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Sorption Rate and Thermal Barriers in a Gas-Zeolite System: Investigation of n-Hexane Sorption in MFI-Type Zeolite J. Wloch*,† and J. Kornatowski‡ Faculty of Chemistry, Nicholas Copernicus University, 7 Gagarin Street, 87-100 Torun, Poland, and Lehrstuhl II fuer Technische Chemie, Technische Universitaet Muenchen, Lichtenbergstrasse 4, 85747 Garching bei Muenchen, Germany Received December 20, 2002. In Final Form: October 28, 2003 The nonequilibrium gravimetric sorption method was used to determine diffusion coefficient values for n-hexane in MFI-type materials. Improvements in the measurement device and experimental conditions resulted in high values of the corrected diffusion coefficient, which are comparable to the literature data obtained by the methods of pulsed field gradient nuclear magnetic resonance (PFG NMR) and frequency response (FR). The results indicate that thermal effects of sorption affect practically neither the rate of the sorption nor the diffusion coefficient.
Introduction Investigations of diffusion phenomena result in obtaining valuable information on the behavior of sorption systems. This concerns primarily sorption in zeolites as materials with a defined regular structure, which may be expected to give unambiguous relationships between theoretical predictions and experimental results. However, after over 30 years of effort and use of numerous experimental methods, the discrepancies between the determined values of the diffusion coefficient still remain large and reach up to several orders of magnitude. These large differences between the results obtained with various methods1 are an essential question. Pulsed field gradient nuclear magnetic resonance (PFG NMR) and quasi-elastic neutron scattering (QENS) are techniques commonly accepted as the most accurate and yielding the highest values of the diffusion coefficients.1,2 Macroscopic methods like, e.g., frequency response (FR) give comparable results.1,3 As commonly assumed, this situation originates from the fact that all these methods concern sorption systems being in an equilibrium state or near to it. This opinion seems to be supported by clearly lower values of the diffusion coefficients obtained generally with use of the nonequilibrium methods such as volumetric and gravimetric ones, which are based on monitoring sorption systems during the transition between two equilibrium states. A fundamental cause of the discrepancies in the diffusion coefficient values is commonly seen in differences between physical phenomena associated with the measurements. In the case of transient methods, the final results are believed to depend on (i) the presence of barriers to flow, located inside the particles of studied materials,1,4 and (ii) * Corresponding author: e-mail
[email protected]; phone (48-56) 6114752; fax (48-56) 6542477. † Nicholas Copernicus University. ‡ Technische Universitaet Muenchen. (1) (a) Ruthven, D. M. Stud. Surf. Sci. Catal. 1995, 97, 223. (b) Ka¨rger, J.; Ruthven, D. M. In Diffusion in Zeolites and Other Microporous Solids; Wiley: New York, 1992. (2) Heink, W.; Ka¨rger, J.; Pfeifer, H.; Datema, K. P. J. Chem. Soc., Faraday Trans. 1992, 88, 3505. (3) Song, L.; Rees, L. V. C. J. Chem. Soc., Faraday Trans. 1997, 93, 649.
significant thermal effects accompanying the sorption process.5 The latter factor is accepted to be the most important obstacle as the heat of sorption increases the sample temperature. Nevertheless, an appropriate preparation and/or adjustment of the measurement device and use of samples composed of large particles enable minimization of possible perturbations in the system.1 An intensive heat release occurs on the particle (crystal) surface where the phase transition from the gaseous state to a quasi-liquid one takes place. This may result in formation of surface barriers to diffusion, which can reduce the sorption rate by up to several orders of magnitude.6 This effect is usually accepted as the most significant factor hindering a correct determination of the diffusion coefficients. Consequently, the above considerations imply that the transient methods are basically inapplicable for the determination of the diffusion coefficients and can be used as complementary techniques only. Our initial measurements by the gravimetric method as applied to zeolite samples of various origin confirmed the described situation: the determined diffusion coefficients were as a rule lower by 2 orders of magnitude in relation to the other methods. In some cases, however, the diffusion coefficient values tended to gain higher values.7 As it appeared, some adjustments of the experimental setup could strongly increase the sorption rates in the examined materials and the calculated diffusion coefficients were of the same order as those obtained with PFG NMR (several times lower only).2 This was the driving force for exploring a possible influence of the thermal effects on both the sorption rate and the diffusion coefficient values presented in the following discussion. Experimental Section The measurements were performed on samples of MFI-type zeolite with crystal sizes of 120 × 90 × 45 µm, synthesized by (4) Vasenkov, S.; Bo¨hlmann, W.; Galvosas, P.; Geier, O.; Liu, H.; Ka¨rger, J. J. Phys. Chem. B 2001, 105, 5922. (5) Grenier, P.; Meunier, F.; Gray, P. G.; Ka¨rger, J.; Xu, Z.; Ruthven, D. M. Zeolites 1994, 14, 242. (6) Bu¨low, M.; Struve, P.; Mietk, W.; Kocirik, M. J. Chem. Soc., Faraday Trans. 1 1984, 80, 813. (7) Wloch, J.; Rozwadowski, M. Ann. Univ. M. Curie-Sklodowska (Lublin, Poland) 2002, 56, 124.
10.1021/la020979x CCC: $27.50 © 2004 American Chemical Society Published on Web 01/22/2004
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Figure 2. Spherical model of a sorbent particle. Figure 1. SEM image of SbSil-1. the method developed for growing large crystals.8 Approximately 2 mol % antimony in relation to silicon was introduced into the framework during the synthesis; the product was designated as SbSil-1.9 The crystal morphology was examined by scanning electron microscopy (SEM) (Figure 1). The measurements of the n-hexane uptake were carried out with a gravimetric technique, using a greaseless vacuum device with an automated Sartorius balance of 0.001 mg accuracy and a set of MKS Baratron pressure transducers. The main vacuum channel was connected directly to the measurement tube with a sample holder in order to minimize the flow of the n-hexane vapor through the balance and to decrease its pathway from the feeder to the sample. The sample holder was connected to the balance with a platinum wire. The wire passed through central openings in a number of aluminum plates that formed a vapor trap. In a typical experiment, a 10-mg zeolite sample was placed on a sample holder and spread into a thin layer. Before each measurement, the sample was degassed for 24 h at 423 K and then cooled for 45 min down to 298 K, which was the measurement temperature. Determination of the uptake curves was performed in two ways: Method I: Classical. The n-hexane vapor was fed to the vacuum device from an ampule, by use of a metering solenoid valve, until the first required pressure was achieved. The vapor was continuously added to maintain the pressure at a constant level. The growth of the weight was recorded until the sorption equilibrium was established. Then, the next target pressure was set and the weight gain was recorded until a new sorption equilibrium was attained. Method II: Modified. The procedure was carried out similarly as described above, with the difference, however, that the sample was degassed at 423 K for 24 h after attaining each consecutive sorption equilibrium under each target pressure. These two ways of carrying out the measurements differ in the route of establishing the equilibrium state. Although the final level of sorption should be independent of this route, the sorption rate and diffusion coefficient may be different if any deviations from the classical concentration-dependent diffusion occur, e.g., when significant thermal effects appear. The applied vapor pressures were within the range of 0.0050.05 mbar. Higher pressures were not used in order to avoid both substantial perturbations of the balance equilibrium caused by a considerable increase in the sorption rate and significant deviations of the calculated values of the diffusion coefficient from those observed under low pressures.
Calculations A simple theoretical model was applied for the description of the course of the uptake curves and determination of the diffusion coefficient values. The studied material was assumed to exist in the form of spherical particles with the volume equal to that of a real crystal. The individual particle may hypothetically be divided into (8) Kornatowski, J. Zeolites 1988, 8, 77. (9) Kornatowski, J. Manuscript in preparation.
spherical sections (Figure 2) of the same thickness, ∆r. Then sorption can be considered as a unidimensional flow and described with the following differential equation:
[
] ()
∂c ∂2c 2 ∂c ∂D ∂c )D 2+ + ∂t r ∂r ∂r ∂r ∂r
()
(1)
where c is the sorbate concentration, t is time, D is the diffusion coefficient, and r is the inner radius of a section. This is a general relation taking into account that the diffusion coefficients depend on the concentration, which is typical of zeolites. The latter dependence is usually expressed by the Darken equation:
∂ ln p D ) D0 ∂ ln c
(2)
where (∂ ln p/∂ ln c) is the reciprocal of the first derivative of the logarithmic form of the sorption isotherm and D0 is the corrected diffusivity. Since the uptake measurements were made under low pressures, it can be accepted that the obtained sorption isotherms correspond to Henry’s isotherm. Thus, the derivative in eq 2 is equal to 1 and D ) D0. When it is assumed that the D0 coefficient is independent of the sorbate concentration, eq 1 can be transformed into
(
)
∂2c 2 ∂c ∂c )D 2+ ∂t r ∂r ∂r
()
(3)
Equation 3 is a limit form of the following expression that includes the difference quotient:
[
c(r + ∆r) - 2c(r) + c(r - ∆r) ∆c )D + ∆t (∆r)2
- c(r - ∆r) (2r) c(r + ∆r)2∆r ] (4)
The diffusion coefficient has been calculated from eq 4 by use of a numerical method. ∆r was set to R/50, where R, the radius of the spherical particle, is equal to 50 µm. The value of R was calculated with the assumption that the volume of the particle was equal to the volume of a mean crystal. At time t ) 0, a homogeneous concentration of n-hexane, corresponding to a given sorption equilibrium, is present inside the particle. At the particle surface, however, a sorbate concentration relating to the next sorption equilibrium is set and it remains constant during the sorption process. The values of the internal and external concentrations were obtained as asymptotic (at t f ∞) values of the concentrations, determined from the experimental uptake curves. The numerical method was chosen because it is a simple, highly intuitive approach and it provides a possibility to modify easily the theoretical model in the case of a dependence of the diffusion
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Figure 3. Uptake of n-hexane by SbSil-1 as determined by method I (cf. Experimental Section) under the pressures of 0.005 (a), 0.010 (b), 0.015 (c), and 0.020 (d) mbar. Circles are the experimental points and solid lines are curves calculated by use of eq 3. Sorption is determined as concentration (c) given in grams of sorbate per cubic centimeter of sorbent.
Wloch and Kornatowski
Figure 4. Uptake of n-hexane by SbSil-1 as determined by method II (cf. Experimental Section) under the pressures of 0.005 (a), 0.010 (b), 0.015 (c), 0.020 (d), 0.025 (e), and 0.030 (f) mbar. Circles are the experimental points and solid lines are curves calculated by use of eq 3. Sorption is determined as concentration (c) given in grams of sorbate per cubic centimeter of sorbent.
coefficient on concentration or occurrence of barriers (of any orientation) to flow as well as in the case of a two- or three-dimensional flow. The results obtained with the numerical method agreed very well with those from the standard analytical diffusion equations. The numerical method yielded a fit to the uptake curves within the initial time range even slightly better. Results and Discussion Despite large dimensions of the zeolite crystals and independently of the measurement methods, the observed rates of the n-hexane sorption were unexpectedly high. In each experiment, the sorption equilibrium was achieved after ca. 60 s (Figures 3 and 4). The diffusion coefficients were equal to 1.7 × 10-11 and 1.9 × 10-11 m2/s as determined by methods I and II, respectively (cf. Experimental Section). These values are close to those obtained with PFG NMR [(5-10) × 10-11 m2/s]2 and FR [(2-10) × 10-11 m2/s].3,10 In the case of the classical method (I), the highest weight gain and, thus, the highest rate of n-hexane sorption (equal to the sorbate flow) were observed for the lowest pressure (Figure 3). The subsequent steps in the sorbate pressure caused much lower weight gains. A discrepancy between the total amount of n-hexane sorbed at a given stage of the uptake process by methods I and II was observed. Nevertheless, no significant difference in the rate of establishing the equilibrium state was found, and the calculated values of the diffusion coefficient appeared close to one another (Figure 5). Unlike for method I, the increase in the amount of n-hexane, sorbed at a given stage, with rising target (equilibrium) pressure was observed in the case of method II. However, the uptake curves obtained under each pressure appeared to be very similar to one another (Figure (10) van den Begin, N. G.; Rees, L. V. C. Stud. Surf. Sci. Catal. 1989, 49, 915.
Figure 5. Diffusion coefficients vs pressure for the sorption of n-hexane by SbSil-1 as determined by methods I (O) and II (0).
4) and the diffusion coefficient values varied within the limits of experimental error. An average value obtained by method II (1.9 × 10-11 m2/s) was close to that from method I (1.7 × 10-11 m2/s). The above findings suggest that the route of establishing the equilibrium state of sorption does not markedly influence either the rate of attaining this state or the value of the sorbate diffusion coefficient. The latter appeared to be essentially independent of concentration. This presumably means also that thermal effects of sorption do not noticeably affect the rate of attaining the sorption equilibrium state and the value of the sorbate diffusion coefficient. The independence of the diffusion coefficients of the measurement method (I or II) becomes even more significant when it is taken into account that the released heat of sorption is carried away practically through the sample holder only. The amount of the heat dissipated
Gas-Zeolite Sorption Rate and Thermal Barriers
through the n-hexane vapor can be assumed as negligible at least because of a very low pressure of the latter. This means that although the sorption thermal effects might cause a considerable increase in the sample temperature, they do not influence the diffusion coefficients. Conclusions The diffusion coefficient values determined by sorption gravimetric methods are independent of the way of attaining the sorption equilibrium. The gravimetric methods, based on monitoring of the transition states, can give high values of the diffusion coefficients. These values are comparable to those obtained with the techniques used for systems in or close to the equilibrium
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state, e.g., PFG NMR and FR. The decreased values of the diffusion coefficients, obtained usually with use of nonequilibrium methods, appear to result mainly from the measurement device limitations and/or experimental conditions. The thermal effects of the sorption do not create significant surface barriers to the sorbate diffusion process under the applied measurement conditions. Acknowledgment. Thanks are due to Dr. K. Erdmann (Nicholas Copernicus University, Torun, Poland) for valuable help. This work was partially supported by the State Committee for Scientific Research (KBN), Grant 4 T09A 147 23. LA020979X
