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SCIENCE E L S E V I E R Journal of Membrane Science 104 (1995) 27-42

Single component and mixed gas transport in a silica hollow fiber membrane

Mohammed H. Hassan, J. Douglas Way *, Paul M. Thoen, Anne C. Dillon Department of Chemical Engineering and Petroleum Refining, Colorado School of Mines, Golden, CO 80401-1887, USA

Received 12 August 1994; accepted 29 December 1994

Abstract

The permeances of gases with kinetic diameters ranging from 2.6 to 3.9 A were measured through silica hollow fiber membranes over a temperature range of 298 to 473 K at a feed gas pressure of 20 atm. Permeances at 298 K ranged from 10 to 2.3.105 Barrer/cm for CH 4 and He, respectively, and were inversely proportional to the kinetic diameter of the penetrant. From measurements of CO2 adsorption at low relative pressures, the silica hollow fibers are microporous with a mean pore size estimated to be between 5.9 and 8.5 A. X-ray scattering measurements show that the orientation of the pores is completely random. Mass transfer through the silica hollow fiber membranes is an activated process. Activation energies for diffusion through the membranes were calculated from the slopes of Arrhenius plots of the permeation data. The energies of activation ranged from 4.61 to 14.0 kcal/mol and correlate well with the kinetic diameter of the penetrants. The experimental activation energies fall between literature values for zeolites 3A and 4A. Large separation factors were obtained for O2/N2 and COJCI-I4 mixtures. The O2/N2 mixed gas separation factors decreased from 11.3 at 298 K to 4.8 at 423 K and were up to 20% larger than the values calculated from pure gases at temperatures below 373 K. Similar differences in the separation factors were observed for CO2/CH4 mixtures after the membrane had been heated to at least 398 K and then cooled in an inert gas flow. The differences between the mixture and ideal separation factors is attributed to a competitive adsorption effect in which the more strongly interacting gases saturate the surface and block the transport of the weakly interacting gases. Based on Fourier transform infrared (FFIR) spectroscopy results, this unusual behavior is attributed to the removal of physically adsorbed water from the membrane surface.

Keywords: Inorganic membranes; Ceramic membranes; Glass membranes; Gas separations; Microporous membranes

1. Introduct ion

Membrane processes can require less energy and capital investment than many other separation technol- ogies such as distillation, absorption, and extraction. In addition to applications such as macromolecule separation and water desalination, membrane technology has been applied to large scale industrial gas separa-

* Corresponding author, phone: (303) 273-3519, fax: (303) 273- 37~30, email: [email protected].

0376-7388/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSD10376-7388(95)00009-7

tions such as H 2 recovery, removal of acid gases from

CH4, and the production of nitrogen from air [ 1,2].

New applications of membrane technology for gas and liquid separations will result from new materials pro-

viding better selectivity and thermal and chemical stability than existing materials [3] . Therefore, new membrane materials with improved properties and ade-

quate selectivities must be identified and developed in order to increase the industrial applications of

membrane technology.

28 M.H. Hassan et al. /Journal of Membrane Science 104 (1995) 27-42

(1) Knudsen diffusion

(2) Surface diffusion

• o e o V I / I / I o i • Oi° o O o o

0o • ° O i l o • • I / I / I / 1

• ° • o I / / / / o-(, I o o • o ilOOOoO% o • o • • ~o •IF 0 o

kinetic diameters of several gases of industrial interest. The kinetic diameter is the interrnolecular distance of closest approach for two molecules colliding with zero initial kinetic energy [ 7 ].

An example of a selective microporous inorganic membrane is the developmental silica hollow fiber material manufactured by PPG Industries [ 9-11 ]. The focus of this paper is an experimental investigation of the structure, surface chemistry, and transport mechanisms in the PPG silica hollow fiber membrane.

• o I ~ l l l I I I o O ° ~ l ~ o o o

(3) Capillary condensation eo o • o

e^ e I I I I I 1 1 o 0 u • O 0 0 Q 0 0 0

(4) Molecular sieving o ° e o l / / / / / I o • o o o • o

"o I771111° Fig. 1. Mechanisms of mass transfer through microporous membranes.

Porous metal oxides (ceramics) are promising membrane materials for gas separations at high temperatures or in aggressive chemical environments [4,5]. The pore size and surface properties of porous inorganic membranes dictate their ability to perform gas separations [5]. As shown in Fig. 1 [6], there are four basic mechanisms for the transport of gases and vapors through microporous materials including: Knudsen diffusion, surface diffusion, capillary condensation, and activated diffusion which is also referred to as molecular sieving [7,8].

The pore diameters in commercially available o

porous inorganic membranes are greater than 50 A, and gas transport occurs by Knudsen diffusion or capillary condensation. Unfortunately, it is difficult to obtain high selectivities with Knudsen diffusion. A calculation of the selectivity with a large molecular weight difference, such as between H2 and N2, yields a selectivity of 3.7. For non-condensable gases, the selectivities obtained are too small for industrial applications. If smaller pores can be fabricated with diameters approaching molecular dimensions, better selectivity may be achieved by utilizing the activated diffusion and surface diffusion mechanisms. Table 1 shows the

2. Background

The fabrication of selective, porous, inorganic membranes for gas separations is an extremely active research area. Over the past ten years, investigators have prepared porous carbon, ceramic, and silica membranes by a variety of techniques (pyrolysis, chemical vapor deposition, sol-gel, and acid leaching) with the objective to increase selectivities above those obtained with Knudsen barriers. While several of these techniques have been successful in increasing separation factors over Knudsen values, the ~ansport mechanisms through these membranes are not yet well understood.

Koresh and Sofer [ 12,13] have reported molecular sieve carbon membranes prepared by the pyrolysis of polymer films. These membranes have ideal separation factors much higher than those predicted from Knudsen diffusion (e.g., He/O2 and O2/N2 selectivities of 20 and 8.0, respectively), Koresh and Sofer attribute the high selectivity to a molecular sieving or size discrim- ination effect. An 02 permeability of 110 Barrer was

Table 1 The kinetic diameters of gases discussed in this paper ~

Gas molecule Kinetic diameter (]~)

He 2.6 H2 2.89 CO2 3.3 At 3.40 Oz 3.46 N2 3.64 CO 3.76 e l l 3.8 C:I-L 3.9

"From [7].

M.H. Hassan et al. / Journal of Membrane Science 104 (1995) 27--42 29

reported, which is very large compared to typical polymer values [ 13].

Recently, Rao and Sircar [ 14,15] have reported the fabrication of microporous carbon membranes by the pyrolysis of poly(vinylidene chloride) that will selectively permeate alkanes over hydrogen. In contrast to the approach of Koresh and Sofer described above, Rao and Sircar chose to optimize the microstructure of their membranes such that surface diffusion is the controlling mechanism. Although the ideal separation factors from pure gas measurements suggested that the membranes were selective for H2, in mixed gas transport measurements the membranes were selective for C2 to C4 alkanes over hydrogen. At 295 K and a feed pressure of 4.4 atm, the mixture CaH1o//H2 separation factor was 94.

Chemical vapor deposition has been recently used to decrease the pore size of inorganic membranes. Okubo and Inoue [16,17] used chemical vapor deposition techniques to modify microporous Vycor-type glass membranes. The chemical modification resulted in a He/O2 mixture separation factor of 6, which is twice as high as the Knudsen value. A vapor phase alkoxy- silane was reacted with the silica surface in order to reduce the pore size of the glass membrane. The smaller pore size changed the mass transfer mechanism from Knudsen diffusion to either surface diffusion or molecular sieving. Lin and Burggraf used a CVD process to deposit ZrO2 in order to decrease the pore size of an alumina ultrafilter [ 18]. They used the opposing reac- tants approach developed by Gavalas and coworkers [191.

Hwang and coworkers have also modified ceramic membranes to reduce the pore size [20,21]. In their work, they pyrolyzed silicon-containing polymer films supported on porous Vycor glass tubes. A Hz/SF 6 separation factor 38 times larger than the Knudsen diffusion selectivity was reported for their composite membrane [ 21 ].

Uhlhorn et al. [22] have recently deposited SiO: sols on T-A1203 supports to produce gas separation membranes which demonstrate molecular sieving behavior. A H=/N2 separation factor of 2000 was observed at 723 K. However, the microporous SiOz layer was unstable and was reported to densify with prolonged contact with ambient air containing water vapor.

Brinker and coworkers [23] have also prepared microporous inorganic membranes by the sol-gel technique. Polymeric silicate sols were deposited on commercial alumina ultrafilters and the resulting membranes were extensively characterized. A mean pore size of less than 10 ,~ for the silica top layer was inferred from reductions in He and N2 pure gas permeance values compared to the alumina support. How- ever, the He/N2 ideal separation factors were less than the calculated Knudsen value.

In previous work, we reported permeabilities of pure gases as a function of temperature for microporous silica hollow fiber membranes [ 11 ]. These developmental hollow fiber membranes were manufactured by PPG Industries [9,10]. The transport mechanism for gas permeation was shown to be non-Knudsen since several heavier gases such as CO2 permeated faster than lighter gases such as N2. High ideal selectivities of 163 and 62.4 were observed at 343 K for H2/N2 and H2/ CO, respectively, which compare very favorably with polymeric gas separation membranes. It was proposed that the controlling transport mechanisms were surface diffusion and molecular sieving.

Ma and co-workers [20,24,25] have studied gas adsorption and the permeability characteristics as a function of temperature using a different sample of the PPG silica hollow fiber membrane. Bhankarkar et al. [24] measured equilibrium adsorption isotherms for C O 2, H20, C2H4, CH4, C2HsOH, and CH2CI 2 at high pressure and at temperatures of 303 and 343 K. The Dubinin-Radushevich isotherm was found to give the best fit of the data. No multilayer adsorption or capillary condensation was observed at the experimental conditions. Shelekhin et al. [ 25 ] observed an Al"rhenius type relationship between pure gas permeability and temperature for He, CO2, 02, N2, and CH 4. The pure gas permeabilities were inversely proportional to the kinetic diameter of the penetrants. High ideal separation factors were observed. It was concluded that adsorption plays a minor role in mass transport in the silica hollow fiber membranes. Shelekhin et al. [25] used percolation theory to describe the microstructure of the silica hollow fiber membranes. Monte-Carlo methods were used to estimate the membrane tortuosity factor, porosity, and surface area. The tortuosity was found to depend on the total porosity of the membrane and the surface area was inversely proportional to the

30 M.H. Hassan et al. / Journal of Membrane Science 104 (1995) 27-42

pore diameter. The pore diameter was estimated to be between 5 and 20 ,~.

In this paper we present experimental measurements of the pore size distribution and present pure and mixed gas permeance data for PPG silica hollow fiber membranes. Transmission Fourier transform infrared (FTIR) spectroscopy was used to investigate the surface chemistry of the membranes to elucidate the role of water in the mass transport process.

3. Experimental

3.1. Membrane materials

PPG Industries provided the microporous hollow fiber silica membranes used in this work. The fibers were manufactured by melt extrusion of borosilicate glass followed by acid leaching to remove the metallic oxides producing a network of pores less than 20 ,~ in diameter [9,10]. The inside and outside diameter of the hollow fibers were measured to be 35 and 45/zm, respectively, using scanning electron microscopy. The specific sample of silica hollow fibers used in this work was different than those previously reported [ 11 ].

The preparation of single hollow fiber test cells for transport measurements was described previously [ 11 ] with the exception that a high temperature polymeric adhesive (Aremco 631, Aremco Products, Ossining, NY) was used as a potting compound.

3.2. Physical adsorption of gases

The pore size distribution of the silica hollow fibers was estimated by measuring the physical adsorption of CO2 at 201 K using a high resolution pore size analyzer (Omnisorp 100, Coulter Electronics, Hialeah, FL). CO2 was found to be a more suitable adsorbate than Nz or Ar, which are not adsorbed in significant amounts at liquid nitrogen and argon temperatures. The adsorption isotherm was obtained in very small (10-~)partial pressure increments starting at a very low adsorbate partial pressure. This technique has been previously applied to analyze the structure of zeolites [26,27] and molecular sieve carbon [28].

The experiments were run in the static mode to ensure that equilibrium between the adsorbate and adsorbent was achieved for each data point. Prior to the

experiments, 60 mg of the silica fibers were outgassed at 175°C under vacuum until a residual pressure of less than 1 x 10 - 6 Torr was achieved. Helium was used to determine the volume of the sample chamber and is assumed not to adsorb at experimental temperatures. Both helium and COz were purchased from General Air Inc. at 99.999% and 99.9% purity, respectively, and used without further purification.

3.3. Small angle X-ray scattering (SAXS)

In addition to physical adsorption measurements, SAXS experiments were performed as an alternative analytical method to determine the pore size distribution of the fibers. The details of the SAXS instrumen- tation and experimental method are described elsewhere [ 29].

3.4. Infrared spectroscopy

FTIR spectroscopy was employed to characterize the stability of physisorbed water and chemisorbed surface hydroxyl species on the silica hollow fiber membranes as a function of pressure and annealing temperature. In addition, water adsorption on the silica membranes was examined. Sensitivity requirements limit transmission FTIR studies to high surface area materials because typical infrared cross sections are low [ 30]. Silica hollow fiber membranes with 8 .~ pore diameters and a porosity of ~ 20% provide a surface area enhancement of ~ 400 x which is sufficient for facile infrared studies.

The silica hollow fiber membranes were mounted on a 10 x 11 mm single crystal Si (100) wafer with a thick- ness of 400/~m. Aremco 618 high temperature ceramic adhesive was applied at the top and bottom edges of the silica hollow fiber membranes. The silicon crystal mounting design and techniques for sample heating have been described previously [ 31 ]. A schematic of the UHV chamber for in-situ transmission FTIR studies has also been given earlier [32]. For these studies, the UHV chamber was equipped with a diffusion pump which was employed to achieve pressures of approximately 1 × 10 - 3 Torr. An isolation valve could then be opened to a 1901/s Balzers turbomolecular pump ena- bling pressures of 5-6X 10 - 6 Torr to be obtained within ~ 10 min.

M.H. Hassan et al. / Journal of Membrane Science 104 (1995) 27-42 31

A Nicolet 740 FI 'IR spectrometer and an MCT-B infrared detector were employed in these studies. The infrared beam passed through a pair of 0.5-inch thick CsI windows on the vacuum chamber. The CsI windows could be isolated from the chamber using gate valves to prevent species from being deposited inad- vertently on the windows.

Thermal annealing studies were employed to moni- tor the thermal stability of both the physisorbed HzO and chemisorbed silica surface hydroxyl species. The annealing studies were performed under ultra high purity (UHP) nitrogen. The silica surface temperature was increased using a heating rate of 7 K/s. The sample was held at the annealing temperature for 5 min. For temperatures < 600 K FTIR spectra were subsequently recorded at the annealing temperature. Because of increased infrared absorption by free carriers at higher temperatures [ 33,34], FTIR spectra were recorded at 600 K for annealing temperatures > 600 K. The experimental sequence was performed for annealing temperatures up to 700 K.

Water adsorption was also monitored on the silica hollow fiber membranes. An FTIR spectrum of the porous silica hollow fiber membranes was initially

obtained at room temperature and atmospheric pressure. The UHV chamber was then evacuated to 1 X 10 -5 Torr and an infrared spectrum was recorded. The silica sample was subsequently exposed to atmospheric pressure for 10 min, and an FTIR spectrum was recorded. The sample was then annealed to 450 K in N2 for 5 min and an infrared spectrum was obtained at 450 K. Finally, the silica sample was cooled at,room temperature for ~ 10 min at atmospheric pressure and an FTIR spectrum was subsequently recorded.

3.5. Transport measurements

The mass transport measurements were performed with an automated, multicomponent apparatus shown in Fig. 2. The apparatus consists of a 35 atm gas flow system capable of producing three component feed gas mixtures of any composition using pure bottled gases, an electric furnace, and an automated gas chromatograph for measurement of gas compositions. A helium sweep stream carries the permeating gas from the end of the fiber to the gas chromatograph. Bubble flow meters are used to measure the flow rates of the residue and permeate streams. For pure gas experiments, the

. 4==-- Vent

250 °C Electr ic Ovt~n

r-SZ

r, S2

Exhaust

J

10- °°rt Gas ~ Chromatograph

Exhaust

Fig. 2. Schematic diagram of the inorganic hollow fiber membrane test system. MFC refers to a mass flow controller. Mixed gases flow into the oven where the membrane cell is located. Feed to the membrane flows over the outside of the fiber; a small portion permeates through the fiber. The nonperrneate, or residue, stream and the permeate stream are analyzed by gas chromatography. Flow of the permeate is determined with a bubble flow meter.

32 M.H. Hassan et al. / Journal of Membrane Science 104 (1995) 27--42

only experimentally measured quantity is the permeate flow rate. In most cases a bubble-flow meter is utilized for this measurement. However, if the permeate flow rate is below 10 ml/min, a helium sweep stream and gas chromatographic analysis are necessary. In multicomponent experiments, the relevant measured quan- tities are the mole fractions of the permeating gases and the permeate flow rate. Reported separation factors were calculated by taking the ratios of the gas permeabilities (ai j = Pi/Pi).

4. Results and discussion

4.1. Membrane microstructure

Physical adsorption of C O 2 at 201 K was used to provide the primary characterization of the microstructure of the silica hollow fiber membranes. Alternate potential functions were used to calculate the pore size distribution because the Kelvin equation cannot be used for pore diameters below 20/~ since the adsorbed molecules will not display bulk fluid behavior [35].

Fig. 3 is a pore size distribution for the silica hollow fiber sample calculated using the Horvath-Kawazoe

. • 0.30

E

r~ uJ m n," O O.2O ( / ) r~ < UJ

,- I o > 0.10 .- I

I-- Z IJJ

W i, IJ- N o.oo

O

Z~

. . . . i . . . .

A H-K (slab) model

O S-F (cylinder) model

O O A O

° o A ~ 0 0

. . . . . .

5 10 15 20

P O R E D I A M E T E R (A)

Fig. 3. The pore size distribution for the silica hollow fiber membrane material calculated from CO2 physical adsorption at 201 K using the Horvath-Kawazoe (parallel plate) and Saito-Foley (cylinder) potential functions.

Table 2 Parameters for pore size calculations

Parameter Silica surface CO2

Diameter, d (nm) 0.264 a 0.33 b Polarizability, a (cm 3) 2.74 X 10 - ~ a 2.911X 10 - ~ Magnetic susceptibility, X (cm3) 4 .6× 10 -29a 3.49 X 10 -2~ Density, N (molecules/cm 2) 8.48 X 1014a 6.10 X 1014e

aUsed in H-K computer program provided by Coulter Electronics. bKinetic diameter. CCalculated from CO2 liquid density listed in CRC Handbook. From CRC Handbook.

(H-K) and Saito-Foley (S-F) potential functions [27,28] The H-K function models the pores as two parallel plates, while the S-F function models the pores as perfect cylinders. The silica hollow fiber sample exhibited a Type I isotherm characteristic of microporous materials [ 36]. The calculated average pore diameters are 5.9/~ using the H-K model and 8.5/~ using the S-F model. The pore geometry of the silica hollow fibers is tortuous and neither model describes the actual physical situation. However, the pore size of the silica hollow fiber membranes should be between the geo- metrical extremes of two flat parallel plates and a right cylinder. It is also quite possible that the microstructure of the fibers consists of a network of pores connected by narrow channels or constrictions. Table 2 gives the values of the physical constants used in the pore size calculations with both the H-K and S-F models.

To examine the validity of the alternate potential functions, we have performed CO2 physical adsorption measurements using zeolites with a range of known pore sizes [ 37 ]. Using the Horvath-Kawazoe potential function and the model parameters listed in Table 2, we calculated pore sizes from our adsorption measurements that are within 10% of the known pore size.

The pore size distribution measurements in Fig. 3 are significant because it has long been speculated that extremely small pores and a very narrow pore size distribution, such as those found in zeolite A, are necessary to obtain high selectivities with microporous inorganic membranes. However high selectivities for difficult separations such as O 2 / N 2 have been observed for the silica hollow fiber material where virtually all of the pores are larger than 4/k . These observations would support a more complex mechanism than simple size exclusion.


The SAXS data and calculated results are given in Fig. 4 which shows a plot of scattered X-ray intensity multiplied by h vs. h, where h = 27r(20)/A. By assum- ing the pores are spherical voids, an average pore size of approximately 13/~, was calculated. This small characteristic dimension is consistent with the pore size distribution measurements in Fig. 3. In future work, we will modify the data analysis computer program to fit the data to cylindrical pores. Changing the angle of incidence of the X-rays resulted in no detectable change in the intensity of the transmitted X-rays, indicating that the pores are oriented in a completely random configuration.

4.2. Single component permeance measurements

Permeation data were obtained for pure gases (He, H2, CO2, 02, N2, Ar, CH4, CO, and C2H4), and binary gas mixtures (O2/N 2 and CO2/CH4). Arrhenius plots of permeance for pure gases as a function of temperature (298 to 473 K) are presented in Figs. 5, 6, and 7. A different membrane cell containing a single hollow fiber from the same membrane material was used to obtain the data for each figure.

Arrhenius plots for the permeability data were orig- inally prepared using the classical Eyring equation to model an activated mass transport process:

D = D * e -E/Rr (1)

where D is the diffusion coefficient, D* is the pre- exponential factor, E is the activation energy, R is the gas constant, and Tis absolute temperature. Plots of the logarithm of pure gas permeance as a function of 1/RT were linear for all of the gases with the exception of He, where the plot flattened out at higher temperatures.

Recent papers by Xiao and Wei [38,39] discussed the development of a unified theory for activated diffusion of alkanes in zeolites. The Eyring equation was generalized to the form:

D = guLe - e/Rr (2 )

where g is a geometric factor, u is the velocity of the penetrant from kinetic theory, and L is the average distance between jumps or collisions. Xiao and Wei modified the Eyring equation to include the temperature dependence of both the velocity and a factor describing the partitioning of the penetrant into the

" ~ - 9 . D

U') t -

-10 t -

" O

~ - 1 1 N

E -12 L.

O f -

- - 1 3 C-

.--/

i i i

k

I I I

1 0 2 0 3 0

h2(nm -2

A

I

E C

I o

¢-

>, ,

[..-

-4,-,

m

6 . 0 i i i

5o ~ 7 \ ,0 / \

5 . 0

t 2 . 0

1 . 0 #

I I I

0 1 2 3

\ \

I I

4 5

h(nm -1 )

Fig. 4. Small angle X-ray scattering spectrum (top) and calculated size distribution for spherical voids in the silica hollow fiber membrane material. The mean size from the lower graph is 13/~.

zeolite pore. The diffusion coefficient had the following relationship with temperature:

D v ~ a e -E/RT (3)

From the relationship in Eq. 3, the logarithm of the permeance. 7~- was plotted as a function of 1/RT. This produced a much better linear fit for the He permeance data. Using the Xiao and Wei form of the diffusion equation did not affect the goodness of the linear fit for any of the other gases compared to the Eyring form. A sensitivity analysis revealed that the effect of higher temperatures is greatest for molecules with small activation energies, such as He.

34 M.H. Hassan et al. / Journal of Membrane Science 104 (1995) 27--42

E

i , .

.Q

uJ

Z

uJ

E uJ I1.

1 E+08

1E+07

1 E+06

• • • i - • • i , • • i - • •

o

I ° . e I • . i . i . . . i

1.2 1.4 1.6 1.8

IO00/RT (g-mole/kcal)

Fig. 5. Arrhenius plot of pure gas He permeation data. A single hollow fiber test cell was used in all of the experiments.

1E+07

1E+06 E

~ 1 E+05 m

UJ ~ 1 E+04 Z < UJ

UJ O- 1 E+03

1E+02

<> ,,,

0 O .&

[ ] 0 O

V [ ] A

v 8 o

0 V

[ ]

A o2

0 Ar

o CO

[ ] N2

V CH4

0 / ,

0

[ ] 0 A

V 0 n

o

A V 0

0

n V 0

• . . i . . . i . . . i . . .

1.2 1.4 1.6

1000/RT (g-mole/kcal)

1.8

Fig. 6. Arrhenius plot for pure gas oxygen, argon, carbon monoxide, nitrogen, and methane permeation data. A single hollow fiber test cell was used for all of the experiments.

The pure gas permeation data are plotted in Figs. 5, 6, and 7 according to Eq. 3. Excellent linear fits of the Arrhenius plots were obtained~ For gases other than He,

the square of the correlation coefficients ( r 2) were all greater than 0.997. In the worst case, the linear fit of the He data had an r 2 value of 0.929.

Table 3 is a comparison of H2 permeance values and H2/N2 ideal separation factors measured in this study with literature values for similar microporous membrane materials and a cellulose ester commercial polymer membrane at or close to 298 K. The silica hollow fiber membrane used in the present work has the lowest H2 permeance and the largest separation factor. The H2 permeance of the silica hollow fiber membrane material is a factor of 40 smaller than the permeance of the cellulose ester polymer membrane. A similar silica hollow fiber membrane also manufactured by PPG Industries used by Shelekhin et al. [20] had an H2 permeance that was an order of magnitude larger than the membrane material we used. However, the H2/N2 ideal separation factor of the membrane used by Shelekhin and co-workers was a factor of 6.5 smaller than the value we obtained. The remaining microporous materials in Table 3 were molecular sieve carbon membranes prepared by the pyrolysis of polymer films. The Air Products selective surface flow membrane [ 14,15 ] was designed to selectively permeate hydrocarbons and had an order of magnitude higher flux, but a very low

1E+09

"~" 1E+08

~, 1E+07 L -

e 1E+06

~ 1E+05

U,I 0 1E+04 Z

UJ ~; 1E+03 n" LU Q.

1E+02

1E+01

[ ] O

[ ]

0 0

0

O A o

A O A

O A

O A

D H2

o CO2

Q CH4

A C2H4

• , i

1.2

[ ] 0

[ ]

o 0 [ ]

o

0

o

0

¢

A 0 A

¢

i . , - i . . .

1.4 1.6 1.8

1000/RT (g-mole/kcal)

Fig. 7. Arrhenius plot for pure gas hydrogen, carbon dioxide, methane, and ethylene permeation data. A single hollow fiber test cell was used for all of the experiments.

M.H. Hassan et al. / Journal of Membrane Science 104 (1995) 27-42

Table 3 Comparison of H2 permeance values and H2/N2 separation factors for several membrane materials

35

Membrane material Temperature (K) H2 Permeance (Barrer/cm) Ideal H2/N 2 separation factor Reference

PPG silica hollow fiber 298 5.23 × l04 545 This work membrane PPG silica hollow fiber 298 5.78 × t05 84 membrane Asymmetric cellulose ester 298 2 × l06 67 polymer membrane Composite microporous carbon 295.1 5.20 X 105 1.73 membrane Molecular sieve carbon hollow 298 2.43 × l06 26 fiber

Shelekhin et al. [20]

Grace, Gracesep product literature (1985) Rao and Sircar [ 14]

Koresh and Sofer [40]

H2/N 2 selectivity. Finally, the molecular sieve carbon membrane of Koresh and Sofer [ 12,13,40] had an H 2

permeance larger than the cellulose ester polymer material and a modest separation factor of 26. For the microporous materials in Table 3, it appears that the permeance and ideal separation factor are inversely proportional.

Ideal separation factors (ratios of pure gas permeances) corresponding to the permeance data in Figs. 5, 6, and 7 are presented in Table 4 at three temperatures: 298, 348, and 423 K. All of the separation factors decrease as the temperature increases which is due to the lesspermeable penetrant having a larger activation energy. Consequently, the differences in flux are smaller as the temperature increases. The separation factors are generally quite large when compared to polymer membranes that operate via a solution-diffusion mechanism [41 ]. At 298 K, the ideal separation factors for O2/N2, CO2/CH4, N2/CH4, and He/CH4 are 9.20, 156, 7.76, and 2.34.104, respectively.

The ideal separation factors reported here for silica hollow fiber membranes are similar to other microporous materials designed to separate penetrants via activated diffusion. Koresh and Sofer reported an ideal 02/

Table 4 Ideal separation factors for hollow fiber silica membrane a

Temperature CO2/ N2/ 02// H2/ H2//CH 4 He/CH4 (K) CH4 CH4 N2 N2

298 156 7.76 9.20 545 4.97× 103 2.34× 104 348 67.0 2 .82 7 .89 351 1.16×103 4.65× l03 423 20.8 2 .31 4 .81 103 2.35 × l02 3.10× 102

aFeed pressure, 21.4 atm.

N2 separation factor of 7.1 [ 12]. Shelekhin et al. [20] reported ideal separation factors at 303 K using similar silica hollow fiber membranes. They observed very large N2/CH4 and CO2/CH4 ideal separation factors of 50 and 1675, respectively. These values are over a factor of six larger than we observed. However, She- lekhin et al. [20] measured an ideal O2/N2 separation factor of 3 to 4 which is substantially smaller than what we observed for pure gases and mixtures. These differences could be due to a larger mean pore size for She- lekhin's silica fibers compared to the membrane material used in the present work. In any case, the microstructure of the silica hollow fiber samples used by Shelekhin et al. are significantly different than those used in the present work. The differences in the micros- tructures of different fiber samples are due mostly to the leaching process, which involves a concentrated acid solution to remove alkali and alkaline earth oxides. The strength of the acid as well as the time and temperature of the leaching process determine the microstructure of the fiber. Interestingly, the separation factors we obtained for gases possessing large differences in kinetic diameter, such as He/CH 4 and H2/CH4, are similar to those reported by Shelekhin.

The slopes of the Arrhenius plots correspond to the activation energy for diffusion in the silica hollow fiber membranes. Fig. 8 shows the influence of kinetic diameter of the penetrant on the activation energy. The kinetic diameter is the hard sphere diameter for the penetrant molecules calculated from a transport property such as viscosity or thermal conductivity [ 7 ]. Con- sequently, the kinetic diameter is an approximate measure of molecular size. Since the gas molecules are not spherical, other measures of molecular size could

3 6 M.H. Hassan et al. /Journal of Membrane Science 104 (1995) 27-42

0 E | ==

v >. CO n" UJ Z IJJ

Z 0 I - -

I-- (3 <C

2 0

15

10

. . . . =

[ ] Sil ica hol low f i b e r

ZL Zeoli te 4A

o Zeol i te 3A

. . . . i . . . . O 2 CO C 21,.I 4

o

! l ± } -'l

[] ±

T z= '~ A ,, o &

1

He H 2 CO 2 Ar N 2 CH 4

0 . . . . J . . . . i . . . .

2 . 5 3 .0 3 .5 4 . 0

K I N E T I C D I A M E T E R (~)

Fig. 8. The influence of kinetic diameter on the activation energy for diffusion in silica hollow fiber membranes.

improve the correlation. The error bars in Fig. 8 are 95% confidence intervals. There is a very high correlation between the kinetic diameters of the permeates and their activation energies, which range from 4.61 (He) to 14.0 kcal/g mol for C2H4. As shown in Fig. 8, the activation energies for the silica hollow fiber membranes are between the activation energies reported for zeolites 3A [42] and 4A [43].

The activation energies obtained in the present work are a factor of 2 to 11 times larger than those previously reported by Ma and co-workers [20] for a different sample of PPG silica hollow fiber membranes. An inter- esting observation made was that 02 and N2 have the same activation energy of 3.1 kcal/mol. The lower activation energy values reported by Shelekhin et al. correspond to much higher permeability values than those measured in this research.

In addition to the influence of temperature on the pure gas permeance, the dependence of differential pressure was also investigated. Fig. 9 shows that both the CO2 and He permeance values increase to a constant value above differential pressure values of 5 bar. Meas- urements were made at 303 and 348 K for CO2 and at 348 K for He. This behavior is consistent with a con- ceptual model of permeation through the silica hollow fiber membranes of both surface diffusion and activated diffusion occurring in parallel. Increasing pressure

E

t - t~

O3 v

LLI L~ Z < LU

n" UJ 13_

1 E + 0 6

1 E + 0 5

1 E + 0 4

1 E + 0 3

. . . . 'O . . . . d " " "O ' "o " " ' o " v - , - "u "

O O

O He @ 348K

/x CO2 @ 348K

[ ] CO2 @ 303K

A 6 A A & A A A

.A

i [~0~0 0 0 0 [] []

5 10 15 2 0 2 5 3 0

D I F F E R E N T I A L P R E S S U R E (atm)

Fig. 9. The influence of differential pressure on the permeance of helium at 348 K and carbon dioxide at 303 K and 348 K.

would increase surface coverage and the surface diffusion flux up to the saturation pressure of the adsorption isotherm at the temperature and pressure corresponding to the permeation measurements.

Ash et al. [44] observed that the NH 3 permeability in a microporous carbon membrane increased with increasing differential pressure below 273 K. Xiao and Wei [38,39] reported that the diffusivities of benzene and toluene increased sharply with increasing concen- tration at temperatures of 338 K and below.

This trend of increasing permeability with increasing differential pressure is opposite of what Koresh and Sofer [ 13] reported for CO2, CH4 and N20 permeation in molecular sieve carbon membranes. Shelekhin et al. [ 20] reported that the CO2 permeability was constant as the differential pressure decreased to 1 bar.

4.3. Binary mixtures

Additional information about the mass transfer mechanism in the PPG silica hollow fiber membranes was obtained by performing permeation experiments with gas mixtures and comparing the results with those obtained using only pure gases. The comparison experiments were performed using the same single hollow fiber for both pure gases and gas mixtures.

It is very common in the polymer membrane literature that the ideal or pure gas separation factors are

M.H. Hassan et al. / Journal o f Membrane Science 104 (1995) 27-42 37

12.0

n" O I - 0 10.0

LL

Z _o ,~ 8.0

<

LLI ffl e~ 6.0

0

. . . . i . . . . i . . . . i . . . . i . . . . i . . . .

O O Mixed gas data

A Pure gas data

O

A 0 &

4 . 0 . . . . i . . . . i . . . . i . . . . i . . . . i . . . .

275 300 325 350 375 400 425

TEMPERATURE (K)

Fig. 10. Comparison of the mixed and pure gas oxygen/nitrogen separation factors for a single fiber membrane test cell. The mixed gas separation factors are larger for temperatures up to 375 K (lOOOC).

larger than the mixed gas values [41]. For both O2/N2 and CO2/CH4 mixtures, we have observed an unusual behavior where the mixture separation factors are larger than the ideal separation factors obtained with pure gas permeability data. Fig. 10 presents O2/N2 separation factor data for both mixture and pure gas experiments that nicely illustrate this unusual behavior for the silica hollow fiber membranes. At temperatures from 298 K to 373 K, the mixed gas O 2 / N 2 separation factors are up to 20% larger than the pure gas values. Above 373 K the pure gas and mixed gas separation factors coin- cide.

Separation factor values of 10 to 12 for 02 over N2 are large and they compare very favorably to separation

factors reported for polymer membranes. An O 2 / N 2

separation factor of 11.3 is over 50% higher than the most selective commercial polymer membrane material in the literature [45].

Rat and Sircar [ 14 ] have recently described a microporous carbon membrane where the mixture separation factors exceed the pure gas values for the separation of light hydrocarbons from hydrogen. The greatest difference was seen for butane, the penetrant with the highest affinity for the carbon membrane surface. The mixed gas separation factor for C4Hlo o v e r H2 was 94 compared to a pure gas value of 1.2. The authors attribute the large difference in separation factors to competitive adsorption, where the hydrocarbons preferentially occupy adsorption sites over hydrogen. Competitive adsorption reduces the surface diffusion flux of hydrogen compared to the pure gas experiments.

As shown in Table 5, the mixed gas 02 permeance values were larger than those measured for pure 02 at all temperatures. However, the percent difference between the mixed gas and the pure gas O2 permeance values decreased as the temperature increased. The opposite trend was observed for N2. At 298 K, there was a small difference between the mixed gas and pure gas permeance N2 values. As the temperature increased, the mixed gas N2 permeances increased faster than the pure gas values and the difference between them increased to about 15%. Therefore, the activation energy for diffusion was slightly larger for N2 in the binary mixture than pure N2.

Rat and Sircar [ 15] also have observed situations where the mixed gas permeability is larger than the pure gas value. In their experiments with microporous carbon membranes at 295 K, they measured a mixed

Table 5 Comparison of pure and mixed gas permeances for the O2/N2 separation"

Temperature (K) Pure gas N2 permeance Mixed gas N2 permeance Pure gas 02 permeance Mixed gas 02 permeance (Barrer/cm) (Barrer/cm) (Barrer/cm) (Barrer/cm)

298 4.46 × 101 4.67 X 101 4.17 × 102 5.29 X 102 323 1.93 X 102 2.13X 102 1.69× 103 2.10X 103 348 6.53 X 102 7.54× 102 5.19X 103 6.39X 103 373 2.13X 103 2.50x 103 1.45× 104 1.77X 104 398 5.87 X 103 6.95 X 103 3.40 X 104 3.89 × 104 423 1.43 X 104 1.68 X 104 6.89 X 104 8.00 X 104

aFeed pressure, 21.4 atm in all experiments. The composition of the mixtures is 80% N2 and 20% 02.


250 n"

Z 0

150

n" ,< O.. 100 UJ 0')

"1-

o

Pure Gas

Mixed Gas

Pure Gas after Heating

Mixed Gas after Heating

• A

0

0 • A •

!

0

6

. . . . i . . . . i

320 370

6 n

0 . . . . i . . . .

270 420 470

TEMPERATURE (Kelvin)

Fig. 11. Comparison of the mixed gas and pure gas carbon dioxide/ methane separation factors for a single silica hollow fiber membrane test cell. The open symbols represent the measurements that were done first. After the experiment at 423 K, the silica hollow fiber test cell was cooled in He, and the experiments were repeated.

gas butane permeability of 230 Barrer compared to the pure gas butane permeability of 190 Barrer.

A similar comparison of pure and mixed gas permeation was performed for the CO2/CH4 separation. As shown by the open symbols in Fig. 11, the difference between the mixture separation factors and the pure gas values is much smaller than we observed for the air separation on a percentage basis. The experiments were performed by starting at 298 K and increasing the temperature up to 423 K. At that point, the hollow fiber membrane cell was cooled to 298 K in high purity He. Then the experiments were repeated at 298 K and 323 K before the hollow fiber test cell developed a leak. Surprisingly, the CO2/CH4 separation factors increased. After cooling, the mixture separation factor at 298 K was 10% larger than the pure gas value. The mixed gas CO2/CH4 separation factor at 298 K increased by 40% after cooling.

Very similar results were obtained in an experiment where the hollow fiber membrane was heated to 398 K in He, and then cooled to 298 K where pure and mixed gas permeation experiments were performed. Subse- quently, both pure and mixed gas permeation experiments were performed over a temperature range of 298 to 423 K. At 298 K, the mixed gas separation factor was 21% larger than the pure gas separation factor. Comparing the activation energies of diffusion for

these experiments to prior pure and mixed gas permeation studies, the activation energies for CO2 and CH4 diffusion decreased by 10 to 17%.

In the CO2/CH4 experiments, the pure gas permeances were always 10 to 20% larger than the mixed gas values at all experimental conditions. The difference between pure gas and mixed gas permeance values was largest for CH4, which is less interacting than CO2 based on adsorption data for silica hollow fiber membranes [24]. The difference between the pure and mixed gas permeances was largest at 298 K. However, after heating to 423 K, all of the pure and mixed gas CO2 and C H 4 permeance values increased by up to a factor of two. The 40% increase in the CO2/CH4 separation factor at 298 K after heating and cooling was primarily due to the fact that the mixed gas CO2 permeance increased by 158% compared to 84% for the CH4 permeance.

The differences in permeability and selectivity due to heating the hollow fiber membrane may be due to the removal of physically adsorbed water from the membrane surface. The water may have been "screen- ing" the penetrant molecules from the polar SiO2 surface. Removal of the water would increase the interaction between the CO2 and the membrane surface which could possibly increase the surface diffusion contribution of the total flux. It is also possible that removal of physisorbed water may increase the effective cross section of the pores. As described below, FTIR spectroscopy was used to investigate the interaction of water with the silica membrane surface.

An analogous situation occurs for zeolites used for a pressure swing adsorption separation [ 46]. The zeolites are ion exchanged to leave a multivalent cation in the zeolite cavity such as Ca 2 +. The Ca zeolites are then activated by heating in a high purity inert gas to remove water from the adsorption sites. Removal of the water increases the interaction between the exchanged cation and the adsorbate, improving the selectivity of the adsorption separation.

Our proposed explanation for the higher mixture separation factors is that during the surface diffusion of mixtures, competitive adsorption takes place on the surface of the membrane. The more strongly adsorbed gas would preferentially occupy the adsorption sites on the pore surface, impeding adsorption and surface diffusion of the more weakly adsorbed gas. From the extensive literature on adsorption in microporous zeo-


lites, carbons, and ceramics, it is well established that gas adsorption in porous solids decreases drastically as the temperature increases [ 7,36]. Our pure and mixed gas data for the O2/N2 and CO2/CH4 separations with silica hollow fiber membranes are also consistent with this observation. The mixed gas separation factors and the pure gas permeance ratios approach each other as temperature is increased.

4.4. FTIR spectroscopy

Fourier transform infrared spectroscopy was used to investigate the role of surface water and the reversibility of water adsorption. Fig. 12 displays the changes in the infrared absorption spectra of silica hollow fiber membranes versus annealing temperature. The broad infrared feature between 3750-2500 cm-1 is characteristic of the O-H stretching vibrations of physisorbed molecular water and hydrogen bonded surface silica hydroxyl species [47,48]. As shown by Thoen et al. [37] annealing the silica hollow fiber membranes to 450 K results in the disappearance of the infrared absorption feature at 1635 cm-~ of the H20 bending

0.6 us Silica Fibers

o . ,

450 K

o , , , , . . ; , ; 4000 3600 3200 28 0 24 0

Frequency (cnl I )

Fig. 12. FTIR spectra showing the effect of temperature on the SiO- H stretch over the temperature range of 300 K to 700 K. At 700 K, the sharper feature at 3720 cm- l is assigned to hydrogen bonded silanol groups.

vibration [47,48] indicating the complete desorption of the physisorbed molecular water. The broad infrared absorption feature between 3770-2700 cm- ~ in the 450 K spectrum of Fig. 12 is therefore attributed to the O- H stretching vibrations of hydrogen bonded surface silica hydroxyl species [48-52]. Hence, annealing the silica hollow fiber membranes to 450 K is sufficient to remove all of the physisorbed molecular H20.

Fig. 12 also demonstrates that as the silica membrane is annealed above 450 K, the broad SiO-H stretching vibration decreases and gradually evolves into a sharper infrared absorption feature at 3720 cm- 1. This decrease in the infrared absorption feature of the SiO-H stretching vibration is consistent with the desorption of molecular water from the surface as: 2SiOH ~ H20 (g) + Si- O-Si.

Previous infrared studies of silica surface hydroxyls have attributed sharp infrared features between 3750- 3740 cm- ~ to the SiO-H stretching vibrations of isolated silica hydroxyl species [47-52]. Pronounced infrared features between 3750-3740 cm- ~ of isolated surface hydroxyl species have been observed at temperatures as low as 300 K on a variety of silica surfaces [47,48,52]. The feature at 3720 cm- 1 in Fig. 12 is red shifted and broader than absorption peaks typically attributed to isolated SiOH species on silica surfaces. Marrow et al. have attributed bands near 3720 cm- 1 to hydrogen bonded pairs or chains of silanols [49]. The feature at 3720 cm- 1 in Fig. 12, therefore, most likely is a result of the SiO-H stretching vibration of surface silica hydroxyls which are still hydrogen bonded to neighboring hydroxyl species. The absence of isolated hydroxyls on silica hollow fiber membranes annealed to 700 K may be due to a negative radius of curvature in the micropores of the membrane bringing the SiOH groups closer together [53]. It is also possible that the SiO-H stretching vibration of isolated surface hydroxyls is observed in Fig. 12 but is red shifted as a result of boron present in the silica hollow fibers or as a consequence of the N2 ambient employed for these annealing studies [ 54 ].

Fig. 13 displays the adsorption of water on the porous hollow fiber silica membranes. The initial spectrum in Fig. 13 is of a silica hollow fiber membrane at room temperature and atmospheric pressure. The broad infrared absorption feature between 3750-2500 cm- ~ corresponds to the O-H stretching vibrations of physisorbed molecular water and hydrogen bonded sur-

40 M.H. Hassan et al. / Journal of Membrane Science 104 (1995) 27~12

8 c

o

~ r Fibers

__j ' ' ; o ' ~o ' ' ' o 4000 3 0 32 2800 24 0

Frequency (crn 1 )

Fig. 13. FTIR spectra showing the reversibility of physisorption of water that was removed by exposure to a pressure of 10 -5 torr by heating to 450 K.

face silica hydroxyl species. The second spectrum in Fig. 13 was recorded following evacuation of the UHV chamber to 1 × 10- 5 Torr while the silica substrate was held at room temperature. Evacuation to 1 X 10 -3 Torr is sufficient to remove all of the physisorbed molecular water on the silica hollow fiber surface as evidenced by the disappearance of the H20 bending vibration at 1635 cm- l [47,48]. The decrease in the broad infrared absorbance of the O-H stretching vibration below 3400 cm- l as displayed in Fig. 13 is also consistent with the desorption ofphysisorbed molecular H20 [47,48]. The third spectrum in Fig. 13 was recorded following exposure of the sample to atmospheric pressure for ~ 10 min. at room temperature. The broad infrared feature in the third spectrum of Fig. 13 is nearly identical to the initial spectrum of the porous hollow fiber membranes. These spectral results reveal the rapid adsorption of water on the silica membrane surface.

The fourth spectrum in Fig. 13 exhibits the SiO-H stretching region for the silica fibers annealed to 450 K in N2. A decrease is observed in the broad infrared absorbance of the O-H stretching vibration below 3400 cm -1. As discussed previously at 450 K, all of the physisorbed molecular water has been removed from

the silica membrane surface. The final spectrum in Fig. 13 was then recorded upon cooling at room temperature at atmospheric pressure for ~ 10 min. This spectrum is also nearly identical to the initial spectrum of the porous silica hollow fiber membranes. These results indicate that the adsorption of water on the silica membrane surface is not inhibited following annealing temperatures < 450 K. These observations are consistent with those of Thoen et al. who showed that the silica hollow fiber membrane surface becomes saturated with water after several hours in ultrahigh purity N2. [ 37].

5. Conclusions

5.1. Membrane microstructure

From measurements of C02 adsorption at low relative pressures, the silica hollow fibers are microporous with a mean pore size estimated to be between 5.9 and 8.5 ,~. This corresponds to approximately two to three kinetic diameters of the penetrant gases of interest. X- ray scattering measurements also give evidence of micropores and suggest that the orientation of the pores is completely random.

5.2. Pure gas permeation

The permeances of gases with kinetic diameters o

ranging from 2.6 to 3.9 A were measured through silica hollow fiber membranes over a temperature range of 298 K to 473 K at a feed gas pressure of 20 atm. Permeances at 298 K range from 10 to 2.3 × 105 Barrer/ cm for CH4 and He, respectively, and were inversely related to the kinetic diameter of the penetrant. Mass transfer through the silica hollow fiber membranes is an activated process. Activation energies for diffusion through the membranes were calculated from the slopes of Arrhenius plots of the permeation data. The energies of activation ranged from 4.61 to 14.0 kcal/mol and correlate well with the kinetic diameter of the penetrants. The experimental activation energies fall between literature values for zeolites 3A and 4A.

5.3. Binary mixture permeation

High selectivities were obtained for 02/N2 and C02/ C H 4 mixtures. The O 2 / N 2 mixed gas selectivities


decreased from 11.3 at 298 K to 4.8 at 423 K and were up to 20% larger than the values calculated from pure gas permeances at temperatures below 373 K. At temperatures above 373 K, the mixture and pure gas separation factors were equal. The mixture separation factor for CO2/CH4 decreased from 186 to 22.3 over the same temperature range. The differences between the mixture and ideal separation factors is attributed to a competit ive adsorption effect in which the more strongly interacting gases saturate the surface and impede the transport of the weakly interacting gases. The more strongly adsorbed gas would preferentially occupy the adsorption sites on the pore surface, pre- venting adsorption and surface diffusion of the more weakly adsorbed gas. Similar differences in the separation factors were observed for CO2/CH4 mixtures after the membrane had been heated to above 398 K and then cooled in flowing He to 298 K. At 298 K after annealing, the C Q / CH4 separation factor increased by 40% and the CO2 permeance more than doubled. The increase in CO2 and CH4 permeances corresponded to a 10 to 17% decrease in the activation energy for transport after heating to 423 K and then cooling in He. Based on the FTIR results, this unusual behavior is attributed to the removal of physically adsorbed water from the membrane surface.

5.4. Surface chemistry

Transmission FTIR spectroscopy was used to investigate the surface chemistry of the silica hollow fiber membranes. The results show that the hydroxylated membrane surface is covered by physically adsorbed water at ambient conditions. The physisorbed water can be removed by heating the silica membrane to 450 K or exposure to pressures below 1 × 10 -4 torr. Water adsorption is reversible, and the silica membrane surface can be easily saturated with water by exposure to UHP N2.

Acknowledgements

The authors gratefully acknowledge support from grants DE-FG06-92ER 14290 and DE-FG03- 93ER14363 from the Department of Energy Office of Basic Energy Sciences, Department of Chemical Sci- ences. We also acknowledge PPG Industries for the donation of the silica hollow fiber membranes used in

this research. J.D. Way would like to acknowledge Professor Steven George of the University of Colorado, Professors Mark Davis and George Gavalas at the Cal- ifornia Institute of Technology, and Dr. John B. Nich- olas at Battelle Pacific Northwest Laboratories for suggestions and helpful discussions. Finally, we would like to thank Dr. Don Wil l iamson and Yan Chen of the Colorado School of Mines for performing the SAXS measurements.

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