Experimental and Theoretical Study on Small Gas Permeation

Article pubs.acs.org/JPCC

Experimental and Theoretical Study on Small Gas Permeation Properties through Amorphous Silica Membranes Fabricated at Different Temperatures Masakoto Kanezashi,*,† Takanori Sasaki,† Hiromasa Tawarayama,‡ Hiroki Nagasawa,† Tomohisa Yoshioka,† Kenji Ito,§ and Toshinori Tsuru† †

Department of Chemical Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japan Optical Communications R&D Laboratories, Sumitomo Electric Industries Ltd, Japan 1, Taya-cho, Sakae-ku, Yokohama 244-8588, Japan § National Metrology Institute of Japan, National Institute of Advanced Industrial Science and Technology, 1-1-1 Higashi, Tsukuba 305-8565, Japan ‡

ABSTRACT: The sol−gel method was applied to fabrication of amorphous silica membranes, which have different silica network sizes caused by control of the calcination temperatures. The effects of fabrication temperature on small gas (He, H2, Ne, NH3, CO2, N2, and CH4) permeation properties through silica membranes were evaluated quantitatively using modified gas translation (GT) model. A silica membrane fired at 550 °C showed He and H2 permeances of 8.6 × 10−7 and 5.5 × 10−7 mol m−2 s−1 Pa−1 with He/CH4 and H2/CH4 permeance ratios of 2350 and 1500 at 500 °C, respectively. The thermal stability was dramatically improved by the fabrication of deposited silica glass intermediate layer because N2 permeance showed slight change, and the membrane showed a H2/N2 permeance ratio above 100 even heat-treated at 750 °C. The estimated silica network size decreased from 0.385 to 0.347 nm when a membrane was fabricated at 750 °C, which was consistent with the trend in activation energy of gas permeation. H2 molecules were more permeable than Ne when passing through amorphous silica membranes despite their larger molecular size (H2, 0.289 nm; Ne, 0.275 nm), and the H2/Ne permeance ratios were approximately the same as the Knudsen ratio and were independent of the activation energy of Ne permeation, which was almost the same as that of H2 permeation.

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INTRODUCTION Silica is one of the most attractive materials for H2 separation due to its amorphous structure across a wide range of temperatures.1 At the end of the 1980s, silica membranes that consist of Si−O−Si bonding and silanol groups derived by sol−gel and CVD methods showed excellent separation properties for both hydrogen and helium at high temperatures.2−11 The structure of amorphous silica membranes is thought to have random networks consisting of 4-, 5-, 6-, 7-, and 8-membered siloxane rings. Duke et al. reported the novel use of positron annihilation lifetime spectroscopy for rapid quantitative measurement of subnanometer pores in amorphous silica gels.12 PALS detected hierarchical trimodal porosity in all silicas, peaking at approximately 0.3 corresponding to the silica network sizes, 0.8 and 1.2 nm, as defined by the grain boundaries. However, no work has been published on the estimation of silica network size with different fabrication temperatures, where small molecules such as He and H2 can permeate, based on experimentally obtained gas permeation results such as the temperature dependence of gas permeance. Permeation mechanisms of gases through porous membranes can be classified into viscous flow, Knudsen-diffusion, surfacediffusion, and activated-diffusion, depending on the structures © XXXX American Chemical Society

(molecular size and shape, pore size), the interaction between diffusing molecules and the pore wall in the membrane, and the operating conditions (pressure and temperature).13,14 In these transport mechanisms, high selectivity can be obtained by activated-diffusion in the case of the microporous inorganic membrane. Thus, the molecular diameter of diffusing molecules should be quite important to determine the transport property through microporous membrane. However, the molecular diameters depend upon the method of measurement, and there is even a significant variation in size. The kinetic diameter reported by Breck15 and the Lennard-Jones (L-J) length constant16 can be utilized as the effective diameter for the permeating molecules. The kinetic diameter, dk, defined by the minimum cross-sectional diameter, has been utilized most commonly to discuss adsorption in adsorbents and permeation through porous material.15 By contrast, the L-J length constant that is a collision diameter, σLJ, can be determined either from the transport properties (viscosity and thermal conductivity) or the second virial coefficients.16 Received: May 20, 2014 Revised: July 18, 2014

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dx.doi.org/10.1021/jp504937t | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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Figure 1. Schematic diagram of single-gas permeation measurement and thermal stability testing.

He, Ne, and H2 for amorphous silica membranes at high temperatures.21−23 The published studies listed above indicate that the only way to estimate the effective molecular size for permeation through amorphous silica membranes is to measure several gas permeances with different molecular sizes across a wide temperature range, particularly at high temperatures where the effect of the surface diffusion is negligible. However, no published studies have reported on small gas permeation behaviors such as for He, H2, Ne, NH3, CO2, N2, or CH4 through amorphous silica membranes, which have a different silica network size across a wide temperature range (∼800 °C), particularly at high temperatures. In order to understand the small gas permeation behaviors of silica membranes, more thorough investigations are needed. This paper reports on the fabrication of amorphous silica membranes, which have different average pore size caused by control of the calcination temperatures and on an evaluation of small gas permeation behaviors in a wide temperature range of 300−750 °C. A modified gas translation (GT) model was applied to quantitatively evaluate small gas (He, H2, Ne, NH3, CO2, N2, and CH4) permeation behaviors through amorphous silica membranes.

Only a few papers have been published concerning the effective molecular size for permeation through amorphous silica networks, particularly at high temperatures. Tsuru et al.17,18 reported that the kinetic diameter of polar molecules such as H2O (dk: 0.265 nm) and NH3 (dk: 0.26 nm) was not an effective molecular size for permeation through amorphous silica networks at high temperatures, since the order of gas permeance is always He > H2 > H2O and He > H2 >NH3, which is not a consistent kinetic diameter order. In accordance with Breck,15 L-J potential was used to obtain the kinetic diameter of He, H2, and N2 molecules, that is spherical and nonpolar molecules, while for H2O and NH3 molecules that is polar molecules, Stockmayer potential, which consists of L-J potential and electric dipole interaction, was used. When NH3 or H2O molecules permeated through a silica structure with an average pore size of 0.3−0.5 nm at high temperatures, there was a possibility that the interaction between the permeating molecules and silica structure would be much stronger than that between the permeating molecules. In this case, the electric dipole interaction, which is attributed to the interaction between NH 3 −NH 3 or H 2 O−H 2 O molecules, can be neglected. Leeuwen19 reported molecular sizes for NH3 and H2O of 0.326 and 0.2995 nm, respectively, by reducing the dipole moment, which resulted in a larger molecular size than that of the kinetic diameter, which is consistent with the order of gas permeance for amorphous silica membrane. For permeation of hydrocarbons through amorphous silica membranes, the kinetic diameters of C3H6 (dk: 0.45 nm) and C3H8 (dk: 0.43 nm) were also not an effective molecular size, since diffusivity seems to strongly depend on molecular length (σLJ) due to the rotation of molecules.20 Oyama et al.21−23 also claimed the unusual order of gas permeance (He, H2, and Ne) through CVD-derived silica membranes, which were He > H2 > Ne because it followed neither the order of kinetic diameter nor the molecular weight (He: 4 g mol−1; H2: 2 g mol−1; and Ne: 20.1 g mol−1). The unusual order of permeance was quantitatively explained by a statistical mechanical model24 based on a mechanism involving jumps between solubility sites. However, they did not claim the effective molecular diameter of

1. EXPERIMENTAL SECTION 2.1. Fabrication of Silica Membranes on Silica Glass Intermediate Layer. The silica sols were prepared by hydrolysis and the polymerization reaction of tetraethoxysilane (TEOS) with water and nitric acid as a catalyst. Six types of sols (equivalent weight % of TEOS in sol: 0.5, 1.0, 1.5, 2.0, 3.0, and 4.0 wt %) were prepared to control the sol size as reported previously.11 Details of the preparation procedure were described in the previous paper.11 Glass tubes with a porosity of 50% and an outer diameter of 10 mm, which were supplied from Sumitomo Electric Industries Ltd., Japan, were for the substrates of silica membranes. The details of information on the substrate were reported in our previous paper.11 Before coating the silica sol to form an active separation layer, in the present study, in order to B



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ularly above 650 °C, irrespective of what materials were used for the intermediate layer (colloidal silica, silica glass). This is due to the densification of silica matrix, through which He and H2 molecules would permeate. A clearly different trend was confirmed in N2 permeance. The permeance of N2 for a SM-1 showed little change, and the membrane showed a H2/N2 permeance ratio that was above 100, even after heat-treated at 750 °C. By contrast, a membrane on a colloidal silica intermediate layer showed an increase in the N2 permeance with increased heat-treated temperature, which resulted in a large decrement of the He/N2 (= 30) and H2/N2 (= 10) permeance ratio after being heat-treated at 750 °C. This is caused by enlarged grain boundaries in the membrane due to the sintering of colloidal silica, as reported previously.11 Figure 3 shows the SEM images of a surface cross section of a membrane on a silica glass intermediate layer heat-treated at 800 °C. The membrane showed an asymmetric structure with a thin silica separation layer (less than 200 nm) on a silica glass intermediate layer deposited onto the porous glass support even heat-treated at 800 °C, showing a thermally stable structure. A membrane on a colloidal silica intermediate layer heat-treated at 800 °C was reported previously11 and is shown here again in Figure 3 (panels c and d). When colloidal silica was used to form an intermediate layer, no clear boundary layer, which should be between the silica separation layer and the intermediate/deposited layer, was observed due to the melting-induced adhesion of colloidal silica caused by sintering at 800 °C. Thus, it can be concluded that silica glass particles, which can prevent the sintering process during the enhanced condensation of Si−OH groups, structural relaxation, and viscous sintering above 780 °C,25 were quite effective in improving the thermal stability of SiO2 membrane structures. 3.2. Densification of Amorphous Silica Networks Fabricated at High Temperatures. The gas translation (GT) or activated-Knudsen diffusion model that was used to describe the gas permeation properties through microporous membranes was originally proposed by Xiao and Wei13 and Shelekhin,14 and can be expressed by eq 1.

enhance the thermal stability, silica glass particles (particle diameter of approximately 0.3 μm) mixed with silica sols were coated to form an intermediate layer. Then, an active separation layer was fabricated by coating with the silica sol diluted to approximately 0.5 wt %, followed by drying and calcination at 550 to 750 °C for 0.5 h under an air atmosphere. 2.2. Measurement of Gas Permeance and Thermal Stability Testing. In the present study, measurement of the permeation rate as well as evaluation of the thermal stability of membranes was conducted using the gas permeation equipment shown in Figure 1.11 He, H2, Ne, NH3, CO2, N2, and CH4 of high purity was fed on the outside of the membrane (membrane surface) at atmospheric pressure, while the permeate side (downstream) was evacuated using a vacuum pump. The feed-flow rate was controlled using a mass-flow controller. Silica membranes were put in the permeation cell, and the temperature was controlled using an electric furnace (300−800 °C). Thermal stability was evaluated by the same procedure reported in our previous paper, and a detailed description can be found there.11

3. RESULTS AND DISCUSSION 3.1. Improved Thermal Stability of Silica Membranes on Silica Glass Intermediate Layer. Figure 2 shows the gas

Pi = εd pρg, i

⎛ Ep, i ⎞ 8RT 1 exp⎜ − ⎟ πMi RTτL ⎝ RT ⎠

(1)

In eq 1, dp is the pore size, ε is the porosity, τ is the tortuosity, L is the thickness, ρg,i is the probability of the ith component, Ep,i is the kinetic energy of the ith component, R is the gas constant, and T is the absolute temperature. It should be noted that the definition of dp is the diameter between the surface of the oxygen atoms, and the GT model assumes no molecular size of permeating molecules. Recently, a modified GT model, which assumes the diffusion distance of (dp − di) instead of dp for the ith component (molecular size: di) was proposed as expressed in eq 2.26

Figure 2. Single-gas permeance and H2/N2 perm-selectivity at 500 °C for a silica membrane fabricated at 550 °C after heat-treated from 550 to 800 °C (closed symbols: membrane with silica glass intermediate layer (SM-1); open symbols: membrane with colloidal silica intermediate layer).

permeances (He, H2, and N2) and H2/N2 permeance ratio at 500 °C for a silica membrane, which was originally fired at 550 °C and heat-treated from 550 to 800 °C. A silica membrane was also fired at 550 °C on a colloidal silica intermediate layer, by following a previously reported procedure.11 A membrane on a silica glass intermediate layer (SM-1) just after preparation showed He and H2 permeances of 6.0 × 10−7 and 3.0 × 10−7 mol m−2 s−1 Pa−1 with He/N2 and H2/N2 permeance ratios of 800 and 400, respectively. A membrane deposited onto a colloidal silica intermediate layer showed almost the same He and H2 permeance as that on a silica glass intermediate layer. It should be noted that gas permeance of either membrane (colloidal silica, silica glass) showed no appreciable change in N2 atmosphere at 550 °C. He and H2 permeances for both membranes decreased with heat-treated temperature, partic-

Pi =

(d p − di)2 ε (d p − di) 3τL d p2

=

k 0, i = C

⎛ Ep, i ⎞ 8 exp⎜ − ⎟ πMiRT ⎝ RT ⎠

⎛ Ep, i ⎞ exp⎜ − ⎟ ⎝ RT ⎠ MiRT

(2)

3 ε (d p − di) 3τL d p2

(3)

k 0, i

8 = a(d p − di)3 π



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Figure 3. SEM images of a surface and cross section of a membrane on a silica glass intermediate layer (a) (scale bar: 10 μm) and (b) (scale bar: 200 nm), and that on a colloidal silica intermediate layer (c) (scale bar: 10 μm) and (d) (scale bar: 1 μm)11 after heat treatment at 800 °C.

Figure 4 shows the temperature dependence of He and H2 permeances for a silica membrane (SM-1) heat-treated from

Figure 5. Activation energy of He and H2 permeation and He/H2 permeance ratio for two amorphous silica membranes (including SM1) on a silica glass intermediate layer fabricated at 550 °C as a function of heat-treated temperatures from 550 to 800 °C.

Figure 4. Temperature dependence of He and H2 permeances for a silica membrane (SM-1) heat-treated from 650 to 800 °C.

silica membranes (including SM-1) on a silica glass intermediate layer fabricated at 550 °C as a function of heattreated temperatures (550−800 °C). The activation energy of He permeation was slightly increased with heat-treated temperature. On the other hand, a drastic increase, from 12.5 to 27.5 kJ mol−1 in the H2 activation energy, was confirmed after heat-being treated above 650 °C. Since the activation energy generally requires a larger value in order to overcome a large repulsive force when molecules permeate through smaller pore size,27 it can be concluded that amorphous silica structures can be densified by calcination at high temperatures, which is caused by the enhanced condensation reaction of Si−OH groups.11,28 The increase in the activation energy of H2 (0.289 nm) that was drastically greater than that of He (0.26 nm) can be ascribed to its larger molecular size. He/H2 permeance ratio was also increased with heat-treated temperature. This is because the He/H2 permeance ratio, which can also be regarded as one of the indicators for the densification of the

650 to 800 °C. He and H2 permeances were decreased with a decrease in the temperature, showing an activated-diffusion mechanism, and the slope of temperature dependence increased with heat-treated temperatures. The activation energy of He and H2 permeation (Ep) was obtained by regressing a modified gas-translation model as expressed in eq 2 with a temperature dependence of He and H2 permeance above 300 °C. It should be noted that the obtained activation energy, which is the activation energy of gas permeation, Ep, is the “apparent activation energy”, since molecular permeation occurs through adsorption with the heat of adsorption, ΔH, and is followed by diffusion from activation energy, Ed, resulting in the activation energy of permeance (Ep = Ed −ΔH). Figure 5 shows the activation energy of He and H2 permeation and the He/H2 permeance ratio for two amorphous D



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Figure 6. Temperature dependence of gas permeance for a silica membrane fired at (a) 550 °C (SM-2) and (b) 750 °C (SM-3) (solid curves fitted with eqs 2 and 4 for NH3 and CO2).

silica structures that He and H2 molecules would permeate,18 was increased due to the molecular sieving properties. It should be noted that a correlation between the He/H2 permeance ratio and the activation energy was obtained; that is, the He/H2 permeance ratio increased when the activation energy of both He and H2 permeation were increased. This correlation is reasonable, since the decreased ratios of H2 permeance was much larger than that of He permeance because of a larger effect of molecular sieving, when these molecules permeated monomodal amorphous silica networks. The molecular sieving separation increased with decreased pore size, corresponding to the increased activation energy of gas permeation. 3.3. Estimation of the Average Pore Size for Amorphous Silica Membranes Using a Modified Gas Translation (GT) Model. The temperature dependence of gas permeances (He, H2, Ne, NH3, CO2, N2, and CH4) was observed at temperatures between 300 and 750 °C. Figure 6a shows the temperature dependence of gas permeances (He, H2, Ne, NH3, CO2, N2, and CH4) at temperatures ranging from 300 to 550 °C for a silica membrane (SM-2) fired at 550 °C. The permeances of He, H2, Ne, N2 and CH4 were increased with increased temperature, showing an activated-diffusion property. The permeance of NH3 and CO2 increased with decreasing temperature; a surface diffusion mechanism wherein a larger degree of adsorption for CO2 and NH3 onto a silica surface at a lower temperature was because of an affinity that was stronger than that of other gases.17,29 An SM-2 showed He and H2 permeances of 8.6 × 10−7 and 5.5 × 10−7 mol m−2 s−1 Pa−1 with He/CH4 and H2/CH4 permeance ratios of 2350 and 1500 at 500 °C, respectively, and the selectivity of both increased with temperature. Figure 6b shows the temperature dependence of gas permeances (He, H2, Ne, NH3, CO2, N2, and CH4) at temperatures ranging from 300 to 750 °C for a silica membrane (SM-3) fired at 750 °C. The permeances of He, H2, and Ne largely increased with increasing temperature, clearly showing an activated permeation mechanism. The H2/N2 permeance ratio was higher than 250 in this temperature range and increased with increasing temperature due to a larger temperature dependence of H2 permeance than that of N2.

The values for the permeance of N2 and CH4 were on the order of 10−10 mol m−2 s−1 Pa−1 and were slightly increased with a decrease in temperature, which was caused by Knudsen-like permeation behavior. The permeance of NH3 increased as the temperature was increased above 500 °C but was independent of temperatures below 500 °C. CO2 permeance also showed a similar permeation behavior; the permeance increased with measurement temperature above 600 °C but also increased with a temperature below 600 °C. The activation energy of gas permeation (Ep,i), which is the “apparent activation energy,” and the pre-exponential factor, k0,i, for He, H2, Ne, N2, and CH4 molecules (following Henry’s law) was obtained by regressing the modified gas-translation model, which assumes a monomodal structure, as expressed in eq 2, with the temperature dependence of gas permeance above 300 °C, and these values are summarized in Tables 1 and 2. Table 1. Activation Energy of Gas Permeation for Amorphous Silica Membranes (SM-2, SM-3) Fitted with Eq 2 activation energy E(1) p (kJ mol−1)

sample code SM-2 SM-3

He

Ne

H2

N2

CH4

7.7 14.6

13.1 23.0

14.1 23.1

12.3 2.36

7.8 0.32

Since the temperature dependence of adsorptive molecules such as NH3 and CO2 showed a combination of surface diffusion and activated diffusion, the activation energy of gas permeation (Ep,i) and the pre-exponential factor, k0,i, for NH3 and CO2 was obtained by eq 4, which takes into account the bimodal structures (pore 1, pore 2). These values are summarized in Table 3. It should be noted that He, H2, Ne, and N2 generally follow the Henry-type adsorption properties and showed less heat of adsorption (∼10 kJ mol−1) in comparison with CO2 and NH3 molecules. The heat of adsorption of NH3 and CO2 by silica was reported to be approximately 40−60 kJ mol−1 and 25 kJ mol−1, respectively.30−32 E



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Table 2. Pre-Exponential Factor, k0,i, for Amorphous Silica Membranes (SM-2, SM-3) Fitted with Eq 2 k(1) 0,i [−]

sample code SM-2 SM-3

He

Ne

H2

N2

CH4

5.2 × 10−4 6.0 × 10−4

3.0 × 10−4 3.5 × 10−4

4.6 × 10−4 4.9 × 10−4

3.2 × 10−6 9.3 × 10−8

4.1 × 10−7 7.2 × 10−8

Table 3. Activation Energy and Pre-Exponential factor, k0,i, of NH3 and CO2 Molecules for Amorphous Silica Membranes (SM-2, SM-3) Fitted with Eq 4 sample code SM-2 SM-3

Pi =

gas NH3 CO2 NH3 CO2

E(1) p (kJ mol−1) 15.9 18.3 24.0 26.2

E(2) p (kJ mol−1) −37.0 −24.0 −41.0 −25.0

⎛ E (1) ⎞ p, i ⎟ exp⎜⎜ − ⎟+ RT MiRT ⎝ ⎠ k 0,(1)i

k(1) 0 [−] 3.1 2.5 5.5 4.0

× × × ×

−5

10 10−5 10−6 10−6

On the contrary, when a linear correlation was drawn for the plotted points of k0(2) for NH3 and CO2 molecules as well as N2 and CH4, the effective pore size was estimated at larger than 0.7 nm, corresponding to the size of the large pores in a membrane. Thus, it can be concluded that silica membranes fired at 750 °C are supposed to have a bimodal structure comprised of pores in amorphous silica networks, and fewer large pores, which are formed as spaces between gel particles. The values of k0(1) for NH3 and CO2 molecules were approximately 105 times higher than the values of k0(2) for NH3 and CO2, indicating the presence of a negligible amount of large pores in a membrane. The estimated silica network size was decreased from 0.385 to 0.347 nm when a membrane was fabricated at 750 °C, which was consistent with the trend in activation energy (i.e., the activation energy of He, Ne, and H2 for SM-3 was much higher than that for SM-2). A similar trend was also confirmed in the activation energy (Ep(1)) for NH3 and CO2 permeation. It should be noted that the obtained apparent activation energy of NH 3 and CO 2 for permeation through pore 2 was approximately the same as the heat of adsorption, as shown in Table 3. The activation energy of N2 and CH4 permeation for SM-3 was smaller than that for SM-2, which can be ascribed to the Knudsen diffusion through large pores, which were formed by sintering at high temperatures. 3.4. He, H2, and Ne Permeation Properties through Amorphous Silica Membranes. Reportedly, the order of kinetic diameters for He, H2, and Ne is as follows: He (0.26 nm), Ne (0.275 nm), and H2 (0.289 nm). It should be noted that the L-J length constant for Ne is also smaller than that for H2 molecules.16 On the other hand, the order of gas permeance, that was irrespective of permeation temperatures (350−750 °C) and silica network size, was He > H2 > Ne. Figure 8a shows a relationship between He/Ne permeance ratio at 500 °C and the activation energy of Ne permeation for

k(2) 0 [−] 2.0 1.2 1.4 8.0

⎛ E (2) ⎞ p, i ⎟ exp⎜⎜ − ⎟ RT MiRT ⎠ ⎝

× × × ×

10−9 10−9 10−11 10−10

k 0,(2)i

(4)

(1) In eq 4, k(1) 0,i and Ep,i are the pre-exponential factor and the activation energy for the ith component through pore 1, while (2) k(2) 0,i and Ep,i are the equivalent through pore 2, respectively. The mean effective pore size can be determined by the plot of k0,i1/3 against di, since the cubic root of eq 3 gives a linear relationship between di and k0,i1/3 with a slope of −a1/3 and an intercept of a1/3dp.33 Figure 7a shows the relationship between k0,i1/3 and di for a membrane fabricated at 550 °C (SM-2). The plotted points of k0(2)1/3 for NH3 and CO2 clearly deviated from the correlation line since these were approximately 1/10000th of the value of k0(1). A good linear correlation was observed in the obtained k0(1)1/3 for He, Ne, H2, NH3, CO2, N2, and CH4 molecules, and the effective pore size of a membrane fabricated at 550 °C was approximately 0.385 nm. Figure 7b shows the relationship between k0,i1/3 and di for a membrane fabricated at 750 °C (SM-3). Two linear correlations were obtained. When a linear correlation was drawn for the plotted points of He, Ne, and H2, which included the k0(1) for NH3 and CO2 molecules, the effective pore size was estimated at approximately 0.347 nm, corresponding to the size of amorphous silica networks.

Figure 7. Relationship between k0,i1/3 and di for membranes fabricated at (a) 550 °C (SM-2) and (b) 750 °C (SM-3) (closed symbols: the values of k0,i(1); open symbols: the values of k0,i(2)). F



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Figure 8. (a) He/Ne and (b) H2/Ne permeance ratios at 500 °C as a function of the activation energy of Ne permeation for amorphous silica membranes (closed symbols: sol−gel-derived; open symbols: CVD-derived21−23). Each point corresponds to one membrane.

Figure 9. Activation energy of (a) He and (b) Ne permeation for silica membranes derived by sol−gel5,6,11,18 and CVD21−23,34−37 methods, as well as vitreous glass,38,39 as a function of the activation energy of H2 permeation. Each point corresponds to one membrane.

activation energy of He and H2 permeation, as discussed in the previous section. Figure 8b shows a relationship between H2/Ne permeance ratio at 500 °C and the activation energy of Ne permeation for amorphous silica membranes prepared via sol−gel and CVD21−23 methods. Surprisingly, the H2/Ne permeance ratio was approximately the same as the Knudsen ratio and was independent of the activation energy of Ne permeation. It should be noted again that H2 was more permeable than Ne, despite having a larger kinetic diameter. These results suggest that the difference in the effective molecular size is negligible between H2 and Ne for permeation through an amorphous silica structure. Thus, the molecular sieving mechanism cannot separate H2 and Ne, and H2/Ne selectivity is approximately the same as the Knudsen ratio (=3.17), which is the ratio of the square root of the molecular weight, according to the modified gas-translation model (GT model), as expressed in eq 2. Figure 9a shows a relationship between the activation energy of He permeation through amorphous silica membranes prepared by sol−gel,5,6,11,18 CVD,21−23,34−37 vitreous glass,39 and activation energy of H2 permeation. The activation energy of He permeation increased with increased activation energy of

amorphous silica membranes prepared in this work and via the CVD21−23 method. It should be noted that each point in this figure corresponds with one membrane. The activation energy of Ne permeation was calculated by regressing eq 2 with the temperature dependence of Ne permeance. A linear correlation between the He/Ne permeance ratio and the activation energy of Ne permeation was obtained, irrespective of membrane preparation methods (sol−gel, CVD21−23); the He/Ne permeance ratios increased with increased activation energy of Ne permeation, which was much higher than the Knudsen ratio. This is because the molecular diameter of He is smaller than Ne, and the area available for permeation (diffusion) is larger for He than for Ne. Thus, the decreased ratio of Ne permeance was much higher than that of He permeance because of the larger effect of molecular sieving. On the contrary, the activation energy of Ne permeation corresponded to the pore size in a membrane where Ne molecules could permeate, as discussed in the previous section. Thus, it can be concluded that the He/Ne permeance ratio increased largely with increased activation energy of Ne permeation, corresponding to smaller network sizes. This trend is acceptable and consistent with the trend for He/H2 permeance ratio and the G



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properties through amorphous silica membranes were quantitatively explained via a modified gas translation (GT) model, irrespective of fabrication temperatures. The estimated silica network size was decreased from 0.385 to 0.347 nm when a membrane was fabricated at 750 °C, which was consistent with the trend in the activation energy of gas permeation. (4) H2 molecules were more permeable than Ne molecules through amorphous silica membranes despite a larger molecular size (0.289 nm vs 0.275 nm, respectively); H2/Ne permeance ratios were approximately the same as the Knudsen ratio and were independent of the activation energy of Ne permeation. By contrast, the activation energy of Ne permeation approximated that of H2 permeation, irrespective of either the pore size of the amorphous silica network or the fabrication method. Thus, the present results suggest that there is a possibility that the effective molecular size of H2 for its permeation through an amorphous silica network might be slightly larger than that of Ne.

H2 permeation, showing an approximately linear correlation. The activation energy of H2 increased more rapidly than that of He with a decrease in pore size, due to its larger molecular size. It should be noted that the calculated activation energy data of He and H2 diffusion through planar H2nSinOn (n = 6−8) rings using the ab initio calculation27 were also plotted in this figure and also expressed with one correlation curve. Figure 9b shows a relationship between the activation energy of Ne permeation through amorphous silica membranes prepared by sol−gel, CVD,21−23 and vitreous glass,38,39 and the activation energy of H2 permeation. The activation energy of Ne permeation also increased with an increase in H2 permeation. However, the activation energy of Ne permeation approximated that of H2 permeation, irrespective of the pore sizes of amorphous silica networks. When Ne and H2 molecules permeate through a monomodal silica network, H2 molecules should have a larger activation energy compared to Ne molecules if kinetic diameter15 and/or L-J length constant16 is appropriate (i.e., H2 > Ne) for an effective molecular size. As shown in Table 2, the value of k0,i was decreased with increased molecular size, except for H2 and Ne. The value of k0,i for H2 was larger than that for Ne, irrespective of fabrication temperatures. It should be noted that the value of k0,i, as expressed by eq 3, depends on the molecular size and decreases with an increase in molecular size due to the decrease in effective diffusion distance. Thus, the present results suggest again that there is a possibility that the effective molecular size of H2 for permeation through an amorphous silica network might be slightly larger than that of Ne.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +81-82-424-7714. Fax: +81-82-424-5494. Notes

The authors declare no competing financial interest.

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REFERENCES

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4. CONCLUSIONS The sol−gel method was applied to the fabrication of amorphous silica membranes, which have different silica network sizes caused by control of the calcination temperatures. The silica separation layer with thickness less than 200 nm was fabricated on a deposited silica glass intermediate layer. Single gas permeation (He, H2, Ne, NH3, CO2, N2, and CH4) properties through amorphous silica membranes were measured to evaluate small gas permeation behaviors in a temperature range from 300 to 750 °C. A modified gas translation (GT) model was applied to quantitatively evaluate small gas permeation properties through porous silica membranes. (1) A silica membrane fired at 550 °C showed He and H2 permeances of 8.6 × 10−7 and 5.5 × 10−7 mol m−2 s−1 Pa−1 with He/CH4 and H2/CH4 permeance ratios of 2350 and 1500 at 500 °C, respectively. Thermal stability was dramatically improved by the fabrication of deposited silica glass intermediate layer, which prevented the sintering process caused by structural relaxation and viscous sintering at high temperatures, due to the fact that N2 permeance showed slight change and a membrane showed a H2/N2 permeance ratio of above 100, even heat-treated at 750 °C. (2) The activation energy of He permeation was slightly increased with increased heat-treated temperature. On the other hand, a drastic increase, from 12.5 to 27.5 kJ mol−1 in the activation energy of H2, was confirmed after heat-treated above 650 °C. The increased activation energy of H2 (dm: 0.289 nm) that was much greater than that of He (dm: 0.26 nm) can be ascribed to a larger molecular size. The trend in increased activation energy suggests that amorphous silica structures can be densified by calcination at high temperatures, which is caused by the enhanced condensation reaction of Si−OH groups. (3) Small gas (He, H2, Ne, NH3, CO2, N2, and CH4) permeation H



Article

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Experimental and Theoretical Study on Small Gas Permeation

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