Gas Permeation Properties and Pore Size Evaluation of Microporous Silica Membranes

CHAPTER 5

Gas Permeation Properties and Pore Size Evaluation of Microporous Silica Membranes Masakoto Kanezashi, Toshinori Tsuru Department of Chemical Engineering, Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima, Japan

1 Introduction Membrane-based separation is a simple energy-conservative method with many advantages, particularly for gas separations with no phase change. These methods represent viable alternatives to conventional distillation, cryogenic separation, and pressure-swing adsorption in applications such as purification of natural gas, CO2 separation, air separation, and H2 separation as well as olefin/paraffin separation. Membranes generally are classified as either polymer or inorganic according to their materials. Inorganic membranes have the substantial advantage of thermal and chemical stability compared with conventional polymeric membranes (Lin et al., 2002; Ockwig and Nenoff, 2007; Verweij et al., 2006; Tsuru, 2008; Basile and Gallucci, 2011; Yun and Oyama, 2011). Thus, many researchers have tried to develop inorganic membranes using various materials, and examples include palladium, silica, alumina, titania, and zirconia. Inorganic membranes can be categorized as either dense derived by palladium (palladium alloy) or porous (silica, alumina, etc.). Dense palladium membranes and their alloys only allow H2 molecules to permeate by the mechanism of solution-diffusion (SD), which results in high H2 selectivity (Yun and Oyama, 2011). The gas separation mechanisms of porous inorganic membranes consist mainly of Knudsen diffusion, surface diffusion, and molecular sieving (Xiao and Wei, 1992; Shelekhin et al., 1995; Yoshioka et al., 2001; Tsuru et al., 2011). Amorphous silica networks have ultramicroporous pores, through which small molecules such as helium (kinetic diameter: 0.26 nm) and hydrogen (0.289 nm) can permeate, in a wide temperature range below 1000°C. In the 1980s, several researchers demonstrated the molecular sieving properties of microporous silica membranes (Lin et al., 2002; Ockwig and Nenoff, 2007; Verweij et al., 2006; Tsuru, 2008; Basile and Gallucci, 2011). Microporous Membranes and Membrane Reactors. https://doi.org/10.1016/B978-0-12-816350-4.00005-2 # 2019 Elsevier Inc. All rights reserved.

101

102 Chapter 5 Fig. 1 displays a transmission electron microscopy (TEM) image of the cross-section of a typical microporous silica membrane (Tsuru et al., 2011). Porous supports, which are usually manufactured using powders by extrusion or slip-casting, have pore sizes in excess of 1 μm and a thickness on the order of millimeters, and are designed for mechanical strength. An intermediate layer is coated on the support layer to reduce pore sizes to accommodate the addition of a top layer. In general, intermediate layer pore size distributions (PSDs) that range across several nanometers are evaluated by nanopermporometry measurement using condensable gas (hexane and water) (Tsuru, 2008; Tsuru et al., 2001). The basic principle of nanopermporometry is based on the controlled blocking of the pores via the capillary condensation of a vapor and measurement of the permeate flux of noncondensable gas through the remaining open pores. The measurement capability of this technique is reported to range from 0.5 to 30 nm (Tsuru, 2008; Tsuru et al., 2001). The separation top layer, which has separation ability and must have controlled pore sizes suitable for specific separations, is formed as thinly as possible on the intermediate layer. In the subnanometer range, it is quite difficult to obtain exact PSDs of porous membranes for gas separation. The only way to estimate the PSD is to take several measurements of gas permeance at temperatures higher than 150°C where the effect of surface flow is negligible, as a function of the molecular size of gas molecules. Fig. 2A shows the degree to which gas permeance is dependent on the kinetic diameter of sol-gel-derived microporous silica membranes (Mem-A, -B, -C) at 200°C. Because the absolute value of gas permeance depends on the thickness, the

Fig. 1 TEM images of a cross-section of a typical sol-gel-derived silica membrane (A) cross-section with a 10 μm depth, and (B) the cross-section of a top layer at high magnification (Tsuru et al., 2011).

Gas Permeation Properties and Pore Size Evaluation of Microporous Silica Membranes 103 10 -5

10 1

He H2

He

H2 CO2

N2

10 -6

Dimensionless permeance (-)

Permeance (mol m-2 s-1 Pa-1)

CO2 CH4 C3H8

10 -7

Mem-A 10 -8 Mem-B

SF6

Mem-C 10

-9

10 -10 0.2

0.3 0.4 0.5 Kinetic diameter (nm)

0.6

N2 CH4

10 0

10 -1

C3H8

10 -2

Mem-A

Mem-B 10

-3

10 -4 0.2

Mem-C

0.3

0.4

0.5

SF6

0.6

Kinetic diameter (nm) (B) Fig. 2 Kinetic diameter dependence of gas permeance (A) and dimensionless permeance based on He permeance (B) at 200°C for sol-gel-derived microporous silica membranes (Mem-A, -B, -C).

(A)

order of the average pore size is estimated using dimensionless permeance based on He permeance (Duke et al., 2008). Fig. 2B shows the dimensionless permeance based on He permeance at 200°C for sol-gel-derived silica membranes (Mem-A, -B, -C) as a function of kinetic diameter. The broken line shows the calculated dimensionless permeance under Knudsen mechanism based on He. Membrane C showed the sharpest cutoff between He and N2 (permeance ratio: 1500), which was much higher than the value expected for a Knudsen diffusion mechanism (He/N2 Knudsen selectivity: 2.65). The permeation cutoff of Membrane A roughly followed the Knudsen mechanism in the range of He (0.26 nm) to CO2 (0.33 nm). Membrane B showed a much higher He to CH4 and C3H8 permeance ratio compared to that for Membrane A. Based on He selectivity and deviation from the Knudsen ratio, it is possible to estimate the order of the average pore size (Mem-A > Mem-B > Mem-C). With this method, however, it is difficult to quantitatively obtain the values of pore sizes. This chapter reviews subnanometer pore size evaluation methods based on a modified gas translation (GT) model and on derived normalized Knudsen-based permeance (NKP) (Lee et al., 2011; Yoshioka et al., 2013; Kanezashi et al., 2014; Nagasawa et al., 2014; Li et al., 2015), which is based on a GT model originally proposed by Xiao and Wei (1992) and Shelekhin et al. (1995), for zeolite and amorphous silica membranes. The effective molecular size of H2 for permeation through an amorphous silica network is discussed based on the results of a k0 plot, activation energy, and each permeance ratio. In addition, theoretical analysis of He and H2 permeation properties through microporous organosilica membranes derived from bridged organoalkoxysilanes with different linking units is also introduced to discuss the permeation differences between SiO2 and organosilica networks.

104 Chapter 5

2 Modified Gas Translation Model for Pore Size Evaluation 2.1 Modified Gas Translation Model (Lee et al., 2011; Yoshioka et al., 2013; Kanezashi et al., 2014; Nagasawa et al., 2014; Li et al., 2015) Gas permeation of microporous membranes can be accomplished by a combination of Knudsen diffusion, surface diffusion, and molecular sieving mechanisms (Xiao and Wei, 1992; Shelekhin et al., 1995; Yoshioka et al., 2001; Tsuru et al., 2011). Several theoretical models have been proposed to describe the gas permeation properties of microporous membranes. Xiao and Wei first developed a model, which is referred to as the GT or activated Knudsen diffusion model, to analyze the diffusion of hydrocarbons in zeolites (Xiao and Wei, 1992). The GT model was derived for diffusion through microporous inorganic membranes using probability, ρi, as expressed in Eq. (1). rffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8 εi Pi ¼ dp ρi  (1)  πMi RT τi Li In Eq. (1), the membrane structural factors (pore size, porosity, tortuosity, thickness) are expressed as dp, εi, τi, and Li. Because the probability, ρi, is expressed in Eq. (2) using preexponential, ρg,i, and kinetic energy, Ep,i, to overcome the diffusion barrier, the permeance in Eq. (1) can be expressed in Eq. (3). This equation replicates a version derived by assuming gas permeation of cylindrical and straight micropores of a homogeneous potential field (Yoshioka et al., 2001).   Ep, i (2) ρi ¼ ρg, i exp  RT rffiffiffiffiffiffiffiffiffiffiffiffiffiffi     8 εi Ep, i k0 Ep, i  ¼ pffiffiffiffiffiffiffiffiffiffiffiffi exp  (3) Pi ¼ dp ρg, i   exp  RT RT πMi RT τi Li Mi RT In 2011, the authors proposed a modified GT model and derived the NKP for the determination of pore sizes less than 1 nm (Lee et al., 2011), which was based on original proposals by Xiao and Wei (1992) and by Shelekhin et al. (1995). NKP is the ratio of permeance of the ith component to that predicted using the jth component under a Knudsen diffusion mechanism, as expressed in Eq. (4). rffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffi Pi Mi Pi Mi (4) fNKP ¼ pffiffiffiffiffiffi ¼ Pj Mj PHe MHe qffiffiffiffiffiffi When He, the smallest molecule, is taken as a reference (jth component), PHe MMHei is the permeance of the ith component predicted from He permeance under the Knudsen diffusion mechanism, and therefore, fNKP corresponds to the ratio of experimentally obtained permeance to predicted permeance based on He. It should be noted that fNKP equals 1 for the Knudsen

Gas Permeation Properties and Pore Size Evaluation of Microporous Silica Membranes 105 mechanism, and fNKP indicates how much the experimentally obtained permeance is decreased due to the effect of molecular sieving. In the original GT model, the geometrical probability, ρg,i, was decided based only on the physical structure of the membrane matrix. On the other hand, in the modified GT model, ρg,i can be defined by Eq. (5). ρg, i ¼

1 Ai 3 A0

(5)

In Eq. (5), Ai is the area of the pore opening for the effective permeation of the ith component, and A0 is the cross-sectional area of the pore. The diffusion distance in Eqs. (1), (3) is assumed to be (dp – dm,i) instead of dp for the ith component (molecular size: dm,i), because the center of the ith component cannot approach the wall. Therefore, Ai, the area of the pore opening effective for diffusion, is proportional to the effective pore area (Eq. 6), which leads to the modified GT model as shown in Eq. (7). 2.  2 π ðdp dm, i Þ 1 Ai 1 1 dp  dm, i 4 . ¼ ¼ (6) ρg, i ¼ dp2 3 A0 3 πdp 2 3 4

  rffiffiffiffiffiffiffiffiffiffiffiffiffiffi      dp  dm, i 2 εi  8 Ep, i k0, i Ep, i dp  dm, i exp  ¼ pffiffiffiffiffiffiffiffiffiffiffiffi exp  Pi ¼ 3τi Li dp2 RT RT πMi RT Mi RT  3 rffiffiffi  3 εi dp  dm, i 8 ¼ a dp  dm, i k0, i ¼ 2 3τi Li dp π rffiffiffi εi 8 a¼ 2 3τi Li dp π

(7)

(8)

(9)

In Eqs. (7)–(9), a is a constant that depends only on the structure of the membrane pores and is independent of the permeation molecules. Based on the previous discussion, the following expression for NKP can be obtained as shown in Eq. (10) with the assumption that membrane structural factors such as tortuosity, τi, and membrane thickness, Li, are rationally assumed to be equal, irrespective of the molecules, due to the cylindrical pore structure. 3      dp  dm, i k0, i Ep, i  Ep, He Ep, i  Ep, He  exp  ¼ (10) fNKP ¼ 3  exp  k0, He RT RT dp  dHe In the authors’ previous paper (Lee et al., 2011), for simplicity, the activation energies, Ep,i, were assumed to be equal for any type of gas to easily evaluate the pore sizes of microporous membranes, which led to the expression for fNKP shown in Eq. (11).

106 Chapter 5  3 dp  dm, i fNKP ¼  3 dp  dHe

(11)

If there is a large difference in the activation energy in each gas molecule, the mean effective pore size can be determined using the experimental data on the temperature dependence of single gas permeance. Once k0,i and Ep,i are obtained by fitting a set of experimental data to the temperature dependence of permeance using Eq. (7), the mean effective pore size can be determined by the plot of k1/3 0,i against di, because the cubic root of Eq. (8) gives a linear 1/3 and an intercept of a1/3dp. relationship between di and k1/3 0,i with a slope of  a

2.2 Verification of Normalized Knudsen-based Permeance by Zeolite Membranes (Lee et al., 2011) NKP was verified with the permeance of zeolite membranes such as MFI and DDR, which are reported to have intrinsic pores of 0.55  0.56 and 0.36  0.44 nm, respectively. Fig. 3A and B shows NKP for MFI- and DDR-zeolite membranes as a function of kinetic diameter (Lee et al., 2011). By assuming dp ¼ 0.55 nm for MFI membranes, normalized Knudsen-based values for permeance experimentally obtained at 200°C were accurately predicted in a curve calculated using Eq. (11).

He

1.0

SF6

CO2

Ref. 28[1] MFI Ref. 30[2] MFI MFI Ref. 31[3]

0.8 0.6

calculated (dp = 0.55 nm)

0.4 0.2 MFI-200°C

0.0

(A)

2

3

Ar CO H2 Ne He CO2 N2 CH4

CO N2

H2

4

5

Kinetic diameter (Å)

6

Normalized Knudsen-based permeance (-)

Normalized Knudsen-based permeance (-)

NKP for DDR membranes was calculated for dp ¼ 0.36 and 0.44 nm and is shown with solid and dotted curves, respectively. NKP for CO2 and CO for DDR zeolite membranes decreased as the permeation temperature increased from 100°C to 400°C (Lee et al., 2011). As expressed in Eq. (10), NKP consists of configurational factors

i-C4H10

1.0 Ref. 29-200°C Ref. 32-100°C Ref. 33-400°C

0.8

0.6 dp = 0.44nm

0.4

0.2

0.0

DDRnm = 0.36 dp(b)

2

3 4 5 Kinetic diameter (Å)

6

(B) Fig. 3 NKP for MFI- (A) and DDR- (B) zeolite membranes as a function of kinetic diameter (Lee et al., 2011).

Gas Permeation Properties and Pore Size Evaluation of Microporous Silica Membranes 107 (temperature-independent) and the interaction between permeating molecules and the membrane (expressed as the temperature-dependent activation energy). CO2 showed a level of NKP that was larger than the calculated values even at 400°C, which was due to the contribution of surface diffusion. Because the exponential term in Eq. (10) approaches unity, and the contribution of surface diffusion decreases at high temperatures, Eq. (11) shows that permeation experiments at high temperatures are preferable for obtaining pore size.

2.3 Comparison of Theoretical and Experimental Gas Permeation Properties (Nagasawa et al., 2014; Li et al., 2015) Considerable effort has been devoted to applying microporous membranes to gas separation, particularly for some important separation processes, such as CO2/CH4 and O2/N2 separations. However, effective separation of these gas pairs by porous membranes is challenging, because the difference in their molecular sizes is quite small, and the membrane pore size is very difficult to control in such a narrow range. Theoretically, when a membrane has a uniform pore size between the molecular sizes of the gas pairs of CO2/CH4 or O2/N2, neither CH4 nor N2 will permeate the membrane for CO2/CH4 and O2/N2 separations, respectively, and infinite selectivity can be obtained under this circumstance. However, when the membrane pore size is larger than the molecular sizes of both permeating gases, the gas pairs can simultaneously permeate the membrane, so that the pore size of the membrane should be controlled within a reasonable range to effectively separate the gas mixtures. The ideal selectivity of the ith to the jth component, αi/j, can be estimated using Eq. (7) as the ratio for permeance. 3 rffiffiffiffiffiffiffi    Mj dp  dm, i Ep, i  Ep, j Pi (12) αi=j ¼ ¼    exp  Pj Mi dp  dm, j 3 RT For a specified separation system operated at a constant temperature, Eq. (12) clearly shows that the ideal selectivity for the membrane is affected by both the pore size of the membrane and the differences in activation energies for gas permeation. Therefore, in addition to pore size control, control of the adsorption properties between preferentially permeating molecules and the membrane material is an important factor in enhancing membrane selectivity (PeraTitus, 2014). When the differences in activation energy for gas permeation are small, or when membrane separation is operated at a quite high temperature, the effect that the exponential term in Eq. (12) exerts on membrane selectivity becomes insignificant, and, thus, the selectivity of the membrane can be approximately expressed as in Eq. (13). Eq. (13) shows that selectivity is only dependent on the pore size of the membrane for a given separation system under these conditions, and the selectivity decreases with increases in the pore size when the molecular size of the i-th component is smaller.

108 Chapter 5 Pi αi=j ¼  Pj

3 rffiffiffiffiffiffiffi  Mj dp  dm, i   Mi dp  dm, j 3

(13)

Fig. 4 displays the CO2/CH4 (A) and O2/N2 (B) permeance ratios through microporous membranes (zeolite, silica) as a function of pore size (Li et al., 2015). It should be noted that the theoretical curves were calculated using the molecular size of each molecule and pore diameter with no fitting parameters. The experimental results agreed well with the theoretical curves across a wide range of permeance ratios, irrespective of the phase structure of a membrane (zeolite crystal, amorphous silica). The results suggest that the selectivity of any given combination of gases can be predicted in a wide range of permeance ratios if the value of the mean pore diameter is given. The predicted curves show that the selectivities of CO2/CH4 and O2/N2 decrease rapidly with increases in the membrane pore size and finally begin to approximate the Knudsen selectivity, which suggests that membrane selectivity is very sensitive to pore size. For example, the membrane pore size should be smaller than 0.391 nm to obtain CO2/CH4 selectivity higher than 100. Fig. 5 displays the He/C3H8 (A) and He/SF6 (B) permeance ratios for microporous silica and organosilica membranes as a function of the He/N2 permeance ratio (Nagasawa et al., 2014). For the correlations of He/C3H8 with He/N2, the experimental results agreed well with the theoretical curves across a wide range of permeance ratios; when the He/C3H8 permeance ratio increased from 10 to 104, the He/N2 permeance ratio increased from 2 to 80. The calculated curves accurately predicted the wide range of permeance ratios obtained in the gas permeation experiments. This suggested that the permeation of He, N2, and C3H8 through organosilica

107

105

[17,18]

[17,18,19]

LTA

LTA

MFI

FAU

105

DDR

[24,25] [26,27]

SAPO-34 [9,28]

silica Knudsen Calculated using Eq.28

103

101

10–1

(A)

0.4

0.5

0.6

[19–21]

MFI

[22,23]

0.7

Pore diameter (nm)

0.8

O2/N2 ideal selectivity (-)

CO2/CH4 ideal selectivity (-)

[19–21]

[22,23]

FAU

[9]

silica

103

Knudsen Calculated using Eq.28

101

10–1

(B)

0.4

0.5

0.6

0.7

0.8

Pore diameter (nm)

Fig. 4 CO2/CH4 (A) and O2/N2 (B) permeance ratios for microporous membranes (zeolite, silica) as a function of pore size (Li et al., 2015).

Gas Permeation Properties and Pore Size Evaluation of Microporous Silica Membranes 109

Fig. 5 He/C3H8 (A) and He/SF6 (B) permeance ratios for microporous silica and organosilica membranes as a function of the He/N2 permeance ratio (Nagasawa et al., 2014).

membranes derived from bis(triethoxysilyl)ethane (Si-C2H4-Si unit, BTESE) followed the modified-GT model similar to microporous silica membranes. On the other hand, the experimental relationship between He/N2 and He/SF6 was somewhat scattered. More specifically, the permeance ratio of He/SF6 for the corresponding He/N2 ratios tended to be low compared with the theoretical values. This behavior could be attributed to the fact that the membranes might have had a small number of large pores. The lower permeance ratio of He/SF6 compared with the theoretical prediction indicates that SF6 mainly permeated the larger pores such as defects or pinholes, whereas He and N2 permeated the micropores formed by the organosilica network pores.

3 Pore Size Evaluation by k0-Plot and Effective Molecular Size of H2 Through Amorphous Silica Membranes Fig. 6 shows the molecular size dependence of gas permeance at 500°C for amorphous silica membranes calcined at 550°C and 750°C. When an amorphous SiO2 membrane was calcined at 750°C, permeance was significantly decreased, but H2 selectively was increased due to densification of the SiO2 structure via condensation of the Si-OH groups (Kanezashi et al., 2013). Kinetic diameters for gases are listed in the literature: He (0.26 nm), Ne (0.275 nm), and H2 (0.289 nm) (Breck, 1974). It should be noted that the Lennard-Jones (L-J) length constant for Ne is also smaller than that for H2 molecules (Hirchfelder et al., 1964). The order for the gas permeance of silica membranes is independent of calcination temperatures and average pore size: He > H2 > Ne.

110 Chapter 5

Permeance (mol m–2 s–1 Pa–1)

10–6

He

H2

SiO2 (550°C)

10–7

Ne

10–8

NH3 CO2 N2

° 10–9 SiO2 (750 C)

10–10 0.25

CH4

0.3 0.35 Molecular size (nm)

0.4

Fig. 6 Molecular size dependence of gas permeance at 500°C for amorphous silica membranes calcined at 550°C and 750°C.

Fig. 7 shows the temperature dependence of gas permeance (He, H2, Ne, NH3, CO2, N2, and CH4) for silica membranes calcined at 550°C at temperatures ranging from 300°C to 550°C (Kanezashi et al., 2014). The permeance of He, H2, Ne, N2, and CH4 was increased with an increase in the temperature, showing an activated permeation mechanism. The permeance of Temperature (°C)

Permeance (mol m–2 s–1 Pa–1)

10–6

10–7

10–8

550 500 450

400

350

1.5

1.6

300

He H2 Ne

NH3 CO2

10–9

N2 CH4

10–10 1.1

1.2

1.3

1.4

1.7

1.8

1000/T (K–1)

Fig. 7 Temperature dependence of gas permeance for an amorphous silica membrane fabricated at 550°C (solid curves fitted with Eqs. 7, 14 for NH3 and CO2) (Kanezashi et al., 2014).

Gas Permeation Properties and Pore Size Evaluation of Microporous Silica Membranes 111 NH3 and CO2 increased with decreases in temperature, which involved the surface diffusion mechanism. This greater level of adsorption by CO2 and NH3 on the silica surface at lower temperatures was due to an affinity that was stronger than that of other gases (Armandi et al., 2011; Zhao et al., 2012). It should be re-emphasized that the permeance of H2 was higher than that of Ne, irrespective of permeation temperature. The activation energy of gas permeation, Ep,i, and the preexponential factor, k0,i, for nonadsorptive molecules such as He, H2, Ne, N2, and CH4 were obtained by regressing a modified GT model, which assumes a monomodal structure, as expressed in Eq. (7) with the temperature dependence of gas permeance above 300°C. Because 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 preexponential factor, k0,i, for NH3 and CO2 were obtained using Eq. (14), which accounts for the bimodal structures (pore 1, pore 2). ! ! ð1Þ ð2Þ ð1Þ ð2Þ Ep, i Ep, i k0, i k0, i + pffiffiffiffiffiffiffiffiffiffiffiffi exp  (14) Pi ¼ pffiffiffiffiffiffiffiffiffiffiffiffi exp  RT RT Mi RT Mi RT (1) In Eq. (14), k(1) 0, iand Ep, i are the preexponential factor and the activation energy for the ith (2) component through pore 1, whereas k(2) 0, i and Ep, i represent that through pore 2.

Fig. 8 shows the relationship between k1/3 0,i and di for a membrane fabricated at 550°C for NH3 and CO2 clearly deviated from the (Kanezashi et al., 2014). The plotted points of k(2)1/3 0 0.1 He H2

ko,i1/3 (-)

Ne

0.05

NH3

CO2 N2 CH4

0 0.2

0.25

0.3

0.35

0.4

Molecular size (nm)

Fig. 8 Relationship between k1/3 0,i and di for a silica membrane fabricated at 550°C (closed symbols: the (2) values of k(1) 0,i , open symbols: the values of k0,i ) (Kanezashi et al., 2014).

112 Chapter 5 correlation line because these were approximately 1/10,000 of the value for k(1) 0 . A good linear for He, Ne, H , NH , CO , N correlation was observed in the obtained k(1)1/3 0 2 3 2 2, and CH4 molecules, and the effective pore size of a membrane fabricated at 550°C was approximately 0.385 nm. Importantly, the value of k0,i for H2 was larger than that for Ne. It should be noted that the value of k0,i, as expressed using Eq. (8), depends on the molecular size, and decreases with an increase in the molecular size due to the effective decrease in the diffusion distance. Thus, the present results suggest the possibility that the effective molecular size of H2 for permeation through amorphous silica networks might be slightly smaller than that of Ne and can be estimated at approximately 0.27 nm. Fig. 9A shows the He/Ne permeance ratio at 500°C as a function of the activation energy of Ne permeation for amorphous silica membranes (sol-gel, CVD method), as originally reported in the authors’ previous paper (Kanezashi et al., 2014). Recent results reported by Oyama et al. (Ahn et al., 2017, 2018) were added to this figure. It should be noted that each point corresponds with one membrane. A linear correlation between the He/Ne permeance ratio and the activation energy of Ne permeation was obtained, irrespective of membrane fabrication methods (sol-gel, CVD) and calcination temperature; the He/Ne permeance ratio increased as the activation energy of Ne permeation increased, which was much higher than the Knudsen ratio.

6

30

H2/Ne permeance ratio (-)

He/Ne permeance ratio (-)

5 20

10

4

3

2

0

0

10

20

30 –1

(A)

Activation energy of Ne permeation (kJ mol )

1 0

10 20 30 Activation energy of Ne permeation (kJ mol–1)

(B) Fig. 9 He/Ne (A) and H2/Ne (B) 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: CVDderived). Data are from Kanezashi, M., Sasaki, T., Tawarayama, H., Nagasawa, H., Yoshioka, T., Ito, K., Tsuru, T., 2014. Experimental and theoretical study on small gas permeation properties through amorphous silica membranes fabricated at different temperatures. J. Phys. Chem. C 118, 20323–20331.

Gas Permeation Properties and Pore Size Evaluation of Microporous Silica Membranes 113 Because the molecular size of He is smaller than that of Ne, the area available for permeation is larger for He than it is for Ne. Thus, the permeance of Ne decreased more rapidly than that of He due to the larger effect of molecular sieving. On the contrary, the activation energy of Ne permeation corresponds to the membrane pore sizes that Ne permeates, so that the He/Ne permeance ratio increased as the activation energy of Ne permeation increased, which corresponded to smaller network sizes. Fig. 9B displays the H2/Ne permeance ratio at 500°C as a function of the activation energy of Ne permeation for amorphous silica membranes (sol-gel, CVD method), as originally reported in the authors’ previous paper (Kanezashi et al., 2014). The recent results reported by Oyama et al. (Ahn et al., 2017, 2018) were also added in this figure. 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 re-emphasized that H2 was more permeable than Ne, despite a larger kinetic diameter. These results suggest only a small difference in the effective molecular sizes of H2 and Ne for permeation through an amorphous silica structure. Thus, the molecular sieving mechanism cannot be separated for H2 and Ne, and H2/Ne selectivity was approximately the same as that of the Knudsen ratio (¼ 3.17), which is the ratio of the square root of the molecular weight, according to the modified GT model as expressed in Eq. (7).

4 Comparison of Permeation Models Through Microporous Membranes The mechanisms of porous membrane permeation include viscous flow (molecular diffusion), Knudsen, surface diffusion, and molecular sieving. These mechanisms are based on the ratios of the sizes of the molecules permeating a membrane pore and on the interactions between permeating molecules and membrane pore walls. High separation factors can be achieved via surface diffusion and molecular sieving mechanisms. Xiao and Wei (1992) categorized the diffusion mechanisms according to molecular diffusion in liquid, gas, and solid phases; Knudsen diffusion; and configurational diffusion. It should be noted that configurational diffusion, which corresponds to a molecular sieving mechanism, is critical when the molecular diameter is comparable to the pore size, and includes GT and solid vibration. Xiao and Wei (1992) described how the diffusion of molecules in zeolite pores of comparable size plays an important role in this shape-selective process. This type of diffusion remains poorly understood and has been coined “configurational diffusion.” In the case of activated diffusion, molecules permeate micropores even when exposed to repelling forces from the pore walls, because kinetic energy is sufficient to overcome the repelling forces. Permeance in activated diffusion has been formulated based on several models. As described in Section 2.1, the authors proposed a modified GT model (mGT) that describes the permeation mechanism through microporous membranes. Table 1 summarizes the permeation models that include conventional SD, GT, mGT, and solubility site (SS), all of which have been used for activated diffusion through microporous

Model Sorption-diffusion model     E s + Ed Pi ¼ P0 exp  RTp, i ¼ P0 exp  4HRT Pi: preexponential, Ep,i: activation energy of permeation, Hs: enthalpy of sorption, Ed: activation energy of diffusion Gas-translation model, activated Knudsen model Assumption: gas diffusion through capillary   qffiffiffiffiffiffiffiffiffiffi E Pi ¼ dp ρg , i  πM8i RT  τεi Li i  exp  RTp, i   Ep, i k0 exp  ¼ pffiffiffiffiffiffiffiffi RT M RT i

Variables are explained in Section 2.1 Modified gas-translation model Assumption: gas diffusion through capillary   ffi   ðdp di Þ2 qffiffiffiffiffiffiffiffiffi Ep, i 8 Pi ¼ 3τεiiLi dp  di exp  2 RT πMi RT d  p Ep, i k 0, i exp  ¼ pffiffiffiffiffiffiffiffi RT Mi RT Variables are explained in 2.1

Comments

Reference

Simple model Pore size and permeation molecules are not explicitly incorporated in the equation Fitting parameters: P0, Ep,i

(Tsuru et al., 2011)

Pore structure: pore size, length, number, porosity, tortuosity are explicit variables of permeance Permeating molecules: molecular size is not explicitly included, size.ffi The but Ep,i is the function of pore size and the molecular pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi molecular mass affects the kinetic velocity ( 8=πMi RT ) Temperature: two terms (kinetic velocity and activation energy) Fitting parameters: k0, Ep,i

(Shelekhin et al., 1995) (Yoshioka et al., 2001)

Pore structure: pore size, length, number, porosity, tortuosity are explicit variables of permeance Permeating molecules: molecular size is explicitly included, and Ep,i is the function of pore size and the molecular size. Theffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi molecular mass (Mi) affects the kinetic velocity ( 8=πMi RT ) Temperature: two terms (kinetic velocity and activation energy) Fitting parameters: k0,i, Ep,i

(Lee et al., 2011) (Yoshioka et al., 2013) (Kanezashi et al., 2014) (Nagasawa et al., 2014) (Li et al., 2015) (Oyama et al., 2004) (Gu and Oyama, 2007) (Oyama et al., 2011) (Ahn et al., 2017) (Ahn et al., 2018)

Solubility site model, Pore structure: thickness (L), the number of solubility (Ns) are Assumption: site hopping explicit variables of permeance  2  h2 3=2  σh2 α Permeation molecules: jumping frequency between solubility ðNs, i =NA Þ 1 di Pi ¼ 6L eEa, i =RT sites (ν*) h hνi ∗=2kT hνi ∗=2kT 2 2 e 2πmi kT 8π IkT ðe Þ Temperature: four terms (kinetic velocity, rotation loss (H2), L: the thickness of the top layer. mi: the mass of ith component. vibration of matrix, activation energy) T: absolute temperature. h: Planck’s constant. k: Boltzmann’s Fitting parameters: Ns, νi*, Ea,i, di (di: correlation equation with constant. NA: Avogadro’s number. R: the gas constant. α: an Ns is reported) exponent accounting for incomplete loss of rotation (0 for He and Ne, and 0.2 for H2). σ: the symmetry factor of the species (2 for H2). I: the moment of inertia. di: distance between solubility site expressed as di ¼ A + BNs + CNs 2 + DNs 3 where A ¼ 0.84649, B ¼ 1.74523  1029, C ¼ 5.60055  1058, and D ¼ 7.66678  1087. Ns,i: the number of solubility sites. νi*: vibrational frequency in the passageways between the sorption sites. Ea: activation energy of diffusion

114 Chapter 5

Table 1 Permeation models through microporous membranes

Gas Permeation Properties and Pore Size Evaluation of Microporous Silica Membranes 115 membranes. As discussed in Section 2.1, the mGT model is an improved model derived from the GT model, which considers the effect that the size of molecules permeating micropores can exert on diffusivity and on the effective area for diffusion. The SD model, which was originally derived for nonporous polymeric membranes, offers the simplest and most frequently used formulation. P0 reflects the pore structure, which includes pore area and volume in the silica matrix, and can be further analyzed similar to GT and mGT models by assuming cylindrical and straight micropores with a homogeneous potential field (Yoshioka et al., 2001). Therefore, mGT and SS models are often recent versions that represent an attempt to explain “configurational diffusion.” Eq. (15) is an SS model proposed by Oyama et al. (Oyama et al., 2004, 2011; Gu and Oyama, 2007; Ahn et al., 2017, 2018).   3=2  α 1 di2 h2 σh2 ðNs, i =NA Þ e4Ea, i =RT (15) Pi ¼ 2 2πmi kT 8π IkT ðehνi ∗=2kT  ehνi ∗=2kT Þ2 6L h In Eq. (15), L is the thickness of the top layer, mi is the mass of the ith component, T is the absolute temperature, h is Planck’s constant, k is Boltzmann’s constant, NA represents Avogadro’s number, R is the gas constant, α is an exponent accounting for an incomplete loss of rotation (0 for He and Ne, and 0.2 for H2), σ is the symmetry factor of the species (2 for H2), and I is the moment of inertia. Thus, Eq. (15) has four fitting parameters: the number of SSs for the ith component (Ns,i), the vibrational frequency of the ith component in the passageways between the sorption sites (νi*), the activation energy of diffusion for the ith component (Ea,i), and the jump distance for the ith component (di). The SS model confers great advantages in that the physical meaning of each fitting parameter in Eq. (15) is clear for amorphous silica. On the other hand, the mGT model assumes cylindrical capillaries for the amorphous silica networks. To analyze the permeation data via either an mGT or an SS model, the primary data reflects gas permeance as a function of temperature. As pointed out in Table 1, the parameters used to fit the experimental data (permeance, temperature) to the models are k0 and Ep for mGT, whereas the number of SSs (Ns,i), the vibrational frequency (νi*), activation energy of diffusion (Ea,i), and jumping distance (di) are required to evaluate the permeation properties for the SS model. The obtained parameters were further analyzed and will be discussed based on the physical meaning of each. Fig. 10A and B shows permeance calculated by mGT and SS models using the parameters shown in Tables 2 and 3, respectively, as a function of reciprocal temperature, which are

Table 2 Parameters used for mGT model calculation k0 (2) mGT-1 mGT-2 mGT-3

4

2.8  10 8.4  104 2.8  104

Ep (kJ mol21)

Comment

18.5 18.5 27.8

Base k0:  3 Ep:  1.5

116 Chapter 5

Fig. 10 Arrhenius plot of permeance calculated using the mGT (A) and SS models (B) and the parameters shown in Tables 2 and 3, respectively.

Table 3 Parameters used for SS model calculation SS-1 SS-2 SS-3 SS-4 a

Ns (Site m23)

ν* (s21)

Ea (kJ mol21)

di (nm)a

Comment

9.2  10 46.0  1026 9.2  1026 9.2  1026

3.9  10 3.9  1012 15.6  1012 3.9  1012

12.1 12.1 12.1 18.2

0.8309 0.7731 0.8309 0.8309

Base Ns:  5 ν*:  4 Ea:  1.5

26

12

di was obtained from the correlation equation (Oyama et al., 2004; Ahn et al., 2018).

so-called Arrhenius plots. As shown in Fig. 10A, mGT-1 represents a typical temperature dependency (base case). With an increase in k0, permeance was increased but maintained the same slope against the reciprocal temperature, which means the activation energy of permeance was unchanged. On the other hand, with an increase in Ep, permeance was decreased and the slope (activation energy of permeance) increased, which can be easily explained using Eq. (7) and the mGT model. The mGT model has the advantage of a permeation mechanism that is simple to understand. Fig. 10B summarizes permeance based on the SS model. It should be noted that the parameters calculated using mGT-1 as a base case were chosen to show approximately the same levels of permeance for SS-1, as shown in Fig. 10A. With the SS model, increases in Ns and ν* cause permeance increases and decreases, respectively, while maintaining approximately the same slope (activation energy of permeance). On the other hand, an increase in Ea caused a decrease in permeance and an increase in slope, which shows that the observed activation energy had increased.

Gas Permeation Properties and Pore Size Evaluation of Microporous Silica Membranes 117 Fig. 11 shows the He, H2, and Ne permeance of a microporous membrane, and highlights the dependence on temperature. The experimental data and calculated curves were taken from the literature (Ahn et al., 2017). The temperature dependence of permeance, as displayed by He-1, H2-1, and Ne-1, can be successfully fitted to an SS model by using the parameters summarized in Table 4. More importantly, the order of the number of SSs, Ns, was as follows: He > Ne > H2, which was consistent with the order of kinetic diameter, because more sites would be able to accommodate the smaller species. On the other hand, the vibrational frequency, ν*, follows the order H2 > He > Ne, which shows an order that

Fig. 11 Temperature dependence for He, H2, and Ne permeance of a microporous membrane. Points are experimental, and curves are calculated based on an SS model using the parameters summarized in Table 4. Data are from Ahn, S.-J., Takagaki, A., Sugawara, T., Kikuchi, R., Oyama, S.T., 2017. Permeation properties of silica-zirconia composite membranes supported on porous alumina substrates. J. Membr. Sci. 526, 409–416.

Table 4 Parameters used to establish the temperature dependence of He, H2, and Ne permeance via SS model calculation Ns (Site m23)

a

ν* (s21)

Ea (kJ mol21)

di (nm)a

Reference (Ahn et al., 2017) (Ahn et al., 2017) (Ahn et al., 2017)

He-1

9.32  10

6.70  10

6.0

0.8306

Ne-1

9.20  1026

3.90  1012

12.1

0.8308

H2-1

9.10  1026

7.03  1012

15.8

0.8309

He-2 Ne-2 Ne-3

2.33  1026 13.80  1026 43.2  1026

3.35  1012 4.68  1012 7.8  1012

6.0 12.1 12.1

0.8426 0.8235 0.7809

26

12

di was obtained from the correlation equation (Oyama et al., 2004; Ahn et al., 2018).

118 Chapter 5 decreases as molecular weight increases, and is consistent with the vibrational frequency of harmonic oscillation. Thus, the authors of that study concluded that the observed order of permeance was the result of a trade-off between the size and mass of the permeating species (Oyama et al., 2004, 2011; Gu and Oyama, 2007; Ahn et al., 2017, 2018). Three additional curves, He-2, Ne-2, and Ne-3, were calculated using different parameters from the originally fitted parameters listed in Table 4 and added to the figure. The three curves show almost complete agreement with the experimental data for He and Ne. As discussed in Fig. 10B, the slope of the temperature is mainly decided by activation energy, which could possibly allow the determination of Ns and ν*. In particular, fitting Ns and ν* to He (He-2) and Ne (Ne-2 and Ne-3) would require an approach that is completely opposite to the previous discussion. Therefore, although the physical meaning of the SS model is clear, careful fitting would be very important for further discussion such as with silica network structures.

5 Comparing the Properties That Govern the He and H2 Permeation of Silica and Organosilica Membranes The selection of Si precursors made it possible to control the network size of a silica structure (Cao et al., 1996; Castricum et al., 2008, 2011, 2015; Kanezashi et al., 2009, 2012, 2017; Paradis et al., 2013; Agirre et al., 2014; Niimi et al., 2014; Tsuru, 2018; Song et al., 2017). In 2008, sol-gel-derived organosilica membranes utilizing bridged-type alkoxysilanes such as bis(triethoxysilyl)ethane (Si-C2H4-Si unit, BTESE) and bis(triethoxysilyl)methane (Si-CH2-Si unit, BTESM) showed superior n-butanol dehydration properties and hydrothermal stability in comparison with conventional SiO2 membranes during pervaporation at 150°C (Castricum et al., 2008; Paradis et al., 2013; Agirre et al., 2014). The gas permeation properties of organosilica membranes were also reported (Nagasawa et al., 2014; Kanezashi et al., 2009, 2012, 2017; Castricum et al., 2011, 2015; Paradis et al., 2013; Niimi et al., 2014; Tsuru, 2018; Song et al., 2017), and the network pore size was successfully tuned by utilizing BTESE, which showed high H2 permeance for H2/organic compounds such as methylcyclohexane (MCH) and toluene (TOL) (Niimi et al., 2014). Recently, several types of organoalkoxysilane (BTESM, BTESE, bis(triethoxysilyl)propane (BTESP), bis(trimethoxysilyl)hexane (BTMSH), bis(triethoxysilyl)benzene (BTESB), and bis(triethoxysilyl)octane (BTESO)) were utilized for the fabrication of organosilica membranes (Kanezashi et al., 2017), as shown in Fig. 12. Bridged organoalkoxysilanes with different linking units were evaluated for their effect on network size and microporous structure. Also, the permeation properties of He and H2 molecules, where both molecules could permeate network pores, were compared with that for SiO2 membranes to discuss the differences in permeation between SiO2 and organosilica networks (Kanezashi et al., 2017).

Gas Permeation Properties and Pore Size Evaluation of Microporous Silica Membranes 119

OEt EtO

OEt

Si

Si

OEt

OEt

OEt

Si

Hydrolysis and Condensation

O

OEt

O

Si

Si

O

Si Si

Si EtO

O

Si

=C1-C8, aromatic

O O

O

Si

Si Si

BTESM (Si-CH2-Si) : C1 BTESE (Si-C2H4-Si) : C2, BTESP (Si-C3H6-Si) : C3 BTMSH (Si-C6H12-Si) : C6, BTESB (Si-Ph-Si) : C6, Aromatic BTESO (Si-C8H16-Si) : C8

Si

O

O

O

Si Si

OH

OH

He/H2 permeance ratio (-)

10

5

0

(A)

Silica BTESM BTESE BTESP BTMSH BTESB BTESO

0

2

4

6

8

10

Activation energy of H2 permeation (kJ mol –1)

Fig. 12 Schematic image of a sol-gel-derived organosilica network structure composed of organoalkoxysilane with different linking units.

20

10 BTESM BTESE BTESP BTMSH BTESB BTESO

0 0

2

4

6

8

10

(B) Carbon number (-) Fig. 13 Relationship between the carbon number of linking units and the He/H2 permeance ratio (A) and the activation energy of H2 permeation (B) (closed symbols: permeance ratio higher than 150°C, open symbols: permeance ratio below 100°C) (Kanezashi et al., 2017). Carbon number (-)

Fig. 13 shows the relationship between the carbon number of linking units and the He/H2 permeance ratio (A), and the activation energy of H2 permeation (B) (Kanezashi et al., 2017). The He/H2 permeance ratios of SiO2 membranes were plotted at a carbon number of zero, and they were much higher than those of organosilica membranes. The He/H2 permeance ratios of SiO2 membranes tend to increase with decreases in temperature. This trend proved reasonable, because the slope of the temperature dependence of H2 permeance was greater than that of He due to a larger molecular size (He: 0.26 nm, H2: 0.289 nm), so that the decreased ratio of H2 remained higher than that of He as the temperature decreased. Organosilica membranes showed approximately the same value of He/H2 permeance ratio, irrespective of temperature and

120 Chapter 5 carbon number of linking units, which indicated a slope for the temperature dependence of He and H2 that remained approximately unchanged. The activation energy for the H2 permeation of organosilica membranes increased from 10 to 15 kJ mol1 with an increase in the carbon number between two Si atoms. Fig. 14 shows the activation energy of He permeation as a function of H2 permeation for SiO2 (CVD, sol-gel) (Tsuru et al., 2011; Kanezashi et al., 2014; Oyama et al., 2004, 2011; Gu and Oyama, 2007; Ahn et al., 2017, 2018) and organosilica (BTESM (Kanezashi et al., 2012, 2017), BTESE (Nagasawa et al., 2014; Niimi et al., 2014; Kanezashi et al., 2017), BTESP (Kanezashi et al., 2017), BTMSH (Kanezashi et al., 2017), BTESB (Kanezashi et al., 2017), and BTESO (Kanezashi et al., 2017)) membranes. It should be noted that each point corresponds to one membrane. The activation energy of He permeation clearly increased along with that of H2, irrespective of either the membrane fabrication method or the materials (SiO2, organosilica). The activation energy indicates the repulsive force of gas molecules for diffusion through network pores, so that a higher level of activation energy corresponds to a smaller network pore size (Tsuru et al., 2011; Kanezashi et al., 2014; Hacarlioglu et al., 2008).

Activation energy of He permeation (kJ mol –1)

For SiO2 and metal-doped SiO2 membranes, the activation energy of H2 was larger than that of He and was increased to a greater degree with a decrease in pore size, due to its larger molecular 50 SiO2 (Sol-gel) Vitreous glass Ni, Co-SiO2 SiO2 (CVD) Ab initio calculation BTESM BTESE BTESP BTMSH BTESB BTESO

40

30

20

10

0

0

10 20 30 40 50 Activation energy of H 2 permeation (kJ mol–1)

Fig. 14 Activation energy of He permeation as a function of H2 permeation for SiO2 (CVD, sol-gel) (Tsuru et al., 2011; Kanezashi et al., 2014; Oyama et al., 2004, 2011; Gu and Oyama, 2007; Ahn et al., 2017, 2018) and organosilica (BTESM (Kanezashi et al., 2012, 2017), BTESE (Nagasawa et al., 2014; Niimi et al., 2014; Kanezashi et al., 2017), BTESP (Kanezashi et al., 2017), BTMSH (Kanezashi et al., 2017), BTESB (Kanezashi et al., 2017), and BTESO (Kanezashi et al., 2017)) membranes (closed symbols: organosilica, open symbols: SiO2).

Gas Permeation Properties and Pore Size Evaluation of Microporous Silica Membranes 121 size. The activation energies of He and H2 were 5 and 10 kJ mol1 with H2 activation energies of 20 and 30 kJ mol1, respectively. The activation energy was determined by ab initio calculation for the permeation of H2 and He molecules through silica n-membered rings (H2nSinOn (n ¼ 4–8)) (Hacarlioglu et al., 2008), which corresponded to the network size, and showed a trend similar to that of the experimental correlation in SiO2 membranes. For organosilica membranes, however, the activation energy of He permeation was approximately the same as that of H2 permeation across a wide range of activation energy levels for H2 permeation, irrespective of network pore size. Fig. 15 shows the He/H2 permeance ratio at 200–300°C as a function of the activation energy for the H2 permeation of SiO2 and organosilica (BTESM, BTESE, BTESP, BTMSH, BTESB, BTESO) membranes (Kanezashi et al., 2017). Also shown in Fig. 15 is the He/H2 permeance ratio at 25°C as a function of the activation energy of H2 permeation for polymeric membranes (polyimide, polyamide, PIM, polysulfone). SiO2 membranes prepared with TEOS and tetramethoxysilane (TMOS) as Si precursors tended to show a He/H2 permeance ratio that was clearly increased with increases in the activation energy of H2 permeation, irrespective of the membrane fabrication method (sol-gel, CVD). The experimental results of SiO2 membranes following steam treatment (ST) showed higher activation energy and He/H2 permeance ratios, which was caused by the condensation of Si-OH groups that formed dense structures under a steam atmosphere (Tsuru, 2008; Tsuru et al., 2011; Kanezashi et al., 2013). This trend is 10

BTESM SiO2 (Sol-gel) BTESE SiO2 (CVD) BTESP SiO2 (after ST) BTESB BTMSH BTESO Polyimide Polyamide PIM Polysulfone

He/H2 permeance ratio (-)

8

6

SiO2

4

2

Organosilica Knudsen

0

0

10

20

30

40 –1

Activation energy of H 2 permeation (kJ mol )

Fig. 15 He/H2 permeance ratios at 200–300°C as a function of the activation energy of H2 permeation for SiO2 and organosilica (BTESM, BTESE, BTESP, BTMSH, BTESB, BTESO) membranes (Kanezashi et al., 2017).

122 Chapter 5 reasonable, because activation energy and the He/H2 permeance ratio both depend on the network pore size (Tsuru et al., 2011; Kanezashi et al., 2014; Hacarlioglu et al., 2008). The activation energy and He/H2 permeance ratios of BTESM and BTESE membranes were smaller than those of SiO2 membranes, and the plotted results approximated the correlation curve for SiO2 membranes. This indicates that network size derived by BTESM and BTESE was much larger than that derived by TEOS, because Si-R-Si units can work as “spacers” for the construction of amorphous networks (Kanezashi et al., 2009, 2012; Tsuru, 2018). On the other hand, BTESP, BTMSH, BTESB, and BTESO membranes showed activation energies ranging from 10 to 20 kJ mol1, which was higher than that of BTESM and BTESE membranes, despite a larger network size (Kanezashi et al., 2017). Interestingly, these organosilica (BTESP, BTMSH, BTESB, BTESO) membranes showed high activation energy, but the He/H2 permeance ratio was approximately the same as the Knudsen ratio, which was much smaller than that for SiO2 membranes. For example, SiO2 and organosilica membranes showed He/H2 permeance ratios ranging from 2 to 5 and 0.7 to 0.8, respectively, with activation energies that ranged from 10 to 20 kJ mol1. The plotted results for polymeric membranes (polyimide, polyamide, PIM, and polysulfone) approximated the correlation curve for organosilica membranes (Kanezashi et al., 2017). The SD mechanism is generally accepted as the gas transport mechanism through polymeric membranes (Stern et al., 1986; Villaluenga and Seoane, 2001). Gas diffusivity of permeating molecules can be determined by the relationship between molecular size and the segment mobility of the polymer matrix, so that the activation energy of diffusion strongly depends on the polymer chain mobility, because polymer chain vibration can significantly affect pore spaces as the temperature increases. On the other hand, the solubility coefficient is thermodynamic in nature and is affected by polymer gas interactions. Because the interaction between He and H2, and organic bridges in networks is small, a large activation energy of permeation can be ascribed to diffusivity rather than to solubility. Thus, molecular sieving is a dominant He and H2 permeation property due to the rigid microporous structure constructed by TEOS, BTESM, and BTESE. With an increased carbon concentration in silica, the polymer chain vibration in organic bridges, which is a type of solution/diffusion mechanism, dominates the permeation properties.

6 Conclusion and Future Trends Subnanometer pore size evaluation methods were reviewed. These methods were based on an mGT model and on the NKP of microporous membranes. In both evaluation methods, it was necessary to accurately grasp the effective molecular size of the permeation molecules when estimating the pore size of the membrane. Kinetic and LJ diameters are generally used as the effective molecular sizes for permeation through porous membranes, but there remains a possibility that these are not valid as the effective molecular size. Theoretical approaches are

Gas Permeation Properties and Pore Size Evaluation of Microporous Silica Membranes 123 considered important. These include proposing the experimentally effective molecular size via k0 plots of microporous membranes (silica, zeolite, carbon, metal-organic framework (MOF), etc.) and prediction of gas permeability by molecular dynamics (MD) simulation. The differences in He and H2 permeation properties through silica and organosilica networks were discussed based on the results of activation energy and on each of the permeance ratios. Molecular sieving can dominate He and H2 permeation properties via the rigid microporous structures constructed by BTESM and BTESE. With increases in the carbon concentration in silica, polymer chain vibration in organic bridges—a type of solution/diffusion mechanism—dominates the permeation properties.

List of Acronyms BTESB BTESE BTESM BTESO BTMSH CVD GT L-J MCH MD mGT MOF NKP PSDs SS TEM TOL

bis(triethoxysilyl)benzene bis(triethoxysilyl)ethane bis(triethoxysilyl)methane bis(triethoxysilyl)octane bis(trimethoxysilyl)hexane chemical vapor deposition gas translation Lennard-Jones methylcyclohexane molecular dynamics modified gas translation metal-organic framework normalized Knudsen-based permeance pore size distributions solubility site transmission electron microscope toluene

List of Symbols a Ai A0 di dm,i dp Ed,i Ep,i fNKP

structural constant given by Eq. (9), m3 area of the pore opening for effective permeation of ith component, m2 cross-sectional area of the pore, m2 jump distance for the ith component, m molecular size of the ith component, m pore diameter, m activation energy of diffusion for ith component, J mol1 activation energy of permeation for ith component, J mol1 normalized Knudsen-based permeance, dimensionless

124 Chapter 5 h I k k0 k0,i Li mi Mi NA Ns,i Pi R T

Planck’s constant, J s moment of inertia, kg m2 Boltzmann’s constant, J K1 structural parameter of ith component given by Eq. (3), dimensionless permeation constant for ith component given by Eq. (8), dimensionless membrane thickness for ith component, m mass of ith component, kg molecular weight of ith component, kg mol1 Avogadro’s number, mol1 number of solubility sites for the ith component, m3 permeance for ith component, mol m2 s1 Pa1 gas constant, J mol1 K1 absolute temperature, K

Greek Letters α αi/j ε ν i* ρi ρg,i σ τ

exponent accounting for an incomplete loss of rotation (0 for He and Ne, and 0.2 for H2), dimensionless ideal selectivity for ith and jth components, dimensionless membrane porosity, dimensionless vibrational frequency of the ith component in the passageways, s1 geometrical probability for ith component, dimensionless probability of diffusion for ith component, dimensionless symmetry factor of the species (2 for H2), dimensionless tortuosity, dimensionless

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