091.

(18) Szekely, J.; Evans, J. W. A Structural Model for Gas-SolidReactions 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 Gas-Solid 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 Oxidewith 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 AtmosphereUsing 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 HydrogenAtmosphere. Chem. Eng. Sci. 2008, 63, 567.

(23) Utigard, T. A.; Wu, M.; Plascencia, G.; Marin, T. ReductionKinetics of Goro Nickel Oxide Using Hydrogen. Chem. Eng. Sci. 2005,60, 2061.

(24) Gonzalez, J. L.; Havel, J. Computation in Kinetics, IV. Regres-sion Estimation of Arrhenius Equation Parameters from Non-IsothermalKinetic Data. React. Kinet. Catal. Lett. 1989, 39, 147.

(25) Telea, C.; Chilom, O.; Geambas, G.; Popa, V. Comparative Studyof Isothermal and Non Isothermal Thermokinetic Processes. J. Therm.

Anal. Calorim. 1997, 50, 647.

(26) Riva, M.; Schiraldi, A. Kinetic Parameterization of Transitionsand Reactions in Food Systems from Isothermal and Non-IsothermalDSC Traces. Thermochim. Acta 1993, 220, 117.

Table 4. Basic Characteristics of Density Distribution Functions(ddf) of the Apparent Activation Energies, g( Ea), for the Isothermaland Nonisothermal Reduction Process of Nickel Oxide in HydrogenAtmosphere

E a,max

(kJ mol-1)g( E a)max

(mol kJ-1)shape

factor, SFhalf-wide, HW

(kJmol-1)

isothermalreduction process

95.2 0.0176 0.7349 43.2

nonisothermalreduction process

91.1 0.2571 0.3333 2.0




(27) Rios, P. R. Relationship Between Non-Isothermal TransformationCurves and Isothermal and Non-Isothermal Kinetics. Acta Mater. 2005,53, 4893.

(28) Liu, F.; Yang, C.; Yang, G.; Zhou, Y. Additivity rule, Isothermaland Non-Isothermal Transformations on the Basis of an AnalyticalTransformation Model. Acta Mater. 2007, 55, 5255.

(29) Friedman, H. L. Kinetics of Thermal Degradation of Char-formingPlastics from Thermo gravimetry - Application to Phenolic Plastic. J. Polym.

Sci. 1965, C6 , 183.

(30) Baitalow, F.; Schmidt, H.-G.; Wolf, G. Formal Kinetic Analysisof Processes in the Solid State. Thermochim. Acta 1999, 337 , 111.

(31) Vyazovkin, S. Computational Aspects of Kinetic Analysis: PartC. 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-FittingApproaches to Kinetic Analysis of Isothermal and Nonisothermal data.Thermochim. Acta 1999, 340-341, 53.

(34) Mentus, S.; Majstorovic, D.; Tomic, B.; Dimitrijevic, R. Reductionof 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. Influenceof Some Parameters on the Synthesis of Nanosized NiO Material byModified Sol-Gel Method. Mater. Lett. 2007, 61, 3174.

(36) Vyazovkin, S.; Lesnikovich, A. I. Preobrazovanie kineticheskikhdannikh “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. NormalizedWeibull Distribution Function for Modelling the Kinetics of Non-IsothermalDehydration 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 IsokineticRelationships: The Thermal Decomposition of Solids Under NonisothermalConditions. J. Chem. Inf. Comput. Sci. 1994, 34, 1273.

(42) Galwey, A. K.; Brown, M. E. Compensation Parameters inHeterogeneous 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 k 0( E )in the Distributed Activation Energy Model from Three Sets of ExperimentalData. Energy Fuels 1995, 9, 302.

(45) Miura, K.; Maki, T. A Simple Method for Estimating f ( E ) and k 0( 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


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