Influence of interfacial layer parameters on gas transport properties through modeling approach in MWCNTs based mixed matrix composite membranes

Journal Pre-proofs Influence of Interfacial layer parameters on gas transport properties through modeling approach in MWCNTs based Mixed Matrix Composite Membranes Sidra Saqib, Sikander Rafiq, Nawshad Muhammad, Asim Laeeq Khan, Ahmad Mukhtar, Nurhayati Binti Mellon, Sami Ullah, Abdullah G. AlSehemi, Farrukh Jamil PII: DOI: Reference:

S0009-2509(20)30075-0 https://doi.org/10.1016/j.ces.2020.115543 CES 115543

To appear in:

Chemical Engineering Science

Received Date: Revised Date: Accepted Date:

7 October 2019 25 January 2020 2 February 2020

Please cite this article as: S. Saqib, S. Rafiq, N. Muhammad, A. Laeeq Khan, A. Mukhtar, N. Binti Mellon, S. Ullah, A.G. Al-Sehemi, F. Jamil, Influence of Interfacial layer parameters on gas transport properties through modeling approach in MWCNTs based Mixed Matrix Composite Membranes, Chemical Engineering Science (2020), doi: https://doi.org/10.1016/j.ces.2020.115543

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Influence of Interfacial layer parameters on gas transport properties through modeling approach in MWCNTs based Mixed Matrix Composite Membranes Sidra Saqib1,4, Sikander Rafiq2*, Nawshad Muhammad3, Asim Laeeq Khan1, Ahmad Mukhtar4, Nurhayati Binti Mellon4, Sami Ullah5, Abdullah G. Al-Sehemi5 , Farrukh Jamil1 1Department

of Chemical Engineering, COMSATS University Islamabad, Lahore Campus, Defense Road, Punjab, 54000, Pakistan

2Department

of Chemical, Polymer & Composite Materials Engineering, University of

Engineering and Technology, Lahore, New Campus, Pakistan 3Interdisciplinary

Research Centre in Biomedical Materials (IRCBM), COMSATS University

Islamabad, Lahore Campus, Defense Road, Punjab, 54000, Pakistan 4Department

of Chemical Engineering, Universiti Teknologi PETRONAS (UTP), Seri Iskandar, Perak, 32610, Malaysia

5Department

of Chemistry, College of Science, King Khalid University, Abha,61413, Saudi Arabia

*Corresponding author email address: [email protected]; [email protected]

1

Abstract: Precise prediction of the gas permeability behavior through the mixed matrix Composite membranes (MMMs) composed of the tubular fillers using existing theoretical approaches are infrequent. This is normally due to the neglecting the interfacial characteristics of the tubular filler particles i.e. multi-walled structured carbon nanotubes (MWCNTs) and a matrix composed of polymeric material in the existing theoretical models, especially, the Kang-Jones-Nair (KJN) model and Hamilton-Crosser model (HC) which were developed for the prediction of gas permeability behavior through the mixed matrix membranes (MMMs) composed of the tubular fillers. In this work, raw- and functionalized MWCNTs filler based MMMs in polysulfone (PSF) matrix were synthesized successfully, followed by morphological analysis on matrix interfacial layers parameters. KJN model was modified by introducing pseudo-dispersed phase fillers that influenced the interfacial layer and consequently overall gas permeabilities, which was ignored in existing models. The new proposed theoretical model is able to predict the gas permeability behavior with significantly reduced average absolute relative error (%AARE) of 1.26% compared to 52.43% and 42.71% for unmodified KJN and HC models, respectively. Furthermore, the mKJN model revealed that the interfacial layer thickness is a unique characteristic and is autonomous of the penetrant molecules of gas which may be influenced by the heterogeneity in the experimental conditions. The cross-sectional morphology and mKJN model revealed that the filler functionalization may lead to the improvement in filler-polymer interaction which thus reduced interfacial layer thickness. Keywords: Mixed matrix Composite membranes, interfacial layer, multi-walled carbon nanotubes, permeability, modeling, and gas separation.

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Introduction: CO2 emissions which lead to an increase in the risk of global warming is threatening the environment and human health [1-4]. The heating value of the natural gas which is one of the most prominent energy resources is significantly affected by the presence of CO2 contents as an impurity and leads to pipeline corrosion [5-8]. To address these challenges, there is an urgent need to develop state-of-the-art pre-post- and oxy-fuel CO2 separation technologies [9-12]. Polymeric membranes are considered as one of the potential alternatives for CO2 separation as compared to the traditional CO2 separation processes from different sources such as nitrogen recovery from the air, oxygen-nitrogen mixture and hydrocarbons separation in the petrochemical industry and the purification of raw natural gas [13-17]. Although, there are many advantages of polymeric membranes such as high processability, excellent intrinsic properties characteristics, and cost-effective synthesis [18-21]. However, the CO2 separation capability of polymeric membranes is affected by a characteristic trade-off between the permeabilities and the selectivities of gases [22-24]. While on the other side, the inorganic materials-based membranes composed of zeolites are being utilized for separation of gases due to their excellent, mechanical, thermochemical stability and good resistance to erosion. However, due to the deficiency of technological advancement to develop the continuous and detect-free membranes, highly expensive in manufacturing and handling problems such as brittleness, the applications of inorganic membranes at commercial level is still limited [14, 25, 26]. A promising and alternative strategy to address this issue of trade-off in polymeric-based membranes is the addition of nanofiller into the polymerbased membranes, so-called mixed as the matrix composite membranes (MMMs) that associate the benefits of both the organic or inorganic nanofillers and well as organic polymer matrix and also yields the high selectivity and permeability well above the upper-bound limit [27, 28]. 3

The gas transport behavior of MMMs containing nanofillers and polymer matrix is not only influenced by the transport properties of the nanofillers and polymer matrix but also affected by the interfacial layer characteristics developed between the nanofillers and polymer matrix surfaces [29, 30]. The final properties of MMMs are based on the dispersion of the nanofillers in the polymer matrix i.e. the nanofillers and polymer matrix compatibility governs by the interface morphology [31]. Nanofillers and polymer matrix poor compatibility is will be expected due to the development of interfacial voids in case of absence of strong interaction between the nanofillers and polymer matrix [32-38]. Considerable research efforts have been made to fabricate the interfacial voids free MMMs to improve the gas permeability and selectivity as it is very difficult and challenging to control the formation of the interfacial void-free MMMs. For the design and efficient utilization of MMMs for industrial applications, the variation in the gas permeability and selectivity with the nature, properties, and concertation of the nanofillers should be estimated accurately. Therefore, there is a need to deeply understand the effect of different gases penetrants on the selectivity and permeability of MMMs for the selection of their effective and optimum operating conditions [39]. Therefore, from the technological significance point of view, the relative permeability modeling of the MMMs is of great significance to such materials having industrial significance [40]. The existing classical models for the prediction of gas permeability through MMMs are derived and published by many academic researchers and these models are derived based on the concept of electrical and thermal conductivity. Therefore, these models are readily applied to characterize the gas permeation behavior in MMMs due to the analogy between the electrical and thermal conductance in composite materials and gas permeation through MMMs [41]. There are many theoretical models reported in the literature for the prediction of gas permeability through the MMMs. These models include Maxwell model [42], Pal model 4

[39], Bruggeman model [43], Lewis-Nelson model [44], Higuchi model [45], KJN, model [46], and Hamilton-Crosser (HC) model [47]. However, in the above-mentioned well-known predictive models, the Kang-Jones-Nair (KJN) model and the HC model are known to be suitable for the prediction of gas permeability behavior through MMMs containing tubular-shaped fillers i.e. MWCNTs. The KJN model was derived on the basis of the parallel-series resistance model in fixed orientation i.e. one-dimensional orientation of fillers in the polymer matrix. However, the KJN model and HC model have been developed on the concept of the two-phase system i.e. continuous phase i.e. polymer matrix and dispersed phase i.e. fillers particle and neglect the influence of the interfacial layer i.e. the third phase known as a pseudo-dispersed phase. The synthesis of raw functionalized MWCNT filler dependent MMMs via the solution casting method can be defined in the following study. Cross-sectional morphological analysis of fillers polymer interfacial layer was observed followed by gas permeation analysis for (CO2, CH4, N2) selective separation at 2-10 bar feed pressure and 298-338 K temperature. Modification of the KJN model by incorporating the interfacial layer thickness parameters was carried out which has not yet explored according to the best of the author’s knowledge. The developed model was validated with the experimental data. Materials and Methods: Chemicals: All chemicals including multi-walled carbon nanotubes (MWCNTs) (≥98%, carbon, 800-1000 m2/g, synthesis-growth method), Monoethanolamine (MEA), Dimethyl formaldehyde (DMF), Acetone, Nitric acid (HNO3), Cetyltrimethylammonium bromide (CTAB), Acetic acid, Ethanol,

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Polysulfone (PSF), and Tetrahydrofuran (THF) with purity >95% were purchased from SigmaAldrich and used without any further purification. Amine Functionalization of MWCNTs: The functionalization of MWCNTs with primary amine i.e. monoethanolamine carried out by a known method [48] which involves the suspension of MWCNTs (0.3 mg) with monoethanolamine (5 mL) in a solution of organic solvent i.e. dimethyl formaldehyde (DMF) (50 mL) with ultrasonication for 1 hour under nitrogen atmosphere. The mixture is further subjected to heating at 70 °C for 3 days leading to the grafting of amine functional groups onto the surface of MWCNTs. The resulting reaction mixture was vacuum filtered through a 0.45 µm PTFE membrane and washed with acetone. Finally, the samples were dried at 80 °C for 24 hours to get amine-MWCNTs. Oxidation of MWCNTs: To oxidize the MWCNTs with HNO3, MWCNTs (500 mg) were weighed and mixed with 100 mL of HNO3 (6 M) in a conical flask and mixture for stirred for homogenous mixing. Then, the mixture was subjected to ultrasonication for 4 hours and the temperature was maintained at 40 °C. After that, the mixture was separated via filter paper and washed with distilled water until it becomes neutral (pH=7.0). The final product was dried in vacuum overnight at a temperature of 80 °C. Synthesis of Deep Eutectic Solvent (DES): The synthesis of deep eutectic solvent involves the formation of a mixture of hydrogen bond donor (HBD) and hydrogen bond acceptor (HBA). In this work, an equal amount of Cetyltrimethylammonium bromide (CTAB) as an HBA and acetic acid as an HBD was used to

6

prepare DES exhibiting gel-like nature exhibiting solid state below 70 °C and liquid state at above 70 °C. Deep Eutectic Solvent (DES) Functionalization of MWCNTs: The raw-MWCNTs functionalization with the DES involves the mixing of the raw-MWCNTs and DES with a ratio of (9:1) in the presence of organic solvent i.e. ethanol. The mixing was subjected to rigorous mixing and the organic solvent was evaporated and the powder was obtained by filtering the DES and MWCNTs mixture. The resulted materials in known as DES-MWCNTs. Development of Raw and Functionalized MWCNTs-PSF based MMMs: Three important components, including PSF, raw and functionalized MWCNT fillers and solvent, have been synthesized to form the doping solution. Through combining Tetrahydrofuran with Polymer PSF (THF 99.9%), a casting solution of about 7g was produced. Upon constant mixing and stirring up to the end of a clear solution, raw and functionalized MWCNTs were applied, like (5 wt.%, 10 wt.% and 20 wt.%) with various filler loading. To obtain complete and uniform homogenization with heating, the solution was stirred. After the continuous heating and agitation, membrane was poured into a flat petri platter with various loadings of filler and held for 24 hours to evaporate. Within 24 hours, the finely and thinly compressed membrane was heated, and any boundary moisture could be extracted. Characterizations of MMMs: A field-emissions electron (FESEM, Hitachi S4800, Japan) microscope was used to analyze the morphology based on cross-section of prepared MMMs. Vacuum-dry MMMs is freeze in liquidphase nitrogen and eventually gold coated in cross-sectional morphology review of MMMs. An attenuated total complete reflectance spectrometer (ATR-FTIR, BRUKER Vertex 70) of Fourier 7

transform-infrared (Perkin Elmer, Germany) was used to analyze the functional groups inside functionalized MWCNTs and MMMs. With aa resolution of 4 cm-1, spectral transmission was taken within the range of 400-4000 cm-1. Gas Permeation Testing: A gas permeation test was performed in a modified gas permeation test device in accordance with raw and functionalized PSF-based MMMs samples from MWCNTs (Fig. 1) for the pure and mixed gas permeation study of CH4, CO2, and N2 at pressure range of 2-10 bar and temperature within the range of (298.15 K to 338.15 K). For each run, pure PSF membrane along with the raw and functionalized MWCNTs-PSF based MMMs samples were mounted into the membrane test cell with an effective area of 1.77 cm2. The regeneration experiments were carried out in a total of 3 films 1 section of three separately cast MMMs. The film was subjected to the vacuum test overnight before the gas permeation test to the vapor or gas that could be surroundings in MMM film after the film was mounted on the membrane cell. Measures have begun once the gas is added into the membrane cell and the velocity of the gas streams has been measured using the atmospheric pressure soap flux meter. i.e. atmospheric pressure. The permeability of the pure CO2 and CH4 gases were estimated using (Eq. 1) as follows [49]:

𝑃𝐴 =

𝑉𝑝𝑡 𝐴𝑚(𝑝ℎ ― 𝑝𝑙)

(1)

Where PA denotes the gas membrane permeation (Barrer) and subscript A denotes the CH4 or CO2 or N2, Vp denotes the permeate flow rate (cm3/s) at ambient conditions, Am denotes the = area of membrane (cm2), ph and pl denote the pressure (cmHg) in the feed as well as the permeate direction, respectively. The gas membrane permeation can be presented in the unit of Barrer (1 Barrer = 1×10-10 cm3 (STP) cm/s.cm2 cmHg). 8

ideal membrane selectivity (Eq. 2), the permeability ratio of different gasses, i.e. can be shown. The following equations can be given for CO2 and CH4 [50]:

𝛼𝐶𝑂2/𝐶𝐻4 =

𝑃𝐶𝑂2

(2)

𝑃𝐶𝐻4

Where, α denotes the ideal CO2/CH4 selectivity and P denotes the gas membrane permeation (Barrer). On the other hand, the binary gases permeation (CO2/CH4) was acquired using a binary gas mixture i.e. (CO2:CH4 50:50) at a pressure within the range of 2-10 bar at ambient conditions. The gas membrane permeation of components in binary gas mixture were estimated by using (Eq. 3 & 4) as follows:

𝑃𝐶𝑂2 =

𝑃𝐶𝐻4 =

𝑉𝑝𝑦𝐶𝑂2𝑡

(3)

𝐴𝑚(𝑝ℎ𝑥𝐶𝑂2 ― 𝑝𝑙𝑦𝐶𝑂2) 𝑉𝑝𝑦𝐶𝐻4𝑡

(4)

𝐴𝑚(𝑝ℎ𝑥𝐶𝐻4 ― 𝑝𝑙𝑦𝐶𝐻4)

Where, PCH4 and PCO2 and indicate the CH4 and CO2 permeation behavior, respectively. Whereas, the x and y indicate the respective gas components mole fraction in the direction of the feed as well as retentate side, respectively. The selectivity of the binary gas membrane permeation can be estimated as follows (Eq. 5).

( ) ( ) 𝑦𝐶𝑂2

𝑦𝐶𝐻4

𝛼𝐶𝑂2/𝐶𝐻4 =

𝑥𝐶𝑂2

𝑥𝐶𝐻4

9

(5)

Fume Hood

Future Expansion

Oven

Pressure Gauge Thermocouple

Oven

Fume Hood To the Filler

Heater

N2

CH4

Coriolis Membrane Flow Meter Cell

Saturation Vessel

CO2 Flow Controllers

Feed Vessel

Static Mixer

Compressor

Drain

Gas Analyzer

Thermocouple Pressure Gauge Thermocouple

Pressure Coriolis Gauge Flow Meter

Drain

To the Filler

Fig. 1. Schematic illustration of the apparatus for the pure and mixed gas permeation testing. Results and Discussions: Cross-Sectional Morphology: The interactions of raw-MWCNTs, OH-MWCNTs, amine-MWCNTs, and DES-MWCNTs fillers with the polymer matrix to form π-π bonds, hydrogen bonding, and electrostatic interactions are illustrated in (Fig. 2 and 3). The surface morphology of the fillers has been reported in our previously published work [21]. The cross-section morphology of the synthesized MMMs which include the fillers particles i.e. raw-MWCNTs-PSF, OH-MWCNTs-PSF, amine-MWCNTs-PSF, and DES-MWCNTs-PSF were investigated by the field emission scanning electron microscopy (FESEM). The FESEM images to demonstrate the cross-section morphology of the MMMs i.e. raw-MWCNTs-PSF, OH-MWCNTs-PSF, amine-MWCNTs-PSF, and DES-MWCNTs-PSF are illustrated in (Fig. 4). It is an admitted fact that the cross-sectional morphology of the MMMs strongly influences the overall gas transport properties through the MMMs. Overall, in all prepared membranes a spongy asymmetric structure can be observed. Furthermore, the strong interactive forces between the raw and functionalized MWCNTs fillers and the PSF polymer matrix along

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with the poor affinity of the organic solvent i.e. tetrahydrofuran (THF) may lead to the development of the emerging skin-like structure during the drying step. The incorporation of the raw and functionalized MWCNTs fillers into the PSF polymer matrix with an increase in the loading from 5 wt.% to 20 wt.% leads to the minimization in the thickness of MMMs. In the case of raw-MWCNTs-PSF based MMMs, thickness reduced from 51.60 µm to 36.52 µm. For OHMWCNTs-PSF based MMMs, thickness reduced from 44.23 µm to 37.97 µm. The amineMWCNTs-PSF based MMMs demonstrated the thickness reduction from 80.86 µm to 37.64 µm. Finally, the DES-MWCNTs-PSF based MMMs demonstrated the thickness minimization from 51.94 µm to 30.38 µm. Normally, the MMMs with thin structures preferred in gas separation applications as it imposes less resistance to the flux towards the gas permeation through MMMs [28, 51, 52]. From the cross-sectional morphology, the raw and functionalized MWCNTs fillers were incorporated into the polymer matrix after a rough cross-section was formed, which can be due to the uniform distribution of fillers in the polymer matrix. However, when the filler loading increased, the formation of the agglomerates is obvious due to the stronger interactive forces between the organic fillers i.e. raw and functionalized MWCNTs compared to the interactions between the raw and functionalized MWCNTs fillers and the PSF polymer matrix. This may lead to the formation of macro-voids or channels which is an indication of the flexibility of the molecular chains in the PSF polymer matrix [53]. The pore structure can be observed in the crosssection images of the synthesized MMMs which pay a significant contribution in the selective gas permeabilities of the MMMs and provides mechanical strength to the MMMs [54, 55]. Finally, the homogenous and uniform distribution of the raw and functionalized MWCNTs fillers into the PSF polymer matrix can be directed to the improved compatibility between the raw and functionalized

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MWCNTs fillers and the PSF polymer matrix especially at higher loadings of raw and functionalized MWCNTs fillers.

Raw-MWCNTs

Pi-Pi Bonds

CH3 C

Polysulfone (PSF)

°° O °°

O O

S O

CH3

Pi-Pi Bonds OH

Hydrogen Bonding

O

OH-MWCNTs

Fig. 2. Interaction of Raw-MWCNTs and OH-MWCNTs with the PSF polymer matrix.

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Amine-MWCNTs

O

Hydrogen Bonding

NH

Pi-Pi Bonds

CH3

O °° O °°

C

°° O

S+

°° O

CH3 Polysulfone (PSF) Pi-Pi Bonds

Electrostatic Interactions

O

C

OH CH3

BrDES-MWCNTs

N+ CH3

Fig. 3. Interaction of Amine-MWCNTs and DES-MWCNTs with the PSF polymer matrix.

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FESEM images revealed that the homogenous and uniform distribution of the raw and functionalized MWCNTs fillers into by using a general chemical reaction tactics between surface functional groups in raw-MWCNTs, the PSF polymer matrix can be accomplished [56]. In the case of MWCNTs, the walls of the MWCNTs do not support selective gas transport as these walls are considered as impermeable and only the internal cylindrical space is accounted as the responsible for the selective gas transport [57]. The gas transport properties of the MWCNTs incorporated MMMs are dependent not only on the gas transport properties of the MWCNTs and the polymer matrix but especially also affected by the interfacial layer thickness or characteristics at the interface of the MWCNTs and polymer matrix [29, 30]. The interfacial surface morphology of the MMMs leads to the interfacial compatibility between the MWCNTs i.e. filler particle and the polymer matrix leading to the final gas transport properties of the MMMs which are accounted the model developed in this work [31]. The FT-IR spectral analysis and the assignment of peaks to the respective bonds have been illustrated and tabulated in (Fig. 5) and (Table 1), respectively. (a)

(b)

(c)

(d)

(e)

(f)

14

(g)

(h)

(i)

(j)

(k)

(l)

Fig. 4. Influence of filler loadings on the thickness of MMMs: (a-c): raw-MWCNTs-PSF at 5 wt.%, 10 wt.%, and 20 wt.%, (d-f): OH-MWCNTs-PSF at 5 wt.%, 10 wt.%, and 20 wt.%, (g-i): amine-MWCNTs-PSF at 5 wt.%, 10 wt.%, and 20 wt.%, and (j-l): DES-MWCNTs-PSF at 5 wt.%, 10 wt.%, and 20 wt.%. (a)

Raw-MWCNTs OH-MWCNTs Amine-MWCNTs DES-OH-MWCNTs 4000

3500

3000

2500 2000 1500 Wavenumber (cm-1 )

15

1000

500

(b)

PSF Raw-MWCNT-PSF (5%) Raw-MWCNT-PSF (10%) Raw-MWCNT-PSF (20%) 4000

3500

3000

2500 2000 1500 Wavenumber (cm-1 )

1000

500

(c)

PSF OH-MWCNT-PSF (5%) OH-MWCNT-PSF (10%) OH-MWCNT-PSF (20%) 4000

3500

3000

2500 2000 1500 Wavenumber (cm-1 )

16

1000

500

(d)

PSF Amine-MWCNT/PSF (5%) Amine-MWCNT/PSF (10%) Amine-MWCNT/PSF (20%) 4000

3500

3000

2500 2000 1500 Wavenumber (cm-1 )

1000

500

(e)

PSF DES-OH-MWCNT-PSF (5%) DES-OH-MWCNT-PSF (10%) DES-OH-MWCNT-PSF (20%) 4000

3500

3000

2500 2000 1500 Wavenumber (cm-1 )

1000

500

Fig. 5. FT-IR spectral analysis of the fillers, polymers, and synthesized MMMs; (a): fillers, (b): raw-MWCNTs-MMMs, (c): OH-MWCNTs-MMMs, (d): amine-MWCNTs-MMMs, and (e): DES-OH-MWCNTs-MMMs.

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Table 1. FT-IR peaks and their respective functional group's assignments [58-62]. Peaks

Assignment

3429.78 cm-1

-OH bonds

2855.1 cm-1

Symmetric -CH2 stretching vibrations

2922.59 cm-1

Asymmetric -CH2 stretching vibrations

1654.62 cm-1

N-H stretching vibrations

1186.97 cm-1

C-N stretching vibrations

1218 cm-1

C-O bending vibrations

1476 cm-1

C-H bending vibrations

1293 cm-1

O=S=O stretching vibrations

1584 cm-1

C=C stretching vibrations

2967 cm-1

C-H stretching vibrations

1615 cm-1

C=C stretching vibrations in the benzene ring of MWCNTs

2850 cm-1

C-H stretching vibrations

1714 cm-1

C=O bonds

Pure Gas Permeation Analysis: The pure gas permeation performances of three gases including CO2, CH4, N2 have been investigated over the raw and functionalized MWCNTs fillers and PSF polymer matrix based MMMs. Three different loadings of the fillers in each case have been investigated including 5 wt.%, 10 wt.%, and 20 wt.% at a pressure of 10 bar and 29815. K temperature. The results of the

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pure gas permeation of the MMMs based on raw-MWCNTs, OH-MWCNTs, amine-MWCNTs, and DES-MWCNTs fillers are tabulated in (Table 2). The results showed that in case of CO2 permeation the pure PSF membranes exhibited a permeability of 6.8 Barrer followed by the successive improvement by the addition of functionalized fillers i.e. MWCNTs. The gas permeation performance of the MMMs can be improved further by the surface functionalization of raw-MWCNTs to attach different nitrogen-rich surface functional groups [28]. These results showed remarkable enhancement in the permeability of pure gas with a rise in the loading i.e. 5 wt.%, 10 wt.%, and 20 wt.% of the filler in PSF demonstrating that the filler have permeability behavior intrinsically. The effective incorporation of MWCNTs filler into the matrix composed of the PSf polymer results in the additional development of the channels responsible for the transport for gas permeation and improves the internal molecular free volume in the matrix composed of the PSf polymer. The synergetic impact of additional transport channels developed, and improvement of internal molecular free volume results to the support of the diffusion of molecules of the gas through the MWCNTs-PSF based MMMs. The improvement in the internal molecular free volume of the matrix composed of the PSf polymer can be accomplished by the effective addition of the MWCNTs fillers which are supposed to the linking of the polymeric chains and to dislocate the packing following to an enhancement in the internal molecular free volume in the matrix composed of the PSf polymer [63]. CO2 demonstrated the significant gas permeation behavior followed by the other two gases i.e. N2 and CH4 in all synthesized membranes. It should be well-intentioned to note that the N2, CH4, CO2 permeability values through PSf may be different from the published literature [64]. This variation in the pure gas permeabilities through the pure PSF membranes can be attributed to the different PSf exhibiting different molecular weights as well as differences in the methods employed for the effective synthesis of the PSF, operational parameters, differences

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in the solvent evaporation time, gas in casting, uniformity of membranes, and the thickness, etc. [63]. However, in the case of MMMs prepared by the effective addition of MWCNTs fillers into the polymer composed of the PSf polymer resulted in such a significant improvement in the gas permeation behavior can be directed to the both adsorption-controlled and sieving mechanism of the gas permeability of CO2 through the raw-MWCNTs filler pores [65]. In case of amineMWCNTs-PSF based MMMs, the CO2 permeability improved from 27.5 barrer to 67.8 barrer by increasing the loading of amine-MWCNTs into PSF polymer matrix from 5 wt.% to 20 wt.% , respectively. In case of CH4, the effective incorporation of amine-MWCNTs into the matrix composed of the PSf polymer results to the improvement of gas permeation from 1.31 barrer to 1.86 barrer by increasing amine-MWCNTs loading from 5 wt.% to 20 wt.%, respectively. Similarly, in case of N2 permeation behavior, the effective addition of amine-MWCNTs into the matrix composed of the PSf polymer resulted in the improved gas permeability from 1.22 barrer to 1.76 barrer by increasing the loading of amine-MWCNTs from 5 wt.% to 20 wt.%, respectively. In case of DES-MWCNTs-PSF based MMMs, the CO2 permeability raised from 198.5 barrer to 490.5 barrer by increasing the loading of DES-MWCNTs into PSF polymer matrix from 5 wt.% to 20 wt.% , respectively. In case of CH4, the effective incorporation of DES-MWCNTs into the matrix composed of the PSf polymer results to the improvement of gas permeation from 2.71 barrer to 5.98 barrer by increasing DES-MWCNTs loading from 5 wt.% to 20 wt.%, respectively. Similarly, in case of N2 permeation behavior, the effective addition of DES-MWCNTs into the matrix composed of the PSf polymer resulted the improved gas permeability from 2.24 barrer to 5.037 barrer by increasing the loading of DES-MWCNTs from 5 wt.% to 20 wt.%, respectively. These improved gas permeation behavior after the effective addition of amine-MWCNTs filler can also be attributed to the improved collaborative forces because of the existence of CO2-philic

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surface functionalities in the amine-MWCNTs filler which is consistent with the published research on a 4-aminophenazone(4-AMP) decorated silica extracted from the rice husk and matrix composed of the PSf polymer based MMMs [66]. Moreover, the amine-MWCNTs-PSF based MMMs can develop interactive forces with the molecules of CO2 through the assistance of the CO2 philic surface functionalities such as the presence of nitrogen fractions in the amineMWCNTs-PSF based MMMs structures which is N2 phobic and CO2 philic nature resulting to the improved polar gas i.e. solubility of CO2 along with the gases with non-polar nature i.e. N2 and CH4 with less soluble nature [67, 68]. Also, the smaller kinetic size of the molecules of the CO2 comparatively to the molecules of the N2 along with the large affinity come into play between the highly basic molecules of N2 and highly acidic molecules of CO2 which can be attributed to the high CO2 permeation behavior over CH4 and N2 [69]. It can be predictable that the effective addition of amine-MWCNTs fillers into the matrix composed of the PSf polymer can develop interactive forces with the chains of the PSf polymer, as demonstrated in the cross-sectional morphological analysis based on the FESEM based analysis. The effect of the pressure of the gas feed on the selective permeation behavior of the gases i.e. CH4, N2, and CO2 through pure PSF and raw and N2 rich functionalized MWCNTs-PSF based MMMs also have been studied. The gas selective permeation behavior in all cases i.e. CO2, CH4, and N2 raised which demonstrated that the Langmuir adsorption sites do not reach its level of saturation. The results also obey Henry’s law which states that the each gas solubility that passes through pure PSF and amine-MWCNTsPSF based MMMs is directly proportional to the applied pressure of the gas feed [70]. However, in the case of DES-MWCNTs-PSF based MMMs, these improved results can be directed to the hydrogen formation nature along with the nitrogen-rich nature of the DES employed in this work for the synthesis of MMMs.

21

Table 2. CO2, CH4, and N2 permeability behavior through raw- and functionalized MWCNTs-PSF based MMMs. MMMs

Gas

Pressure

Permeabilities (Barrer)

(bar) Fillers particle weight fractions Raw-MWCNTs-PSF

CO2

CH4

N2

OH-MWCNTs-PSF

CO2

5 wt.%

10 wt.%

20 wt.%

2

7.7

10.7

14.7

4

8.2

11.6

15.5

6

9

12.2

16.4

8

9.7

13.1

17.5

10

10.5

14.12

18.43

2

0.359

0.385

0.396

4

0.364

0.392

0.4

6

0.37

0.408

0.418

8

0.375

0.416

0.427

10

0.38

0.42

0.43

2

0.349

0.375

0.386

4

0.354

0.382

0.39

6

0.36

0.398

0.408

8

0.365

0.406

0.417

10

0.37

0.41

0.42

2

16.4

23.2

30.5

4

17.6

24.7

31.8

6

18.5

25.4

32.7

22

CH4

N2

Amine-MWCNTs-PSF

CO2

CH4

N2

8

19.7

26.3

33.5

10

20.98

27.08

34.74

2

0.486

0.575

0.654

4

0.497

0.589

0.668

6

0.508

0.596

0.676

8

0.519

0.61

0.684

10

0.539

0.623

0.697

2

0.482

0.545

0.647

4

0.496

0.565

0.655

6

0.507

0.574

0.668

8

0.515

0.587

0.675

10

0.526

0.592

0.682

2

22.8

39.3

63.4

4

24.3

40.5

64.5

6

25.1

41.8

65.6

8

26.2

42.7

66.5

10

27.5

43.5

67.8

2

1.18

1.48

1.74

4

1.22

1.5

1.77

6

1.26

1.52

1.81

8

1.28

1.55

1.84

10

1.31

1.58

1.86

2

1.11

1.41

1.68

23

DES-MWCNTs-PSF

CO2

CH4

N2

4

1.14

1.43

1.7

6

1.17

1.46

1.72

8

1.19

1.49

1.74

10

1.22

1.51

1.76

2

194.6

311.1

486.4

4

195.7

312.4

487.6

6

196.5

313.2

488.7

8

197.8

314.6

489.5

10

198.5

315.8

490.5

2

2.62

3.89

5.92

4

2.65

3.91

5.94

6

2.66

3.94

5.95

8

2.68

3.96

5.97

10

2.71

3.98

5.98

2

2.18

3.38

5.063

4

2.2

3.4

5.058

6

2.21

3.42

5.05

8

2.23

3.44

5.042

10

2.24

3.45

5.037

Development of New Model: There are many theoretical models reported in the literature for the prediction of gas permeability through the MMMs. These models include Maxwell model [42], Pal model [39], Bruggeman 24

model [43], Lewis-Nelson model [44], Higuchi model [45], KJN, model [46], and the HamiltonCrosser (HC) model [47]. However, in the above-mentioned well-known predictive models, the Kang-Jones-Nair (KJN) model and HC model are known to be suitable for the prediction of gas permeability behavior through MMMs containing tubular-shaped fillers i.e. MWCNTs. The KJN model was derived on the basis of the parallel-series resistance model in fixed orientation i.e. onedimensional orientation of fillers in the polymer matrix. In this work, modified KJN model based on three-phase i.e. MWCNTs-interface-polymer matrix has been proposed using a rational methodology. To best of our knowledge, for the first time in this paper we are going to develop a new model based on KJN model by incorporating the influence of interfacial layer on the permeability of the MMMs. The schematic illustration of the MWCNTs in tubular shaped is shown in (Fig. 6). The mathematical form of the KJN model is given in (Eq. 6). Polymer Matrix

Pseudo-Dispersed Phase

Interfacial Layer

MWCNTs

Polymer Matrix Thickness of Interfacial Layer

Radius of MWCNTs

Fig. 6. Schematic illustration of dispersion of tubular fillers i.e. MWCNTs into the polymer matrix.

25

𝑃𝑒𝑓𝑓 𝑃𝑚

[(

) (

) ]

―1

𝑃𝑚 cos 𝜃 1 = 1― 𝜑𝑁𝑇 + 𝜑𝑁𝑇 1 𝑃𝑁𝑇 1 cos 𝜃 + sin 𝜃 cos 𝜃 + sin 𝜃 𝛼 𝛼

(6)

Where, and θ denotes the aspect ratio of tubular fillers i.e. MWCNTs aspect ratio (length/diameter, L/dNT) and filler orientation angle with respect to the transport direction in the MMMs. The value of θ varied from 0 to π/2 in radians. By comparing the platelet and the spherical filler particles, the tubular filler particles such as the MWCNTs have gained much attraction for their application in MMMs for efficient gas separation because of their high aspect ratio and the hollow structural network. This can lead to a significant enhancement in the selective gas permeation behavior of the MMMs [71-73]. Due to the high inner diameter of the MWCNTs, it does not exhibit any significant improvement in the selective gas separation of binary mixtures i.e. CO2/N2 and CO2/CH4 which can be improved by the surface functionalization of the MWCNTs with the CO2philic surface functional groups. The influence of the aspect ratio (α) of the MWCNTs incorporated as a filler particle into the polymer matrix to synthesize the MMMs can be estimated by using the (Eq. 6). Form the (Eq. 6), it can be observed that the effective permeability of the MMMs is directly proportional to the aspect ratio of the MWCNTs [74]. As mentioned earlier that the (Eq. 1) form of KJN model is derived for the one-dimensional orientation of fillers in the polymer matrix which is considered as an ideal case. However, in real conditions i.e. for completely random distribution of tubular fillers into the polymer matrix, the KJN model (Eq. 1) can be rewritten as follows (Eq. 7).

𝑃𝑒𝑓𝑓 𝑃𝑚

=

[∫

𝜋 2

𝜋 2

𝑃𝑚

0 𝑃𝑒𝑓𝑓,𝜃

𝑑𝜃

]

―1

26

(7)

Specifically, for the MMMs composed of the tubular fillers i.e. MWCNTs, the incompatibility between the fillers and the matrix composed of PSf polymer polymer matrix leads to the formation of interfacial voids in the surroundings of the fillers. Furthermore, the polymer in the MMMs may contain intrinsic holes extending from the feed side to the permeate side within the MMMs. By considering these two defects, the KJN model can be extended based on the real conditions i.e. incompatibility and non-ideal morphology of the tubular fillers incorporated into the polymer matrix. Hence, the modified KJN model for the effective permeability of gas through MMMs can be written as follows (Eq. 8).

𝑃𝑒𝑓𝑓 =

𝜑𝑁𝑇

𝑃𝑒𝑓𝑓,𝑑 +

𝜑𝑁𝑇 + 𝜑𝑣 + 𝜑𝑝

𝜑𝑣

𝑃𝑒𝑓𝑓,𝑣 +

𝜑𝑁𝑇 + 𝜑𝑣 + 𝜑𝑝

𝜑𝑝

𝑃 𝜑𝑁𝑇 + 𝜑𝑣 + 𝜑𝑝 𝑒𝑓𝑓,𝑝

(8)

Where Peff.d denotes the effective permeability of a gas through an ideal composed MMMs based on MWCNTs filler and polymer matrix. Peff.v denotes the effective permeability of the interfacial voids in MMMs based on voids and polymer matrix. Peff.p denotes the effective permeability of a gas through a pinhole MMMs based on MWCNTs filler and polymer matrix. The φNT, φv, and φp denote the volume fractions of the MWCNTs fillers, interfacial void, and pinholes, respectively. The Peff.d can be estimated by using the following equations (Eq. 9-12) [75]. 𝑃𝑒𝑓𝑓 = 𝑃𝑒𝑓𝑓.𝑚𝜑𝑐 + 𝑃𝑒𝑓𝑓.𝑑𝜑𝑑

(9)

Where 𝜑𝑐 = 1 ― 𝜑𝑑

(10)

Substituting the (Eq. 5) into the (Eq. 4) results (Eq. 6) as follows. 𝑃𝑒𝑓𝑓 = 𝑃𝑒𝑓𝑓.𝑚(1 ― 𝜑𝑑) + 𝑃𝑒𝑓𝑓.𝑑𝜑𝑑

27

(11)

Finally, the Peff.d can be estimated as follows (Eq. 7).

𝑃𝑒𝑓𝑓.𝑑 =

[

𝑃𝑒𝑓𝑓 ― 𝑃𝑒𝑓𝑓.𝑚(1 ― 𝜑𝑑)

]

𝜑𝑑

(12)

Peff.v can be predicted by using the HC model by considering that the permeability of the interfacial voids and the permeability of the pseudo-dispersed phase are identical, and both are isotropic in shape i.e. cylindrical or tubular. From these identical interfacial voids and pinholes, the transport of gas molecules is dominated by the phenomenon of Knudsen diffusion [40]. Hence, the Peff.v can be estimated by using the HC model as follows (Eq. 13) [47]. 𝑃𝑝𝑠 𝑃𝑖𝑛𝑡

=

𝑃𝑒𝑓𝑓.𝑣 𝑃𝑐

=

𝑃𝑁𝑇 + 5𝑃𝑖𝑛𝑡 ― 5𝜑𝑠(𝑃𝑖𝑛𝑡 ― 𝑃𝑁𝑇)

(13)

𝑃𝑁𝑇 + 5𝑃𝑖𝑛𝑡 + 𝜑𝑠(𝑃𝑖𝑛𝑡 ― 𝑃𝑁𝑇)

Where Pps, PNT, and Pint denote the permeabilities of the pseudo-dispersed phase, MWCNTs, and the interfacial layer, respectively. In addition, the φs denotes the volume fractions of the pseudodispersed phase and can be estimated as follows (Eq. 14) [1].

𝜑𝑠 =

𝜑𝑁𝑇 𝜑𝑁𝑇 + 𝜑𝑖𝑛𝑡

=

𝑟𝑁𝑇2

(𝑟𝑁𝑇 + 𝑙𝑖𝑛𝑡)2

(14)

Where, rNT and lint denote the radius (m) of the MWCNTs and the thickness of the interfacial layer (nm), respectively. The gas permeability of the polymer matrix (PM) is considered as the permeability of the pure membrane with zero filler loadings. Furthermore, the permeability of the fillers i.e. MWCNTs is usually considered as a variable parameter by using the linear or non-linear regression analysis approach also known as curve fitting approach. However, in this proposed methodology, the permeability of the fillers i.e. MWCNTs is estimated based on the dusty gas model (Eq. 15) [76].

28

𝑅𝑁𝑇 ―1 = (𝑅𝐾 + 𝑅𝑀) ―1 + 𝑅𝑃 ―1

(15)

Where RNT, RK, RM, and RP are the resistances to the transport of gas molecule inside the fillers i.e. MWCNTs, to the transport of gas molecules based on Knudsen diffusion, to the transport of gas molecules based on molecular diffusion, and viscous flow mechanism, respectively [77]. The mean free path will determine which kind of mechanism governs the transport of gas molecules through the respective membrane. There are three types of mechanisms as mentioned earlier which describe the transport of gas molecules through the membranes including the Knudsen diffusion, molecular diffusion, and viscous flow. These mechanisms are also distinguished by the operational parameters including the pressure and temperature of the gas of feed side along with the kinetic diameter of the gas molecule of the feed gas and the diameter of the tubular fillers i.e. MWCNTs in this case [78]. Based on the kinetic theory, the mean free path (Eq. 16) or the average distance between the collisions of gas molecules can be predicted. The detailed procedure of the determination of the mean free path is provided in the supplementary information.

𝜆=

𝐾 𝐵𝑇

(16)

2𝜋𝜎2𝑃

Based on the mean free path (Eq. 16), there are three fundamental mechanisms that can be described to investigate the transport of gas molecules through the MWCNTs fillers based MMMs. If the diameter of the MWCNTs is smaller than the mean free path, the Knudsen diffusion mechanism will be dominant. The resistance based on Knudsen diffusion (RK) (Eq. 17) and the permeability based on the Knudsen diffusion mechanism (PK) through the transport of the gas molecules through the MWCNTs fillers based on MMMs can be described as follows (Eq. 18).

𝑅𝐾 =

𝐿 𝑃𝐾

(17) 29

2𝑟𝑁𝑇 8𝑅𝑇 𝑃𝐾 = 3𝑅𝑇 𝜋𝑀

0.5

( )

(18)

Where L, rNT, and M denote the length of the MWCNTs (m), the radius of the MWCNTs (m), and molecular weight of the gas (Kg/mole) transported through the MWCNTs fillers based MMMs, respectively. If the diameter of the MWCNTs is larger than the mean free path, the Molecular diffusion mechanism will be dominant. The resistance based on Molecular diffusion (RM) (Eq. 19) and permeability based on the Molecular diffusion mechanism (PM) through the transport of the gas molecules through the MWCNTs fillers based MMMs can be described as follows (Eq. 20).

𝑅𝑀 =

𝑃𝑀 =

3

𝐿 𝑃𝑀

𝐾 𝐵𝑇

(19)

0.5

( )

(20)

8𝑅𝑇𝜎2𝑛 𝜋𝑀

Where σ and n denote the kinetic diameter of the gas molecule (m) and number density (1/m3) of gas which is supposed to be transported through the MWCNTs fillers based MMMs, respectively. If the diameter of the MWCNTs is found to be very larger than the mean free path, the Viscous flow mechanism will be dominant. The resistance on the basis of the Viscous flow mechanism (RV) (Eq. 21) and the permeation of gas on the basis of the Viscous flow mechanism (PV) through the transport of the gas molecules through the MWCNTs fillers based MMMs can be described in (Eq. 22). The value of PV (Eq. 32) is estimated based on the Hagen-Poiseuille equation.

𝑅𝑉 =

𝐿 𝑃𝑉

(21)

30

𝑃𝑉 =

𝑟𝑁𝑇2𝑝

(22)

8𝜇𝑅𝑇

Where p and µ denote the feed pressure of the gas (pascal) and viscosity of gas (Pa.s) which is supposed to be transported through the MWCNTs fillers based MMMs, respectively. By substituting the values of from (Eq. 17) to (Eq. 22) into the dusty gas model (Eq. 10), the overall permeability of the gas through the MWCNTs can be estimated as follows (Eq. 23) [57].

𝑃𝑁𝑇 =

𝑃𝐾 𝑃𝑚 + 𝑃𝑉 𝑃𝑚 + 𝑃𝑉 𝑃𝐾

(23)

𝑃𝐾 +𝑃𝑚

Additionally, the existence of incompatibility between the MWCNTs fillers and the PSF polymer matrix leads to the formation of the interfacial voids which must be accounted for their influence on the overall gas permeability of the MMMs. Therefore, the permeability of the gas through the interfacial layer (Pint) (Eq. 26) can be predicted by taking the product of the sorption and diffusion coefficients in accordance with the Knudsen diffusion mechanism [3]. The gas sorption coefficient (Sint) (Eq. 24) and diffusion coefficient (Dint) (Eq. 25) are given as follows [79].

𝑆𝑖𝑛𝑡 =

𝐷𝑖𝑛𝑡 =

1 𝑅𝑇

(24)

(

32𝑅𝑇𝑙𝑖𝑛𝑡2 9𝜋𝑀

0.5

)

(25)

2 1 32𝑅𝑇𝑙𝑖𝑛𝑡 𝑃𝑖𝑛𝑡 = 𝑆𝑖𝑛𝑡 × 𝐷𝑖𝑛𝑡 = 𝑅𝑇 9𝜋𝑀

(

)

0.5

31

(26)

Where lint is the interfacial layer thickness (m) of MWCNTs/polymer matrix in the MMMs. The interfacial layer thickness is an adjustable parameter that can be estimated by fitting the experimental gas permeability data of MWCNTs fillers based MMMs into the mKJN model developed in this work. The methodology to evaluate the performance of the developed model is illustrated in (Fig. 7). Analysis of Existing Models: Prior to verifying the performance of the proposed model i.e. mKJN model, it is necessary to discuss the performance evaluation of the existing models i.e. KJN model and the HC model. The performance of the KJN model and HC model for the permeation of CO2, CH4, and N2 through the MMMs based on four different types of fillers i.e. raw-MWCNTs, OH-MWCNTs, amineMWCNTs, and DES-MWCNTs into the PSF polymer matrix are illustrated in (Fig. 8-10), respectively. The KJN model performance was evaluated by considering the random distribution of the tubular fillers particles i.e. MWCNTs into the polymer composed of PSf polymer. It can be seen that in all cases, the KJN model failed to predict the overall gas permeation of the MMMs for CH4, N2, and CO2. This behavior of the KJN model i.e. failed to predict the relative permeability of the CO2, CH4, and N2 through the MMMs can be directed to the fact that in resistance-based prediction model including the KJN model, the permeability is strongly influenced by the resistance of the tubular fillers particles. In this case, such as MWCNTs, if tubular fillers have higher permeability then the PSF polymer matrix, the KJN model failed to predict the further permeability enhancement for the permeation of CO2, CH4, and N2 through the MMMs [46].

32

Step-I

Step-II

Mean Free Path (λ) Sorption Coefficient (Sint) Knudsen Diffusion (PK) (λ > dNT)

Molecular Diffusion (PM) (λ < dNT)

Viscous Flow Mechanism (PV) (λ <<< dNT)

Diffusion Coefficient (Dint)

Permeability of Interfacial Layer (Pint)

Permeability of MWCNTs (PNT)

Step-III

Permeability of PseudoDispersed Phase (Pps)

Step-IV

Modified Kang-JonesNair (mKJN) Model

Thickness of Interfacial Layer (lint) (Minimum Value of %AARE)

Fig. 7. Flowchart for the evaluation of the proposed model for the determination of the thickness of the interfacial layer. 33

Therefore, the KJN model demonstrated the prediction behavior of the permeabilities of CO2, CH4, and N2 through the MMMs in decreasing trend with an increase in the weight fraction of the fillers particles. The KJN model failed behavior of the permeation of CO2, CH4, and N2 through the MMMs can also be directed to the fact that the KJN model prediction is based on the continuous polymer matrix phase which means that the role of the tubular fillers is almost ignored. Therefore, with a rise in the loadings of filler the KJN model demonstrated that the overall gas permeation behavior of CH4, CO2, and N2 through the MMMs decreased which means that increase in the proportion of the MWCNTs which is being neglected by the KJN model also reduces the overall permeability performance of the PSF polymer matrix which is accounted by the KJN model. Therefore, a decreasing prediction trend with an increase in filler loading can be observed by the KJN model. However, it is an admitted fact that the interfacial layer between the tubular particle i.e. MWNCTs and the polymer matrix i.e. PSF plays a significant role to influence the over permeabilities of the CO2, CH4, and N2 through the MMMs. Similarly, in the case of the HC model performance for the permeation of the CO2, CH4, and N2 through the MMMs it underestimates the prediction results. Although, it demonstrated the increasing trend of the permeability prediction of the permeation of CO2, CH4, and N2 through the MMMs the predicted values of the permeabilities are still very low [1]. Actually, both models i.e. KJN model and the HC model have been developed on the basis of the ideal assumptions which means that there should be ideal contact between the filler particles and the polymer matrix which means these two models simply neglect the influence of the interfacial characteristics. However, in real conditions, due to the different filler particles and polymer matrix exhibiting different surface chemistry lead to the formation of the interfacial voids between the filler particles and polymer matrix [6]. In other words, these models have been developed on the basis of ideal conditions which means that these models accounted two-phase

34

system including the continuous phase i.e. polymer matrix and the dispersed phase i.e. fillers particles. However, in real conditions, the influence of the interfacial voids in between the filler particles and the polymer matrix on the overall gas permeability of the CO2, CH4, and N2 through the MMMs cannot be neglected and should be accounted. Therefore, in this work, to address this issue, the KJN model has been modified to the three-phase system which include the continuous phase i.e. polymer matrix, the dispersed phase i.e. fillers particles, and the interfacial layers existed between the fillers particles and the matrix composed of PSf polymer. The third phase i.e. interfacial layers existed between the fillers particles and the polymer matrix also known as the pseudo-dispersed phase which means that the tubular fillers particles i.e. MWCNTs dispersed into the matrix composed of PSf polymer surrounded by the interfacial voids [80, 81]. The comparison of the KJN model and HC model with respect to the proposed mKJN model are tabulated in (Table 2) on the basis of %AARE. Verification of Proposed Model: To investigate the proposed model i.e. mKJN model, the experimentation has been performed for the permeation of the CO2, CH4, and N2 through the MMMs. The MMMs were composed of the four different types of fillers particles including the raw-MWCNTs, OH-MWCNTs, amineMWCNTs, and DES-MWCNTs into the PSF polymer matrix. The results are illustrated in (Fig. 8-10) and comparison with the existing models i.e. KJN model and the HC model on the basis of the %AARE is tabulated in (Table 3). To evaluate the modified model proposed in this work i.e. mKJN model, the average absolute relative errors (%AARE) between the experimental data points of the permeation of CO2, CH4, and N2 through the MMMs and the predicted data points acquired by the mKJN model are found to be in better agreement comparatively to the existing models i.e. HC model and KJN model. From the findings (Table 3), it can be observed that the for all MMMs 35

i.e. raw-MWCNTs, OH-MWCNTs, amine-MWCNTs, and DES-MWCNTs into the matrix composed of PSf polymer, the value of %AARE for mKJN for the permeation of CO2, CH4, and N2 through these MMMs are found to be within the range of 1.2588% to 10.8046%, while, for HC model and KJN model, these values are found to be within the range of the 42.7096% to 97.9371% and 52.4228% to 265.5154%, respectively. The results are consistent with the published literature [1]. Again, these high values of %AARE for KJN model and the HC model compared to the modified model i.e. mKJN model can be directed to the fact that the KJN model and HC model are developed on the concept of the ideal two-phase system i.e. continuous phase i.e. polymer matrix and the dispersed phase i.e. fillers particles. However, the proposed model i.e. mKJN model exhibited remarkably lower values of %AARE for all MMMs which can be attributed the fact that it has been developed on the basis of three-phase system which means the continuous phase i.e. polymer matrix, the dispersed phase i.e. fillers particles, and the interfacial layers existed between the fillers particles and the matrix composed of PSf polymer. Hence, the better performance of the mKJN model as compared to the KJN model and HC model can also be directed to the fact that mKJN model accounts for the influence of the interfacial layer between the filler particles and the polymer matrix on the over gas permeabilities through the MMMs while the other two models i.e. KJN model and HC model simply neglect the impact of the interfacial layer. Therefore, based on the results presented here in this work, it can be concluded that the proposed model mKJN model can predict the permeability behavior of the CH4, CO2, and N2 through these MMMs composed of tubular fillers particles more accurately comparatively to the other two existing models i.e. HC model and KJN model. In addition to the precise prediction of the gas permeability behavior by the mKJN model, a new term has been introduced in this modified model i.e. mKJN model which is known as the thickness of the interfacial layer (pm). This term i.e. thickness of the interfacial

36

layer (pm) provides a new directive for the exploration of the role of the interface between the filler particles i.e. MWCNTs and the polymer matrix i.e. PSF, especially, in this work. The values of the thickness of the interfacial layer for the permeation of CH4, CO2, and N2 through these MMMs composed of tubular fillers including the raw-MWCNTs, OH-MWCNTs, amineMWCNTs, and DES-MWCNTs are tabulated in (Table 4). Surprisingly, it can be observed that the values of the thickness of the interfacial layer are found to be similar for all gases through specific MMMs. For the raw-MWCNTs-PSF based MMMs the values of the thickness of the interfacial layer were found to be 6.5841 µm, 10.2867 µm, and 9.6541 µm for the permeation of CO2, CH4, and N2 through these MMMs, respectively. For the OH-MWCNTs-PSF based MMMs the values of the thickness of the interfacial layer were found to be 4.9076 µm, 6.5047 µm, and 6.4031 µm for the permeation of CO2, CH4, and N2 through these MMMs, respectively. More interestingly, for the amine-MWCNTs-PSF and DES-MWCNTs-PSF, for all gases, i.e. CO2, CH4, and N2, the values of the thickness of the interfacial layer were found to be similar and that was 3.7754 µm and 3.2864 µm, respectively. In the case of raw-MWCNTs-PSF and OH-MWCNTsPSF, the small difference in the values of the thickness of the interfacial layer for three different gases i.e. CO2, CH4, and N2 can be directed to the fact of heterogeneity of the experimental data points during the curve fitting procedure. However, for the case of amine-MWCNTs-PSF and DES-MWCNTs-PSF, the values of the thickness of the interfacial layer CO2, CH4, and N2 through these MMMs were found to be exactly similar which can be directed to the fact that the thickness of the interfacial layer is one of the unique property of the interface of the tubular fillers particles i.e. MWCNTs and the polymer matrix i.e. PSF and this property is independent of the nature of the gas molecules which are to be penetrated through the respective MMMs. Furthermore, it can be observed from the values of the thickness of the interfacial layer that it decreased after the

37

surface functionalization of the filler particles. This can be directed to the fact that after the surface functionalization of the fillers particles, the strength of the interfacial interaction between the tubular fillers particles i.e. MWCNTs and the polymer matrix i.e. PSF are enhanced which leads to the reduction in the thickness of the interfacial layer. To explore the role of the thickness of the interfacial layer on the over gas permeabilities of the MMMs, the decrease in the thickness of the interfacial layer after the surface functionalization of the fillers particles is another evidence for the validity of the modified model i.e. mKJN model proposed in this work. These findings are found to be higher in agreement with the reported work [57]. The comparison of mKJN model with reported mHC model on the basis of %AARE for CO2 permeation through different MMMs are provided in (Table 5).

38

CO2 Permeability (Barrer)

70

(a)

50 40 30 20 10 0 0.01 70

CO2 Permeability (Barrer)

Experimental mKJN Model KJN Model HC Model

60

0.04

0.07

0.1 0.13 0.16 Filler Fraction

0.19

0.22

0.25

Experimental mKJN Model KJN Model HC Model

(b)

60 50 40 30 20 10 0 0.01

0.04

0.07

0.1 0.13 0.16 Filler Fraction

39

0.19

0.22

0.25

CO2 Permeability (Barrer)

110 (c) 100 90 80 70 60 50 40 30 20 10 0 0.01 0.04

0.07

0.1 0.13 0.16 Filler Fraction

0.19

0.22

0.25

Experimental mKJN Model KJN Model HC Model

CO2 Permeability (Barrer)

1000 (d) 900 800 700 600 500 400 300 200 100 0 0.01 0.04

Experimental mKJN Model KJN Model HC Model

0.07

0.1 0.13 0.16 Filler Fraction

0.19

0.22

0.25

Fig. 8. Analysis of modified KJN model in comparison with the KJN model and HC model for CO2 permeation through MMMs; (a): raw-MWCNTs-PSF-MMMs, (b): OH-MWCNTs-PSFMMMs, (c): amine-MWCNTs-PSF-MMMs, and (d): DES-MWCNTs-PSF-MMMs.

40

CH4 Permeability (Barrer)

3 2.5 2 1.5 1 0.5

0 0.01

3

CH4 Permeability (Barrer)

Experimental mKJN Model KJN Model HC Model

(a)

0.04

0.07

0.1 0.13 0.16 Filler Fraction

0.19

0.22

0.25

Experimental mKJN Model KJN Model HC Model

(b)

2.5 2 1.5 1 0.5 0 0.01

0.04

0.07

0.1 0.13 0.16 Filler Fraction

41

0.19

0.22

0.25

CH4 Permeability (Barrer)

3.5

2.5 2 1.5 1 0.5 0 0.01

CH4 Permeability (Barrer)

Experimental mKJN Model KJN Model HC Model

(c)

3

0.04

10 (d) 9 8 7 6 5 4 3 2 1 0 0.01 0.04

0.07

0.1 0.13 0.16 Filler Fraction

0.19

0.22

0.25

Experimental mKJN Model KJN Model HC Model

0.07

0.1 0.13 0.16 Filler Fraction

0.19

0.22

0.25

Fig. 9. Analysis of modified KJN model in comparison with the KJN model and HC model for CH4 permeation through MMMs; (a): raw-MWCNTs-PSF-MMMs, (b): OH-MWCNTs-PSFMMMs, (c): amine-MWCNTs-PSF-MMMs, and (d): DES-MWCNTs-PSF-MMMs.

42

N2 Permeability (Barrer)

3 2.5 2 1.5 1 0.5

0 0.01

3

N2 Permeability (Barrer)

Experimental mKJN Model KJN Model HC Model

(a)

0.04

0.07

0.1 0.13 0.16 Filler Fraction

(b)

0.19

0.22

0.25

Experimental mKJN Model KJN Model HC Model

2.5 2 1.5 1 0.5 0 0.01

0.04

0.07

0.1 0.13 0.16 Filler Fraction

43

0.19

0.22

0.25

N2 Permeability (Barrer)

3 2.5 2 1.5 1 0.5

0 0.01

N2 Permeability (Barrer)

Experimental mKJN Model KJN Model HC Model

(c)

0.04

10 (d) 9 8 7 6 5 4 3 2 1 0 0.01 0.04

0.07

0.1 0.13 0.16 Filler Fraction

0.19

0.22

0.25

Experimental mKJN Model KJN Model HC Model

0.07

0.1 0.13 0.16 Filler Fraction

0.19

0.22

0.25

Fig. 10. Analysis of modified KJN model in comparison with the KJN model and HC model for N2 permeation through MMMs; (a): raw-MWCNTs-PSF-MMMs, (b): OH-MWCNTs-PSFMMMs, (c): amine-MWCNTs-PSF-MMMs, and (d): DES-MWCNTs-PSF-MMMs.

44

Table 3. Comparison of mKJN model with existing HC and KJN model on the basis of %AARE for CO2, CH4, and N2 permeation through different MMMs. MMMs

Gases

Raw-MWCNTs-PSF

OH-MWCNTs-PSF

Amine-MWCNTs-PSF

DES-MWCNTs-PSF

%AARE values HC model

KJN model

mKJN model

CO2

56.0700

197.9367

10.8046

CH4

42.7096

265.5154

4.3125

N2

45.6134

253.8221

3.5559

CO2

77.4333

93.8326

1.6751

CH4

61.7930

165.5442

2.8839

N2

63.2750

159.1622

1.2588

CO2

85.0778

79.7288

7.5414

CH4

84.7884

61.1815

7.6897

N2

85.0620

61.8976

7.3849

CO2

97.9371

84.0714

4.1890

CH4

93.7227

52.4228

6.0798

N2

93.0962

54.0433

6.7383

Table 4. The thickness of the interfacial layer estimated by the mKJN model for CO2, CH4, and N2 permeation through different MMMs. MMMs

Interfacial layer thickness (µm) CO2

45

CH4

N2

Raw-MWCNTs-PSF

6.8541

10.2867

9.6541

OH-MWCNTs-PSF

4.9076

6.5047

6.4031

Amine-MWCNTs-PSF

3.7754

3.7754

3.7754

DES-MWCNTs-PSF

3.2864

3.2864

3.2864

Table 5. Comparison of mKJN model with reported mHC model on the basis of %AARE for CO2 permeation through different MMMs. MMMs

Gases

%AARE values Ref. mKJN model

mHC model

Raw-MWCNTs-PSF

CO2

10.8046

This work

OH-MWCNTs-PSF

CO2

1.6751

This work

Amine-MWCNTs-PSF

CO2

7.5414

This work

DES-MWCNTs-PSF

CO2

4.1890

This work

HNT-NH2/PI

CO2

8.05

[32]

HNT-PANi/PSf

CO2

7.87

[33]

MWCNTs-COOH/PI

CO2

9.84

[36]

Conclusions: In summary, we proposed a new theoretical model by modifying the existing KJN model which was developed to explore the gas permeation behavior through MMMs by accounting two-phase systems i.e. continuous phase (polymer matrix) and the dispersed phase (MWCNTs fillers particles). However, these KJN and HC models ignored the influence of the interfacial layer. A 46

new strategy has been proposed for the development of a new model based on the KJN model to predict the gas permeability behavior through MMMs more precisely by incorporating the influence of their most significant phase which is known as the pseudo-dispersed phase. The pseudo-dispersed phase accounts for the interfacial layer influence on the overall gas permeability. The new proposed theoretical model is able to estimate the gas permeability behavior with significantly reduced average absolute relative error (%AARE) of 1.26% compared to 52.43% and 42.71% for unmodified KJN and HC models, respectively. Furthermore, the mKJN model demonstrated that the interfacial layer thickness is a unique characteristic and is independent of the penetrant gas molecules which may be influenced by the heterogeneity in the experimental conditions. The cross-sectional morphology and mKJN model revealed that the surface functionalization of the fillers may lead to the enhancement in the interactive forces between the filler-polymer interface which thus reduced interfacial layer thickness. Acknowledgment: The authors are thankful to COMSATS University Islamabad, Lahore Campus, Higher Education Commission (HEC) financial support under NRPU Project #3957 and NRPU Project # 998. The authors would like to acknowledge the Yayasan-UTP (YUTP-0153AA-H01) research grant, Department of Chemical Engineering at Universiti Teknologi PETRONAS (UTP), Malaysia, King Khalid University, Saudi Arabia (Deanship of Scientific Research) for financial support through the Research Groups Project under the grant number (R.G.P.2/59/40).

47

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“The authors declare that there is no conflict of interest regarding the publication of this paper.”

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Declaration of interests

☐ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

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It is stated that the corresponding author is responsible for all the descriptions in the manuscript are accurate and agreed by all authors.

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Research Highlights: 

Raw- and Functionalized MWCNTs fillers and PSF polymer matrix based MMMs were synthesized, characterized.



A new theoretically modified KJN model has been proposed explore the three-phase system of gas transport through MMMs.



The mKJN model precisely predict the gas transport behavior by accounting the influence of interfacial layer.



The mKJN model revealed that interfacial layer is independent of penetrant molecules and reduced with the functionalization of fillers.

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