Frequency Response Study of Adsorbate Mobilities of Different

J. Phys. Chem. B 1999, 103, 7469-7479

7469

Frequency Response Study of Adsorbate Mobilities of Different Character in Various Commercial Adsorbents Gyo1 rgy Onyestya´ k† and Lovat V. C. Rees*,‡ Institute of Chemistry, Chemical Research Center, Hungarian Academy of Sciences, P.O. Box 17, H-1525 Budapest, Hungary, and Department of Chemistry, UniVersity of Edinburgh, West Mains Road, Edinburgh EH9 3JJ, United Kingdom ReceiVed: February 23, 1999; In Final Form: May 27, 1999

The sorption of strong basic ammonia, acidic carbon dioxide, and apolar propane in different commercial adsorbents: activated alumina, charcoal, and silica gel porous particles and 4A, 5A, and 13X zeolite pellets has been investigated using the frequency response (FR) method. Despite differences in the sorption and diffusion processes of the sorbates in 4A, 5A, and 13X zeolite crystals, in the pelletized samples, intercrystalline diffusion was found to be the rate-controlling process with macropore diffusivities being the same within 1 order of magnitude for NH3 or CO2. The mass transport rates of the apolar propane seemed to be more sensitive to differences in the meso- and macropore size distributions of the zeolitic pellets. The micropore adsorption capacity played a significant role in the uptakes controlled by macropore diffusion. For ammonia and carbon dioxide, sorption proved to be the rate-determining process inside the zeolite crystals, but for propane, intracrystalline diffusion was rate controlling. Micropore diffusivities were determined in both 5A crystals and pellets, and good agreement was obtained. Carbon dioxide intercrystalline diffusivities were determined from the pellet responses, and the same rates were obtained for all three zeolite pellets. Micropore diffusion was 1 order of magnitude faster in 5A (Ca-form) compared with zeolites 4A and 13X (Na-form), which indicates the strong influence of cations. The other adsorbents show more varied sorption behaviors. Interesting findings are the bimodal intracrystalline diffusion rate spectra of ammonia, carbon dioxide, and propane in charcoal. An outstanding advantage of the FR method is its ability to study diffusion in anisotropic systems. The usefulness of the FR technique for dynamical characterization of various adsorbents has been demonstrated.

1. Introduction Commercial adsorbents and heterogeneous catalyst supports which exhibit ultraporosity and which are frequently used for the separation of gas and vapor mixtures or for heterogeneous chemical processes include activated alumina, activated carbons, inorganic gels such as silica gel, and crystalline microporous materials among which the most well-known are zeolites. Activated alumina, activated carbons, and silica gel do not possess uniform pore structures of molecular size. The distribution of the pore diameters within these adsorbent particles may be narrow (5-50 Å) or wide (5 to several thousand Å), depending on the preparation. The pore size distribution of zeolites or zeotypes is quite different having pores of uniform and narrow size (generally less than 20 Å) determined uniquely by the structure of the crystal. However commercial zeolite crystals are quite small, and to prepare a practically useful adsorbent or catalyst, these crystals must be formed into macroporous pellets of suitable dimensions, porosity, and mechanical strength. Generally, a clay mineral is added as a binder to achieve satisfactory physical strength. Such composite pellets offer mainly two diffusional resistances to mass transfer: micropore diffusional resistance in the individual zeolite crystals and macropore diffusional resistance in the pellet. So * Corresponding author. Fax: (44-131)-650 6472. E-mail: Lovat.Rees@ ed.ac.uk. † Hungarian Academy of Sciences. ‡ University of Edinburgh.

the zeolite adsorbents or catalysts used in industrial applications have also a wide pore size distribution. All of the sorbents mentioned above play important roles in various technologies depending on the separation problem and the composition of the mixtures involved. The first step in the development of an adsorption separation process is to determine the most suitable adsorbent having the best separation factor and with a high adsorption capacity. However, the dynamical behavior of the adsorbate-adsorbent system is also of great significance. Transient methods are generally used to study the dynamics of physical and chemical systems applying, for example, step, pulse, or harmonic perturbations. The last method follows the change in amplitude and phase produced in a dynamic system when a small periodical perturbation is carried out around its equilibrium point. The resulting amplitude changes, and phase shifts are related to the dynamics of the processes controlling the return of the system to the equilibrium. Analogously to resonances observed in various spectroscopic methods, “rate spectra” which are characteristic of the gas/surface dynamics are obtained. The added experimental complexity of this frequency response method is balanced by its ability to trace and distinguish directly the rates of several concurrent kinetic processes operating inside a complex system. Two reviews1,2 summarize early frequency response studies of all processes occurring in adsorption and heterogeneous catalytic systems. The frequency response technique has been

10.1021/jp990662e CCC: $18.00 © 1999 American Chemical Society Published on Web 08/18/1999

7470 J. Phys. Chem. B, Vol. 103, No. 35, 1999 shown to be a most powerful method for determining intracrystalline diffusivities in well-shaped zeolite crystals. Diffusion coefficients in the micropores of different zeolite/adsorbate systems obtained by the FR technique have been found to agree closely with PFG NMR results.3,4 Various models have been developed to interpret experimental data. In 1993, Jordi and Do5 reported models and analysis of the frequency response method to describe the sorption kinetics in bidispersed structured sorbents. In these models, macropore and micropore diffusion and film and surface barrier resistances coupled with adsorption were considered, i.e., all the processes that influence the responses in a bidisperse structured porous solid under isothermal adsorption conditions. CO2 diffusion in commercial zeolite 5A powder and pellets has been systematically investigated by the frequency response technique.6 Assignment of different peaks in the spectra was made, and pure CO2 macropore diffusivity was determined in pressed and commercial 5A pellets between 75 and 125 °C. Under the same experimental conditions, the mass transport in commercial 13X pellets from different manufacturers was compared and found to be well characterizable when CO2 was the sorbate.7 The same set of 13X particles was also found to be characterizable using isobutane macropore diffusion at 75125 °C.7 The intercrystalline diffusion of ammonia was found to be the rate-controlling process in pellets formed by pressing strongly acidic H-mordenite samples and found to be independent of the conditions in the 100-450 °C temperature range.8 Dynamical sorption characterization was carried out using CO2 as the sorbate in mined zeolitic rocks from various locations.9 The experimental data were interpreted using the new models developed for bidispersed pellets.5,10 Intraparticle diffusivities in the Knudsen regime were measured for N2, Xe, Xe/N2 mixtures, and isobutane in mesoporous silica particles.11 Although the theoretical solutions of the frequency response technique have been comprehensively developed in the past decade for microporous systems1 and for bidispersed porous systems5,10 and the potential of the FR technique for investigation of sorption dynamics in practically useful sorbent pellets has been demonstrated, only a few experimental studies have been reported. Although the technique is not very complicated, only a few laboratories have frequency response equipment. The other major difficulty in the application of this method is that the rate spectra are not always unique and there are generally several combination of parameters which could yield virtually the same amplitude ratio/frequency or phase lag/frequency relationships. The only way to cope with this difficulty is to study systems over a range of reasonable or possible parameter values, e.g., variation of particle size or temperature. The aim of this work is to extend previous studies to gain a more general knowledge and to show the wide complexity of the results offered by the flexibility of the frequency response technique in the field of macro- and mesopore diffusivities with adsorbates of different character in various adsorbents. Ammonia, carbon-dioxide and propane are used as basic, acidic, and neutral probe molecules in various kinds of industrial porous adsorbent pellets, e.g., activated alumina, activated charcoal, silica gel, and commercial zeolite beads 4A, 5A, and 13X. 2. Theory Frequency response parameters (phase lag and amplitude) are derived from equivalent fundamental sine wave perturbations by a Fourier transformation of volume and pressure square

Onyestya´k and Rees waves. The phase lag φZ-B ) φZ - φB, where φZ and φB are the phase angles determined in the presence and absence of sorbent, respectively. The amplitude ratio PB/PZ is determined, where PB and PZ are the pressure responses to the (1% volume perturbations in the absence and presence of sorbent, respectively. The experimental FR data, the “FR spectra” of a system, are described by the in-phase (real) and out-of-phase (imaginary) components, respectively1:

in-phase (PB/PZ) cos φ Z-B - 1 ) Kδin

(1)

out-of-phase (PB/PZ) sin φ Z-B ) Kδout

(2)

where δin and δout are the overall in-phase and out-of-phase characteristic functions, which are of the form for sorption kinetics in bidispersed structured sorbents,5

(

δin ) ∆sMReal σ1 +

(

)

( )

)

( )

σ2 σ2 ∆ - ∆sMImag ∆ 1 + λ sµReal 1 + λ sµImag (3)

δout ) ∆sMImag σ1 +

σ2 σ2 ∆ + ∆sMReal ∆ 1 + λ sµReal 1 + λ sµImag (4)

where ∆sMReal and ∆sMImag are the macroparticle in-phase and out-of-phase characteristic functions for macroparticle shape factor sM; ∆sµReal and ∆sµImag are the microparticle in-phase and out-of-phase characteristic functions for microparticle shape factor sµ. The parameter σ1 is the fractional adsorption capacity in the macropore void, and σ2 is the fractional adsorption capacity in the microparticles; they are taken as 0.01 and 0.99, respectively, which are reasonable estimates for most industrial pellets. The parameter λ is a measure of the approach to saturation of the Langmuir isotherm and is defined by

λ)

ka C kd Be

(5)

where CBe is a bulk sorbate concentration under equilibrium conditions and ka and kd are the rate constants for adsorption and desorption. The value K(σ1 + (σ2/1 + λ)) is directly proportional to the gradient of the equilibrium isotherm; therefore, the intensity of the frequency response spectrum is proportional to the gradient of the adsorption isotherm at equilibrium. The associated dynamic parameters of the FR spectra could be determined by fitting the characteristic functions generated by an appropriate theoretical model describing the frequency response of the batch system to the spectra.5 Two different in-phase and out-of-phase characteristic functions for spherical macroparticle and microparticle geometry among models developed by Jordi and Do5 are used in this study to fit the experimental response data in pellets (model 1 and 2). The following assumptions in the analysis are considered: the system is isothermal; the diffusional processes are time and position invariant; the adsorption at the pore mouth of the micropore follows Langmuirian kinetics with constant rate constants; adsorption on the microparticle exterior surface is negligible; only one adsorbable component is present; each sorbent particle is exposed to the same bulk-phase environment; sorbent particles are identical to one another. The last two assumptions reduce the sorption mass balance equations to

Frequency Response Study of Adsorbate Mobilities

J. Phys. Chem. B, Vol. 103, No. 35, 1999 7471

single-particle analysis. In this study the following three mass transfer processes are considered in the analysis: macropore diffusion through the large pores; adsorption at pore mouth of the microparticle; activated diffusion in the micropores. Negligible film mass transfer resistance was assumed. Model 1: Macropore-Micropore Diffusion. Macropore Characteristic Functions.

γ)

δ3R )

(

3

xr{cosh[2xr cos(θ/2)] - cos[2xr sin(θ/2)]}

-

)

cos θ (6) r δ3I )

(

cos(θ/2) sin[2xr sin(θ/2)] + sin(θ/2) sin[2xr cos(θ/2)]

xr{cosh[2xr cos(θ/2)] - cos[2xr sin(θ/2)]}

-

)

sin θ (7) r

where

ηM ) r exp(iθ) ηM )

2 1 DµR σ1 R 2D µ

cos(θ/2) sinh[2xr cos(2θ/2)] - sin(θ/2) sin[2xr sin(θ/2)]

3

The parameter Dp is the macropore diffusivity, r is the radial coordinate in microparticle, R is the radius of the pellet, and ω is the angular frequency. The parameter γ is the ratio of the micropore to the macropore diffusion rates, which is defined by

3σ2γ{ηµ[sinh ηµ + sin ηµ] - 2} 2(1 + λ){cosh ηµ - cosηµ}

(8) + + iωR /Dp (9) 2

2(1 + λ){cosh ηµ - cos ηµ} and

x( ) 2ωRµ2 Dµ

(10)

Microparticle Characteristic Functions.

3[sinh ηµ - sin ηµ]

δ3R ) δ3I )

(11)

ηµ[cosh ηµ - cos ηµ]

3[sinh ηµ + sin ηµ] ηµ[cosh ηµ - cos ηµ]

-

6 ηµ2

(12)

Model 2: Macropore Diffusion and Adsorption. Macropore Characteristic Functions. As for model 1, with ηM given by

ηM )

ωR2σ2ηµ Dp(1 + λ)(1 +

ηµ2)

[

+ iω σ1 +

σ2

]

(1 + λ)(1 + ηµ2)

(13) ηµ )

ωRµ2 3BDµ

(14)

Micropore Characteristic Functions.

δ3R ) δ3I )

1 (1 + ηµ2) ηµ (1 + ηµ2)

where Dµ is intracrystalline diffusivity and Rµ is the radius of the zeolite crystals. The parameter B is the ratio of the adsorption rate to the micropore diffusion rate. When B is large, equilibrium at the pore openings of the micropores is rapidly attained.

B ) kaCBeCµsRµ/CµeDµ

(18)

where Cµe is the sorbate concentration in the microparticle in equilibrium with CBe, and Cµs is the sorbate concentration in the microparticle at saturation. Rate spectra controlled by processes taking place inside the micropores were fitted by Yasuda’s well-known models for sorption on different sites,12 diffusion in micropores associated with surface barrier,13 and two independent intracrystalline diffusion processes. 3. Experimental Section

i3σ2γηµ[sinh ηµ - sin ηµ]

ηµ )

(17)

p

(15)

(16)

The frequency response apparatus working with square wave perturbations has been described previously. 15,16 The frequency window used in this study was 0.01-10 Hz. Samples were dispersed in a glass-wool plug in a sorption chamber of 3 cm diameter and outgassed at 300 °C for 1 h before carrying out the perturbation measurements. The sorbates were admitted to pretreated samples and allowed to come to adsorption equilibrium in a pressure range of 1-6 Torr at 100 °C or lower temperatures only in two runs with CO2. Measurements were carried out in the presence and absence of sorbent samples to eliminate any influence of the apparatus. In some experiments, quantities of sorbent as large as 5000 mg were used. To obtain the correct blank response for such systems, inert glass beads of volume equal to that of the sample were added to the sorption chamber to bring the blank free gas volume equal to that of the experimental system. The sorbate CO2 of 99.998% purity and ammonia of 99.96% purity were from ARGO International, and propane of 99.95% purity from Linde Gas UK. The frequency response method was used for studying the “rate spectra” of NH3, CO2, and C3H8 in commercial (Lancaster Synthesis, United Kingdom) zeolite 4A, 5A and 13X powders and spherical pellets. The charge of different anionic lattices (4A ) LTA and 13X ) X, FAU) was compensated with the same cation, sodium, while 4A and 5A have the same zeolite structure (LTA) containing Na+ (4A) or Ca2+ (5A) ions. So 5A or 13X has wider pores compared to 4A. The beads of 0.40.8 mm in diameter were sieved into narrower, 0.71-0.50 and 0.50-0.25 mm, particle fractions. For comparison, laboratorysynthesized Ca-A and Ca-ZK-4 crystals were also investigated. Scanning electron micrographs of these powders showed that the laboratory synthesized Ca-A sample contained nearly uniform cubic crystals and some intergrown crystals, while the commercial 4A, 5A, and 13X powders consist of aggregates and intergrown agglomerates of crystals. The dimensions of the crystals used are given in Table 1.

7472 J. Phys. Chem. B, Vol. 103, No. 35, 1999

Onyestya´k and Rees

TABLE 1: Powder Samples Used in This Study sample

label

diameter/µm

commercial lancaster 4A laboratory-synthesized Ca-A laboratory-synthesized Ca-ZK-4 commercial Lancaster 5A commercial Lancaster 13X

4A Ca-A Ca-ZK-4 5A 13X

2.6 6 3 2.8 1.2

TABLE 2: Mercury Porosimetric Data of Lancaster Zeolite Beads samples

total cum. vol cm3 g-1

spec. surf. area m2 g-1

avg. pore radius nm

4A 5A 13X

0.26 0.27 0.39

14.8 10.8 17.9

199 79 99

The pore distributions of the zeolitic beads were investigated by mercury porosimetry; the parameters are summarized in Table 2. The mercury porosimeter (Micrometrics) operated in the 1 to 2000 bar pressure range. Thus, the distribution of the pore volume was calculated as a function of the pore radius in the 3-10000 nm range. After recording volume versus pressure curves, cumulative pore distributions (see Figure 4) were calculated using the cylindrical model, and on the basis of these pore size distributions, the specific surface areas and average pore radii were also determined. Three other commercial adsorbents: activated alumina (Edwards, U.K.) of 3-5 mm in diameter; charcoal, granular activated for gas adsorption (BDH, U.K.) of 0.85-1.7 mm; silica gel (Fisons, U.K.) of 1-3 mm diameter were also studied. These big particles were ground and sieved into narrow size fractions of 1.00-0.71, 0.71-0.50, 0.50-0.25, and 0.25-0.15 mm. The charcoal sample was studied by the small-angle X-ray scattering (SAXS) technique.17,18 A classical Kratky camera with slit geometry and a proportional counter (Anton Paar, Graz, Austria) were used. Data were evaluated by the method based on the moments of the scattering intensity function. 4. Results and Discussions The frequency response method is sensitive to interparticle mass transfer resistances, which arise even when a small bed depth of sorbent is involved. When zeolite particles, crystals, or pellets are well dispersed in a plug of glass wool, these effects are eliminated and correct intracrystalline or intercrystalline diffusivities are obtained by the FR method.6 If macroporous pellets are formed from zeolite crystals, intercrystalline mass transfer is found to be rate controlling. 4.1. Sorbent Interactions with Propane. Propane is a symmetric, apolar, neutral, highly resistant hydrocarbon having zero dipole moment and a kinetic diameter of 4.3 Å. Figure 1 demonstrates the different frequency response characteristic functions for propane sorption in well-separated, different zeolite crystallites (R, β, γ), in pelletized beads (R ) 0.30 mm) (a, b, c), and in beds built up from ∼15 layers of these beads (A, B, C). In Na-A, i.e., zeolite 4A, Na+ cations are located in each eight-membered framework oxygen ring which partially block the entrances to the supercages. Propane is too large to penetrate these windows, so no response can be observed with this sorbent (Figure 1,R). The situation is the same with beads manufactured from crystals of this zeolite (Figure 1a). However, a response can be detected if the sample mass is increased from 200 to 5000 mg to form a bed of approximately 15 layers of 4A beads. The macropore network is available for propane in 4A pellets, but this hydrocarbon can adsorb only on the outer surface of the crystals and/or binder material, so the sorption capacity is

Figure 1. Frequency response data points for the in-phase (0) and out-of-phase (O) characteristic functions for propane adsorption/ desorption in ca. 100 mg 4A (R), 5A (β), and 13X (γ) zeolite powder; ca. 200 mg 4A (a), 5A (b), and 13X (c) zeolite beads (R ) 0.30 mm), and in ca. 5000 mg 4A (A), 5A (B), and 13X (C) beds of zeolite beads at 100 °C under 4 Torr propane. The continuous lines are the fits of the characteristic functions.

very small (Figure 1A). The resonance frequency in beds of 4A beads is much higher than in beds of 5A and 13X pellets (Figure 1B,C), indicating a faster mass transport with 4A. This difference can be due to the different pore size distribution in the various zeolite pellets and to different sorption mechanisms in these three samples. Propane can adsorb in the micropores of 5A and 13X. In (Ca,Na)-A (i.e., 5A), the eight-ring apertures are free of cation, and propane molecules can now pass through the eight-ring apertures, resulting in intracrystalline diffusion (see Figure 1,β) when the crystals are well-separated. In 13X zeolite, the apertures of the channel system are much wider and micropore diffusion is faster by more than 2 orders of magnitude, as indicated by the response curves appearing at high frequencies outside the experimental frequency window (Figure 1γ). The intracrystalline diffusivities can be determined therefore only in the three-dimensional channel system of 5A. Larger crystals of zeolite 13X are required to bring the response curves into the frequency window available. The fits with Yasuda’s isothermal single diffusion model13 are not perfect; the out-of phase data points give somewhat wider peaks than the theoretical curves. However, as a bimodal response behavior is improbable and heat of sorption effects can be eliminated by choosing appropriate experimental conditions established previously [see refs 3 and 4] (higher temperatures produce small or zero heat effects). The wider peaks can be explained by the nonuniformity of 5A crystallites and some aggregation and/or intergrowths of the crystals. The frequency response spectra of 5A and 13X zeolite crystallites when compacted into beads show a great change compared with the intracrystalline diffusion spectra of the separated zeolite crystals. The resonance positions appear at lower, similar frequencies, although the intracrystalline diffusivities are quite different. 13X beads give a pure, regular, perfect macropore diffusion spectra (Figure 1c). The characteristic response functions of 5A intersect near the top of the out-of-phase response signal (Figure 1b), demonstrating a more complicated resistance to propane penetration. The response spectra of propane in the pellets is mainly associated with intercrystalline diffusion processes since (i) if micropore diffusion is the rate-controlling step in the pellet, the response will be the same as those obtained in the case of separated crystals,



Figure 2. Macropore diffusion time constant versus square particle radius as obtained from model 1 of commercial 5A (0) and from model 2 of 13X (O) beads at 100 °C and 2 Torr propane.

(ii) if the uptake is controlled by both micropore and macropore diffusion, the response curves will appear at some lower frequency than that found for micropore diffusion and the inphase characteristic function curve will intersect the out-of-phase characteristic function curve where the intersected area is influenced by the shorter but comparable micropore diffusion time constant as found for propane in 5A beads, (iii) the positions of the response curves move to lower frequencies with increasing pellet sizes and the macropore diffusion coefficients determined by the macropore diffusion model are independent of pellet dimensions as can be seen in Figure 2. This latter type of observation was found for most adsorbate-zeolite systems studied. A similar linear relationship between the square of bead size and intercrystalline diffusion time constant were also obtained with other adsorbates such as ammonia and carbon dioxide. The experimental data points could be fitted, quite accurately, using three different models. These models are (a) macropore diffusion with a film resistance, (b) micro- and macropore diffusion, and (c) macropore diffusion with a surface barrier resistance. Macropore diffusion with a film resistance can be eliminated because film resistances are not likely when pure zeolites and single sorbates are involved. Model (b) involving micropore and macropore diffusion is the most likely explanation for the kinetics of propane sorption in 5A (see model 1 in the theoretical section). However, micro- and macropore dif-

fusion can be ruled out for propane diffusion in 13X pellets because the intracrystalline diffusion coefficient obtained from the fit is about 3 orders of magnitude smaller than the value estimated for the pure crystals. Therefore, the response spectrum of propane in the 13X pellets is most likely to be associated with pure macropore diffusion. Bed effect seems to be negligible in these systems (see Figure 1, parts b and B). The change of signal intensities is proportional to mass (Figure 1, cf parts b,B and c,C), but the resonance frequencies are unaffected. Difference can be observed in the shape of the 13X zeolite bead and bed spectrum (Figure 1, parts c and C). The appearance of an intersection in Figure 1C near the top of out-of-phase signal indicates a more complex sorption behavior, due to a complicated combination of intercrystalline and interparticle diffusion. In these deep bed configurations, the response is influenced by the concentration distribution in the bed among the bead particles. The sorbent particles are not exposed to the same bulk-phase environment, and the Jordi-Do model for the sorption of gases onto bidispersed structured sorbent in a batch system5 is inapplicable. Investigations of flow systems are more convenient and useful for deep bed situations, as shown by early attempts to study axial interparticle and intraparticle diffusion effects.19,20 The intracrystalline propane transport diffusivities determined by the FR method in Lancaster 5A crystallites and beads can be compared in Table 3. The intracrystalline transport rates determined in beads are approximately half of the values measured in the separated crystals (compare Dµ values from model 1 and Yasuda model). However, the response curves determined for beads (see Figure 1b) are not fully developed in the frequency window used. Lower frequencies are required. However, comparison of the K values for both systems indicates that the surface of the crystals must be partly covered by binder material which may decrease the mass transport of the crystals in the beads compared to that in the separated crystals. The increasing diffusivities (Dµ) of propane with increasing equilibrium pressure in the 5A crystals at 100 °C (as shown in Table 3) was also observed in early PFG NMR studies.21 Although such a comparison of diffusivities is not strictly justified, because of the different experimental conditions, the results do indicate that the diffusivity of propane does increase with increasing loading in 5A zeolite. A linear relationship between the square of the pellet size and the macropore diffusion time constant was found which proves that the propane uptakes are controlled by intercrystalline diffusion in the beads. The position of the resonance peaks in

TABLE 3: Propane Diffusivities Determined in Lancaster 5A and 13X Beads Jordi-Do model 15

5A

13X

a

t °C

Pe Torr

100 100 100 125 150 175 100 100 100 100 125 150 175

2 4 6 6 6 6 1 2 4 6 6 6 6

10-7

Yasuda1,13 a 10-13

K

γ

DP m2 s-1

Dµ m2 s-1

Dµ m2 s-1

0.83 0.79 0.74 0.38 0.20 0.12

3 3 3 3 3 3

0.95 1.03 1.03 1.72 2.41 3.28

1.6 1.7 2.2 2.8 3.9 5.3

3.3 3.9 4.4

pure macropore diffusion w

Pure intracrystalline diffusion determined in separated crystals of the 5A powder.

Jordi-Do model 25

10-13 K

B

DP 10-7 m2 s-1

0.85 0.81 0.76 0.40 0.21 0.13 0.60 0.58 0.56 0.55 0.30 0.17 0.10

60 60 60 60 60 60 ∞ ∞ ∞ ∞ ∞ ∞ ∞

0.24 0.26 0.26 0.45 0.69 0.80 4.29 4.29 4.29 4.29 7.20 12.6 16.4



Figure 3. Arrhenius plots of propane macrodiffusivities under an equilibrium pressure of 6 Torr in Lancaster 5A as obtained from model 1 and in 13X beads from model 2 (A) and microdiffusivities in the graphite microcrystallites of charcoal granules (B).

the 5A and 13X beads do not change significantly with the propane equilibrium pressure in the range of 1-8 Torr (see DP values in Table 3 for both models 1 and 2); that is, intercrystalline diffusion in the zeolite beads in the meso/macropore range is independent of pressure, which is contrary to the effect of increasing pressure on the micropore diffusion of propane in 5A as shown above. The macropore diffusivities determined are in the Knudsen diffusion regime where Dp is independent of pressure. The temperature dependencies of propane intercrystalline diffusivities in Lancaster 5A and 13X beads are shown in Figure 3A, from which the activation energies for diffusion can be calculated. The macropore diffusivity in 13X beads is 4 times faster than the corresponding diffusivity in 5A beads. Although the diffusivities in the beads are different, the activation energies were found to be very similar: 21.2 kJ/mol in 5A and 25.5 kJ/mol in 13X beads. Thus, the macropore channel systems must be quite similar, which is not surprising since Lancaster 4A, 5A, and 13X zeolite beads are pelletized in the same plant, with the same binder and technology. Although the pore size distribution of these pellets is similar, as shown in Figure 4, some important quantitative differences can be observed in Table 2. The average pore radius is the smallest in the 5A beads where the slowest macropore diffusivities were found. Since negligible bed effect was observed in 5A and 13X beads/propane systems when large adsorbent masses were used (Figure 1, compare parts b and B and c and C), the weak response found in Figure 1A for a large mass of 4A beads can be assigned to intercrystalline diffusion. The macropore diffusivity of 5 × 10-6 m2 s-1 estimated for 4A beads is the highest among the Lancaster zeolite beads and is consistent with the largest average macropore radius of 199 nm for this sample. As this pore radius is outside the upper limit of the Knudsen diffusion range, this diffusivity is high enough to be ascribed to molecular diffusion. The apolar propane molecule seems, therefore, to be a sensitive probe to study meso- and macropore size distribution differences in commercial zeolitic pellets. In Figure 5, the characteristic curves obtained with propane for various other adsorbents are presented. Alumina and silica are sorbents containing surface charges. The interactions with the apolar propane as sorbate are weak, which results in weak

Figure 4. Relative meso- and macropore volume against pore radius curves of (A) Lancaster 4A, (B) 5A, and (C) 13X commercial beads determined by mercury porosimetry.

response signals. As their surface areas are smaller than those in zeolites, the responses are hardly detectable even when sample masses as large as ∼1000 mg are used. The shape of the spectra is characteristic of macropore diffusion, and a linear relationship between the square of pellet size and the macropore diffusion time constant was observed in agreement with Jordi and Do’s macropore diffusion and adsorption model. The rate of mass transfer in the silica pellets is similar to that found in zeolite pellets, but in alumina, the rate of mass transfer is much faster



Figure 7. Maxwellian distribution of Gunier radius for charcoal in the higher region of the scattering variable.

Figure 5. Comparison of the propane spectra of ca. 1000 mg alumina (a), 200 mg charcoal (b), and 1000 mg silica (c); particles (R ) 0.43 mm) dispersed in glass/wool plug and the same adsorbents in beds of ∼5000 mg labeled with the corresponding capital letters (A, B, C, respectively).

Figure 6. Comparison of response spectra for charcoal with propane (A) (1 Torr, ∼200 mg, R ) 0.30 mm); ammonia (B) (1 Torr, ∼1000 mg, R ) 0.30 mm), and carbon dioxide (C) (2 Torr, ∼1000 mg, R ) 0.19 mm) as the sorbate.

since resonances appears at high frequencies. The mass exchange between the gas and solid phase is small, and the concentration gradients in the bed are thus minute, so the effect of bed depth is not detectable even when the sample size is increased to 5000 mg. The intensity of responses, although small, is found, however, to be proportional to the sample mass. Charcoal interacts strongly with apolar sorbates (e.g., hydrocarbons), so their uptake in charcoal is much larger than in inorganic adsorbents and their FR signals are strong associated with the high gradient of the adsorption isotherms at the equilibrium pressures studied (compare the respective K values at low frequencies). The response spectra cannot be fitted as a single peak. The rate-determining steps can be sorption on different sorption sites or independent parallel diffusion processes. However, the experimental data points could not be fitted by the Yasuda’s sorption model12 developed for parallel adsorption on various sorption centers. The experimental results can, however, be fitted perfectly if two independent, parallel diffusion processes14 are assumed in the charcoal particles (see Figure 6A). Two similar diffusion processes also describe the results obtained with ammonia and carbon dioxide in this sample (see Figure 6, partsB and C). The ratio of the intensities of the resolved diffusion peaks is quite different with the various

sorbates, which probably indicates different strengths of sorption for these three sorbates in the two channel systems. However, such an interpretation of the data, although reasonable, should be treated with circumspect at present until more detailed studies are carried out. The molecular weight of propane and carbon dioxide is the same; however, their mobilities in charcoal and their frequency response resonances are quite different. The much slower mass transport of propane is probably due to its kinetic diameter of 4.3 Å being 1 Å larger than that of carbon dioxide and the stronger sorption interaction energy of propane with the carbonaceous surface. This latter reason is the most probable explanation of the slower diffusion of the smaller (2.6 Å diameter) ammonia molecule compared with that of CO2. These results confirm that diffusion in these systems is not Knudsen in character. Propane responses in charcoal seem to be independent of pressure in the 1-6 Torr pressure range, so molecular diffusion can be also excluded. Bimodal intercrystalline diffusion seems to be the rate-determining process in these systems. A linear relationship between the square of pellet size and macropore diffusion time constant was not obtained, which proves that the propane uptakes are not controlled by macropore diffusion in the charcoal particles. Very similar responses were recorded with 5-6 mm pellets of charcoal and with pellets less than 0.25 mm. The pore and matrix structures were studied by small-angle X-ray scattering (SAXS).17,18 The primary structural parameter generally obtained from SAXS is a Gunier radius (see Figure 7). The average size of the pores and the matrix units can be derived from the moments of the scattering curves. On the basis of these SAXS measurements on the BDH charcoal sample, the distribution of the Gunier radii shown in Figure 7 was obtained, and assuming spherical particles, the average diameter of these particles is 2R ) 2(5/3)1/2RG ) 45 Å. The propane diffusivities determined for the two different channel systems in the charcoal particles of 45 Å average diameter are presented as Arrhenius plots in Figure 3B. The activation energies were found to be 34.7 kJ/mol for the slower and 28.5 kJ/mol for the faster diffusion process. The sorption energies of propane with the carbonaceous surface in the two different pore structures are similar, and it is only the mass transport rates which are different. The known structure of charcoals is consistent with the bimodal diffusional response found.17 The lower frequency peak is not associated with a heat of sorption effect, as the intensity of this low frequency peak decreases more slowly with increasing temperature than the higher one. Propane sorption on charcoal shows the strongest bed effects. The two response curves change from lines meeting asymptotically to ones which intersect with increasing bed depths. The intensity of the in-phase response signal at low frequencies is


Figure 8. Response spectra for 6 Torr of propane sorbed on alumina particles of radius (A) R ) 0.42 mm and (B) R ) 0.30 mm.

not proportional to the sample mass. When the sample is increased from 200 to 5000 mg, the K value changes only from 0.85 to 4.30 as shown in Figure 5, parts b and B. Because of the strong sorption of propane in charcoal, only the upper layers of the bed are in equilibrium with the pressure change. The lower layers of the bed do not attain equilibrium under the times involved in the pressure modulations. In the Lancaster 4A zeolite pellets, propane molecular diffusion in the wide macropore system was found to be the rate-determining process. Propane diffusion in the alumina particles of 0.84 mm average diameter is also fast and a diffusivity value of 1.18 × 10-5 m2 s-1 was determined, which is faster than that for Knudsen diffusion. However, on decreasing the particle size, an interesting mechanism change can be observed in Figure 8. In the case of propane sorption on alumina, the time constants of the sorption/desorption processes will be longer than that for mass transfer when particles of 0.60 mm or slightly less diameter are involved. With the increase in surface area when particles of 0.30 mm are used, a complicated sorption rate spectra appears, demonstrating that sorption involving weaker sorption energies must be present in sufficient concentration to introduce the additional responses found in Figure 8B as compared to the simple macropore diffusion in Figure 8A. The additional peaks can be fitted perfectly by Yasuda’s sorption model.12 4.2. FR Responses Using Carbon Dioxide as an Acidic Probe Molecule. Compared to the apolar propane, carbon dioxide has a large quadrupole moment, which makes it of particular interest as a probe molecule in the characterization of various types of surfaces. CO2 binds strongly to cations through a quadrupole/field gradient interaction and also reacts with basic zeolite oxygens to form bidentate and ionic carbonate species. The FR response spectra of CO2 are presented in Figure 9 for the six different sorbents. The sorption interaction of CO2 with silica and charcoal surfaces (which do not contain metal cations) is very weak, and the intensities of the responses are weak (see Figure 9, parts B and C). Signals can only be obtained with 1000 mg sample mass, and the K values are small. Characteristic peaks are obtained at quite high frequencies, indicating fast diffusion. Zeolite pellets give nicely developed, more intense macropore sorption spectra, but at lower frequencies (see Figure 9, parts a-c). The similarity of these spectra is surprising compared with the more complicated propane zeolite pellet spectra shown in Figure 1. The intersections found in the response curves in Figure 9a-c differ with the intersected areas


Figure 9. Carbon dioxide FR spectra of ∼50 mg 4A (R), 5A (β), and 13X (γ) zeolite powder; ∼100 mg 4A (a), 5A (b), and 13X (c) zeolite beads and ∼1000 mg alumina (A), charcoal (B), and silica (C) granules at 100 °C under 4 Torr of CO2.

Figure 10. Comparison of carbon dioxide responses for ∼50 mg of various LTA zeolites recorded at 100 °C under 2 Torr of CO2 fitted using the sorption model: Lancaster 5A (A); laboratory-synthesized Ca-5A (B); Ca-ZK-4 (C); Lancaster 4A (D).

decreasing in the sequence 4A > 5A > 13X. The FR spectra of the zeolite powders (see Figure 9, parts R, β, and γ) are different and strongly depend on the zeolite structure, cationic composition, and water content (i.e., pretreatment temperature).22 The FR characteristic functions recorded for carbon dioxide sorption on zeolite crystals cannot be fitted as a single peak, and for this reason, the use of the diffusion models in the case of LTA and FAU structures is impossible. In zeolite crystallites, parallel sorption processes may be present involving sites of different sorption energies and various sorption rates which results in complicated FR spectra. In previous studies, CO2 response spectra were fitted by one set of characteristic curves satisfactorily where micropore diffusion was considered to be the one and only rate-limiting process.6,7 However, in a recent study, CO2 responses on cationic A, X, and Y zeolites were found to be more complicated.22 Figure 10 gives some examples which demonstrate that carbon dioxide sorption is the ratedetermining step in zeolite crystallites. Commercial Ca-A (5A) zeolite shows the same spectrum as a laboratory-synthesized sample, even though the dimension of the commercial crystals is half that of the laboratory-synthesized sample (see Figure 10, parts A and B). Ca-ZK-4 (a higher Si/Al ratio form of zeolite A) shows a drastically different spectrum, although it is only the Ca cation density which differs (see Figure 10C). In Na-A (see Figure 10D), there are two Na+ cations for every Ca2+ ion in Ca-A zeolites, and some cations are now sited in the eight-membered oxygen rings separating adjacent supercages. The resulting response spectrum is much wider than that found with 5A zeolites.



TABLE 4: Carbon Dioxide Intra- and Intercrystalline Diffusivities in the Zeolitic Beads at 100 °C model 1 zeolite 4A

5A 13X

Pe Torr 1 2 4 6 1 2 4 1 2 4

model 2

K

Dµ 10-15 m2 s-1

DP 10-7 m2 s-1

K

B

DP 10-7 m2 s-1

0.77 0.67 0.60 0.55 0.49 0.43 0.38 0.73 0.57 0.43

1.7 3.4 4.2 5.6 8.9 20.6 49.0 1.8 3.2 6.4

1.8 1.8 1.8 1.8 1.6 1.9 2.2 1.8 2.0 2.0

0.76 0.66 0.60 0.56 0.48 0.43 0.37 0.69 0.55 0.43

130 130 130 130 500 500 500 900 900 900

0.41 0.47 0.50 0.52 0.77 0.86 0.90 0.82 0.82 0.90

A complicated sorption spectrum is demonstrated in Figure 9A for alumina due to various carbon dioxide chemisorption interactions. In this sample, the influence of intraparticle diffusion can be neglected. As found for propane diffusion in zeolite pellets (see Figure 2) a linear relationship between the square of pellet size and the macropore diffusion time constant can be obtained for CO2 diffusion in zeolites indicating that the carbon dioxide uptakes are controlled by intercrystalline diffusion in the beads. The positions of the resonance peaks do not change with CO2 equilibrium pressure in the range of 1-6 Torr, i.e., intercrystalline diffusion in the zeolite beads in the meso/macropore range is independent of pressure. Thus, the diffusivities determined are in the Knudsen diffusion regime, where Dp is independent of the pressure. Equally good fits were obtained from both JordiDo models 1 and 2. K and D values calculated by the macropore-micropore (model 1) and the macropore diffusion and adsorption (model 2) models can be compared in Table 4. From model 2 the intercrystalline diffusivities (DP) obtained are 0.5-0.2 times slower than those derived from model 1 (compare columns 5 and 8 in Table 4). Table 4 also shows that the B values (ratio of the adsorption and micropore diffusion rates) obtained from model 2 increase from 130 for 4A zeolite to 500 for 5A zeolite and is 900 for 13X zeolite. This surprising observation is the result of the interplay of different micropore diffusivities through the 8- and 12-ring zeolites and differences in the interaction energies of CO2 with the Na+ and Ca2+ ions sited in the different sets of sites in these zeolites. The strong interaction between carbon dioxide and the walls of the macroand mesopores of the pellets seems to be very important, since the macropore diffusion constants are the same in these three pellets which have different pore size distributions (see Table 2) and which demonstrated different macropore diffusivities when the apolar propane was the sorbate (see Figure 2). Micropore diffusivities, as listed in column 4 of Table 4, are shown to increase with increasing pressure, which suggests that at higher coverages sites of lower interaction energies are mainly involved in the diffusion jumps. Carbon dioxide sorption on zeolite beads shows a strong bed effect. The response curves in Figure 11 change from a slightly overlapping situation to one involving a large intersection when a bed is involved. This latter spectrum is very similar to that obtained for strong sorption on cationic sites. The intensity of the response signal in the bed is not proportional to the sample mass. When the 13X bead samples are increased from 98 to 10000 mg, the K value changes from 0.72 only to 34.3, instead of the theoretical ∼73. Figure 12 shows the influence of temperature on the FR spectra of carbon dioxide in 13X crystals at 1 Torr equilibrium pressure. The response curves recorded at temperatures below

Figure 11. Carbon dioxide response spectra of 98 mg of well-separated beads (A) and 10 000 mg of 13X beads in bed (B) at 100 °C and 1 Torr.

Figure 12. Temperature influence on the frequency response spectra for 1 Torr of CO2 and 60 mg 13X powder at 100 °C (A), 50 °C (B), and 0 °C (C).

100 °C could not be fitted with a single chemisorption time constant. Additional signals appeared at lower frequencies, and their intensities increased with decreasing temperature. Since the 60 mg of 13X crystals were well dispersed in the glass wool plug, bed-depth effects could be eliminated. The second peak which appears at low frequencies and low temperatures may be due to heats of sorption effects as proposed by Sun at al.11 However, the fits using the Sun model do not describe the inphase curves well (see Figure 12, parts B and C). A better fit is obtained using the Yasuda’s sorption model;12 consequently, low-temperature sorption on different sorption sites is the more probable explanation of the data. 4.3. FR Response Using Ammonia as a Basic Probe Molecule. Ammonia, which possesses a large dipole moment, has been used to study the strong interactions which arise with various cations. This strong basic molecule is a useful probe for the characterization of both Lewis and Bro¨nsted acidic sites. In Figure 13, the FR spectra obtained with NH3 sorbed in zeolites are similar to those obtained with CO2 in the same zeolites, but in some cases lower resonance frequencies are


Onyestya´k and Rees different frequencies, different macropore diffusivities are involved. The intensities of the responses are also quite different. The interaction of ammonia with apolar charcoal and weakly acidic alumina is much weaker than with acidic silica or strongly acidic zeolites. 5. Conclusions

Figure 13. Ammonia response spectra recorded with ca. 30 mg 4A (a); 5A (b), and 13X (c) well-dispersed zeolite powder and 4A (A), 5A (B), and 13X (C) beads at 100 °C under 1 Torr of NH3.

Figure 14. Comparison of ammonia responses in adsorbent particles of 0.30 mm diameter under 1 Torr of NH3 at 100 °C: ca. 30 mg Lancaster 5A (A); alumina (B); and silica (C).

found. Most probably, the main sorptive sites for these two sorbates are the cations sited in the same locations. The detailed description of ammonia chemisorption on Na-A, Ca-A, and Na-X will be described in a later paper. In the case of sorption of ammonia in zeolite pellets, the rate-controlling step was found to be macropore diffusion (see Figure 13, parts A-C) despite the much stronger sorption of NH3 in the micropores of the zeolite crystals (compare Figure 9, parts R, β, and γ, with Figure 13, parts a, b, and c). The resonances with the pellets occur at similar frequencies to those found with carbon dioxide (compare Figure 9, parts a, b, and c, with Figure 13, parts A, B, and C). The intersections of the characteristic functions tend to occur nearer to the maximum of the out-of phase function with NH3 compared with CO2. Ammonia sorption in the 13X pellets shows pure macropore diffusion spectra. The resonance frequencies occur at lower frequencies than those found with CO2, and the fits are less accurate. The intensities of the intercrystalline diffusion-controlled responses are approximately half of that found with the separated crystallites, presumably because the mass of the binder material in the pellets is not negligible and part of the surface of the crystals is covered by binder which blocks the uptake of the sorbate into the micropores. Figure 14 shows a comparison of ammonia spectra recorded on three different types of adsorbent particles (the charcoal spectrum is shown in Figure 6). All of the spectra demonstrate that the sorption of ammonia in pellets is determined by macropore diffusion but, as the resonance peaks appear at

In this study, the frequency response technique has been shown to be an effective method for the investigation of diffusion processes in the macro- and mesopores of various adsorbent particles with sorbates of different chemical character. Generally, the macropore diffusivities were found to be rate controlling in most of the adsorbent particles under study, with the exception of carbon dioxide and propane sorption on alumina and propane sorption in charcoal. The micropore sorption properties, sorption interactions, and capacity of zeolite crystallites played a significant role in the uptake rates of zeolite pellets, but macropore diffusion was the dominant process in all cases. The similar responses found with zeolite pellets demonstrate that the pelletization processes and binder materials used by the manufacturer result in similar meso/macropore diffusivities. However, the apolar propane showed a sensitivity to differences in the pore structures in the zeolite pellets. Part of these differences originated from the different structures and compositions of the zeolite crystallites, but the similarity of NH3 and CO2 responses in zeolite pellets suggested that the strong interaction of these sorbates and the binder material smoothed out these differences. It was interesting to find that the uptakes in the charcoal investigated in this study were controlled by two independent, different micropore diffusion processes. The FR technique has a unique advantage among the techniques available in that it is capable of distinguishing different mobilities in separated pore systems. Acknowledgment. Gyo¨rgy Onyestya´k thanks the Royal Society, London and the Hungarian Academy of Sciences for the fellowship and the University of Edinburgh for the facilities which made this study possible. The authors are grateful to Dr. Miha´ly Hegedu¨s, Central Research Institute for Chemistry (Budapest, Hungary) for the mercury porosimetry measurements and Dr. Attila Bo´ta, Department of Physical Chemistry, Technical University Budapest for the SAXS data. The valuable assistance of Mrs. Agnes Wellisch (CRIC, Budapest) is gratefully acknowledged. References and Notes (1) Yasuda, Y. Heterog. Chem. ReV. 1994, 1, 103. (2) Reyes, S. C.; Iglesia, E. Catalysis 1994, 11, 51. (3) Song, L.; Rees, L. V. C. Micropor. Mater. 1996, 6, 363. (4) Song, L.; Rees, L. V. C. J. Chem. Soc., Faraday Trans. 1997, 93, 649. (5) Jordi, R. G.; Do, D. D. Chem. Eng. Sci. 1993, 48, 1103. (6) Onyestya´k, Gy.; Shen, D.; Rees, L. V. C. Micropor. Mater. 1996, 5, 279. (7) Onyestya´k, Gy., Shen, D.; Rees, L. V. C. J. Chem. Soc., Faraday Trans. 1995, 91, 1399. (8) Onyestya´k, Gy.; Valyon, J.; Rees, L. V. C. Presented at the International Symposium on Acid-Base Catalysis III, Rolduc, The Netherlands, 1997. (9) Onyestya´k, Gy.; Valyon, J.; Rees, L. V. C. Presented at Zeolite ’97, Ischia, Italy, 1997. (10) Sun, L. M.; Meunier, F.; Grenier, Ph.; Ruthven, D. M. Chem. Eng. Sci. 1994, 49, 373. (11) Reyes, S. C.; Sinfelt, J. H.; DeMartin, G. J.; Ernst, R. H.; Iglesia, E. J. Phys. Chem. B 1997, 101, 614. (12) Yasuda, Y. J. Phys. Chem. 1976, 80, 1867. (13) Yasuda, Y.; Suzuki, Y.; Fukada, H. J. Phys. Chem. 1991, 95, 2486. (14) Yasuda, Y.; Yamamoto, A. J. Catal. 1985, 93, 176.

Frequency Response Study of Adsorbate Mobilities (15) Rees, L. V. C.; Shen, D. Gas Sep. Purif. 1993, 7, 83. (16) Van Den Begin, N. G.; Rees, L. V. C. In Zeolites: Facts, Figures, Future; Jacobs, P. A., van Santen, R. A., Ed.; Elsevier: Amsterdam, 1986; p 915. (17) Bo´ta, A.; La´szlo´, K.; Nagy, L. Gy.; Copitzky, T. Langmuir 1997, 13, 6502. (18) La´szlo´, K.; Bo´ta, A.; Nagy, L. Gy.; Subklew, G.; Schwuger, M. J. Colloids Surf. 1998, 138, 29.

J. Phys. Chem. B, Vol. 103, No. 35, 1999 7479 (19) Deisler, P. F.; Wilhelm, R. H. Ind. Eng. Chem. 1953, 45, 1219. (20) Boniface, H. A.; Ruthven, D. M. Chem. Eng. Sci. 1985, 40, 2053. (21) Ka¨rger, J.; Ruthven, D. M. J. Chem. Soc., Faraday Trans. 1981, 77, 1485. (22) Onyestya´k, Gy.; Valyon, J.; Rees, L. V. C. In Proc. 12th IZC; Treacy, M. M. J., Marcus, B. K., Bisher, M. E., Higgins, J. B., Eds.; Materials Research Society: Warrendale, PA, 1998; p 159.

Frequency Response Study of Adsorbate Mobilities of Different

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