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Improved Hydrogen Separation Using Hybrid Membrane Composed of Nanodiamonds and P84 Copolyimide Alexandra Pulyalina 1, *, Galina Polotskaya 1,2 , Valeriia Rostovtseva 1 , Zbynek Pientka 3 and Alexander Toikka 1 ID 1 2 3

*

Institute of Chemistry, Saint Petersburg State University, Universitetskiy pr. 26, 198504 Saint Petersburg, Russia; [email protected] (G.P.); [email protected] (V.R.); [email protected] (A.T.) Institute of Macromolecular Compounds, Russian Academy of Sciences, Bolshoy pr. 31, 199004 Saint Petersburg, Russia Institute of Macromolecular Chemistry, Czech Academy of Sciences, Heyrovsky Sq. 2, 16206 Prague, Czech Republic; [email protected] Correspondence: [email protected]; Tel.: +78-124-284-805

Received: 22 June 2018; Accepted: 23 July 2018; Published: 27 July 2018

 

Abstract: Membrane gas separation is a prospective technology for hydrogen separation from various refinery and petrochemical process streams. To improve efficiency of gas separation, a novel hybrid membrane consisting of nanodiamonds and P84 copolyimide is developed. The particularities of the hybrid membrane structure, physicochemical, and gas transport properties were studied by comparison with that of pure P84 membrane. The gas permeability of H2 , CO2 , and CH4 through the hybrid membrane is lower than through the unmodified membrane, whereas ideal selectivity in separation of H2 /CO2 , H2 /CH4 , and CO2 /CH4 gas pairs is higher for the hybrid membrane. Correlation analysis of diffusion and solubility coefficients confirms the reliability of the gas permeability results. The position of P84/ND membrane is among the most selective membranes on the Robeson diagram for H2 /CH4 gas pair. Keywords: membrane; gas separation; nanomodifiers; hydrogen separation; methane steam reforming

1. Introduction Membrane technologies provide a number of advantages in terms of environmental requirements, high energy efficiency, and low capital and operating cost over their conventional counterpart technologies [1]. Membrane gas separation has been successfully developed and is widely used in chemical and petrochemical plants. Separation of hydrogen from its mixtures with nitrogen or hydrocarbons, nitrogen purification, and carbon dioxide removal from natural gas are recognized as the most significant industrial applications of membranes [2]. Hydrogen separation and purification is among the global problems; hydrogen is considered to be the most promising source of alternative energy that could replace fossil fuel. Hydrogen is a “green” fuel, since the only product of its combustion is water, which does not damage the environment [3]. Hydrogen is commonly produced by steam methane reforming [4]: CH4 + H2 O ↔ CO + 3H2 CO + H2 O ↔ CO2 + H2

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Hydrogen is purified to satisfy the various purity requirements for different applications [5]: high purity < 99.99% is required in fuel cells, ~70–80% purity is sufficient for hydrocracking. Hydrogen can be enriched by various methods such as pressure-induced adsorption [6], cryogenic distillation [7], and membrane separation [8]. Membrane gas separation is a promising technology for hydrogen purification [9]. The process of selective separation is based on the different permeability of membranes for individual components of the gas mixture. The search for new membrane materials with improved transport properties is one of the priority scientific tasks. Among various membrane polymers, aromatic polyimides and their derivatives are of undoubted interest due to their unique gas separation properties, which are combined with high chemical and thermal stability [10–12]. The problem of the hydrogen separation from CO2 and CH4 has been studied using membranes based on aromatic polyimides [13,14], their mixtures with polymers of another nature [15], and the products of polyimide chemical modification with cross-linking agents [16–20]. It has recently been found that gas separation properties can be improved by development of hybrid membranes consisting of nanoparticles dispersed in a polymer matrix: zeolites [21], carbon molecular sieves [22], carbon nanotubes [23], graphene [24], others [25] or nanoparticles of a different nature [26–28]. Nanodiamonds (ND) or ultradispersed diamonds are specific carbon particles produced by detonation synthesis using explosive mixtures [29,30]. Subsequent chemical purification of ND using strong oxidizing agents (sulfuric acid, oleum, nitric acid, etc.) completes the formation of the ND particles. ND is a compound particle with a three-layer structure including (i) a diamond core (4–6 nm), in which up to 70–90 wt% C atoms are located; (ii) a transition carbon shell, an intermediate X-ray amorphous layer (0.4–1.0 nm), where 10–30% C atoms are located; and (iii) a surface layer containing (in addition to C) N, O, H atoms forming functional groups. ND particles attract special attention due to the chemical stability of their diamond core and the surface activity given by various functional groups (-OH, -COOH, =C=O, etc.) that appear during the chemical purification of detonation ND using strong acids. ND have already found application as a component of mixed matrix membranes for the solving of different industrial problems. Nanocomposite membranes based on poly(vinylidene fluoride) modified with ND have been applied to water desalination by distillation [31]. The polyphenylene-iso-phthalamide membrane containing ND in the matrix has been successfully used in pervaporation [32] and gas separation [33]. ND particles have been selected as an inorganic modifier of poly(phenylene oxide) membranes for gas separation [34]. In the present work, ND were chosen as the filler of the P84 copolyimide matrix to develop novel hybrid membrane. Figure 1 shows the structure of P84 copolyimide and nanodiamonds. The P84 copolyimide {BTDA-TDI/MDI, co-polyimide of 3,30 ,4,40 -benzophenone tetracarboxylic dianhydride (BTDA) and 80% toluene diisocyanate (TDI) + 20% methylene diphenyl diisocyanate (MDI)} is a commercially available polymer that demonstrates good mechanical properties, chemical resistance, and low hydrophilicity; it has already been studied as a membrane material for ultrafiltration [35], nanofiltration [36], gas separation [37], and pervaporation [38]. The aim of the present work is to obtain the hybrid membrane based on P84 copolyimide modified with ND particles, to study its structure, physicochemical and gas transport properties in hydrogen separation from components of steam methane reforming.

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Figure 1. 1. Structure Structure of of nanodiamonds nanodiamondsand andP84 P84copolyimide. copolyimide. Figure

2. Materials Materials and and Methods Methods 2. 2.1. Materials Materials 2.1. TheP84 P84 copolyimide was purchased HPGmbH Polymer GmbH (Lenzing, Austria). The copolyimide was purchased from HPfrom Polymer (Lenzing, Austria). Nanodiamonds 3 3 Nanodiamonds with density 3.0 g/cm by were produced by detonation synthesis and provided by with density 3.0 g/cm were produced detonation synthesis and provided by SCTB ‘Technolog’ SCTB Petersburg, ‘Technolog’ (Saint N,N-Dimethylacetamide Petersburg Russia). N,N-Dimethylacetamide by (Saint Russia). (DMA) manufactured by(DMA) Vekton manufactured (Saint Petersburg, Vekton was (Saint Petersburg, was used purification. as solvent without further purification. Russia) used as solventRussia) without further 2.2. 2.2. P84/ND P84/ND Composite Composite Preparation Preparation The The P84/ND P84/ND composite was obtained by thoroughly mixing powders of 99 wt% P84 and and 11 wt% wt% ND ND in in agate agate mortar mortar for for 11 h. h. Thereafter, Thereafter, the the composite composite powder powder was was dissolved dissolved in in DMA DMA to to obtain obtain aa solid solid phase phase concentration concentration of of 88 wt%. wt%. To To achieve achieve complete complete homogenization homogenization of of the the composite composite solution, solution, ◦ C for 40 min were intensive stirring with a mechanical stirrer for 1 h and then ultrasonic bath at 40 intensive stirring with a mechanical stirrer for 1 h and then ultrasonic bath at 40 °C for 40 min were used. used. After After that, that, the the P84/ND P84/ND composite solution was filtered to remove any mechanical impurities. 2.3. 2.3. Membrane Membrane Formation Formation Dense Dense membranes membranes ~30 ~30 µm µm thick thick were were prepared prepared by by casting casting the the 88 wt% wt% polymer polymer solution solution in in DMA DMA ◦ C for 48 h; the membranes were onto a glass plate. The solvent was removed by evaporation at 40 onto a glass plate. The solvent was removed by evaporation at 40 °C for 48 h; the membranes were ◦ C for about 2 weeks in order to achieve separated and dried in ainvacuum ovenoven at 60 at separatedfrom fromthe thesupport support and dried a vacuum 60 °C for about 2 weeks in order to constant weight. weight. achieve constant 2.4. Characterization of P84 and P84/ND 2.4. Characterization of P84 and P84/ND A multimode Atomic Force Microscope Nanoscope IIIa (Digital Instruments, Santa Barbara, CA, A multimode Atomic Force Microscope Nanoscope IIIa (Digital Instruments, Santa Barbara, USA) was used to observe the nanoparticles in situ in tapping mode using OTESPA silicon cantilevers CA, USA) was used to observe the nanoparticles in situ in tapping mode using OTESPA silicon (Veeco Instruments, Dourdan, France) with a radius of 5 nm and oscillating at 300 kHz. cantilevers (Veeco Instruments, Dourdan, France) with a radius of 5 nm and oscillating at 300 kHz. For investigating the membrane cross-sectional morphology, the membranes were cracked in For investigating the membrane cross-sectional morphology, the membranes were cracked in liquid nitrogen, coated with carbon, and observed using Zeiss Merlin scanning electron microscope liquid nitrogen, coated with carbon, and observed using Zeiss Merlin scanning electron microscope (Zeiss AG, Oberkochen, Germany). (Zeiss AG, Oberkochen, Germany). The membrane density, ρ, was estimated by the flotation method in a solution of isopropanolThe membrane density, ρ, was estimated by the flotation method in a solution of carbon tetrachloride at 25 ◦ C [ρ(iPrOH) = 0.786 g/cm3 , ρ(CCl4 ) = 1.594 g/cm3 ]. isopropanol-carbon tetrachloride at 25 °C [ρ(iPrOH) = 0.786 g/cm3, ρ(СCl4) = 1.594 g/cm3]. Fractional free volume of P84 membrane, FFV, was calculated by the Bondy method [39]: Fractional free volume of P84 membrane, FFV, was calculated by the Bondy method [39]: FFV = V00 -−1.3 1.3V FFV = ((V Vww) /V /V00

(1) (1)

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where V 0 = 1/ρP84 is the polymer specific volume and Vw is the van der Waals volume of P84 estimated via Askadskii’s group contribution method. Fractional free volume of P84/ND composite, FFVc , was calculated by the following equation [40]: FFVc = 1 − ρc (1 −

wt ND % 1 wt ND % )·(1 − FFV)ρ P84 −1 − ρC ρ− ND 100 100

(2)

where ρP84 , ρND , and ρC are the densities of polymer, nanodiamonds, and composites, respectively, and wtND is the weight fraction of the ND modifier in the polymer matrix. Water contact angles of investigated membranes were measured by the sessile drop method on the Drop Shape Analyzer DSA 10 (KRÜSS GmbH, Hamburg, Germany) at 20 ◦ C and atmospheric pressure. Thermogravimetric analysis (TGA) was carried out using samples of 8–15 mg at a heating speed of 10 ◦ C/min in a nitrogen atmosphere. A TG 209 F3 Iris thermo-microbalance (Netzsch, Selb, Germany) was used for the analysis. 2.5. Gas Permeation Measurement Gas permeability of membranes was measured using single gases with high purity (H2 , CO2 , CH4 ) by the barometric technique using a laboratory high-vacuum apparatus with a static permeation cell with an effective area of 5.25 cm2 at 30 ◦ C. The membrane sample was placed and sealed in a module which was evacuated. At the beginning of the permeation experiment, the gas under constant pressure, p (150 kPa), was brought into the feed part of the permeation cell. The permeability was determined from the increase of pressure ∆pp in a calibrated volume Vp of the product part of the cell per the time ∆t interval during steady-state permeation. The gas permeability coefficient, Pexp , was estimated by the following equation [41]: Pexp =

∆p p Vp ·l 1 · · ∆t S· p RT

(3)

where l is a membrane thickness, S is its area, T is the absolute temperature, and R is the gas constant. The permeability coefficient P was expressed in Barrers (1 Barrer = 10−10 cm3 (STP)cm/(cm2 s cmHg)). Each experiment was repeated 3–5 times; several membranes of approximately the same thickness and prepared under the same conditions were used. The relative error of permeability value was 1–3%. The ideal selectivity of gas i relatively gas j, αi/j , was calculated with the accuracy ± 0.05 according to the following equation: P αi/j = i (4) Pj The diffusion coefficient, D, was calculated from the initial transient regime, which determines the x-intercept that is a time-lag, θ: l2 D= (5) 6θ The solubility coefficient, S, was calculated using the main gas transport equation: P = S·D Correlation analysis of gas transport parameters was performed using the data in Table 1.

(6)

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Table 1. Effective diameter, d, and the depth of the Lennard-Jones potential, (ε/k), for the gases under5 of 12 study [42]. Table 1. Effective diameter, d, and the Gas depth of d,the nmLennard-Jones (ε/k), K potential, (ε/k), for the gases under study [42].

H2 CO2 Gas CH4

0.210 0.302 d, nm 0.318

62.2 213.4 (ε/k), K 154.7

H2 0.210 62.2 CO2 0.302 213.4 The gas permeability coefficient for P84/ND film154.7 prepared by inclusion of non-porous CH4 0.318

impermeable filler in a continuous polymer matrix, PMaxwell, was calculated using Maxwell model [43]:

 film prepared  The gas permeability coefficient for P84/ND by inclusion of non-porous  1−ϕ  ND impermeable filler in a continuous polymer matrix, PMaxwell , was   calculated using Maxwell model [43]: = PP 84 PMaxwell (7)  1 + ϕ ND   ! 2  1−ϕ ND PMaxwell = PP84 (7) ϕ ND 1+ where PP84 is the gas permeability coefficient for pure polymer and ϕND is the volume fraction of 2 nanodiamonds. where PP84 is thefraction gas permeability coefficient for pure polymer and φND is the fraction The volume of the filler in the polymer matrix was estimated using thevolume equation: of nanodiamonds. wt ND % was estimated using the equation: The volume fraction of the fillerϕinNDthe = polymer matrix ρ (8) wt ND % + ND (1 − wND ) wtρND % P 84 ϕ ND = (8) ρ wt ND % + ρND (1 − w ND ) P84 where ρP84 and ρND are the density of P84 and ND, respectively, and wtND is the weight fraction of the filler polymer matrix. whereinρthe P84 and ρND are the density of P84 and ND, respectively, and wtND is the weight fraction of the

filler in the polymer matrix. 3. Results 3. Results Hybrid P84/ND membrane was obtained by dispersing 1 wt% ND particles in a matrix of P84 copolyimide. The certainty that allwas the obtained calculatedbyamount of ND usedND for particles the composite preparation Hybrid P84/ND membrane dispersing 1 wt% in a matrix of P84 is present in the membrane is guaranteed by the method of the composite preparation and copolyimide. The certainty that all the calculated amount of ND used for the composite preparation is subsequent hybrid membrane formation. Tomethod reveal of specific features preparation of the hybrid present in the membrane is guaranteed by the the composite and membrane, subsequent comparative research of P84/ND andspecific pure P84 membranes on structure, physical and transport hybrid membrane formation. To reveal features of the hybrid membrane, comparative research properties was performed. of P84/ND and pure P84 membranes on structure, physical and transport properties was performed. 3.1. Membrane Membrane Structure Structure 3.1. The change of of membrane structure with inclusion of ND in the P84 matrix was studied by SEM The and AFM. AFM. As As seen seen from the AFM images images of the membrane membrane surfaces surfaces in in Figure Figure 2, 2, the the inclusion inclusion of of ND ND and nanoparticles in to atomore complex structure in comparison to the smooth surface nanoparticles inthe themembrane membraneleads leads a more complex structure in comparison to the smooth of pure of P84. Namely, sphericalspherical fragmentsfragments are formed the surface of surface P84/NDofmembrane due to the surface pure P84. Namely, areonformed on the P84/ND membrane aggregation of macromolecules in solution in upon the addition of nanoparticles. Such a reliefSuch of the due to the aggregation of macromolecules solution upon the addition of nanoparticles. a modified membrane can be formed as a result of the spontaneous movement of ND and aggregates to relief of the modified membrane can be formed as a result of the spontaneous movement of ND and the surface to of the the surface hybrid membrane during the solvent evaporation. aggregates of the hybrid membrane during the solvent evaporation.

(а)

(b)

Figure 2. 2. AFM of membrane membrane surfaces: surfaces: (a) (a) Р84 and (b) (b) P84/ND. Р84/ND. Figure AFM images images of P84 and

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SEM was used to study the morphology of membrane cross-sections (Figure 3). The cross-section SEM was to study the 3a) morphology of membrane cross-sections (Figureof3). of unmodified P84 used membrane (Figure is homogenous and uniform. The structure theThe hybrid cross-section of unmodified P84 membrane (Figure 3a) is homogenous and uniform. The structure P84/ND membrane is more complicated. The fracture lines can be observed across the of entire the hybrid P84/ND membrane is more complicated. The fracture lines can be observed across the micrograph with the inclusion of ND in P84 matrix. This observation would typically be an indication entire micrograph with the inclusion of ND in P84 matrix. This observation would typically be an of reduced flexibility in the membrane. This fact can probably be explained by the aggregation of indication of reduced flexibility in the membrane. This fact can probably be explained by the macromolecules and the formation of a denser structure of the P84/ND membrane. The inclusion of aggregation of macromolecules and the formation of a denser structure of the Р84/ND membrane. ND The leads to less of flexibility membrane. However, theHowever, absence the of visible in the inclusion ND leadsin to the lesshybrid flexibility in the hybrid membrane. absencedefects of visible P84/ND cross-section indicates the good compatibility the nanoparticles with P84 andwith the stability defects in the Р84/ND cross-section indicates the goodof compatibility of the nanoparticles P84 of the hybrid membrane and the stability of the [25]. hybrid membrane [25]. 200 nm

200 nm

(a)

(b)

Figure 3. SEM micrographsofofthe themembrane membrane cross-section: (b)(b) P84/ND. Figure 3. SEM micrographs cross-section:(a)(a)P84, P84, P84/ND.

3.2. Physical Properties

3.2. Physical Properties

Table 2 lists some physical properties of the membranes under study: water contact angle, Table 2 lists some physical properties of the membranes under study: water contact angle, density, density, fractional free volume (FFV) and glass transition temperature (Tg). The water contact angle fractional free volume (FFV) and glass transition temperature (T ). The water contact angle on the on the surface of P84/ND membrane is decreased compared to the gP84 membrane; this points to the surface of P84/ND membraneof is the decreased compared the membrane; this points to the moderate moderate hydrophilization membrane surface to due toP84 modification with nanoparticles.

hydrophilization of the membrane surface due to modification with nanoparticles. Table 2. Physical properties of membranes.

Table 2. Physical properties of membranes. Membrane Contact Angle of Water, ° Membrane Contact Angle Water, ◦ P84 72.0 ±of0.5 P84 P84/ND P84/ND

72.0 ± ±0.5 70.0 0.4 70.0 ± 0.4

Density, g/cm3 3 Density, 1.323 ± g/cm 0.005 1.323 1.343±± 0.005 0.003 1.343 ± 0.003

Fractional Free Volume Tg, °C ◦ Fractional 0.082 Free ± 0.01Volume 344T±g ,3 C 0.082±±0.01 0.01 0.073 0.073 ± 0.01

346344 ± 3± 3 346 ± 3

According to Table 2, the membrane density increases when the ND particles are incorporated into the polymer matrix. Fractional free volume P84/ND membrane decreased with According to Table 2, the membrane densityofincreases when the is ND particlescompared are incorporated the pure P84. These facts indicate that the membrane structure becomes more compact after inclusion into the polymer matrix. Fractional free volume of P84/ND membrane is decreased comparedofwith the nanomodifier polymerthat matrix. Only a very weak increase of Tg value registeredafter as a result the pure P84. These into factsthe indicate the membrane structure becomes moreiscompact inclusion of the inclusion of ND into P84 matrix. of the nanomodifier into the polymer matrix. Only a very weak increase of T value is registered as a g

result of the inclusion of ND into P84 matrix. 3.3. Transport Properties

3.3. Transport Properties The selective separation of H2/CH4 and H2/CO2 is an important task due to the promising role of hydrogen as an energy source. The CO2/CH4 separation is an urgent problem, since the CO2 presence The selective separation of H2 /CH4 and H2 /CO2 is an important task due to the promising obstructs the development of oil and gas fields. Thus, industrial problems promote research on the roletransport of hydrogen as anofenergy source. The CO2 /CHfor is an urgent problem, since the CO2 4 separation properties P84 and P84/ND membranes the following gases: H2, CO 2, and CH4. Table 3 presence obstructs the development of oil and gas fields. Thus, problems promote research lists gas permeability and ideal selectivity in the separation of theindustrial industrially significant gas pairs. It on the transport properties of P84 and P84/ND membranes for the following gases: H , CO 2 2 was found that the gas permeability coefficients of the P84/ND membrane are lower than those of, and CH4pure . Table 3 lists ideal selectivity invalues the separation of theafter industrially P84. This gas fact permeability is determinedand by the decreasing FFV of membrane inclusion significant of ND 2), because depends directly onof thethe FFV value of membrane the membrane gas modifier pairs. It(Table was found that the the permeability gas permeability coefficients P84/ND are[1]. lower

than those of pure P84. This fact is determined by the decreasing FFV values of membrane after inclusion of ND modifier (Table 2), because the permeability depends directly on the FFV value of the membrane [1].

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Particular attention was paid to the ideal selectivity in the separation of three gas pairs: H2 /CO2 , H2 /CH4, and CO2 /CH4 . Our glassy polymer membranes were selectively permeable to H2 , which can be explained by the diffusion selectivity due to the smaller size of H2 molecules. In the case of the CO2 /CH4 pair, both diffusion and sorption factors facilitate CO2 selective permeability. Table 3 shows that values of the ideal selectivity of the P84/ND membrane are greater than those of pure P84 for all gas pairs. ND filler containing amino groups improves the interaction of the polymer matrix and the dispersed phase; this may lead to the rigid structure at the interface, which decreases the gas permeability but increases H2 /CO2 , H2 /CH4 , and CO2 /CH4 ideal selectivity. Table 3. Transport properties of membranes, 30 ◦ C. Membrane P84 P84/ND

Permeability, Barrer

Ideal Selectivity

H2

CO2

CH4

H2 /CO2

H2 /CH4

CO2 /CH4

8.0 6.7

2.25 1.61

0.040 0.022

3.6 4.1

200 310

56 75

To study the influence of the composition and structure changes in membranes based on P84 copolyimide on gas transport properties, analysis of diffusion and solubility coefficients is required, because they are components of the permeability coefficient according to Equation (6). Data on diffusion and solubility coefficients are presented in Table 4. Table 4. Diffusion coefficients and solubility coefficients for H2 , CO2 , and CH4 . Membrane P84 P84/ND

Diffusion Coefficient, D × 10−12 m/s

Solubility Coefficients, S × 10−3 mol/(m3 Pa)

H2

CO2

CH4

H2

CO2

CH4

44.7 7.3

0.18 0.10

0.034 0.018

0.31 0.06

5.0 4.0

1.0 0.4

With an increase of the gas molecule size (Table 1) the diffusion coefficients decrease. This is also reflected to the lowering of the gas permeability (Table 3). The decrease in both diffusion and sorption coefficients with the introduction of ND is probably connected with the strong interaction between nanoparticles and P84 and the formation of a denser structure around the modifiers. This fact will be discussed in more detail below Correlation analysis of the membrane transport parameters was carried out using the Teplyakov technique [42]. The first correlation for the polymer–gas system is the dependence of the gas diffusion coefficient on the effective diameter of gas molecules. Figure 4 shows this dependence in the logarithmic coordinates lgD = f (d2 ) for both membranes. The diffusion coefficients follow a linear correlation with gas molecule diameters, and there is no discernible difference between the trends for P84 and P84/ND membranes. This indicates that the diffusion during gas separation occurs mainly due to elements of the free volume. Another kind of correlation for the polymer–gas system is the dependence of the solubility coefficient on the depth of the Lennard-Jones potential (ε/k) of gases [42]. Figure 5 shows the dependence in logarithmic coordinates lgS = f (ε/k) for P84 and P84/ND membranes. The linear type of this correlation for both membranes confirms the reliability of the experimental results. Numerous models have been developed to describe the effect of modifiers on permeability in gas separation [44–47]. One of the most widely known is Maxwell’s model, which was used to calculate permeability coefficients of H2 , CO2 , and CH4 for the P84/ND membrane and to estimate the deviation of experimental permeability coefficients Pexp from PMaxwell . Figure 6 shows the relative permeability deviation for the P84/ND membrane, which is located in the negative region, since the experimental permeability of all gases is less than the calculated one. The reason is apparently associated with the stronger interaction of nanoparticles with a polymer matrix, which was not accounted for in the model.

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-10 -10 -10

-11 -11 -11

LgD LgD LgD

P84 P84 P84/ND P84 P84/ND P84/ND

-12 -12 -12

-13 -13 -13

H2 H H22 CO2 CO CO22

-14 0.04 -14 -140.04 0.04

0.05 0.05 0.05

0.06 0.06 0.06

0.07 0.072 0.07 d,

0.08 0.08 2 nm0.08

d2, nm2 d2, nm2

0.09 0.09 0.09

CH4 CH CH44

0.10 0.10 0.10

0.11 0.11 0.11

Figure Dependence of of diffusion diffusion coefficient coefficient on effective gas forfor P84 and Figure 4. 4. on effectivediameter diameterof gasmolecules molecules P84 and Figure 4.Dependence Dependence of of diffusion diffusion coefficient coefficient on on effective effective diameter ofofgas gas molecules for P84 P84 and Figure 4. Dependence diameter of molecules for and P84/ND membranes. P84/ND membranes. P84/ND membranes. P84/ND membranes. -2.0 -2.0 -2.0

P84 P84 P84/ND P84 P84/ND P84/ND

-2.5 -2.5 -2.5

LgS LgS LgS

-3.0 -3.0 -3.0 -3.5 -3.5 -3.5 -4.0 -4.0 -4.0

H2 H -4.5 H2 -4.5 60 2 80 -4.5

60 60

80 80

CH4 CH CH44 100 100 100

120 120 120

140 140

160 160

140Κ 160 ε/κ, ε/κ, Κ ε/κ, Κ

CO2 CO CO22 180 180 180

200 200 200

220 220 220

Figure 5. Dependence of solubility coefficients on the depth of the Lennard-Jones potential of gases Figure 5. Dependence Dependence of solubility coefficientsonon onthe thedepth depthofof ofthe theLennard-Jones Lennard-Jonespotential potentialofof ofgases gasesfor Figure 5. 5. Dependence ofof solubility coefficients Figure solubility coefficients the depth the Lennard-Jones potential gases for P84 and P84/ND membranes. for P84 and P84/ND membranes. P84 membranes. forand P84P84/ND and P84/ND membranes. CH4 CH CH44

(P-Р -РМaxwell )/РМaxwell (P(P )/Р -Р )/Р exp Мaxwell expexp Мaxwell Мaxwell Мaxwell

-0.5 -0.5 -0.5 -0.4 -0.4 -0.4

CO2 CO CO22

-0.3 -0.3 -0.3 -0.2 -0.2 -0.2

H2 H H22

-0.1 -0.1 -0.1 0.0 0.0 0.0

Figure 6. Relative deviation of gas permeability coefficients Pexp from PMaxwell for the P84/ND membrane. Figure 6. 6. Relative deviation deviation of of gas gas permeability permeability coefficients coefficients P Pexp exp from PMaxwell for the P84/ND membrane. Figure from PMaxwellPfor P84/ND membrane. Figure 6. Relative Relative deviation of gas permeability coefficients from PMaxwell for the expthe P84/ND membrane. It should be noted that the transport properties of hybrid membranes containing nanoparticles

It should should be be noted noted that that the the transport transport properties properties of of hybrid hybrid membranes membranes containing containing nanoparticles nanoparticles It depend directly on their morphology. Gas permeability coefficients of hybrid membranes, where the depend directly on their morphology. Gas permeability coefficients of hybrid membranes, where the the depend directly on their morphology. Gas permeability coefficients of hybrid membranes, where interaction particles is absent, be membranes predicted bycontaining the Maxwell model. It shouldbetween be notedmatrix that theand transport properties of can hybrid nanoparticles interaction between matrix and particles is absent, can be predicted by the Maxwell model. interaction an between matrix and particles is absent, can be predicted by the Maxwell model. However, inadequate description of permeability P84/ND permeability data this model indicates thethe depend directly on their morphology. coefficients of by hybrid where However, an inadequate inadequate descriptionGas of P84/ND P84/ND permeability permeability data by this this membranes, model indicates indicates the However, an description of data by model the dependence of the decrease in permeability on changes in the membrane morphology. interaction between matrix and particles is absent, can beinpredicted by themorphology. Maxwell model. However, dependence of the decrease in permeability on changes the membrane dependence of the decrease in permeability in thebecause membrane morphology. In general, formation of an ideal structureonischanges very difficult of the different physicochemical an inadequate description of P84/ND permeability data by this model indicates the dependence of the In general, formation of an ideal structure is very difficult because of the different physicochemical In of general, formation an tendency ideal structure is very difficult because of thein different physicochemical nature two phases and of their towards aggregation. A decrease the permeability of the nature in of permeability two phases phases and and their tendency towards aggregation. A decrease decrease in in the the permeability permeability of of the the decrease ontheir changes in thetowards membrane morphology. nature of two tendency aggregation. A

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In general, formation of an ideal structure is very difficult because of the different physicochemical 9 of 13 13 towards aggregation. A decrease in the permeability 9ofofthe P84/NDmembrane membranecan canprobably probably be be explained explained by by aa decrease decrease in in the the mobility mobility of of polymer polymer chains chains due due to to P84/ND P84/ND membrane can probably be explained by a decrease in the mobility of polymer chains due to an increase in the packing density around the nanoparticle [48,49]. Figure 7 shows the scheme of the an increase in the packing density around the nanoparticle [48,49]. Figure 7 shows the scheme of the an increase in the packing density around the nanoparticle [48,49]. Figure 7 shows the scheme of the ideal structure of the hybrid membrane (a) and the structure with a dense polymer layer around the ideal structure of the hybrid membrane (a) and the structure with a dense polymer layer around the nanoparticle (b). nanoparticle (b). Polymers 2018, 10, x FOR PEER REVIEW Polymers of 2018, 10,phases x FOR PEER nature two andREVIEW their tendency

(a) (a)

(b) (b)

Figure 7. A morphology of polymer membrane membrane with dispersed dispersed nanoparticles: (a) Figure A schematic schematic (a) ideal ideal Figure 7. 7. A schematic morphology morphology of of polymer polymer membrane with with dispersed nanoparticles: nanoparticles: (a) ideal structure; (b) with rigidified polymer layer. structure; structure; (b) (b) with with rigidified rigidified polymer polymer layer. layer.

For an objective evaluation of the efficiency of the membranes under study, their gas transport For an an objective objective evaluation the membranes membranes under their gas gas transport transport For evaluation of of the the efficiency efficiency of of the under study, study, their properties were plotted in a Robeson diagram [50]. Figure 8 shows the Robeson diagram for the properties were were plotted plotted in in aa Robeson Robeson diagram diagram [50]. [50]. Figure Robeson diagram diagram for the properties Figure 88 shows shows the the Robeson for the Н2/СН4 gas pair, i.e., the dependence of the ideal selectivity αН2/СН4 on the permeability coefficient Н 2 /СН 4 gas pair, i.e., the dependence of the ideal selectivity α Н2/СН4 on the permeability coefficient H /CH gas pair, i.e., the dependence of the ideal selectivity α on the permeability coefficient PН22 . The4straight line in Figure 8 represents the upper bound ofH2/CH4 the gas separation capabilities of all PH2 Н2.. The P The straight straight line line in in Figure Figure 88 represents represents the the upper upper bound bound of of the the gas gas separation separation capabilities capabilities of of all all membranes known from scientific literature up to 2008 [50]. As can be seen from Figure 8, the P84 membranes known 2008 [50]. [50]. As 8, the the P84 P84 membranes known from from scientific scientific literature literature up up to to 2008 As can can be be seen seen from from Figure Figure 8, membrane is located among the most selective membranes, and the P84/ND hybrid membrane is membrane is hybrid membrane is membrane is located located among among the the most most selective selectivemembranes, membranes,and andthe theP84/ND P84/ND hybrid membrane displaced to a more advantageous position. This fact shows a promising means of membrane displaced to to a amore membrane is displaced moreadvantageous advantageousposition. position.This Thisfact factshows showsaa promising promising means means of of membrane modification by nanodiamonds. modification by nanodiamonds. modification by nanodiamonds.

P84 P84 P84/ND P84/ND

Figure 8. 8. Robeson diagram for hydrogen/methane hydrogen/methane gas Figure gas pair pair [50]. [50]. Figure 8. Robeson diagram for for hydrogen/methane gas pair [50].

The transport properties of the Р84/ND membrane were also compared with the latest literature The transport transport properties properties of of the the P84/ND Р84/ND membrane The membrane were were also also compared compared with with the the latest latest literature literature data on the gas separation properties of modified polyimide membranes for the cases of H2/CO2, data on the gas separation properties of modified polyimide membranes for the cases 2/CO2,, data on the gas separation properties of modified polyimide membranes for the cases ofofHH2 /CO 2 H2/CH4 and CO2/CH4 separation (Table 5). H22/CH 2/CH 4 separation (Table 5). H /CH4 4and andCO CO /CH separation (Table 5). 2 4 It can be seenTable that 5.ideal selectivity of P84/ND exceeds this parameter for other presented Gas transport properties of modified polyimide membranes. Table 5. Gas transport properties lower. of modified membranes. membranes, but the permeability is noticeably Thispolyimide can be explained by the difference in Permeability, Barrer Ideal Selectivity membrane topology. A promising way to improve for industrial applications is the Permeability, Barrer permeability Ideal Selectivity Membrane Ref. Membrane Ref. H2 CO2 CH4 H2/CO2 H2/CH4 CO2/CH4 creation of a bilayer composite membrane with aCH thin~P84/ND H2 CO 2 4 H2/CO2 selective H2/CH4 layer. CO2/CH4 P84/ND P84/ND Matrimid/ZIF-1 (10%) Matrimid/ZIF-1 (10%) 6FDA-TTM/Si-H (5%) 6FDA-TTM/Si-H (5%) PI/MWCNT@GONRs (2%) PI/MWCNT@GONRs (2%)

6.7 6.7 28.11 28.11 62.6 62.6 42.5 42.5

1.61 1.61 6.75 6.75 29.7 29.7 25.2 25.2

0.022 0.022 0.29 0.29 0.39 0.39 2.3 2.3

4.1 4.1 4 4 2.1 2.1 1.7 1.7

310 310 97 97 160.5 160.5 18.5 18.5

75 75 23 23 76 76 11 11

This work This work [51] [51] [52] [52] [53] [53]

Polymers 2018, 10, 828

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Table 5. Gas transport properties of modified polyimide membranes.

Membrane P84/ND Matrimid/ZIF-1 (10%) 6FDA-TTM/Si-H (5%) PI/MWCNT@GONRs (2%)

Permeability, Barrer

Ideal Selectivity

Ref.

H2

CO2

CH4

H2 /CO2

H2 /CH4

CO2 /CH4

6.7 28.11 62.6 42.5

1.61 6.75 29.7 25.2

0.022 0.29 0.39 2.3

4.1 4 2.1 1.7

310 97 160.5 18.5

75 23 76 11

This work [51] [52] [53]

4. Conclusions A novel hybrid membrane was obtained by dispersing ND particles in a matrix of P84 copolyimide and was characterized by high selectivity in separation of hydrogen from gases formed during steam reforming of methane: H2 , CO2 , and CH4 . The introduction of ND particles into the P84 matrix leads to a more compact macromolecular packing in the membrane. As a result, the experimental permeability of all gases through the P84/ND membrane is lower than the permeability calculated by the Maxwell model; this is due to stronger interaction of the nanoparticles with the polymer matrix than that model provided. Transport properties of membranes were studied for the following gases: H2 , CO2 , and CH4 . Gas permeability coefficients of the hybrid P84/ND membrane are lower than that of the unmodified P84 membrane, whereas ideal selectivity in separation of H2 /CO2 , H2 /CH4 , and CO2 /CH4 is higher for the hybrid membrane. Analysis of transport properties using correlation dependencies for diffusion and solubility coefficients of P84 and P84/ND membranes confirms the reliability of the gas permeability measurements and indicates that diffusion during gas separation occurs mainly due to elements of free volume. Author Contributions: Membrane formation, structure characterization, physicochemical investigation, analysis of transport properties in pervaporation and article writing were carried out by A.P., G.P., V.R. and A.T., Z.P. was involved in scientific discussions and analyzed the data. All authors read and approved the final manuscript. Funding: This work was funded by the Russian Science Foundation (RSF) [grant 16-13-10164]. Acknowledgments: The authors are gratefully acknowledged SCTB ‘Technolog’ Saint-Petersburg for the samples of ND Equipment of Resource Centers of St. Petersburg State University, namely, “Chemical Analysis and Materials Research Centre”, Interdisciplinary Resource Centre “Nanotechnologies”, “Thermogravimetric and Calorimetric Research Centre”, “Centre for X-ray Diffraction Studies” and Education Resource Centre in the direction of chemistry were used for membrane investigation. Conflicts of Interest: The authors declare no conflict of interest.

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