A Frequency-Response Study of the Diffusion and Sorption Dynamics

Nov 11, 1999 - Master curves for mass transfer in bidisperse adsorbents for pressure-swing and volume-swing frequency response methods. Yu Wang , M. D...
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Langmuir 2000, 16, 1331-1336

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A Frequency-Response Study of the Diffusion and Sorption Dynamics of Ammonia in Zeolites J. Valyon,*,† Gy. Onyestya´k,† and L. V. C. Rees‡ Institute of Chemistry, Chemical Research Center, Hungarian Academy of Sciences, H-1525 Budapest, P.O. Box 17, Hungary, and Department of Chemistry, University of Edinburgh, West Mains Road, Edinburgh EH9 3JJ, Scotland, U.K. Received July 2, 1999. In Final Form: September 28, 1999 The dynamics of diffusion and sorption of NH3 was studied in zeolites Na-A, K-A, Na-X, H-Y, H-mordenite, and H-ZSM-5. The batch frequency-response (FR) technique was applied. The NH3 pressure was 133 Pa and the temperature was in the 373-873 K range. The FR spectra were interpreted according to the model of the isotherm, batch-type FR system containing uniform, isotropic, and spherical sorbent particles. Results suggest that any one of the consecutive process steps of the ammonia transport between the gas and the sorbent can control the rate of the process under the near-equilibrium conditions of the measurement. The nature of the rate-controlling step depends on the structure, composition, and size of the sorbent particles. Diffusion in the macropores was found to determine the rate in commercial zeolite pellets and in large particles built of aggregated zeolite crystallites. When this rate-controlling process was eliminated by grinding the particles, either micropore diffusion or sorption became the slowest rate-controlling step. The dimensions of NH3 molecules and the free diameter of the pores of zeolite K-A are comparable. As a result, the diffusion resistance of the zeolitic micropores controls the NH3 mass transport. The other zeolite samples have wider channels and bind ammonia more strongly than K-A. Owing to the high NH3 coverage and activation energy of desorption, the adsorption-desorption process was much slower than the rate of diffusion. For H-zeolites, different parallel transports could be distinguished. A fast process, dominating at high near-equilibrium ammonia coverage, was assigned to sorption on Lewis acid sites, such as NH4+ ions. The slower processes, appearing mainly at lower coverage, can represent the direct interactions between the NH3 and the Bro¨nsted acid sites. The FR method can be effectively used for most of the zeolites to characterize the dynamics of NH3 sorption.

1. Introduction The interest in reactions initiated by solid acid catalysts motivates efforts to develop theories and techniques that can be used to characterize the acidity of solids.1 Acidity is a general term for the properties that determine the effectiveness of an acid for reaction with a base. NMR and IR spectroscopic methods,2-7 temperature-programmed desorption (TPD),5,8-12 and microcalorimetry13,14 are routinely used for the examination of the acid-base interac* To whom correspondence should be addressed. Fax: (36-1) 3257750. Phone: (36-1) 325-7868. E-mail: [email protected]. † Hungarian Academy of Sciences. ‡ University of Edinburgh. (1) Acidity and Basicity of Solids: Theory, Assessment and Utility; Fraissard, J., Petrakis, L., Eds.; Kluwer Academic Publishers: London, 1994. (2) Ka¨rger, J.; Pfeifer, H. Zeolites 1987, 7, 90. (3) Blumenfeld, A. L.; Coster, D.; Fripiat, J. J. J. Phys. Chem. 1995, 99, 15181. (4) Yin, F.; Blumenfeld, A. L.; Gruver, V.; Fripiat, J. J. J. Phys. Chem. 1997, 101, 1824. (5) Karge, H. G. In Catalysis and Adsorption by Zeolites; O ¨ hlmann, G., Pfeifer, H., Fricke, R., Eds.; Studies in Surface Science and Catalysis; Elsevier: Amsterdam, 1991; Vol. 65, p 133. (6) Lercher, A. J.; Gru¨ndling, C.; Eder-Mirth, G. Catal. Today 1996, 27, 353. (7) Paze´, C.; Bordiga, S.; Lamberti, C.; Salvalaggio, M.; Zecchina, A. J. Phys. Chem. 1997, 101, 4740. (8) Guimon, C.; Zouiten, A.; Boreave, A.; Pfister-Guillouzo, G.; Schulz, P.; Fitoussi, F.; Quet, C. J. Chem. Soc., Faraday Trans. 1994, 90, 3461. (9) Forni, L.; Vatti, F. P.; Ortoleva, E. Zeolites 1992, 12, 101. (10) Forni, L.; Vatti, F. P.; Ortoleva, E. Microporous Mater. 1995, 3, 367. (11) Karge, H. G.; Dondur, V. J. Phys. Chem. 1990, 94, 765. (12) Camiloti, A. M.; Jahn, S L.; Velasco, N. D.; Moura, L. F.; Cardoso, D. Appl. Catal. 1999, 182, 107. (13) Auroux, A.; Jin, Y. S.; Vedrine, J. C. Appl. Catal. 1988, 36, 323. (14) Jozefowicz, L. C.; Karge, H. G.; Coker, E. N. J. Phys. Chem. 1994, 98, 8053.

tion using NH3 as a basic probe. From the analysis of the IR spectra, conclusions can be drawn about the nature of acidity, such as Bro¨nsted or Lewis, and the concentration of the different sites. Adsorption calorimetry and TPD can be employed to determine the amount and the strength of the various acid sites. Various methods often need to be applied in parallel to obtain a more complete description of the acidity. Spectroscopic and calorimetric methods study the acid-base interaction usually under equilibrium conditions, while the TPD measurement is of dynamic method. TPD peaks appear at the temperatures where desorption rates are maximal. These temperatures or preferably the activation energies of desorption can be used to characterize the acid strength of the sites releasing the NH3. The TPD results must be treated by an appropriate model to obtain the activation energies. However, if the rate of desorption is controlled by the rate of NH3 diffusion, nothing can be learned about the acidity.9,10 Recently it was shown that the dynamics of NH3 sorption in different zeolite catalysts could be studied by the frequency-response (FR) method.15-17 In this method the equilibrium of a gas-solid system is periodically perturbed. A pressure wave is generated which, owing to the gas-solid interaction, has its amplitude and phase angle delayed relative to the perturbing volume wave. If perturbation and reequilibration proceeds at comparable time scale, resonance occurs. The resonance frequency (15) Onyestya´k, Gy.; Shen, D.; Rees, L. V. C. J. Chem. Soc., Faraday Trans. 1996, 92, 307. (16) Valyon, J.; Onyestya´k, Gy.; Rees, L. V. C. J. Phys. Chem. 1988, 92, 8994. (17) Rees, L. V. C.; Onyestya´k, Gy. Microporous Mesoporous Mater. 1999, 28, 293.

10.1021/la990867e CCC: $19.00 © 2000 American Chemical Society Published on Web 11/11/1999

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gives the time constant of the transport process. It follows from the theory that parallel processes with different time constants can be distinguished.18,19 It was suggested that the FR parameters, like the data determined by TPD, could be correlated with the acidity of the solids.15-17 An important difference from the conventional TPD is that the FR method gives the dynamic parameters of the NH3 transport under quasi-equilibrium conditions at controlled temperatures. If the dynamic parameters of the acidbase interaction are required, evidently the rate of sorption must control the transport between the gas and the adsorbed phases. The theory of such systems has continued to be developed. The models are integrating the various factors influencing the FR results, e.g., mass and heat transports, bed effects, and particle- and pore-size distributions.18-22 However, it is not possible to obtain an unambiguous interpretation of the experimental FR curves based on a theoretical model. Even the most complex models fail in describing FR results obtained with gas-solid systems involving both adsorption and catalytic processes. The present work is an attempt to expand the use of the theoretical treatments in their applications to the results obtained by the FR method. From this aspect it is advantageous to work with NH3/zeolite system since the FR results can be analyzed with an extensive knowledge of possible sorption interactions and the micropore structure of the solid sorbent already obtained. It is shown in the present work that meaningful dynamic parameters can be obtained for the NH3/zeolite system if system is simplified to such extent that a single process of interest exclusively or predominantly determines the rate of transport. We shall demonstrate that, depending on the zeolite sample and the measurement conditions, any of the consecutive diffusion and sorption steps may control transport kinetics. Representative examples are given for the various different cases. The potentials and the difficulties of using the FR technique for the characterization of zeolitic acid sites are discussed. 2. Experimental Section 2.1. Materials. The ammonia was obtained from Argo International. It was of 99.96% purity and was used, therefore, without further purification. The zeolites studied are described in Table 1. 2.2. FR Measurements. The principles and the technical details of the FR technique have been given previously.23 Twenty-five to fifty milligrams of commercially manufactured zeolite powder or zeolite pellets were placed into the FR chamber. The zeolite powder was normally finely distributed in a plug of glass wool, but, when the bed effect was examined, it was allowed to form a thin layer at the bottom of the sample holder. A pressure wave was generated by applying a periodic square wave perturbation to the volume of the FR chamber containing ammonia gas and the solid sample in sorption equilibrium at a pressure of 133 Pa. A maximum perturbation of (1% of the gasphase volume was applied. The perturbation frequency was changed between 0.01 and 10 Hz. The higher odd harmonics of the Fourier transformation of the response signals were used to extend the frequency range to about 90 Hz. Measurements were carried out with and without sorbent under the same conditions. The phase difference and the amplitude ratio of the pressure (18) Yasuda, Y. Heterog. Chem. Rev. 1994, 1, 103. (19) Jordi, R. G.; Do, D. D. Chem. Eng. Sci. 1993, 48, 1103. (20) Bourdin, V.; Grenier, Ph.; Malka-Edery, A. In Fundamentals of Adsorption 6; Meunier, F., Ed.; Elsevier: Amsterdam, 1998; p 1167. (21) Petkovska, M.; Do, D. D. In Fundamentals of Adsorption 6; Meunier, F., Ed.; Elsevier: Amsterdam, 1998; p 1189. (22) Song, L.; Rees, L. V. C. J. Chem. Soc., Faraday Trans. 1997, 93, 649. (23) Rees, L. V. C.; Shen, D. Gas Sep. Purif. 1993, 7, 83.

Valyon et al. Table 1. Characterization of the Zeolite Samples sample ID 4Aa Na-Ab K-Ac H-ZSM-5d H-MORe 13Xf H-Yg

structure

composition of the unit cell

LTA LTA LTA MFI MOR FAU FAU

Na11.5Al11.3Si12.7O48 Na11.8Al11.6Si12.3O48 K11.6Na0.1Al11.7Si12.3O48 H3.91Na0.16Al4.06Si91.6O192 H6.6Na0.39Al7.16Si40.7O96 Na79.5Al79.4.5Si112.3O384 H50.7Na1.6Al52.3Si139.7O384

a Na-A powder and pellets prepared from the powder were examined. Both are zeolite 4A products of Lancaster Synthesis, U.K. The average diameter of the powder crystallites was 2.6 µm. The pellets contained about 10 wt % binder. b 4A powder; product of Hungalu, Ajka, Hungary. The average size of the crystallites was 1.2 µm. c Prepared from the Na-A powder by ion exchange. d The sample was provided by Degussa, Germany with the identification CAZ 49. Sample consists of 0.1-0.2-µm size crystallites intergrown into 100-200-µm aggregates. 47% of the total Al content is present in extraframework species. e NH4+ form was prepared from Na-mordenite (product of the Chemical Works, Wolfen, Germany) and was in situ thermally decomposed before the FR measurement. f Na-X powder and beads manufactured from the powder were examined. Both are zeolite 13X products of Lancaster Synthesis, U.K. The average diameter of the crystallites was 1.2 µm. The granules contained about 10 wt % binder. g The sample was provided by the Linde Co. with the identification LZY82. The framework Si-to-Al ratio is 4.8.

waves were determined, and a response function was derived. The in-phase (real) and out-of-phase (imaginary) components of the response function were plotted against the perturbation frequency to generate the FR spectrum. The effect of temperature was studied in the 373-873 K temperature range. Spectra show a step in the in-phase and a peak in the out-of-phase function at the frequency of resonance. The sorption capacity defines the intensity of the FR response and is a function of the pressure change effected by the volume perturbation of the FR system and is proportional to the slope of the adsorption isotherm at the equilibrium pressure. The relative magnitude of an out-of-phase peak reflects the fractional sorption capacity of the associated process. The characteristic FR functions derived by Jodi and Do19 were used to fit the experimental FR spectra. These functions were obtained by solving the general mathematical model of a periodically perturbed, isotherm batch system containing gas and isotropic adsorbent particles of uniform size and shape. The model includes processes of coupled mass-transfer resistance, such as transport through an external film or surface barrier and macro- and micropores diffusion. When it was possible the experimental conditions were chosen such that only one specific mass-transfer resistance was controlling the FR spectra of the system. The characteristic FR functions of rate-controlling sorption were determined using Yasuda’s model.18

3. Results Differences in the type of particles and in the structure of the adsorbent bed were found to have a pronounced effect on the FR characteristics of the NH3/zeolite systems. Figures 1 and 2 demonstrate these two effects. Parts A and a of Figure 1 show that relatively simple FR spectra can be obtained if measurements are carried out with particles smaller than about 20 µm and finely dispersed in the FR chamber. The H-MOR was used in its as-synthesized form. The finer grain of the H-ZSM-5 sample was obtained by grinding the parent material. The characteristic curves that fitted the experimental data most closely were derived using the model assuming ratecontrolling isothermal sorption (i.e., the sorption model). A weak resonance signal was resolved at about 0.2 Hz and a much more intense peak in the 10-20 Hz range. The data suggest that at least two parallel transport processes are involved. A broad, featureless spectrum was obtained if the finegrained H-MOR powder was not carefully distributed in

Diffusion and Sorption Dynamics of NH3 in Zeolites

Figure 1. FR spectra of NH3 mass transport on H-ZSM-5 (A, B) and H-MOR samples (a, b) at 133 Pa NH3 pressure and 723 K. The in-phase and out-of-phase components of the measured response functions are given by the symbols. Full and dotted lines were obtained by formal mathematical curve fitting and peak resolution (B, b) or by determining the parameters of the best-fit sorption model (A, a). 50 mg of H-ZSM-5 powder was dispersed over glass wool in ground (A) and in nonground (B) form, and 50 mg of H-MOR powder was dispersed over glass wool (a) or was allowed to form a shallow bed (b). Samples were pretreated by evacuation at 723 K for 1 h.

Figure 2. NH3 FR spectra of (a, b) powder and (A, B) pellet form (a, A) 4A and (b, B) 13X zeolites. Samples were pretreated by evacuation at 573 K for 1 h. Spectra were recorded at 133 Pa NH3 pressure and 373 K.

the FR chamber but allowed to form a thin layer (see Figure 1b). A broad spectrum was also recorded with the nonground H-ZSM-5, regardless of the method applied for dispersing the powder in the FR chamber (see Figure 1B). These spectra could be resolved into two or more components. The high-frequency component appeared at about the frequency of the intense peak on the corresponding spectra shown in Figure 1A, a. Comparison of the spectra indicates that most of the low-frequency components are removed if only small particles are involved, and these are distributed in the sample chamber in a plug of glass wool (see Figure 1A, a). The spectra of Figure 1B, b is broad, suggesting that many processes of different characteristic times are proceeding in parallel. Processes such as diffusion in poorly defined adsorbent beds and in particles of various sizes, furthermore, sorption, and, possibly, heat transport may also be involved. It is impossible to simulate theoretically such complex phenomenon and determine the dynamic parameters of these processes. Valuable information can be obtained, however, if the bed effect is avoided and the

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particle-size distribution is included in the applied model. The latter problem was not involved in the present work as particles or granules of uniform size were used. In absence of particle-size heterogeneity and bed effects, it is relatively easy to analyze experimental spectra that can be described by one of the degenerate FR models, preferably by a model involving only a single source of mass transport resistance. The first point to note is the relative form the out-of-phase and the in-phase components of the FR function. It follows from the theory that, if rates of sorption govern the transport, then the in-phase curve and the out-of-phase FR peak intersect at half the step height and at the maximum of the out-of-phase peak. The spectra shown in Figure 1A, a satisfy this requirement, and, therefore, the characteristic curves were derived using the sorption model. If diffusion is the rate-controlling process, the highfrequency end of the out-of-phase peak approaches the high-frequency tail of the in-phase curve asymptotically. The experimentally determined FR curves for ammonia transport in commercial 13X beads follow this diffusion case (see Figure 2B). For an isotropic spherical particle of radius r, the characteristic time of diffusion can be given as r2/D, where D is the diffusivity. The measured characteristic time, or the time constant (D/r2), can correspond to diffusion in either micropores or macropores. The time constant depends on the bead size if the rate of the process is determined by diffusion in the intercrystalline voids. In contrast, the bead size is irrelevant if the diffusion resistance of the micropores in the zeolite crystallites is controlling the rate of the process. The effect of bead size was, therefore, experimentally tested. It was concluded that the FR spectrum in Figure 2B had to be interpreted according to a model that assumes that the diffusion in the macropores controls the transport process. The sizes of the 4A and the 13X beads and the zeolite crystallites, of which the beads were formed, were similar in both zeolites. However, for the 4A beads the intersection behavior of the component FR curves in Figure 2A was different from that found for either the 13X beads or the powdered zeolite samples in Figure 2B and Figure 2a, b. Obviously, the rate spectrum of NH3 transport in the 4A beads, shown in Figure 2A, cannot be described by either a simple diffusion or a sorption model. According to theory such spectra can be fitted by characteristic FR curves generated by a model involving coupled resistance of consecutive transport processes. The condition of coupling is determined by the time constants of the consecutive processes. Considering that the 4A sample is comprised of beads similar to those of the 13X sample, it is conceivable that one of these processes is the diffusion in the macropores of the beads. The most pronounced difference of the two samples is the size of the zeolitic micropores. It seems rational, therefore, to assign the second coupled transport resistance to the diffusion resistance of the 4A micropores. The time constants of the two diffusion processes is comparable if rc2/rp2 is about equal to Dµ/DM, where rc and rp are the particle radii associated with the zeolite crystallites and the beads, and Dµ and DM are the diffusivities in the micro- and macropores, respectively. This condition is satisfied for the 4A but not for the 13X; thus, coupled macro- and micropore diffusion is observed with the 4A but not with the 13X sample. The FR curves of the fine-grain 4A and 13X powders are different, but both can be interpreted as rate spectra involving two parallel sorption processes (see Figure 2a, b). Different FR spectra of NH3 were measured for welldispersed, uniform-size fine grains of Na- and K-A zeolites

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Figure 3. FR characterization of the interaction of zeolite Na-A (A, B) or K-A (C, D) and NH3 at 400 (A, C) and at 700 K (B, D). The measurements were carried out using about 25 mg of samples at 133 Pa NH3 pressure following a 1-h evacuation at 723 K. Symbols give the measured response functions; full and dotted lines were obtained as the best-fit characteristic functions.

Valyon et al.

Figure 5. Temperature dependence of the total FR intensity for different H-zeolites. Sorption rate spectra were recorded at 133 Pa NH3 pressure. About 50 mg of sample was used. Samples were pretreated in situ by 1-h evacuation at 873 K.

relative intensities of the out-of phase peaks depend on the temperature. The peaks at 10 and 0.1-0.2 Hz monotonically lose intensity as the temperature is increased, indicating that the sorption capacities associated with the related processes are decreasing. The peak at about 1-2 Hz gains intensity in the 473-673 K range, but as the temperature is increased above 673 K this peak also decreases. The temperature dependence of the total H-Y FR intensity is shown in Figure 5 and may be compared with the corresponding plots for some other zeolites. A maximum appears in the temperature range of 650-750 K for all H-zeolites, suggesting that this feature is a general characteristic of these zeolites. 4. Discussion

Figure 4. NH3 FR spectra of H-Y at 373 (A), 473 (B), 673 (C), and 773 K (D). The measurements were carried out using about 50-mg samples at 133 Pa NH3 pressure after 1-h evacuation of the sample at 773 K.

(see Figure 3). Since the K-A was prepared from the Na-A by ion exchange, it is reasonable to attribute the different FR properties of the samples to the variance introduced by the cation and not to structural differences of the particles. The characteristic function of the Na-A was determined by a fitting procedure using the sorption model as shown in Figure 3. In contrast, the diffusion model of the FR experiment was giving the best-fit function for the K-A data. These results suggest that the NH3 molecules diffuse through the windows of Na-A, which have a free diameter of 0.4 nm, rapidly relative to the rate of sorption. The critical diameter of the NH3 molecule is 0.26 nm, while the pore openings of the K-A are about 0.3 nm in size. These openings can pose steric hindrance to the uptake of the NH3 molecules and control the transport dynamics. The FR spectra of NH3 sorption in H-Y zeolite are given in Figure 4. These spectra, in conjunction with those in Figure 1A, a, demonstrate the different characteristic functions that can be observed among the different kinds of H-form zeolites. A resonance signal appears at about 10 Hz and one or more less intense resonance peaks at lower frequencies. For H-Y, signals were discerned at about 1 and 0.1 Hz. These resonance frequencies are hardly dependent on the temperature, but the absolute and

The dynamics of a gas-solid interaction is studied essentially to recognize the rate-controlling mechanism and to determine the kinetic parameters of the process. A unique feature of the FR method is that it can distinguish and characterize parallel transports. The batch-type FR technique is relatively simple, and the data collection is quite rapid. However, the effective use of the method is hindered by ambiguities in the interpretation of the spectra. All the adsorption-desorption processes are accompanied by heat of sorption effects. The problem then is that it is difficult to distinguish rate-controlling heat and mass-transfer processes. Moreover, it is often impossible to avoid random heterogeneity of the particle size and shape, as well as the adsorbent bed depth effects. As a result the measured FR spectrum can often be fitted according to more than one model. If the time constants of the heat transport and mass transport are comparable, the FR spectrum contains nonisothermal response characteristic curves. When the heat transport is rapid relative to the mass transport, the system is considered isothermal. In case of a very slow heat transport, the system can be treated as adiabatic. For such a system the temperature of the sorptive gas and the sorbent can be different but are virtually invariant in time. On the basis of the pressure response function, the adiabatic and the isotherm FR systems cannot be distinguished. It seems more than probable that the NH3/ zeolite systems studied in the present work were not isothermal, but models assuming isotherm behavior still give a good fit of the FR responses. If curve fitting results in a perfect fit, an error is still present from the use of an imperfect model. It can be shown, for example, that the

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value of the calculated diffusion coefficient can vary as much as an order of magnitude depending on the particle geometry adopted by the model. However, such difficulties are not specific to the FR method since any model describing a complex phenomenon must be used with consideration of the limitations of the model. The rate-controlling mechanism of NH3 transport was substantiated for some well-defined NH3/zeolite systems using models assuming isothermal processes over isotropic and spherical particles. 4.1. Adsorption. Using the Langmuir rate equation, the FR parameters, κj and κ-j, of a process generating adsorbed species j can be expressed with the rate constants of adsorption, ka(j), and desorption, kd(j), and with Pe equilibrium pressure, or θe(j), the fractional coverage of site j at Pe as

κ-j ) ka(j)Pe + kd(j) ) kd(j)[(θe(j)/1 - θe(j)) + 1]

(1)

and

κj/κ-j ) const.(∂θ(j)/∂P)e ) const.kd(j)ka(j) κ-j-2 (2) or (j)

(j)

(j) 2

κj/κ-j ) const.(ka /kd )(1 - θe )

(3)

κj and κ-j are the partial derivatives of the sorption rate by the variables of pressure and adsorbed amount; thus, κ-j is the time constant of the sorption process which can be determined from the position of resonance signal j on the out-of-phase FR curve. κj/κ-j is proportional to the slope of the adsorption isotherm at Pe and gives the intensity of peak j. Usually the adsorption isotherms of ammonia on zeolites do not follow the Langmuir isotherm quantitatively.24 However, it gives a more accurate description of the adsorption over a definite kind of sorption site, e.g., over site j. A recent FR study15 verified the validity of the Langmuir model for the NH3/H-ZSM-5 zeolite system. It was shown that the relationship between κ-j and Pe is linear (eq 1) and that the slope of the linear ln κj/κ-j vs ln κ-j plot is -2 (eq 2). Equation 1 points out that the κ-j frequency of the out-of-phase peak decreases and tends to approach kd(j) if the pressure and, correspondingly, the coverage are decreased. Also, κj/κ-j increases until a constant value, proportional to the slope of the isotherm in the Henry region, ka(j)/kd(j), is reached for the j resonance. In contrast, if pressure is increased the intensity decreases, and at saturation (θe(j) ) 1) the signal completely vanishes (see eqs 2 and 3). Owing to the difficulty of measuring small, for example (1%, changes of very low pressures accurately, the FR experiments are usually carried out at pressures where the coverage of the sorption sites is far from the Henry region. As a result the resonance appears at a frequency (κ-j) higher than the corresponding rate constant of desorption (kd(j)). At a given pressure the fractional NH3 coverage of the sites of different acid strength must be different; thus, the shift of κ-j from kd(j) toward the higher frequencies is more pronounced for the stronger acid sites since these sites are more fully covered. A large difference in the fractional coverage can thus cause a situation in which resonance signals of sorption processes on sites of different acidity overlap and may remain unresolved by any curve-fitting procedure. However, if coverage is decreased, under isothermal conditions, κ-j approaches (24) Barrer, R. M.; Gibbons, R. M. Trans. Faraday Soc. 1963, 59, 2569; 2875.

kd(j), and the peaks, that could not be distinguished at higher coverage can be separated and exhibit increased intensity. If Pe is kept constant but the temperature, T, is varied, kd(j) and ka(j) change simultaneously but in opposite directions. At each higher T a new equilibrium is established at a lower coverage. Since Ed(j) exceeds Ea(j) with the heat of adsorption (Qa) due to the increase of kd(j), the resonance signal j shifts to higher frequencies as temperature is increased. The simultaneous decrease of coverage acts in the opposite way (see eq 1). A significant upward shift of the NH3 signal was observed for the sorption of NH3 over Na-A if the temperature was raised from 373 to 723 K (Figure 3A, B). In contrast, a similar temperature change had hardly any effect on the positions of the FR peaks of the NH3/H-Y system. The ratio ka(j)/kd(j) obtained from the Langmuir isotherm equation was inserted into eq 2. If isobar conditions are maintained, Pe can be included in the constant, and we obtain

κj/κ-j ) const.′θe(j)(1 - θe(j))

(4)

where θe(j) ) f(T). Obviously, the κj/κ-j vs θe(j) function passes through a maximum at θe(j) ) 0.5. The effect of increasing temperature on ∑κj/κ-j as shown in Figure 5 must be interpreted with this in mind. As the coverage of sites j is decreased toward θe(j) ) 0.5, the intensity of the FR signal becomes more intense. If θe(j) decreases below 0.5, the intensity drops. In our opinion the sorption on the acid sites proceeds essentially according to the following sorption equilibria: (i) NH3 + H+ h NH4+, and (ii) NH4+ + NH3 h NH3H+-NH3. The temperature and the pressure of the measurement determine the degree of participation of these two processes in the gross sorption process. Under 133 Pa of NH3 pressure, equilibrium i is shifted to the right up to about 500-600 K; i.e., the acid sites are virtually saturated. No or only a weak FR signal of process i can be detected. The NH4+ ions are weak Lewis acid sites, which can bind NH3 according to equilibrium ii. The resonance at about 10 Hz is assigned to the faster sorption processes of equilibrium ii. If the temperature is increased above about 400 K, the intensity of the 10-Hz signal decreases, suggesting that the coverage of the NH4+ ion sorption center was 0.5 or lower. If the temperature is raised further, the intensity of some peaks at lower frequency starts to increase (see Figure 4). This can happen if the coverage of some strong acidic sorption sites decreases below saturation; e.g., equilibrium i is shifted somewhat to the left. At a temperature where the gained intensity exceeds the intensity loss of the high-frequency peak, the total FR intensity starts to increase (see Figure 5). It follows from eq 3 that the intensity of resonance j begins to decrease if the coverage of sites j drops below 0.5. Referring to the above discussion, we assign the signals losing intensity at lower temperatures to sorption of NH3 on the weak Lewis acid sites and those growing in the range of 600-800 K to direct NH3-Bro¨nsted acid interaction (see Figure 5). The maximum on the ∑κj/κ-j vs T plots gives the temperature (Tmax) where about half of the Bro¨nsted acid sites are covered. By correlating this temperature and the average acid strength of the sites, the order of increasing acidity can be given as H-M g H-ZSM-5 > H-Y. In the case of the Na-mordenite, ∑κj/κ-j monotonically decreases in the temperature range examined. The

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Table 2. Transport Diffusivity of NH3 in the Micropores (Dµ,) and Macropores (DM) of Zeolitic Adsorbentsa sample 4Ab K-Ac 13Xb

Dµ, m2 s-1 10-13

1.6 × 3.6 × 10-14 (4.5 × 10-13)d

DM, m2 s-1 5.6 × 10-8 4.8 × 10-8

a

Samples were evacuated at 623 K for 1 h, cooled to 373 K, and equilibrated with NH3 at 133 Pa pressure, and the FR spectra were recorded. b The measurement was carried out with 0.25-0.5-mm diameter beads manufactured from Na-zeolite by Lancaster Synthesis, U.K. c Ion-exchanged Na-A powder. The Na-A was the product of Hungalu, Ajka, Hungary. The average crystallite size was 1.2 µm. d Measured at 723 K.

coverage of the weak Lewis acid Na+ ions even at the lowest temperature of 373 K must have been below 0.5. The curves in Figure 5 have some similarities to the results of conventional temperature-programmed desorption (TPD) measurements. However, some distinct differences have to be indicated. At all temperatures, the FR data are obtained at the same NH3 pressure and the systems are always in adsorption quasi-equilibrium. An advantage of the FR-TPD is that the profile of the FR spectra directly indicates if rate-controlling diffusion resistance, heterogeneity, or bed effects are involved. If rate constants and activation energies of desorption can be determined for the parallel sorption processes, these parameters are suggested to be used to characterize acidity instead of κ-j or Tmax. 4.2. Diffusion. Coefficients of transport diffusivities of ammonia determined by the FR method are given in Table 2. The FR results suggested that the macro- and micropore diffusions in the pore system of the 4A beads have similar time constants (D/r2). In such special case the coefficients of both transports can be obtained from the FR model of coupled diffusions. For the 13X beads the rate-controlling process step was the diffusion in the macropores and only DM could be calculated. The DM values are quite the same for the 4A and the 13X samples as shown in Table 2. Conceivably, pellets of similar texture were formed from crystallites of the two zeolites, which are about the same size (1-3 µm). The macropore diffusivity is about 1 order of magnitude lower than the Knudsen diffusivity calculated for cylindrical pores of 2-nm diameter. However, if calculation accounts for the random pore network, lower diffusivities are obtained that are in harmony with those measured.25 For both Na-zeolites the micropore diffusion was rapid relative to sorption rates, thus, it was not possible to determine Dµ when the diffusion resistance of the macropores were eliminated. Although the value of (25) Onyestya´k, Gy.; Shen, D.; Rees, L. V. C. J. Chem. Soc., Faraday Trans. 1995, 91, 1399.

transport Dµ was not obtained, the undisturbed macropore diffusion in the pellets suggests that Dµ must be much higher for 13X than for 4A. This is not surprising when the channel sizes of the zeolites are considered. The selfdiffusivity of NH3 within Na-X crystallites as determined by the pulsed field gradient NMR method2 was about 10-11-10-10 m2 s-1 at 293 K, i.e., much higher than the Dµ we obtained for 4A (Na-A) by the FR method. In contrast with that in Na-A, the diffusion in the zeolitic micropores controlled the rate of NH3 transport in the K-A. The movement of NH3 is generally constrained in the narrower pores of the potassium form zeolite. However, energetic factors may also be involved. The K+ ions are weaker Lewis acid sites than the Na+ ions. It is conceivable that because of the lower heat of ammonia adsorption (Qa) and activation energy of desorption (Ed) the rate constant (kd) is higher. If the coverage is the same, the sorption time constant (κ-j) is also higher (see eq 1). The micropore diffusion in K-A is the rate-limiting step since the sorption rates are more rapid in K-A than in Na-A. Earlier NH3-TPD studies on H-ZSM-5 zeolites suggested that, depending on the properties of the sample, either the diffusion or desorption rate can control the rate of NH3 release. The energetic factor, namely, the differences in the strength of NH3-acid site interaction, was mentioned to explain the findings.9,10 However, since the particle size of the samples were not examined and compared, it seems dubious that the different ratecontrolling mechanisms can be attributed simply to different sample acidities. 5. Conclusions Any one of the steps of the consecutive diffusion and adsorption processes can control the rate of NH3 transport in zeolites depending on the structure of the sample and on the conditions of the measurement. Owing to textural heterogeneity of a sample, one or more kinds of processes with numerous different time constants can give resonance with modulation frequencies that result in spectra of minor scientific value. The rate spectra reflecting purely the sorption processes of NH3 can be used to characterize zeolite acidity. However, the relationship between FR property and acidity is not fully understood yet. The seemingly simple FR results can only be interpreted fully when a more complete understanding of the underlying processes and the nature of the technique is achieved. Acknowledgment. The financial support provided by the Royal Society CEE Project Grant, the Hungarian Academy of Sciences, and the National Science Foundation of Hungary (Grant No. T16761) is gratefully acknowledged. LA990867E