1331
J . Phys. Chem. 1986, 90, 1331-1337
Determination of the Reduction Mechanism by Temperature-Programmed Reduction: Application to Small Fe,O, Particles 0. J. Wimmers, P. Arnoldy,+ and J. A. Moulijn* Institute for Chemical Technology, University of Amsterdam, Nieuwe Achtergracht 166, 1018 WV Amsterdam, The Netherlands (Received: May 15, 1985; In Final Form: October 22, 1985)
A method is described to calculate profiles generated by temperature-programmed reduction (TPR), using kinetic expressions derived for gassolid reactions. Subsequently,it is shown that the activation energy of a reduction can be determined, irrespective of the reduction mechanism, from the shift of the TPR peak maximum as a function of the heating rate. Using the thus-established activation energy and the temperature of the peak maximum of the measured TPR pattern, we found that for each reduction mechanism selected one single TPR pattern can be calculated. By comparing the measured pattern with a set of calculated patterns, the reduction mechanism can be selected which describes the measured TPR pattern best. As an example, the reduction of small Fe203particles (diameter ca. 0.3 pm) to Fe metal has been studied. This reduction is a two-step process with Fe304as an intermediate. At very low H 2 0 pressures, this reduction can be described best by the three-dimensional nucleation model of Avrami-Erofeev. Addition of 3% H20to the reducing gas affects especially the TPR peak for reduction of Fe3O4to Fe metal: this peak shifts to higher temperatures, while its shape changes considerably. These changes will be discussed by considering self-catalyzed nucleation as the rate-determining step.
Introduction
TABLE I: /(a)and p(a) Functions of Different Reduction Models
Temperature-programmed reduction (TPR) has been used to gain qualitative information on the reducibility of oxidic species, such as metal oxides dispersed on a support.' Kissinger2developed a method to determine activation energy values from differential thermal analysis (DTA) patterns by measuring the displacement of the DTA peak maximum as a function of the heating rate. His method has been implemented successfully for the determination of activation energy values from TPR patterns measured at several heating rates, e.g. for the reduction of oxidic Cu, Fe, Mo, Ni, and R e catalyst^.^-^ In order to determine the mechanism for decompositions of solids from DTA peak shapes, Kissinger also presented a method to calculate DTA patterns using an analytical procedure.2 In these calculations he assumed that decompositions of solids can be described by nth order kinetics. Monti and Baiker' have recently used this procedure to calculate TPR profiles assuming that the mechanism for reduction can be presented by first-order kinetics. nth order expressions mostly have little physical meaning: gas-solid reactions such as reductions generally show complex kinetics which cannot be described by a single nth order expression over the entire conversion range.'^^-^^ It is the objective of the present work to extend Kissinger's approach for the calculation of TPR patterns by using kinetic expressions which are more realistic for gas-solid reactions. A convenient method will be presented which contains only a single numerical differentiation step for the calculation of a TPR pattern. Subsequently, it will be shown that the equation for the determination of the activation energy value developed by Kissinger2 can be applied irrespective of the specific reduction mechanism. A reduction mechanism will be selected by comparison of calculated and measured patterns, using the thus-established activation energy value. As an example of the application of this procedure for selecting the reduction mechanism, the reduction of small Fe203 crystallites (ca. 0.3 pm) has been investigated. This reduction has been chosen because of its relevance for iron production and preparation of ammonia synthesis catalysts. Consequently, a large number of studies have been executed on the reduction of iron oxides (e.g., ref 12-33) and they are used for comparison with the present TPR results. It must be emphasized, however, that the literature data diverge to a large extent, since different oxides exist ( F q 0 3 , Fe304, and FeO) and, moreover, these can contain impurities (in the case of ores: Ca, Mg, Mn, Si20)) or dopes (in the case of ammonia synthesis catalysts: AI, Ca, K, Mg, Furthermore, there are large differences in the literature with respect to, for instance, Present address: Koninklijke/Shell-Laboratorium, Badhuisweg 3, 1031 CM Amsterdam. The Netherlands.
0022-3654/86/2090- 1331$01.50/0
A4
id.)d
reduction model three-dimensional nucleation according to Avrami-Erofeev
(1 - a)(+ (1 - a ) ) 2 / 3 (-3 In (1 - a))'/'
two-dimensional
(1 - a)(-2 In (1 -
(-2 In ( I -
2( 1 -
1 - (1 - a)1/2
3( 1 -
1 - (1
1-a 3/2(1 - a)'/' X ((1 - l)-I
-In (1 - a ) (1 - (1 - a)1/3)2
nucleation according to Avrami-Erofeev two-dimensional phase boundaryab three-dimensionalphase boundaryasb unimolecular decay three-dimensional diffusion according to Janderasc
- a)'/3
a These models are geometrically defined as shrinking/unreacted core or contracting sphere models, with reaction proceeding topochemically. Chemical reaction as the rate-determining step. 'Gas diffusion through the product layer as the rate-determiningstep. d g ( a )
=
1: da/Aa).
the selection of reduction temperatures, H,O partial pressure, and particle/crystallite sizes. (1) N. W. Hurst. S. J. Gentrv. ,, A. Jones. and B. D. McNicol. Catal. Reu.. 2 4 . 3 3 (1982). (2) H. E. Kissinger, Anal. Chem., 29, 1702 (1957). (3) S. J. Gentry, N. W. Hurst, and A. Jones, J . Chem. SOC.,Faraday Trans. 1. 65. 1688 (1979). (4) E: E.'Unmuth, L.'H. Schwartz, and J. B. Butt, J . Catal., 61, 242 (1980). (5) P. Amoldy, J. C. M. de Jonge, and J. A. Moulijn, J . Phys. Chem., 89, 4517 (1985). (6) B. Scheffer, P. Arnoldv. and J. A. Mouliin, to be published. (7) D. A. M. Monti and Baiker, J . Card.; 83, 323'(1983). (8) P. Arnoldy, 0. S. L. Bruinsma, and J. A. Moulijn, J . Mol. Catal., 30, 111 (1989. (9) J. Sestlk and G. Berggren, Thermochim. Acta, 3, 1 (1971). (10) L. G. Harrison in "Comprehensive Chemical Kinetics", Vol. 2, C. H. Bamford and C. F. H. Tipper, Eds., Elsevier, Amsterdam, 1969, p 377. (1 1) J. Sestlk, V. Sastava, and W. W. Wendtland, Thermochim. Acta, 7 , 333 (1973). (12) J. 0. Mstrom. J . Iron Steel Znst.. 175. 289 (1953). (13j J. M. Quets, M. E. Wadsworth, and J. R. Lehs, Trhns. Metall. SOC. AIME, 218, 545 (1960). (14) J. M. Quets, M. E. Wadsworth, and J. R. Lewis, Trans. Merall. SOC. AZME,221, 1186 (1961). (15) N. J. Themelis and W. H. Gauvin, AZChE J., 8, 437 (1962). (16) N. J. Themelis and W. H. Gauvin, Trans. Merall. SOC.AIME, 227, 290 (1963). (17) A. Endom, K. Hedden, and G. Lehmann, React. Solids, Proc. Int. Symp., 5th, 1964, 632 (1965).
A.
0 1986 American Chemical Society
1332 The Journal of Physical Chemistry, Vol. 90, No. 7, 1986 The present study gives TPR results of well-defined Fe203 crystallites. It will be shown that different reduction mechanisms correlate with clearly different TPR peak shapes, allowing selection of one reduction mechanism by comparing calculated and measured Fe203 TPR patterns. At very low H 2 0 pressure, the three-dimensional nucleation model of Avrami-Erofeev is selected, whereas at higher H20pressure none of the reduction mechanisms gives a reasonable fit. In the latter case, self-catalyzed nucleation (autocatalysis) is suggested as the rate-determining step.
Wimmers et al.
eq 4 giving a explicitly as a function of T, and subsequently (ii) differentiation of the latter function. First, the variables in eq 4 are separated:
Table I gives besides f ( a ) functions also the g(a) functions. Equation 5 has been solved by partial i n t e g r a t i ~ n ; ' ' it, ~can ~ be rewritten as
Theory Generally, the reaction rate equation of a solid reacting with a gas to form another solid can be represented as a product of a temperature-dependent and two "concentration"-dependent factors: r = d a / d t = k , ( T ) f(a) ~ ( P H ~ P H ~ o )
x = E/RT
(7)
(1)
where a is the degree of conversion of the solid reactant. Table I givesfla) functions for some gassolid reaction models which are relevant to describe reduction mechanisms. The models selected are representative of the different rate-determining processes as proposed in solid-state kinetics. Their physical meaning has been described in ref 9, 10, and 11 and references cited therein. The model of Jander describes diffusion less accurately than the model of Ginstling-BrounshteinIo but is preferred because of its more convenient mathematical form. Under differential conditions, the gas-phase-dependent term f ' ( P H 2 , ~ H 2 0 ) is approximately a constant, reducing eq 1 to d a / d t = k( T ) f ( a )
where
(2)
When in a TPR experiment the temperature increases linearly with time at a heating rate 4, eq 2 can be rewritten as
(3) In eq 3 the temperature dependence of the rate constant k can be expressed by using the Arrhenius equation
(4) It should be noted that the gas-phase-dependent term is incorporated in A. Calculation of TPR Patterns. TPR patterns (Le. dcu/dT as a function of 73 can be calculated by (i) solution of the differential
(18) A. Nielsen, 'An Investigation on Promoted Iron Catalysts for the Synthesis of Ammonia", 3rd ed, Jul. Gjellerups Forlag, 1968. (19) P. K. Strangway, H. 0. Lien, and H. U. Ross, Can. Metall. Q., 8, 235 (1969). (20) E. T. Turkdogan and J . V. Vinters, Metall. Trans., 2, 3175 (1971). (21) E. T. Turkdogan, R.G. Olsson, and J. V. Vinters, Metall. Trans., 2, 3189 (1971). (22) E. T. Turkdogan and J. V. Vinters, Metall. Trans., 3, 1561 (1972). (23) R. H . Tien and E. T. Turkdogan, Metall. Trans., 3, 2039 (1972). (24) Y . Hara, Trans. Iron Steel Inst. Jpn., 12, 358 (1972). (25) A. Barabski, A. Bielabski, and A. Pattek, J . Catal., 26, 286 (1972). (26) R. P. Viswanath, B. Viswanathan, and M. V. C. Sastri, React. Kinet. Catal. Lett., 2, 5 1 (1975). (27) P. R. Khangaonkar and V. N. Misra, J . Sci. Ind. Res., 35.23 1 (1976). (28) M. Shimokawabe, R.Furuichi, and T. Ishii, Thermochim. Acta, 28, 287 (1979). (29) J. Bessibres, A. Bessibres, and J. J. Heizmann, Int. J . Hydrogen Energy, 5, 585 (1980). (30) A. Ozaki and K. Aika in "Catalysis", Vol. 1, J. R . Anderson and M. Boudart, Eds., Springer, Berlin, 1981, p 87. (31) A. Baraiiski, J. M. Lagan, A. Pattek, and A. Reizer, Appl. Catal., 3, 207 (1982). (32) R. Brown, M E. Cooper, and D. A. Whan, Appl. Catal., 3, 177 (1982). (33) M. V. C. Sastri, R. P. Viswanath, and B. Viswanathan, In?. J . Hydrogen Energy, 7, 951 (1982).
Doyle34has tabulated the most commonly found values of p ( x ) . For computing purposes, the following simplification" was found to be most convenient: P(X)
=
c(1699.066 + 8 4 1 . 6 5 5 ~+ 4 9 . 3 1 3 ~- ~8 . 0 2 ~ x4~ ) (9) 614.567
+ 5 7 . 4 2 1 ~- 6 . 0 5 5 -~ ~x3
X
-
Equation 9 can be used for x values between 9 and 174'' which correspond to TPR conditions generally applied. From a combination of eq 6, 7, and 9 and Table I, a can be calculated as a function of T. Differentiation of this function gives the calculated TPR pattern, Le. d a / d T as a function of T. Determination of the Activation Energy. To predict the reduction mechanism from TPR measurements, the value of the activation energy (E) must be known. Kissinger* has established a method to obtain the activation energy for decomposition reactions from DTA measurements by variation of the heating rate, assuming nth order kinetics (see the Introduction). The applicability of Kissinger's method can be extended to reactions with more complex kinetics, such as reductions, as will be shown in the following. For the maximum of a TPR peak the following equation holds:
Combination of eq 10 with eq 4 leads, via eq 11, to eq 12:
(12)
Because (da/dT)T=T,,, is not equal to zero, eq 12 reduces to
From eq 13 it follows that
+
In (4/TmaX2) In (E/AR) =
Assuming thatf(a) (the reduction model) and CY^=^,,, are indeis not equal pendent of the heating rate and that (dfla)/da)T=Tm8x to zero, eq 14 can be rewritten as (34) C. D. Doyle, J . Appl. Polym. Sci., 5 , 285 (1961).
The Journal of Physical Chemistry, Vol. 90, No. 7, 1986 1333
Determination of Reduction Mechanism by TPR In ( 4 / T m a X z=) - E / R T , , ,
+ In ( A R / E ) + C
(15)
where C is a constant. Consequently, plots of In (4/Tma?) vs. 1/ T,, (temperature-programmed “Arrhenius plots”) are expected to give straight lines with slope - E / R . For three different reduction models (the three-dimensional phase boundary model, the three-dimensional nucleation model of Avrami-Erofeev, and the three-dimensional diffusion model of Jander), the applicability of eq 15 has been checked by calculating T,,, from eq 14 assuming several values for A , E , and 4. Plotting of In (4/ TmU2)as a function of 1/ Tm always resulted in perfect straight lines with a slope of precisely - E / R . Consequently, it is concluded that eq 15 can be generally applied to determine the activation energy E from TPR measurements by using several heating rates. Method f o r Selecting the Reduction Mechanism from TPR Patterns. In order to determine the reduction mechanism, the following procedure can be used: Determine the E value from temperature-programmed “Arrhenius plots” by using eq 15, in a generalized Kissinger approach. Select representative reduction models such as those given in Table I. Calculate a matrix of T P R patterns by using the procedure described above, varying both the reduction mechanism and the A value and applying fixed E and 4 values. From this matrix, one single pattern is selected for each reduction mechanism, namely the one which has its calculated Tma, value at the measured T,,, value; this selection determines the A value for each reduction mechanism. Compare the thus-established set of calculated patterns (one for each reduction model selected) with the measured pattern; the best-fitting calculated pattern gives the reduction mechanism. With this procedure, reduction mechanisms can be established in a rapid and convenient way from measured TPR patterns, as will be shown in the following for the reduction of small Fez03 crystallites.
Experimental Section The TPR measurements were performed in an apparatus which has been described in detail p r e v i o ~ s l y . ~As ~ reducing gas a 67% H2/Ar mixture (Matheson, UHP) was used (flow rate 12 pmol/s; 1.O bar). In some experiments, the reducing gas was saturated with H 2 0at room temperature, resulting in about 3% H 2 0in the reducing mixture. The sample size was varied reciprocally with the heating rate. The TPR reactor was a quartz tube (internal diameter 4 mm). The contribution of the apparatus to the peak broadening was measured with the impulse-response technique; it was found that the full width at half-maximum height (fwhm) for a Dirac input equalled 39 s. The structure of a-FezO3 (Merck, pro analysi) was checked by X-ray diffraction (Co K a radiation). Scanning electron microscopy (SEM) pictures showed a sharp particle size distribution; it was found that the Fe203 particles were spherical, with an average diameter of ca. 0.3 bm. The BET specific surface area was determined to be 2.6 m2/g. If it is assumed that all particles are spherical, nonporous, and of identical size, the particle diameter can be estimated from the measured BET specific surface area as 0.46 pm. This value agrees well with the result obtained by means of SEM. Results Figures 1-3 give TPR patterns of Fe2O3 under various experimental conditions. Quantitative TPR analysis indicated that the reduction is completed to Fe metal in the TPR peaks shown. When “dry” H2/Ar is used as reducing gas (Le. no HzO added), an increase of the base line can be observed as a result of CH4 formation from organic i m p ~ r i t i e s . ~ ~ The patterns shown in Figure la-c were obtained with different F e 2 0 3sample sizes. The pattern shifts to higher temperatures (35) P. Arnoldy and J. A. Moulijn, J . Cutul., 93,38 (1985).
d
C
b
a 500 600 -temperature
700
(K)-
Figure 1. TPR patterns (6 = 0.2 K/min) of Fe203in dry H2/Ar (a-c) and in H,/Ar saturated with 3% H,O (d). Fe203sample sizes: (a) 3.6 mg; (b) 8.2 mg; (c) 15.9 mg; (d) 7.0 mg.
with increasing sample size, suggesting that the reduction rate is affected by the H20 produced by reduction. In agreement with this, TPR in “wet” H2/Ar (saturation with H 2 0 ) (see Figure Id) shows that H 2 0 indeed induces a significant shift. On the lowtemperature side of the TPR patterns, a shoulder (Figure la-c) or small peak (Figure Id) preceeds the main peak. It is concluded that the TPR patterns of Fe2O3, obtained in this study, correspond with a two-step reduction to Fe metal, in agreement with the reduction path found previously at temperatures below ca. 850 K where FeO (wustite) cannot be formed:4J2-14,28,29s33
--
+ H2 2Fe304(magnetite) + H 2 0 Fe304 + 4H2 3Fe + 4 H 2 0
3Fe203(haematite)
(i) (ii)
As the TPR patterns are highly influenced by the H 2 0pressure, two series of measurements were performed, viz. a “dry” and a “wet” series. In the dry series (see Figure 2), no H 2 0 was added to H2/Ar and the sample size was chosen as small as possible in order to approach as close as possible differential conditions with regard to the H 2 0 pressure. In the wet series (see Figure 3), H2/Ar was saturated with H 2 0 (3%). Comparison of Figures 2 and 3 shows that the small low-temperature peak and the main peak are shifted 10-30 and 75-95 K, respectively, to higher temperature by HzO addition to H2/Ar; the precise magnitude of the shift depends on the heating rate.
1334 The Journal of Physical Chemistry, Vol. 90, No. 7 , 1986 1
I
I
1
Wimmers et al.
I
a I
I
500 600 -temperature
700
(K)-
Figure 2. TPR patterns of F e 2 0 3in dry H2/Ar a s a function of heating rate ("dry" series): (a) 0.2 K/min (m = 3.6 mg); (b) 0.5 K/min (m = 2.8 mg); (c) 1 K/min (m = 1.8 mg); (d) 2 K/min (m = 0.91 mg); (e) 5 K/min (m = 0.19 mg); (f) 10 K/min (nz = 0.08 mg).
Small changes in peak shape can be observed in Figures 2 and 3, especially for the higher heating rates. This is caused by the small sample sizes used at these higher heating rates, since these result in nonhomogeneous packed beds in the TPR reactor. The relatively large broadening of the main peak in Figure 3f, at the highest heating rate applied, might be caused by changes in the reduction mechanism at one border of the experimental conditions selected. However, since the temperatureprogrammed "Arrhenius plots" shown in Figure 4 are straight lines, major changes in the reduction mechanism are not likely to occur within the large range of heating rates studied. From the lines of Figure 4, values of the activation energy E were established for all separate peaks observed. The T,,, value measured from Figure 2 will correspond essentially with the T,,, value of Fe304 Fe metal, since the also occurring reaction F%03 Fe304consumes only one-ninth of the total H2uptake. Under the dry conditions of Figure 2, an E value of 111 kJ/mol was established for Fe304 Fe metal. Under the wet conditions of Figure 3, E values of 124 and 172 kJ/mol were determined for Fe304 Fe metal, respectively. the steps Fe203 For the determination of the reduction mechanism of Fe304 t o Fe metal, the TPR patterns measured at the lowest heating rate (0.2 K/min) were chosen. These constitute the most optimal experimental data because of (i) the least influence of instrumental peak broadening and (ii) the relatively large sample size, giving
-
-
-
-
-+
500
600
700
800
temperature (K)Figure 3. TPR patterns of Fe203in wet H2/Ar (3% H20) as a function of heating rate ("wet" series): (a) 0.2 K/min (m = 7.0 mg); (b) 0.5 K/min ( m = 2.6 mg); (c) 1 K/min (m = 1.5 mg); (d) 2 K/min (m = 0.90 mg); (e) 5 K/min (m = 0.33 mg); (f) I O K/min ( m = 0.17 mg).
12
13
14
15
16
l i
Id
- -
Figure 4. Temperature-programmed "Arrhenius plots" for the reduction of Fe,03: (a) main peak (Fe304 Fe metal) for wet series (E = 172 kJ/mol); (b) low-temperature peak (Fe,03 Fe304) for wet series (E = 124 kJ/mol); (c) main peak (Fe304 Fe metal) for dry series (E = 11 1 kJ/mol).
the most ideal packed bed and the most random sample selection. From the T,,,, E , and 6 values of the TPR pattern shown in Figures l a and 2a (dry H,/Ar), A values were calculated for each
The Journal of Physical Chemistry, Vol. 90, No. 7, 1986 1335
Determination of Reduction Mechanism by T P R TABLE 11: A and fwhm Values, Calculated by Using E = 111 kJ/mol, 6 = 0.2 K/min, and T,, = 587 K for the Reduction Models Stated reduction model A , s-' fwhm, K 1.5 X lo6 20 three-dimensional nucleation according to Avrami-Erofeev two-dimensional nucleation according to Avrami-Erofeev two-dimensional phase boundary" three-dimensional phase boundary" unimolecular decay three-dimensional diffusion according to Jander"
1.5 X
lo6 los 105 lo6
5.0 X 3.5 x 1.0 X 9.5 x 104
30
42 55 63 io5
"See the caption of Table I.
3-
4-
I
650 temperature ( K )
I
-
700
Figure 6. Comparison between measured TPR patterns for F e 2 0 3and calculated TPR peaks for the Fe304 Fe metal reduction step, using the three-dimensional nucleation model according to Avrami-Erofeev (6 = 0.2 K/min). The area of the F e 3 0 4 reduction peak is the same for measured and calculated patterns: (a) dry patterns, calculated (dotted line; see Figure Sa) and measured (full line; see Figures l a and 2a); (b) wet patterns, calculated (dotted line; E = 172 kJ/mol; A = 3.5 X lo9 s-I) and measured (full line; see Figures Id and 3a).
3-
500
600
550
650
-
temperature ( K )
Figure 5. Calculated Fe304 Fe metal T P R peaks for six different reduction models using E = 1 1 1 kJ/mol (TPR in dry H,/Ar), 6 = 0.2 K/min, and the A values from Table 11: (a) three-dimensional nucleation according to Avrami-Erofeev; (b) two-dimensional nucleation according to Avrami-Erofeev; (c) two-dimensional phase boundary; (d) three-dimensional phase boundary; (e) unimolecular decay; (f) three-dimensional diffusion according to Jander.
of the six reduction models from Table I, according to the procedure described above (see Table 11). With these A values, TPR patterns for reduction of Fe304to Fe metal were calculated (see Figure 5 ) . From this figure, it is concluded that a good discrimination can be made between the models, and that the simple first-order kinetics (curve 5e) are not representative of the calculation of T P R patterns. Comparison of the full width at half-maximum height (fwhm) of the calculated TPR patterns (see Table 11) with the fwhm value of 19 K obtained from Figure 2a suggests that the three-dimensional nucleation model according to Avrami-Erofeev describes the measured pattern best. In Figure 6a the TPR pattern calculated for this Avrami-Erofeev-type reduction of Fe304to Fe metal is compared with the measured TPR pattern of Fe2O3. The agreement between the measured and calculated curves is satisfactory (deviation less than 2 K, except for the leading edge) in light of the fact that the method presented in this study does not contain an adjustable parameter allowing curve-fitting procedures. Moreover, the deviation on the leading edge can be explained as follows. Firstly, the shoulder present on the leading edge of the measured pattern represents Fe203 Fe304prereduction which has not been included in the calculations. Secondly, the reduction of Fe304 to Fe metal is slightly delayed in the measured pattern in comparison with the calculated pattern, obviously because progression of the Fe203 Fe304reduction step is a prerequisite for the start of reduction of Fe304. Consequently, it can be concluded that, despite of the small differences observed in Figure 6a, the reduction of small Fe304crystallites (formed in-situ from Fe20,) is well described by the three-dimensional nucleation model of Avrami-Erofeev at very low H 2 0pressures in the temperature range of the present study (570-700 K). In Figure 6b, the simulation is presented f o r a "wet" TPR measurement (Figures Id and 3a). Comparison of the measured
-
-
I
600
-
'Y
I
550
pattern with the calculated one, which is, again, based on the three-dimensional nucleation model of Avrami-Erofeev, shows that the calculated peak is ca. two times too broad, especially related to significant deviations in the low-temperature edge. As simulation using the other reduction models from Table I gave even broader peaks, it is concluded that none of the models from Table I describes Fe304 reduction under wet conditions well.
Discussion Calculation of TPR Patterns. The procedure for calculation of TPR patterns, described in the previous sections, can be applied to the determination of the reduction mechanism of welldefined-i.e. homogeneous-solids, viz. metal oxides, unsupported as well as supported on inert carriers such as activated carbon. In principle, it might also be suited for heterogenous systems containing a metal oxide which is bonded to a carrier in many different ways (e.g., M0O,/Al~036.~~); in that case, heterogeneity should be described by mathematical models which, however, do not exist yet. It should be noted that the use of differential conditions with regard to the H2 and H 2 0pressure during TPR is not generally found in the literature. For instance, two TPR studies on the reduction of unsupported iron o ~ i d e s have * ~ ~ reported ~~ TPR patterns which are strongly deformed and broadened with respect to the differentially measured patterns of the present study, probably due to the use of integral conditions. Other authors),' have calculated E values from TPR measurements under integral conditions and, for this purpose, needed the assumption of simple reduction kinetics, viz.f(a) = (1 - a)". Such kinetic expressions, however, seldom have physical meaning for the description of reduction mechanisms. Generally, in TPR literature differential H, conversion has been applied, but hardly any attention has been given to the H 2 0 pressure, resulting, typically, in integral conditions with regard to the H,O pressure. It is concluded that TPR measurements must be executed under differential conditions with respect to both the H, and the H 2 0 pressure in order to be able to apply quantitative procedures, such as the calculation of E values and TPR patterns. Reduction Mechanism of Fe,04 i n the Absence of H 2 0 . The present study shows that Fe metal is formed at 570-750 K from (36) F.E. Massoth, J . Coral., 30, 204 (1973).
1336 The Journal of Physical Chemistry, Vol. 90, No. 7 , 1986 Fe304,after prereduction of Fe203to Fe304at 560-690 K. In the literature, the reduction of both Fe203and Fe304to Fe metal has been studied, generally in the isothermal mode. In the present study, we sought to determine the reduction mechanism of the step Fe304 Fe, for various reasons: The experimental conditions (especially the sample size) were optimized toward evaluation of this reduction step; the Fez03 Fe304peaks were generally of too low an intensity for accurate quantitative analysis, due to the relatively small H2 consumption involved. The reduction step Fe203 Fe304cannot be observed as a distinct peak under dry TPR conditions (see Figure 2). The reduction of F e 3 0 4to Fe metal has been studied most extensively in the literature, with Fe304as a starting material or formed as an intermediate in the reduction of Fe203. Moreover, generally those reduction conditions were chosen for Fez03 which resulted in completion of the reduction to Fe metal and in the occurrence of the Fe203 -+ Fe304step as a fast prereduction. The isothermal reduction curves (degree of reduction cy as a function of time) for the reduction of Fe304at 475-850 K have been reported to be S-shaped.13,17-20,28.33 Furthermore, it was found that this induction period becomes more important with decreasing The occurrence of reduction temperature or particle size.17~20~28 such an induction period has been associated with nucleation processes as the rate-determining step in a uniform internal reduction.20,22 With increasing particle size or reduction temperature the rate-determining step was found to change from nucleation (uniform internal reduction) to phase boundary reaction, i.e. chemical reaction at the Fe304/Fe metal interface, and/or diffusion through the (porous) Fe metal product layer.15,16i20,23 The latter two rate-limiting processes are both associated with a topochemical mode of reduction. As in most literature relatively large particles have been used, the topochemical reaction and/or diffusion have generally been found to be rate limiting. In the present study, however, extremely small Fez03 particles (ca. 0.3 km) have been used. The selection of the three-dimensional nucleation model of Avrami-Erofeev, for the description of the (dry) reduction of in-situ formed small Fe304particles, is supported by the literature, since the model of Avrami-Erofeev represents a uniform internal reduction mechanism: first-order formation of nuclei throughout the particles is followed by linear growth of the nuclei in three dimensions, taking into account the overlap of growing nuclei.I0 The occurrence of such internal, Avrami-Erofeev-type reduction is supported by the fact that Fez03 Fe304 prereduction is advanced extensively (Figure 2 ) or is even completed (Figure 3) when the Fe304 Fe metal reduction starts, showing that the whole particle is accessible for the gas phase, and the reported increase of porosity by reduction of iron oxides. 18-22,30 Besides the Avrami-Erofeev model, there exist other models which describe uniform internal reduction by different mathematical expression^.^^^^^^^' For instance, the crackling core model of Park and Levenspiel has been applied successfully for the description of the reduction of Fe304by C0.37 This model assumes that, at the reduction start, an initially nonporous particle becomes porous by formation of cracks, followed by uniform internal reduction. It is obvious that this model and the Avrami-Erofeev model differ little physically; when many pores are formed initially, nuclei can be formed along the pore walls throughout the entire particle from which the reduction can proceed in three directions. We have preferred the Avrami-Erofeev model with respect to other models describing uniformal internal reduction, since the mathematics of the former model are much more convenient for the presented procedure for the calculation of TPR patterns. The Role of H 2 0 in the Reduction Mechanism. It was observed that the reduction rate decreases with increasing H 2 0 pressure, especially for Fe304 Fe metal and to a much smaller extent for Fe203 Fe304. In the literature, conflicting observations have been reported on the influence of H 2 0 , probably due to
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-
-
-
-
- -
(37) J Y Park and 0 Levenspiel, Chem Eng Sci , 30. 1207 (1975)
Wimmers et al.
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differences in the reduction temperatures, the H 2 0 pressures, and the presence of impurities. With regard to the Fe203 Fe304 reduction, H 2 0 might influence the rate slightly n e g a t i ~ e l y ' ~ . ~ ~ or positively.26 The Fe304 Fe metal reduction has generally However, this been reported to be retarded by reduction appears to be catalyzed in the combined presence of fresh Fe metal and H 2 0 in some cases, due to acceleration of H2 dissociation (by Fe metal) and hydrogen spillover (by Also the unsuccessful simulation of the wet TPR pattern for the Fe304 Fe metal reduction step (see Figure 6b) suggests a special role of H 2 0 in the reduction mechanism. To find an explanation for the influence of H 2 0 , first the thermodynamics of the system Fe203/Fe304/Femetal in H 2 0 / H 2 medium was calculated from the JANAF tables.38 It was found that, in the range of temperatures and pressures studied, either Fe304or Fe metal is the stable phase. Already at room temperature Fe metal can be stable, at H 2 0 pressures below 0.02 mbar. Even when the H 2 0 pressure is 1 mbar (found as the maximum H 2 0pressure during dry TPR measurements), Fe metal is already stable above 400 K. Therefore it is concluded that Fe metal is the stable phase throughout the complete temperature range during dry TPR measurements. When the H 2 0pressure is 30 mbar (typical during wet TPR measurements over the entire temperature range studied), Fe metal can only be formed above 590 K. It is expected from these thermodynamic data that the shifts of the reduction peaks for Fez03 Fe304and Fe304 Fe metal as a result of H 2 0 addition are absent and significant, respectively. The slight shift of the Fe203 Fe304reduction peak can be easily explained kinetically, considering some blocking of reduction nuclei by adsorbed H20. In the case of the Fe304 Fe metal reduction, two questions remain: Why does the reduction start shift, due to H 2 0 addition, to a higher temperature (ca. 650 K at 0.2 K/min) than required by the thermodynamics (590 K)? Why could a reasonable fit not be obtained for the wet TPR pattern (see Figure 6b)? It is concluded that kinetic concepts other than those presented in Table I are needed for the description of the influence of H,O on the reduction of Fe304. In the following, self-catalyzed nuclei formation (autocatalysis)10%'6 will be considered as an alternative rate-determining step. Unfortunately, no mathematical models without adjustable parameters are available yet for the precise description of self-catalyzed n u c l e a t i ~ n .The ~ ~ steep ~ ~ increase of the reduction rate around 650 K, however, supposedly can be fitted by use of power-law-type equations as proposed for selfcatalyzed nucleatior~.~*'~ Probably nuclei formation in the presence of 3% H 2 0 starts around 590 K but is very slow up to ca. 650 K. In support of this, an increase of the induction period has been found by the addition of H 2 0 in isothermal reduction m e a s ~ r e m e n t s . ' Such ~ a slow initial nuclei formation can be explained, for instance, by destruction, by H 2 0 , of surface defects needed for nuclei formation, This nuclei as has been found in a study on MOO, r e d u ~ t i o n . ~ destruction might be enhanced by higher temperatures where nucleation takes place in the presence of H 2 0 . The strong acceleration of the reduction rate above 650 K is associated with self-catalyzed nucleation (autocatalysis).'0s16 Apparently, nuclei catalyze further nuclei formation, due to branching of nuclei or to the catalytic role of the Fe metal in H 2 dissociation. H 2 0 might assist during the acceleration by assuring fast hydrogen spillover.33 It is obvious that the rate-determining step will change further during reduction once the explosive nuclei formation is finished. Probably overlap of nuclei will start around the TPR peak maximum according to an Avrami-Erofeev-type mechanism. The E value of 172 kJ/mol obtained under wet conditions for the Fe304 Fe metal reduction is tentatively associated with self-catalyzed nucleation as the rate-determining step, because the T,,, value
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H20.14517,26329,33
H20).26333
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+
+
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-
(38) JANAF Thermochemical Tables, 2nd edition, Natl. Stand. Ref. Data Ser., Natl. Bur. Stand., No. 37 (1971).
J. Phys. Chem. 1986, 90, 1337-1344 is mainly determined by the reduction rates on the low-temperature side of the TPR peak.
ConcIusions
Foundation for Chemical Research (S.O.N.) with financial aid from the Netherlands Organization for the Advancement of Pure Research (Z.W.O.). The authors thank Dr. Ir V.H.J. de Beer (Eindhoven University of Technology) for his helpful comments.
The activation energy value E can be determined independent of the reduction mechanism, using the position of the TPR peak maximum at several heating rates. A procedure for the calculation of TPR patterns is described, which shows that the T P R peak shape is clearly different for various reduction mechanisms. Therefore, the reduction mechanism can in principle be determined by comparison of the measured TPR pattern with a set of TPR patterns calculated on the basis of several reduction mechanisms. The reduction of Fe,O, to Fe metal (heating rates 0.2-10 K/min; particle size 0.3 Fm) was found to be a two-step process: Fe203 Fe30, (560-690 K) and Fe30, Fe metal (570-750 K) . When the calculation procedure proposed in this paper was applied, the reduction of small Fe304particles under dry conditions was shown to proceed with three-dimensional nucleation according to Avrami-Erofeev as the rate-determining step ( E = 1 1 1 kJ/mol). As this mechanism represents uniform internal reduction, this finding is supported by the literature. The reduction of small Fe30, particles in the presence of 3% H 2 0is retarded significantly and could not be described by regular solid-state kinetics. The rate-determining step supposedly is self-catalyzed nucleation (autocatalysis) on the low-temperature side of the T P R peak ( E = ca. 172 kJ/mol), while it cha,nges during reduction to, probably, Avrami-Erofeev-type nucleation.
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1337
preexponential factor, s-' constant in eq 15 activation energy for reduction, J mol-l mechanism-dependent term of reduction rate equation (see eq 1) gas-phase-dependentterm of reduction rate equation (see eq 1)
full width at half-maximumheight of a TPR pattern, K or
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S
mechanistic part of eq 5 and 6 reduction rate constant, s-I reduction rate constant, s-l sample weight, kg function defined by eq 8 H2 pressure in reactor, bar H 2 0 pressure in reactor, bar gas constant, R = 8.31434 J mol-' K-' reduction rate (see eq I), SKI time, s
temperature, K temperature where the reduction rate is at maximum, K temperature where cy = 0, K dummy variable used in eq 8 parameter defined by eq 7 degree of reduction of solid reactant heating rate, K s-l Registry No. Fe203,1309-37-1.
Acknowledgment. This study was supported by the Netherlands
Surface Acidity of Vanadyl Pyrophosphate, Active Phase in n-Butane Selective Oxidation Guido Busca: Gabriele Centi,! Ferruccio Trifirii,*$ and Vincenzo Lorenzellis Istituto Tecnologie Chimiche Speciali. 401 36 Bologna, Italy, Istituto di Chimica, Facoltci di Ingegneria, 401 36 Bologna, Italy, and Istituto di Chimica, Facoltci di Ingegneria. Universitci di Genova, Genova, Italy (Received: June 4, 1985)
The surface acidity of two (VO)zPz07catalysts with similar specific activities per square meter of surface area in 1-butene selective oxidation, but different specific activitiesin n-butane selective oxidation, was studied by ammonia, pyridine, acetonitrile, CO, and COz adsorption, by ammonia temperature-programmed desorption, and by 2-propanol oxidation. The results for both catalysts indicate the presence of strong Bransted sites attributed to surface P-OH groups and of medium strong Lewis sites attributed to V(IV) coordinatively unsaturated ions exposed on the surface. The presence of these centers was related to the (VO)zPz07structure itself and is fairly independent of the (VO)zP207preparation method. However, in the (VO)2P207 prepared in an organic medium and to a lesser extent in the (V0)2Pz0, prepared in an aqueous medium, the presence of very strong Lewis sites also was observed. The enhancement of the rate of n-butane activation in the (VO)2P207 prepared in an organic medium was attributed to the presence of these sites. The role of the preparation method in the formation of such very strong Lewis sites also is discussed.
Introduction In addition to the industrial importance of the selective oxidation reaction of n-butane on vanadium-phosphorus oxides for the synthesis of maleic anhydride, this reaction is an interesting model for studies of the characteristics of the catalysts able to selectively *Correspondence should be sent to F.T. at Istituto Tecnologie Chimiche Speciali, Viale Risorgimento 4, 1-40136 Bologna, Italy. Istituto di Chiml'ca. Istituto Tecnologie Chimiche Speciali. 8 Universiti di Genova.
*
0022-3654/86/2090-1337$01.50/0
activate paraffins. In fact, in contrast to the well-studied allylic mechanisms of oxidation, no comparable data have been published on the mechanism of selective oxidation of n-butane.'-6 It was ( I ) Centi, G.; Trifir6, F.; Vaccari, A.; Pajonk, G. M.; Teichner, S.J. Bull. Sor. Chim. Fr. 1981, 7-8, 1. (2) Centi, G.; Fornasari, G.; Trifir6, J . Card. 1984, 89, 44. (3) Varma, R. L.; Saraf, D.N. Ind. Eng. Chem. Prod. Res. Deu. 1979, 18, I
(4) Hodnett, B. K.; Delmon, B. Znd. Eng. Chem. Fundam. 1984,23,465. (5) Wolf, H.; Wuestneck, N.; Seeboth, H.; Belousov, V . M.; Zazhigalov, V. Z . Chem. 1982, 22, 193.
0 1986 American Chemical Society
