Comparative Study of the Excess versus Absolute Adsorption of CO2

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Langmuir 2003, 19, 2683-2690

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Comparative Study of the Excess versus Absolute Adsorption of CO2 on Superactivated Carbon for the Near-Critical Region† Li Zhou,* Shupei Bai, and Wei Su High Pressure Adsorption Laboratory, School of Chemical Engineering, Tianjin University, Tianjin 300072, People’s Republic of China

Jun Yang and Yaping Zhou Department of Chemistry, School of Science, Tianjin University, Tianjin 300072, People’s Republic of China Received July 29, 2002. In Final Form: December 10, 2002 The adsorption of CO2 on superactivated carbon was measured for the near-critical region, and a comparative study between the excess and the absolute adsorption was presented. The quantity of absolute adsorption was determined based on the principle that it is equal to the excess one if the product of the gas-phase density and the volume of the adsorbed phase can be neglected. However, all isotherms in the ranges of 273-360 K and 0-18 MPa can be satisfactorily modeled by properly accounting for such product. The number of molecular layers in the adsorbed phase was estimated based on the density and volume of the adsorbed phase as evaluated. It was shown that multilayer adsorption is possible for near-critical temperatures but seems impossible if the temperature is fairly far away from the critical. Finally, it was shown that the difference between the absolute and the excess isotherms of CO2 at 273 K could yield about 20% difference in adsorbent characterization.

1. Introduction Supercritical adsorption is a special name for adsorption at above-critical temperatures, which did not attract much research interest for a long time because the amount adsorbed was usually very low at low pressures. However, research on this type of adsorption increased considerably in recent years following the need for clean fuels, such as natural gas and hydrogen. Storage of these fuels aboard vehicles constitutes the key technique, and adsorptive storage seemed promising. New adsorbents such as superactivated carbon with very high specific surface area and novel materials with nanostructures have been developed recently for fuel storage purposes.1-6 Besides, radioactive krypton can be safely stored by adsorption at above-critical temperatures.7 However, the storage temperature of interest is much higher than the critical temperature of the fuel gases; therefore, supercritical adsorption is the theoretical foundation of such storage technology. Aside from adsorptive storage, supercritical * To whom correspondence should be addressed. Phone & Fax: +86 22 87891466. E-mail: [email protected]. † This work was accomplished in the High Pressure Adsorption Laboratory, Tianjin University, Tianjin 300072, P. R. China. (1) Cannon, J. S. Hydrogen Vehicles Programs in the U.S.A. Int. J. Hydrogen Energy 1994, 19, 905-909. (2) Ewald, R. Requirements for Advanced Mobil Storage Systems. Int. J. Hydrogen Energy 1998, 23, 803-814. (3) Matranga, K. R.; Mayers, A. L.; Glandt, E. D. Storage of Natural Gas by Adsorption on Activated Carbon. Chem. Eng. Sci. 1992, 47, 1569-1579. (4) Dillon, A. C.; Jones, K. M.; Bekkedahl, T. A.; Kiang, C. H.; Bethune, D. S.; Heben, M. J. Storage of hydrogen in single-walled carbon nanotubes. Nature 1997, 386, 377-379. (5) Chambers, A.; Park, C.; Terry, R.; Baker, K.; Rodriguez, N. M. Hydrogen Storage in Graphite Nanofibers. J. Phys. Chem. B 1998, 102, 4254-4256. (6) Sircar, S. Activated carbon for gas separation and storage. Carbon 1996, 34, 1-5. (7) Findenegg, G. H.; Korner, B.; Fischer, J.; Bohn, M. Supercritical Gas Adsorption in Porous Materials, I. Storage of Krypton in Carbon Molecular Sieves. Ger. Chem. Eng. 1983, 6, 80-84.

adsorption is also the foundation of adsorptive separation processes. Such separation processes are applied conventionally for the separation or purification of light hydrocarbons, as well as for the separation of air to produce oxygen or nitrogen through pressure swing adsorption or other adsorption processes.8,9 Supercritical adsorption of N2, CH4, and so forth was also proposed for the characterization of porous materials.10,11 Most studies on supercritical adsorption were devoted to the range much above the critical temperatures; only a few studied the region near the critical point, which is, however, very important for understanding the variation of the adsorption mechanism in crossing over the critical temperature. Findenegg studied the adsorption behavior of C2H4 and SF6 on graphitized carbon black12 crossing the critical temperature. Zhou and co-workers observed the transition of the adsorption mechanism in crossing the critical temperature basing on the adsorption of N2 and CH4 on activated carbon13 and on silica gel.14 However, the adsorption behavior near the critical zone could be (8) Ruthven, D. M.; Farooq, S.; Knaebel, K. S. Pressure Swing Adsorption; VCH: New York, 1994; p 235. (9) Yang, R. T. Gas Separation by Adsorption Processes; Butterworth: London, 1987. (10) Nguyen, C.; Do, D. D. Adsorption of Supercritical Gases in Porous Media: Determination of Micropore Size Distribution. J. Phys. Chem. B 1999, 103, 6900-6908. (11) Suzuki, T.; Koboro, R.; Kaneko, K. Grand Canonical Monte Carlo Simulation Assisted Pore Width Determination of Molecular Sieve Carbons by Use of Ambient Temperature N2 Adsorption. Carbon 2000, 38, 630. (12) Findenegg, G. H. High-pressure physical adsorption of gases on homogeneous surfaces. In Fundamentals of Adsorption; A. L. Myers and Belford; Engineering Foundation: New York, 1983; pp 207-219. (13) Zhou, Y.-P.; Bai, Sh.-P.; Zhou, L.; Yang, B. Studies on the Physical Adsorption Equilibria of Gases on Porous Solids over a Wide Temperature Range Spanning the Critical Region: Adsorption on Microporous Activated Carbon. Chin. J. Chem. 2001, 19, 943-948. (14) Zhou, L.; Zhou, Y.-P.; Bai, Sh.-P.; Yang, B. Studies on the Transition Behavior of Physical Adsorption from the Sub- to the Supercritical Region: Experiments on Silica Gel. J. Colloid Interface Sci. 2002, 253, 9-15.

10.1021/la020682z CCC: $25.00 © 2003 American Chemical Society Published on Web 03/08/2003

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quite different to that far from the critical point. According to Findenegg,12 the density of the adsorbed phase is a function of distance normal to the interface for the range of Tc < T < 1.2Tc, which means multilayer adsorption is possible. The result of Monte Carlo simulation for T/Tc ) 1.0215 revealed that the adsorbed phase was a monolayer at low gas-phase density; however, a second layer, a third layer, and even a fourth layer appeared as the gas-phase density increased. As shown presently, the volume and density of the adsorbed phase could be estimated based on both the excess and absolute adsorptions, which will provide more insights into the nature of the adsorbate for the near-critical region. Studies on the adsorption of CO2 for the near-critical region bear special meaning because the so-called supercritical CO2 fluid is applied widely for extraction, regeneration of adsorbents, supercritical chromatography, and catalysis. Only a few related experimental studies have been published.16-19 The precision of the experimental results of earlier works was limited by the techniques available at that time. The experiments of Humayun and Tomasko16 used an apparatus based on dynamic principles and having high resolution, but the effect of compressibility factors was not explained and the temperature range was relatively narrow (300-318 K). A static volumetric method whose principle was described previously20 was used in the present study. The relative error of pressure readings is less than 0.05% for the range of 20 MPa. The constancy of the reference temperature is higher than (0.05 K, and that of the adsorption temperature is higher than (0.1 K. Such accuracy in measuring pressure and temperature was no less or even higher than that achieved previously.16 Attention was also paid to the determination of compressibility factor, which exerts considerable effect on the result of adsorption measurement especially for the nearcritical region.21 Carbon dioxide of purity higher than 99.995% was used to collect nine isotherms in the range of 273-360 K and at pressures up to 18 MPa. A carbon sample of about 3000 m2/g specific surface area was used in the experiments. Adsorption data of CO2 on activated carbon of such high surface area have never been reported. Because the critical temperature of CO2 is much higher and the equilibrium pressure before saturation is also much higher than that of H2, N2, and CH4 previously studied,20,13,14 the typical phenomenon of supercritical adsorption appeared on the subcritical isotherms. Such an observation was explained by a comparison between the excess and the absolute adsorption. To evaluate the absolute adsorption, the method presented by the authors previously22-24 was applied for both the sub- and super(15) Van Megen, W.; Snook, I. K. Physical adsorption of gases at high pressure, I. The critical region. Mol. Phys. 1982, 45, 629-636. (16) Humayun, R.; Tomasko, D. L. High-Resolution Adsorption Isotherms of Supercritical Carbon Dioxide on Activated Carbon. AIChE J. 2000, 46, 2065-2075. (17) Strubinger, J. R.; Parcher, J. F. Surface Excess (Gibbs) Adsorption Isotherms of Supercritical Carbon Dioxide on Octadecyl-Bonded Silica Stationary Phases. Anal. Chem. 1989, 61, 951-955. (18) Chen, J. Hs.; Shan, D.; Wong, H.; Tan, Ch. S.; Subramanian, R.; Lira, C. T.; Orth, M. Adsorption and Desorption of Carbon Dioxide onto and from Activated Carbon at High Pressures. Ind. Eng. Chem. Res. 1997, 36, 2808-2815. (19) Jones, W. M.; Isaac, P. J.; Philips, D. The Adsorption of Carbon Dioxide and Nitrogen at High Pressure by Porous Plugs of Lampblack. Trans. Faraday Soc. 1959, 55, 1953. (20) Zhou, Y.-P.; Zhou, L. Experimental study on high-pressure adsorption of hydrogen on activated carbon. Sci. China, Ser. B 1996, 39, 598-607. (21) Zhou, L.; Sun, Y.; Zhou, Y.-P. An Experimental Study on the Adsorption Behavior of Gases Crossing the Critical Temperature. Chin. J. Chem. Eng. 2002, 10, 1-10. (22) Zhou, L.; Zhou, Y.-P. Linearization of Adsorption Isotherms for High-Pressure Applications. Chem. Eng. Sci. 1998, 53, 2531-2536.

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Figure 1. DRK plot of the CO2 isotherm at 273.15 K.

critical regions. The isotherms of 292.15 and 298.15 K, which are lower than the critical temperature (304.2 K) but show a maximum, were satisfactorily interpreted and modeled by applying the quantity of absolute adsorption as evaluated. The adsorption data are densely distributed in a region near the critical point, and drastic descent was observed at isotherms near the critical temperature, but a perfect fit of the model was achieved for all isotherms in the region studied. Such success has not been achieved in applying other models for the near-critical region before. This suggested, therefore, that the difference between the classical isotherms25 and the abnormal supercritical isotherm that has features of a maximum and a negative increment was caused merely by the product of the gas phase density and the volume of the adsorbed phase. The present study shows that the difference between the “abnormal” isotherm and the classical isotherms and problems caused by the difference can be pertinently managed by appropriately accounting for the product. However, to achieve the goal, the absolute adsorption isotherms must be determined from the excess isotherms that are experimentally available. Finally, it was noticed that the difference between the excess and the absolute isotherms of CO2 at 273.15 K could yield a difference in pore volume and specific surface area of adsorbent of about 20%. 2. Experimental Section 2.1. The Adsorbent. The adsorbent used in the experiments was carbon from carbonated coconut shells, physically activated in a rotary kiln of our laboratory. The carbon sample was characterized by the adsorption isotherm of CO2 at 273 K, which is presented in a subsequent figure. The isotherm belongs to type I; therefore, the DRK plot shown in Figure 1 was applied to estimate the surface area.26 As shown in Figure 2, the plot is composed of three sections indicating a wide pore size distribution, which was estimated by the method proposed by Cazorla-Amoros et al.27 The total surface area was estimated from the intercept (23) Zhou, L.; Zhou, Y.-P. A Mathematical Method for the Determination of Absolute Adsorption from Experimental Isotherms of Supercritical Gases. Chin. J. Chem. Eng. 2001, 9, 110-115. (24) Zhou, L. Adsorption Isotherms for the Supercritical Region. In Adsorption: Theory, Modeling & Analysis; Toth, J. Ed.; Marcel Dekker: New York, 2002; Chapter 4, pp 211-249. (25) IUPAC Commission on Colloid and Surface Chemistry Including Catalysis. Pure Appl. Chem. 1985, 57, 603. (26) Gregg, S. J.; Sing, K. S. W. Adsorption, Surface Area and Porosity; Academic Press: London, 1982.

Excess versus Absolute Adsorption of CO2

Figure 2. Pore size distribution of the activated carbon sample.

Figure 3. The apparatus of adsorption measurement: (1) vacuum pump; (2) CO2 cylinder; (3) compressor; (4) filter; (5) pressure transmitter; (6) filter; (7) reference cell in a double thermostat; (8) adsorption cell; (9) cutoff valve; (10) metering valve. of the plot (1.43) and the area occupied by a CO2 molecule at 273.15 K, which was determined by the density of liquid CO2:28

(

)

10-6 0.927432/44 × 6.023 × 1023

2/3

) 18.4 × 10-20 m2

A ) 101.43 × 10-3 × 6.023 × 1023 × 18.4 × 10-20 ) 2980 m2/g The total pore volume of the sample was estimated by the saturation adsorption at p/ps ) 0.95,26 and 1.27 cm3/g was obtained. 2.2. The Experimental Apparatus and Procedure. The experimental apparatus used for the adsorption measurement was based on a volumetric principle and is shown schematically in Figure 3. The reference cell, which functions as a gas meter, was put in a double thermostat in order to guarantee the constancy of temperature within (0.05 K. Pressure in the reference cell was detected by a pressure transmitter, model PAA-23/8465.1-200 made by Keller Druckmesstechnik, Switzerland. Deviation from linearity of the transmitter output was less than 0.05% for the whole range of 20 MPa. Systematic measurements of the adsorption equilibrium of CH4 and N2 on activated carbon and silica gel were completed using the (27) Cazorla-Amoros, D.; Alcaniz-Monge, J.; De la Casa-Lillo, M. A.; Linares-Solano, A. CO2 As an Adsorptive to Characterize Carbon Molecular Sieves and Activated Carbons. Langmuir 1998, 14, 45894596. (28) Span, R.; Wagner, W. A New Equation of State for Carbon Dioxide Covering the Fluid Region From the Triple-Point Temperature to 1100 K at Pressure up to 800 MPa. J. Phys. Chem. Ref. Data 1996, 25, 15091595.

Langmuir, Vol. 19, No. 7, 2003 2685 apparatus.13,14 Because the cylinder pressure of CO2 is only about 6.4 MPa at room temperature, an air-operated diaphragm compressor from Newport Scientific Inc. (USA) was used to pump up the pressure of CO2 for the supercritical condition. The whole experimental system including the pressure-pumping part was prewashed three times by the supercritical CO2 fluid and vacuumed afterward to prevent contamination by organic impurities that might exist. A filter filled with activated carbon was added between the compressor and the adsorption measurement system to remove any impurities and minor content of water that might be contained in CO2. A residual gas analyzer with high sensitivity was used to monitor the purity of CO2 before it entered the measurement system. The stainless steel tubes connecting the reference cell and the adsorption cell were heated by an electric wire that surrounded the outside, and the heating load was controlled by a controller AL-708P to maintain a temperature of 45 ( 0.5 °C to prevent any possible condensation of CO2 inside the connecting tube. About 10 g of sample was dried at 150 °C and 0.1 Pa for 24 h before adsorption measurement. Helium of purity higher than 99.9995% was used to determine the void space of the adsorption cell. It took less than 1 h to reach adsorption equilibrium at subcritical temperatures; however, 3-4 h was needed when the condition approached the critical point due to the long-term variation of the fluid density. It took 3-4 days to complete the measurement of an isotherm, and measurements were carried out twice for each isotherm. The results of the two measurements were in good agreement. The sample was characterized once again after the adsorption measurements. The result was the same as the previous one, indicating no change in pore size distribution of the sample during high-pressure adsorption measurements. 2.3. Determination of the Compressibility Factor. Determination of the compressibility factor is very important for adsorption measurement because the amount adsorbed is calculated based on an equation of state of real gases (EOS) in the volumetric method. It is also important for the gravimetric method because of the buoyancy correction. Generally, the compressibility factors obtained from different equations of state do not differ much if the condition is fairly far from the critical point. However, the values of the compressibility factors of different origins may have a remarkable difference, which may considerably change the isotherm orientation for the near-critical region.21 Therefore, the determination of the compressibility factor is even more important for studying the adsorption behavior in the near-critical region. Three representative equations of state, the Wagner equation,28 the Lee-Kesler equation,29 and the Ely equation,30 were used to calculate the compressibility factor of CO2 at 307 and 313 K for pressures of 5-14 MPa (F/Fc ) 0.7-1.8). The results were compared with the experimental data.31,32 As shown in Figure 4 for 307 K (the temperature closest to critical in the experiments), the Wagner equation showed the least discrepancy for the whole range of interest. Better agreement between the equation-calculated values and the experimental values was shown for the Wagner equation in the nearcritical region of CO2, and this equation was thus applied in the present work.

3. The Experimental Excess Isotherms Nine isotherms were collected for the ranges 273-360 K and 0-18 MPa. Three of them are located in the subcritical region (273.15, 292.15, and 298.15 K) and six in the supercritical region (307, 313, 318, 323, 340, and 360 K), as shown in Figures 5 and 6, respectively. (29) Lee, B. I.; Kesler, M. G. A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States. AIChE J. 1975, 5, 510. (30) Ely, J. F.; Haynes, W. M.; Bain, B. C. Isochoric (P, Vm, T) measurements on CO2 and (0.982 CO2+0.018N2) from 250 to 330k at pressures up to 35Mpa. J. Chem. Thermodyn. 1989, 21, 879-894. (31) Duschek, W.; Klelnrahm, R.; Wagner, W. Measurement and Correlation of the (pressure, density, temperature) relation of carbon dioxide, I. The homogeneous gas and liquid regions in the temperature range from 217 to 340 K at pressure up to 9 MPa. J. Chem. Thermodyn. 1990, 22, 827-840. (32) Gilen, R.; Kleinrahm, R.; Wagner, W. J. Chem. Thermodyn. 1992, 24, 1493.

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Figure 4. A comparison of the calculated z-values from the EOS with the experimental data for CO2 at 307 K.

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Figure 6. Adsorption isotherms for the supercritical region: (dots) experimental; (curves) predicted by model.

The excess isotherm near the critical temperature drops down fast after the maximum. The closer the temperature to the critical, the more drastic the descent shown on the isotherm and reverse intersection of isotherms was observed. Humayun16 et al. collected four isotherms of CO2 on activated carbon at 305, 309, 313, and 318 K. A plateau before the drastic descent was observed on these isotherms; however, such a plateau was not shown in Figure 6. 4. The Absolute Adsorption Isotherms

Figure 5. Adsorption isotherms for the subcritical region: (dots) experimental; (vacant triangles) desorption; (curves) predicted by model.

Desorption data were also measured for 273 K, and they coincided with the adsorption data as shown in Figure 5. This is different from the observations previously reported18 where hysteresis was found at 284 and 300 K, but no hysteresis existed at all if the initial pressure of desorption was just a little less than the saturation pressure. It was observed in our experiments that hysteresis may be caused by the condensation of CO2 in the tubing system. Such condensation would happen in the tube connecting the reference cell and the adsorption cell when the adsorption pressure is higher than the saturation pressure at room temperature. Although pressure decreases at desorption, it takes time for the liquid CO2 to evaporate, and fictitious hysteresis was thus recorded. To prevent CO2 condensation in any part of the system, all valves, the tubing, and the reference cell were set at 318 K, higher than the critical temperature, and the hysteresis phenomenon never appeared again. A maximum was observed in 292 and 298 K isotherms as shown in Figure 5, although it was not a feature of subcritical isotherms. A similar observation was also reported by Keller and co-workers.33

Determination of the absolute adsorption is the impediment of further development of supercritical adsorption theory presently. It cannot be measured directly by any means,34 yet it is the real mass confined in the adsorbed phase. Therefore, many properties of the adsorbed phase depend on the absolute amount, but not on the excess adsorption. A simple method to determine the absolute adsorption based on the experimental excess isotherm was proposed by the authors.22-24 The principle of the method comes from the Gibbs definition of adsorption:

n ) nt - VaFg

(1)

where n is the excess adsorption, nt is the absolute adsorption, Va is the volume of the adsorbed phase, and Fg is the density of bulk gas. If the product of VaFg can be neglect compared to the value of n, we have n ) nt. Therefore, we can use the experimental values of n that comply with the constraint to formulate the model of absolute adsorption isotherms. As is the usual practice in formulating experimental data, a linear plot was preferably obtained. The experimental data were transformed twice to reach a linear representation.23 The experimental data were utilized ultimately, and the data that did not comply with the constraint were sifted out during the transformations. A plot of ln[ln(δn)] versus 1/ln p (p in kPa) was thus constructed and is shown in Figure 7 for the nine isotherms collected. Parameter δ ) 1 for the present set of data, but it was set to 10 (ref 13) or 100 (ref 14) according to the magnitude of n values to avoid (33) Dreisbach, F.; Staudt, R.; Keller, J. U. High-Pressure Adsorption Data of Methane, Nitrogen, Carbon Dioxide and their Binary and Ternary Mixtures on Activated Carbon. Adsorption 1999, 5, 215-227. (34) Sircar, S. Ind. Eng. Chem. Res. 1999, 38, 3670.

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Figure 7. Linear plot of the excess adsorption for modeling the isotherms of absolute adsorption.

Figure 8. Parameters of the absolute adsorption isotherms as functions of temperature.

evaluating the logarithm of a negative number. A model with two parameters was obtained from the linear plots for the absolute adsorption isotherms:

[ (

nt ) exp exp R +

β ln p

)]

(2)

The value of parameters R and β is a function of temperature as shown in Figure 8. The absolute adsorption isotherms generated by the model are shown in Figures 9 and 10, respectively, for each side of the critical temperature. The absolute isotherms always continue to increase with pressure no matter how the excess isotherms behave. The difference between the absolute and the excess isotherm becomes remarkable on approaching the maximum at above-critical temperatures or when the excess isotherm approaches saturation for the subcritical conditions. 5. Discussion 5.1. Modeling the Subcritical Isotherms. Adsorption isotherms collected on a microporous adsorbent at subcritical temperatures show type-I features and are usually

Figure 9. Comparison of the excess with the absolute isotherms for the subcritical region.

Figure 10. Comparison of the excess with the absolute isotherms for the supercritical region.

modeled by the Langmuir or the Dubinin-Astakhov equation. However, these equations were initially derived for absolute adsorption and, therefore, must not describe the excess isotherms if the difference between them becomes remarkable as in those shown in Figure 9. The absolute adsorption determined above was presently used for modeling the excess isotherm based on the definition of adsorption shown in eq 1:

n ) n0t [1 - exp(-bpq)] - VaFg

(3)

where the first term of the right-hand side is an isotherm equation proposed recently35 for the absolute adsorption; Va, the volume of the adsorbed phase, was evaluated from

Va )

nt - n Fg

(4)

(35) Zhou, L.; Zhang, J.-Sh.; Zhou, Y.-P. A Simple Isotherm Equation for Modeling the Adsorption Equilibria on Porous Solids over Wide Temperature Ranges. Langmuir 2001, 17, 5503-5507.

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By a fit of eq 3 to the experimental isotherms through nonlinear regression, parameters of the model were evaluated. The excess isotherms predicted by the model are shown by curves in Figure 5. The model fits the experimental data (the dots) very well. 5.2. Modeling the Supercritical Isotherms. Modeling supercritical isotherms has attracted much research interest recently because these isotherms could not be modeled by conventional methods, and a successful modeling will help in understanding the nature of supercritical adsorption. Different strategies including the Ono-Kondo equation36,37 and nonlocal38 or simplified local density approaches39,40 were introduced into the modeling of supercritical isotherms. Different forms of equations of state were also proposed for the modeling.41,42 Each method achieved success for some conditions. However, these models are too complicated to use and the physical nature of the adsorption was to some extent blurred by complicated mathematical expressions. Besides, a problem deserves to be considered in choosing models: does the method or the prerequisite of using the method comply with the physical state of the adsorbed phase at abovecritical temperatures? For example, any equation of state of real gases is applied only to fluids without borders, which limits the interaction between molecules only to the fluid. However, the behavior of the adsorbed phase, no matter in small pores or on a flat surface, is dominated mainly by the interaction between gas molecules and solid atoms at the interface. There are arguments43 that the adsorbate can only be a monolayer at supercritical temperatures. The legality of applying an EOS to such a layer is doubtful. Any EOS was derived from many experiments that were carried out on massive fluids. The applicability of the EOS to a fluid confined in a pore space of nanometer dimensions is also doubtful. Besides, a continuous change of density cannot exist in the normal direction of the solid surface at supercritical temperatures, which is the assumption of some mathematical models. In fact, as shown by eq 1, it is the second term of the right-hand side of the equation, that is, the product of gas-phase density and the volume of the adsorbed phase, that caused the difference between the excess and the absolute adsorption. The excess adsorption isotherms would be pertinently described if the product term could be properly accounted for. The problem is how to determine the volume of the adsorbed phase, Va. A method was proposed for the determination of the absolute adsorption based on the experimental excess adsorption data as shown above, and Va was calculated according to eq 4. This (36) Aranovich, G. L.; Donohue, M. D. Adsorption of supercritical fluids. J. Colloid Interface Sci. 1996, 180, 537-541. (37) Be´nard, P.; Chahine, R. Modeling of High-Pressure Adsorption Isotherms above the Critical Temperature on Microporous Adsorbents: Application to Methane. Langmuir 1997, 13, 808-813. (38) Jiang, S. Y.; Zollweg, J. A.; Gubbins, K. E. High-pressure adsorption of methane and ethane in activated carbon and carbon fibers. J. Phys. Chem. 1994, 98, 5709-5713. (39) Chen, J. H.; Wong, D. S. H.; Tan, C. S.; Subramanian, R.; Lira, C. T.; Orth, M. Adsorption and desorption of carbon dioxide onto and from activated carbon at high pressures. Ind. Eng. Chem. Res. 1997, 36, 2808-2815. (40) Soule, A. D.; Smith, C. A.; Yang, X.-N.; Lira, C. T. Adsorption modeling with the ESD equation of state. Langmuir 2001, 17, 29502957. (41) Aranovich, G. L.; Donohue, M. D. Surface compression in adsorption systems. Colloids Surf., A 2001, 187-188, 95-108. (42) Ustinov, E. A.; Do, D. D.; Herbst, A.; Staudt, R.; Harting, P. Modeling of gas adsorption equilibrium over a wide range of pressure: A thermodynamic approach based on equation of state. J. Colloid Interface Sci. 2002, 250, 49-62. (43) Zhou, L.; Zhou, Y.-P.; Li, M.; Chen, P.; Wang, Y. Experimental and Modeling Study of the Adsorption of Supercritical Methane on a High Surface Carbon. Langmuir 2000, 16, 5955-5959.

Zhou et al.

Figure 11. A comparison of the DRK plot between the excess and the absolute adsorption.

method does not have assumptions or prerequisites. It has been satisfactorily applied for modeling the gas/solid adsorption equilibrium over wide ranges of temperature and pressure.13,14,35,43 As has just been shown above, the method applies also for a subcritical isotherm with a maximum. However, it has not been applied for the experimental isotherms that are densely distributed as near to the critical temperature as the isotherms shown in Figure 6. There are three parameters in eq 3: n0t , b, and q. Parameter n0t is the saturation quantity of absolute adsorption since nt ) n0t when p approaches infinity, b is a parameter related to the adsorption energy, and q is a parameter related to the surface heterogeneity. By a fit of eq 3 to the six isotherms in the range of 307-360 K and 0-18 MPa by nonlinear regression, model parameters were evaluated and the model was thus established. As shown by the curves in Figure 6, the model fits all experimental data very well. The discrepancy between the model and experimental isotherms was measured by

d%)

1

Nt

[

1

Nm 100

∑ ∑ N j)1 N i)1 t

m

]

× ABS(ncal - nexp) nexp

(5)

where nexp is the experimentally measured amount adsorbed, ncal is the value predicted by the model, Nm is the number of data of an isotherm, and Nt is the number of isotherms. The general discrepancy of the model with the experimental isotherms is less than (1% for the subcritical isotherms and less than (2% for the supercritical isotherms. Numerical consistency is important for a model, but still not enough to be physically meaningful. Parameters of the model have definite physical meaning, because of which they must reasonably vary with temperature. As shown in Figures 12-14, the variation of parameters with temperature is reasonable. Parameter n0t decreases with increasing temperature; however, it becomes constant when the temperature departs from the critical44 as is the case at 340 and 360 K. Parameter b is (44) Zhou, L.; Zhou, Y.-P.; Bai, Sh-P.; Lu¨, Ch.-Zh.; Yang, B. Determination of the Adsorbed Phase Volume and Its Application in Isotherm Modeling for the Adsorption of Supercritical Nitrogen on Activated Carbon, J. Colloid Interface Sci. 2001, 239, 33-38.

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Figure 12. Variation of n0t with T.

Figure 14. Variation of q with T.

Figure 13. Variation of b with T.

Figure 15. Density of the adsorbed phase.

much higher in the subcritical region than in the supercritical one, indicating a large difference in adsorption energy. Parameter q relates to the energetic heterogeneity of the surface, and the surface would be uniform if q ) 1. It seems that the energetic heterogeneity of the surface would be detected less at the critical temperature since q showed the highest value. 5.3. Estimation of the Number of Adsorbate Layers in the Adsorbed Phase. The adsorption mechanism would be clear if the number of adsorbate layers in the adsorbed phase could be evaluated. The number of adsorbate layers can be estimated via a simple relation:

Va ) Aσλ

(6)

where Va is the volume of the adsorbed phase; A is the specific surface area of the adsorbent, and A ) 3424 m2/g as determined by the absolute adsorption isotherm in the subsequent section and as shown in Figure 11; λ is the average number of adsorbate layers; and σ is the average reach of an adsorbed adsorbate molecule, which is estimated by

σ ) [1/(10-3FaAv)]1/3 (cm)

(7)

where Fa is the density of the adsorbed phase (mmol/cm3) and Av is the Avogadro number. It is clear that the values of Va and Fa must be known for the determination of λ. As mentioned above, Va was calculated from the value of nt via eq 4, and Fa ) nt/Va. As indicated previously,45 the value of Fa determined as such became stable only at relatively high pressure due to numerical reasons and the larger experimental error at low pressures. The stable value of Fa is shown in Figure 15. An average value of 19.86 mmol/cm3 was obtained for 307-318 K, and 19.03 mmol/cm3 was the average for 323-360 K. The value of σ was 4.37 × 10-8 and 4.44 × 10-8 cm, respectively, as determined from eq 7. The volume of the adsorbed phase is a function of temperature and of pressure.44 However, the highest value of Va at each temperature should be used for the evaluation of λ and is shown in Figure 16. The result of the calculation of λ is shown in Table 1. As shown in the table, a multilayer adsorption mechanism was possible for the near-critical region due to the special property of the fluid. However, the average number of adsorbate layers is less than unity at temperatures fairly (45) Zhou, L.; Li, M.; Zhou, Y.-P. Measurement and theoretical analysis of the adsorption of supercritical methane on superactivated carbon. Sci. China, Ser. B 2000, 43, 143-153.

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Figure 16. Volume of the adsorbed phase. Table 1. Adsorbate Layers in the Adsorbed Phase T, K λ

307

313

318

323

340

360

1.20

1.12

1.06

1.00

0.87

0.82

far away from the critical zone, and monolayer adsorption seems the inevitable mechanism. 5.4. What Isotherm Should Be Used for the Characterization of Adsorbent? The volume of pores was usually estimated by dividing the amount adsorbed at a relative pressure of p/ps ) 0.95 (saturation is actually reached) by the density of saturated liquid if the isotherm is type I.26 The underlined assumption of the method is assuming the space of pores was filled by liquid adsorbate. Therefore, the quantity of adsorbate should be the total amount that fills in the pore space. However, any quantity determined on an excess isotherm is not the total mass of the adsorbed phase but only a part, although the major part, of it. As shown in Figure 9 for 273 K, the difference between the absolute and the excess isotherms is considerable when the excess adsorption seems saturated. Because the absolute isotherm corresponds to the total mass in the adsorbed phase, pore volume should be determined based on it. It is seen also that the absolute isotherm intersects the “condensation line” when pressure approaches saturation, which proves a convention that the adsorbed phase has the same state as the saturation liquid. The amount determined on the absolute isotherm at ps is the saturated amount of absolute adsorption, which does not include any amount of condensation since ps is the border between adsorption and condensation. Any amount condensed should be located on the vertical line of p ) ps. It was thus concluded that pore volume should be evaluated by dividing the absolute amount adsorbed at the pressure approaching saturation by the liquid density. For example, the pore volume of the sample would be 1.52 cm3/g based on the absolute adsorption compared to 1.27 cm3/g based on the excess adsorption. The relative difference is as large as 20%. The difference in the DRK plot between the excess and the absolute adsorption is

also considerable as shown in Figure 11. The intercept of the two plots is 1.43 and 1.49, respectively, yielding a relative difference of 15% in the surface area. Both pore volume and the specific surface area of the adsorbent will have a minus 15-20% error if they are evaluated based on the excess isotherm. Such a difference cannot be neglected and should be considered for all cases when the excess adsorption isotherm, on which the characterization relied, is type I. Characterization of porous solids is still a lively topic of research, yet the adsorption isotherm of N2 at 77 K and that of CO2 at 273 K are widely applied for the characterization of microporous adsorbents. The latter was claimed to discover even smaller pores for adsorbents of a nonpolar surface such as activated carbon. The excess isotherm of CO2 at 273 K can be easily transformed to the absolute adsorption isotherm as shown above. Most experimental points would be on the linear plot because the adsorption pressure is lower than the saturation one as shown in Figure 7; therefore, the absolute adsorption determined is more reliable. However, some points at the lowest pressure might not be on the linear plot due to the large relative error of measurement when the pressure is close to zero. 6. Conclusions 1. One has to pay attention to the precision and constancy of pressure and temperature readings and also to how the compressibility factor was determined to have a reliable result for adsorption measurement for the nearcritical region. Any larger error will mask the behavior of isotherms collected. 2. The product of gas-phase density with the volume of the adsorbed phase is the exclusive reason causing the difference between the excess and the absolute adsorption. It causes the appearance of a maximum and a negative increment on isotherms not only in the supercritical region but also possibly in the subcritical region. All the experimental excess isotherms could be pertinently modeled by properly accounting for the product term. 3. On the basis of the volume and density of the adsorbed phase that were evaluated from experimental data, one can conclude that a multilayer adsorption mechanism could function for near-critical temperatures, but not for temperatures fairly far away from the critical. 4. Instead of the excess isotherm, the absolute isotherm should be used to characterize adsorbents if the adsorption isotherm of CO2 at 273 K is relied on and the isotherm shows the features of type I. About 15-20% relative error might be produced otherwise. Such an excess isotherm can be transformed to the absolute one easily and reliably using the method proposed. Acknowledgment. This work was subsidized by the Special Funds of Major State Basic Research Projects (G2000026404) and supported by the National Natural Science Foundation of China (No. 29936100). The software for calculating the p-V-T data of CO2 was kindly provided by Professor W. Wagner, whom the authors gratefully acknowledge. LA020682Z