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with initial condition and other symbols same as before and a! is the number of particles present initially in state D.
(10) I. G. Darvey, B. W. Ninham, and P. J. Staff, J. Cbem. Pbys., 45, 2145 (1966). (11) I. G. Darvey and B. W. Ninham, J . Chem. Phys., 46, 1626 (1967). (12) A. Renyi, Magy. Tud. Akad. Alkalm. Mat. Int. Kozl., 2, 93 (1954). P. J. Staff, J. Chem. Phys., 46, 2209 (1967). C. J. Jachimowski, D. A. McQuarrie, and M. E. Russel, Blochemistry, 3, 1732 (1964). C. DeLisi, Biopo/ymers, 11, 2251 (1972). M. G.Kendaii, “The Advanced Theory of Statistics”, Voi. I, Griffin, London, 1943. H. Cramer, “Mathematical Methods of Statistics”, Princeton University Press, Princeton, N.J., 1946. W. P. Eiderton and N. L. Johnson, “Systems of Frequency Curves”, Cambridge University Press, London, 1969. A. K. Thakur and C. DeLisi, Biopo/ymers, in press. N. Dubin, “A Stochastic Model for Immunological Feedback in Carcinogenesis” in “Lecture Notes in Biomathematics”, Vol. 9, Springer-Veriag, Berlin, 1976, D. E. Barton and K. E. Dennis, Biometrika, 39, 425 (1952). R. A. Fisher, Phil. Trans. R. SOC.London, Ser. A, 222, 309 (1922). L. R. Shenton, Biometrlka, 38, 58 (1951).
References and Notes A. F. Barthoiomay, Bull. Math. Blopbys., 20, 175 (1958). A. T. Bharucha-Reid, “Elements of the Theory of Markov Processes and Their Applications”, McGraw-Hili, New York, N.Y., 1960. D. A. McQuarrie, “Methuen’s Monographs on Applied Probability and Statistics”, Voi. 8, Methuen, London, 1967. A. K. Thakur, A. Rescigno, and D. E. Schafer, Bull. Math. Biol., 34, 53 (1972). A. K. Thakur, A. Rescigno, and D. E. Schafer, Bull. Math. Biol., 35, 263 (1973). A. K. Thakur, Ph.D. Thesis, University of Minnesota, Minneapolis, Minn., 1975. D. A. McQuarrie, Adv. Cbem. Phys., XV, 149 (1969). D. A. McQuarrie, C. J. Jachimowski, and M. E. Russel, J . Cbem. Phys., 40, 2914 (1964). K. Ishida, J . Chem. Phys., 41, 2472 (1964).
Carburization of Supported Iron Synthesis Catalysts J. A. Amelse,+ J. 8. Butt,* and L. H. Schwartd Department of Chemlcal Englneerlng, and Department of Material Science and Engineerlng, North western Unlversity,Evanston, Illinois 6020 1 (Received October 17, 1977) Publication costs assisted by the Petroleum Research Fund
The chemical state of iron in a 4.94 wt % Fe/SiOz catalyst was examined by Mossbauer spectroscopy at various stages of calcination and reduction, and after use as a synthesis catalyst. About 90% of the iron in the initial oxide (a-Fez03)was reduced to a-Fe metal during 24 h reduction in Hzat 425 “C. Under reaction conditions the catalyst carburized within 90 min to the extent that no metallic iron could be detected in the Mossbauer spectra. The carbide formed is the 6’ form, as opposed to the x form previously reported for unpromoted fused or precipitated catalysts or the F form reported for KzO or Cu promoted catalysts. Reaction rates were measured in a differential reactor system. Methane formation rates increased monotonically as the catalyst carburized to a steady value of turnover frequency of 0.0037 f 0.0003 s-l. Product selectivity shifted toward a higher alkane content at the expense of methane formation as the catalyst carburized.
Introduction In the recently reawakened interest in the catalysis of Fischer-Tropsch ahd related synthesis reactions much work has centered on catalysts dispersed on high area supports such as silica or alumina rather than the fused or precipitated types originally employed. Primary topics of interest have been the determination of specific rates or turnover frequencies per unit surface area of the metal, the mechanism(s) of the synthesis reactions, and the role that electronic and alloying effects play in determining activity and ~electivity.l-~ Some caution must be exercised in the interpretation of recent attempts to deal with these topics, since much of the characterization which has been presented does not deal with the fact that Fischer-Tropsch catalysts apparently change their state under reaction conditions. It has been known for some time that the three principle catalysts, iron, cobalt, and nickel, all form carbides, at least in the fused or precipitated state.5 Controversy continues as to whether the synthesis reactions involve these carbides or whether some form of oxygenated species is the active *To whom correspondence should be addressed. Department of Chemical Engineering, Ipatieff Catalytic Laboratory. ‘Department o f Chemical Engineering. %Department of Material Science and Engineering, Ipatieff Catalytic Laboratory, Materials Research Center. 0022-3654/78/2082-0558$01 .OO/O
intermediate.2i6-8 It is not our present purpose to engage in details of the synthesis reaction mechanism, rather we wish to investigate the possible formation of carbide phases under reaction conditions for a typical metal synthesis catalyst dispersed on a high area support. No information exists in the literature concerning the rate of formation or the form of carbide produced in supported catalysts. In the following we report the results of a detailed investigation of an iron on silica catalyst. Silica was chosen as the support material as it is generally considered more inert than alumina or silica/alumina. Mossbauer spectroscopy was used for characterization of the chemical state of the iron after various oxidation-reduction cycles and after use as a synthesis catalyst. Chemical reactivity studies were also carried out to provide information on synthesis rates and the rate of carburization as a function of time of catalyst use in addition to data on product selectivity.
Experimental Section Catalyst. The support material used was 80-120 mesh Davison Grade 62 silica gel, BET area 340 m2/g, average pore diameter 14 nm. The gel was repeatedly washed with redistilled water and 0.1 N HN09 to remove alkali metal impurities, then dried and impregnated with an Fe(N03)3 solution (Mallinckrodt Reagent Grade, Lot AVL) via the incipient wetness technique. About 1.1cm3of solution per 0 1978 American Chemical Society
The Journal of Physical Chemistry, Vol. 82, No. 5, 1978 559
Carburization of Supported Iron Catalysts
TABLE I: Mossbauer Parameters for Figure 1 Spectrum
Phase
6 f mm/s
5.1-la
a-Fe,O, Superparamagnetic a-Fe,O, a-Fe Superparamagnetic a-Fe,O,
0.42 i: 0.01 0.40 i: 0.01
0.33 i 0.01
0.00* 0.01 0.36i: 0.01
-0.03 i: 0.01 1.02i: 0.01
5.1-lb
a Isomer shift reported with respect to iron metal. pole doublet. Magnetic field strength.
A E ~ mm/s , ~
H,c kOe
Re1 area
1
0.818 0.182
330 i. 1
0.673 0.327
500
i
Quadrupole splitting reported as the full width between a quadru-
gram of silica was required to reach the point of incipient wetness, with a calculated metal loading of 4.94 wt %. The impregnated catalyst was then dried under a sun lamp for 2 h and calcined in air for 4 h at 450 "C. Mossbauer Spectra. Spectra were obtained with a constant acceleration NSEC-AM1 spectrometer coupled to a Nuclear Data-2200 multichannel analyzer. Counting electronics are capable of handling the rates associated with the 50-100 mCi 57C0 source used in this work. Spectrometer calibration was with either natural iron foil or a foil enriched in 57Fe. Catalyst samples were mounted in the spectrometer in the form of a pressed pellet contained within a controlled atmosphere cell. The pellet was placed in a movable aluminum block which could be slid to the head of the cell for heating or other pretreatment while maintaining the mylar windows on the tail section at room temperature. Details of the cell design are given by Amelse.lo Lorentzian line shapes were fit to the spectra using a sum of squares deviation minimization via the method of Powell, developed by Dr. B. S. Garbow of Argonne National Laboratory. Reaction Measurements. Measurements of reaction turnover frequencies were obtained in a small flow reactor of conventional design operated under differential conversion conditions. Catalyst reduction was with ultra high purity hydrogen (Union Carbide Corp., 99.99% minimum, less than 3 ppm H20), further purified by passage through a Deoxo unit (Englehard Model 10-2500). For reaction experiments a 24.9% CO in H2 mixture (Union Carbide Corp.) was employed as the feed in all cases. The CO was CP grade (99.0% minimum, less than 15 ppm H 2 0 and 5 ppm 0,) and H2 of the same ultra high purity grade used for reduction. Oxygen was removed from the feed mixture by passage through a magnesia in silica trap previously reduced in flowing hydrogenall Flow rate was measured via a thermal mass flow meter (Brooks Model 5310). The reactor consisted of a 0.25-in. 0.d. Pyrex tube, typically containing about 0.15 g of catalyst, mounted in an insulated ceramic coil furnace. Temperature control to f l "C was provided by a Weather Measure Model IPC-R proportional-derivative controller. All reaction measurements were carried out at 255 "C and 1 atm total pressure with the 1:3 mixture of CO in H2. Standard prereduction of the catalyst was a t 425 "C in flowing hydrogen a t 100 cm3/min (SC) for 24 h. The product analysis via GC resolved H20,C02, and C1 through C4 alkanes and alkenes, but with no separation of C4 or Cd2- isomers.1°
Results Characterization by Mossbauer Spectroscopy. Two goals were set for the Mossbauer experiments: (1) determination of the degree of reduction before use as a synthesis catalyst, and (2) observation of any changes in the chemical nature of the catalyst during reaction. In the present experiments it is necessary to fully reduce the iron before use as a catalyst, since the rate of carbide
a
,970
,970
-9 -6
-3
0
3
6
9
VELOCITY, mm/a
Flgure 1. Mossbauer spectra of the 4.94 wt % Fe/SiO, catalyst: (a) calcined; (b) reduced in H, for 12 h; (c) spectrum of (b) after exposure to 0,at room temperature; (d) reduced in H, at 425 "C for 24 h in the differential reactor.
formation is obtained via mass balance on oxygen containing species. For this reason a series of oxidationreduction cycles was conducted on a sample with Mossbauer characterization at various stages in the treatment. The series was initiated by placing a 2-cm disk of the catalyst, 0.015 cm thick, in the controlled atmosphere cell and drying by heating in helium, raising the temperature in 50 "C increments every 0.5 h from 50 to 300 "C, and holding a t 300 "C for 2 h. The sample was then cooled to room temperature in He overnight. The spectrum of this calcined oxide is shown in Figure la. Seven Lorentzian lines were fit to the data and the Mossbauer parameters calculated by the procedure outlined above. The parameters associated with Figure 1 are presented in Table I. The spectrum of Figure l a shows a six-line pattern with an additional broad central peak. The state of the iron here can be identified as cr-Fe203 from the isomer shift, and the large value of the quadrupole splitting of the six-line pattern.12 This identification is confirmed by x-ray diffraction. The central peak is believed to be an unresolved doublet of superparamagnetic
580
The Journal of Physical Chemistry, Vol. 82, No. 5, 1978
J. A. Amelse, J. B. Butt, and L. H. Schwartz
TABLE 11: Mossbauer Parameters for Figure 2 Spectrum
Phase
5.1-2a
e-Fe,.,C Superparamagnetic €'-Fez,,C €'-Fez, 2 C E' -Fez. C Superparamagnetic e'-Fe,,,C
5.1-2b 5.1-2~
mm/s 0.22 f 0.01 0.25 i: 0.01
A EQ ,b mm/s
H,c kOe
-0.13 f 0.01 0.96 f 0.01
173f 1
0.25 i: 0.01 0.25 i: 0.01 0.23 rt 0.01
-0.15 -0.29 0.90
189 i: 1 173rt 1
6f
a Isomer shift reported with respect to iron metal. pole doublet. Magnetic field strength.
f
f f
0.01 0.01 0.01
Re1 area 0.713 0.287 0.806 0.194
Quadrupole splitting reported as the full width between a quadru-
a-FezO3 since the isomer shift of this peak corresponds very well to that of the six-line pattern. The average particle size of the a-FezO3 is about 16 nm, as determined by x-ray line broadening.lg The fraction of superparamagnetic material, and the hyperfine field calculated from Figure la, is consistent with that found by Kundig and Bomme124 for particles of a-FezO3 with an average particle size in this range. The a-Fez03/SiOzcatalyst was then reduced in flowing hydrogen while the temperature was increased from 100 to 400 "C, holding after each 50 "C increment for 0.5 h, then maintaining temperature at 425 "C for 1 2 h. The Mossbauer pattern for this reduced specimen (Figure l b ) shows a six-line pattern characteristic of iron metal plus a superimposed central doublet which can be attributed to superparamagnetic a-FezO3.l3 This spectrum was recorded at room temperature in hydrogen. The Lorentzian lines were fit to the data for the reduced catalyst by constraining only the line widths and the intensities of the inner two lines of the iron metal pattern to be in the same ratio to the parameters for the outer peaks as the inner to outer parameters for the spectrum of a natural iron foil. The central doublet was not constrained, since several reasons exist why these lines should not be expected to be of equal intensity.14 The ratio of the recoil-free fraction of a-FezO3 to that of iron metal is 1.22 f 0.10.15 If one makes the assumption that this ratio remains the same for small particles, then the fraction of iron atoms present as oxide after 12 h of reduction is estimated as about 40% based on the area under the Lorentzian lines. It is interesting to note that there is no change in the Mossbauer spectrum of this partially reduced catalyst on exposure to air a t room temperature for several hours, as shown in Figure IC. We do not understand the reason for this passivation, however, both partially and fully reduced catalysts were consistently found resistant to reoxidation under such conditions, allowing a considerable simplification in experimental procedure. A second sample of a-Fez03/SiOz(Figure l a ) was reduced in the reactor for 24 h following the procedure above. The spectrum of this reduced specimen, recorded in air, is presented in Figure Id. An unsuccessful attempt was made to determine quantitatively the amount of oxide present by fitting six Lorentzians for the metal and two for the superparamagnetic oxide to the data, but it is visually evident that oxide can only be present in very small amounts. Hence, we feel the 24-h reduction procedure sufficient to produce a fully reduced iron metal surface for this catalyst. Changes in the catalyst under synthesis reaction conditions were investigated by mounting another a-FezO3/ SiOz pellet in the controlled atmosphere cell, and reducing according to the 24-h schedule. The cell was cooled to reaction temperature (255 "C) in H2and then the reaction mixture of 24.9% CO in H2 passed through the cell for 6 h. The spectrum of this material is shown in Figure 2a;
I
J W
,984 -9
-6 - 3
0
3
6
9
V E L O C I T Y , mm/s
Flgure 2. Mossbauer spectra of carburized Fe/Si02 catalysts: (a) carburized by 1:3 CO in H, at 250 "C for 6 h; (b) spectrum of (a) at liquid N2 temperature (77 K); (c) carburized by 1:3 CO in H, at 255 "C for 1.5 h in the differential reactor.
parameters for all spectra of Figure 2 are given in Table 11. Only six lines were fit to Figure 2a. The spectrum appears to have a central doublet superimposed on a six-line magnetically split pattern. The small magnetic field indicated by the six-line pattern is suggestive of a carbide phase. At least four iron carbide phases have been identified by their Curie temperatures: E' carbide (Fez.&) about 450 "C; t carbide (Fe,C) 380 "C; x carbide (FeSC,) 247-256 "C; and 19 carbide, or cementite (Fe3C) 205-220 0C.5J6 Arents et al.17 speak of two other phases x' and x" arising during the E x 0 transformation. All of these phases have iron atoms at three magnetically inequivalent sites, except the E' and 8 carbides.17Js The e' and 0 carbides are thus the only carbides which exhibit Mossbauer spectra with only six lines. A Mossbauer spectrum of the E' carbide has not been previously reported; however, the hyperfine field of 173 f 1kOe calculated for the spectrum of Figure 2a is in agreement with the field of about 170 kOe which Maksimov and his co-worker~~',~* speculate that the E' carbide should have. Futhermore, the field is substantially less than 208-kOe field of the B carbide at room temperature. Further evidence that the carbide formed is the t' carbide and not the B carbide is provided by x-ray
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The Journal of Physical Chemistry, Vol. 82, No. 5, 1978 561
Carburization of Supported Iron Catalysts
diffraction data. The first six low angle reflections of the hexagonal e' structure were observed, whereas the 6' carbide is orthorhombic. The carbides may be arranged in the following order of increasing stability: E ' - F ~ ~
