Gas permeation through micropores of carbon molecular sieve membranes derived from Kapton polyimide

Article abstract of DOI:10.1021/jp963997u

The evolution of micropores and the gas permeation properties have been investigated on carbon molecular sieve dense membranes prepared by pyrolysis of Kapton polyimide films under several conditions. With decreasing the pore sizes upon pyrolization under vacuum, the gas permeability decreased, whereas the permselectivity increased. The change in the heating rate was found to affect the permeation properties to a lesser extent; however, the pyrolysis atmosphere (vacuum or inert purge pyrolysis) did not appreciably influence the properties within the experimental conditions studied. The highest permselectivities attained by a membrane were H₂/N₂ 4700, He/N₂ 2800, CO₂/N₂ 122, and O₂/N₂ 36, respectively, at 308 K. The permeabilities of the selected gases were shown to be in the order H₂ > He > CO₂ > O₂ > N₂ for almost all the membranes, whose order was not exactly in accordance with the order of kinetic gas diameters. From the temperature dependencies of permeability, diffusivity, and sorptivity of the membrane, the anomalous behavior that H₂, with a larger kinetic diameter, permeated faster than the smaller He was explained to originate in the larger sorptivity of H₂ than that of He.

Full text of DOI:10.1021/jp963997u

3988
J. Phys. Chem. B 1997, 101, 3988-3994
Gas Permeation through Micropores of Carbon Molecular Sieve Membranes Derived from
Kapton Polyimide
Hiroyuki Suda* and Kenji Haraya
National Institute of Materials and Chemical Research, 1-1 Higashi, Tsukuba 305, Japan
ReceiVed: December 6, 1996; In Final Form: February 18, 1997X
The evolution of micropores and the gas permeation properties have been investigated on carbon molecular
sieve dense membranes prepared by pyrolysis of Kapton polyimide films under several conditions. With
decreasing the pore sizes upon pyrolization under vacuum, the gas permeability decreased, whereas the
permselectivity increased. The change in the heating rate was found to affect the permeation properties to a
lesser extent; however, the pyrolysis atmosphere (vacuum or inert purge pyrolysis) did not appreciably influence
the properties within the experimental conditions studied. The highest permselectivities attained by a membrane
were H2/N2 4700, He/N2 2800, CO2/N2 122, and O2/N2 36, respectively, at 308 K. The permeabilities of the
selected gases were shown to be in the order H2 > He > CO2 > O2 > N2 for almost all the membranes,
whose order was not exactly in accordance with the order of kinetic gas diameters. From the temperature
dependencies of permeability, diffusivity, and sorptivity of the membrane, the anomalous behavior that H2,
with a larger kinetic diameter, permeated faster than the smaller He was explained to originate in the larger
sorptivity of H2 than that of He.
Introduction
hydride (BPDA), and 5,5-[2,2,2-trifluoro-1-(trifluoromethyl)-
ethylidene]-1,3-isobenzofurandione. Hayashi et al.7 prepared
CMS membranes by dip-coating of BPDA-4,4′-oxydianiline
(ODA) solution on an R-Al2O3 porous support tube followed
by pyrolysis. We have reported that both the flat, dense8,9 and
asymmetric capillary10 CMS membranes prepared by pyrolysis
of a Kapton type polyimide under controlled conditions
exhibited the highest gas permselectivities among those in the
past. The Kapton type polyimide was derived from pyromellitic
dianhydride (PMDA) and ODA.
A growing interest can be seen in the synthesis of novel
inorganic membranes for gas separation mainly because of their
chemical and thermal stability. One of the candidates is a
carbon molecular sieve (CMS) membrane, which is obtained
by pyrolysis of a polymeric precursor. The CMS membrane
has extensively been studied and shown to exhibit excellent gas
separation performance.1-11 A distinctive feature is that the
controlled pyrolysis of a precursor can yield a series of CMS
membranes that possess micropores of desired dimension.
Nevertheless, the factors determining the microstructure and gas
permeation properties of CMS membranes are not completely
open to control, because these properties are significantly
affected by several factors and vary from sample to sample.
These factors include (a) the choice of polymeric precursor, (b)
the membrane formation method, and (c) the pyrolysis condition.
The choice of polymeric precursor (a) is the first important
factor since pyrolysis of each precursor may bring about
different CMS membranes, sometimes even leaky ones. Poly-
furfuryl alcohol was used by Bird and Trimm1 to prepare
unsupported and supported CMS membranes, but it proved
impossible to prepare a continuous membrane. Koresh and
Soffer2,3 carried out detailed studies on the gas separation
performance of CMS hollow fiber membranes derived from
thermosetting polymers. Rao and Sircar4 prepared nanoporous
carbon membranes by pyrolysis of a polyvinylidene chloride
layer coated on a graphite disk support, in order to separate gas
mixtures by selective surface flow. Shusen et al.5 proposed a
one-step preparation method of asymmetric CMS membranes,
consisting of the formation of phenol formaldehyde film
followed by pyrolysis and unequal oxidation steps. In recent
years, polyimides are considered to yield CMS membranes with
better separation properties. Jones and Koros6 reported gas
separation properties of CMS asymmetric hollow fiber mem-
branes prepared by pyrolysis of 6F-containing polyimide. The
polyimide used was derived from a reaction of 2,4,6,-trimethyl-
1,3-phenylene diamine, 3,3′,4,4′-biphenyltetracarboxylic dian-
Whether the membrane formation (b) is carried out either by
coating of the precursor on porous support or by phase inversion
techniques, both followed by pyrolysis steps, or by one-step
pyrolysis of precursor dense film is another factor. In some of
the past studies5,6,11 asymmetric membranes have been prepared,
because the thinner skin layer formed on a porous support is
desirable for practical use in providing higher fluxes. Our
previous study,10 however, revealed that the microstructure and
gas permeation properties of asymmetric CMS membranes
prepared on the basis of the phase inversion technique were
difficult to control and were sensitively influenced by prepara-
tion conditions particularly at the gelation step. The formation
method1,4,7 of repeating the coating-pyrolysis cycle for several
times until no pinholes are depicted also needs time and special
care. The simplest method8,9 of pyrolysis of commercially
available Kapton film instead can produce dense CMS mem-
branes with better reproducibility. These dense membranes are
not practical from the viewpoint of industrial application;
however, they are preferable to asymmetric ones in making clear
the factors that determine the basic properties.
The pyrolysis condition (c), such as the pyrolysis temperature,
the heating rate, and the pyrolysis atmosphere, is the third factor.
Although the pyrolysis temperature should be varied in ac-
cordance with the precursor polymer, all the temperatures in
the past studies fall within the range 773-1273 K. The heating
rate, typically in the range 1-13.3 K/min, may also affect the
membrane performance. The choice of pyrolysis atmosphere
has drawn increasing attention, especially because the atmo-
sphere can change the pore size and geometry or even the nature
X Abstract published in AdVance ACS Abstracts, April 1, 1997.
S1089-5647(96)03997-1 CCC: $14.00 © 1997 American Chemical Society

Gas Permeation through Carbon Molecular Sieve Membranes
J. Phys. Chem. B, Vol. 101, No. 20, 1997 3989
Figure 2. Illustration of the apparatus for gas permeation measurement
by the time-lag method.
as precursor, in order to measure accurate time lags for the
smaller penetrants such as He and H2. Heating rate (1.33-
13.3 K/min) and pyrolysis atmosphere (under vacuum or Ar
flow) were also controlled so as to study the effects of pyrolysis
conditions on the CMS membrane properties. All the mem-
branes were allowed to cool to room temperature under each
atmosphere. The microstructure of the prepared CMS mem-
branes was investigated by Fourier transform infrared spectros-
copy (Nicolet, Magna 550), elemental analysis (Carlo Erba, 1106
& EA-1108), XPS (X-ray photoelectron spectroscopy) (Perkin
Elmer, PHI 5600ci), X-ray diffractometry (Rigaku, RAX 12),
high-resolution transmission electron microscopy (Jeol, JEM-
2000FX), and gas sorption measurements (Nihon Bell, Belsorp
28).
Figure 1. Pyrolization process of Kapton polyimide membranes.
of the surface by sintering (pore closure) or activation (pore
opening by removal of surface groups or by burn-off) effects.
4,5,7
The atmospheres of He,11 Ar,8,11 or N2
were used for the
inert purge pyrolysis, whereas the vacuum pyrolysis technique
was employed by Koros et al.6,11 and Suda et al.9,10 Geiszler
and Koros11 compared the two pyrolysis techniques on asym-
metric CMS membranes derived from 6F-containing polyimide
and concluded that the vacuum pyrolysis produced more
selective but less productive membranes than the inert purge
pyrolized membranes. They also investigated the other variables
and discussed effects of residual oxygen in inert gases. All of
the above factors may diversify the resulting membrane proper-
ties, and thus should be controlled to yield better CMS
membranes, but are not compared thoroughly.
2. Analysis of Pore Size Distribution. Pore size distribu-
tions were estimated by the molecular probe method from
analysis of sorption isotherms at 298 K of probe gas molecules
with different kinetic diameter σ13 (CO2, C2H6, n-C4H10, i-C4H10)
by application of Dubinin-Astakhov equation:14
W ) W0 exp{-(A/E)n}
(1)
Another significant problem is that few studies have inves-
tigated gas permeation properties in connection with the
microstructure of a membrane and the diffusivity and the
sorptivity of a penetrant. One of the interesting phenomena
encountered is the anomalous behavior4,8-10 that H2, with a
larger kinetic diameter, permeates through CMS membranes
faster than the smaller He. Considering that the permeability
of a given membrane may be the product of the diffusivity
(kinetic factor) and the sorptivity (thermodynamic factor),12
studies on the two factors are indispensable for understanding
the permeation behavior. Therefore a systematic study on both
the microstructure and the gas permeation properties of well-
characterized flat, dense CMS membranes may serve to explain
all aspects of CMS membrane properties.
One of the objectives in the present study is a clarification
of the factors that determine the microstructure and the
permeation properties of CMS dense membranes derived from
Kapton polyimide film. The other is to gain insight into the
permeation mechanism through the study of permeability versus
kinetic diameter in connection with diffusivity and sorptivity.
where W is the pore volume, E is the characteristic energy of
sorption, and W0 is the limiting pore volume whose pore size
is assumed to be larger than the kinetic diameter of each sorbate.
The sorption potential A [)RT ln(ps/p)] is calculated from the
saturated vapor pressure ps, the equilibrium vapor pressure p,
the gas constant R, and the measurement temperature T. The
obtained sorption data were analyzed with the parameter n )
2, in accord with those for microporous carbon.7 The W0 values
were obtained from y-axis intersections in the plots of ln W
against A2 [)(RT ln(ps/p))2]. Samples were degassed at 573 K
for 2 h prior to each sorption measurement.
3. Gas Permeation Measurements. Gas permeabilities
were measured at 308-373 K with a high-vacuum time-lag
method15,16 under the pressure difference of 1 atm (Figure 2).
Permeability values were calculated by using the following
equation:
VT0L
dp
P )
(2)
(
)
dt p0TpfAm
Experimental Section
where P is the permeability expressed in Barrer [1 Barrer ) 1
× 10-10 {cm3(STP)‚cm}/{cm2‚s‚cmHg}], dp/dt is the rate of
the pressure increase under the steady state, V is the volume, L
is the membrane thickness, pf is the feed pressure, T is the
measurement temperature, Am is the membrane area, and p0 and
T0 are the standard pressure and temperature, respectively. Both
the feed and permeate sides of the membrane cell were
1. Preparation of CMS Membranes and Characteriza-
tion. The CMS membrane was fabricated by pyrolysis of
Kapton polyimide film 100H (Toray, Dupont Inc., thickness
25 µm) between graphite blocks at mainly 873-1273 K for 2
h with a heating rate of 10 K/min under a vacuum of 10-5 Torr9
(Figure 1). Films of 125 µm thickness (500H) were also used

3990 J. Phys. Chem. B, Vol. 101, No. 20, 1997
Suda and Haraya
Figure 3. Changes in the weight and film diameter as a function of
pyrolysis temperature.
Figure 4. Infrared spectra of (a) original Kapton film and Kapton films
pyrolized at (b) 873, (c) 1073, and (d) 1273 K under vacuum for 2 h.
evacuated (<10-5 Torr) prior to each time-lag measurement.
The rate of pressure rise on the permeate side was monitored
by thermostated Baratron sensors. The temperature of the
membrane cell set in a ventilated oven was kept at a desired
value within an accuracy of (0.5 K. Permselectivity is defined
in the present study as the ratio of permeability of chosen gas
over that of N2:ideal separation factor.
Figure 5. High-resolution transmission electron micrographs of the
CMS membranes.
oxygen, 5.9% nitrogen, 1.0% hydrogen, and 0.5% other ele-
ments. The unexpected large amount of oxygen may be due to
surface-sorbed oxygen, as was suggested by Jones and Koros,6
where the oxygen was able to be etched away by Ar ablation.
The O1s peak located at around the binding energy of 532.5 eV
in XPS spectra of our 1273 K membrane indeed became
negligibly small after Ar etching for only 30 s, while the peaks
of C1s (284 eV) and N1s (399 eV) were almost unchanged even
after the etching, resulting in a carbon content of about 95%.
These CMS membranes were essentially X-ray amorphous,
and the crystallinity became higher with increasing the pyrolysis
temperature.9 The carbon prepared by the pyrolysis of organic
materials is known to have a turbostratic structure,19 in which
layer-planes of graphite-like microcrystallines are dispersed in
a noncrystalline carbon. The high-resolution transmission
electron micrographs (Figure 5) demonstrate that such a
graphite-like structure starts to appear and develops at higher
pyrolysis temperature. The abrupt evolution of gases in the early
stage of pyrolization through either imide ring cleavage or C-N
bond cleavage processes18 changes the crystalline state of
polyimide to an amorphous state, and the evolution of mainly
N2 gas in the further pyrolysis steps makes the layer-planes of
graphite-like microcrystallines grow.
Results and Discussion
1. Pyrolization Process of Kapton Polyimide Film under
Vacuum. Upon heating, the color of the film changed from
transparent yellow to dark brown, and then black due to
pyrolization. The weight and the film diameter decreased
abruptly at around 800-900 K and then gradually (Figure 3).
The weight loss at a lower pyrolysis temperature of about 800-
900 K is attributed to O217 or CO and CO2,18 at an intermediate
temperature of 900-1100 K to H2,18 and at higher than 1100
17,18
K mainly to N2
released during thermal degradation of
Kapton polyimide. The ATR infrared spectra shown in Figure
4 indicate that the peak intensities for the aliphatic or aromatic
C-N (1100-1200 cm-1, 1300-1400 cm-1), CdO (∼1700
cm-1, 1200-1300 cm-1), and C-H bonds (600-900 cm-1
,
1000-1200 cm-1) were reduced at higher pyrolysis tempera-
tures.
It is characteristic of the Kapton polyimide film that pyrolysis
of the film yields CMS dense membranes without pinholes
despite the rather large weight loss of about 40% and shrinkage
of about 25% at 1273 K. The micropores of CMS membranes
are considered to be developed by the evolved gases channeling
out of the matrix during pyrolysis. Thus the pyrolysis condition
is expected to strongly affect the pore structure, which will be
described later.
The CMS membrane obtained at 1273 K under vacuum was
revealed to consist of almost only carbon by the infrared
spectrum (Figure 4 (d)). The elemental analysis revealed that
the membrane KP1273 contains about 85% carbon, 7.6%
2. Pore Analysis of the Vacuum-Pyrolized CMS Mem-
branes. To gain further insight into the structural change of
the CMS membranes, we estimated pore size distribution.
Sorption isotherms of probe molecules (Figure 6) imply how
the pore size changes with increase in pyrolysis temperature.
The membrane prepared at lower temperature (KP873) sorbed
to some extent even i-C4H10, the largest sorbate (σ ) 5.0 Å),

Gas Permeation through Carbon Molecular Sieve Membranes
J. Phys. Chem. B, Vol. 101, No. 20, 1997 3991
Figure 6. Sorption isotherms of probe molecules for the CMS membranes (measured at 298 K).
Figure 7. Typical Dubinin-Astakhov plots for the CMS membrane
KP1073.
whereas the membrane prepared at 1273 K (KP1273) sorbed
only CO2, the smallest sorbate (σ ) 3.3 Å). All these isotherms
were well fitted with the Dubinin-Astakhov equation14 (Figure
7). The pore size distributions, plots of the limiting micropore
volume W0 against the kinetic diameters of probe sorbate
molecules, are shown in Figure 8a. It is clear from the
distributions that with increasing the pyrolysis temperature, both
the limiting pore volume and pore size decrease. The plots also
indicate that pore size distributions become sharper when the
pyrolysis temperatures rise. Figure 8b shows that pyrolysis at
Figure 8. (a, top) Pore size distributions of the CMS membranes; plots
higher temperatures reduces the portion of larger pores. The
W0 values for CO2 increased from 0.15 (KP1273) to 0.22 cm3/g
(KP873) with decreasing pyrolysis temperature, all of which
were larger than that of the silica microporous membrane (W0
) 0.11 cm3/g).20 Hayashi et al.7 reported that the W0 increased
from 0.16 to a maximum of about 0.36 cm3/g at a pyrolysis
temperature of 1073 K for BPDA-ODA polyimide-derived
CMS membranes. The results may indicate the possibility of
larger micropore volume for CMS membranes derived from the
other polymers than from Kapton. Assuming that the charac-
teristic energy of sorption E obtained by CO2 sorption is related
to average pore size,7 the values of 10.7, 11.4, and 11.5 kJ/
mol, for KP873, KP1073, and KP1273, respectively, were in
accordance with the pore size reduction upon heating. The
microstructure (pore size, pore volume, etc.) can therefore be
tailored by controlling the pyrolysis temperature.
of limiting micropore volume W0 against kinetic diameters of probe
sorbate molecules. (b, bottom) Change in volume of each pore size of
the CMS membranes.
greatest effect on the microstructure and the gas permeation
behavior for the vacuum-pyrolized CMS membranes; that is,
the permeabilities of the selected gases measured at 373 K
became lower, whereas the gas permselectivities became higher
with increasing the pyrolysis temperature. For H2/N2 and CO2/
N2 gas pairs, the permselectivities reached up to 1450 and 101
at 308 K, respectively, for the membrane KP1273 (Table 1),
whose values were much higher than those reported1-7 by 1 or
2 orders of magnitude. Such extremely high gas permselec-
tivities imply that the CMS membrane has a molecular sieving
effect, by which the membrane can discriminate between the
small and larger molecules. Thus the larger molecules such as
N2 are more restricted than the smaller ones to diffuse into the
narrower pore whose size is close to or smaller than their kinetic
gas diameters. In view of the turbostratic structure, gases are
likely to permeate both through the cross-linked voids of the
amorphous region and the interlayer spacing of the graphite-
3. Gas Permeation Properties of the Vacuum-Pyrolized
CMS Membranes. Figure 9 compares the permeation perfor-
mance of the CMS membranes pyrolized under various condi-
tions (pyrolysis temperature, heating rate, and pyrolysis atmo-
sphere). The pyrolysis temperature was found to have the

3992 J. Phys. Chem. B, Vol. 101, No. 20, 1997
Suda and Haraya
4. Effects of the Other Pyrolysis Conditions on Gas
Permeation Properties. Figure 9 also shows that the perme-
ability decreases with decreasing the heating rate from 13.3 to
1.33 K/min. The reason for this trend may be that with
decreasing the heating rate the pyrolization proceeds very
slowly, which may make the pore smaller. The longer total
time for pyrolysis may also contribute to the pore size reduction
due to a sintering effect. The membrane pyrolized at the slowest
heating rate of 1.33 K/min under Ar flow exhibited the highest
permselectivity of all the membranes studied (H2/N2 4700 and
O2/N2 36 at 308 K), indicating the possibility of their use in
the processes of hydrogen recovery, oxygen enrichment of air,
etc.
It is worthwhile mentioning the effects of pyrolysis atmo-
sphere, because from a study on several factors of an inert purge
pyrolysis technique Geiszler and Koros11 concluded that even
the residual trace levels of oxygen (0.3 ppm) in the inert gases
affected the membrane properties. They also mentioned that
the trace of oxygen made the pore larger, but the reduction in
the purge flow rate from 200 to 20 cm3(STP)/min had the
opposite effect of reduction of pore size presumably due to
deposition of carbon. To investigate the inert gas effect, the
pyrolization was carried out also in the present study under high
purity Ar flow (purity >99.9995%, flow rate 500 cm3(STP)/
min). According to the supplier Nihon-sanso. Co. Ltd., the Ar
contained at most 0.2 ppm of oxygen. The trace of oxygen
was thus reduced by passing the Ar through heated graphite
blocks at the inlet side of a furnace. Comparing the difference
in the pyrolysis atmosphere from the two curves for KP1273
(10 K/min, vac) and KP1223 (13.3 K/min, Ar) (also in Table
1), the trace of oxidative gases was shown not to exhibit a severe
effect on the permeation performance owing to the reduction
of the trace level and to the higher flow rate.
Figure 9. Gas permeabilities (measured at 373 K) of the CMS
membranes prepared at 873, 1073, and 1273 K under vacuum and at
1223 K under Ar flow. Permeabilities are given in Barrer, where 1
Barrer equals 1 × 10-10 cm3(STP)‚cm / cm2‚s‚cmHg.
like microcrystallines. The question is which path mainly
contributes to the molecular sieving effect, and it is the subject
of further investigation.
The reasons that we obtained the highest permselectivity for
the selected gases are having pyrolized the film at appropriate
temperature and selecting the polymer film suitable for the
pyrolysis. The membrane pyrolized at lower temperatures
(KP873) exhibited higher permeability (for instance, PH2 )
1600 Barrer at 308 K) with relatively much loss in permselec-
tivity (H2/N2 ) 19.6). This is because of a large amount of
micropore volume whose size is large enough for N2 molecules
(σ ) 3.64 Å) to permeate through. This means that the pyrolysis
temperature should be varied in accordance with target gases
to be separated. Pyrolysis of the films other than Kapton
polyimide might bring about the presence of a large amount of
an amorphous portion or larger pores or even cracks,1 resulting
in the preference for permeation of larger gases through these
voids. Rao’s nanoporous carbon membranes4 prepared by
pyrolysis of polyvinylidene chloride layer coated on a graphite
disk support may be one of the cases, although the membranes
could efficiently separate hydrocarbons from H2 by competitive
adsorption and surface diffusion of the more strongly adsorbed
components.
5. Order of Gas Permeabilities against Kinetic Diameters
of Gas Molecules. The permeabilities of the selected gases
measured at 373 K (Figure 9) and at 308 K (Table 1) were
shown to be in the order H2 > He > CO2 > O2 > N2 for all
the CMS membranes except for KP873. The order was not
exactly in accordance with the order of kinetic gas diameter,13
since the kinetic diameter sequence is He < H2 < CO2 < O2 <
N2. Similar results have been obtained for our asymmetric CMS
membranes10 and for Rao’s nanoporous carbon membranes,4
while the silica microporous membrane with a pore size of less
than 20 Å used by Shelekhin et al.21 exhibited an “expected”
ordinary trend; that is, the permeabilities followed the order of
kinetic diameter. It is valuable to give an interpretation for the
order of gas permeabilities against kinetic diameter, since this
kind of correlation is related to the estimation of molecular
TABLE 1: Gas Permeabilities and Permselectivities Measured at 308 K for the CMS Membranes Prepared At 873, 1073, and
1273 K under Vacuum, and at 1223 K under Ar Flow; The Data for the Thicker Membrane (Thickness 113 µm) Are Shown
within Parentheses
KP873
KP1073
KP1273
KP1223
KP1223
KP1223
(10 K/min, vac)
(10 K/min, vac)
(10 K/min, vac)
(13.3 K/min, Ar)
(4.5 K/min, Ar)
(1.33 K/min, Ar)
PHea
He/N2
PH2
H2/N2
PCO2
CO2/N2
PO2
O2/N2
PN2
N2/N2
534
6.54
1600
19.6
1820
22.2
383
4.70
81.6
1
248
81.4
669
220
128
42.2
34.8
11.5
3.04
1
27.9
680
59.4
1450
4.15
101
0.96
23.4
0.04
1
26.4
618
53.1
1240
3.54
82.7
0.92
21.6
0.04
1
21.1
739
41.3
1450
2.51
87.7
0.66
23.0
0.03
1
11.6 (4.97)
2810
19.4 (6.89)
4700
0.50
122
0.15
36.0
0.004
1
b
a Permeability [in Barrer] measured at 308 K; 1 Barrer ) 1 × 10-10 {cm3(STP)‚cm}/{cm2‚s‚cmHg}. b Permselectivity for A and B gases:
PA/PB.

Gas Permeation through Carbon Molecular Sieve Membranes
J. Phys. Chem. B, Vol. 101, No. 20, 1997 3993
TABLE 2: Properties of Penetrants and Gas Permeation Data (Permeability P, Diffusivity D, and Sorptivity S) for the
Membrane KP1223 (1.33 K/min, Ar, thickness 22 µm) Obtained at 373 K, and the Corresponding Pre-exponential Factors P0,
D0, S0, Apparent Activation Energies for Permeation EP, for Diffusion ED, and Heat of Sorption HS; The Latter Values Were
Determined through Temperature Dependencies of Permeability, Diffusivity, and Sorptivity within the Temperature Range
308-373 K; The Data for the Thicker Membrane (Thickness 113 µm) Are Shown within Parentheses (1 Barrer ) 1 × 10-10
{cm3(STP)‚cm}/{cm2‚s‚cmHg})
kinetic
diameter potential
penetrant σ [Å]13 ꢀ/k [K]25 [Barrer]
L-J
P
D
S
P0
[Barrer]
D0
S0
EP
ED
HS
[cm2/s]
[cmHg-1
]
[cm2/s]
[cmHg-1
]
[kJ/mol] [kJ/mol] [kJ/mol]
He
2.60
10.2
18.1
152
(143)
151
6.61
(8.62)
5.27
(8.90) (3.90 × 10-7
)
)
(2.28 × 10-3
(7.25 × 10-3
)
(1.83 × 10-5
(1.91 × 10-5
)
)
(7.82 × 10-4
(6.50 × 10-4
5.22 × 10-4
3.93 × 10-4
)
(11.9)
(-3.32)
H2
2.89
59.7
28.1
(11.4)
0.47
(1.57 × 10-7
)
(124)
)
(7.42)
(14.9)
15.9
21.9
31.8
(-7.47)
-16.9
-14.2
-15.1
CO2
O2
N2
3.30
3.46
3.64
195
107
71.4
1.13 × 10-10 4.18 × 10-1
5.01 × 10-10 5.11 × 10-2
0.35 1.88 × 10-8
3.05 5.85 × 10-7
2.86 7.31 × 10-7
1.87 × 10-3 -0.95
0.26
7.74
0.013 2.75 × 10-11 4.84 × 10-2
16.7
dimensions from sorption kinetics22 and the theoretical calcula-
tion of critical pore dimensions.23
where D(C) is the local concentration-dependent diffusivity at
a local point of concentration C, and Ch and Cl are the sorbed
penetrant concentrations at the feed and permeate sides,
respectively. As shown in the sorption isotherms (Figure 6), a
straight line tangent to the isotherms at each point of pressure
that corresponds to each sorptivity is not constant. Consequently
the values of D and S reported in the present study are apparent
ones expressed respectively by the eqs 5 and 6. Recalling the
permeability being given as the product of the diffusivity and
the sorptivity, the permeability may be expressed as follows:
A detailed study was thus conducted for the membrane
KP1223 (1.33 K/min, Ar) in order to understand the permeability
order. As is well-known, a CMS membrane produced by
pyrolysis of a polymeric precursor is essentially a microporous
material (the pore size is a few angstroms) with a turbostratic
structure.19 There seems no complete theory that is applicable
to totally explain the gas permeation behavior through such a
small micropore with a size comparable to the dimensions of
the penetrant molecules. However considering the rather high
sorptivity of gases in CMS than in the polymer and the fact
that the so-called sorption time-lag16 is observed on our
membranes, it seems acceptable to apply a sorption-diffusion
theory12 of the polymer membrane to the gas permeation in CMS
membranes in an analogous way.
Phenomenologically in the sorption-diffusion model, the
permeation process of gas molecules through a membrane under
a pressure difference is explained to consist of three steps: (I)
sorption of gas molecules at the membrane surface of a higher
pressure side, (II) diffusion of the sorbed gas molecules through
the membrane under a pressure gradient, and (III) desorption
of gas molecules at the membrane surface of a lower pressure
side. In an ideal case where the diffusivity D and the sorptivity
S are constant, applications of Fick’s law of diffusion to step II
and a linear relationship of the external gas pressure and the
corresponding equilibrium concentration to the steps I and III
give a simple expression:
P ) P0 exp(-EP/RT) ) DS
) D0 exp(-ED/RT)S0 exp(-HS/RT)
) D0S0 exp(-(ED + HS)/RT)
(7)
Therefore in the present study, the apparent activation energy
for permeation EP was assumed to be the sum of the apparent
activation energy for diffusion ED and the apparent heat of
sorption HS.
Table 2 lists the data of the permeability P, diffusivity D,
sorptivity S at 373 K, and the apparent activation energies for
permeation EP, for diffusion ED, and the heat of sorption HS,
those parameters being estimated from the temperature depend-
encies of permeability, diffusivity, and sorptivity. The diffu-
sivities decreased from 10-7 to 10-11 [cm2/s] in order with the
kinetic diameters σ of penetrants, whereas the sorptivities
increased from 10-3 to 10-1 [cmHg-1] in order with the
Lennard-Jones potential ꢀ/κ.25 This greater change in the
diffusivity compared to that in the sorptivity implies that the
excellent permselectivity of the CMS membranes is attributed
to the molecular sieving effect that comes mainly from the
dependence of diffusivity on the pore size. Rao’s comment4
that “a very small change (∼0.5 Å) in the pore diameter in the
3-10 Å range reduces the diffusivity by an order of magnitude”
is instructive in this respect. Comparison of the calculated
diffusivity of N2 as a function of pore diameter at 296 K4 with
the measured N2 diffusivity (order of 10-8 to 10-11 [cm2/s]) on
our CMS membranes suggests that the average pore sizes of
the membranes are around 4 Å, consistent with those estimated
from the molecular probe method (Figure 8). The ED data and
-HS data were correlated linearly at a positive slope with the
square of kinetic diameter and with ꢀ/κ, respectively. It was
thus also implied that gases with larger cross-sectional area need
greater activation energies for diffusion and that the more
condensable gases are more easily sorbed.
P ) DS
(3)
where the permeability P equals by definition the steady state
flux divided by the driving pressure across the membrane
normalized by the membrane thickness. The expression (3)
means that the product of the diffusivity (kinetic factor) and
the sorptivity (thermodynamic factor) determines the perme-
ability of a penetrant through the membrane. The apparent
diffusivity D was calculated by the equation24
D ) L2/6θ
(4)
where θ is the sorption time-lag observed in the early stage of
permeation. Accordingly the apparent sorptivity S can be
estimated from the expression (3) by using the obtained P and
D values, while in the case where the diffusivity and the
sorptivity are concentration dependent, they are given as
Ch
Ch
D )
D(C) dC/
dC
(5)
(6)
∫
∫
C1
C1
The anomalous behavior that the larger H2 gas (σ ) 2.89 Å)
permeates faster than the smaller He gas (σ ) 2.60 Å) through
our membranes including the previous ones8-10 and Rao’s
S ) (Ch - C1)/(ph - p1)

3994 J. Phys. Chem. B, Vol. 101, No. 20, 1997
Suda and Haraya
nanoporous membranes4 may be connected with the sorptivity
difference. The present study revealed that at 373 K the
diffusivity of He is about 2 times larger than that of H2, while
the sorptivity of He is about one-third of that of H2 (Table 2).
The above mentioned results imply that the larger sorptivity of
H2 than that of He contributes the higher H2 permeability. The
phenomenon that CO2 (σ ) 3.30 Å) permeates faster than the
smaller He (σ ) 2.60 Å) observed for the membrane KP873
(Figure 9, Table 1) and for Hayashi’s CMS membrane pyrolized
at 873 K7 may be explained in a similar manner. It should be
born in mind, however, that the present study reports only the
ideal separation factors and not the mixed gas separation factors.
Considering that the heavier hydrocarbons permeated faster than
the smaller H2 or CH4 by selective surface flow through Rao’s
nanoporous carbon membranes,4 the present CMS membranes
are also expected to exhibit different behavior on mixed gas
separations. Mixed gas permeation measurements now under-
taken may give further insight into the permeation mechanism.
Acknowledgment. We would like to express our thanks to
Mr. Satoshi Yoda of the National Institute of Materials and
Chemical Research for taking TEM photographs.
References and Notes
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Conclusions
It was proven in the present study that a series of CMS dense
membranes with tailored microstructure (pore size, pore volume,
etc.) can be obtained by controlling pyrolysis conditions
(pyrolysis temperature, heating rate, and pyrolysis atmosphere).
Of the pyrolysis conditions, the heating temperature had the
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