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The structural characterization of carbon molecular sieve membrane (CMSM) via gas adsorption
Journal of Membrane Science 220 (2003) 177–182
Short communication
The structural characterization of carbon molecular sieve membrane (CMSM) via gas adsorption C. Nguyen a , D.D. Do b , K. Haraya c , K. Wang d,∗ a
d
CSIRO Manufacturing & Infrastructure Technology, Gate 4 Normanby Road, Clayton, 3168 Vic., Australia b Department of Chemical Engineering, University of Queensland, St. Lucia, 4067 Qld, Australia c National Institute of Advanced Industrial Science & Technology, Central 5, Tsukuba 305-8565, Japan School of Mechanical & Production Engineering, Nanyang Technological University, Singapore 639798, Singapore Received 1 November 2002; received in revised form 9 May 2003; accepted 10 May 2003
Abstract The microstructure of a carbon molecular sieve membrane (CMSM) is characterized using adsorption equilibrium information. The pore size distributions of the CMSM derived from N2 and CH4 adsorption isotherm are found to be consistent with each other and in agreement with the results of gas permeation experiments as well as the general characteristics of such molecular sieve materials. © 2003 Elsevier B.V. All rights reserved. Keywords: CMSM; PSD; Permeation; Adsorption
1. Introduction Carbon molecular sieve membrane (CMSM) is produced from the controlled pyrolysis of polymeric precursors. Its microstructure resembles that of the precursor but with superior selectivity, thermal stability and strength [1–3]. A CMSM generally possesses pores of relatively uniform sizes which enable the discrimination of gas molecules with very similar dimensions. CMSMs are promising materials for the separation of a number of important gas mixtures. Due to the specific structural characteristics (ultramicropores with narrow PSD) of a CMSM, the traditional/conventional characterization methods, such as N2 sorption at its liquid temperature (−196 ◦ C) may become unpractical because of the extremely slow ∗ Corresponding author. E-mail address: [email protected] (K. Wang).
sorption rate. Some researchers depend largely on such methods as gas permeation [1], Dubinin–Raduskevich (DR) plot [2], molecular probe [2], or SEM [4], etc. These methods have been known to require arduous experimental efforts or expensive facilities and yet the interpretation of the results still bears some difficulties. Statistical methods like GCMC or DFT are theoretically very revealing, but may require some special molecular properties and are complicated to use. A dynamic method such as the permeation technique appears the most suitable for the purpose of characterizing the pore structure due to the sieving usage of the molecular sieve materials like CMSM. An alternative way is to characterize the CMSM pore system by analyzing the adsorption equilibrium (isotherm) of a suitable adsorbate at room temperature. Adsorption of nitrogen at its normal boiling point (sub-critical temperature) is a very useful tool for
0376-7388/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0376-7388(03)00219-9
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C. Nguyen et al. / Journal of Membrane Science 220 (2003) 177–182
materials having pores of larger sizes or a system of pore of a wide distribution, where surface layering and capillary condensation are always parts of the adsorption process [7]. In the case of CMSM, where pores are exclusively in micro-size range with narrow distributions, adsorption of supercritical gases seems to be more appropriate, because (1) supercritical adsorption in micropores is by and large faster than sub-critical adsorption and, (2) supercritical gas adsorption takes place mostly in micropores while sub-critical adsorption may occur even on outer surface of the membrane. This paper is an attempt to characterize the PSD of a CMSM by the gas adsorption at higher (room) temperatures using a model proposed by Nguyen and Do [5].
2. Adsorption of supercritical gases in porous media In the model proposed by Nguyen and Do [5], new concepts are introduced to account for the enhancement of the potential energy of interaction between ad-molecules (adsorbate molecules) and surface atoms within the pore interior. With these concepts, a structure-based model is developed to describe the adsorption equilibria in pore system. The model requires only molecular properties of the adsorbate and adsorbent, and the structural heterogeneity is accounted for using the distribution of micropore size. The model is briefly presented as follows. Once finding themselves in a pore system, some of the gas molecules will be attracted very close, i.e. adsorbed, to the solid surface while the others will remain in the gas phase within the pore. These gas phase molecules are referred to as the confined gas molecules, the pressure ppore of which can be calculated from the bulk pressure pbulk as follows: g −Epore ppore = pbulk exp (1) RT g
with Epore being the potential energy of the gas phase molecules confined in the pore interior. A molecule adsorbed in a micropore is under the force field from all sides of the pore. Such interaction depends on the distance between the walls as well as the position of the ad-molecule relative to the pore
walls. At equilibrium, this interaction and hence the heat of adsorption is a function of the pore size. We denote Es and bs as the heat released and the affinity of adsorption on a flat surface, respectively. Similarly, we denote Epore and bpore as those of adsorption in a pore. The affinity coefficient of adsorption in the pore bpore then can be calculated from the affinity coefficient of adsorption on flat surface bs by the formula: Epore − Es (2) bpore = bs exp RT √ with bs = (β/ MT) exp(Es /RT) and M is the molecular weight. β is a parameter characterizing the solid surface. This parameter takes a value of 0.426 for adsorption on a flat surface as found by Hobson [6]. The resulting affinity has a unit of inverse Mpa. In our previous work [5] we argued that due to the restriction of movement in pore space the parameter takes a smaller value and in this paper, β is assigned a value of 0.08. If f(r) is the pore size distribution function and H(p, r) is the single pore isotherm equation, the amount adsorbed at pressure p can be calculated as: ∞ C (p) = H(p, r)f(r) dr. 0
Using Langmuir equation as the local isotherm, we get ∞ bpore (r)ppore (r) C (p) = f(r) dr (3) Cs (r) 1 + bpore (r)ppore (r) 0 with Cs (r) the maximum capacity of all pores of size r. The PSD, f(r), can be derived by comparing Eq. (3) to the isotherm data. Details of the algorithm are presented in [5,7] while the basic principles are described as follows. The micropores of CMSM are assumed to be slit-shaped, similar to the one described by the 10-4-3 potential (pore walls consist of several graphite layers in parallel) [7]. The adsorption potential of a molecule confined in such a pore is the summation of the Lennard–Jones’ (LJ) 12-6 potentials between the ad-molecule and each carbon atom on the pore walls. For an ad-molecule confined in a pore of size r, g the related energy parameters [Epore , Es , and Epore in Eqs. (1) and (2)] can be calculated from the summation of the LJ potentials according to their definitions. The LJ parameters used in the simulations are listed in Table 1.
C. Nguyen et al. / Journal of Membrane Science 220 (2003) 177–182
179
Table 1 Gas permeation properties of the KP 800 CMSM at room temperature and atmospheric pressure Gases (10−10
Kinetic diameter σ /κ (T) Permeability (Barrer) Selectivity (PHelium /Pi ) a
m (Å))
H2
He
N2
O2
CH4
CF4
C
2.89 – 507.62 0.31
2.60 – 158.86 1.00
3.64 71.4 7.13 22.28
3.46 – 41.40 3.84
3.80 148.6 1.24 128.11
4.70 – 0a ∞
3.5 28 – –
Observation in 12 h only.
3. Experimental A CMSM (referred to as KP 800) was prepared via the controlled pyrolysis of Kapton® polyimide film under vacuum. The highest pyrolysis temperature is 800 ◦ C and the thermal treatment program is described in [2,8]. A Cahn 2000 microbalance (resolution: 10−3 g) was used to measure gas sorption isotherms on the KP 800. The microbalance is fitted in a high pressure vessel for which the temperature can be controlled in the range of −20 to 92 ◦ C. About 0.6 g of KP 800 in small crushes was loaded in the sample basket. An aluminum block was used as the counterweight. To minimize the effect of buoyancy, gold is added in the sample basket to ensure that both density and weight of the sample basket are (nearly) the same as those of the counterweight. This is achieved via trial and error. Helium is assumed to be the non-adsorbing gas at room temperature and is used to check the effect of buoyancy. The sample was cleaned at high temperature and under vacuum. The weight of the sample was monitored during the cleaning process until there was no change observable within 12 h. The zero point of the microbalance is then set accordingly. The adsorption isotherm of N2 was measured in the pressure range of 0.005–4 MPa at the temperatures 35, 60 and 90 ◦ C, respectively. At lower pressure and temperature, the sorption rate of N2 was seen slow on the KP 800 and it may take three more days for the equilibrium to be reached (weight change less then 10−3 g in 12 h). Such slow sorption kinetics of N2 at its supercritical temperature was also reported on an ultra-microporous carbon by Koresh et al. [9]. A conventional time lag rig was used to measure gas permeations on the KP 800 CMSM with a diameter of approximately 3 cm and a thickness of 125 m. The detailed experimental setup and procedures are
described in [2]. Table 1 shows the permeation fluxes (permeability) and selectivities (versus Helium) of several gases on the KP 800 at room temperature and at atmospheric pressure. It can be seen that this membrane presents reasonable sieving effect for gas molecules with different kinetic diameters, which suggests that the CMSM is predominantly microporous with no major contribution from Knudsen diffusion or viscous flow in its overall mass transfer. This is in agreement with our previous results from molecular probing experiments on a CMSM prepared under the similar thermal treatment conditions [2].
4. Results and discussion Adsorption/desorption isotherms of nitrogen at three temperatures are shown in Fig. 1. No hysteresis is observed for this system. It is understood that no hysteresis due to capillary condensation is possible in this case since there is no mesopore in the CMSM and
Fig. 1. Nitrogen adsorption on KP 800 at different temperatures (solid-adsorption, hollow-desorption).
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C. Nguyen et al. / Journal of Membrane Science 220 (2003) 177–182
more over, it is about supercritical adsorption. The lack of a hysteresis on the isotherm may also point to the absence of very narrow micropores, which may be a reason for micropore hysteresis [9]. The model equations are then employed to fit the experimental data. It is known that the maximum pore capacity Cs is a function of temperature. However, the thermal expansion coefficient was found to be rather small (in the order of 1×10−5 mol/◦ C), [10], i.e. the effect of the thermal expansion is minimal within the experimental temperature range (35–90 ◦ C). The fitting is carried out for nitrogen adsorption at three different temperatures simultaneously. In the fitting process, the whole pore spectrum is divided into a number of pore sub-ranges, and then the optimization procedure is invoked to find the volume of each sub-range such that the calculated isotherm closely matches the experimental data [7]. This method does not assume any particular form for the distribution function, and as a result the PSD reflects the “real” distribution better than methods assuming an a-priori form for the distribution. The fitting results (lines) are satisfactory for all temperatures as shown in Fig. 2a and b, where pressure is presented in normal and log scales, respectively to highlight the goodness of fit at low- and high-pressure ranges. The derived PSD in Fig. 2c is consistent with the permeation experiment: a narrow distribution of micropores without a significant presence of mesopores, and the majority of pores are smaller than 10 × 10−10 m (10 Å) in diameter. It is important to note that the PSD in Fig. 2c is in terms of adsorption capacity, which is different but related to the common
volumetric PSD. The absence of mesopores and larger micropores is a must for any sieving materials and this is supported by our observations in the permeation experiments, e.g. CF4 , a molecule with the kinetic diameter of approximately 4.7 × 10−10 m (4.7 Å), virtually cannot penetrate the 125 m (thickness) CMSM in 12 h at room temperature and pressure. The model is further tested with the adsorption data of the other gas adsorbate, methane, for which the isotherm was measured on KP 800 at 90 ◦ C. The isotherm data and fitting are shown in Fig. 3a and b while the PSD derived is shown in Fig. 3c, respectively. We see that the PSD derived is more homogeneous (with a pore size range of (8–9) × 10−10 m (8–9 Å)) and qualitatively agree with the PSD derived from N2 sorption data. The difference may result from the difference in the size and geometries of methane and nitrogen molecules, because (1) some of the smaller micropores accessible to N2 (3.64 × 10−10 m (3.64 Å)) may not be “felt” by the methane (3.80 × 10−10 m (3.80 Å)) molecule, and (2) the dump-bell (3.64 × 10−10 m × 3.01 × 10−10 m (3.64 Å × 3.01 Å)) shaped N2 molecule is likely to experience slightly different sorption potential compared with the spherical methane molecule. For example, a slit-shaped pore with the size of 10 × 10−10 m (10 Å) (center to center) may accommodate up to two layers of N2 , but only one layer of methane at the experimental pressure range. Thus the KP 800 can be more “heterogeneous” to N2 than to CH4 molecules. In a previous study [2], molecular probing (sorption) were performed on a CMSM prepared under similar thermal treatment conditions (T = 800 ◦ C, but
Fig. 2. The fitting of nitrogen adsorption isotherms at three temperatures (a and b) and the derived PSD (c). Symbols and solid lines represent the experimental data and model fitting, respectively.
C. Nguyen et al. / Journal of Membrane Science 220 (2003) 177–182
181
Fig. 3. The fitting of methane adsorption isotherm at 90 ◦ C (a and b) and the derived PSD (c). Symbols and solid lines represent the experimental data and model fitting, respectively.
with the thickness of 23 m). Several gases, including CO2 , C2 H6 , n-C4 H10 and i-C4 H10 , were used as probing molecules. i-C4 H10 (5.0 × 10−10 m (5.0 Å)) was seen to marginally adsorb on that CMSM. The sorption capacity of i-C4 H10 is comparable to that of n-C4 H10 (4.3 × 10−10 m (4.3 Å)) but much less than that of CO2 (3.3 × 10−10 m (3.3 Å)). The PSD of that CMSM was then calculated from the micropore volumes derived from the DR equation for various gas molecules and was found in the range below 4.5 × 10−10 m (4.5 Å) (effective pore size, wall to wall), which makes the center-to-center PSD below 8 × 10−10 m (8 Å). These ‘physical’ characterization results are in a reasonable consistency with the PSD derived from N2 data (Fig. 2). Thus the PSD derived from the N2 sorption data is more applicable with this model. However, because of the complicated nature of the microporous structure of the CMSM (known as turbostratic structure). The PSD derived from equilibrium information may not be immediately applicable for a permeation (dynamic) process in which not only the size of pores but also the way they connected with each other also plays a decisive role. Some discrepancy can also be found by comparing the results from our equilibrium and permeation experiments. For example, at sub-critical temperatures i-C4 H10 and n-C4 H10 are seen to marginally adsorbable on such CMSMs, yet molecules of approximately same size (CF4 ) are not permeable. This phenomenon may point to the importance of the pore connectivity in the CMSM and constitutes a challenging issue in future study.
5. Conclusions Adsorption isotherms of nitrogen and methane were measured on a CMSM at raised temperature and under wide pressure range. The PSD of the CMSM is derived from the equilibrium information using the model proposed by Nguyen and Do. The PSD is found predominantly in the upper-ultra-micropore range, without any significant mesopore contribution. The results are supported by our gas permeation as well as molecular probing experiments. The study confirms the suitability of the model and forms a basis for further study on gas permeation in microporous media.
References [1] J.B. Koresh, A. Soffer, The carbon molecular sieve membrane. General properties and the permeability of CH4 /H2 mixture, Sep. Sci. Technol. 22 (1987) 973. [2] H. Suda, K. Haraya, Gas permeation through micropores of carbon molecular sieve membranes derived from Kapton polyimide, J. Phys. Chem. B 101 (20) (1997) 3988. [3] W.J. Koros, R. Mahajan, Pushing the limits on possibilities for large scale gas separation: which strategies? J. Membr. Sci. 175 (2000) 181. [4] M.C. Sedigh, M. Jahangiri, P.K. Liu, M. Sahimi, T.T. Tsotsis, Structural characterization of polyetherimide-based carbon molecular sieve membrane, AIChE J. 46 (2000) 2245. [5] C. Nguyen, D.D. Do, Adsorption of supercritical gases in porous media: determination of micropore size distribution, J. Phys. Chem. B103 (1999) 6900. [6] J.P. Hobson, A new method for finding heterogeneous energy distributions from physical adsorption isotherms, Can. J. Phys. 43 (1965) 1934.
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[7] C. Nguyen, D.D. Do, Simple optimization approach for the characterization of pore size distribution, Langmuir 16 (2000) 1319. [8] J. Petersen, M. Matsuda, K. Haraya, Capillary carbon molecular sieve membranes derived from Kapton for high temperature gas separation, J. Membr. Sci. 131 (1997) 85.
[9] J.E. Koresh, T.H. Kim, W.J. Koros, Study of ultramicroporous carbons by high pressure adsorption, J. Chem. Soc., Farad. Trans. 85 (1989) 1537. [10] K. Wang, D.D. Do, Characterizing micropore size distribution of activated carbon using equilibrium data of many adsorbates at various temperatures, Langmuir 13 (1997) 6226.
Short communication
The structural characterization of carbon molecular sieve membrane (CMSM) via gas adsorption C. Nguyen a , D.D. Do b , K. Haraya c , K. Wang d,∗ a
d
CSIRO Manufacturing & Infrastructure Technology, Gate 4 Normanby Road, Clayton, 3168 Vic., Australia b Department of Chemical Engineering, University of Queensland, St. Lucia, 4067 Qld, Australia c National Institute of Advanced Industrial Science & Technology, Central 5, Tsukuba 305-8565, Japan School of Mechanical & Production Engineering, Nanyang Technological University, Singapore 639798, Singapore Received 1 November 2002; received in revised form 9 May 2003; accepted 10 May 2003
Abstract The microstructure of a carbon molecular sieve membrane (CMSM) is characterized using adsorption equilibrium information. The pore size distributions of the CMSM derived from N2 and CH4 adsorption isotherm are found to be consistent with each other and in agreement with the results of gas permeation experiments as well as the general characteristics of such molecular sieve materials. © 2003 Elsevier B.V. All rights reserved. Keywords: CMSM; PSD; Permeation; Adsorption
1. Introduction Carbon molecular sieve membrane (CMSM) is produced from the controlled pyrolysis of polymeric precursors. Its microstructure resembles that of the precursor but with superior selectivity, thermal stability and strength [1–3]. A CMSM generally possesses pores of relatively uniform sizes which enable the discrimination of gas molecules with very similar dimensions. CMSMs are promising materials for the separation of a number of important gas mixtures. Due to the specific structural characteristics (ultramicropores with narrow PSD) of a CMSM, the traditional/conventional characterization methods, such as N2 sorption at its liquid temperature (−196 ◦ C) may become unpractical because of the extremely slow ∗ Corresponding author. E-mail address: [email protected] (K. Wang).
sorption rate. Some researchers depend largely on such methods as gas permeation [1], Dubinin–Raduskevich (DR) plot [2], molecular probe [2], or SEM [4], etc. These methods have been known to require arduous experimental efforts or expensive facilities and yet the interpretation of the results still bears some difficulties. Statistical methods like GCMC or DFT are theoretically very revealing, but may require some special molecular properties and are complicated to use. A dynamic method such as the permeation technique appears the most suitable for the purpose of characterizing the pore structure due to the sieving usage of the molecular sieve materials like CMSM. An alternative way is to characterize the CMSM pore system by analyzing the adsorption equilibrium (isotherm) of a suitable adsorbate at room temperature. Adsorption of nitrogen at its normal boiling point (sub-critical temperature) is a very useful tool for
0376-7388/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0376-7388(03)00219-9
178
C. Nguyen et al. / Journal of Membrane Science 220 (2003) 177–182
materials having pores of larger sizes or a system of pore of a wide distribution, where surface layering and capillary condensation are always parts of the adsorption process [7]. In the case of CMSM, where pores are exclusively in micro-size range with narrow distributions, adsorption of supercritical gases seems to be more appropriate, because (1) supercritical adsorption in micropores is by and large faster than sub-critical adsorption and, (2) supercritical gas adsorption takes place mostly in micropores while sub-critical adsorption may occur even on outer surface of the membrane. This paper is an attempt to characterize the PSD of a CMSM by the gas adsorption at higher (room) temperatures using a model proposed by Nguyen and Do [5].
2. Adsorption of supercritical gases in porous media In the model proposed by Nguyen and Do [5], new concepts are introduced to account for the enhancement of the potential energy of interaction between ad-molecules (adsorbate molecules) and surface atoms within the pore interior. With these concepts, a structure-based model is developed to describe the adsorption equilibria in pore system. The model requires only molecular properties of the adsorbate and adsorbent, and the structural heterogeneity is accounted for using the distribution of micropore size. The model is briefly presented as follows. Once finding themselves in a pore system, some of the gas molecules will be attracted very close, i.e. adsorbed, to the solid surface while the others will remain in the gas phase within the pore. These gas phase molecules are referred to as the confined gas molecules, the pressure ppore of which can be calculated from the bulk pressure pbulk as follows: g −Epore ppore = pbulk exp (1) RT g
with Epore being the potential energy of the gas phase molecules confined in the pore interior. A molecule adsorbed in a micropore is under the force field from all sides of the pore. Such interaction depends on the distance between the walls as well as the position of the ad-molecule relative to the pore
walls. At equilibrium, this interaction and hence the heat of adsorption is a function of the pore size. We denote Es and bs as the heat released and the affinity of adsorption on a flat surface, respectively. Similarly, we denote Epore and bpore as those of adsorption in a pore. The affinity coefficient of adsorption in the pore bpore then can be calculated from the affinity coefficient of adsorption on flat surface bs by the formula: Epore − Es (2) bpore = bs exp RT √ with bs = (β/ MT) exp(Es /RT) and M is the molecular weight. β is a parameter characterizing the solid surface. This parameter takes a value of 0.426 for adsorption on a flat surface as found by Hobson [6]. The resulting affinity has a unit of inverse Mpa. In our previous work [5] we argued that due to the restriction of movement in pore space the parameter takes a smaller value and in this paper, β is assigned a value of 0.08. If f(r) is the pore size distribution function and H(p, r) is the single pore isotherm equation, the amount adsorbed at pressure p can be calculated as: ∞ C (p) = H(p, r)f(r) dr. 0
Using Langmuir equation as the local isotherm, we get ∞ bpore (r)ppore (r) C (p) = f(r) dr (3) Cs (r) 1 + bpore (r)ppore (r) 0 with Cs (r) the maximum capacity of all pores of size r. The PSD, f(r), can be derived by comparing Eq. (3) to the isotherm data. Details of the algorithm are presented in [5,7] while the basic principles are described as follows. The micropores of CMSM are assumed to be slit-shaped, similar to the one described by the 10-4-3 potential (pore walls consist of several graphite layers in parallel) [7]. The adsorption potential of a molecule confined in such a pore is the summation of the Lennard–Jones’ (LJ) 12-6 potentials between the ad-molecule and each carbon atom on the pore walls. For an ad-molecule confined in a pore of size r, g the related energy parameters [Epore , Es , and Epore in Eqs. (1) and (2)] can be calculated from the summation of the LJ potentials according to their definitions. The LJ parameters used in the simulations are listed in Table 1.
C. Nguyen et al. / Journal of Membrane Science 220 (2003) 177–182
179
Table 1 Gas permeation properties of the KP 800 CMSM at room temperature and atmospheric pressure Gases (10−10
Kinetic diameter σ /κ (T) Permeability (Barrer) Selectivity (PHelium /Pi ) a
m (Å))
H2
He
N2
O2
CH4
CF4
C
2.89 – 507.62 0.31
2.60 – 158.86 1.00
3.64 71.4 7.13 22.28
3.46 – 41.40 3.84
3.80 148.6 1.24 128.11
4.70 – 0a ∞
3.5 28 – –
Observation in 12 h only.
3. Experimental A CMSM (referred to as KP 800) was prepared via the controlled pyrolysis of Kapton® polyimide film under vacuum. The highest pyrolysis temperature is 800 ◦ C and the thermal treatment program is described in [2,8]. A Cahn 2000 microbalance (resolution: 10−3 g) was used to measure gas sorption isotherms on the KP 800. The microbalance is fitted in a high pressure vessel for which the temperature can be controlled in the range of −20 to 92 ◦ C. About 0.6 g of KP 800 in small crushes was loaded in the sample basket. An aluminum block was used as the counterweight. To minimize the effect of buoyancy, gold is added in the sample basket to ensure that both density and weight of the sample basket are (nearly) the same as those of the counterweight. This is achieved via trial and error. Helium is assumed to be the non-adsorbing gas at room temperature and is used to check the effect of buoyancy. The sample was cleaned at high temperature and under vacuum. The weight of the sample was monitored during the cleaning process until there was no change observable within 12 h. The zero point of the microbalance is then set accordingly. The adsorption isotherm of N2 was measured in the pressure range of 0.005–4 MPa at the temperatures 35, 60 and 90 ◦ C, respectively. At lower pressure and temperature, the sorption rate of N2 was seen slow on the KP 800 and it may take three more days for the equilibrium to be reached (weight change less then 10−3 g in 12 h). Such slow sorption kinetics of N2 at its supercritical temperature was also reported on an ultra-microporous carbon by Koresh et al. [9]. A conventional time lag rig was used to measure gas permeations on the KP 800 CMSM with a diameter of approximately 3 cm and a thickness of 125 m. The detailed experimental setup and procedures are
described in [2]. Table 1 shows the permeation fluxes (permeability) and selectivities (versus Helium) of several gases on the KP 800 at room temperature and at atmospheric pressure. It can be seen that this membrane presents reasonable sieving effect for gas molecules with different kinetic diameters, which suggests that the CMSM is predominantly microporous with no major contribution from Knudsen diffusion or viscous flow in its overall mass transfer. This is in agreement with our previous results from molecular probing experiments on a CMSM prepared under the similar thermal treatment conditions [2].
4. Results and discussion Adsorption/desorption isotherms of nitrogen at three temperatures are shown in Fig. 1. No hysteresis is observed for this system. It is understood that no hysteresis due to capillary condensation is possible in this case since there is no mesopore in the CMSM and
Fig. 1. Nitrogen adsorption on KP 800 at different temperatures (solid-adsorption, hollow-desorption).
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C. Nguyen et al. / Journal of Membrane Science 220 (2003) 177–182
more over, it is about supercritical adsorption. The lack of a hysteresis on the isotherm may also point to the absence of very narrow micropores, which may be a reason for micropore hysteresis [9]. The model equations are then employed to fit the experimental data. It is known that the maximum pore capacity Cs is a function of temperature. However, the thermal expansion coefficient was found to be rather small (in the order of 1×10−5 mol/◦ C), [10], i.e. the effect of the thermal expansion is minimal within the experimental temperature range (35–90 ◦ C). The fitting is carried out for nitrogen adsorption at three different temperatures simultaneously. In the fitting process, the whole pore spectrum is divided into a number of pore sub-ranges, and then the optimization procedure is invoked to find the volume of each sub-range such that the calculated isotherm closely matches the experimental data [7]. This method does not assume any particular form for the distribution function, and as a result the PSD reflects the “real” distribution better than methods assuming an a-priori form for the distribution. The fitting results (lines) are satisfactory for all temperatures as shown in Fig. 2a and b, where pressure is presented in normal and log scales, respectively to highlight the goodness of fit at low- and high-pressure ranges. The derived PSD in Fig. 2c is consistent with the permeation experiment: a narrow distribution of micropores without a significant presence of mesopores, and the majority of pores are smaller than 10 × 10−10 m (10 Å) in diameter. It is important to note that the PSD in Fig. 2c is in terms of adsorption capacity, which is different but related to the common
volumetric PSD. The absence of mesopores and larger micropores is a must for any sieving materials and this is supported by our observations in the permeation experiments, e.g. CF4 , a molecule with the kinetic diameter of approximately 4.7 × 10−10 m (4.7 Å), virtually cannot penetrate the 125 m (thickness) CMSM in 12 h at room temperature and pressure. The model is further tested with the adsorption data of the other gas adsorbate, methane, for which the isotherm was measured on KP 800 at 90 ◦ C. The isotherm data and fitting are shown in Fig. 3a and b while the PSD derived is shown in Fig. 3c, respectively. We see that the PSD derived is more homogeneous (with a pore size range of (8–9) × 10−10 m (8–9 Å)) and qualitatively agree with the PSD derived from N2 sorption data. The difference may result from the difference in the size and geometries of methane and nitrogen molecules, because (1) some of the smaller micropores accessible to N2 (3.64 × 10−10 m (3.64 Å)) may not be “felt” by the methane (3.80 × 10−10 m (3.80 Å)) molecule, and (2) the dump-bell (3.64 × 10−10 m × 3.01 × 10−10 m (3.64 Å × 3.01 Å)) shaped N2 molecule is likely to experience slightly different sorption potential compared with the spherical methane molecule. For example, a slit-shaped pore with the size of 10 × 10−10 m (10 Å) (center to center) may accommodate up to two layers of N2 , but only one layer of methane at the experimental pressure range. Thus the KP 800 can be more “heterogeneous” to N2 than to CH4 molecules. In a previous study [2], molecular probing (sorption) were performed on a CMSM prepared under similar thermal treatment conditions (T = 800 ◦ C, but
Fig. 2. The fitting of nitrogen adsorption isotherms at three temperatures (a and b) and the derived PSD (c). Symbols and solid lines represent the experimental data and model fitting, respectively.
C. Nguyen et al. / Journal of Membrane Science 220 (2003) 177–182
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Fig. 3. The fitting of methane adsorption isotherm at 90 ◦ C (a and b) and the derived PSD (c). Symbols and solid lines represent the experimental data and model fitting, respectively.
with the thickness of 23 m). Several gases, including CO2 , C2 H6 , n-C4 H10 and i-C4 H10 , were used as probing molecules. i-C4 H10 (5.0 × 10−10 m (5.0 Å)) was seen to marginally adsorb on that CMSM. The sorption capacity of i-C4 H10 is comparable to that of n-C4 H10 (4.3 × 10−10 m (4.3 Å)) but much less than that of CO2 (3.3 × 10−10 m (3.3 Å)). The PSD of that CMSM was then calculated from the micropore volumes derived from the DR equation for various gas molecules and was found in the range below 4.5 × 10−10 m (4.5 Å) (effective pore size, wall to wall), which makes the center-to-center PSD below 8 × 10−10 m (8 Å). These ‘physical’ characterization results are in a reasonable consistency with the PSD derived from N2 data (Fig. 2). Thus the PSD derived from the N2 sorption data is more applicable with this model. However, because of the complicated nature of the microporous structure of the CMSM (known as turbostratic structure). The PSD derived from equilibrium information may not be immediately applicable for a permeation (dynamic) process in which not only the size of pores but also the way they connected with each other also plays a decisive role. Some discrepancy can also be found by comparing the results from our equilibrium and permeation experiments. For example, at sub-critical temperatures i-C4 H10 and n-C4 H10 are seen to marginally adsorbable on such CMSMs, yet molecules of approximately same size (CF4 ) are not permeable. This phenomenon may point to the importance of the pore connectivity in the CMSM and constitutes a challenging issue in future study.
5. Conclusions Adsorption isotherms of nitrogen and methane were measured on a CMSM at raised temperature and under wide pressure range. The PSD of the CMSM is derived from the equilibrium information using the model proposed by Nguyen and Do. The PSD is found predominantly in the upper-ultra-micropore range, without any significant mesopore contribution. The results are supported by our gas permeation as well as molecular probing experiments. The study confirms the suitability of the model and forms a basis for further study on gas permeation in microporous media.
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