ARTICLE pubs.acs.org/Langmuir
High Pressure Excess Isotherms for Adsorption of Oxygen and Nitrogen in Zeolites Yu Wang,† Bernardus Helvensteijn,‡ Nabijan Nizamidin,† Angelae M. Erion,† Laura A. Steiner,† Lila M. Mulloth,‡ Bernadette Luna,‡ and M. Douglas LeVan*,† † ‡
Department of Chemical and Biomolecular Engineering, Vanderbilt University, Nashville, Tennessee 37235, United States NASA Ames Research Center, Moffett Field, California 94035, United States
bS Supporting Information ABSTRACT: High-pressure oxygen is an integral part of fuel cell systems, many NASA in situ resource utilization concepts, and life support systems for extravehicular activity. Due to the limited information available for system designs over wide ranges of temperature and pressure, volumetric methods are applied to measure adsorption isotherms of O2 and N2 on NaX and NaY zeolites covering temperatures from 105 to 448 K and pressures up to 150 bar. Experimental data measured using two apparatuses with distinctly different designs show good agreement for overlapping temperatures. Excess adsorption isotherms are modeled using a traditional isotherm model for absolute adsorption with a correction for the gas capacity of the adsorption space. Comparing two models with temperature-dependent coefficients, a virial isotherm model provides a better description than a Toth isotherm model, even with the same number of parameters. With more virial coefficients, such as a cubic form in loading and quadratic form in reciprocal temperature, the virial model can describe all data accurately over wide ranges of temperature and pressure.
’ INTRODUCTION The adsorption behavior of high-pressure, supercritical gases on porous materials has attracted research interest because of important applications, such as carbon dioxide sequestration,1 adsorptive storage of natural gas and hydrogen,2 and separation and purification of hydrogen and light hydrocarbons. Isotherm data and equilibrium models at high pressures are needed for design and development of these processes. High-pressure oxygen is an integral part of fuel cell systems, in situ resource utilization concepts, and life support systems for extravehicular activity. NASA has program needs for an in-flight supply of high-pressure oxygen using a temperature swing adsorption system that accepts liquid propellant tank boil-off and produces a supply of compressed oxygen at 3000 psig. For high-pressure storage, isotherms over wide ranges of temperature and pressure are required to assess the feasibility of capturing oxygen from propellant boil-off or adsorbing it at cryogenic temperatures. Owing to the extreme flammability and explosion hazard involved in high pressure oxygen containing systems, experimental apparatuses and isotherm data for oxygen have been reported only for a few adsorbents at moderate pressures. Adsorbents considered most commonly are inorganic materials, such as zeolites, which are not combustible in contrast to carbonaceous materials. Izumi and Suzuki3,4 studied oxygen adsorption on NaX zeolite at a total pressure of 120 kPa and temperatures of 213, 243, 273, and 298 K. Isotherm data at r 2011 American Chemical Society
pressures up to 30 bar have been reported for several zeolite-type materials,510 including 5A,5,6 LiLSX,7 ETS-4 (a small pore titanium silicate),8 AlPO4-5,9 and SAPO-5.9 Higher pressure oxygen isotherm data are found in the literature for only AX-21, a superactivated carbon, for pressures up to 100 bar and temperatures of 118313 K.11 These experimentally measured isotherms are exclusively represented as excess quantities adsorbed because it is impossible to differentiate between molecules confined in the adsorbed phase and molecules in the bulk fluid phase. As a consequence of the adsorption potential, the adsorbed-phase density increases in a narrow layer adjacent to the surface of the adsorbent and approaches a bulk gas density at greater distances. This region of altered density at the solid surface is referred to as the “adsorption space” or “adsorbed phase”.12,13 The integral of adsorbate density over the adsorbed-phase volume is considered to be the “absolute adsorption” occurring at the surface.14,15 Unfortunately, the size and structure as well as the density of the adsorbed phase cannot be measured directly in any experiment. To avoid this difficulty, the excess adsorbed amount is rigorously defined based on the concept of Gibbs surface excess16 as the difference between the actual amount of gas present in a volume minus the amount of gas that would be present in the same volume at the Received: May 6, 2011 Revised: June 13, 2011 Published: July 11, 2011 10648
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Langmuir prevailing bulk density of the gas. Thus, the excess adsorption is the absolute adsorption minus a product of the bulk gas density and the adsorption space volume.13,17 Depending on the relative values of the adsorbed-phase density and bulk gas density, the excess isotherms have long been reported to have maxima,18 and even negative values are possible at very high pressures,19,20 for which the adsorbed-phase density is less than the bulk gas-phase density. This has prompted the development of theories to account for the maxima, and literature reviews on supercritical adsorption studies are available.12,21 A simple way to describe excess isotherms has been developed on the basis of the relationship between excess adsorption and absolute adsorption, which has a monotonic form and can be described by traditional isotherm models21,22 or molecular simulations.23,24 Molecular simulations are able to provide guidance in optimizing the properties of materials by depicting dynamic and equilibrium behaviors. Furthermore, they can provide accurate prediction of mixture behavior from data for single components.14 Simulation methods have been developed to understand and describe excess adsorption data, and these depend on the estimation of void volume.25 Typical simulation methods include Monte Carlo simulations,14,23,25,26 density functional theory,24,27,28 and molecular dynamics.29 By defining the adsorbed-phase volume, the excess adsorption can be obtained from an absolute adsorption model and compared with experimental data. The adsorbed-phase volume is typically treated as the pore volume of the adsorbent23,24 or estimated by assuming that the adsorbed-phase density can be approximated by a liquid density. Depending on the system, some high-pressure data can be described quantitatively, whereas others can be described only qualitatively. Another approach is to treat this adsorbed-phase volume as a constant for a given gassolid system.21,30 Do and Do21 used this approach to study literature data on nonporous and microporous materials and found that the adsorbed phase is confined mostly to a geometrical volume having a thickness of up to a few molecular diameters. At high pressure, the adsorbed phase density was found to be very close to but never equal to or greater than the liquid phase density. In contrast to considering a constant value for adsorbed-phase volume or density, Dreisbach et al.22 proposed a model that fits a pressure-dependent density of the adsorbed phase from isotherm data measured for He, CH4, N2, and Ar on a microporous activated carbon at different pressure ranges. Results show that densities of the adsorbed phases have a linear dependency on the upper pressure limit. A similar observation has been reported with the nonconstant adsorbedphase volume varying with pressure and temperature for supercritical nitrogen adsorption on activated carbon.31 It is noteworthy that differences between adsorbed-phase volumes and micropore volumes exist mostly for activated carbons. This can be attributed to the pore size distributions of carbons, which have macropores. For zeolites with uniform micropores and no macropores, the adsorbate molecules cannot escape the attraction from adsorbent walls. Thus, the accessible micropore volume inside the microporous zeolites is considered to be the adsorbed-phase volume. This is widely accepted and has been applied successfully to describe high-pressure adsorption in zeolites.14,23,24,32 The objective of the present work is 2-fold. First, we construct and validate two distinctly different apparatuses to measure oxygen and nitrogen adsorption data over broad pressure and
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Figure 1. Schematic diagram for VU volumetric apparatus: 15, pneumatic valves; 6, 7, needle valves.
temperature ranges of interest for cryogenic and ambient temperature applications. Nitrogen was chosen in addition to oxygen because it is inert and safer for high-pressure-isotherm measurements, and the measurements can be compared with published results to verify the methods. Second, we analyze data with an approach that combines traditional isotherm models for absolute adsorption with an adsorbed-phase volume to describe experimental excess adsorption. Two models with temperature-dependent parameters, the Toth and virial models, are applied and compared. Furthermore, the models and the resulting parameters allow prediction of adsorption loadings over wide ranges of temperature and pressure. To the best of our knowledge, this is the first report of high pressure oxygen isotherm measurements on zeolites.
’ EXPERIMENTAL SECTION Materials. NaX zeolite (lot 534413X344) and NaY zeolite (Y-54) were supplied by UOP. Both zeolites were in 1/16” pellet form. All gases were obtained from Air Liquide and Matheson Tri-Gas and had nominal cylinder pressures of about 150 bar. The oxygen was research grade (99.9995%), and the helium and nitrogen were ultrahigh purity (99.99%). Apparatus. Two volumetric apparatuses were designed and built for isotherm measurements over wide ranges of temperature and pressure. One was constructed at Vanderbilt University (VU) for measuring equilibrium adsorption data from 248.15 to 448.15 K. The other was constructed at the NASA Ames Research Center (ARC) to target lower temperatures, ranging from 105 K, the saturation temperature of oxygen at 50 psia, to 300 K. Room temperature data were collected using both apparatuses and compared to verify the systems. All parts of both apparatuses were oxygen compatible. Prior to assembly, special treatments were performed to remove any contaminants such as oils, greases, solvents, and dusts, which are combustible in an oxygen system and can cause an accidental fire or explosion. We used the following cleaning procedure to clean parts if they had not been specially cleaned for oxygen service by the manufacturer. First, parts were cleaned in an ultrasonic bath with detergent added to remove oils/ solvents. This was followed by a triple rinse with deionized water and then an isopropyl alcohol (IPA) rinse. Lastly, parts were dried with pure inert gas. VU Volumetric Adsorption Apparatus. A schematic diagram of the volumetric apparatus constructed at Vanderbilt University is shown in Figure 1. It has several pneumatic valves (Swagelok SS-HBS4-C) and needle valves (Swagelok SS-31RS4) to control gas flow in the system. The main manifold was placed inside an environmental chamber 10649
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Table 1. Characteristics of Adsorbents
Figure 2. Schematic diagram for ARC cryogenic volumetric apparatus. (Thermotron, model SM-8-8200), which can maintain temperatures from 68 to 180 °C with 0.1 °C precision. Two pneumatic valves were actuated to control the dosing of gas into a reference cell and an adsorption cell. Pneumatic actuation instead of manual operation was used to prevent ice formation during low-temperature measurements, which can occur as the result of the repetitive opening of the door to the environmental chamber. The reference cell consisted of a tubing section between the two pneumatic valves. For calculations, its volume was divided into two parts based on the temperature profile along the tubing, with the major part contained inside the environmental chamber. The adsorption cell was constructed of stainless steel VCR parts (from Swagelok), including a 1/2 in. bulkhead union body (SS-8-VCR61P) and 1/2 in. cap (SS-8-VCR-CP). The volume of the adsorption cell could be expanded by connecting more 1/2 in. VCR union bodies. This enlargeable adsorption cell provides flexibility for measurements with low capacity samples and improved accuracy with more adsorbent. The adsorption cell was sealed with VCR gaskets to minimize leakage. Specifically, a snubber gasket with a 10 μm frit was used to minimize the passage of sample dust from the adsorption cell to other parts of the system when it was evacuated by vacuum. The apparatus operates on the volumetric principle with pressures being read using a high accuracy transducer (Paroscientific, model 745), which has a range of 3000 psi and an accuracy of better than 0.008% of full scale. The system was designed to measure high-pressure isotherms of flammable and/or inert gases. Considering that at high pressure oxygen is highly reactive with many materials (including stainless steel), safety considerations are important for the design and operation of the apparatus. Several features were added to address the safety concerns, including (a) adding a vent line for pressure reduction prior to using a dry turbo pump to exhaust the system, (b) adding a needle valve in both the vent line and vacuum line to prevent rapid pressure changes, and (c) using pneumatically actuated valves to permit the system to be operated from a safe distance. Another unique feature was related to the adsorbent regeneration procedure used. A heating mantle was added around the adsorption bed to have in situ regeneration temperatures of up to 250 °C . This feature avoids both the postregeneration transferring of samples in air and the heating of the whole system, which can create leaks from thermal expansion of metal parts. After leak testing the apparatus at a pressure of 150 bar over an extended time period, we measured system volumes for different regions using a gas expansion method. First, the relative volume ratio between the buffer and adsorption region was measured. Then, a known volume was substituted for the adsorption region and the volume ratio was measured again. Thus, the reference volume and the adsorption region volume could be calculated using a material balance; they were 11.45 and 18.75 mL, respectively. The internal volume of the 1/8” tubing outside of the chamber to connect to the pressure transducer was determined to be 1.515 mL. The mass of adsorbent used was typically about 5 g. The system was designed to have low void volume and high adsorbent mass in order to partition a large fraction of the adsorbable component in
zeolite
BET surface area (m2/g)
DA micropore volume (cm3/g)
NaX
558
0.269
NaY
508
0.244
the adsorbed phase. This improves the accuracy of measurements as the quantities adsorbed are obtained by material balance as the difference between the quantity of adsorbable component input to the system and the amount remaining in the gas phase. The error is small as the result of minimizing the contribution from the gas phase. In initial measurements, we found that results were very repeatable with slightly different void volumes for different setups. ARC Cryogenic Adsorption Apparatus. The ARC apparatus is shown schematically in Figure 2. The adsorbent bed and its fill line were housed inside a vacuum can placed within a liquid nitrogen Dewar, the liquid nitrogen providing the means for cooling down to cryogenic temperatures. A copper strap, connecting the liquid nitrogen soaked base of the vacuum can to the adsorbent bed, facilitated cooling the sorbent to cryogenic temperatures. An attached heater enabled equilibrium temperatures greater than 77 K, while the surrounding vacuum helped to reduce the power needed for heating. Thermal insulation was applied around the fill line and the adsorbent bed to reduce heat transfer to these components. The external components (vacuum pump, high-pressure gas cylinder, valves, and buffer) permitted pressurization, bleed down, and evacuation of the system. Fomblin oil, which is oxygen compatible, was used in a fore-pump connected to a dry turbo pump. To permit accurate quantitative measurements of the oxygen adsorbed, pressure measurements were made with the same model of high-accuracy Paroscientific pressure transducer as used on the VU apparatus. At low pressures, a 3.4 MPa (500 psi) Heise pressure transducer (model DXD; 0.02% F. S. accuracy) was used as well. The temperatures of the cooled components were measured using calibrated LakeShore Cryotronics diode thermometers ((0.03% accuracy), while the room temperature hardware temperatures were measured using type E thermocouples.
’ RESULTS AND DISCUSSION Adsorbent Characterization. Adsorbent samples were characterized using a Micromeritics ASAP 2020 porosimeter to measure ultrahigh purity N2 adsorption isotherms at 77.35 K. Prior to measurement, approximately 0.1 g of each sample was degassed with heating to 100 °C for 1 h and then continuously at 350 °C for an additional 10 h under a vacuum below 10 μbar. Some characteristics of the adsorbents are summarized in Table 1. The micropore volumes are 0.269 cm3/g for NaX and 0.244 cm3/g for NaY based on the DubininAstakhov (DA) method. The micropore volume for our NaX sample is close to the value of 0.26 cm3/g reported for a commercial faujasite-type zeolite (13X) in pellet form33 but is less than reported values of 0.30 cm3/g for the sample in powder form34 and 0.32 cm3/g in crystal form.35 For NaY zeolite, our sample has a lower micropore volume compared to reported values of 0.30 cm3/g for the sample in powder form34 and 0.36 cm3/g for a lab-synthesized NaY.36 Compressibility Factor. To determine an appropriate equation of state (EOS) to describe fluid properties, we examined three: PengRobinson, Soave, and a viral equation with B and C terms. Compressibility factors (z) were calculated using these EOSs and were compared with tabulated data from the National Bureau of Standards37 for N2 at pressures of 0.1100 atm and temperatures of 105450 K. As shown in Figure 3, it is clear that data are described well by the solid lines, which represent the virial equation, but show slight discrepancies at high pressures for the PengRobinson and Soave EOSs. We also calculated 10650
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Virial coefficients (B and C) for nonpolar gases, including quantum gases, have been correlated using three characteristic parameters, i.e., the critical temperature (Tc), the critical pressure (Pc), and the acentric factor (ω).38,39 The critical properties of O2 are Tc = 154.58 K, Pc = 50.43 bar, and ω = 0.022, and those of N2 are Tc = 126.20 K, Pc = 33.96 bar, and ω = 0.037.40 The generalized correlation forms for B and C terms are functions of TR T/Tc as follows:38,39 BPc ¼ fB0 ðTR Þ þ ωfB1 ðTR Þ RTc
ð2Þ
fB0 ðTR Þ ¼ 0:1445 0:330=TR 0:1385=TR 2 0:0121=TR 3 0:000607=TR 8
ð3Þ
fB1 ðTR Þ ¼ 0:0637 þ 0:33=TR 2 0:423=TR 3 0:008=TR 8 ð4Þ
Figure 3. Comparison of compressibility factors from different equation of states with tabulated data for N2.
CPc 2 ¼ fC0 ðTR Þ þ ωfC1 ðTR Þ ðRTc Þ2
ð5Þ
fC0 ðTR Þ ¼ 0:01407 þ 0:02432=TR 2:8 0:00313=TR 10:5 ð6Þ fC1 ðTR Þ ¼ 0:02676 þ 0:01770=TR 2:8 þ 0:040=TR 3:0 0:003=TR 6:0 0:00228=TR 10:5 ð7Þ
Figure 4. Effect of compressibility factor on N2 isotherms for NaX zeolite at 348 K.
compressibility using the commercial NIST REFPROP program, which has less than (0.1% error and gives good agreement with data, as shown by the dotted line in Figure 3. Measured isotherms can be affected significantly at high pressures by the EOS chosen. This is confirmed by comparison of N2 isotherms at 75 °C using the different EOSs. The excess isotherms, shown in Figure 4, are quite different for pressures greater than 40 bar. Thus, it is crucial to choose an appropriate equation of state to describe PVT properties of the adsorbable gas. We further investigated the virial equation with B and C terms for O2. The calculated compressibilities are in good agreement with tabulated data from the National Bureau of Standards37 at pressures of 0.1100 atm and temperatures of 105400 K. Thus, we chose the virial equation truncated after the third virial coefficient to calculate compressibility factors for isotherm data measured using the VU volumetric apparatus. It is of the form z
Pυ B C ¼1 þ þ 2 RT υ υ
ð1Þ
Isotherm data measured using the ARC cryogenic apparatus were analyzed using the NIST REFPROP program to calculate bulk gas density at the measured temperature and pressure. Accessible Volume. The operating principle of the volumetric method consists of expanding a pure adsorbable gas from a reference side of known volume (VR) into a region containing an adsorption bed with a known mass (ms) of adsorbent. The accessible volume for the sample side Vac is also called dead space or void volume.14 By monitoring P before and after opening the valve between the reference and adsorption region, we obtain the initial pressures for the reference cell (PR) and the adsorption bed (Pa) and the final equilibrium pressures for both regions (Pe). Corresponding densities (FR, Fa, and Fe) can be calculated using the EOS as discussed previously. By continuing to dose the reference cell and expanding the adsorbable gas into the adsorption cell, the excess adsorption isotherm can be calculated from a material balance for each step (i) using VR FR, 1 ¼ ðVR þ Vac ÞFe, 1 þ ms nex Pe, 1
ð8Þ
VR FR, i þ Vac Fe, i1 ¼ ðVR þ Vac ÞFe, i ex þ ms ðnex Pe, i nPe, i1 Þ
ð9Þ
i ¼ 2, ::: n where nex has units of mol adsorbate/mass adsorbent. It is clear that the value of the accessible volume Vac for the adsorption bed with adsorbent is important in calculating accurate excess adsorption. The common method is to use helium expansion as a control experiment based on the assumption that helium is not adsorbed. Thus, Vac can be calculated using eq 8 with nex = 0. However, this has been criticized because 10651
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Figure 5. Excess adsorption isotherms for N2 on NaX zeolite for 105473 K. Symbols, experimental data; curves, virial isotherm with Vad = 0.269 cm3/g.
helium has been shown to be weakly adsorbed for a wide range of conditions.13 Malbrunot et al.20 measured the adsorbent helium density (i.e., with volume based on helium displacement) up to 400 °C for various adsorbents and found that values measured at room temperature could be erroneous due to a non-negligible effect of helium adsorption. With a new helium density measured at high temperature for activated carbon, they reexamined their previous data,19 which had shown negative excess adsorption at very high pressures. They found no negative excesses and even a renewed increase in excess adsorption at the highest pressures. In addition, their reported helium densities at 473 and 673 K are similar for zeolite NaX,20 indicating negligible He adsorption at these temperatures. In another study,27 the agreement between the adsorbent volume obtained by DFT simulation and helium pycnometry assuming nonadsorbable helium was shown to be good at a temperature of 343 K. To minimize the possible helium adsorption effect, we used helium expansion to measure the accessible volume (void volume in the system) at the highest measured isotherm temperature for each zeolite, i.e., 448.15 K for NaX and 348.15 K for NaY. In comparison to many experiments with helium expansion at room temperature, we could obtain slightly lower values for Vac by using high temperature expansion. Excess Adsorption. Equilibrium excess isotherms for pure nitrogen and oxygen on zeolites were measured by the techniques described above. Tables of our isotherm data are available as Supporting Information. Figure 5 shows nitrogen isotherms on NaX zeolite. Nine isotherms were measured at temperatures of 248.15448.15 K with steps of 25 K using the VU volumetric adsorption apparatus. These data are shown as filled symbols. Six isotherms, at 105, 150, 175, 200, 225, and 300 K, were measured using the ARC cryogenic adsorption apparatus with the data shown as open symbols. All isotherms are still monotonic (i.e., loading increasing with pressure) except for isotherms at 248.15 and 273.15 K, which show maxima at high pressures. As pressure is increased, maxima are expected to be observed first for the lower-temperature isotherms. However, measurements of low-temperature isotherms up to high pressures were not within the capability of the apparatus designed for low-temperature measurements. Principally, condensation at the saturation pressure for subcritical temperatures, but also temperature variations
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Figure 6. Excess adsorption isotherms for N2 on NaY zeolite for 248348 K. Symbols, experimental data; curves, virial isotherm with Vad = 0.244 cm3/g.
Figure 7. Excess adsorption isotherms for O2 on NaX zeolite for 105348 K. Symbols, experimental data; curves, virial isotherm with Vad = 0.269 cm3/g.
along system lines, prohibited measurements at low temperatures up to high pressures. Two isotherms, one at 300 K obtained using the ARC cryogenic adsorption apparatus and the other at 298.15 K measured with the VU volumetric adsorption apparatus, agree well with each other. This verifies the consistency of measurement made with the two apparatuses. We also compare our data for nitrogen at 273.15 K with data at this temperature published by Salem et al.,32 which are shown in the figure. Both isotherms show a similar trend up to the maximum pressure measured in our system, but the data of Salem et al. continue to show a decreasing trend at higher pressures beyond our limit. Also, our data, which extend to lower pressures, show slightly higher equilibrium loadings compared to their data, which could be caused by different sources of NaX zeolite. Also, it could result from the accessible volume being measured at different temperatures, as we measured Vac at 448.15 K and they measured it at 273.15 K. Three nitrogen isotherms at 248.15, 298.15, and 348.15 K on NaY zeolite, measured using the VU volumetric apparatus, are shown in Figure 6. These isotherms have monotonic shapes with loadings continuing to increase for pressures up to 150 bar. 10652
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bulk density, the excess adsorption is related to absolute adsorption by Z ex FðrÞ dV Fg Vad ¼ n Fg Vad ð11Þ n ¼ Vad
Figure 8. Excess adsorption isotherms for O2 on NaY zeolite for 105348 K. Symbols, experimental data; curves, virial isotherm with Vad = 0.244 cm3/g.
where n is the absolute loading. For the faujasite-type zeolites NaX and NaY, Vad is the micropore volume, as the adsorption potential fields inside microporous zeolites impact the densities everywhere relative to bulk gas densities. For our samples, the values of Vad are equal to the micropore volumes listed in Table 1. Using this approach, we can describe surface excess isotherms having maxima through the use of a traditional isotherm model. Generally, the traditional isotherm model can only describe monotonic forms, as the model has a mathematically monotonic function of loading and a given loading corresponds to only one pressure. However, when combined with the Vad term to deduct the gas quantity at the bulk gas density, the resulting expression can describe a maximum. Two isotherm models, the Toth and virial models, were considered, as both allow for a temperature dependence. The Toth model has a relatively simple form and can effectively describe many systems. Also, it has the correct limiting (Henry’s law) behavior at low pressures. The standard Toth equation has three parameters and is of the form n¼
ns bP ½1 þ ðbPÞt 1=t
ð12Þ
where b is an equilibrium constant, ns is the saturation capacity, and t characterizes the heterogeneity of the adsorbent. When the surface is homogeneous, the heterogeneity parameter t is equal to unity and the Toth isotherm reduces to the Langmuir isotherm. In applying the Toth equation over a temperature range, the parameters b, ns, and t can be considered temperature-dependent with the following forms41 b ¼ b0 expðE=TÞ
ð13Þ
Figure 9. Comparison of adsorption isotherms for O2 on NaX and NaY zeolites at different temperatures.
ns ¼ ns0 exp½Hð1 T=273:15Þ
ð14Þ
Similarly, oxygen isotherms on NaX and NaY zeolites are shown in Figures 7 and 8. Close agreement is observed for isotherms having overlapping temperatures measured by the two apparatuses. For both zeolites, O2 excess isotherms show maxima at some temperatures but remain monotonic for the majority of temperatures. This is caused by the pressure limitation in the measurement, especially at low temperatures. Thus, maxima are not observed for most of the excess isotherms. When comparing oxygen isotherms on NaX and NaY zeolites in Figure 9, we note that oxygen has a higher loading in NaX at high pressures, but a lower loading in NaX at low pressures. Thus, NaX zeolite is a better adsorbent for oxygen storage at high pressures in comparison to NaY zeolite, because it has a higher capacity at the storage pressure and retains less at the delivery pressure. Model Description. Surface excess adsorption is defined as the difference between the total amount of adsorbate in any accessible volume and the amount of bulk gas that would occupy such a volume. This can be written as Z ex ð10Þ n ¼ ðFðrÞ Fg Þ dV
t ¼ t0 þ a=T
ð15Þ
V
With an adsorbed-phase volume Vad, which is chosen such that the density at any point outside this volume will be equal to the
Another temperature-dependent isotherm is based on the virial formalism. Given its solid foundational basis in the fundamental concept of spreading pressure and given that the temperature dependences of gasadsorbate equilibrium at constant loading and vaporliquid equilibrium are quite similar, with both having latent heats firmly grounded in the ClausiusClapeyron equation, the virial isotherm is quite successful in describing adsorption equilibrium very accurately. For a pure adsorbed component, the virial equation can be written as6,42 lnðP=nÞ ¼ A þ
2 3 Bn þ Cn2 þ ::: A 2A 2
ð16Þ
where A is the specific surface area of the adsorbent (m2/kg) and A, B, C,... are virial coefficients, which can be expressed as functions of 1/T using A ¼ Að0Þ þ
Að1Þ Að2Þ þ 2 þ ::: T T
ð17Þ
with expressions of identical form for B, C, etc. A least-squares approach is generally used to evaluate parameters by minimizing an objective function. We defined a 10653
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variance as42 var
E 1 N N
N
∑1 ½Δ ln ðP=nÞ2
ð18Þ
where Δ ln (P/n) is the difference between a calculated and an experimental value of ln (P/n). The calculated ln (P/n) is given by the polynomial form of n and 1/T in eqs 16 and 17. However, the coefficient matrix tends to become ill-conditioned for a large number of equations.42 To avoid this complication, we utilized the method of polynomials orthogonal to summation following the procedure of Taqvi and LeVan42 to generate the coefficients in eqs 16 and 17 without iteration. To compare the capability of the Toth and the virial models for describing these high-pressure data, we applied both models to the O2 isotherms on NaX with the same number of parameters. As the Toth model has six parameters (b0, E, ns0, H, t0, and a), we truncated the virial equation at six parameters, which corresponds to cases of expansions either quadratic in n and linear in 1/T or linear in n and quadratic in 1/T. Combining eqs 1115 and using nonlinear regression, we obtain the Toth isotherms, which are shown as solid lines in Figure 10. Similarly, on the basis of eqs 11, 16, and 17, the virial model results are shown as dashed lines in Figure 10. It is clear that the virial model provides a better description than the Toth equation, especially for data at high pressures. The Toth model tends to have a maxima and then drops quickly. This is caused by the absolute isotherm shape described by the Toth model having a long, fairly flat plateau. When the adsorbed-phase volume is not negligible, the excess loadings decrease rapidly as the FVad term in eq 11 increases with pressure. Thus, the Toth model predicts a negative excess at high pressures. However, as emphasized by Talu et al.,6
the virial model cannot be extrapolated far outside of the range of the data due to its polynomial form. We have also compared the Toth and the virial models with six parameters for the other three systems, N2 on NaX, N2 on NaY, and O2 on NaY, and observe the same trend that the Toth equation fails to describe data well at high pressures. That the virial model describes data at high pressures better than the Toth model is a somewhat surprising result, since the virial model is of greatest theoretical utility at low pressures, where it exactly describes an ideal surface gas in the limit as n f 0. We further examined the Toth expression to compare it with the virial model. The Toth equation can be written as " t # 1 n ð19Þ lnðP=nÞ ¼ lnðbns Þ ln 1 s t n If we expand the right side of this equation in a Taylor series in n about zero loading, it should be possible to compare the Toth and virial equations on a term-by-term basis to understand the relationships among parameters. However, we find that the Toth equation gives an infinite first derivative when t is less than 1 and an infinite second derivative when t is less than 2. Thus, in comparison with the virial equation given by eq 16, the Toth model as represented by eq 19 cannot be expanded in a series about a loading of zero. Considering that our data cover a wide range of temperatures and pressures, we have also included higher powers in both loading and reciprocal temperature to improve the accuracy of the virial model. The appropriate form can be chosen by comparing the variances from the virial model with different values of highest powers of n and 1/T. We calculated the variances for all cases with highest powers of loading and Table 3. Coefficients for Virial Equation coefficient of term O2 on NaX
term
Figure 10. Comparison of results for the Toth and virial models with six parameters for O2 on NaX zeolite. Symbols, experimental data; solid curves, multitemperature Toth model; dashed curves, virial model.
N2 on NaX 7.22 0.972
O2 on NaY
1 n
6.06 0.991
n2
1.19 10 2
3
n
1.68 10
2
1/T
9.95 10
1.50 10
9.45 10
2.43 103 37.6
2
6.15 2.35
N2 on NaY
0.225
8.92 0.276 7.41 10 2
0.736
1.84 10
3 3
5.07 10
2 2
2.00 10 2
n/T
4.50 10
5.07 10
9.69 10
n2/T
78.0
2.12 102
3.82 102
64.1
n3/T
0.743
15.7
32.1
0.756
1/T2 n/T2
5.38 104 4.43 104
1.06 105 7.12 104
8.42 104 1.01 105
n2/T2
1.07 104
2.41 104
4.05 104
5.85 10
2.25 10
3.91 103
3
n /T
2
2
2
2
3
2
Table 2. Variances for the Virial Equation Truncated at Different Points 2 var 1/N ∑N 1 [Δ ln (P/n)]
O2 on NaX N2 on NaX
(n, 1/T)
(n2, 1/T)
(n, 1/T2)
(n2, 1/T2)
(n3, 1/T)
(n, 1/T3)
(n3, 1/T2)
0.09 0.1137
0.0183 0.053
0.0773 0.039
0.016 0.0271
0.0118 0.0416
0.0772 0.037
0.0066 0.02
0.0439
0.0089
O2 on NaY
0.1471
0.0423
0.0495
0.0179
0.0335
N2 on NaY
0.0051
0.0030
0.0030
0.0020
0.0005
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Figure 11. Isosteric heat of adsorption as a function of loading at 300 K.
reciprocal temperature from (n, 1/T) up to (n3, 1/T2). The results are summarized in Table 2. It is evident that increasing the highest power on loading in the equation decreases the variance more significantly than increasing the power on reciprocal temperature for O2 adsorbed on both zeolites, but not for N2 systems. With the cubic polynomial in loading and quadratic polynomial in temperature, the virial model gives an accurate description for the data over several decades of pressure and temperature. Note that we only have three isotherms for N2 on NaY and that the series for 1/T only needs to be linear for this system. Figures 58 show the results for adsorption on zeolites with the virial equation truncated at n3 and 1/T2. All data are described precisely with this approach, and the related virial coefficients are summarized in Table 3. Compared to the common approach of fitting isotherms at each temperature, we have reduced the total number of parameters required dramatically. Isosteric Heat of Adsorption. The isosteric heat of adsorption for a pure component can be calculated using the Clausius Clapeyron equation from isotherms at different temperatures using43 ∂ðln PÞ 2 ∂ðln PÞ ΔHad ¼ zR ð20Þ ¼ zRT ∂ð1=TÞ ∂T n
n
The isosteric heat of adsorption is generally defined on the basis of absolute adsorption. Indeed, Salem et al.32 have discussed the nonphysical nature of the isosteric heat on the basis of excess adsorption. Thus, we use the absolute isotherm model to calculate the isosteric heat of adsorption instead of using isosteres constructed from excess isotherms. Following eq 20, the isosteric heat of adsorption is obtained by differentiating the virial model (eq 17) with respect to 1/T. Values of isosteric heat calculated for zeolites NaX and NaY at 300 K are shown in Figure 11. For N2, the isosteric heats decrease slightly with the amount adsorbed. The average ΔHad is about 18 kJ/mol, which can be compared to a previously reported value of 12.8 kJ/mol for the isosteric heat of N2 on NaX.44 The isosteric heats for O2 remain nearly constant at about 14 kJ/mol.
’ CONCLUSIONS Two volumetric apparatuses have been designed and constructed for high pressure isotherm measurement and have been used to obtain surface excess isotherms for N2 and O2 adsorbed on NaX and NaY zeolites. Isotherms over the temperature range
of 105450 K and pressures up to 150 bar have been measured. Maximum excess loadings occur for low temperatures and high pressures. These are the first reported high pressure oxygen isotherms on zeolites. We have analyzed experimental surface excess loadings with traditional isotherm models with consideration of the adsorbedphase volume. Two absolute isotherm models, the Toth and virial models, have been considered in their temperature-dependent forms. To compare the two models, the virial model was truncated to have the same number of parameters as the Toth model. We found that N2 and O2 isotherms on NaX and NaY were described better with the virial equation than with the Toth model, as the Toth model fails at higher pressures. Also, the Toth model, written as ln (P/n) = f(n), was found not to be expandable in a Taylor series about zero loading. By comparing the variance for the virial model with different values of the highest powers of n and 1/T, we found that increasing the power in loading dramatically decreases the variance for O2 systems, but no obvious trend was observed for N2 systems. Generally, the virial model gives an accurate description for the isotherm data over several decades of pressure and temperature with a cubic polynomial in loading and a quadratic polynomial in reciprocal temperature. Compared to the common approach of fitting isotherms at each temperature, we have reduced the total number of parameters required dramatically. Isosteric heats of adsorption were calculated from the absolute virial isotherm model. For N2 adsorbed on zeolites NaX and NaY, the isosteric heat is about 18 kJ/mol, which is higher than the value of 14 kJ/mol for O2.
’ ASSOCIATED CONTENT
bS
Supporting Information. Tables of isotherm data for O2 and N2 on NaX and NaY zeolites. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*Tel: (615) 343-1672. Fax: (615) 343-7951. E-mail: m.douglas.levan@ vanderbilt.edu.
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