CO2 Permeation in Carbon Membranes with Different Degrees of

Jan 17, 2007 - CO2 Permeation in Carbon Membranes with Different Degrees of Carbonization. Kean Wang,*Leslie S. Loo, andK. Haraya. School of Chemical ...
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CO2 Permeation in Carbon Membranes with Different Degrees of Carbonization Kean Wang,*,† Leslie S. Loo,† and K. Haraya‡ School of Chemical & Biomedical Engineering, Nanyang Technological UniVersity, Singapore, and National Institute of AdVanced Industrial Science and Technology (AIST), AIST Tsukuba Central 5, Tsukuba 305-8565, Japan

CO2 adsorption and permeation were measured on two carbon molecular sieve membranes over a wide pressure range. The two membrane samples were fabricated under similar conditions but with different degrees of carbonization. The pressure dependence of the permeation time lag was investigated, and it is found that the diffusion coefficient takes a stronger functional dependence on loading than the Darken relation and this dependence increases with the degree of carbonization. The experimental data and diffusion models from the literature were employed for the purpose of analysis and comparison. Introduction Carbon molecular sieve membranes (CMSMs) are prepared from the controlled pyrolysis of polymer precursors. The micostructure of a CMSM, which dictates the separation performance (selectivity and permeability), is determined by the carbonization parameters such as the temperature ramping rate, thermal soak time, final temperature, polymer precursor used, etc.1,2 A number of studies investigated the relation between the membrane performance and the controlled carbonization parameters. For example, Foley prepared a supported carbon membrane using the ultrasonic coating technique and studied the effect of temperature and coating.3 Yamamoto et al.4 compared several CMSMs prepared under various conditions and identified some optimal parameters for certain applications. Sedigh et al.5 prepared a supported tubular carbon membrane and characterized its structure/performance with a number of standard techniques. Recently, Lua and Su studied the effect of the carbonization parameters on the transport properties of CMSMs with the statistical analysis from the factorial designed (two levels, eight runs) experiments.6,7 Steel and Koros8 fabricated four CMSM samples with two types of polymer precursors and two sets of carbonization parameters. They found that, with the aid of permeation experiments and the density function theory (DFT) analysis on the low-temperature CO2 sorption isotherm, the microporous network of a CMSM can be characterized as the sieving pores and sorption pores. The study on mass transport properties in CMSMs also attracted a lot of attention. The early works of Koresh and Soffer proposed the sorption-diffusion mechanism for gas permeation in CMSM9 and the surface barrier model for permeation at high pressure.10 They also found the permeability is dependent on the permeation pressure for adsorbing species, and this dependence is the result of the nonlinearity in the sorption isotherm. Ash et al. measured the sorption and permeation of several gases in a microporous carbon membrane11 and pointed out that blind pores play an important role in the transit permeation process and the diffusion coefficient is not the same for the transit permeation and steady-state flux. The diffusion coefficient could be time dependent and may present a strong dependence on loading for an adsorbing gas such as CO2.12 * To whom correspondence should be addressed. E-mail: mkwang@ ntu.edu.sg. † Nanyang Technological University. ‡ AIST.

Petropoulos and Roussis carried out a series of studies on the time lag analysis of diffusion anomalies and found that the distance-dependent diffusion can be the main reason for the anomalies as well.13 Strano and Foley studied the permeation of several gases in a supported nanoporous carbon membrane prepared by the spray coating process.14 The time lag and steady-state flux were analyzed together to derive the adsorption/diffusion properties of the system. The Darken relation and a Langmuir isotherm were found to be adequate for adsorbing gases such as CO2. Lagorsse et al.15 studied gas sorption and permeation in a hollow fiber CMSM and concluded that the Darken relation is adequate for the permeation of weakly adsorbing species such as O2 and N2, but inadequate for adsorbing species such as CO2. Molecular simulations were also performed to study the diffusion in CMSMs; e.g., Seaton et al. simulated the diffusion of hydrogen and light hydrocarbons and found that the surface diffusion is the predominant mechanism of mass transport16 and the pore network connectivity plays an important role in gas separation.17 It is well-known that the diffusion coefficient is dependent on the adsorbed concentration. The Darken relation provides a popular correlation, but many exceptions exist.18,19 A stronger functional dependence has been reported for diffusion in microporous media such as CMSM. Wang et al. measured CO2 sorption and permeation in a CMSM carbonized at 950 °C and found that the diffusion coefficients derived from both the transit permeation and the steady-state permeation flux present a strong dependence over a wide pressure range.20,21 Do attributed such an anomaly to the structural heterogeneity of the adsorbents.22,23 The effect of the isotherm and loading on the concentration dependence of the diffusion coefficient was recently studied by Ruthven.24 In this paper we will report the experimental results of CO2 adsorption and permeation on a CMSM carbonized at 800 °C. The pressure dependence of the permeation time lag will be analyzed and compared with the previous results obtained from the CMSM carbonized at 950 °C. Theory The diffusion flux of the adsorbed phase, Jµ, can be written as

Jµ ) -Dµ

10.1021/ie060617a CCC: $37.00 © 2007 American Chemical Society Published on Web 01/17/2007

∂Cµ ∂r

(1)

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where Cµ is the adsorbed-phase concentration and Dµ is the apparent diffusion coefficient, which is related to the diffusion coefficient at zero loading, D0µ, via the isotherm

Dµ D0µ

)

(

∂ ln P ∂ ln Cµ

)

(2)

T

In eq 2, P is the bulk-phase pressure in equilibrium with the adsorbed phase and T is the temperature. D0µ is assumed to be independent of surface loading and specific to the adsorbatesurface system. Equation 2 is the popular Darken relation, and its actual functional dependence on the adsorbed concentration (loading) depends on the local isotherm.24 With the Langmuir isotherm, Cµ ) CµsbP/(1 + bP), eq 2 reduces to

Dµ )

D0µ D0µ ) 1 - Cµ/Cµs 1 - θ

(3)

Equation 3 is the same as the HIO model for a homogeneous surface.25 With the Toth isotherm, Cµ ) CµsbtP/[1 + (btP)t]1/t, eq 2 will become

Dµ )

D0µ

(4)

1 - θt

where Cµs is the adsorption capacity, b and bt are the affinities, t is the surface heterogeneity, and θ is the surface loading. The use of the Langmuir isotherm implicitly assumes a homogeneous surface, while the choice of the Toth isotherm suggests a heterogeneous surface for both adsorption and diffusion processes. In addition to the Darken relation, two diffusion models were also employed in this study to investigate the experimental data. Model A was used by Wang et al.20 and Lagorsse et al.15 It is a modified HIO model allowing a flexible dependence on loading:

Dµ )

D0µ (1 - Cµ/Cµs)

) n

D0µ (1 - θ)n

(5)

The value of n in eq 5, as will be shown later, represents the heterogeneity for diffusion. Equation 5 reduces to the Darken relation with the Langmuir isotherm and n ) 1, that is, a homogeneous surface for both adsorption and diffusion. Model B was proposed by Do,22 which is a structural model for the adsorption kinetics in activated carbons. The model allows a strong dependence on loading. The feature of this model will be discussed later. With the Toth isotherm, the apparent diffusion coefficient of model B takes a functional dependence on loading as

Dµ )

D0µ [1 - θt](1/t)+1

Figure 1. Pore volume distribution vs pyrolysis temperature of three CMSM samples (KP600, KP800, and KP1000). (Reprinted from ref 1. Copyright 1997 American Chemical Society.) Table 1. Pyrolysis Parameters and Properties of the Two Membrane Samples sample

temp (°C)

soaking time (h)

heating rate (°C/min)

weight loss (%)

thickness (µm)

density (g/cm3)

KP950 KP800

950 800

1 1

10 10

35 12

23 125

∼2.14 ∼1.99

treatment programs are similar but with different soaking temperatures. The first membrane sample was carbonized at 950 °C (thereafter referred to as KP950), while the second sample was treated at 800 °C (referred to as KP800). The carbonization parameters and some of the membrane properties are listed in Table 1. Previous studies showed that the membranes are pinholefree and symmetric in structure.1 The pore volume development (evolution) against the pyrolysis temperature was previously investigated in detail for a total of three membrane samples (KP600, KP800, and KP1000) and will be used as the benchmark. The derived pore volume distributions are shown in Figure 1 against their pyrolysis temperatures.1 It is seen that, as the pyrolysis temperature increases from 600 to 1000 °C, the membrane samples will develop more fractions of micropores below 4 Å. Table 2 shows the permselectivities (vs helium) of the two membrane samples at room conditions (∼25 °C, 1 atm). It can be seen that the permselectivity (e.g., N2/O2) is good for KP950 and reasonably good for KP800, confirming the samples are predominantly microporous with no major contribution from Knudsen diffusion or viscous flow in the overall mass transfer. CO2 permeation experiments were conducted on a time-lag rig, while the adsorption isotherms were measured on a volumetric rig for KP95020 and a Cahn 2000 microbalance for KP800. The experimental setup and procedures can be found in refs 20 and 21. Results and Discussion

(6)

The four diffusion models (eqs 3-6) present various functional dependences on loading. They are employed to analyze the experimental permeation time lags. The details of the time lag analysis with the four diffusion models are complicated, but details are available in ref 20 for eq 3, ref 21 for eq 5, and ref 23 for eqs 4 and 6. Experiment CMSM samples were prepared by the controlled pyrolysis of a Kapton polyimide thin film under high vacuum. The thermal

Figure 2a shows the CO2 adsorption isotherm measured on KP950 at 298 K (dots). As CO2 is not an ideal gas at high pressure, the pressure reading is converted to fugacity. The isotherm data are fitted to the Langmuir isotherm (solid line) and Toth isotherm (dashed line). The fitting is reasonably good for the Langmuir isotherm and good for the Toth isotherm. The fitting results are listed in Tables 3 and 4, respectively. Figure 2b shows the CO2 isotherms measured on KP800 at 308, 333, and 363 K as symbols. The fittings are shown as solid lines for the Langmuir isotherm and dashed lines for the Toth isotherm. The isotherm parameters are listed in Tables 3 and 4, respectively.

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Figure 2. (a, left) Adsorption isotherm of CO2 on KP950 at 298 K (dots): Langmuir (s); Toth (- - -). (b, right) Adsorption isotherm of CO2 on KP800 (symbols): Langmuir (s); Toth (- - -). Table 2. Permselectivity of the Two Membrane Samples at Room Conditions permselectivity of KP800 (P800 helium/Pi) permselectivity of KP950 (P950 helium/Pi) a

H2 0.31 0.446

He 1.00 1.00

N2 22.28 356.7

O2 3.84 19.06

Ar 1550

CO2 0.67 3.54

CF4 infa inf

Observation for 12 h.

Table 3. Parameters of the Langmuir Isotherm and Fitting Results of Model A Langmuir Isotherm sample KP800 KP950 Carbolac

Model A

temp (K)

Cµs (mmol/g)

b (kPa-1)

n

D0µ (cm2/s)

308 333 363 298 190

4.59 4.14 3.71 3.67 6.57

1.16 × 10-2 6.89 × 10-3 3.38 × 10-3 1.22 × 10-2 8.82 × 10-2

1.58 1.59 1.63 2.06 1.91

1.33 × 10-8 2.71 × 10-8 4.33 × 10-8 6.37 × 10-12 2.83 × 10-5

Table 4. Parameters of the Toth Isotherm and Fitting Results of Model B Toth Isotherm sample KP800 KP950 Carbolac

Model B

temp (K)

Cµs (mmol/g)

b (kPa-1)

t

D0µ (cm2/s)

308 333 363 298 190

4.99 4.64 4.52 4.12 24.5

2.19 × 10-2 1.13 × 10-2 4.91 × 10-3 3.69 × 10-2 0.6163

0.671 0.663 0.627 0.571 0.241

5.55 × 10-9 1.42 × 10-8 2.46 × 10-8 2.57 × 10-12 1.23 × 10-6

The Toth isotherm indicates that KP950 is more heterogeneous (t ≈ 0.57 at 298 K) than KP800 (t ≈ 0.66 at 308 K) for CO2 adsorption. This is in agreement with the pore volume development in Figure 1. As the pyrolysis temperature progresses from 800 to 1000 °C (while other parameters are kept constant), the micropores shrink steadily toward smaller sizes (e4 Å), and the portion (∼0.07 cm3/g) of micropores in the 4-4.3 Å range for KP800 disappears. However, Figure 1 cannot tell us the “shrinkage” of micropores below 4 Å when the pyrolysis temperature reaches 1000 °C, because the molecular probe experiment cannot resolve pores below 4 Å (the smallest probe molecule is generally CO2). To get some qualitative information on the shrinkage of pores below 4 Å, the isosteric heats of CO2 adsorption on KP800 and KP1000 were calculated and are plotted in Figure 3a, respectively. The two curves are derived from the low-pressure CO2 isotherm data (5 Torr < P < 90 Torr) measured on the two samples at multiple temperatures (30-60 °C) with a standard BEL (BEL Japan Inc.) pore and surface analyzer. It is seen that, in general, KP1000 is more heterogeneous than KP800 and, specifically, the isosteric heat of CO2 is about 35 kJ/mol on KP800 and 27kJ/mol on KP1000

at low surface loadings. These values are seemingly high, but are comparable to the values reported for CO2 on such carbon molecular sieves as Takeda 3A (30 kJ/mol), Bergbau CMS (37 kJ/mol), and Air Product CMS (28 kJ/mol).26 Figure 3b plots the adsorption potential of a CO2 molecule in slit-shaped micropores, which is taken as the negative of 10-4-3 potential minimum.27 The potential is normalized with respect to Slp*, the potential minimum of a CO2 molecule adsorbing on a single layer of a graphite lattice (basal plane), the value of which has been calculated as ∼16 kJ/mol by Rao et al.28 The dashed lines in Figure 3b indicate the pore sizes in which the heats of CO2 adsorption will correspond to the isosteric heats of CO2 at low loading. We can therefore deduce that, when the pyrolysis temperature progresses from 800 to 1000 °C, the membrane will develop more micropores below 3 Å so that the heat of adsorption is lower and is more sensitive to the variation of pore sizes. KP950 is closer to KP1000 in synthetic conditions, and this explains its higher heterogeneity for CO2 adsorption. It should be noted that, even with higher heterogeneity and low isosteric heat, KP950 possesses much higher permeation selectivity for gas molecules listed in Table 2, due to the stronger molecular sieving (size exclusion) effect. It should also be pointed out that Figure 1 is derived from the molecular probe experiments in which gas molecules of various dimensions (CO2, C2H6, n-C4H10, and iso-C4H10) were used to probe the membrane samples for their capacities. Therefore, the pore volume distribution obtained does not assume any specific pore geometry and is dictated by pore connectivity as well. For example, big blind pores (or ink-bottle pores) accessible to smaller probe molecules such as CO2 may not be “felt” by large molecules such as n-C4H10. This is different from the pore size distribution derived from a single isotherm using the popular methods such as H-K, DFT, or GCMC, etc., Lua and Su recently investigated the pore development in polyimide-derived CMSMs vs pyrolysis temperature (pyrolysis from 823 to 1273 K under vacuum). Their results showed a trend similar to that in Figure 1 but with more diversified pore sizes (4.0-8.5 Å). This discrepancy is expected as their distributions were derived from the CO2 isotherm (273 K) via the H-K equation. Generally, such an approach requires the assumptions of pore geometry and an interaction potential.19

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Figure 3. (a, left) Isosteric heat of CO2 adsorbing on KP800 and KP1000 samples. (b, right) Normalized adsorption potential of CO2 in slit pores by the 10-4-3 potential minimum. The dashed lines indicate the pore size for the isosteric heats on each sample at low loading.

Figure 4. (a, left) Permeation time lag of CO2 on KP950 at 298 K: experimental data (dots); model A (s); model B (- - -). (b, right) Permeation time lag of CO2 on KP800: experimental data (symbols); model A (s); model B (- - -).

Figure 4a shows the CO2 permeation time lag vs permeation pressure on KP950 at 298 K. The experimental data are dots, while the fittings of models A and B are a solid line and a dashed line, respectively. The fitting results of the two models are listed in Tables 3 and 4, respectively. It is seen that model A gives a good fit with n ) 2.06. Model B gives a reasonable fit, but slightly overestimates the pressure dependence of the time lag. The performances of the other two diffusion models are also compared in the figure. The dotted line represents the DarkenLangmuir model (eq 3, with Dµ0 ) 6.9 × 10-12 cm2/s), while the dashed-dotted line shows the Darken-Toth model (eq 4, with Dµ0 ) 5.6 × 10-12 cm2/s). It is seen that the Darken relation underestimates the pressure dependence of the time lag (as a result of underestimating the concentration dependence of the diffusion coefficient) by a large margin with either the Langmuir or Toth isotherm. Therefore, we can conclude that the apparent CO2 diffusion coefficient in KP950 presents a much stronger dependence on loading than the Darken relation. Next, CO2 permeation time lags measured on KP 800 were investigated. Figure 4b shows the permeation data at three temperatures (308, 333, and 363 K) as symbols. It is seen that model A (solid lines) again well simulates the data at each temperature with n ≈ 1.6 (the optimal parameters are listed in Table 3). Model B (dashed lines), however, shows a much too strong dependence on the permeation pressure, as exemplified by the fittings of the time lag data at 308 and 333 K. Compared with KP950, KP800 is the sample with a lower degree of carbonization and less heterogeneity for CO2 adsorption. Therefore, it can be generally concluded that the anomaly of CO2 diffusion depends on the structural heterogeneity of the molecular sieve membrane and an increase in the degree of

Figure 5. Functional dependence on loading for eqs 5 and 7 with n ) Eij/RT ) 1.6 and D0µ ) 1.

carbonization will result in stronger concentration dependence for the apparent diffusion coefficient (n ≈ 2.0 for KP950 vs n ≈ 1.6 for KP800). The different performances of models A and B deserve some attention, and this leads us to explore more about the mechanisms and assumptions behind these two models. Both models attribute the structural heterogeneity as the source of diffusion anomaly, but their approaches are very different. Model A assumes a homogeneous surface (Langmuir equation) for the adsorption equilibrium and sets a correction factor, 1/(1 - θ)n-1, for the apparent diffusion coefficient. This factor represents the “diffusional heterogeneity” and lumps the effects of the nonideality/structural heterogeneities for diffusion in the molecular sieves.21,25,29 It is possible for the diffusional hetero-

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Figure 6. (a, left) Sorption isotherm of CO2 on Carbolac carbon at 190 K:11 experimental data (dots); Langmuir isotherm (s); Toth isotherm (- - -). (b, right) Permeation time lag of CO2 on a Carbolac plug at 190 K: experimental data (dots); model A (s); model B (- - -).

geneity to present on a mostly homogeneous surface via, e.g., blind pores or pore connectivities. The value of “n” is generally larger than 1. Model A can be treated as a modified HIO model on a heterogeneous surface, by assuming that the activation energy for diffusion is a function of loading, interaction between adsorbed molecules, and the structure heterogeneity. Equation 7

Dµ(θ) )

0 Dµ∞

1-θ

(

)

E - θEij ) RT E 0 exp Dµ∞ D0µ/(1 - θ) RT ) (7) Eij θEij (1 - θ) exp -θ exp RT RT

exp -

(

)

( )

( )

0 demonstrates the mathematical derivation, where Dµ∞ is the diffusion coefficient at zero loading and infinite temperature, E is the activation energy on a homogeneous surface, and Eij represents the interaction between the adsorbed molecules and structural heterogeneity for diffusion. The term D0µ/(1 - θ) is the HIO model for a homogeneous surface, and the term exp(-θEij/RT) is the correction factor. Figure 5 compares eqs 7 and 5 for their dependence on loading (with D0µ ) 1). It is seen that, with the arbitrary choice of n ) 1.6 ) Eij/RT (corresponding to the heterogeneity of KP800), eq 5 shows a trend of dependence on loading very similar to that of eq 7 up to θ ) 0.93. Since Eij cannot be quantified at this stage, eq 5 provides a good approximation correlation for the corrected (heterogeneous) HIO model (eq 7). The microscopic structure of a CMSM is complicated, with open channels and blind pores of various shapes and sizes.10,11 These factors play important roles in kinetics but cannot be adequately addressed by the heterogeneity parameter(s) derived from the analysis of a single isotherm. Molecular probe experiments can give us some insight into the pore connectivity but require tedious experimental efforts and are noted for their inability to characterize pore size accurately and to resolve pores below 4 Å. Model A treats all these uncertainties with the correct factor and is able to account for the diffusion anomalies on the two CMSM samples. Model B directly applies Do’s model to the diffusion in carbon molecular sieves and assumes the same surface heterogeneity (derived from the Toth isotherm) will dictate both the adsorption equilibrium and kinetics. In Do’s model, the activated carbon is assumed to consist of numerous “unit cells”, in which graphites (micropores) randomly dispersed in amorphous car-

bons (macro/mesopores). The surface flow is paralleled by the bulk flow and is characterized by the repeated diffusion, evaporation, and readsorption in and between the unit cells. Therefore, the apparent diffusion coefficient presents strong functional dependence on loading, and the model does not reduce to the Darken relation with the Langmuir isotherm. The diffusion in a dense CMSM is very different from that described in activated carbons. The CMSM is characterized by micropores in the range of a few angstroms in which diffusing molecules never escape the potential fields of the pores and “sorption-diffusion” is the dominant (if not the sole) mechanism for the overall mass transfer.9,10,20 Therefore, it is not surprising that Do’s model, which is very successful for kinetics on activated carbons, overestimates the pressure dependence of the time lag data on CMSMs, as the surface heterogeneity is much higher in the case of activated carbons (generally with t ≈ 0.29 in the Toth isotherm23) and diffusion mechanisms are more complicated. Finally, the published data of Ash et al.11 were employed to further examine the two models (A and B) and the allegations above. Ash measured CO2 adsorption and permeation on a Carbolac carbon pellet (with a thickness of 9.1 mm) at 190 K. Gas permeation experiments showed that the surface flow is the predominant mechanism in the microporous carbon pellet. The isotherm data are reproduced in Figure 6a as symbols and fitted to the Langmuir (solid line) and Toth (dashed line) isotherms. The fitting results are listed in Tables 3 and 4, respectively. It is seen that the Langmuir equation fits the experimental data poorly while the Toth equation fits the data well. The Toth isotherm gives an unreasonably high capacity (24.5 mmol/g) because the experimental pressure is low (P < 1 atm). The heterogeneity parameter of the Toth isotherm, t ) 0.24, suggests that the Carbolac carbon is structurally more heterogeneous than the two membrane samples. This is expected, as the pellet is formed by compressing the fine powders of microporous carbon molecular sieves. Figure 6b shows the CO2 permeation data (dots) at 190 K and the fittings from model A (solid line) and model B (dashed line). It is seen that model A is flexible enough to fit the data well with n ) 1.91, indicating the concentration dependence in Carbolac carbon is comparable to that of KP950 and is much stronger than that given by the Darken relation. Model B again overestimates the pressure dependence of the permeation time lag.

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Conclusions The CO2 diffusion coefficient in the carbon molecular sieve membranes presents a stronger functional dependence on loading than that described by the Darken relation over a wide pressure range and at multiple temperatures. This dependence is dictated by the surface heterogeneity of the membrane sample and increases with the degree of carbonization. The model of Wang et al. is based on the traditional HIO model and modified with a correction factor of diffusional heterogeneity. The model is capable of addressing the diffusion anomalies in the samples with different degrees of carbonization and structure. The model of Do is based on the structural characteristics of activated carbons and may overestimate the functional dependence on loading for the diffusion in carbon molecular sieves, due to the difference in the diffusional mechanisms and structural characteristics between these two types of porous media. Literature Cited (1) Suda, H.; Haraya, K. Gas permeation through micropores of carbon molecular sieve membranes derived from Kapton polyimide. J. Phys. Chem. B 1997, 101, 3988. (2) Foley, H. Carbogenic molecular sieves: synthesis, properties and application. Microporous Mater. 1995, 4, 407. (3) Shiflett, M.; Foley, H. Reproducible production of nanoporous carbon membrane. Carbon 2001, 39, 1421. (4) Yamamoto, M.; Kusakabe, K.; Hayashi, J.; Morooka, S. Carbon molecular sieve membrane formed by oxidative carbonization of a copolyimide film coated on a porous support tube. J. Membr. Sci. 1997, 133, 195. (5) Sedigh, M. G.; Onstot, W. J.; Xu, L.; Peng, W. L.; Tsotsis, T. T.; Sahimi, M. Experiments and simulation of transport and separation of gas mixtures in carbon molecular sieve membranes. J. Phys. Chem. A 1998, 102, 8580. (6) Su, J.; Lua, A. Influence of carbonization parameters on the transport properties of carbon membranes by statistical analysis. J. Membr. Sci. 2006, 278, 335-343. (7) Lua, A.; Su, J. Effects of carbonization on pore evolution and gas permeation properties of carbon membranes from Kapton polyimide. Carbon 2006, 44, 2964. (8) Steel, K. M.; Koros, W. J. An investigation of the effect of pyrolysis parameters on gas separation properties of carbon materials. Carbon 2005, 43, 1843. (9) Koresh, J. E.; Soffer, A. mechanism of permeation through molecular sieve carbon membrane. J. Chem. Soc., Faraday Trans. 1 1986, 82, 2057. (10) Koresh, J. E.; Soffer, A. Molecular sieve carbon, part 3: adsorption kinetics according to a surface barrier model. J. Chem. Soc., Faraday Trans. 1 1981, 77, 3005.

(11) Ash, R.; Baker, R. W.; Barrer, R. M. sorption and surface flow in graphitized carbon membranes II, time lag and blind pore character. Proc. R. Soc. London, A 1968, 304, 407. (12) Ash, R.; Barrer, R. M.; C. G. Flow of adsorbable gases & vapors in a microporous media. Proc. R. Soc. London, A 1963, 271, 1. (13) Roussis, P. P.; Petropoulos, J. H. Permeation time lag analysis of anomalous diffusion. J. Chem. Soc., Faraday Trans. 2 1976, 72, 737. (14) Strano, M. S.; Foley. Temperature and pressure dependent transit analysis of single component permeation through nanoporous carbon membranes. Carbon 2002, 40, 1029. (15) Lagorsse, S.; Magalhaes, F.; Mendes, A. Carbon molecular sieve membranes, sorption, kinetics and structural characterization. J. Membr. Sci. 2004, 241, 275. (16) Seo, Y. G.; Kum, G. H.; Seaton, N. A. Monte Carlo simulation of transport diffusion in nanoporous carbon membrane. J. Membr. Sci. 2002, 195, 65. (17) Vieira, A. M.; Seaton, N. A. Pore network connectivity effects on gas separation in a microporous carbon membrane. Chem. Eng. Sci. 2003, 58, 5251. (18) Kapoor, A.; Yang, R. T.; Wong, C. Surface diffusion. Catal. ReV. 1989, 31, 129. (19) Yang, R. T. Adsorbents, Fundamentals and Applications; John Wiley & Sons: New York, 2003. (20) Wang, K.; Suda, H.; Haraya, K. Permeation time lag and concentration dependence of the diffusion coefficient of CO2 in a carbon molecular sieve membrane. Ind. Eng. Chem. Res. 2001, 40, 2942. (21) Wang, K.; Suda, H.; Haraya, K. The characterization of CO2 permeation in a CMSM derived from polyimide. Sep. Purif. Technol. 2003, 31, 61. (22) Do, D. D. A model for surface diffusion of ethane and propane in activated carbon. Chem. Eng. Sci. 1996, 51, 4145. (23) Rutherford, S. W.; Do, D. D. Permeation time lag and heterogeneity in adsorbed phase transport. Chem. Eng. Sci. 2000, 55, 3542. (24) Ruthven, D. M. Sorption kinetics for diffusion-controller systems with strongly concentration-dependent diffusivity. Chem. Eng. Sci. 2004, 59, 4531. (25) Higashi, K.; Ito, H.; Oishi, J. J. At. Energy Soc. Jpn. 1963, 5, 846. (26) Rutherford, S. W.; Coons, J. E. Adsorption equilibrium and transport kinetics for a range of probe gases in Takeda 3A carbon molecular sieve. J. Colloid Interface Sci. 2005, 284, 432. (27) Everett, D. H.; Powl, J. C. Adsorption in slit-like and cylindrical micropores in the Henry’s law region. J. Chem. Soc., Faraday Trans. 1 1976, 72, 619. (28) Rao, M. B.; Jekins, R. G.; Steele, W. A. Potential functions for diffusive motion in carbon molecular sieve. Langmuir 1985, 1, 137. (29) Okazaki, M.; Tamon, H.; Toel, R. Interpretation of surface flow phenomenon of adsorbed gases by hopping model. AIChE J. 1981, 27, 262.

ReceiVed for reView May 18, 2006 ReVised manuscript receiVed November 19, 2006 Accepted December 4, 2006 IE060617A