Free volume, gas permeation, and proton conductivity in MIL-101-SO3H/Nafion composite membranes

Chongshan Yin*a, Chunqing He*b, Qicheng Liua, Bangyun Xiongc, Xiaowei Zhangb, Libing Qianb, Jingjing Lic and Yawei Zhoub
aSchool of Physics and Electronic Science, Changsha University of Science and Technology, Changsha 410114, China. E-mail: c.sh.yin@foxmail.com
bKey Laboratory of Nuclear Solid State Physics Hubei Province, School of Physics and Technology, Wuhan University, Wuhan 430072, China. E-mail: hecq@whu.edu.cn
cSchool of Materials Science and Energy Engineering, Foshan University, Foshan 528000, China

Received 31st August 2019 , Accepted 18th October 2019

First published on 19th October 2019


A series of MIL-101-SO3H/Nafion composite membranes was synthesized. They show an improved proton conductivity, due to the abundance of SO3H groups, which fosters proton conduction by binding the water molecules and enabling a larger number of conducting sites. Gas (including water vapor, hydrogen, and oxygen) permeability, crystallinity, and free volumes of the MIL-101-SO3H/Nafion composite membranes were investigated, as well as their correlation. By increasing the MIL-101-SO3H content, the gas permeability of the membranes significantly decreases, since the crystalline region is larger and the water-bearing MIL-101-SO3H particles are efficient barriers for the gas molecules. The gas permeation in the composite membranes is a very complex process and the results indicate no simple linear relation between the gas permeability and the free volume size (VFV), or between the gas permeability and the crystallinity. Moreover, it is very interesting to observe that the influence of VFV on the gas permeability is closely related to the size of the particular gas molecules: the larger the size of the gas molecules, the larger the free volume needed to achieve their rapid diffusion in the membrane. The results suggest the presence of a threshold value for VFV, which depends on the size of the gas molecules: when VFV is lower than this value, the gas molecules cannot easily jump through neighboring free volumes to a neighboring site, and, as a result, the permeability drops quickly.


1 Introduction

Perfluorosulfonic acid (PFSA) ionomer-based proton exchange membranes (PEMs) such as Nafion are one of the most promising PEMs for proton exchange membrane fuel cells (PEMFCs), due to their excellent structural stability, prominent proton conductivity, and efficient gas barrier properties. However, there exist several technical limitations, which restrict the further commercialization of Nafion, such as the permeation of gas reactants, the degradation of proton conductivity at high temperatures, its high cost, heat rejection, and intolerance to impurities in fuels.1–8 In order to reduce the proton resistance and the membrane cost, thinner PEMs are preferred. However, one of the limits of such composites is the increase in the reactant permeation through the membrane. Results show that, except for the direct fuel loss due to fuel gas permeation, the gas permeation generates adverse effects on the durability, the steady state, and the dynamic response of the PEMFCs.6–11 For instance, the crossover of H2 and O2 accelerates the membrane degradation and generates a reduction process in the Pt ions, which constitute the cathode.9,12,13 In addition, the diffusing gases induce the formation of hydroxyl and hydroxyl-peroxyl on the metal catalyst within the PEM, which is harmful for the Nafion chains.12,13 One possible approach to reduce gas permeation in PEMs is to modify their microstructure by using gas barrier additives.4–6,14,15 Metal–organic frameworks (MOFs) are crystalline nanoporous materials16 that have recently attracted attention in the scientific community, due to their unique features, such as selective separation17–23 and proton conductivity.24–31 Different types of MOFs, which can be decorated with special functional groups to meet specific requirements, have been reported.24–33 For instance, MOFs functionalized with protonated groups, such as sulfonic acid, amidogen, imidazole, and phosphate, have been synthesized to enhance their proton conductivity.24–31 However, their value is still very low when compared to the proton conductivity of conventional proton exchange materials such as Nafion and SPPO, since the bulk phase and the grain boundaries of the MOFs sharply decrease the mobility of the proton carriers.25 Nevertheless, with the selective separation of gas molecules and the proton conducting capacity, functionalized MOFs are expected to play an important role as additives in PEMs.28–30 Since sulfonic acid groups are known to increase the efficiency of proton conduction by enabling a larger number of proton conducting sites in the PEMs,30,34 studies on the application of sulfonic acid group-functionalized MOFs in PEMs are of high interest.

Researchers have investigated the gas permeation and the diffusion mechanism of gas molecules (such as vapor water, oxygen, hydrogen, and methyl alcohol) in Nafion.11,35–41 In terms of the free volumes, the diffusion of small molecules in polymers occurs if large enough free volume holes are present around them. Thus, the free volume in a polymer is of primary importance in the diffusion of small molecules.42–45 However, the microstructure of a polymer is complex, as is the gas permeation process within the polymer. The gas permeation in the Nafion membrane can be influenced by several factors, such as the ionic-water cluster phase,46 the amorphous phase,47 the crystalline structure,48 the overall phase structure of the membrane,49 and the solubility coefficient of the gas molecules.36 Therefore, the free volume and the gas permeation always show a complex relation, which requires further investigation to be fully understood. In this work, MIL-101-SO3H/Nafion composite membranes were synthesized. Positron annihilation lifetime spectroscopy (PALS), a popular method to perform free volume measurements,34,50–58 was employed to characterize the free volume holes of the composite membranes. Details about the PALS measurements and their theoretical basis are provided in the ESI, and in previous works of this research group.59 The microstructure dependence on the gas permeation in the membranes was extensively studied in terms of the free volumes.

2 Experimental

2.1 Preparation of MIL-101 and MIL-101-SO3H

MIL-101-SO3H was synthesized according to the previously reported procedure:32 a mixture of monosodium 2-sulfoterephthalic acid (2 g, 7.5 mmol), CrO3 (0.75 g, 7.5 mmol), and concentrated HCl (12 N, 0.546 g) was dissolved in deionized water (30 g). The solution was hydrothermally treated at 180 °C for 168 hours. The resulting crystallized MIL-101-SO3H green powder was thoroughly rinsed with deionized water and methanol. As reported by Pro. Kitagawa and co-workers, MIL-101-SO3H can remain stable in structure up to the temperature of 600 K, which is much higher than the operating temperature of Nafion.32 MIL-101 was synthesized for comparison according to a previously reported procedure,60,61 and the details are provided in the ESI.

2.2 Preparation of the MIL-101-SO3H/Nafion composite membranes

The MIL-101-SO3H/Nafion composite membranes were prepared via a self-assembly sol–gel process. Initially, a certain amount of purified MIL-101-SO3H was suspended in a mixture of deionized water (50%) and ethanol (50%) and then stirred and sonicated for 3 hours. Successively, a given mass of commercial Nafion solution was added into the suspension and the mixture was sonicated at 50 °C until about two-thirds of its original volume evaporated. The solution was then transferred into a flat-bottomed quartz dish and evaporated at 60 °C for 8 hours. The resulting membranes were thermally treated under vacuum at 135 °C for 2 hours. The weight ratio MIL-101-SO3H[thin space (1/6-em)]:[thin space (1/6-em)]Nafion was varied in the 0–12% range. The membranes obtained by following this process are denoted by their corresponding MIL-101-SO3H content as 2.5-MIL-101-SO3H/Nafion, 5.0-MIL-101-SO3H/Nafion, 7.5-MIL-101-SO3H/Nafion, 10.0-MIL-101-SO3H/Nafion, and 12.0-MIL-101-SO3H/Nafion. Pristine Nafion membranes were prepared by following an identical procedure, but without the addition of MIL-101-SO3H. Finally, the samples were thoroughly rinsed by employing the standard procedure, which is reported in the ESI. The thickness of the membranes measures 50 ± 10 μm. After the addition of MIL-101-SO3H, the thickness of the membranes increased.

2.3 Characterization

In this work, techniques including PALS, Fourier transform infrared (FTIR) spectroscopy, scanning electron microscopy (SEM), X-ray diffraction (XRD), and X-ray powder diffraction (XRPD) were employed. The mechanical properties, the proton conductivity, the gas (hydrogen and oxygen) permeation, the water vapor transmission rate (WVTR), the water uptake, and the swelling ratio of the membranes were measured. Moreover, the N2 adsorption–desorption (BET) and particle size distribution of the MIL-101-SO3H particles were measured. Further details about the experimental procedures and the materials are provided in the ESI.

3 Results and discussion

3.1 Synthesis of the MIL-101-SO3H/Nafion composite membranes

The XRPD patterns of MIL-101 and MIL-101-SO3H are shown in Fig. 1. Both patterns are in very good agreement with the previously reported simulated spectrum of MIL-101.60 This result demonstrates that the structure of MIL-101-SO3H is identical to MIL-101 except for its substituents. Fig. 2(A) displays the comparison between the FTIR spectra of MIL-101 and MIL-101-SO3H. The region between 3700 cm−1 and 2500 cm−1, with the center at ∼3400 cm−1, shows an asymmetric stretch, which is generally attributed to the presence of water traces.62 Moreover, the intensity of this feature in the MIL-101-SO3H spectrum is higher than in the MIL-101 one, since MIL-101-SO3H can retain a larger number of water molecules around the sulfonic acid by forming strong hydrogen bonds.
image file: c9cp04832d-f1.tif
Fig. 1 Simulated spectrum of MIL-101, and XRPD patterns of MIL-101 and MIL-101-SO3H.

image file: c9cp04832d-f2.tif
Fig. 2 (A) FTIR spectra of MIL-101-SO3H compared to that of MIL-101 and (B) the fingerprint region.

The SO3H stretch is located in the 1750–950 cm−1 fingerprint region, as reported in Fig. 2(B). The two bands, which are located at 1235 cm−1 and 1185 cm−1 in the MIL-101-SO3H spectrum, correspond to the O[double bond, length as m-dash]S[double bond, length as m-dash]O asymmetric and symmetric stretching modes, respectively. The peak at 1085 cm−1 is attributed to the S–O stretching vibration. The feature, which appears at 1025 cm−1 in the MIL-101 spectrum, is shifted to 1030 cm−1 in the MIL-101-SO3H spectral pattern. This slight shift is most likely due to the influence of the SO3H substitution on the aromatic ring.63 These observations agree well with the data reported in previously published literature.65 Therefore, the XRPD data and the FTIR spectra confirm the successful synthesis of MIL-101-SO3H.

As shown in Fig. S1 (ESI), in the SEM images, MIL-101 and MIL-101-SO3H exhibit a very similar morphology and particle size. By measuring the particle-size distribution via a laser particle analyzer, the particle diameter of the MIL-101-SO3H sample can be estimated to be in the 70–650 nm range, with an average of 250 nm (Fig. S2, ESI). The surface area of the two samples was calculated from the N2 adsorption–desorption isotherms at 77 K (Fig. S3, ESI). The results show that in the case of MIL-101 (3050 m2 g−1), the surface area is about twice that of MIL-101-SO3H (1530 m2 g−1), due to the partial occupation of the pores of MIL-101-SO3H by the sulfonic acid groups. The concentration of the detectable sulfonic acid groups (IEC) in the MIL-101-SO3H particles was obtained via a back-titration method and found to be 1.84 mmol g−1.

A series of MIL-101-SO3H/Nafion composite membranes was prepared with different contents of MIL-101-SO3H. As suggested by the mechanical properties of the membranes (Fig. S4, ESI), upon an increase in the MIL-101-SO3H content higher than 12 wt%, the break strength of the membranes drops quickly. This phenomenon may be attributed to the distortion of the cross-linking geometry of the Nafion backbones due to the addition of the MIL-101-SO3H particles. Based on these observations, this work investigates the MIL-101-SO3H/Nafion composite membranes with a content of MIL-101-SO3H lower than 12 wt%.

3.2 Water uptake and proton conductivity of MIL-101-SO3H/Nafion composite membranes

The water uptake under different relative humidity (RH) conditions and the swelling behavior of the MIL-101-SO3H/Nafion composite membranes are presented in Fig. S5 and S6 (ESI), respectively. Upon an increase in the amount of the MIL-101-SO3H dopant, the water uptake at different humidity levels and the swelling ratio of the MIL-101-SO3H/Nafion composite membranes increase. This indicates that the incorporation of MIL-101-SO3H into the Nafion membranes favors both the water adsorption and the water swelling of the membranes, due to the large number of hydrophilic sulfonic acid groups present in MIL-101-SO3H.

It is well-known that water content plays a pivotal role in proton conduction.47 Moreover, the high proton conductivity of the Nafion membranes is mainly attributed to their efficient proton conduction in the water channels (i.e. the channel-like hydrophilic phase). Thus, proton conduction may benefit from an enhanced water uptake of the composite membranes.64 The proton conductivity of the MIL-101-SO3H/Nafion composite membranes was investigated at various temperatures. The results were obtained via the Nyquist plot, which was measured by employing an AC impedance technique, under a ∼100% RH condition. Several Nyquist plots of the 12-MIL-101-SO3H/Nafion composite membranes, which were acquired at different temperatures, are presented in Fig. 3(A). The semicircle located in the high-frequency region corresponds to the bulk and grain boundary resistances of the membranes.34 The proton conductivity of all the membranes initially increases and then decreases, as shown in Fig. 3(B). Above the temperature of ∼50 °C, the proton conductivity of all the MIL-101-SO3H/Nafion composite membranes is higher than that of the pristine Nafion ones. Furthermore, it increases with the increase of the MIL-101-SO3H content for various temperatures (Fig. S7, ESI). The maximum value of the proton conductivity measures 0.198 cm2 s−1 at 12 wt% MIL-101-SO3H-loading at 109 °C. Beyond the temperature of 110 °C, the proton conductivity of all membranes drops sharply because of the rapid evaporation of water molecules, regardless of the MIL-101-SO3H additives (Fig. 4).


image file: c9cp04832d-f3.tif
Fig. 3 (A) Nyquist plots from AC impedance data of MIL-101-SO3H/Nafion composite membranes at different temperatures, and (B) proton conductivity of membranes as a function of temperature, at 100% RH relative humidity.

image file: c9cp04832d-f4.tif
Fig. 4 Activation energy (Ea) values of membranes according to the Arrhenius equation.

The enhancement of the proton conductivity of the MIL-101-SO3H/Nafion composite membranes is mostly attributed to the formation of numerous ion-rich contact regions for proton conduction between the Nafion matrix and MIL-101-SO3H. The IEC value of MIL-101-SO3H measures 1.84 mmol g−1 and it is about twice that of the pristine Nafion matrix (0.91 mmol g−1). The detectable sulfonic acid groups foster the proton conduction in PEMs and the binding of water molecules.14,34 Thus, upon water adsorption, the interface between the Nafion matrix and MIL-101-SO3H is an ion-rich region: numerous ionic-water clusters are formed. As a result, the water channel network in the membrane becomes more interconnected, which is conducive to proton conduction.

In this study, the relative activation energy (Ea) of the membranes was obtained according to the Arrhenius equation.66 The results show that the activation energy of the MIL-101-SO3H/Nafion composite is slightly higher than that of the pristine Nafion. This indicates that the proton diffusion in the MIL-101-SO3H/Nafion membranes tends to avoid the MIL-101-SO3H particles and this results in a higher tortuosity of the proton diffusion path. Upon an increase in the MIL-101-SO3H content, Ea decreases, due to the enhanced water uptake of the membranes, which fosters the formation of water channels for proton conduction. It is noticeable that the MIL-101-SO3H/Nafion composite exhibits an enhanced proton conductivity, and the tortuosity of the proton diffusion path is increased. Since the high tortuosity of the proton diffusion path is unfavorable to proton conductivity, in this case, the enhancement in the water uptake is believed to play the dominant role in promoting proton conduction in the composite membranes.

3.3 Gas permeability and crystallinity of the MIL-101-SO3H/Nafion composite membranes

Hydrogen and oxygen permeabilities were measured via the differential pressure method. The water vapor transmission rate (WVTR) was used to investigate the water-vapor barrier properties of the MIL-101-SO3H/Nafion composite membranes (Fig. 5). The incorporation of MIL-101-SO3H into the Nafion membranes results in an evident decrease in the WVTR and oxygen permeability, whereas the hydrogen permeability decreases slightly. This indicates that the water-bearing MIL-101-SO3H particles prevent the penetration of the gas molecules (especially H2O vapor and O2, in this study) because the MIL-101-SO3H nanopores are largely occupied by the sulfonic acid groups and the ionic-water clusters. Moreover, the trapping effect of the gas molecules of the residual pores in MIL-101-SO3H particles may also play an important role in the decrease in the gas permeability of the membranes.17–20,30 Consequently, the water-bearing MIL-101-SO3H particles exhibit efficient gas-barrier properties. As shown in Fig. 5, the H2 permeability only drops slightly and this phenomenon may have two possible explanations: (1) H2 may either penetrate into the membrane through the water-bearing MIL-101-SO3H particles, due to their small molecular size, or (2) H2 molecules may be difficult to trap in the MIL-101-SO3H pores due to their relatively large diffusion coefficient.67
image file: c9cp04832d-f5.tif
Fig. 5 (A) Hydrogen permeability, oxygen permeability and (B) water vapor transmission rates of MIL-101-SO3H/Nafion composite membranes.

The enhanced gas barrier properties of the MIL-101-SO3H/Nafion composite membranes can play a very important role, since the working efficiency of PEMFCs can be extremely affected by the direct permeation of gas reactants and water vapors across the PEMs.68–72 The gas permeation in water-bearing Nafion membranes has been investigated by many researchers36,46–49 by using the well-known three phase physical model.3,6,7,47 Their results show that this is a very complicated process, which can be influenced by the ionic-water cluster phase,46 the amorphous phase,47 the crystalline structure,48 the overall phase structure of the membrane,49 and the solubility coefficient of the gas molecules.36 Due to the complex microstructure present in the water-bearing MIL-101-SO3H/Nafion composite membranes, it is almost impossible to identify the specific diffusion path of the gas molecules across the membranes.

Nevertheless, the Nafion crystalline region can prevent the penetration of a large number of gas molecules. Therefore, the crystallinity of these pre-dried composite membranes was investigated via XRD, as shown in Fig. 6(A), to elucidate the role of their crystalline region in the gas permeation process. The broad peak in the 10–20° range is generated from a crystalline peak, which is located at around 2θ = 17.5°, and an amorphous peak.73–75 The relative degree of crystallinity of the membranes was obtained by calculating the ratio between the area of the crystalline peak and the overall XRD pattern, as shown in the inset of Fig. 6(A). By increasing the content of MIL-101-SO3H, the membrane crystallinity increases as well, since the MIL-101-SO3H particles act as physical crosslinkers and they increase the crystallinity of the composite membranes. In addition, the incorporation of MIL-101-SO3H particles into Nafion leads to the formation of new interfaces. During the annealing process at 135 °C, the Nafion chains are exposed at the interfaces. Their arrangement is influenced by the strong molecular interaction, which may facilitate the formation and the growth of the crystallites.


image file: c9cp04832d-f6.tif
Fig. 6 (A) XRD patterns and crystallinity of MIL-101-SO3H/Nafion composite membranes, and (B) WVTR, (C) oxygen permeability and (D) hydrogen permeability of membranes as a function of crystallinity. The solid lines in (B)–(D) are guides to the eyes.

The increment in the crystallinity fosters the gas barrier properties of the membranes by forcing the gas molecules (H2O vapor, H2, and O2 in this study) to avoid the crystalline regions. This results in an increased tortuosity of the gas molecules' diffusion path.48 The trends of the WVTR, the O2 permeability, and the H2 permeability are displayed as a function of the crystallinity of the membranes in Fig. 6(B)–(D), respectively. None of these three gas permeabilities shows a linear correlation with the crystallinity, since this is only one of the multiple factors that effect the gas permeation in Nafion.

3.4 Gas permeability and free volumes in MIL-101-SO3H/Nafion composite membranes

The free volumes have a strong effect on several physical properties of polymers, such as their diffusion coefficient.52,76–78 Moreover, they are considered to be of primary importance in the diffusion of small molecules.42–45,79 Despite the fact that the diffusion path of H2O vapor may differ from that of O2 and H2 in water-bearing Nafion, the free volumes are surely necessary for the diffusion of these gas molecules. In this study, the o-Ps component (spin parallel ortho-positronium) measured via PALS was used to evaluate the free volume holes within the membranes. The free volume radius is calculated from the o-Ps lifetime (τo-Ps) according to the spherical approximation of the Tao-Eldrup model.80,81

The resulting τo-Ps and its corresponding intensity (Io-Ps) are shown in Fig. 7(A) and (B), respectively. Upon an increase in the MIL-101-SO3H content, both τo-Ps and Io-Ps decrease. Such a decrease in Io-Ps is mostly attributed to the increment in the crystallinity of the sample, as shown in Fig. 6(A), since the o-Ps formation probability in the crystalline region of Nafion (i.e. the perfluoronated polymer backbone) is very low.82,86 Moreover, the inhibition effect generated by the high content of SO3H groups in the membranes contributes to the decrease of Io-Ps. Generally, the positively charged positrons (e+) are efficiently trapped by the negatively charged SO3 groups and they form a bound state, which is known as the [SO3e+] complex.83–85 Subsequently, the formation of a positronium (including o-Ps and spin antiparallel p-Ps) is suppressed. As previously mentioned, the IEC of MIL-101-SO3H is about twice that of the pristine Nafion matrix. Thus, the formation of an o-Ps is limited in MIL-101-SO3H. This hypothesis is confirmed by the nonexistence of an o-Ps lifetime component in MIL-101-SO3H, as shown in Table 1. Since the incorporation of the MIL-101-SO3H particles into Nafion generates a large amount of interfaces, the strong molecular interaction at the interfaces reduces the mobility of the involved Nafion chains. This fosters the formation of a contact region where the Nafion chains are tightly arranged together and the free volumes are small and, as a result, the τo-Ps decreases upon the increase in the MIL-101-SO3H content. Moreover, MIL-101-SO3H improves the water uptake of the composite membranes, which also contributes to the decrement of τo-Ps, since the o-Ps lifetime in an ionic-water cluster (∼1.8 ns) is shorter than that in a Nafion matrix (∼2.8 ns).86


image file: c9cp04832d-f7.tif
Fig. 7 (A) The τo-Ps and corresponding free volume radius R and (B) the intensity of o-Ps (Io-Ps) in MIL-101-SO3H/Nafion composite membranes. Dotted arrow is a guide to the eyes.
Table 1 PALS results of pristine Nafion membranes and MIL-101 and MIL-101-SO3H particles
  τ1 (ns) I1 (%) τ2 (ns) I2 (%) τ3 (ns) I3 (%) τ4 (ns) I4 (%)
Pristine Nafion 0.179 ± 0.016 23.89 ± 1.38 0.436 ± 0.007 68.53 ± 1.39 3.102 ± 0.013 7.58 ± 0.11    
MIL-101-SO3H 0.228 ± 0.009 46.36 ± 2.18 0.448 ± 0.067 53.73 ± 2.16        
MIL-101 0.125 26.90 ± 1.20 0.317 ± 0.001 52.20 ± 1.80 9.11 ± 0.86 4.19 ± 0.46 35.7 ± 1.3 16.71 ± 0.69
  Fixed              


To further examine the role of the free volume holes in the gas permeation in Nafion, the free volume size (VFV) was calculated. According to the average radii of free volumes, the VFV can be calculated by

 
image file: c9cp04832d-t1.tif(1)

The average free volume size in MIL-101-SO3H/Nafion composite membranes is displayed in Fig. 8(A). It is commonly accepted that the gas diffusion coefficient (D) has an exponential relationship with the VFV by87

 
image file: c9cp04832d-t2.tif(2)
where A and B are constants relating to the permeant, Rg is the gas constant and T is the absolute temperature. The permeability coefficient (P) in the polymer depends on the product of solubility coefficient (S) and D as
 
image file: c9cp04832d-t3.tif(3)
where C is a constant decided by the solubility coefficient and the stiffness of Nafion chains.88–90 Fig. S8 (ESI) shows the reciprocal value of VFV of the composite membranes and the trend of ln(P) as a function of it. No simple linear relation can be observed for the H2O vapor, O2, and H2. This abnormal non-linear correlation between the reciprocal value of VFV and ln(P) may be generated by the trapping effect of the MIL-101-SO3H pores on the gas molecules, as described in the previous Section, which disturbs the ordinary diffusion process of the gas molecules in the membranes.


image file: c9cp04832d-f8.tif
Fig. 8 (A) Free volume size in MIL-101-SO3H/Nafion composite membranes, and the trend of (B) WVTR, (C) oxygen permeability and (D) hydrogen permeability as a function of it. Red arrows and solid lines are guides to the eyes.

Generally, small molecules are allowed to make a jump to a neighboring site when there are large enough free volumes surrounding them.87 Moreover, there is a minimum size for the free volume required for the diffusion of the gas molecules to occur. The WVTR, the oxygen permeability, and the hydrogen permeability as a function of VFV are shown in Fig. 8(B)–(D), respectively. The gas permeability decreases upon a decrease in VFV, which is in agreement with the statement that the large free volumes facilitate the diffusion of small molecules in a polymer.37,91 Furthermore, no simple linear relation is observed between VFV and the gas permeability, since the gas permeation in Nafion is an extremely complex process and it can be influenced by many factors.

Upon a decrease in VFV, a sharp decrease in the permeability of all the investigated gases is observed, as indicated by the red arrows in Fig. 8(B)–(D). For H2O vapor, O2, and H2, this sharp decrement in the permeability occurs in the 0.1970–0.1902 nm3, 0.1946–0.1898 nm3, and 0.1915–0.1870 nm3 VFV range, respectively. Fig. 9 shows the starting and ending values of the VFV radius during the sharp decrement in gas permeability, as a function of the gas molecular radius. The results reveal that the larger the size of the molecular gas, the higher the starting and the ending points of VFV during the sharp decrease of the permeability parameter. This phenomenon reveals that the influence of VFV on the gas permeability is closely related to the size of the gas molecules. Moreover, it is very interesting to notice that the starting points of VFV show a linear trend with the radius of the molecule, as indicated by the dotted arrow in Fig. 9.


image file: c9cp04832d-f9.tif
Fig. 9 Starting and ending points of the radius of VFV during the sharp decrement in gas permeability, as a function of the gas molecular radius. Dotted arrow is a guide to the eyes.

These results suggest that a threshold value for VFV exists in the composite membranes and it depends on the size of the particular gas molecules. When the value of VFV is lower than this threshold value, the gas permeability drops quickly. In other words, the larger the size of the gas molecules, the larger the free volume needed for their rapid diffusion in the membrane. In the water-bearing MIL-101-SO3H/Nafion composite membranes, the threshold radius of VFV measures 0.3610 nm, 0.3595 nm, and 0.3576 nm for H2O vapor, O2, and H2, respectively. If the average free volume size in the membrane is lower than such a threshold, the gas molecules cannot easily jump through neighboring free volumes to a neighboring site, and, as a result, the permeability drops quickly. Fig. 10 displays the schematic permeation process of O2 and H2 through the free volume holes in Nafion membranes.


image file: c9cp04832d-f10.tif
Fig. 10 A schematic illustration of the permeation of O2/H2 molecules through the free volume holes in Nafion membranes. (a) The VFV is higher than the threshold value for O2/H2; (b) The VFV is lower than the threshold value for O2 and higher than that for H2.

Nevertheless, the threshold radius of VFV for a particular gas molecule is 0.8–1.47 times larger than the radius of the gas molecule itself. The reason behind this phenomenon cannot be explained only based on the results of this study and it is out of the scope of this paper. The diffusion theory of gases in water-bearing MIL-101-SO3H/Nafion composite membranes as a function of VFV needs a deeper investigation to be understood.

4 Conclusions

In this work, MIL-101-SO3H particles were synthesized and MIL-101-SO3H/Nafion composite membranes were prepared. These membranes show an enhanced proton conductivity and water uptake, due to the abundance of SO3H groups in MIL-101-SO3H, which fosters the proton migration and the binding of water molecules. The gas permeability, including the H2O vapor, O2, and H2, in MIL-101-SO3H/Nafion composite membranes is decreased. Both the enlarged crystalline region and the water-bearing MIL-101-SO3H particles are efficient barriers for the gas molecules: they prevent or retard the penetration of such gas molecules and this results in longer diffusion paths. The free volumes and the crystallinity of the membranes were characterized: the gas permeability shows a positive correlation with the free volume size (VFV) and a negative correlation with the membrane crystallinity. However, the results show that there is no simple linear relation between the gas permeability, VFV, and the crystallinity in the MIL-101-SO3H/Nafion composite membranes. In particular, when VFV is lower than a certain threshold value, the gas permeability drops sharply. This threshold value is closely related to the size of the gas molecules. In the MIL-101-SO3H/Nafion composite membranes, the threshold radii of VFV are 0.3610 nm, 0.3595 nm, and 0.3576 nm for H2O vapor, O2, and H2, respectively.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The work is supported by the National Natural Science Foundation of China (NSFC) under Grants No. 11875209 and 11705029, the National Key R&D Program of China under Grant No. 2019YFA02100003, the Natural Science Foundation of Guangdong Province under Grant No. 2017A030313038, and the Scientific Research Funds of Hunan Provincial Education Department under Grant No. 18C0186. The author (C. Yin) thanks Miss Qing Liu for her helpful assistance in experiments.

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Footnote

Electronic supplementary information (ESI) available: SEM images, N2 adsorption–desorption isotherms, and particle-size distribution of MIL-101-SO3H particles; break strength, water uptake, swelling behavior, and proton conductivity of MIL-101-SO3H/Nafion composite membranes; the reciprocal value of VFV (1/VFV) of MIL-101-SO3H/Nafion composite membranes and the trend of logarithmic gas permeability as a function of 1/VFV; and details of experiments. See DOI: 10.1039/c9cp04832d

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