146
Langmuir 2008, 24, 146-154
Kinetic Restriction of Simple Gases in Porous Carbons: Transition-State Theory Study Thanh X. Nguyen and Suresh K. Bhatia* DiVision of Chemical Engineering, The UniVersity of Queensland, St. Lucia, Brisbane QLD 4067, Australia ReceiVed August 10, 2007. In Final Form: October 5, 2007 The separation of simple gases such as N2, Ar, CO2, and CH4 is an industrially important problem, particularly for the mitigation of greenhouse emissions. Furthermore, these gases are widely accepted as standard probing gases for the characterization of the microstructure of porous solids. However, a consistent set of microstructural parameters of a microporous solid determined from the use of adsorption measurements of these different gases is not always achieved because of differences in their pore accessibility. This is a long-standing and poorly understood problem. Here, we present the calculated results of the crossing time of N2, Ar, CO2, and CH4 between two neighboring cages through a constricted window in a realistic structural model of saccharose char, generated from hybrid reverse Monte Carlo (HRMC) simulation (Nguyen, T. X.; Bhatia, S. K.; Jain, S. K.; Gubbins, K. E. Mol. Simul. 2006, 32, 567-577) using transition state theory (TST), as described in our recent work (Nguyen, T. X.; Bhatia, S. K. J. Phys. Chem. 2007, 111, 2212-2222). The striking feature in these results is that whereas very fast diffusion of carbon dioxide within the temperature range of 273-343 K, with crossing time on the molecular dynamics scale (10-4-10-6 s), leads to instantaneous equilibrium and no hysteresis on the experimental time scale, slower diffusion of Ar and N2 at the low temperature of analysis indicates an accessibility problem. These results rationalize the experimental results of hysteresis for N2 at 77 K and Ar at 87 K but not for CO2 at 273 K in Takeda 3 Å carbon molecular sieves. Furthermore, it is shown that CH4 diffusion through narrow pore mouths can be hindered even at ambient temperature. Finally, we show that the use of pore size and wall thickness distributions extracted from the adsorption of Ar at 87 K using the finite wall thickness (FWT) model (Nguyen, T. X.; Bhatia, S. K. Langmuir 2004, 20, 3532-3535 and Nguyen, T. X.; Bhatia, S. K. J. Phys. Chem. B 2004, 108, 14032-14042) provides the correct prediction of experimental CO2 adsorption in BPL and PCB carbons whereas that from N2 at 77 K gives a significant underprediction for both CO2 and CH4 in the BPL carbon. These trends are in excellent agreement with those predicted using the calculated crossing times.
Introduction The separation of carbon dioxide from flue gas, or its mixture with methane, is a problem of immediate importance in industry. In the former case, the separation is a key step in its capture and storage, necessitated by the urgent need to mitigate greenhouse gas emission and combat global warming. In the latter case, the removal of carbon dioxide is also an important means of improving calorific value (e.g., of natural gas or biogas or of coal bed methane in conjunction with carbon dioxide sequestration). The separation of carbon dioxide may be accomplished in various ways, the most common of which are based on chemical absorption or physical adsorption. For instance, an existing and fairly mature technology based on the former is the use of monoethanolamine (MEA) scrubbing to capture carbon dioxide present at low concentration in flue gases. However, this technique is costly because of the large heat requirement for the regeneration of the MEA solvent. It is now recognized that the separation of carbon dioxide on the basis of physical adsorption using pressure swing adsorption (PSA) provides a number of advantages over chemical absorption. For instance, the former technique enables high-temperature operation, which is energetically efficient given the high operating temperature of power plants as well as the low heat requirement for the desorption of the gas physically interacting with the adsorbent surface. In PSA technology, carbon molecular sieves are widely used as selective adsorbents because of their extremely high selectivity and large surface area. The former property distinguishes carbon molecular sieves from normal porous * Author to whom correspondence may be addressed. E-mail: s.bhatia@ eng.uq.edu.au.
carbons. The extremely high selectivity of carbon molecular sieves (CMS) is due to the extremely large difference between the diffusion rates of different species of a mixture resulting from the highly constricted nature of pore entrances having sizes comparable to molecular dimensions. Although experimental methodologies to control the size of the pore mouth such as heat treatment5 or chemical vapor deposition (CVD)6,7 are well known, the effect of the structure of the pore mouth constriction on the adsorbate diffusion rate is not experimentally accessible at the molecular level because of the complexity of the carbonaceous microstructure. There have been numerous theoretical investigations of the effect using an arbitrarily constructed 2D pore mouth.8 However, the microstructure of porous carbons is not strictly ordered, and the microstructure of the pore mouth in porous carbon is expected to be 3D. This means that carbon atoms of the pore mouth, which dominate the interaction with adsorbate molecule located at the saddle point (i.e., the top energy barrier point) do not essentially lie within the dividing surface. As a consequence, an arbitrarily constructed 2D pore mouth may not realistically capture the strength of solid-fluid interaction with carbon atoms of the pore mouth or the activation energy that predominantly dictates the diffusion rate through the pore mouth. For this reason, a realistic carbon structure such as that generated (1) Nguyen, T. X.; Bhatia, S. K.; Jain, S. K.; Gubbins, K. E. Mol. Simul. 2006, 32, 567-577. (2) Nguyen, T. X.; Bhatia, S. K. J. Phys. Chem. C 2007, 111, 2212-2222. (3) Nguyen, T. X.; Bhatia, S. K. Langmuir 2004, 20, 3532-3535. (4) Nguyen, T. X.; Bhatia, S. K. J. Phys. Chem. B 2004, 108, 14032-14042. (5) Mochida, I.; Yatsumani, S.; Kawabuchi, Y.; Nakayama, Y. Carbon 1995, 33, 1611-1619. (6) Verma, S. K.; Walker, P. L., Jr. Carbon 1990, 29, 175-184. (7) Kawabuchi, Y.; Oka, H.; Kawano, S.; Mochida, I.; Yoshiyawa, N. Carbon 1998, 36, 377-382. (8) Rallabandi, P. S.; Ford, D. M. AIChE J. 2000, 46, 99-109.
10.1021/la702471d CCC: $40.75 © 2008 American Chemical Society Published on Web 11/29/2007
Kinetic Restriction of Gases in Porous Carbons
from HRMC simulation1 is crucial for the above task. This research builds on this idea and offers the potential to optimize the size of pore entrances in CMS materials and operating temperature for the complete separation of carbon dioxide from mixtures (flue gas, natural gas, and biogas) with small molecules (CH4, H2, Ar, and N2), which differ in terms of molecular size from carbon dioxide only marginally. The theoretical investigation of the activation diffusion also provides insight into open hysteresis loops, which are experimentally observed from the adsorption of simple gases in microporous carbons.9-15 It is due to the fact that activated diffusion through the pore mouth between two neighboring pores may be extremely slow on practical time scales even under supercritical conditions and prevents true adsorption equilibrium between these pores. In this case, if the desorption time is longer than the adsorption time and outside the experimental time scale, then an open hysteresis loop is normally observed.9-15 Such hysteresis is a very important feature in the long-term storage of carbon dioxide in unused coal mines. However, if the adsorption time is outside the practical time scale, then this creates an accessibility problem that has a serious impact on characterization results and therefore on the subsequent prediction of adsorption equilibrium and dynamics. Finally, the theoretical research of the activation diffusion process helps to elucidate a long-standing problem related to the pore accessibility of N2, Ar, CO2, and CH4 in porous materials. The understanding of this problem plays a key role in the proper selection of the probing gas and conditions used for the characterization of porous materials using adsorption. In particular, N2, Ar, CO2, and CH4 are widely accepted in the existing literature as standard probing gases for the characterization of porous materials. Among these gases, the subcritical adsorption of N2 at 77 K is most commonly used because of its relatively low cost, and in principle, it enables one to detect a full range of micropore sizes. CO2 adsorption at 273 K under subatmospheric pressure is normally utilized to characterize the microstructure of coal and carbon molecular sieves16 in which the N2 molecule has a diffusional problem at 77 K. However, CO2 adsorption under subatmospheric conditions enables the detection of only the lower range of micropore size (10 Å) is difficult to characterize accurately by this method because of the weak adsorption of CH4 in this range. Consequently, the pore size distribution (PSD) determined from CH4 adsorption does not normally provide correct predictions for other gases.19 Ar is a spherical, nonpolar molecule that requires much simpler theoretical treatment in comparison to CO2 and N2. Furthermore,
Langmuir, Vol. 24, No. 1, 2008 147
Ar has a similar molecular size to N2, and the use of subcritical adsorption of Ar at 87 K therefore permits one to probe a similar range of micropore size, as subcritical N2 adsorption. However, Ar liquid is much more expensive than liquid N2, and for this reason, Ar adsorption at 77 K20 is in practice preferred for the characterization of porous materials because of the low cost of N2 liquid. The use of Ar adsorption at 87 K for the characterization of porous carbons has been scarce.3,4,21-22 Consequently, a question asked here is whether Ar at 87 or 77 K and N2 at 77 K have similar accessibility to porous materials. In recent work,2 we have proposed a novel algorithm that enables one to determine the pore accessibility in an atomistic structural model of a disordered nanoporous material. This algorithm has been successfully utilized to determine the pore accessibility of nitrogen and argon in the atomistic structural model of a saccharose char obtained using the hybrid reverse Monte Carlo technique (HRMC)1 and further validated by means of crossing times of pore mouth barriers using transition-state theory (TST). In this earlier work, we found temperaturedependent pore accessibility for nitrogen and argon based on the structural model of saccharose char and a pore accessibility problem for nitrogen at 77 K but not for argon at 87 K. In the present work, we determine the crossing time of CO2 and CH4 in the saccharose char for a wide temperature range using transition-state theory.2 We identify the consequences of the differences in crossing times for three important concerns. These are the issues of selectivity for separation, adsorption hysteresis in micropores, and accessibility of micropores. Furthermore, experimental adsorption measurements of N2 at 77 K, Ar at 87 K, and CO2 at 273 K in porous carbons were also conducted in this work to validate our calculated results. Experimental Section Three commercialized carbons (carbon molecular sieve Takeda 3 Å (CMS-T3A), BPL, and PCB activated carbon) were degassed at 300 °C overnight prior to adsorption measurement. CMS-T3A is supplied by Takeda Chemical Company, and BPL and PCB carbons, by Calgon Corpn. A Micromeritics ASAP 2010 volumetric adsorption analyzer was used to measure adsorption isotherms of N2 at 77 K, Ar at 87 K, and CO2 at 273 K and subatmospheric pressure in T3A. For the BPL and PCB activated carbons only, the adsorption measurement of N2 at 77 K was performed. Adsorption data of Ar at 87 K in this carbon was taken from our previous work.3,4 Mathematical Modeling. Transition-State Theory. We apply transition-state theory, as described in our recent work,2 to determine the crossing time of a single CO2 or CH4 molecule between two cages (cage A to cage B) or adsorption times, τAfB, and vice versa (i.e., desorption time, τBfA) in the atomistic structural model of saccharose char1 at the low loading limit. Cages A and B were identified in our recent work2 and are illustrated in Figure 1 in this work. According to TST, the crossing time is given as τAfB )
(9) Koresh, J. E. J. Chem. Soc., Faraday Trans. 1993, 89, 935-937. (10) Koresh, J. E.; Kim, T-H.; Walker, D. R. B.; Koros, W. J. J. Chem. Soc., Faraday Trans. 1990, 86, 2267-2270. (11) Makashima, M.; Shimda, S.; Inagaki, M. Carbon 1995, 33, 1301-1306. (12) Mangun, C. L.; Daley, M. A.; Braatz, R. D.; Economy, J. Carbon 1998, 36, 123-131. (13) Carrott, P. J. M.; Cansado, I. P. P.; Carrott, M. M. L. R. Appl. Surf. Sci. 2006, 252, 5948-5952. (14) Rychlicki, G.; Terzyk, A. P.; Zawadzki, J. Pol. J. Chem. 1995, 69, 13281334. (15) Busch, A.; Gensterblum, Y.; Krooss, B. M. Int. J. Coal Geol. 2003, 55, 205-224. (16) Lozano-Castello´, D.; Cazorla-Amoro´s, D.; Linares-Solano, A. Carbon 2004, 42, 1233-1242. (17) Fre`re, M.; Weireld, G. D.; Jadot, R. J. Porous Mater. 1998, 5, 275-287. (18) Quirke, N.; Tennison, S. R. R. Carbon 1996, 34, 1281-1286. (19) Heuchel, M.; Davies, G. M.; Buss, E.; Seaton, N. A. Langmuir 1999, 15, 8695-8705.
1 kAfB
(1)
where kAfB is a diffusion rate constant, written2 as kAfB ) κ
x
kBT 2πm
∫ ∫
DS
e-βφsf(r) d2r
Vcage A
e-βφsf(r) d3r
(2)
Here, κ is a transmission coefficient that represents the fraction of particles starting on top of the barrier with velocity toward cage B (20) Ravikovitch, P. I.; Vishnyakov, A.; Russo, R.; Neimark, A. V. Langmuir 2000, 16, 2311-2320. (21) Nguyen, T. X.; Bhatia, S. K. Carbon 2005, 43, 775-785. (22) Olivier, J. P. Carbon 1998, 36, 1469-1472.
148 Langmuir, Vol. 24, No. 1, 2008
Nguyen and Bhatia investigated carbons (T3A, BPL, PCB) as well as to predict gas adsorption in these carbons. The FWT model was previously described in detail elsewhere.3,4 In summary, the FWT model, based on the slit-pore model, approximates the microstructure of porous carbons in terms of a set of unconnected slit-like pores, with carbon walls having a finite number of perfect graphite sheets. Accordingly, the general adsorption isotherm (GAI), in terms of the excess adsorbed amount, Γex(P), is given as Γex(P) )
∫[Fˆ (P, H ) - F ]f(H ) dH in
b
in
(8)
in
where f(Hin) is the pore size distribution of the adsorbent, Hin ) (Hcc - σc) is the geometrical pore width, Hcc is the physical pore width, σc is the effective diameter of the carbon atom, and Fb is the bulk density. Fˆ (P, Hin) is the average density in a pore of width Hin at a given pressure P. The average density is expressed23 as ∞
Fˆ (P, Hin) )
∑
∞
p(m)
that successfully reaches cage B, kB is the Boltzmann constant, T is the temperature, and m is the mass of the particle. As recently shown,2 κ is approximately unity for N2 and Ar. In this work, κ is taken to be unity for CO2 and CH4. φsf is the interaction potential between adsorbate particle i at position r and all solid atoms of the adsorbent phase, given as φsf(r) )
∑ u(|r - r|)
(3)
j
j)1
[( ) ( ) ]
u(r) ) 4sf
12
σsf r
[( ) ( ) ]
φff(r) ) 4ff
6
(4)
In accordance with our recent approach of TST,2 the crossing time of a single particle, τAfB, from cage A to B is finally obtained as τAfB )
x
b κ
2πm βEa e kBT
(5)
where β ) 1/kBT and Ea is the effective activation energy, given as Ea ) 〈φsf〉N,Vbox,T + kBT ln
(∑ n)1
-βφsf(rn)
e
)
(6)
Here, τmax is the number of grid points in cage A or B, rn is the coordinate of grid points in cage A, and b is the width of a small cubic box, which contains the dividing surface. In what follows, we take b to be 0.1 Å, for which the deviation of the minimum-energy point of the surface parallel to the dividing surface from that at the saddle point is negligible and within 0.3%, as described in our recent paper.2 Thus, the width of box, b, seems to be only very slightly sensitive to the investigated species (Ar, N2, CH4, CO2). For the determination of top barrier energy, 〈φsf〉N,Vbox,T, given by the first term on the right-hand side (R.H.S.) of eq 6, the dividing surface for the investigated compounds (CH4, CO2) between two cages A and B is determined using a two-step procedure that was previously presented in detail in our earlier paper.2 Finally, the second term on the R.H.S. of eq 6 or free energy in cages A or B is determined using a grid point size of 0.05 Å. Further details of the determination of the activation energy are provided in our recent work.2 Finite Wall Thickness Model (FWT). In this work, we utilized our recently proposed characterization procedure, the FWT model, to obtain PSD and the pore wall thickness distribution (PWTD) of the
(9)
σff r
12
-
σff r
6
(10)
where r is the interparticle distance, σff is the collision diameter, and ff is the well depth. Following the WCA separation,25 the attractive part of this potential is represented as
[
φatt(|r - r′|) ) φff(|r - r′|) |r - r′| > rm ) -ff |r - r′| < rm
]
(11)
where rm ) 21/6φff. The interaction potential, φwf (z), between a carbon wall and an adsorbate molecule is represented by26,27 n-1
τmax
Fl m(P, Hin, z) dz
in
where p(n) is a wall thickness probability distribution and Flm(P, Hin, z) is the local density profile in a pore of geometrical width Hin, with the left wall having λ graphene layers and the right wall having m layers. Here we assume that the thicknesses of the two opposing walls of a pore are uncorrelated and that the interaction potential between adsorbed molecules in neighboring pores is insignificant in comparison to the fluid-solid potential energy, justified by the recent study from this laboratory.4 The local density profile is determined using Tarazona nonlocal density functional theory (NLDFT)24 with fluid-fluid and solid-fluid potential models that are described as follows Potential Models. The interaction potential between fluid molecules is taken as the Lennard-Jones 12-6 potential
where u is the LJ (12-6) solid-fluid pair potential σsf r
Hcc
0
l )1
m)1
Figure 1. Snapshot of the converged configuration of activated saccharose char.1 Cages A and B depict the open and closed pores, respectively, detected in our recent work.2
1
∑ p(l ) H ∫
φwf(z, n) ) 2πFcσcf2∈cf
∑ i)0
[ ( ) ( )] 2
σcf
5 z + i∆
10
-
σcf
4
z + i∆
z > 0 (12)
Here, z is the center-to-center distance between the fluid molecule and the pore wall surface, n is the number of graphene layers in the pore wall, ∆ is the interlayer spacing, and Fc is the number of carbon (23) Bhatia, S. K. Langmuir 1998, 14, 6231-6240. (24) Tarazona, P. Phys. ReV. A 1985, 31, 2672-2679. Tarazona, P. Phys. ReV. A 1985, 32, 3148-3148. Tarazona, P.; Marconi, U. M. B.; Evans, R. Mol. Phys. 1987, 60, 573-595. (25) Weeks, J. D.; Chandler, D.; Andersen, H. C. J. Chem. Phys. 1971, 54, 5237. (26) Steele, W. A. Surf. Sci. 1973, 36, 317-352. (27) Mays, T. J. Simulations of Adsorption and the Design of Activated Carbons. In Fundamentals of Adsorption: Proceedings of the Fifth International Conference on Fundamentals of Adsorption; Le Van, M. D., Ed.; Kluwer Academic Publishers: Boston, 1996; pp 603-610. (28) Lastoskie, C. M.; Gubbins, K. E.; Quirke, N. J. Phys. Chem. 1993, 97, 4786-4796. (29) Ustinov, E. A.; Do, D. D. Langmuir 2003, 19, 8349-8357. (30) Nguyen, T. X.; Bhatia, S. K.; Nicholson, D. Langmuir 2005, 21, 31873197. (31) Vishnyakov, A.; Ravikovitch, P. I.; Neimark, A. V. Langmuir 1999, 15, 8736-8742.
Kinetic Restriction of Gases in Porous Carbons
Langmuir, Vol. 24, No. 1, 2008 149
Table 1. Lennard-Jonnes (LJ) Parameters for the Investigated Gases Used in This Work gas
σff(Å)
N2 CH4 CO2
3.572 3.6177 3.472
CH4 CO2
3.81 3.6481
ff/kB (Å)
σcf(Å)
sf/kB (Å)
source
53.22 64.14 78.84
28 29 30
Transition-State Calculations 148.1 3.605 64.40 246.15 3.429 81.49
26 31
NLDFT Calculations 93.98 3.494 146.91 3.509 221.98 3.436
Table 2. Calculated Results of the Crossing Time of CO2 and CH4 between Cages A and B for the HRMC-Based Structural Model of Saccharose Char1 Using the TST Approach CO2
CH4
temp (K)
τads(AfB) (s)
τdes(BfA) (s)
temp (K)
τads(AfB) (s)
τdes(BfA) (s)
273 283 293 303 313 323
5.9209 × 10-5 3.7958 × 10-5 2.529 × 10-5 1.7468 × 10-5 1.2408 × 10-5 9.0849 × 10-6
1.7996 × 10-4 9.5426 × 10-5 5.2853 × 10-5 3.0498 × 10-5 1.8187 × 10-5 1.1234 × 10-5
200 253 263 273 283 323
4.4559 × 107 8.2091 × 103 2.4836 × 103 8.2799 × 102 3.0135 × 102 1.0488 × 101
5.3373 × 107 3.8807 × 103 9.9048 × 102 2.7938 × 102 8.6321 × 101 1.6270 × 100
atoms per unit area in a single graphene layer. Following Steele,26 the parameters ∆ ) 0.335 nm and Fc ) 38.17 atoms nm-2, corresponding to graphite, are used. The asymmetric external potential profile, φext(z, l, m), for a slit-shaped pore with pore size H is determined from the superposition of the potentials of the opposing pore walls φext(z, l, m) ) φwf(z, l ) + φwf(H - z, m)
(13)
where λ and m are arbitrary numbers of graphene layers in the two opposing walls. From eq 8, the PSD and PWTD of a porous carbon can be simultaneously determined by minimization of the difference between theoretical and measured excess adsorbed amounts of probing gas such as N2, Ar, CO2, or CH4. Conversely, the theoretical excess adsorbed quantity of adsorbate in a carbon can be determined if the PSD and PWTD are known.
Results and Discussion All Lennard-Jones (LJ) parameters of CO2 and CH4 used to determine their crossing time between cages A and B using TST are presented in Table 1. Solid-fluid LJ parameters, which are determined using Lorentz-Berthelot rules, are also given in this Table. The calculated results of the crossing time of CO2 in the 273-343 K temperature range and the crossing time of CH4 in the 200-343 K temperature range obtained in this work, following eq 5, are given in Table 2. These investigated temperature ranges are selected for their practical interest. At high temperature, the crossing time of CO2 is within the molecular dynamics time scale, as seen in Table 2, where the TST may be less accurate. However, we have already2 validated the TST calculation of the crossing time of N2 at 300 K where the energy barrier is small in comparison with kinetic energy (kBT/2) against equilibrium molecular dynamics (EMD) simulation. At this high temperature, we obtained a mean crossing time of N2 of 455 ns using EMD, which is reasonably close to that calculated using TST (486 ns). Consequently, the verification of the crossing time of CO2 against EMD is unnecessary and is not attempted here because of the fact that it is quite similar to that of N2 at 300 K. A detailed discussion of these results is given below. Selectivity. From Table 2, it can be seen that the crossing times of CO2 and CH4 between cages A and B are strongly temperature-dependent, as observed for Ar and N2 in our recent work.2 Such a strong temperature dependence is characteristic
of adsorption by activated diffusion. It is interesting to see that CO2 diffuses faster than CH4 by several orders of magnitude. In particular, the crossing time of the former at the investigated temperatures (10-6-10-4 s) lies within the molecular dynamics time scale whereas the crossing time of CH4 ranges from several to a few hundred seconds in the same temperature range and is greater than a few hours in the lower temperature range ( 6 Å). From the Figure, it is evident that the PSD in the smaller pore size range ( 6 Å). Hin is the internal pore width.
Figure 4b. It is noted that from our previous work30 the fraction of pore volume of this carbon that is accessible to CH4 (AV ) 0.86) is slightly smaller than that for the BPL carbon (AV ) 0.91). However, the intensity of the second and third peaks of the PSD results of the PCB carbon obtained from Ar adsorption at 87 K is only slightly higher than that from N2 adsorption at 77 K, by an amount that is much less than that observed for the BPL carbon. This may be due to the nonspherical nature of the N2 molecule and is discussed in detail in the following paragraphs. Figure 5a depicts our prediction of the CO2 adsorption isotherms at 273 and 323 K in the BPL carbon using structural parameters (PSD and PWTD) determined from N2 adsorption 77 K and Ar adsorption at 87 K. The experimental adsorption data of CH4 and CO2 in the BPL carbon are taken from Himeno et al.36 Figure 5a shows that the use of the structural parameters (PSD and PWTD), determined from Ar adsorption 87 K, provides the correct prediction (solid and dashed lines) of CO2 adsorption measurements at 273 K (filled triangles) and 323 K (empty triangles). On the contrary, the use of the structural parameters (PSD and PWTD) determined from N2 adsorption at 77 K dramatically underpredicts the adsorption measurements of CO2, especially in the high-pressure range. Similarly, Figure 5b also shows that the use of PSD and PWTD extracted from Ar adsorption at 87 K also gives the correct prediction of adsorption data of CO2 in PCB carbon at 373 and 480 K. The CO2 adsorption measurement in PCB is taken from Ritter et al.37 However, the use of PSD and PWTD of PCB extracted from N2 adsorption at 77 K also predicts (36) Himeno, S.; Komatsu, T.; Fujita, S. J. Chem. Eng. Data 2005, 50, 369376. (37) Ritter, J. A.; Yang, R. T. Ind. Eng. Chem. Res. 1987, 26, 1679-1686.
152 Langmuir, Vol. 24, No. 1, 2008
Figure 5. Experimental adsorption isotherms of CO2 in (a) BPL carbon36 at 273 K (4) and 323 K (0) and (b) PCB carbon37 at 373 K (4) and 480 K (0) and FWT model predictions. Solid and dashed lines depict the predicted CO2 isotherms (a) at 273 and 323 K and (b) at 373 and 480 K, respectively, using the structural parameters (PSD and PWTD) determined from Ar adsorption at 87 K. Similarly, dotted and dashed-dotted lines illustrate the predicted CO2 isotherms (a) at 273 and 323 K and (b) at 373 and 480 K, respectively, using the structural parameters (PSD and PWTD) determined from N2 adsorption at 77 K.
the CO2 data equally well in the low-pressure range ( 6 Å) of the PCB carbon, as discussed in the preceding paragraph. The above results strongly suggest that there is a diffusional problem for N2 adsorption at 77 K but not for Ar adsorption at 87 K and for CO2 adsorption at 273 K or higher temperature in the BPL carbon. This result is similar to that predicted in our recent work.2 As a consequence, it is obvious from this work that the use of Ar adsorption at 87 K for the characterization of microporous materials is a better choice than N2 at 77 K. Figure 6a depicts that the use of N2 adsorption 77 K significantly underpredicts the adsorption measurement of CH4 at 273 K (empty triangle) and 333 K (filled triangle). This is consistent with the prediction of the crossing time of CH4 (< 800 s at T > 273 K) presented in this work. However, whereas the calculated results of the crossing time in the saccharose char for Ar at 87 K, as shown in Figure 2, and CH4 in the 273-343 K range, as seen in Table 2, show no accessibility problem for these gases, the use of Ar adsorption at 87 K overpredicts CH4 adsorption measurements. The fraction of accessible volume, AV, as defined in our previous work,30 for CH4 in BPL carbon is 0.86 at 273 K and 0.91 at 333 K. The latter value is similar to that reported in our previous work.30 Accordingly, the accessibility of CH4 is slightly temperature-dependent. This is consistent with the temperature dependence of the crossing time in the saccharose char, presented in Table 2.
Nguyen and Bhatia
Figure 6. Experimental adsorption isotherms of CH4 in (a) BPL carbon36 at 273 K (4) and 333 K (0) and (b) PCB carbon37 at 296 K (empty triangle) and 373 K (empty square), and FWT model predictions. Solid and dashed lines depict the predicted CH4 isotherms (a) at 273 and 333 K, and (b) at 296 and 373 K respectively, using the structural parameters (PSD and PWTD), determined from Ar adsorption at 87 K. Similarly, dotted and dashed-dotted lines illustrate the predicted CH4 isotherms (a) at 273 and 333 K and (b) at 296 and 373 K, respectively, using the structural parameters (PSD and PWTD) determined from N2 adsorption at 77 K.
Finally, we examine the higher accessibility of Ar at 87 K compared to that of CH4 at 273 and 373 K in both the BPL and PCB carbons. For the saccharose char, the TST calculations presented in the recent2 and current work indicate no accessibility problem for these gases, with reasonably similar crossing times of Ar at 87 K (∼15 min) and CH4 (
