diffusive transport through mesoporous silica membranes

Microporous and Mesoporous Materials 117 (2009) 268–277

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Microporous and Mesoporous Materials

journal homepage: www.elsevier .com/locate /micromeso

Diffusive transport through mesoporous silica membranes

Scott Higgins, William DeSisto, Douglas Ruthven*

Department of Chemical and Biological Engineering, University of Maine, 5737 Jenness Hall, Orono, ME 04469, United States

a r t i c l e i n f o

Article history:Received 9 April 2008Received in revised form 19 June 2008Accepted 26 June 2008Available online 3 July 2008

Keywords:Mesoporous silicaDiffusionPermeanceOctadecyldimethylchlorosilane

1387-1811/$ - see front matter � 2008 Elsevier Inc. Adoi:10.1016/j.micromeso.2008.06.030

* Corresponding author. Tel.: +1 207 581 2277; faxE-mail address: [email protected] (D. R

a b s t r a c t

The results of a detailed study of the permeation of several light gases through unmodified and modifiedmesoporous silica membranes are reported. The base membranes which were synthesized by dip-coatingmultiple layers of a templated silica onto a macroporous alumina support showed relatively high perme-ances with evidence of both support resistance and a contribution from viscous flow, in addition toKnudsen diffusion, through the active layer. The behavior of the modified membranes, which were pre-pared by silanation of the original membranes with octadecyldimethylchlorosilane, was more interesting.Permeances were lower and there was no evidence of support resistance or viscous flow. Permeationthrough the active layer appeared to occur by a ‘‘Knudsen-like” process. Permeance and permeance ratiosmeasured in both single component and binary systems showed the characteristic inverse dependenceon the square root of the molecular weight (or the molecular weight ratio) but the temperature depen-dence was much stronger than expected for classical Knudsen flow. The behavior of CO2 was somewhatanomalous yielding permeances that were about 25% larger than those for propane which has the samemolecular weight.

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1. Introduction

Since the discovery of MCM-41, the first mesoporous silica to beprepared by a surfactant templated synthesis, a great deal of re-search has been devoted to the production of mesoporous mem-branes of this type [1–8]. The pore size (typically 4–20 nm) is toolarge for size selective ‘‘molecular sieve” separation for all butthe largest molecules so surface modification is needed to enhancethe selectivity. Through application of well known silane chemistryit is possible to react the surface hydroxyl groups in the mesoporeswith an organochlorosilane. An article by Singh et al. [9] shows acomparison between the addition of two silanes; octadecyldimeth-ylchlorosilane and octadecyltrichlorosilane, to the surface. Thereactions were performed on a hydrated Vycor surface with tolu-ene as the solvent. The monochlorosilane is shown to have thehighest reaction yield due to the single reacting atom, the chlorine,of the monochlorosilane. This reaction leaves the pores of the inor-ganic matrix with organosilane termination groups, thereby creat-ing a membrane with the robust mechanical strength and high fluxof an inorganic matrix which can be combined with the selectivityof an organic surface. Yoo et al. [10] synthesized mesoporous silicamembranes onto alumina supports achieving a narrow pore sizedistribution with an average pore size of 5 nm. Separation experi-ments of He/N2 and C3H8/N2 showed ideal Knudsen separation val-ues, indicating high quality membranes. In a series of four papers

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: +1 207 581 2323.uthven).

Ford et al. [11–14] report the surface functionalization of aluminamembranes (average pore sizes 5 and 12 nm) with alkylchlorosil-anes. The synthesized membranes had various length alkyl chains(C4–C22) extending from the pore wall to form organic/inorganicmembranes which showed an ability to separate propane fromnitrogen. Ideal separation factors for C3H8/N2 were as high as 32for single gas ideal selectivities and 9 for binary separations. Func-tionalized alumina membranes have also been prepared and stud-ied by McCarley and Way [15]. Both the Ford and Way membranesshowed convincing evidence of surface flow since the heavier spe-cies permeated more rapidly than the lighter species.

Extensive work has also been published on the functionaliza-tion of silica. From 1992 to 1995 Tripp published several studiesshowing the attachment of organosilanes to fumed silica in whichthe resulting surfaces were characterized quantitatively by IR [16–19]. In 1999, Tripp published an article reporting the viability ofsupercritical CO2 as a solvent medium for both volatile and nonvol-atile organosilane reactions [20]. Fumed silica was immersed insupercritical CO2 (SCF CO2), which completely dehydrates the sil-ica. Once dehydrated, a surface reaction with either hexamethyldi-silazane or octadecyltrichlorosilane was carried out by exposingthe silica to the organosilanes dissolved in SCF CO2 solvent. The re-sults showed improved reaction yield due to the drying effect ofSCF CO2, which limits hydrolysis by surface water. The proposedreaction mechanism has been shown also to work on fumed silica[20]. In the reaction, the surface hydroxyl groups are exposed totriethylamine (TEA) as a catalyst. With the TEA bonded to it, thesurface hydrogen has a partial positive charge; when exposed to

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Nomenclature

a average pore radius in support layerDAB molecular diffusivityDK Knudsen diffusivityM molecular weightN flux through membraneP total pressurer pore radius of active layer�r average value of r

R gas constantT temperature (K)YA, YB mole fractionsz membrane thicknessp permeancel viscositye porositys tortusosity, primed values refer to support layer

S. Higgins et al. / Microporous and Mesoporous Materials 117 (2009) 268–277 269

trimethylchlorosilane the chlorine and the hydrogen bond to formHCl and a methylated silane bond to surface oxygen, thus produc-ing a methylated surface.

In this paper we present the results of a theoretical and exper-imental study of the transport of selected probe molecules throughalkyl modified mesoporous silica membranes prepared in this lab-oratory. In contrast to the membranes of Ford and McCarley andWay our membranes showed no evidence of surface flow. At a gi-ven temperature the permeance ratios are always close to the idealKnudsen values and the temperature dependence is similar for allcomponents including He (which is certainly not significantly ad-sorbed at these temperatures). Detailed analysis shows that trans-port through the modified membranes occurs by a ‘‘Knudsen-like”process but the effective pore radius decreases with increasingtemperature. This effect appears to arise from an increase in theeffectiveness with which the attached alkanes obstruct permeationrather than from a surface diffusion effect.

2. Experimental

As described in previous publications from this laboratory [21],mesoporous silica membranes were synthesized by dip-coating atemplated silica sol onto an asymmetric macroporous alumina

0

200

400

600

800

1.000

1.200

1.400

1.600

1.800

2.000

0.00 1.00 2.00 3.00 4.00

pore R

pore

s 10

-17

m3

Fig. 1. Pore size distribution of a typical unmodified membrane as

support disk having an upper layer of thickness 10 lm and anapproximate pore diameter of 100 nm. The thickness of the silicalayer is about 1 lm. The template was removed by calcinationleaving an interconnected porous silica network with an averagepore size of 4.7 nm. Base catalyzed silanation of the surfacehydroxyls was then performed using triethylamine and octadecyl-dimethylchlorosilane with supercritical CO2 as the solvent, to yielda hybrid membrane consisting of a silica surface with C18 chainsattached to the pore walls. These membranes have been character-ized, with DRIFT, perm-porosimetry and permeance measure-ments [22]. Single gas and binary permeance measurementswere performed using mass flow and pressure controllers to main-tain steady state conditions. Typically the feed pressure was main-tained at 2 atm while the permeate was at atmospheric pressure.Permeance measurements were performed before and after silana-tion to quantify the change in the permeance of the membrane.Fig. 1 shows a typical pore size distribution as measured withperm-porosimetry. Fig. 2a is a schematic of the gas permeanceequipment. Mass flow controllers bring the feed stream to the up-stream side of the membrane where a pressure controller main-tains a constant pressure forcing the permeate to diffuse throughthe membrane via the pressure/concentration differential createdfrom the downstream side of the membrane being at atmospheric

5.00 6.00 7.00 8.00 9.00

adius (nm)

measured by perm-porosimetry using n-hexane as the sorbate.

F

F

F

F

F

F

P

He

N2

Ar

CH4

CO2

C3H8 Mass Flow Controllers

Gas ManifoldMembrane cell

Pressure Controller

Gas Chromatograph

Bubble flow meter

Exhaust

n- hexane bubbler

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

0 50000 100000 150000 200000 250000

He

CH4

C3H8

N2

Ar

Δp(pa)

(

(

mol

m2

. s . p

aπ

x107

a

b

Fig. 2. (a) Schematic of the apparatus for permeance measurement, (b) A typical permeance versus pressure measurement for a silica membrane before modification.

270 S. Higgins et al. / Microporous and Mesoporous Materials 117 (2009) 268–277

pressure. The effluent is then brought to a gas chromatograph forbinary permeance analysis or to a bubble flowmeter for singlegas permeance measurements. Fig. 2b shows a typical set ofpermeance measurements for a silica membrane beforemodification.

3. Theoretical model

Transport through mesoporous membranes has been widelystudied and is reasonably well understood. The basic theory hasbeen well reviewed by Jackson [23], Cunningham and Williams[24], Evans et al. [25] and more recently by Do [26]. Momentumbalance arguments show that molecular diffusion plays no role in

single component permeation. Therefore, in the absence of surfaceflow, only Knudsen diffusion and viscous flow mechanisms apply.

For pure Knudsen flow the permeance (p) in S.I. units, is givenby

pmol

m2 � s � Pa

� �¼ N

DP¼ e

s� DK

z� 1RTffi 97

R� er

sz

� �� 1ffiffiffiffiffiffiffi

TMp : ð1Þ

In a typical membrane, however this simple behavior is modified bythe contribution of support resistance and a small contributionfrom viscous flow through the pores of the active layer.

1plRT

¼ 1ersz

� �Pr8 þ 97l

ffiffiffiMT

q� �þ s0z0

e0� 8Pa2 : ð2Þ

Table 1Summary of permeance data

T(K) Viscosity Permeance (p) {mol�m�2�s�1�Pa�1}

Membrane A Membrane B Membrane C

Sorbate l (Pa�s) Unmodified Modified Unmodified Modified Unmodified

298 He 2.03E�05 2.09E�06 5.69E�07 2.53E�06 4.53E�07 3.01E�06N2 1.79E�05 1.07E�06 2.04E�07 1.34E�06 1.67E�07 1.46E�06Ar 2.24E�05 9.13E�07 1.80E�07 1.12E�06 1.43E�07 1.19E�06CH4 1.10E�05 1.60E�06 2.72E�07 2.04E�06 2.23E�07 2.10E�06C3H8 8.15E�06 1.37E�06 1.84E�07 1.89E�06 1.43E�07 1.97E�06



423 He 2.59E�05 1.42E�06 3.39E�07 1.73E�06 2.15E�07 1.90E�06

Fig. 3. Plots of 1plRT versus 1

l

ffiffiffiMT

qfor He in the unmodified membranes.

Table 2Parameters derived from He permeance data for the unmodified membranes

Membrane Slope ersz Intercept ¼ s0z0

e0� �

� 8Pa2

� �(m � Pa)�1

A 935 1.09E�05 4.06E06B 767 1.34E�05 3.4E06C 441 2.26E�05 4.01E06


If we assume that the resistances of the support and the active layerare additive and viscous flow within the active layer is negligibleðPr

8 << 97lffiffiffiTM

qÞ Eq. (2) reduces to:

1plRT

¼ szer� 197l

ffiffiffiffiffiMT

rþ s0z0

e0� 8Pa2 : ð3Þ

Thus, under these conditions, a plot of (plRT)�1 versus 1l

ffiffiffiMT

qshould

be linear with slope 197

szer

� �and an intercept s0z0

e0 � 8Pa2

� �. This latter

term measures the support resistance.These expressions are used as the basis for analysis of the

experimental permeance data.

4. Results and discussion

The experimental permeance data for the five membranes thatwere studied are summarized in Table 1. It is evident that the datafor a given sorbate and temperature are quite consistent, and the

Fig. 4. Plots of 1plRT versus 1

l

ffiffiffiMT

qfor six different gases at 298 K, 323 K and 373 K in the three unmodified membranes: (a) Membrane A; (b) Membrane B; (c) Membrane C; the

diamonds (�) represent experimental data while the line represents the least squares fit of Eq. (2) with the parameters given in Table 3.

Table 3Parameters derived by fitting the permeance data for He, Ar, N2, CH4 and C3H8 in theunmodified membranes to Eq. (2)

Membrane c Pr8 (m � Pa) er

sz

A 4.06E06 0.00161 8.33 � 10�6

B 3.4E06 0.00194 1.03 � 10�5

C 4.01E06 0.00151 1.19 � 10�5

c ¼ support resistance ¼ s0z0e0� �

� 8Pa2

� �from He data (Table 2).


permeances for the three different membranes (A, B, and C) aresimilar, with the permeance of the modified membranes beingsmaller than those of the original unmodified membranes by fac-tors of about 5–10. The permeance decreases modestly with tem-perature and this trend is somewhat stronger for the modifiedmembranes.

4.1. Unmodified membranes

For He the ratio lffiffiffiMp is relatively large so one may expect that

the relative importance of viscous flow within the active layerwill be minimal with the result that the permeance data should

obey Eq. (3). Plots of 1plRT versus 1

l

ffiffiffiMT

qfor the permeation of He

through the three unmodified membranes are shown in Fig. 3.It is clear that Eq. (3) provides a good representation of theexperimental data; the values of the parameters er

sz and s0z0e0 � 8

Pa2

derived from the slopes and intercepts are summarized in Table2.

Fig. 4 shows the plots of 1plRT versus 1

l

ffiffiffiMT

qfor all sorbates studied

in all three (unmodified) membranes. In conformity with Eq. (2)the data show a unique correlation between 1

plRT and 1l

ffiffiffiMT

qfor all

sorbates and temperatures, suggesting that the model correctlyrepresents the behavior of these membranes. Furthermore, it isevident that the relationship is not linear, implying that, for theheavier sorbates (compared to He), the contribution of viscous flowwithin the active layer is significant. The parameters er

sz and Pr8 ; gi-

ven in Table 3 were obtained from a non-linear least squares fitof the experimental data to Eq. (2). In order to avoid the uncertain-ties inherent in the extraction of three parameters the supportresistance s0z0

e0 � 8Pa2 was set to the values obtained from the He per-

meance data (Table 1).It may be seen that the parameters for the three unmodified

membranes, derived from the model, are very similar. Further-

Fig. 5. Plot of 1plRT versus 1

l

ffiffiffiMT

qfor modified membrane (Membrane B).

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6

MembraneA 323K

MembraneA 298K

MembraneB 373K

√M

1 (√ molgm

(

π R

T ×

104

( m

(

s

Fig. 6. Plot showing the variation of permeance with molecular weight and temperature for the modified membrane A at 298 K and 323 K and modified membrane B at 373 K.


more, the values for the ratio of the effective pore radius to themembrane thickness er

sz derived from the data for the heavier probemolecules are quite similar to the He values, thus providing furthersupport for the validity of the theoretical model. However, themean pore radius derived from the estimated viscous flow contri-bution Pr

8 is about 10�7 m which correlates with the finding re-ported in an earlier paper [21] in which perm-porosimetryshowed that 10% of the flux through the membrane occurs in poreslarger than 15 nm.

4.2. Modified membranes

The behavior of the modified membranes is quite different fromthat of the unmodified membranes and, in some respects, it is sim-pler. The permeance is much smaller, reflecting the smaller effec-tive pore size. As a result, for the modified membranes, theimpact of support resistance and viscous flow through the activelayer is insignificant. A plot of 1

plRT versus 1l

ffiffiffiMT

qfor the modified

membrane B is shown in Fig. 5, which may be compared with

Fig. 7. Plot of permeance versus 1M0:5 T2 for modified Membrane B.

Table 4Permeance data and effective pore radius for modified membranes derived from Eq. (1)

T(K) Sorbate Membrane A Membrane B

p � 107 pRffiffiffiffiffiffiffiffiTMp

� 104 ersz p � 107 pR

ffiffiffiffiffiffiffiffiTMp

� 104 ersz

298 He 5.68 1.63 1.8E�06 5.67 1.62 1.42E�06N2 2.05 1.55 1.8E�06 2 1.24 1.42E�06Ar 1.8 1.63 1.8E�06 1.43 1.3 1.42E�06CH4 2.72 1.56 1.8E�06 2.24 1.28 1.42E�06CO2 2.45 2.33 1.8E�06 1.54 1.46 1.42E�06C3H8 1.87 1.78 1.8E�06 1.44 1.37 1.42E�06

323 He 5.21 1.55 1.70E�06 3.87 1.15 1.28E�06N2 1.82 1.44 1.70E�06 1.43 1.35 1.28E�06Ar 1.59 1.5 1.70E�06 1.26 1.19 1.28E�06CH4 2.45 1.46 1.70E�06 1.89 1.13 1.28E�06CO2 2.32 2.31 1.70E�06 1.43 1.4 1.28E�06C3H8 1.66 1.64 1.70E�06 1.24 1.23 1.28E�06

373 He 4.48 1.44 1.55E�06 2.83 0.91 0.93E�06N2 1.52 1.29 1.55E�06 1 0.85 0.93E�06Ar 1.36 1.38 1.55E�06 0.91 0.92 0.93E�06CH4 2.02 1.3 1.55E�06 1.36 0.87 0.93E�06CO2 1.85 1.97 1.55E�06 1.07 1.14 0.93E�06C3H8 1.91 2.03 1.55E�06 0.94 1 0.93E�06

423 He 3.92 1.34 1.39E�06 2.15 0.734 0.75E�06N2 1.32 1.59 1.39E�06 0.72 0.65 0.75E�06Ar 1.19 1.29 1.39E�06 0.581 0.63 0.75E�06CH4 1.7 1.16 1.39E�06 0.97 0.66 0.75E�06CO2 1.55 1.75 1.39E�06 0.81 0.92 0.75E�06C3H8 1.21 1.37 1.39E�06 0.69 0.78 0.75E�06


the corresponding plot for the unmodified membrane (Fig. 4b). It isevident that the behavior of the modified and unmodified mem-branes is qualitatively different. For the unmodified membrane

1plRT or plRT is a unique function of 1

l

ffiffiffiMT

q, for all species and tem-

peratures, in accordance with Eq. (2). However it is obvious thatthe behavior of the modified membranes does not conform to thismodel.

Since the permeance of the modified membranes is substan-tially smaller than that of the unmodified membranes one mightexpect that the intrusion of support resistance and viscous flowin the active layer will be insignificant. In that situation the perme-

ance should be controlled by Knudsen diffusion in accordance withEq. (1). In conformity with this simple model Fig. 6 shows that thepermeance is indeed approximately proportional to 1ffiffiffi

Mp , but the

temperature dependence, shown in Fig. 7, is much stronger thanexpected, approximating 1

T2 rather than 1ffiffiTp . Enhanced temperature

dependence might be explained by assuming a significant contri-bution from surface diffusion but such an explanation seems unli-kely since the same trend is shown by the He permeance data.

The implication appears to be that transport through the mod-ified membranes occurs by a ‘‘Knudsen-like” process but that theeffective pore radius decreases with temperature. Values of the

Table 5Comparison of effective pore radius for modified and unmodified membranes

298 K 423 K

Membrane Unmodified Modified Radius ratio Modified Radius ratio

ersz� 106 er

sz� 106 ersz� 106

A 8.33 1.8 1.67 1.39 1.82B 10.3 1.42 1.94 0.75 2.39


parameter ersz were therefore calculated from the experimental per-

meance data (for the modified membranes) in accordance with Eq.(1). These values are summarized in Table 4. The pattern is similarfor both the modified membranes. The values for the different sor-bates show some variation but are reasonably consistent. The tem-perature dependence of the mean values is shown in Fig. 8. It isevident that the effective radius for the modified membrane B issmaller than that for membrane A and the temperature depen-dence is stronger. If it is assumed that the modification procedurechanges only the pore radius without affecting the membranethickness or tortuosity, the parameter er

sz will be proportional tor3 since e is proportional to r2. The values of the parameter er

sz forthe modified and unmodified membranes and the correspondingratios of their effective radii are presented in Table 5. The modifi-cation procedure evidently reduces the pore size by a factor ofabout two (depending to some extent on the temperature).

Fig. 9 shows the temperature dependence of the experimentalpermeance data (for the modified membrane B) in comparisonwith the values back calculated from Eq. (1) using the (tempera-ture dependent) average effective radii given in Table 4. It is appar-ent that the model of Knudsen diffusion with a temperaturedependent effective pore radius provides a reasonable representa-tion of the experimental data for all sorbates.

4.3. Permeance ratios

An alternative way to examine conformity with the modifiedKnudsen model is to compare the experimental single componentpermeance ratios with the square root of the inverse ratios of themolecular weights (the expected permeance ratio for pureKnudsen diffusion). Such a comparison relative to He is shown inTable 6. Although the permeances are more strongly temperaturedependent than expected for Knudsen diffusion the permeanceratios were all essentially independent of temperature so only

Fig. 8. Variation of parameter ersz with temperature for the modified membra

the average values are given. The agreement between the datafor the two modified membranes (A and B) is excellent. For CH4,N2, Ar and C3H8 the permeance ratios relative to He are all within10% of the theoretical values thus confirming conformity with themodified Knudsen model. The experimental single component per-meance ratio for He/CO2 is however significantly smaller than thetheoretical value (by 25%). This implies that CO2 diffuses fasterthan expected, suggesting that the effective pore radius for CO2 issomewhat larger than for the other species. As a result the perme-ance ratio for CO2/C3H8 is about 1.3 even though the molecularweights of CO2 and C3H8 are the same.

4.4. Binary diffusion

When modeling binary diffusion in a pore it is necessary to con-sider the effects of both Knudsen and molecular diffusion. Momen-tum transfer arguments [25,27,28] show that the combineddiffusivity is given by

1DA¼ 1

DKAþ 1

DAB1� YA 1þ NB

NA

� � ; ð4Þ

with a similar expression for component B. The flux ratio is given by

nes calculated by matching the permeance data to Eq. (1) (see Table 4).

0

1

2

3

4

5

6

290 310 330 350 370 390 410 430

He

CH4

CO2

N2Ar

Fig. 9. Variation of permeance with temperature for the modified membrane B showing the comparison of the experimental data (points) and the values calculated from Eq.(1) (lines) with the (temperature dependant) average values of the parameter er

sz given in Table 4.

Table 6Permeance ratios calculated from single component data

Sorbates (1,2)ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiM2=M1

pðp1=p2ÞAverage % Deviation

Membrane A Membrane B

He/CH4 2.0 2.24 2.22 +10He/N2 2.65 2.89 2.84 �7.4He/Ar 3.16 3.26 3.46 +6.3He/C3H8 3.32 3.14 3.30 �3.0He/CO2 3.32 2.38 2.65 �25CO2/C3H8 1.0 1.32 1.25 +28CH4/CO2 1.66 1.06 1.19 �30

Table 7Comparison of single component and binary permeance data at 373 K

Single component data

Permeance mol=mol m2 � s � Pa� �

Membrane A Membrane B Membrane D Membrane ECH4 2.02 � 10�7 1.36 � 10�7 2.39 � 10�8

CO2 1.85 � 10�7 1.07 � 10�7 2.25 � 10�8

Binary data – Permeance ratioCH4/CO2 1.07 (1.09) (1.27) 1.19 (1.06) 1.10N2/C3H8 (1.085) (1.16) 1.17

Values calculated from single component permeances are in brackets.


NA

NB¼ DA

DB� DPA

DPB¼

1DKBþ 1

DAB1� YB 1þ NA

NB

� �h i1

DKAþ 1

DAB1� YA 1þ NB

NA

� �h i � DPA

DPB; ð5Þ

since YB ¼ NBNAþNB

and YA ¼ NANAþNB

it follows that:

NA

NB¼ DKA

DKB� DPA

DPB; ð6Þ

as the molecular diffusion term cancels. If the feed (total pressurePH) is an equimolar mixture of A, B; then

DPA

DPB¼

PH2 � PL

NANAþNB

PH2 � PL

NBNAþNB

¼PH2 � PLYA

PH2 � PLYB

; ð7Þ

so the ratio DKADKB

for comparison with the single component perme-ance ratio may therefore be calculated directly from Eqs. (6) and (7).

Binary permeation measurements were carried out at 373 Kwith an equimolar mixture of the two components. A HewlettPackard series II gas chromatograph with a TCD detector was usedto monitor the composition of the permeate stream. Measure-ments were made with membrane A which was prepared withthree mesoporous silica layers and two new membranes (D andE) which were prepared with four silica layers. The permeance ra-tio ðDKA

DKBÞ was calculated from Eqs. (6) and (7). The results are sum-

marized in Table 7. As a result of the extra thickness added to themembrane with 4 layers of silica, the permeances shown by mem-branes D and E are an order of magnitude smaller than those for

membranes A and B. However the permeance ratios are very sim-ilar with good agreement between the single component and bin-ary data for both CH4/CO2 and N2/C3H8 in all membranes.

5. Conclusion

The permeation of several probe molecules through modifiedand unmodified mesoporous silica membranes has been studiedin detail. Permeation through the unmodified membranes is rapidand the data show clear evidence of support resistance. Flowthrough the active layer occurs mainly by Knudsen diffusion, butfor all sorbates other than He, there was clear evidence of signifi-cant contribution from viscous flow. A small viscous flow wouldis to be expected as perm-porosimetry shows indicates 10% ofthe pores are larger than 15 nm for the unmodified membranes.

The behavior of the modified membranes (in which alkanegroups are attached to the walls) is more interesting. Permeancesare lower and there is no evidence of support resistance or a vis-cous contribution. Within the active layer the dominant transportmechanism appears to be a ‘‘Knudsen-like” process. For He, CH4, N2

and C3H8 the permeance values vary inversely with the square rootof the molecular weight, as expected for Knudsen diffusion. Fur-thermore, in conformity with Knudsen diffusion, the permeanceratios measured in single component and binary systems, areessentially the same, independent of temperature and coincide clo-sely with the inverse ratio of the square roots of the molecular


weights. The temperature dependence of the permeance is how-ever far stronger than the 1ffiffi

Tp dependence characteristic of classical

Knudsen flow and corresponds more nearly to 1=T2. This result isinterpreted as implying that the effective pore radius decreaseswith increasing temperature presumably as a result of the morevigorous vibration of the tethered alkane groups on the pore walls.

The behavior of CO2 is somewhat anomalous. We again see con-sistency between the single component and binary permeancedata and a stronger than expected temperature dependence ofthe permeance but the permeance of CO2 is about 25% lower thanthat of the propane (which has the same molecular weight) andthis is reflected in lower than expected permeance ratios for thelighter components relative to CO2. Although the effect is relativelysmall it is well outside the limits of experimental error. The Knud-sen model assumes specular reflection of molecules colliding withthe pore wall. This simple model seems to work reasonably well formost molecules but may well break down for a linear molecule onsuch a surface. An incomplete exchange of momentum on collisionwould lead to a higher than expected diffusivity.

One objective of these studies was to investigate whether thetethering of long alkane chains on the pore walls would lead tohigher perm-selectivies then are currently observed with mesopor-ous membranes due to the selective hindrance of particular com-ponents. With the exception of CO2 which permeates somewhatfaster than expected, such effects were not observed with thelow molecular weight species studied. It is of course possible thatsuch effects may occur with larger molecules but the prospects forapplication the membranes prepared in this study in gas separa-tion do not appear promising. Decreasing support defects, decreas-ing support pore size, and increasing functional group size could alllead to improvements in separation of smaller molecules.

Acknowledgment

The authors acknowledge the National Science Foundation CA-REER Award 0547103.

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