Theoretical and Experimental Insights Into the Mechanism for Gas Separation Through Nanochannels in 2D Laminar Mxene Membranes

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Article Theoretical and Experimental Insights into the Mechanism for Gas Separation through Nanochannels in 2D Laminar MXene Membranes

Yun Jin 1, Yiyi Fan 1, Xiuxia Meng 1, Weimin Zhang 1,*, Bo Meng 1, Naitao Yang 1,* and Shaomin Liu 2,* 1 School of Chemical Engineering, Shandong University of Technology, Zibo 255049, China; [email protected] (Y.J.); [email protected] (Y.F.); [email protected] (X.M.); [email protected] (B.M.) 2 Department of Chemical Engineering, Curtin University, Perth 6102, Australia * Correspondence: [email protected] (W.Z.); [email protected] (N.Y.); [email protected] (S.L.) Received: 4 September 2019; Accepted: 10 October 2019; Published: 15 October 2019

Abstract: Clarifying the mechanism for the gas transportation in the emerging 2D materials-based membranes plays an important role on the design and performance optimization. In this work, the corresponding studies were conducted experimentally and theoretically. To this end, we measured the gas permeances of hydrogen and nitrogen from their mixture through the supported MXene lamellar membrane. Knudsen diffusion and molecular sieving through straight and tortuous nanochannels were proposed to elucidate the gas transport mechanism. The average pore diameter of 5.05 Å in straight nanochannels was calculated by linear regression in the Knudsen diffusion model. 1 The activation energy for H2 transport in molecular sieving model was calculated to be 20.54 kJ mol− . From the model, we can predict that the gas permeance of hydrogen (with smaller kinetic diameter) is contributed from both Knudsen diffusion and molecular sieving mechanism, but the permeance of larger molecular gases like nitrogen is sourced from Knudsen diffusion. The effects of the critical conditions such as temperature, the diffusion pore diameter of structural defects, and the thickness of the prepared MXene lamellar membrane on hydrogen and nitrogen permeance were also investigated to understand the hydrogen permeation difference from Knudsen diffusion and molecular sieving. At room temperature, the total hydrogen permeance was contributed 18% by Knudsen diffusion and 82% by molecular sieving. The modeling results indicate that molecular sieving plays a dominant role in controlling gas selectivity.

Keywords: MXene; gas separation; Knudsen diﬀusion; molecular sieving; transport mechanism

1. Introduction Gas separation techniques using membranes have many merits such as high efficiency, facile operation, and low energy cost. [1,2]. Traditionally, polymeric membranes are often used for this application while they suffer from the well-known problem of permeability–selectivity trade-off (e.g., the Robinson upper bound) [3]. Recently, two-dimensional (2D) material membranes have been developed for gas separation because it exhibits the promising potential to overcome the permeability–selectivity trade-off problem. Therefore, in the past decade, they have gained enormous attention [1,2]. Typically, the 2D nanosheets assembled lamellar microporous inorganic membranes have interlayer galleries which can provide abundant molecular pathways [4,5]. For this attractive property, a variety of the 2D materials have been exploited to assemble lamellar membranes for gas separation. From the current published studies, the 2D materials include layered double hydroxides (LDH) [6], graphene (GA) [7,8], MXene 2D materials [2,9], graphene oxide (GO) [10,11], tungsten disulfide (WS2)[12],

Processes 2019, 7, 751; doi:10.3390/pr7100751 www.mdpi.com/journal/processes Processes 2019, 7, 751 2 of 17

molybdenum disulphide (MoS2)[13,14], and metal-organic frameworks (MOFs) [15,16] have been receiving particular interest. Generally, MXene 2D materials are a large family of 2D carbides and nitrides with the general formula of Mn+1XnTx, where M represents a transition metal, X is carbon and/or nitrogen, and T is referred to the surface termination [17,18]. Very recently, MXene-based 2D materials have been introduced to fabricate 2D lamellar membranes because of their tunable nanochannel width, excellent mechanical strength, and easy fabrication and integration [2,19,20]. It has been reported that the assembled MXene 2D membranes exhibit a range of attractive characters in separation, e.g., precise ion sieving [21], ultrafast water permeation [22], and gas separation [19,20]. Even a promising potential for highly efficient gas separation has been proved experimentally, to fully clarify the gas transportation mechanism in 2D lamellar membranes, the insight into the theoretical and simulation clarification is scarce and the corresponding investigation is still needed to be conducted. Especially, there are only a few reports on theoretical simulation of gas separation through 2D lamellar nanochannels [11,23,24] while the mechanism of transportation and separation of gas through 2D nanochannels is far away to be fully clarified. For example, Li et al. [24] studied various gas transportations in MXene nanogalleries with molecular dynamic (MD) simulations and activated and Knudsen diffusion being observed for gas diffusion in through MD simulations. Nevertheless, Fan et al. [20] found the gas transportation in MXene nanogalleries via the molecular sieving mechanism. Therefore, in order to optimize and promote the performance and the efficiency of the 2D MXene lamellar membranes, the gas transport mechanisms are still needed to be further clarified because they can efficiently provide the guidance for tuning the channel width of 2D lamellar membranes and gas molecule–channel wall interactions in gas transportation. That is due to the gas transportation mechanism in porous media is primarily related with pore diameter, pore geometry, and interconnectivity of the interlayer distance and defects in the 2D lamellar membranes structure [25]. In this work, the related parameters were firstly determined theoretically and then the gas transport modeling to permeate through different nanochannels was developed to reveal the diffusion of different gas molecules (H2 and N2) in 2D MXene lamellar membranes. The simulation results are well consistent with the experimental results and their significance to the gas diffusion (e.g., permeance and selectivity) was discussed. The structural effects from MXene nanochannels formed during MXene nanosheets assembling on the transportation of different gas molecules (e.g., size and mass) were studied. Moreover, we provided the effects of temperature, pore diameter of structural defects, and the MXene thickness of the lamellar membrane on hydrogen and nitrogen permeances.

2. Experimental The MXene lamellar membrane was prepared using the similar method illustrated previously [20]. Briefly, Ti3C2Tx was synthesized by etching Ti3AlC2 powders using 50 wt% HF solution at a certain temperature followed with DMSO intercalation. The interlayer interaction became weak due to the removal of Al atom between layers, leading to a facile exfoliation to form MXene nanosheets under sonication. The suspended MXene nanosheets were deposited by filtration on the anodic aluminum oxide (AAO) support with a pore diameter of 200 nm (Whatman Co., Maidstone, UK) by a vacuum pump. The resultant MXene membrane was dried at 120 ◦C for 8 h in a vacuum oven to remove the water molecular between interlayers. H2 and N2 gas permeances were derived from their gas mixture separation performance measurement through the MXene membrane supported on AAO [20]. The gas mixture permeance was carried out in a home-made device as reported previously [20]. The gas mixture containing 50 vol% H2 and 50 vol% N2 as the feed gas was supplied to the membrane feed side with a flow rate of 1 1 50 mL min− , while the argon sweep gas with a flow rate of 40 mL min− at a standard pressure was supplied to the sweep side. The exit gas from the membrane sweep side was transferred to an online Processes 2019, 7, 751 3 of 17

GC (6890N, Agilent Technologies, Inc, Waldbronn, Germany) with TCD to measure the permeated H2 or N2 concentration. The permeance and mixture selectivity or separation factor were deﬁned by:

N F = i (1) i P P i1 − i2 2 1 1 where Fi is the permeance of the derived gas (i) (mol m− s− Pa− ), Ni is the molar ﬂux of the gas (i) 2 1 (mol m− s− ), Pi1 and Pi2 are the partial pressures of gas (i) at the feed side and sweep side.

yi2/yj2 S = (2) yi1/yj1 where S is the mixture selectivity or separation factor yi1, yi2, yj1 and yj2, the volumetric fraction of the gas component i or j in the feed or permeated side gas mixtures, respectively. Experimental results are summarised in Table1.

Table 1. Experimental results of the supported 800-nm-thick MXene lamellar membrane for temperature dependent nitrogen and hydrogen permeances measured from gas mixture separation performance tests [20].

8 2 1 1 7 2 1 1 Testing Temperature (K) Permeance of N2 (10− mol m− s− Pa− ) Permeance of H2 (10− mol m− s− Pa− ) Separation Factor (H2/N2) 295 1.74 2.34 13.45 343 1.13 2.22 19.65 423 0.84 2.11 25.11 443 0.74 2.09 28.24 473 0.64 2.07 32.34 503 0.62 2.06 33.22 533 0.59 2.05 34.74 563 0.55 2.03 36.90 593 0.50 2.03 40.60

The crystalline characteristics of MXene nanosheets and composite membranes were studied by XRD (Bruker D8 Advance with Cu-Kα radiation λ = 0.154 nm at 40 kV and 40 mA, in the 2 θ range 20–80◦ with a sacn step of 0.01◦). The surface topology, cross-section, and microstructures of the MXene lamellar membrane were investigated by using a ﬁeld emission scanning electron microscopy (SEM, FEI Sirion 200, Philips, The Netherlands).

3. Theoretical Models of Transport Mechanism We propose the presence of two kinds of gas transport nanochannels as illustrated in Figure1. One is straight channels from structural defects and its width is assumed between 2 nm and the mean free path of transport gases (λ). Another nanochannel consists of randomly distributed nanoscale wrinkles and interlayer spacing between stacked MXene sheets and its width is between the kinetic diameter of gas molecular (Φk) and 2 nm. Accordingly, two mathematical models of the gas transport mechanism for the permeation through the MXene lamellar membrane can be proposed based on the diﬀerent nanochannels width using the following assumptions:

(1) One-dimensional transport model is used. (2) There are two kinds of transport channels as illustrated in Figure1, which are the straight nanochannels (2 nm < dp < λ) and tortuous nanochannels (Φk < dp < 2 nm). Their size remains unchanged with the temperature. (3) The MXene/AAO lamellar membrane operates at a steady-state isothermal condition. (4) The linear adsorption isotherm (or non-adsorption) for all gases on the surface of MXene lamellar membranes is neglected. (5) The mass transfer resistance of gas within the porous AAO layer is neglected due to its much large pore size [10,26]. ProcessesProcesses2019 2019, 7,, 7517, x; doi: FOR PEER REVIEW 4 of 417 of 17

(5) The mass transfer resistance of gas within the porous AAO layer is neglected due to its much (6) Gaslarge mixture pore size (hydrogen [10,26]. and nitrogen) transport through the membrane is under ideal conditions (6)on Gas which mixture the actual (hydrogen separation and factor nitrogen) is equal transport to the ideal through selectivity the membrane and pure is gas under permeance ideal is equalconditions to the mixtureon which permeance. the actual separation factor is equal to the ideal selectivity and pure gas permeance is equal to the mixture permeance.

FigureFigure 1. Schematic 1. Schematic diagram diagram of the of two the kinds two of kinds gas transport of gas modeltransport through model di ﬀ througherent nanochannels different withinnanochannels the MXene within lamellar the MXene membranes. lamellar membranes.

TheThe relevant relevant schematic schematic transport transport models models for gas gas permeation permeation through through the the MXene MXene lamellar lamellar membranesmembranes are are shown shown in in Figure Figure1 .1. Here, Here, HH2 (kinetic(kinetic diameter diameter of of 2.89 2.89 Å) Å) and and N2 N (3.642 (3.64 Å) Å) diffuse diffuse throughthrough the the MXene MXene lamellar lamellar membrane membrane basedbased on our our experimental experimental results results [20], [20 ],so sothe the geometrical geometrical structurestructure of nanochannels of nanochannels derived derived from from the structural the structural defects defects and interlayer and interlayer spacing spacing plays a plays significant a rolesignificant in the gas role transportation. in the gas transportation. For gas permeation, For gas twopermeation, transport two models transport were models proposed were corresponding proposed corresponding to the nanochannels in order to explain the experimental results. The Knudsen to the nanochannels in order to explain the experimental results. The Knudsen diffusion is assumed to diffusion is assumed to occur within the straight nanochannels with the lager pore diameter (2 nm < occur within the straight nanochannels with the lager pore diameter (2 nm < dp < λ). The tortuous dp < λ). The tortuous nanochannels are mainly composed of randomly distributed nanoscale nanochannels are mainly composed of randomly distributed nanoscale wrinkles, inter-galleries, wrinkles, inter-galleries, and interlayer spacing between stacked MXene sheets. Therefore, the gas and interlayer spacing between stacked MXene sheets. Therefore, the gas transportation within transportation within tortuous nanochannels containing the interlayer spacing (Φk < dp < 2 nm) is tortuousmainly nanochannelsrelated to the molecular containing sieving. the interlayer spacing (Φk < dp < 2 nm) is mainly related to the molecularTherefore, sieving. for MXene lamellar membranes, both Knudsen diffusion and molecular sieving contributeTherefore, to the for total MXene mass lamellar transportation. membranes, The total both permeance Knudsen can di ffbeusion written and bymolecular Equation (3) sieving as contributefollows: to the total mass transportation. The total permeance can be written by Equation (3) as follows: FFtotal defects  Fint erlayer  FF Kn g (3) Ftotal = Fde f ects + Finterlayer = FKn + Fg (3)

Here, Ftotal, Fdefects, and Fint erlayer are the total gas permeance, the gas permeance through straight Here, Ftotal, Fdefects, and Fint erlayer are the total gas permeance, the gas permeance through straightnanochannels nanochannels of structural of structural defects, defects, and and tortuous tortuous nanochannels nanochannels containing containing interlayer interlayer spacing, spacing, respectively. FKn and Fg are the permeances contributed by the Knudsen diffusion and the molecular respectively. FKn and Fg are the permeances contributed by the Knudsen diffusion and the molecular sieving, respectively. sieving, respectively. 3.1. Knudsen Diffusion (KD) Model 3.1. Knudsen Diffusion (KD) Model Typically, Knudsen diffusion dominates in the mesoporous nanochannels with the size range Typically, Knudsen diffusion dominates in the mesoporous nanochannels with the size range between 2 nm and the mean free path of transport gases (2 nm < dp < λ), i.e., the average distance a between 2 nm and the mean free path of transport gases (2 nm < d < λ), i.e., the average distance a molecule traversed by collisions, which is comparable or larger thanp transport channels, transport moleculefalls in traversed Knudsen by regime collisions, [27]. The which mass is comparable transport of or gas larger may than be described transport bychannels, Fick’s first transport law as falls in KnudsenEquation (4). regime [27]. The mass transport of gas may be described by Fick’s first law as Equation (4).

dc ϕDK dP dP JJK,i =ϕ DDK =  (4) (4) Ki, − K dz − RTdz dz where ϕ is the factor for structure geometrical effects by Equation (16). R is the ideal gas constant, T is the absolute temperature. Thus, the expression of Knudsen diffusion flux (JK,i) for gas can be obtained in terms of pressure gradient. In this case, DK is the Fick diffusion coefficient (Knudsen Processes 2019, 7, 751 5 of 17 diffusivity), which may be expressed as the product of a geometric factor by diffusion pore diameter and the velocity of gas molecules by Equation (5):

1 dp 8RT 2 D = ( ) (5) K,i 3 πM where dp is the diffusion pore diameter, the velocity of diffusing molecules is given by the kinetic theory of gases, and M is the molecular weight of the diffusing gas. The geometric factor is 1/3 since only these molecules moving in the considered direction will be taken into account [28]. The expression for Knudsen diffusion flux (JK,i) obtained by combining Equations (4) and (5) is expressed as Equation (6).

1 ϕdp 8 2 dP J = ( ) (6) K,i − 3 πMRT dz The Knudsen diﬀusion permeance through a porous membrane can be determined after integration of Equation (6) over the membrane thickness (δ):

1 J ϕdp 8 2 F = K = ( ) (7) K,i ∆P 3δ πMRT

In order to obtain the diﬀusion pore diameter (dp), Equation (7) was transformed to Equation (8) to reveal the gas permeance dependence on the temperature. Thus, the gas permeance in Knudsen regime is pressure-independent and decreases with temperature as indicated by Equation (8).

1 8 2 8ϕdp 1 F ( ) = ( ) (8) K,i πMRT 3δπMR T

3.2. Molecular Sieving (MS) Model The molecular sieving model was firstly used for zeolite, which can be illustrated by the kinetic theory of gases [28]. In the small channels with the size range between kinetic diameter of gas molecular and 2 nm (Φk < dp < 2 nm), channel size changes into the molecular dimensions and molecules are no longer as free as these in Knudsen diffusion. For simplification purpose, the individual gas molecular adsorption difference is not considered. This is a reasonable assumption for these gases with less adsorption like He, H2, and N2 than CO2. The molecular sieving flux can be expressed in terms of pressure gradient. As a result, the molecular sieving flux (Js,i) can be written as:

dc ϕDs,i dP J = ϕD = (9) s,i − s,i dz − RT dz where Ds,i is the molecular sieving coeﬃcient in the MXene laminates, which is given by Equation (10).

1 l 8RT 2 Ea,g D = s ( ) exp( ) (10) s,i Z πM − RT where ls is the diﬀusion distance (the distance between two adjacent sites of the low energy regions), Z is the number of adjacent sites [28], and Ea,g is the activation energy, which is required for molecules to surmount the attractive constrictions imposed by the nanochannels structure. However, the geometrical factor (1/Z) is the probability of a molecule moving in the direction under consideration. The expression of molecular sieving ﬂux (Js,i) obtained by combining Equations (9) and (10) is shown as the following.

1 ϕls 8 2 Ea,g dP J = ( ) exp( ) (11) s,i − Z πMRT − RT dz Processes 2019, 7, 751 6 of 17

The gas permeance for molecular sieving through a microporous membrane is obtained after integration of Equation (12) over the membrane thickness δ:

1 Js,i ϕls,i 8 2 Ea,g F = = ( ) exp( ) (12) s,i ∆P Zδ πMRT − RT Equation (12) reveals an exponential dependence of gas permeance on the temperature, which is different from that of the Knudsen diffusion model. Taking logs of the both sides of Equation (12) can obtain the activation energy Ea,g and the diffusion distance.

 1  E 2 1 a,g 1 ϕls,i 8  Ln(Fs,iT 2 ) = ( ) + Ln ( )  (13) − R T  Zδ πMR 

The gas permeance tests at diﬀerent temperatures were carried out, the activation energy Ea,g and the diﬀusion distance in the logarithmic plots can be regressed based on experimental data by Equation (13).

3.3. Diffusion Contribution to Total Transport The fractional diffusion of Knudsen diffusion and molecular sieving, respectively can be expressed as the following Equations (14) and (15).

F Zdp f = Kn = Kn E (14) FKn + Fs a,g Zdp + 3ls exp( ) − RT

Ea,g F 3ls exp( ) f = s = − RT s E (15) FKn + Fs a,g Zdp + 3ls exp( ) − RT The relative individual diﬀusion contribution to total transport from Equations (3), (7), and (12) obtained using Equations (14) and (15) can be used to determine the rate-dominated diﬀusion process.

4. Results and Discussion

4.1. Morphology and Structure

The scanning electron microscopy (SEM) images of the cross-section of MXene (Ti3C2Tx), high magnification over the cross-section of MXene membrane, external surface of MXene membrane, and low magnification of the cross-section of MXene membrane are displayed as Figure2a–d, respectively. As shown in Figure2a, the MXene membrane was assembled by the stacked 2D MXene nanosheets. Additionally, the nanosheets exhibit plicate feature on their surface. We can find there are structure defects and interlayer spacing in the bulky membrane, which can provide channels for the gas transportation. It is worth noting that the inner-sheet structural defect is assumed to be correlated with straight channels. The tortuous nanochannels consist of randomly distributed inter-galleries and nanoscale wrinkles between the stacked nanosheets. Here, the 2D MXene laminar membrane with 800-nm-thickness was assembled and supported on the AAO substrate (Figure2b), which shows similar morphology to that of other laminar materials such as GO membranes [11]. MXene (Ti3C2Tx) nanosheets were deposited as an outer layer on top of a porous AAO support with a pore diameter of 200 nm using the vacuum impregnation method to form the supported MXene membrane (Figure2c,d). Processes 2019, 7, x; doi: FOR PEER REVIEW 7 of 17

Processes 2019, 7, 751 7 of 17 Processes 2019, 7, x; doi: FOR PEER REVIEW 7 of 17

Figure 2. SEM images of the cross-section of MXene (Ti3C2Tx) (a), the cross-section of MXene membrane (b), external surface of MXene membrane (c), and the cross-section of MXene membrane (low magnification) (d).

As shown in Figure 2a, the MXene membrane was assembled by the stacked 2D MXene nanosheets. Additionally, the nanosheets exhibit plicate feature on their surface. We can find there are structure defects and interlayer spacing in the bulky membrane, which can provide channels for the gas transportation. It is worth noting that the inner-sheet structural defect is assumed to be correlated with straight channels. The tortuous nanochannels consist of randomly distributed inter- galleries and nanoscale wrinkles between the stacked nanosheets. Here, the 2D MXene laminar membrane with 800-nm-thickness was assembled and supported on the AAO substrate (Figure 2b), which shows similar morphology to that of other laminar materials such as GO membranes [11]. FigureFigure 2. 2.SEM SEM images images of of the the cross-section cross-section of of MXene MXene (Ti3CC22TTx)x )( (a),a ), the the cross-section cross-section of of MXene MXene MXene (Ti3C2Tx) nanosheets were deposited as an outer layer on top of a porous AAO support with membranemembrane (b ),(b external), external surface surface of of MXene MXene membranemembrane ( (cc),), and and the the cross-section cross-section of of MXene MXene membrane membrane a pore diameter of 200 nm using the vacuum impregnation method to form the supported MXene (low(low magniﬁcation) magnification) (d ().d). membrane (Figure 2c,d). From the XRD patterns in Figure 3, the (002) plane at 6.6° can be used to determine the d- FromAs the shown XRD in patterns Figure in 2a, Figure the MXene3, the (002) membrane plane at was 6.6 assembled◦ can be used by to the determine stacked 2D the MXened-spacing betweenspacingnanosheets. the between MXene Additionally, the nanosheets MXene the nanosheets andnanosheets the monolayer and exhibit the monolayerplicate thickness, feature thickness, which on their were which surface. calculated were We calculated to can be find ~13.4 tothere Åbe and ~13.4 Å and 10 Å, respectively. These data are inconsistent with the previous publications [2,20]. 10 Å,are respectively.structure defects These and data interlayer are inconsistent spacing in the with bulky the membrane, previous publications which can provide [2,20]. channels Moreover, for the Moreover, the interlayer spacing of MXene membrane is estimated to be ~3.4 Å (Figure 1), which is interlayerthe gas spacing transportation. of MXene It ismembrane worth noting is estimated that the to inner-sheet be ~3.4 Å (Figure structural1), which defect is is favorable assumed to sieve be favorablecorrelated to with sieve straight small channels.molecules The such tortuous as hydrogen nanochannels (kinetic diameterconsist of ofrandomly 2.89 Å) anddistributed helium inter-(2.60 small molecules such as hydrogen (kinetic diameter of 2.89 Å) and helium (2.60 Å). Å).galleries and nanoscale wrinkles between the stacked nanosheets. Here, the 2D MXene laminar membrane with 800-nm-thickness was assembled and supported on the AAO substrate (Figure 2b), which shows similar morphology to that of other laminar materials such as GO membranes [11]. MXene (Ti3C2Tx) nanosheets were deposited as an outer layer on top of a porous AAO support with a pore diameter of 200 nm using the vacuum impregnation method to form the supported MXene (002) membrane (Figure 2c,d). MXene(Ti3C2Tx) From the XRD patterns in Figure 3, the (002) plane at 6.6° can be used to determine the d- spacing between the MXene nanosheets and the monolayer thickness, which were calculated to be

~13.4 Å and 10 Å, respectively. These data are inconsistent with the previous publications [2,20].

Moreover, the interlayer spacing of MXene membrane is estimated(104) to be ~3.4 Å (Figure 1), which is MAX(Ti AlC ) favorable to sieve small molecules such as hydrogen3 2 (kinetic diameter of 2.89 Å) and helium (2.60

Å). Intensity(a.u.) (002) (105) (101) (103) (107) (109) (004) (108)

10 20 30 40 50 60 (002) MXene(Ti3 C2Tx) 2q (degree)

FigureFigure 3. 3.XRD XRD patterns patterns of of the the MAXMAX (Ti(Ti33AlC22)) and and MXene MXene (Ti (Ti3C32CT2x)T membrane.x) membrane.

The determination of geometrical eﬀects in nanochannel(104) structure is quite critical for the gas MAX(Ti AlC ) transport mechanisms model, and which can be described3 2 by [16]: Intensity(a.u.) a (002) (1 )

ε d (105) ϕ = = −(101) (16) (103) (107) (109) (004) τ τ (108) where ϕ is the geometrical eﬀect of the porous structure (i.e., the ratio of the membrane porosity ε to the tortuosity factor τ), a is the10 thickness 20 of monolayer 30 thickness 40 MXene 50 lamellar 60 which is ~10 Å, d is

2q (degree)

Figure 3. XRD patterns of the MAX (Ti3AlC2) and MXene (Ti3C2Tx) membrane. Processes 2019, 7, x; doi: FOR PEER REVIEW 8 of 17

The determination of geometrical effects in nanochannel structure is quite critical for the gas transport mechanisms model, and which can be described by [16]: a (1 )  d (16)    Processes 2019, 7, 751   8 of 17 where φ is the geometrical effect of the porous structure (i.e., the ratio of the membrane porosity ε to the tortuosity factor τ), a is the thickness of monolayer thickness MXene lamellar which is ~10 Å, the d-spacing of MXene laminates which is about ~13.4 Å, and τ is the tortuosity factor which can be d is the d-spacing of MXene laminates which is about ~13.4 Å, and τ is the tortuosity factor which approximatedcan be approximated as the ratio as the of diratioﬀusion of diffusion length tolength the MXeneto the MXene laminar laminar thickness thickness (Equation (Equation (17)). 17).

lls τ= s (17) (17) δδ In ourIn our work, work, the the thickness thickness of theof the MXene MXene laminar laminar membrane membrane is 800 is 800 nm. nm. The The tortuosity tortuosity factor factorτ can τ be estimatedcan be estimated to be ~1for to be straight ~1 fornanochannels straight nanochannels of inner-sheet of inner-sheet structural structural defects. defects. Moreover, Moreover, the tortuosity the factortortuosityτ (τ > 1) factor in tortuous τ (τ > 1) nanochannels in tortuous nanochannels must be calculated must beusing calculated molecular using sieving molecular model. sieving model. 4.2. The Experimental Nitrogen Permeance and the Parameters Regression of Knudsen Diffusion (KD) Model 4.2. The Experimental Nitrogen Permeance and the Parameters Regression of Knudsen Diffusion (KD) Model There are two transport nanochannels in the MXene lamellar membrane, which are straight nanochannelsThere are from two inner-sheettransport nanochannels structural defects in the MXene and tortuous lamellar membrane, nanochannels which in are wrinkles straight and inter-galleriesnanochannels contained from inner-sheet interlayer structural spacing defects between and stackedtortuous MXene nanochannels sheets. in Additionally, wrinkles and the inter- gases transportgalleries mechanisms contained interlayerfor the diff spacingusion in betweenporous membrane stacked MXene are primarily sheets. dependent Additionally, on the the transport gases channeltransport width, mechanisms geometry, and for the interconnectivity diffusion in porous [2,25,28 membrane]. Therefore, are it is primarily extremely dependent critical to onfigure the out thetransport dimension channel of the width, nanochannels geometry, before and interconnectivity we perform the modeling.[2,25,28]. Therefore, To calculate it is theextremely interlay critical spacing, theto XRD figure measurement out the dimension was conducted. of the nanochannels before we perform the modeling. To calculate the interlay spacing, the XRD measurement was conducted. We can determine from the XRD results (Figure3) for MXene membranes that the interlayer We can determine from the XRD results (Figure 3) for MXene membranes that the interlayer spacing between the MXene sheets is 3.4 Å, which is smaller than the kinetic diameter of N2 (3.64 Å), spacing between the MXene sheets is 3.4 Å, which is smaller than the kinetic diameter of N2 (3.64 CH4 (3.84 Å), C3H6 (4.30 Å), and C3H8 (4.50 Å) (Figure4). Since we assume that the width of straight Å), CH4 (3.84 Å), C3H6 (4.30 Å), and C3H8 (4.50 Å) (Figure 4). Since we assume that the width of nanochannelsstraight nanochannels are larger than are the larger kinetic than diameters the kinetic of these diameters gases, therefore, of these gases,for the therefore,transport permeance for the of N , CH ,C H , and C H , Knudsen diffusion is the main process in the gas transportation in the transport2 4 permeance3 6 of3 N28, CH4, C3H6, and C3H8, Knudsen diffusion is the main process in the gas straighttransportation channels. in Since the straight straight channels. nanochannels Since straight flow dominates nanochannels gas permeation, flow dominates the Knudsengas permeation, diffusion modelingthe Knudsen was performed diffusion by modeling the ordinary was performed least squares by method the ordinary using MATLAB least squares 7.0 (The method Math using Works Inc.,MATLAB Natick, MA,7.0 (The USA) Math [29 ]Works to obtain Inc., the Natick, parameters MA, USA) in Equations [29] to obtain (7) and the (8) parameters and the regression in Equations results were(7) shownand (8)in and Figure the regression5. We can observeresults were that shown the calculations in Figure using5. We thecan Knudsenobserve that di ff theusion calculations model with theusing obtained the Knudsen parameters diffusion can fit model the experimental with the obtained data well parameters with the can resultant fit the experimental correlation coe datafficient well up to 0.9966.with the resultant correlation coefficient up to 0.9966.

) 5 Å 4.50 4.30 3.84 4 3.64 3.4Å 3 2.89 2.60

1 Kinetic diameter of gases ( gases of diameter Kinetic

0 He H N CH C H C H 2 2 4 3 6 3 8

FigureFigure 4. 4.The The kinetickinetic diameterdiameter of gases gases ( (ΦΦk)k )of of different diﬀerent gases. gases. Processes 2019, 7, 751 9 of 17 Processes 2019, 7, x; doi: FOR PEER REVIEW 9 of 17

Experimental data 1.6 Theoretical value ) -1 Pa -1 s

-2 1.2 mol m mol

-8 0.8 (10 N2 F 0.4

250 300 350 400 450 500 550 600 Temperature (K) FigureFigure 5. Comparison 5. Comparison of the of experimental the experimental data and data the and model the modelpredictions predictions of the temperature of the temperature dependent nitrogendependent permeance nitrogen through permeance the MXenethrough lamellarthe MXene membrane. lamellar membrane.

TheThe values values for for the the model model parameters parameters ϕφ andand ddpp can be be obtained obtained from from the the regression. regression. Since Since the the tortuositytortuosity factor factorτ inτ in Equation Equation (17) (17) can can bebe estimatedestimated to ~1 in in inner-sheet inner-sheet structural structural defects defects because because of theof the straight straight di ffdiffusionusion channels. channels. TheThe geometricalgeometrical effects effects ( (φϕ)) of of the the porous porous structure structure derived derived from from EquationEquation (16) (16) is is 0.25, 0.25, and and the the average average didiffusionffusion pore diameter ddp pisis 5.05 5.05 Å Å which which is islarger larger than than the the kinetic diameter of N2 (3.64 Å), CH4 (3.84 Å), C3H6 (4.30 Å), and C3H8 (4.50 Å). It can be concluded kinetic diameter of N2 (3.64 Å), CH4 (3.84 Å), C3H6 (4.30 Å), and C3H8 (4.50 Å). It can be concluded thatthat the the Knudsen Knudsen di diffusionffusion through through straight straight nanochannelsnanochannels for nitrogen nitrogen is is reasonable. reasonable.

4.3.4.3. The The Experimental Experimental Hydrogen Hydrogen Permeance Permeance and and thethe ParametersParameters Regression of of Molecular Molecular Sieving Sieving (MS) (MS) Model Model The interlayer spacing width between the MXene sheets is 3.4 Å which is larger than the kinetic The interlayer spacing width between the MXene sheets is 3.4 Å which is larger than the diameter of He (2.60 Å) and H2 (2.89 Å) (Figure4), thus it is favorable to separate them by molecular kinetic diameter of He (2.60 Å) and H2 (2.89 Å) (Figure 4), thus it is favorable to separate them by sieving diffusion. Therefore, hydrogen transport mechanism models in the MXene membrane are molecular sieving diffusion. Therefore, hydrogen transport mechanism models in the MXene the combined Knudsen diffusion and molecular sieving, which correspond to the diffusion through membrane are the combined Knudsen diffusion and molecular sieving, which correspond to the straight nanochannels of structural defects, and tortuous nanochannels contained interlayer spacing diffusion through straight nanochannels of structural defects, and tortuous nanochannels contained between stacked MXene sheets, respectively. Hence, H2 permeance is higher than N2 permeance in interlayer spacing between stacked MXene sheets, respectively. Hence, H2 permeance is higher than the temperature range of 295~593 K in experimental (Table1 and Figure6). For example, H and N2 permeance in the temperature range of 295~593 K in experimental (Table 1 and Figure 6). For2 7 2 1 1 N permeances were 2.34 and 0.174 10 mol m s Pa−7 , respectively,−2 −1 −1 at 295 K. The calculated 2example, H2 and N2 permeances were× 2.34− and 0.174− −× 10 − mol m s Pa , respectively, at 295 K. separationThe calculated factor orseparation selectivity factor of H or2/ Nselectivity2 was ~13 of basedH2/N2 onwas the ~13 gas based permeance, on the gas and permeance, it greatly exceededand it thegreatly Knudsen exceeded selectivity the Knudsen of 3.74 for selectivity H2/N2 pairs. of 3.74 It for indicates H2/N2 pairs. the promising It indicates potential the promising application potential ofthe 2Dapplication MXene membrane of the 2D to MXene separate membrane H2 from to its separate gas mixture. H2 from The its modeling gas mixture. results The show modeling that molecularresults sievingshow plays that molecular a dominant sieving role inplays the a selectivity dominant ofrole gas in separation.the selectivity of gas separation. Processes 2019, 7, 751 10 of 17 Processes 2019, 7, x; doi: FOR PEER REVIEW 10 of 17

FigureFigure 6. 6.Comparison Comparison of of the the experimental experimental data and the the model model predictions predictions of oftemperature temperature dependent dependent hydrogenhydrogen permeance permeance through through the the MXene MXene lamellarlamellar membrane.

HydrogenHydrogen permeances permeances through through the the MXene lamellar lamellar membrane membrane were were obtained obtained via via the the gas gas permeationpermeation test test as as a a function function of of temperaturetemperature between 22 22 °C◦C (295.15 (295.15 K) K) and and 320 320 °C◦ C(593.15 (593.15 K) K)using using 1 thethe mixture mixture of of hydrogen hydrogen and and nitrogen nitrogen withwith aa flowflow rate of of 50 50 mL mL (STP) (STP) min min−1 −in inthe the feed feed side side of the of the −1 1 membrane,membrane, and and an an argon argon sweep sweep gasgas withwith aa flowflow rate of 40 mL mL (STP) (STP) min min− onon the the permeate permeate side side to to removeremove the the permeated permeated hydrogen hydrogen and and nitrogen. nitrogen. The The values values for for the the model model parameters parametersϕ ,φ, ls ,ls and, andE a,gEa,gcan becan obtained be obtained by Equations by Equations (12) and(12) (13).and (13). The calculated activation energies (Ea,g) for H2 permeance displayed in Figure 6 is 20.54 kJ mol−1. 1 The calculated activation energies (Ea,g) for H2 permeance displayed in Figure6 is 20.54 kJ mol − . Although the geometrical effects of the porous structure (φ) and diffusion distance (ls) are difficult Although the geometrical effects of the porous structure (ϕ) and diffusion distance (ls) are difficult to beto determined be determined in Equation in Equation (12), by (12), performing by performing the ordinary the ordinary least squares least squares method method using MATLAB using MATLAB 7.0 (The Math Works Inc., Natick, MA, USA) [29] for regression, the value of multiple (ls × 7.0 (The Math Works Inc., Natick, MA, USA) [29] for regression, the value of multiple (ls ϕ) can be φ) can be calculated to be 1.73 × 10−12. In addition, φ is the ratio of the membrane porosity× ε to the calculated to be 1.73 10 12. In addition, ϕ is the ratio of the membrane porosity ε to the tortuosity factor tortuosity factor τ× (see− Equation (16)) and the tortuosity factor τ is difficult to be determined in τ (see Equation (16)) and the tortuosity factor τ is difficult to be determined in Equation (17) as transport Equation (17) as transport nanochannels from wrinkles and inter-galleries between stacked MXene nanochannels from wrinkles and inter-galleries between stacked MXene sheets. The calculations using sheets. The calculations using the model incorporating the obtained parameters fit the experimental thedata model well incorporating with the resultant the correlation obtained parameters coefficient of fit 0.9966. the experimental data well with the resultant correlationMolecular coefficient sieving of 0.9966.mechanism is also generally characterized by the activated diffusion [24,30]. Thus,Molecular the hydrogen sieving permeance mechanism contributed is also generally from molecularcharacterized sieving by the increased activated while diff usion that from [24, 30]. Thus,Knudsen the hydrogen diffusion permeance decreased contributed with the temperature from molecular increment, sieving so increased leading to while the totalthat from permeance Knudsen diffchangeusion decreasedwith temperature with the variation. temperature increment, so leading to the total permeance change with temperature variation. 4.4. Temperature Dependent Permeance and Relative Contribution to Total Gas Transport from Knudsen 4.4.Diffusion Temperature and Molecular Dependent Sieving Permeance and Relative Contribution to Total Gas Transport from Knudsen Diffusion and Molecular Sieving To simulate the hydrogen or nitrogen gas permeance through the MXene lamellar membrane underTo simulate the same theconditions, hydrogen we or calculated nitrogen the gas permeance permeance using through the models the MXene (Equations lamellar (7) and membrane (12)) underwith the the same related conditions, regressed we parameters calculated the and permeance analyzed using fractional the models diffusion (Equations to determine (7) and the (12)) rate with thedominates related regressed diffusion parametersdescripted by and Equations analyzed (14) fractional and (15) at di differentffusion to temperatures. determine the rate dominates diffusionFigure descripted 7 displays by Equationsthe gas permeance (14) and of (15) hydrogen at different and nitrogen, temperatures. and selectivity (H2/N2) between 260Figure and 7007 displaysK. We can the see gasthat the permeance hydrogen ofpermeances hydrogen are and higher nitrogen, than nitrogen. and selectivity For example, (H the2/N 2) betweenhydrogen 260 and and nitrogen 700 K. permeance We can see through that the the MXenehydrogen lamellar permeances membrane are is higher 2.11 and than 0.11 nitrogen. ×10−7 Formol example, m−2s−1Pa the−1 at hydrogen363 K, respectively. and nitrogen Moreover, permeance the corresponding through the selectivity MXene of lamellar H2/N2 is membrane ~19 based is on the gas permeance7 calculation.2 1 These1 results can be explained by the gas diffusion mechanism. 2.11 and 0.11 10− mol m− s− Pa− at 363 K, respectively. Moreover, the corresponding selectivity The nitrogen× transport is dominated by Knudsen diffusion through straight nanochannel of of H2/N2 is ~19 based on the gas permeance calculation. These results can be explained by the gas structural defects with the width of ~5.05 Å, while hydrogen transports based on Knudsen diffusion diffusion mechanism. The nitrogen transport is dominated by Knudsen diffusion through straight and molecular sieving through straight nanochannels of structural defects and tortuous nanochannel of structural defects with the width of ~5.05 Å, while hydrogen transports based on nanochannels from interlayer spacing. Knudsen diffusion and molecular sieving through straight nanochannels of structural defects and tortuous nanochannels from interlayer spacing. Processes 2019, 7, 751 11 of 17 Processes 2019, 7, x; doi: FOR PEER REVIEW 11 of 17

2.2 35 ) -1 2.0 F Pa H2 SH2/N2 30 -1 s -2 1.8 )

25 2 /N

F (Theoretical value) 2

mol m mol N2 -7 1.6 F (Experimental data) N2 20 FH2(Theoretical value) 0.2 FH2(Experimental data) 15

FN2 (H Selectivity Permeance(10 10 0.0 300 400 500 600 700

Temperature (K)

FigureFigure 7. 7.The The gas gas permeance permeance and and selectivity selectivity (H(H22/N/N22)) through through the the MXene MXene lamellar lamellar membrane membrane as asa a functionfunction of of temperature. temperature.

Meanwhile,Meanwhile, we we can can also also see that see in that Figure in 7 Figure the nitrogen 7 the nitrogen permeance permeance decay upon decay the temperature upon the increasedtemperature in the increased range between in the 260 range and between 700 K. 260This and trend 700 can K. be This ascribed trend tocan its be Knudsen ascribed di toff usion its mechanismKnudsen diffusion via which mechanism the permeance via which decreased the permeance with temperature decreased with as illustratedtemperature by as Equationillustrated (7). Comparedby Equation with (7). nitrogen, Compared the hydrogenwith nitrogen, permeance the hydrogen displays permeance a different displays trend and a different reaches itstrend maximum and −7 −2 −1 −1 valuereaches of 2.12 its maximum10 7 mol value m 2 sof1 2.12Pa 1× at10 408 mol K. m However,s Pa at the 408 selectivity K. However, of Hthe/ Nselectivityis always of H enhanced.2/N2 is × − − − − 2 2 Suchalways results enhanced. can be Suchinterpreted results by can the be joint interpreted effects by of the molecular joint effects sieving of molecular and Knudsen sieving di ff andusion. Knudsen diffusion. From molecular sieving (Equation (12)), it reveals an exponential dependence of From molecular sieving (Equation (12)), it reveals an exponential dependence of gas permeance on the gas permeance on the temperature, which is obviously different from that of Knudsen diffusion. temperature, which is obviously different from that of Knudsen diffusion. However, these trends are However, these trends are ascribed to the coverage of functional groups such as −OH and −O which ascribed to the coverage of functional groups such as OH and O which will affect the adsorbed will affect the adsorbed amount of hydrogen [31,32]. − − amountThe of hydrogen effect of temperature [31,32]. on the fractional diffusion of Knudsen and molecular sieving for hydrogenThe effect permeance of temperature through on the the MXene fractional membrane diffusion is depicted of Knudsen in Figure and 8. molecular It is clear sieving that the for hydrogenmolecular permeance sieving permeances through theare MXenealways higher membrane than these is depicted of Knudsen in Figure diffusion8. Itbetween is clear 260 that and the molecular700 K. Meanwhile, sieving permeances the fraction are of alwaysmolecular higher sieving than increases these of steadily Knudsen from di ff~80%usion to between~88%, and 260 the and 700Knudsen K. Meanwhile, diffusion the fraction fraction slightly of molecular decreases sieving from increases ~20% to steadily ~12%. On from average, ~80% to the ~88%, molecular and the Knudsensieving didiffusionffusion fractionis about slightlyfour times decreases higher fromthan the ~20% Knudsen to ~12%. diffusion, On average, which the indicates molecular tortuous sieving diffnanochannelsusion is about containing four times interlayer higher than spacing the Knudsen that dominates diffusion, the whichwhole indicatestransport tortuouschannels. nanochannels containing interlayer spacing that dominates the whole transport channels. Figure8 also reveals that the increase of temperature will result in the decrease of Knudsen diffusion permeance which is consistent with Equation (7). However, the molecular sieving permeance increases steadily upon the increase of temperature which reveals that temperature is more readily affected in the exponent than those in pre-exponential coefficients in Equation (12). Processes 2019, 7, 751 12 of 17 Processes 2019, 7, x; doi: FOR PEER REVIEW 12 of 17

Figure 8. Temperature dependent fractional diffusion of H to total transport from Knudsen diffusion Figure 8. Temperature dependent fractional diffusion 2 of H2 to total transport from Knudsen anddiffusion molecular and sieving. molecular Note: sieving. Data point Note: represents Data point experimental represents experimental data while the data continuous while the line indicatescontinuous model line predictions. indicates model predictions. 4.5. The Effect of the Diffusion Pore Diameter of Straight Nanochannels on the Gas Permeance and Relative Figure 8 also reveals that the increase of temperature will result in the decrease of Knudsen Contribution from Knudsen Diffusion and Molecular Sieving to Total Gas Transport diffusion permeance which is consistent with Equation (7). However, the molecular sieving permeanceThe change increases of the gassteadily permeance upon the and increase the transport of temperature fractions ofwhich Knudsen reveals di ffthatusion temperature and molecular is sievingmore withreadily the affected pore diameter in the exponent of the than straight those nanochannels in pre-exponential can becoefficients calculated in Equation from Equations (12). (7) and (12). According to the relationship between the gas permeance and the average pore diameter of straight4.5. The Effect nanochannels of the Diffusion at 295 Pore K Diameter as shown of Straight in Figure Nanochannels9, the hydrogen on the Gas and Permeance nitrogen and permeances Relative increaseContribution with thefrom average Knudsen di Diffusionffusion and pore Molecular diameter Sieving of straight to Total nanochannels Gas Transport in the MXene lamellar membrane.The We change can see of the the hydrogen gas permeance permeance and increased the transport from fractions 1.955 to 9.0 of Knudsen10 7 mol diffusion m 2s 1Pa and1 and × − − − − nitrogenmolecular permeance sieving 0.73 with to the18.6 pore10 diameter8 mol m 2 ofs the1Pa straight1 with the nanochannels pore diameter can of be straight calculated nanochannel from × − − − − alternationEquations between (7) and (12). 0.364 According and 1.0 nm, to the respectively. relationship The between discrepancy the gas betweenpermeance them and becomesthe average more pronouncedpore diameter with of the straight increasing nanochannels average at pore 295 diameterK as shown of straightin Figure nanochannels. 9, the hydrogen This and reflects nitrogen that thepermeances larger nanochannel increase with of structural the average defects diffusion will enhance pore diameter Knudsen of di straightffusion nanochannels more significantly in the for MXene lamellar membrane. We can see the hydrogen permeance increased from 1.955 to 9.0 × 10−7 permeance through the MXene lamellar membrane. Therefore, the selectivity of H2/N2 decreases from −2 −1 −1 −8 −2 −1 −1 26 tomol 4.87 m (closes Pa toand 3.74 nitrogen of the permeance Knudsen selectivity). 0.73 to 18.6 This× 10 indicates mol m s thatPa itwith is important the pore diameter to reduce of the straight nanochannel alternation between 0.364 and 1.0 nm, respectively. The discrepancy between average pore diameter of straight nanochannels resulting from structural defects to ensure the good them becomes more pronounced with the increasing average pore diameter of straight gas selectivity.Processes 2019, 7, x; doi: FOR PEER REVIEW 13 of 17 nanochannels. This reflects that the larger nanochannel of structural defects will enhance Knudsen

diffusion more significantly for permeance through the MXene lamellar membrane. Therefore, the 12 20 36 T=295 K ) selectivity of H2/N2 decreasesT=295 K from-1 26 to 4.87 (close to 3.74 of the Knudsen selectivity). This Pa 15 -1

s F indicates that it is important10 to reduce-2 the averageN2 pore diameter of straight30 nanochannels resulting 10 F

) H2

from structural defects to ensure the good mol m gas selectivity. -8 -1 5 (10 N2 Pa 8 F 24

-1 0

0 15 30 45 60 75 90 105 ) s -1 2 -2 d (10 nm) p /N 6 2 SH2/N2 18 mol m mol -7 4 12 (10 H2 Selectivity (H Selectivity F 2 6

0 0 0 15 30 45 60 75 90 105 Diffusion pore diameter of straight nanochannels (10-1 nm)

Figure 9. The eﬀect of the average pore diameter of straight nanochannels on gas permeance at 295 K. Figure 9. The effect of the average pore diameter of straight nanochannels on gas permeance at 295 K. Figure 10 shows the fractions of Knudsen diffusion and molecular sieving contribution as a function of the average pore diameter of straight nanochannels at 295 K. As can be seen, the increase of the average pore diameter of straight nanochannels from 0.364 to 1.0 nm enlarges the fractions of Knudsen diffusion permeance from 14% to 82%, while the fractions of molecular sieving decreases from 86% to 18%. Moreover, the characteristic pore diameter (dc) of 2.32 nm (23.2 Å) was also obtained from Figure 10, at which the Knudsen diffusion and molecular sieving equally share the transport. in addition, increasing the average diffusion pore diameter of defects more than such characteristic value (dc) will lead to the higher proportion of Knudsen diffusion than molecular sieving in the total permeance (Figure 10).

10 120 T=295 K 8 F H2 100 )

-1 6 Pa

-1 80

s 4 -2 f 2 Kn 60

mol m mol -7 0 f 40 (10 s H2 -2 2.32 nm F

20 (%) diffusion Fraction -4

-6 0 0 15 30 45 60 75 90 105 Diffusion pore diameter of straight nanochannels (10-1 nm)

Figure 10. Average pore diameter of the straight nanochannels dependent fractional diffusion to total transport of Knudsen diffusion and molecular sieving for H2 at 295 K.

4.6. The Effect of MXene Layer Thickness on the Gas Permeance and Fractional Diffusion of Knudsen Diffusion and Molecular Sieving The dependence of the gas permeance and the fractions of Knudsen diffusion and molecular sieving on the effect of the thickness was determined by Equations (7) and (12), and Figure 11 reveals the effect of the MXene membrane thickness on gas permeance at 295 K. From Figure 11 we can see that the decrease of the thickness of the MXene layer leads to the increase for both hydrogen Processes 2019, 7, x; doi: FOR PEER REVIEW 13 of 17

12 20 36 T=295 K ) T=295 K -1 Pa 15 -1

s F 10 -2 N2 30 10 F

) H2 mol m -8 -1 5 (10 N2 Pa 8 F 24

-1 0

0 15 30 45 60 75 90 105 ) s -1 2 -2 d (10 nm) p /N 6 2 SH2/N2 18 mol m mol -7 4 12 (10 H2 Selectivity (H Selectivity F 2 6

0 0 0 15 30 45 60 75 90 105 Diffusion pore diameter of straight nanochannels (10-1 nm) Processes 2019, 7, 751 13 of 17

Figure 9. The effect of the average pore diameter of straight nanochannels on gas permeance at 295 K. Figure 10 shows the fractions of Knudsen diffusion and molecular sieving contribution as a Figure 10 shows the fractions of Knudsen diffusion and molecular sieving contribution as a function of the average pore diameter of straight nanochannels at 295 K. As can be seen, the increase function of the average pore diameter of straight nanochannels at 295 K. As can be seen, the of theincrease average of the pore average diameter pore of diameter straight of nanochannels straight nanochannels from 0.364 from to 1.0 0.364 nm to enlarges 1.0 nm theenlarges fractions the of Knudsenfractions di ff ofusion Knudsen permeance diffusion from permeance 14% to 82%, from while 14% the to 82%, fractions while of the molecular fractions sieving of molecular decreases fromsieving 86% todecreases 18%. Moreover, from 86% the to characteristic18%. Moreover, pore the diametercharacteristic (dc) ofpore 2.32 diameter nm (23.2 (d Å)c) of was 2.32 also nm obtained (23.2 fromÅ) Figurewas also 10 obtained, at which from the Figure Knudsen 10, at di whichffusion the and Knudsen molecular diffusion sieving and equallymolecular share sieving the equally transport. in addition,share the transport. increasing in theaddition, average increasing diffusion the pore average diameter diffusion of defects pore diameter more than of defects such characteristicmore than valuesuch (d characteristicc) will lead to value the higher (dc) will proportion lead to the ofhigher Knudsen proportion diffusion of Knudsen than molecular diffusion sieving than molecular in the total permeancesieving in (Figure the total 10 permeance). (Figure 10).

10 120 T=295 K 8 F H2 100 )

-1 6 Pa

-1 80

s 4 -2 f 2 Kn 60

mol m mol -7 0 f 40 (10 s H2 -2 2.32 nm F

20 (%) diffusion Fraction -4

-6 0 0 15 30 45 60 75 90 105 Diffusion pore diameter of straight nanochannels (10-1 nm)

Figure 10. Average pore diameter of the straight nanochannels dependent fractional diffusion to total Figure 10. Average pore diameter of the straight nanochannels dependent fractional diffusion to transport of Knudsen diffusion and molecular sieving for H2 at 295 K. total transport of Knudsen diffusion and molecular sieving for H2 at 295 K. 4.6. The Effect of MXene Layer Thickness on the Gas Permeance and Fractional Diffusion of Knudsen Diffusion and4.6. Molecular The Effect Sieving of MXene Layer Thickness on the Gas Permeance and Fractional Diffusion of Knudsen Diffusion and Molecular Sieving The dependence of the gas permeance and the fractions of Knudsen diffusion and molecular sievingThe on thedependence effect of theof the thickness gas permeance was determined and the byfractions Equations of Knudsen (7) and diffusion (12), and and Figure molecular 11 reveals sieving on the effect of the thickness was determined by Equations (7) and (12), and Figure 11 the effect of the MXene membrane thickness on gas permeance at 295 K. From Figure 11 we can see reveals the effect of the MXene membrane thickness on gas permeance at 295 K. From Figure 11 we that the decrease of the thickness of the MXene layer leads to the increase for both hydrogen and can see that the decrease of the thickness of the MXene layer leads to the increase for both hydrogen nitrogen permeances. For example, the hydrogen and nitrogen permeances increase from 1.60 to 13.7 and 0.081 to 0.675 10 7 mol m 2s 1Pa 1, respectively, when the MXene thickness is reduced from × − − − − 1000 to 20 nm. On the other hand, the H2/N2 selectivity maintains at 13.5. It indicates that the thinner MXene layer can lead to higher gas permeance for hydrogen or nitrogen (Equations (7) and (12)) but maintain the gas selectivity unaltered. Figure 12 presents the transport fractions of Knudsen diffusion and molecular sieving to the total permeance as a function of the MXene membrane thickness (operated at 295 K). As can be seen, the decrease of the thickness of the MXene layer results in the substantial increase in the hydrogen permeance. However, the fractions of Knudsen diffusion and molecular sieving keep constant at around 18% and 82%, respectively. This can be explained from Equations (14) and (15), where the MXene membrane thickness does not affect the fractional diffusion to total transport from Knudsen diffusion and molecular sieving. Processes 2019, 7, x; doi: FOR PEER REVIEW 14 of 17

and nitrogen permeances. For example, the hydrogen and nitrogen permeances increase from 1.60 to 13.7 and 0.081 to 0.675 × 10−7 mol m−2s−1Pa−1, respectively, when the MXene thickness is reduced from 1000 to 20 nm. On the other hand, the H2/N2 selectivity maintains at 13.5. It indicates that the thinner MXene layer can lead to higher gas permeance for hydrogen or nitrogen (Equations (7) and (12)) but maintain the gas selectivity unaltered.

12 T=295 K 18

Processes 2019, 7, x; doi:) FOR PEER REVIEW 14 of 17 -1 FH2

Pa 8 and nitrogen permeances.-1 For example, the hydrogen and nitrogen permeances increase from 1.60 s )

−7 −2 −1 −1 2 to 13.7 and 0.081-2 to 0.675 × 10 mol m s Pa , respectively, when the MXene15 thickness is reduced /N

4 2 from 1000 to 20 nm. On the other hand, the H2/N2 selectivity maintains at 13.5. It indicates that the thinner MXene layer can lead to higher gas permeance for hydrogen or nitrogen (Equations (7) and Processes 2019, 7, 751 m mol 14 of 17

(12)) but maintain-7 0.6 the gas selectivity unaltered. S H2/N2 F 12 N2 0.4 Selectivity (H Selectivity 12 T=295 K 18 )

-1 0.2 Permeance(10 F H2 9 Pa 8 -1 s

0.0 ) 2 -2 10 8 6 4 2 15 /N

4 2 MXene thickness (102 nm)

mol m mol

-7 0.6 Figure 11. The effectS of MXene membrane thickness on gas permeance at 295 K. H2/N2 F 12 N2 Figure 12 presents0.4 the transport fractions of Knudsen diffusion and molecular sieving to the Selectivity (H Selectivity total permeance as a function of the MXene membrane thickness (operated at 295 K). As can be 0.2

seen, the decreasePermeance(10 of the thickness of the MXene layer results in the substantial increase in the 9 hydrogen permeance. However, the fractions of Knudsen diffusion and molecular sieving keep constant at around0.0 18% and 82%, respectively. This can be explained from Equations (14) and (15), 10 8 6 4 2 where the MXene membrane thickness does not affect the fractional diffusion to total transport MXene thickness (102 nm) from Knudsen diffusion and molecular sieving.

Figure 11. The eﬀect of MXene membrane thickness on gas permeance at 295 K. Figure 11. The effect of MXene membrane thickness on gas permeance at 295 K. 100 Figure 12 presents the T=295transport K fractions of Knudsen diffusion and molecular sieving to the 16 f total permeance as a function of the MXene membranes thickness (operated at 295 K). As can be 80 seen, the decrease of the thickness of the MXene layer results in the substantial increase in the ) hydrogen permeance.-1 12 However, the fractions of Knudsen diffusion and molecular sieving keep Pa

constant at around -1 18% and 82%, respectively. This can be explained from Equations60 (14) and (15), s F where the MXene -2 membrane8 thickness does not affect the fractionalH2 diffusion to total transport from Knudsen diffusion and molecular sieving. 40 mol m mol

-7 4

(10 100 H2

20 (%) diffusion Fraction F T=295 K 160 f f s Kn 80 0 )

-1 12 10 8 6 4 2 2 Pa MXene thickness (10 nm) -1 60 s F -2 H2 Figure 12. Eﬀects of the8 MXene membrane thickness on the transport fractions from Knudsen diﬀusion Figure 12. Effects of the MXene membrane thickness on the transport fractions from Knudsen and molecular sieving to total gas transport operated at 295 K. 40 diffusion and molecular m mol sieving to total gas transport operated at 295 K. -7 4 5. Conclusions (10

20 (%) diffusion Fraction In conclusion, in orderF to determine the diffusion mechanism of gases in the MXene lamellar 0 f membrane, we evaluated the hydrogen and nitrogen permeationKn properties as a function of temperature using the prepared membrane. We proposed Knudsen diffusion and molecular0 sieving through the 10 8 6 4 2 respective straight nanochannels that stemmed from structural defects and tortuous nanochannels MXene thickness (102 nm) formed by interlayer spacing. Furthermore, we performed linear regression on the experimental data to obtain the model parameters values for the MXene lamellar membrane, which were further applied Figure 12. Effects of the MXene membrane thickness on the transport fractions from Knudsen to explain the Knudsen diffusion and molecular sieving mechanisms for hydrogen and nitrogen diffusion and molecular sieving to total gas transport operated at 295 K. transport. Based on the modeling results, we simulated the effects of temperature, the pore size of the structural defects, and the thickness of the lamellar MXene membranes on hydrogen and nitrogen permeances. The relative contribution of Knudsen diffusion and molecular sieving to the total hydrogen permeance was also investigated. The model provides insights into the dominant diffusion at different operational condition and geometry variables. The results of theoretical and experimental study show that molecular sieving through tortuous nanochannels plays a dominant role in controlling the gas selectivity. Processes 2019, 7, 751 15 of 17

Author Contributions: Conceptualization, X.M., B.M. and S.L.; methodology, Y.J.; investigation, Y.F.; writing—original draft preparation, Y.J.; writing—review and editing, W.Z. and S.L.; supervision, N.Y.; funding acquisition, Y.J., W.Z., X.M., B.M., N.Y. and S.L. Funding: The authors gratefully acknowledge the research funding provided by the National Natural Science Foundation of China (No. 21878179, 21776165, and 21776175), Project of Shandong Province Higher Educational Science and Technology Program (J18KA095) and Natural Science Foundation of Shandong Province (ZR2019MB056). S. Liu acknowledges the financial support provided by the Australian Research Council through the Discovery Program (DP180103861). Acknowledgments: The authors would thank the facilities support from Analysis & Testing Center of Shandong University of Technology. Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature a Thickness of monolayer MXene lamellar, m 3 c Concentration of gas species, mol m− 2 1 DK Knudsen diffusivity coefficient, m s− 2 1 Dg,i Molecular sieving coefficient, m s− d d-spacing of MXene laminates, m dp Diffusion pore diameter, m dc Characteristic diffusion pore diameter, m 1 Ea,g Activation energy of gas diffusion, J mol− 2 1 1 F Permeance of the gas, mol m− s− Pa− 2 1 1 Ftotal Total gas permeance, mol m− s− Pa− 2 1 1 Fdefects Permeance through structural defects, mol m− s− Pa− 2 1 1 Finterlayer Permeance through interlayer spacing, mol m− s− Pa− fKn Fractional of Knudsen diffusion contribution f s Fractional of molecular sieving contribution ls Distance between two adjacent sites, m M Molecular weight of the diffusing gas 2 1 N Molar flux of gas, mol m− s− P1 Pressures at the feed side, Pa P2 Pressures at permeate side, Pa 1 1 R Ideal gas constant, J mol− K− S Selectivity of the gas pair T Absolute temperature, K Z Number of adjacent sites z Distance coordinate, m Greek Letters Φk Kinetic diameter, m λ Mean free path, m ϕ Geometrical effects of the porous structure τ Tortuosity factor δ Membrane thickness, m ε Membrane porosity Subscripts i, j Gas species i and j Kn Knudsen diffusion s Molecular sieving

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