J. Phys. Chem. 1995, 99, 2038-2041
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Diffusion in Porous Catalyst Grains As Studied by EPR Imaging 0. E. Yakimchenko,? E. N. Degtyarev,? V. N. Parmon,’ and Ya. S. Lebedev*?+ N. N. Semenov Institute of Chemical Physics RAS, Kosygin Str. 4, 117977, Moscow,Russia, and Institute of Catalysis, Sibierian Department of RAS, Akademgorodok, 630090, Novosibirsk, Russia Received: May 27, 1994@
Diffusion of the spin probe perchlorotriphenylmethylinto the solvent-saturated porous catalyst support prepared from two types of aluminium oxide (Al2O3) and into pure solvent (CC4) is studied by EPR imaging. By comparison of the experimental tomograms (spectra in nonuniform magnetic field) with the computed ones obtained on the basis of the Fick’s diffusional equation solution, the effective diffusion coefficients De are determined and values of tortuosity are estimated. Two-dimensional spatial distribution of spin probe 2,2,6,6tetramethyl-4-hydroxypiperidine- 1-oxy1 at different times of diffusion into alumina support are detected and De is estimated to be less than 6 x lo-* cm2/s.
Introduction
Diffusion and mass transfer in porous catalysts grains are processes of fundamental importance in heterogeneous catalysis. Very often they are determining the upper limit of activity of real industrial catalysts and their behavior in respect to temperature. For a long time such processes were attracting attention of physical chemists.’s2 As a typical catalyst grain contains about 109-1019 units of porous structure, the whole grain may be considered as quasi-homogeneous media characterized by some effective diffusion coefficient De. To define these coefficients. a number of stationary and nonstationary methods had been developed based mostly on detection of the flow of a substance via a microscopic sample of simple configuration. Still existing experimental approaches appear hardly applicable to explore diffusion in rather small grains of catalyst support which are used in modern technologies (cylinders with diameter about 0.4 and about length 1.2 cm), for which one can expect a serious influence of the granules shape, a deflection from the ideal models, describing the mass transfer in the porous matrices, etc. A novel approach to resolve these problems for experimental study of so complicated systems would be the methods of direct imaging allowing to observe diffusion processes in situ. Unfortunately, the known applications were restricted by only X-ray imaging of diffusion of organic molecules with inclusion of heavy halogen atoms3 and NMR imaging of diffusion of D20 in porous cylinder of ~irconia.~ The present study was aimed to demonstrate the efficiency of EPR imaging for exploring diffusion of chosen paramagnetic molecules in small grains of catalyst support. The EPR imaging based on detection of EPR spectra in nonuniform magnetic field was introduced as early as 19735.6and its application to study kinetic and diffusion processes was demonstrated by several authors.’-18 More details about EPR imaging applicationsmay be found in review^.^^,^^ In ref 21 the great efficiency of combination of spin probe technique and EPR imaging to study time-dependent spatial distribution of paramagnetic molecules in heterogeneous media was demonstrated. EPR imaging allows us to observe nondestructively the concentration profiles within the solid samples, thus enabling us to measure the diffusion parameters in samples of different size and shape. Here we N. N. Semenov Institute of Chemical Physics RAS. Institute of Catalysis. @Abstractpublished in Advance ACS Abstracts, January 1, 1995.
investigated the diffusion transport in catalyst supports prepared from porous aluminium oxide A1203 with different parameters of porosity, specific surface, etc. The sample was soaked with liquid CC4 and diffusion of spin probes (stable free radicals) was studied as a model of diffusion stage of catalytic process. Two type of radicals with different polarity were chosen: perchlorotriphenylmethyl (I) as nonpolar molecule and 2,2,6,6tetramethyl-4-hydroxypiperidine-1-oxy1 (II) as representative of polar molecules. The investigation included comparison of diffusion of I and 11 from the solution in CC4 into the A1203 granules soaked with CC4, and for I into the pure solvent (CC4) as well. The spatial distribution of I and I1 were checked at different stages of diffusion, and diffusion coefficients De were thus detemined. The obtained results are discussed within capillary model of porous media and tortuosity factor is estimated. Experimental Technique
Two kind of samples were used both representing industrial catalyst supports made from A 1 2 0 3 as cylinders with radius 0.23 cm and height 1.2 cm. Other parameters of material were as follows: type 1, a-A12O3,specific surface S,, = 10 m2/g, volume of pores V, = 0.42 cm3/g, average pore radii rp = 0.4 pm and 0.02 pm; type 2, y-Al203, s, = 200 m2/g, v, = 0.35 cm3/g, r, -= 100 A. The preevacuated samples were kept for 30 min in pure CC4, then transferred to ampule filled with a concentrated solution of spin probe in CC4. EPR spectra were detected by X-band (9.5 GHz) spectrometer ERS-221 with rectangular resonator (TE102 mode) modified for EPR imaging experiments.22 In particular the ll-shaped ferromagnetic prism was used generating magnetic field gradient V$? = 560 G/cm in the y direction normal to magnetic field B and axis of cylindrical sample. To study diffusion in liquid solution, gradient V,B = 110 G/cm was generated in vertical direction by the ferromagnetic wedge. For the sample tube with 5 mm 0.d. the variations of the microwave field were not taken into account. When EPR spectra is recorded in nonuniform magnetic field with permanent gradient V B along some direction, the detected EPR tomogram I@) is represented by convolution of the EPR line shapefo(B) with the distribution function p ( B ) of paramagnetic centers along the direction of gradient: +-a
Ic(B) = S f o ( B - B*)P(B*>dB -ca
0022-3654/95/2099-2038$09.00/00 1995 American Chemical Society
(1)
Diffusion in Porous Catalyst Grains
J. Phys. Chem., Vol. 99, No. 7, 1995 2039
1/L
H
100
1.00
G
0.90
fi
I\
0.80
0.70
0.60
H
100 G
0.50 0.40
1 ,
0.30 0.00
0.05
0.10
0.15
0.20
0.25
r= Dt/a2 Figure 2. Dependence of 1IL from t for computed tomograms (straight
line). Data points, expressed in dimensionless coordinates, obtained with use of experimentally detected values of De and L,are plotted for two samples of type 1. Figure 1. (A) Experimental tomograms, obtained in process of diffusion of radical I, dissolved in CC4, into the granule of catalyst support (type l), preliminary soaked with solvent, registered at different times of diffusion (1, t = 2 min; 2, t = 8 min). The starting conditions are in accord with nonequial distribution of solution around the granule. (B) Tomograms, computed according eqs 2 and 3, at different t (1, t = 0.005; 2, t = 0.01; 3, t = 0.04).
To restore the spatial distribution function p ( x ) = p(B)/V,B, it is necessary to perform the deconvolution, that is to solve the convolution equation (1). To obtain a two-dimensional (2D) spatial distribution, a set of 18 1D projections was detected by rotating the sample around the vertical axis. Then the 2D function was restored by deconvolution and reconstructionprojection algorithm described elsewhere.21 The simplest and the least time-consuming approach was based on the straightforward analysis of EPR tomograms involving comparison of theoretically predicted and experimental spectra in the magnetic field with a known gradient. Note that the conventional magnetic field modulation technique gives the first derivative of the EPR line shape dfo(B)ldB, and according to eq 1 the recorded EPR tomogram then represents differential function dfo(B)ldB as well.
Experimental Results In Figure 1A we present experimental tomograms (first derivative) obtained after various periods of diffusion of spin probe I into the catalyst support soaked with CC4, as described in the previous section. The differential EPR tomogram has two pairs of extremal points. The distance between outer points corresponds to the geometrical dimension of sample (diameter 6) and is approximately L = d V,B. This value of L does not change in course of diffusion. The distance between internal extremums I decreases in the course of diffusion and may be attributed to the position of diffusional fronts which are separated by distance n = UV@. To check it more quantitatively, we calculated tomograms according to eq 1, assumine one-dimensional diffusion into an infinitely long cylinder with radius a. The local concentration
along radius C(r,t) is governed by the diffusion equation
aciat = lir alar(rD aciar) with the border and initial conditions
c=o,
O> Dm and Dr % Dm. Then we may use eq 6 and experimental values of De to determine values of factor 6 which is important for characterization of catalyst support properties. The corresponding values are given in Table 1. The diffusion of the interacting spin probe I1 into the catalyst support of type 1 looks quite different. The motion of diffusion front (characterized by parameter I in Figure 1 ) is much slower,
J. Phys. Chem., Vol. 99, No. 7, 1995 2041
Diffusion in Porous Catalyst Grains and one has enough time to screen many projections and to restore the two-dimensional spatial distribution of the spin probe at different time of diffusion; see Figure 3. The sample was always immersed in the solution, but prior to the beginning of the 1-D projection collection (t = 18.5 h), spin probe I1 was wholly absorbed on the surfaces of A1203. This was detected both from the experimentally obtained tomograms and visually. The line shape of the EPR signal looked like partially immobilized, but with out spatial resolution near 300 p m we can say only that all radicals are on the surface of the support or in a layer thinner than 300 pm. All further experiments were made in an overmodulated regime of registration in order to overcome the differences in the line shapes of radicals in different spatial positions as was suggested in ref 21. The variations of signal intensity around the sample (Figure 3A) are connected with variations of thickness of the solvent layers surrounding the sample. In the further process of diffusion the radical filled the whole cylinder uniformly. The time of the filling process allowed us to estimate the diffusion coefficient Deas less than ‘ 6 x cm2/s. It is at least 1050 times less than the diffusion coefficient for the noninteracting probe I. We assumed that probe I1 moves in the Knudsen’s regime with Dk
