Journal of Membrane Science 220 (2003) 177–182

Short communication

The structural characterization of carbon molecular sievemembrane (CMSM) via gas adsorption

C. Nguyena, D.D. Dob, K. Harayac, K. Wangd,∗a CSIRO Manufacturing & Infrastructure Technology, Gate 4 Normanby Road, Clayton, 3168 Vic., Australia

b Department of Chemical Engineering, University of Queensland, St. Lucia, 4067 Qld, Australiac National Institute of Advanced Industrial Science & Technology, Central 5, Tsukuba 305-8565, Japan

d 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 infor-mation. The pore size distributions of the CMSM derived from N2 and CH4 adsorption isotherm are found to be consistentwith each other and in agreement with the results of gas permeation experiments as well as the general characteristics of suchmolecular sieve materials.© 2003 Elsevier B.V. All rights reserved.

Keywords: CMSM; PSD; Permeation; Adsorption

1. Introduction

Carbon molecular sieve membrane (CMSM) isproduced from the controlled pyrolysis of polymericprecursors. Its microstructure resembles that of theprecursor but with superior selectivity, thermal stabil-ity and strength[1–3]. A CMSM generally possessespores of relatively uniform sizes which enable thediscrimination of gas molecules with very similardimensions. CMSMs are promising materials for theseparation of a number of important gas mixtures.

Due to the specific structural characteristics (ultra-micropores with narrow PSD) of a CMSM, the tradi-tional/conventional characterization methods, such asN2 sorption at its liquid temperature (−196◦C) maybecome unpractical because of the extremely slow

∗ Corresponding author.E-mail address: mkwang@ntu.edu.sg (K. Wang).

sorption rate. Some researchers depend largely on suchmethods as gas permeation[1], Dubinin–Raduskevich(DR) plot [2], molecular probe[2], or SEM [4], etc.These methods have been known to require arduousexperimental efforts or expensive facilities and yetthe interpretation of the results still bears some dif-ficulties. Statistical methods like GCMC or DFT aretheoretically very revealing, but may require somespecial molecular properties and are complicated touse. A dynamic method such as the permeation tech-nique appears the most suitable for the purpose ofcharacterizing the pore structure due to the sievingusage of the molecular sieve materials like CMSM.An alternative way is to characterize the CMSMpore system by analyzing the adsorption equilib-rium (isotherm) of a suitable adsorbate at roomtemperature.

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 ofpore of a wide distribution, where surface layering andcapillary condensation are always parts of the adsorp-tion process[7]. In the case of CMSM, where poresare exclusively in micro-size range with narrow distri-butions, adsorption of supercritical gases seems to bemore appropriate, because (1) supercritical adsorptionin micropores is by and large faster than sub-criticaladsorption and, (2) supercritical gas adsorption takesplace mostly in micropores while sub-critical adsorp-tion may occur even on outer surface of the membrane.This paper is an attempt to characterize the PSD of aCMSM by the gas adsorption at higher (room) tem-peratures using a model proposed by Nguyen and Do[5].

2. Adsorption of supercritical gases in porousmedia

In the model proposed by Nguyen and Do[5], newconcepts are introduced to account for the enhance-ment of the potential energy of interaction betweenad-molecules (adsorbate molecules) and surfaceatoms within the pore interior. With these concepts, astructure-based model is developed to describe the ad-sorption equilibria in pore system. The model requiresonly molecular properties of the adsorbate and adsor-bent, and the structural heterogeneity is accounted forusing the distribution of micropore size. The model isbriefly presented as follows. Once finding themselvesin a pore system, some of the gas molecules will beattracted very close, i.e. adsorbed, to the solid surfacewhile the others will remain in the gas phase withinthe pore. These gas phase molecules are referred toas the confined gas molecules, the pressureppore ofwhich can be calculated from the bulk pressurepbulkas follows:

ppore = pbulk exp

(−E

gpore

RT

)(1)

with Egpore 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 interactiondepends on the distance between the walls as well asthe position of the ad-molecule relative to the pore

walls. At equilibrium, this interaction and hence theheat of adsorption is a function of the pore size. WedenoteEs andbs as the heat released and the affinity ofadsorption on a flat surface, respectively. Similarly, wedenoteEporeandbporeas those of adsorption in a pore.The affinity coefficient of adsorption in the porebporethen can be calculated from the affinity coefficient ofadsorption on flat surfacebs by the formula:

bpore = bs exp

(Epore− Es

RT

)(2)

with bs = (β/√

MT) exp(Es/RT) andM is the molec-ular weight.β is a parameter characterizing the solidsurface. This parameter takes a value of 0.426 for ad-sorption on a flat surface as found by Hobson[6]. Theresulting affinity has a unit of inverse Mpa. In our pre-vious work[5] we argued that due to the restriction ofmovement in pore space the parameter takes a smallervalue and in this paper,β is assigned a value of 0.08.

If f(r) is the pore size distribution function andH(p,r) is the single pore isotherm equation, the amountadsorbed at pressurep can be calculated as:

C�(p) =∫ ∞

0H(p, r)f(r) dr.

Using Langmuir equation as the local isotherm, weget

C�(p) =∫ ∞

0C�s(r)

bpore(r)ppore(r)

1 + bpore(r)ppore(r)f(r) dr (3)

with C�s(r) the maximum capacity of all pores of sizer. The PSD,f(r), can be derived by comparingEq. (3)to the isotherm data. Details of the algorithm are pre-sented in[5,7] while the basic principles are describedas follows. The micropores of CMSM are assumedto be slit-shaped, similar to the one described by the10-4-3 potential (pore walls consist of several graphitelayers in parallel)[7]. The adsorption potential of amolecule confined in such a pore is the summationof the Lennard–Jones’ (LJ) 12-6 potentials betweenthe ad-molecule and each carbon atom on the porewalls. For an ad-molecule confined in a pore of sizer,the related energy parameters [Epore, Es, andE

gpore in

Eqs. (1) and (2)] can be calculated from the summa-tion of the LJ potentials according to their definitions.The LJ parameters used in the simulations are listedin Table 1.

C. Nguyen et al. / Journal of Membrane Science 220 (2003) 177–182 179

Table 1Gas permeation properties of the KP 800 CMSM at room temperature and atmospheric pressure

Gases H2 He N2 O2 CH4 CF4 C

Kinetic diameterσ (10−10 m (Å)) 2.89 2.60 3.64 3.46 3.80 4.70 3.5ε/κ (T) – – 71.4 – 148.6 – 28Permeability (Barrer) 507.62 158.86 7.13 41.40 1.24 0a –Selectivity (PHelium/Pi ) 0.31 1.00 22.28 3.84 128.11 ∞ –

a Observation in 12 h only.

3. Experimental

A CMSM (referred to as KP 800) was preparedvia the controlled pyrolysis of Kapton® polyimidefilm under vacuum. The highest pyrolysis tempera-ture is 800◦C and the thermal treatment program isdescribed in[2,8]. A Cahn 2000 microbalance (res-olution: 10−3 �g) was used to measure gas sorptionisotherms on the KP 800. The microbalance is fittedin a high pressure vessel for which the temperaturecan be controlled in the range of−20 to 92◦C.

About 0.6 g of KP 800 in small crushes was loadedin the sample basket. An aluminum block was usedas the counterweight. To minimize the effect of buoy-ancy, gold is added in the sample basket to ensurethat both density and weight of the sample basket are(nearly) the same as those of the counterweight. Thisis achieved via trial and error. Helium is assumed tobe the non-adsorbing gas at room temperature andis used to check the effect of buoyancy. The samplewas cleaned at high temperature and under vacuum.The weight of the sample was monitored during thecleaning process until there was no change observablewithin 12 h. The zero point of the microbalance is thenset accordingly.

The adsorption isotherm of N2 was measured inthe pressure range of 0.005–4 MPa at the temperatures35, 60 and 90◦C, respectively. At lower pressure andtemperature, the sorption rate of N2 was seen slow onthe KP 800 and it may take three more days for theequilibrium to be reached (weight change less then10−3 �g in 12 h). Such slow sorption kinetics of N2 atits supercritical temperature was also reported on anultra-microporous carbon by Koresh et al.[9].

A conventional time lag rig was used to measuregas permeations on the KP 800 CMSM with a diame-ter of approximately 3 cm and a thickness of 125�m.The detailed experimental setup and procedures are

described in[2]. Table 1shows the permeation fluxes(permeability) and selectivities (versus Helium) ofseveral gases on the KP 800 at room temperatureand at atmospheric pressure. It can be seen that thismembrane presents reasonable sieving effect for gasmolecules with different kinetic diameters, which sug-gests that the CMSM is predominantly microporouswith no major contribution from Knudsen diffusionor viscous flow in its overall mass transfer. This is inagreement with our previous results from molecularprobing experiments on a CMSM prepared under thesimilar thermal treatment conditions[2].

4. Results and discussion

Adsorption/desorption isotherms of nitrogen atthree temperatures are shown inFig. 1. No hysteresisis observed for this system. It is understood that nohysteresis due to capillary condensation is possible inthis case since there is no mesopore in the CMSM and

Fig. 1. Nitrogen adsorption on KP 800 at different temperatures(solid-adsorption, hollow-desorption).

180 C. Nguyen et al. / Journal of Membrane Science 220 (2003) 177–182

more over, it is about supercritical adsorption. Thelack of a hysteresis on the isotherm may also point tothe absence of very narrow micropores, which maybe a reason for micropore hysteresis[9].

The model equations are then employed to fit theexperimental data. It is known that the maximum porecapacityC�s is a function of temperature. However, thethermal expansion coefficient was found to be rathersmall (in the order of 1×10−5 mol/◦C), [10], i.e. the ef-fect of the thermal expansion is minimal within the ex-perimental temperature range (35–90◦C). The fittingis carried out for nitrogen adsorption at three differenttemperatures simultaneously. In the fitting process,the whole pore spectrum is divided into a number ofpore sub-ranges, and then the optimization procedureis invoked to find the volume of each sub-range suchthat the calculated isotherm closely matches the ex-perimental data[7]. This method does not assumeany particular form for the distribution function, andas a result the PSD reflects the “real” distributionbetter than methods assuming an a-priori form for thedistribution.

The fitting results (lines) are satisfactory for all tem-peratures as shown inFig. 2a and b, where pressureis presented in normal and log scales, respectively tohighlight the goodness of fit at low- and high-pressureranges. The derived PSD inFig. 2cis consistent withthe permeation experiment: a narrow distribution ofmicropores without a significant presence of meso-pores, and the majority of pores are smaller than 10× 10−10 m (10 Å) in diameter. It is important to notethat the PSD inFig. 2c is in terms of adsorption ca-pacity, which is different but related to the common

Fig. 2. The fitting of nitrogen adsorption isotherms at three temperatures (a and b) and the derived PSD (c). Symbols and solid linesrepresent the experimental data and model fitting, respectively.

volumetric PSD. The absence of mesopores and largermicropores is a must for any sieving materials and thisis supported by our observations in the permeationexperiments, e.g. CF4, a molecule with the kineticdiameter 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 adsorptiondata of the other gas adsorbate, methane, for whichthe isotherm was measured on KP 800 at 90◦C. Theisotherm data and fitting are shown inFig. 3a and bwhile the PSD derived is shown inFig. 3c, respec-tively. We see that the PSD derived is more homo-geneous (with a pore size range of (8–9)× 10−10 m(8–9 Å)) and qualitatively agree with the PSD derivedfrom N2 sorption data. The difference may result fromthe difference in the size and geometries of methaneand nitrogen molecules, because (1) some of thesmaller 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 slightlydifferent sorption potential compared with the spher-ical methane molecule. For example, a slit-shapedpore with the size of 10× 10−10 m (10 Å) (centerto center) may accommodate up to two layers ofN2, but only one layer of methane at the experimen-tal pressure range. Thus the KP 800 can be more“heterogeneous” to N2 than to CH4 molecules.

In a previous study[2], molecular probing (sorp-tion) were performed on a CMSM prepared undersimilar thermal treatment conditions (T = 800◦C, but

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 theexperimental data and model fitting, respectively.

with the thickness of 23�m). Several gases, includ-ing CO2, C2H6, n-C4H10 and i-C4H10, were used asprobing molecules.i-C4H10 (5.0 × 10−10 m (5.0 Å))was seen to marginally adsorb on that CMSM. Thesorption capacity ofi-C4H10 is comparable to that ofn-C4H10 (4.3 × 10−10 m (4.3 Å)) but much less thanthat of CO2 (3.3 × 10−10 m (3.3 Å)). The PSD ofthat CMSM was then calculated from the microporevolumes derived from the DR equation for variousgas molecules and was found in the range below4.5 × 10−10 m (4.5 Å) (effective pore size, wall towall), which makes the center-to-center PSD below8 × 10−10 m (8 Å). These ‘physical’ characterizationresults are in a reasonable consistency with the PSDderived from N2 data (Fig. 2). Thus the PSD derivedfrom the N2 sorption data is more applicable with thismodel.

However, because of the complicated nature ofthe microporous structure of the CMSM (known asturbostratic structure). The PSD derived from equilib-rium information may not be immediately applicablefor a permeation (dynamic) process in which not onlythe size of pores but also the way they connectedwith each other also plays a decisive role. Some dis-crepancy can also be found by comparing the resultsfrom our equilibrium and permeation experiments.For example, at sub-critical temperaturesi-C4H10and n-C4H10 are seen to marginally adsorbable onsuch CMSMs, yet molecules of approximately samesize (CF4) are not permeable. This phenomenon maypoint to the importance of the pore connectivity in theCMSM and constitutes a challenging issue in futurestudy.

5. Conclusions

Adsorption isotherms of nitrogen and methanewere measured on a CMSM at raised temperature andunder wide pressure range. The PSD of the CMSMis derived from the equilibrium information using themodel proposed by Nguyen and Do. The PSD is foundpredominantly in the upper-ultra-micropore range,without any significant mesopore contribution. Theresults are supported by our gas permeation as well asmolecular probing experiments. The study confirmsthe suitability of the model and forms a basis for fur-ther 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 microporesof carbon molecular sieve membranes derived from Kaptonpolyimide, J. Phys. Chem. B 101 (20) (1997) 3988.

[3] W.J. Koros, R. Mahajan, Pushing the limits on possibilitiesfor 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 carbonmolecular sieve membrane, AIChE J. 46 (2000) 2245.

[5] C. Nguyen, D.D. Do, Adsorption of supercritical gases inporous media: determination of micropore size distribution,J. Phys. Chem. B103 (1999) 6900.

[6] J.P. Hobson, A new method for finding heterogeneous energydistributions from physical adsorption isotherms, Can. J. Phys.43 (1965) 1934.

182 C. Nguyen et al. / Journal of Membrane Science 220 (2003) 177–182

[7] C. Nguyen, D.D. Do, Simple optimization approach for thecharacterization of pore size distribution, Langmuir 16 (2000)1319.

[8] J. Petersen, M. Matsuda, K. Haraya, Capillary carbonmolecular sieve membranes derived from Kapton for hightemperature gas separation, J. Membr. Sci. 131 (1997) 85.

[9] J.E. Koresh, T.H. Kim, W.J. Koros, Study of ultramicroporouscarbons by high pressure adsorption, J. Chem. Soc., Farad.Trans. 85 (1989) 1537.

[10] K. Wang, D.D. Do, Characterizing micropore size distributionof activated carbon using equilibrium data of many adsorbatesat various temperatures, Langmuir 13 (1997) 6226.