Inﬂuence of Carbon Uniformity on Its Characteristics and Adsorption Capacities of CO 2 and CH 4 Gases

: Activated carbons of resorcinol-formaldehyde aerogels (AC-RFA) were prepared and mixed with multiwall carbon nanotubes (MWCNTs) with various ratios. Samples were characterized by different techniques. The novelty of the study is in evaluating the effect of uniformity of carbon nanocomposites on their performance for the adsorption of CH 4 and CO 2 gases as well predicting the separation of their mixtures. The results indicated that, by increasing the percentage of MWCNTs into the sample, its structural uniformity and order ascend. The capacities of CH 4 and CO 2 by adsorption were measured at various temperatures, and were correlated with the extended dual site Langmuir (DSL) model. Overall, results showed that the adsorption capacity of MWCNTs towards gases is relatively very low compared to that of activated carbons. The DSL model was utilized to forecast the separation of the binary CO 2 /CH 4 mixed gas based on knowledge of single component adsorption isotherm parameters. Adsorption equilibrium data of the CO 2 /CH 4 binary gas mixture was forecasted at different temperatures by DSL model in accordance with the perfect-negative (PN) or perfect-positive (PP) behaviors on the heterogeneous surface of the adsorbent.


Introduction
Methane (CH 4 ) and carbon dioxide (CO 2 ) gases coexist often in nature, forming gas mixtures, such as natural gas, biofuel gas, landfill gas, coal bed methane, etc. [1][2][3][4][5]. Separation of CO 2 gas from CO 2 /CH 4 mixed binary gas is a core and strategic target in enhancing the gas purity and efficiency. The existence of CO 2 impurity within CH 4 gas reduces its heating value and leads to pipeline corrosion, especially if moisture is found [6]. Furthermore, CO 2 and CH 4 gases are key players in the amassing of greenhouse gases, and subsequently in the augmented global warming crisis [7]. The greenhouse warming impact of CH 4 is 21 times bigger than that of CO 2 [8]. Owing to the strong augmentation in the cost of oil and recent rigorous ecological regulations, there is a noticeable rise in the extraction of natural gas as a strong competent source of energy [9]. Therefore, it is desired to establish efficient techniques for removing CO 2 gas from natural gas.
The separation of CO 2 gas from natural gas or biogas mixtures is of a vital importance to their economic value, and is an issue of dire investigations [10,11]. It is reported that that natural gas is principally formed from CH 4 (95%) and C 2 H 6 (5%) while the biogas mainly includes CH 4 (45% to 65%) and CO 2 (30% to 40%). The higher content of CO 2 (30% to 40%) contributes to the much lower energy of biogas comparing to the natural gas [12].
The separation of CO 2 from gas mixtures is conducted by numerous techniques, such as cryogenic distillation, absorption, membrane technology, and adsorption [13]. The use of adsorption is of strategic importance in industry. Numerous materials (e.g., carbons [14,15], zeolites [8,16], metal organic frameworks [17,18], molecular sieves [19,20], and clays [21]) have attracted attention as adsorbents to separate mixtures of CO 2 and CH 4 gases. The distinguished selectivity is the most important and unique feature of adsorption processes over other separation techniques. The informative knowledge of pure and multi-component adsorption equilibrium data is necessary for designing and optimizing industrial units, and is very pivotal for determining the selectivity and the adsorption capability of specific adsorbents [6]. Nonetheless, binary or multicomponent adsorption experiments are very difficult and time-expensive. Thus, it would be advantageous if such findings could be forecasted using the traditional adsorption models. For its simplicity, the extended dual site Langmuir (DSL) model is commonly used to forecast the mixed gas adsorption equilibrium data from single component adsorption data [22][23][24].
Carbon nanotubes (CNTs) have attracted much attention as a result of their distinct chemical and physical properties [25,26]. CNTs are one-dimensional nanoscale substances formed of carbon atoms, where each carbon atom is sp 2 hybrid, and is bonded covalently to three adjacent carbon atoms. Upon the number of their wall layer(s), CNTs can be classified as either single-walled carbon nanotubes (SWCNTs) or multiwall carbon nanotubes (MWCNTs) [27]. It is well-known that the activated carbons are featured with disorder and non-uniformity, while MWCNTs are featured with highly uniform and ordered structures. It is expected that the structure uniformity of MWCNTs may be affected when mixing them with activated carbon nanoparticles, which reflects their changing performance in gas adsorption or separation processes. It is well-known that CNTs are very weak in adsorption capacity; therefore, the addition of other carbon materials may enhance their adsorption performance. In addition, according to the authors' knowledge, there is no work available in the literature to address the carbon-carbon interactions effect on adsorption. Consequently, this work tackles a novel issue and adds value to literature that may open new gates of research for this kind of work and reflect on properties for a wide range of related applications. Therefore, authors believe that this concept of carbon-carbon interaction is novel and needs further investigation by the research community to deduce and extract an integral vision of the reaction mechanism and its reflections on the related product characteristics, performances and potential applications.
This work aims to investigate the structure uniformity of mixed activated carbon (AC) nanoparticles with MWCNTs. It considers mixing different ratios of MWCNTs with nanoparticles of activated carbon resorcinol-formaldehyde aerogel (AC-RFA). The mixed samples will be characterized by various techniques to show the influences of mixing. The adsorption capacity and the adsorption of gas mixtures (i.e., CH 4 and CO 2 ) will be studied on MWCNTAC-RFA mixed adsorbents with variable ratios. Moreover, the influence of temperature on single-component gas adsorption equilibria will be studied. The single gas adsorption capacity and predicted binary CO 2 /CH 4 adsorption equilibria and selectivity onto MWCNT/AC-RFA adsorbents will be examined. Moreover, the novelty of this work lies in addressing the possible effects of carbon-carbon structural interactions and structure uniformity on the adsorption capacity and prediction of the adsorption behavior considering both the perfect-negative (PN) and perfect-positive (PP) behaviors.

Synthesis of Aerogels
Aerogels were prepared from resorcinol and formaldehyde as fundamental reactants, with sodium carbonate as a catalyst. The pH level of the reaction medium was adapted at neutral level with diluted nitric acid and ammonium hydroxide solutions. The quantities of resorcinol, sodium carbonate, formaldehyde, and water that were utilized in the synthesis of the aerogel were 12.44 g, 0.0240 g, 17.40 mL, and 32.60 mL, accordingly. The temperature was kept constant at 70 ± 1 • C. Resorcinol and Na 2 CO 3 were weighed and blended with ultrapure H 2 O in Erlenmeyer flasks, and then stirred until all constituents are entirely dissolved. Afterwards, formaldehyde was combined with the previously dissolved species during the stirring process. After that, the solution acidity was adapted at (pH = 7) by utilizing diluted HNO 3 and NH 4 OH buffers. The resorcinol-formaldehyde mixture solution was poured into vials, sealed tightly and set in an oven at 70 ± 1 • C. In order to prevent the dehydration of the gel, and to increase their cross-linking density, a dilute (2%) acetic acid solution is poured onto the gel after its solidification. After seven days, the samples were retrieved from the oven and left to cool down to ambient temperature.
The remnant solution on top of the cured gel was decanted and disposed. The remaining solution was replaced with fresh acetone at ambient temperature by casting acetone on top of the sample surface and keeping it at ambient temperature for one day, then replacing the leftover acetone with fresh acetone everyday for three consecutive days. Following the 3rd day of solvent replacement with acetone, the drying process was conducted by supercritical CO 2 extraction with the following procedure. Firstly, the gel was put underneath pressure of 20 MPa of liquid CO 2 at a temperature of 25 • C to dissolve the acetone with the liquid CO 2 . The exit valve was opened and the extractor was depressurized to 12 MPa, allowing liquid CO 2 to flow through the gel at 25 • C for times ranging from 1 to 2.5 h. Then, the temperature was elevated to reach the supercritical state at 31 • C and 7.4 MPa, and maintained at this condition for 2 h. After that, the extractor was gradually depressurized to atmospheric pressure and the dried resorcinol-formaldehyde aerogel was attained [28][29][30][31]. The supercritical drying was performed using a critical point dryer (E3100 Critical Point Dryer, Quorum Technologies-Preparation for Excellence, UK). The proposed reaction mechanism of resorcinol and formaldehyde to produce a gel is represented in Figure 1.

Preparation of Carbonized and Activated Carbon Aerogels
The dried resorcinol formaldehyde aerogels (RFA) was set in a ceramic boat in a programmable electrically-heated tube oven (Nabertherm GmbH, Germany), with flowing nitrogen gas (100 cm 3 /min). The oven was initially kept at ambient temperature for 30 min to make sure that the air surrounding the samples was flushed out completely with the nitrogen gas. Next, the oven was heated to 500 °C with ramp of 10 °C/min, kept at 500 °C for 3 h, and then left to reach the ambient Figure 1. Suggested reaction mechanism of resorcinol-formaldehyde gel.

Preparation of Carbonized and Activated Carbon Aerogels
The dried resorcinol formaldehyde aerogels (RFA) was set in a ceramic boat in a programmable electrically-heated tube oven (Nabertherm GmbH, Germany), with flowing nitrogen gas (100 cm 3 /min). The oven was initially kept at ambient temperature for 30 min to make sure that the air surrounding the samples was flushed out completely with the nitrogen gas. Next, the oven was heated to 500 • C with ramp of 10 • C/min, kept at 500 • C for 3 h, and then left to reach the ambient temperature spontaneously whilst passing nitrogen gas flow.
The resultant RF carbon aerogel was then activated in the same oven (after cleaning it thoroughly from previous process residues) with passing a CO 2 gas flow (150 cm 3 /min) in place of nitrogen gas flow, heating the sample once more with a ramp of 10 • C/min to 700 • C, keeping the sample at 700 • C for 1 h, and then letting the sample to reach the ambient temperature spontaneously whilst passing CO 2 gas [32]. The produced sample is considered to be an activated carbon aerogel (AC-RFA). Figure 2 illustrates a schematic diagram of the carbonization and activation processes of RFA sample.

Preparation of Carbonized and Activated Carbon Aerogels
The dried resorcinol formaldehyde aerogels (RFA) was set in a ceramic boat in a programmable electrically-heated tube oven (Nabertherm GmbH, Germany), with flowing nitrogen gas (100 cm 3 /min). The oven was initially kept at ambient temperature for 30 min to make sure that the air surrounding the samples was flushed out completely with the nitrogen gas. Next, the oven was heated to 500 °C with ramp of 10 °C/min, kept at 500 °C for 3 h, and then left to reach the ambient temperature spontaneously whilst passing nitrogen gas flow.
The resultant RF carbon aerogel was then activated in the same oven (after cleaning it thoroughly from previous process residues) with passing a CO2 gas flow (150 cm 3 /min) in place of nitrogen gas flow, heating the sample once more with a ramp of 10 °C/min to 700 °C, keeping the sample at 700 °C for 1 h, and then letting the sample to reach the ambient temperature spontaneously whilst passing CO2 gas [32]. The produced sample is considered to be an activated carbon aerogel (AC-RFA). Figure  2 illustrates a schematic diagram of the carbonization and activation processes of RFA sample.

RF aerogel particle
Carbonization N 2 gas Activation CO 2 gas RF aerogel carbon particle AC-RFA particle

Characterizations
The surface area and porosity of AC-RFA and MWCNTs samples were examined via the adsorption/desorption isotherms of nitrogen at −196 • C by a Micromeritics ASAP2420 ® surface area and porosity analyzer. In advance of each analysis, the specimens were degassed in-situ for 24 h at 150 • C under high vacuum (1 × 10 −4 Pa). The pore properties of samples were determined from the adsorbed volume of N 2 at −196 • C and the relative pressure (P/P 0 ) of 0.99 (99% of the saturation pressure).
The FT-Raman spectra were collected by a Bruker FT-Raman spectrometer of type RFS 100/S that is attached to a Bruker-IFS 66/S spectrometer. The morphology of MWCNT/AC-RFA mixed specimens was observed using an FEI Nova™ nanoscanning electron microscope 450 (Nova NanoSEM). A transmission electron microscope (TEM) of Talos L120C and of FEI Tecnai G2 F20 FE-TEM, available at Qatar Environment and Energy Research Institute (QEERI), were utilized to investigate the samples. Thermogravimetric analyses (PerkinElmer Pyris 6 TGA) were proceeded under nitrogen gas flow with a ramp 10 • C/min from ambient temperature to 800 • C (see Figure S1 in Supplementary Materials).
Adsorption/desorption isotherm measurements of CO 2 and CH 4 gases were carried out by a Rubotherm-Hygra magnetic suspension microbalance with a microgram resolution [22]. Prior to the adsorption measurement process on each sample, a buoyancy measurement using helium gas was conducted at 40 • C to assess the skeleton mass and volume, and hence the skeleton density, of each sample [22]. Furthermore, before conducting every adsorption isotherm, the samples were degassed in-situ at 120 • C for 24 h (see Figure S2 in Supplementary Materials). The adsorption calculations proceed afterwards as reported elsewhere [22,24].
The elemental analysis of MWCNT/AC-RFA mixed samples were carried out using a CHNS/O analyzer (2400, Series II, Perkin Elmer). X-ray diffraction (XRD) measurements were also conducted by utilizing a Miniflex II Benchtop XRD analyzer, manufactured by Rigaku Corporation Japan. The 2θ scan data were collected over the range of 5 • to 90 • . X-ray photoelectron spectroscopy (XPS) was achieved utilizing a Thermo Scientific K-alpha photoelectron spectrometer using monochromatic Al kα radiation.

Theory
Adsorption equilibrium data are among the basic cornerstones for simulating and optimizing adsorption systems. Numerous adsorption models exist to explain and describe these equilibrium data and their consequent physical properties. Some of the adsorption model parameters can indicate some of the adsorbent surface features, such as its adsorption affinity and energetic homogeneity/heterogeneity towards the adsorbed gas molecules.

Equilibrium Adsorption Isotherms
The forecasting of unary and binary adsorption equilibria relies on the precision of single component adsorption data and their description with a reliable adsorption isotherm model. Adsorption equilibrium data of the binary gas system (CO 2 and CH 4 ) is forecasted in this work from single component (unary) adsorption isotherm fitting parameters by applying the extended dual-site Langmuir (DSL) isotherm model.
The unary (single-constituent) DSL model [30] describes the adsorption of constituent i onto a nonhomogeneous surface that consists of two homogeneous, but energetically distinct, sites. Supposing that the adsorbent-adsorbate free energy onto each site is fixed, the adsorbed quantity of constituent i is determined from Equation (1) where n s 1,i and b 1,i correspond, respectively, to the monolayer saturation capacity limit and adsorption affinity on site 1; n s 2,i and b 2,i are, correspondingly, the monolayer saturation limit and adsorption affinity on site 2, and P is pressure. The hypotheses of the traditional Langmuir model are considered valid to each site, and the two sites are assumed not to interact with each other [33]. In this formulation, the monolayer saturation limit for every constituent on each site is let to be dissimilar. The affinity parameter for the adsorption of where j refers to the free-energy level (site 1 or site 2), E j,i is the adsorption energy of constituent i on site j, b j,io is the pre-exponential factor (or adsorption affinity of constituent i on site j at infinite temperature, T) and R is the universal gas constant. The corresponding Henry's law constant can be estimated from Equation (3) as In this formulation, j = 1 always refers to the adsorption site with a higher free energy level, and j = 2 always refers to the adsorption site with a lower free energy level. For unary gas adsorption, this causes the free energy of site 1 always superior than that of site 2.
On the other hand, for binary gas adsorption, the two free energies can be attributed to either site 1 or site 2.
For the extended DSL model, thermodynamic consistency necessitates the overall saturation capacity (n s 1,i + n s 2,i ) to be similar for all the constituents [34]. Equivalently, the amounts n s 1,i and n s 2,i in extended DSL would not depend on the constituent [35]. Unary constituent adsorption equilibrium data for each of CO 2 and CH 4 gases were fitted to the DSL isotherm model (Equations (1) and (2)) by the method of the least sum of squared errors (LSSE) as shown in Equation (4). Moreover, the percentage average relative error (ARE, %) between the measured and correlated quantities adsorbed is assessed from Equation (5).
where i refers to the data point number, N P refers to the total number of data points for every constituent, and the subscripts "exp" and "cal" symbolize, correspondingly, the experimental and correlated amounts. It is important to mention that the theoretical background of binary equilibrium adsorption isotherm is illustrated in the Supplementary Materials.

Selectivity
Further to the forecasting of equilibrium adsorption capacity by extended DSL model, the selectivity of adsorbing constituent A over constituent (S A,B ) in the gas mixture of A and B can be assessed by [36].
where x A and y A refer to the mole fractions of constituent A in the adsorbed and gas phases, correspondingly. The same can be noted about x B and y B . The values of x A and x B can be calculated from where n A,m and n B,m are the amounts adsorbed of constituents A and B, respectively, from the binary mixture, and can be calculated from the extended DSL model as illustrated in the Supplementary Materials. Figure 3 illustrates the Raman spectra of MWCNT/AC-RFA mixed samples with variable compositions. These samples (with MWCNT:AC-RFA weight ratios of 100:0, 60:40, 50:50, 40:60 and 0:100) were labeled as S100, S60, S50, S40, and S0, respectively. The spectra of carbon structures contain two main bands: the G-peak (at 1576 cm −1 ) and D-peak (at 1314 cm −1 ). The G-peak is attributed to the stretching mode of a well-ordered graphitic matrix, whereas the D-peak is assigned to the stretching mode of a defected structure or lattice in the graphite matrix (e.g., vacancies or substitutional heteroatoms or chemically attached heteroatoms) [37]. The quotient of the D-peak (I D ) to the G-peak (I G ) intensities in Raman spectra is a useful parameter to assess the structural ordering/disordering of carbons, comprising carbon nanostyles. A high I D /I G indicates to the existence of disorders within the carbon matrix, whereas a low value of I D /I G refers to a degree of crystalline perfection and less structure defects. The trend in Figure 4 shows that by increasing the ratio of AC-RFA into the sample, the I D /I G ratio value increases. The increment relates to increasing disorder and defects of carbon materials. The peak at 2623 cm −1 (G -peak) for MWCNTs in Figure 3 refers to an overtone of the D-peak [38]. In further observation, it was seen that peak at 856 cm −1 appears for S100 and disappears for S0.    Figure 5a-e shows NanoSEM photomicrographs of S100, S60, S50, S40 and S0 samples, respectively. The difference in the morphology of these samples is observed clearly as a reflection of increasing content of carbon nanospheres among the carbon nanotubes. Figure 6a-e shows TEM images of S100, S60, S50, S40 and S0 samples, respectively. The observations from these images support those deduced from NanoSEM photomicrographs. The elemental analyses of these samples were carried out using CHNS/O and XPS techniques The elemental analyses, either from EDX or XPS, indicate that as the oxygen percentage is higher, the adsorption capacity increases as listed in Table   5a-e shows NanoSEM photomicrographs of S100, S60, S50, S40 and S0 samples, respectively. The difference in the morphology of these samples is observed clearly as a reflection of increasing content of carbon nanospheres among the carbon nanotubes. Figure  6a-e shows TEM images of S100, S60, S50, S40 and S0 samples, respectively. The observations from these images support those deduced from NanoSEM photomicrographs. The elemental analyses of these samples were carried out using CHNS/O and XPS techniques The elemental analyses, either from EDX or XPS, indicate that as the oxygen percentage is higher, the adsorption capacity increases as listed in Table S1 (Supplementary Materials).

Results and Discussion
Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 26 Applied Sciences 2020, 10, x; doi: FOR PEER REVIEW  The nitrogen adsorption/desorption isotherms at −196 °C on S100, S60, S50, S40, and S0 are exposed in Figure 7. The isotherms of N2 gas adsorption/desorption at −196 °C on pure MWCNTs (i.e., the sample of S100) are classified as a type-II adsorption isotherm as defined by IUPAC. This type is often encountered in adsorption by nonporous substances or in substances with macropores The nitrogen adsorption/desorption isotherms at −196 • C on S100, S60, S50, S40, and S0 are exposed in Figure 7. The isotherms of N 2 gas adsorption/desorption at −196 • C on pure MWCNTs (i.e., the sample of S100) are classified as a type-II adsorption isotherm as defined by IUPAC. This type is often encountered in adsorption by nonporous substances or in substances with macropores or unlocked cavities [39]. Furthermore, it is noticed that almost no hysteresis exists for the sample S100, whereas it appears noticeably in the samples S60, S50, S40 and S0. The nitrogen adsorption capacities onto the samples S60, S50, S40 and S0 samples are significantly higher than that onto the sample S100. This might be because the adsorption on mesoporous AC-RFA that is present in the mixed samples ensues through multilayer adsorption pursued by capillary condensation, resulting in type-IV isotherm [40,41]. Generally, hysteresis is attributed to a thermodynamic effect, a network effect (or a combination of these two effects) and capillary condensation as well [42]. It was observed that the hysteresis on pure MWCNTs is almost zero, while the hysteresis on AC-RFA is noticeable. Moreover, the porosity of AC-RFA is higher than that of MWCNTs. Consequently, the capillary condensation effect occurs more significantly in AC-RFA than MWCNTs; and the results listed in Table S2 (Supplementary Materials) support this behavior. Overall, as is reported in the literature, there are five types of hysteresis loops and their related pore shapes. Namely, Type-A is attributed to cylindrical pores; Type-B is assignable to slit pores; Types-C and -D are assignable to wedge shaped pores and Type-E is attribute to bottle neck pores [43]. The hysteresis loops in this work belong to Type-E, which indicates to bottle neck pore type.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 13 of 26 Applied Sciences 2020, 10, x; doi: FOR PEER REVIEW Figure 7. Isotherms of N2 adsorption/desorption at −196 °C onto different MWCNT/AC-RFA sample compositions; namely S100, S60, S50, S40 and S0. Solid circles refer to adsorption data and empty circles refer to desorption data. Figure 8 exposes the XRD patterns of different MWCNT/AC-RFA mixed sample compositions; namely S100, S60, S50, S40 and S0. It is noted that the peaks at 2θ of 26.1°, 42° and 54° are assigned, respectively, to the (002), (100) and (004) planes of the hexagonal graphite structure of the MWCNTs [37,45]. It was observed that the fingerprint band of MWCNTs (2θ = 26.1°) exposed a diminuendo trend when increasing amount of AC-RFA into the mixed sample composition. Furthermore, other two small peaks at 21.4° and 54° were noticed in the samples ranging from S100 to S40 and disappeared in S0. It could be said through outcome results that the sharp peak at 26.1° and broad peaks at 21.4° refer, respectively, to the relative crystallinity and relative amorpohicity regions into the samples. The characteristic peak of MWCNTs at 26.1° diminished gradually when increasing the quantity of AC-RFA into the composition. Figure 9a is a summary of FWHM of XRD peaks at 2θ values of 26.1° and 21.4°, which indicate to the relative crystalline section of MWCNTs and relative amorphous section of AC-RFA, correspondingly. It was observed that the FWHM of the band at 26.1° has a diminuendo trend, whereas that at 21.4° has a crescendo behavior with the increase in the AC-RFA ratio. Figure 9b represents the influence of the hybrid MWCNT/AC-RFA mixed sample composition on the XRD FWHM ratio (I26.1°/I21.4°). The ratio of XRD peaks (I26.1°/I21.4°) increases with the increasing MWCNT content; thereby increasing the relative crystallinity and reducing the relative amorphicity into the matrix of the product. Figure 9c exhibits the impact of sample composition on  Through the results listed in Table 1, it is seen from the S60 to S0 samples that the neck of the mesopore opens at a P/P o range between~0.7 and 1; as shown by the observed hysteresis loops [44]. This indicates that all the samples from S60 to S0 exhibit mesoporous structures. The pore volume of samples changed from 0.026 to 0.767 cm 3 /g when comparing S100 to S0, respectively; and the average pore size changed from 63.7 to 6.1 nm when comparing S100 to S0, respectively (Table 1). Moreover, BET surface area changed from 1.63 to 507 m 2 /g, respectively (Table 1). This conclusion is agreement with the structural properties of the samples as listed in Table 1.  Figure 8 exposes the XRD patterns of different MWCNT/AC-RFA mixed sample compositions; namely S100, S60, S50, S40 and S0. It is noted that the peaks at 2θ of 26.1 • , 42 • and 54 • are assigned, respectively, to the (002), (100) and (004) planes of the hexagonal graphite structure of the MWCNTs [37,45]. It was observed that the fingerprint band of MWCNTs (2θ = 26.1 • ) exposed a diminuendo trend when increasing amount of AC-RFA into the mixed sample composition. Furthermore, other two small peaks at 21.4 • and 54 • were noticed in the samples ranging from S100 to S40 and disappeared in S0. It could be said through outcome results that the sharp peak at 26.1 • and broad peaks at 21.4 • refer, respectively, to the relative crystallinity and relative amorpohicity regions into the samples. The characteristic peak of MWCNTs at 26.1 • diminished gradually when increasing the quantity of AC-RFA into the composition. Figure 9a  FWHM of XRD peaks at 2θ of 42° and 54°, which evidently show that no significant influence on the intensity of these peaks is noticed when adding AC-RFA to MWCNTs, whereas the pure AC-RFA (i.e., the sample of S0) has no such peaks.   Figure 10 shows the isotherms of CO2 and CH4 gases adsorption/desorption isotherms at 40°C versus pressure onto hybrid MWCNT/AC-RFA adsorbents with various compositions, namely S100, S60, S50, S40, and S0. It is observed that the adsorption capacities of CO2 and CH4 increase by increasing the ratio of AC-RFA into the hybrid MWCNT/AC-RFA adsorbent, which can be attributed  Figure 10 shows the isotherms of CO 2 and CH 4 gases adsorption/desorption isotherms at 40 • C versus pressure onto hybrid MWCNT/AC-RFA adsorbents with various compositions, namely S100, S60, S50, S40, and S0. It is observed that the adsorption capacities of CO 2 and CH 4 increase by increasing the ratio of AC-RFA into the hybrid MWCNT/AC-RFA adsorbent, which can be attributed to the increased surface area (see Table 1), and enhance the interactions between the adsorbing surface and gas molecules. The sequential order of hybrid MWCNT/AC-RFA samples towards either CO 2 or CH 4 is as S0 > S40 > S50 > S60 > S100. Furthermore, the adsorption affinity of all samples towards CO 2 is higher than that towards CH 4 . All isotherms described in Figure 10 are classified as Type-I according to IUPAC [46]. However, the sample S100 exposes an almost linear adsorption isotherm for both CH 4 and CO 2 .
Applied Sciences 2020, 10, x; doi: FOR PEER REVIEW Figure 10. Adsorption/desorption isotherms of (a) CO2 and (b) CH4 on different hybrid MWCNT/AC-RFA sample compositions; namely, S100, S60, S50, S40 and S0 at 40°C. Solid and empty symbols indicate, correspondingly, the experimental adsorption and desorption data. Figure 11a,b exposes the adsorption/desorption isotherms of CO2 and CH4 gases onto the sample S50 at 20, 40, and 60°C. The adsorption capability of S50 towards each of CO2 and CH4 reduces noticeably when increasing temperature. The symbols and lines represent experimental points and DSL correlations, respectively. It was observed from Figure 11 that the experimental points are well fitted by the DSL model for both CO2 and CH4 gases; covering the whole range of pressure and temperature scales as well. Therefore, the DSL model is deemed to be an excellent presentation of experimental data over the whole ranges of pressure and temperature. Trials showed that two homogenous sites (i.e., J = 2) are adequate to define the adsorption of CO2 or CH4 gases via the DSL Figure 10. Adsorption/desorption isotherms of (a) CO 2 and (b) CH 4 on different hybrid MWCNT/AC-RFA sample compositions; namely, S100, S60, S50, S40 and S0 at 40 • C. Solid and empty symbols indicate, correspondingly, the experimental adsorption and desorption data.
From Raman results, the trend of uniformity deduced from I D /I G ratio leads to affecting the adsorption capacity; which is also supported by pore and area structure data listed in Table 1. Overall, the higher ratio of I D /I G indicates more defects/disorders into the matrix is, which results in higher adsorption capacities. On other words, the by increasing the amount of AC-RFA into the adsorbent matrix, the adsorption capacity of adsorbent increases.
Further, the XRD profiles indicate that as more RFA-AC is added to MWCNTs, a higher adsorption capacity is attained due to the increasing amorphicity of the structure. It is important to mention that the crystallinity of MWCNTs is higher than that of RFA-AC. The elemental analysis, either from EDX or XPS, indicates that as the oxygen percentage is higher, the adsorption capacity increases as shown in Table S1 (Supplementary Materials). In addition to the former results based on Raman and XRD patterns discussed previously, it could be said that by increasing the AC-RFA, the increasing non-uniformity of the adsorbent corresponds to higher adsorption capacities towards gas molecules. Therefore, the adsorption capacity of adsorbents is enhanced by increasing the non-uniformity order into the structure of sample utilized, which also corresponds to a higher surface area and pore volumes as presented in Table 1. Therefore, structural characteristics such crystallinity, composition, and orders/disorders have a significant impact on the adsorption behavior of CH 4 and CO 2 gases. Figure 11a,b exposes the adsorption/desorption isotherms of CO 2 and CH 4 gases onto the sample S50 at 20, 40, and 60 • C. The adsorption capability of S50 towards each of CO 2 and CH 4 reduces noticeably when increasing temperature. The symbols and lines represent experimental points and DSL correlations, respectively. It was observed from Figure 11 that the experimental points are well fitted by the DSL model for both CO 2 and CH 4 gases; covering the whole range of pressure and temperature scales as well. Therefore, the DSL model is deemed to be an excellent presentation of experimental data over the whole ranges of pressure and temperature. Trials showed that two homogenous sites (i.e., J = 2) are adequate to define the adsorption of CO 2 or CH 4 gases via the DSL model. The optimum fitting parameters, along with the corresponding LSSE and ARE(%) values deduced from cumulative adsorption data of each component over the entire range temperature, are listed in  The unary constituent adsorption of CO2 and CH4 gases onto the sample S50 were fitted well by the DSL isotherm model, as described in the previous section. The adsorption equilibria of dual mixtures of CO2 and CH4 gases were forecasted utilizing both the PP (Equations (S2) and (S3)) and PN (Equations (S4) and (S5)) behaviors of the DSL model with merely the unary gas adsorption regression parameters listed in Table S3 Figure 11. Experimental (symbols) and DSL fitting (lines) adsorption equilibrium points of (a) CO 2 and (b) CH 4 gases onto S50 at various temperatures. Solid and empty symbols refer, respectively, to adsorption and desorption points.
The unary constituent adsorption of CO 2 and CH 4 gases onto the sample S50 were fitted well by the DSL isotherm model, as described in the previous section. The adsorption equilibria of dual mixtures of CO 2 and CH 4 gases were forecasted utilizing both the PP (Equations (S2) and (S3)) and PN (Equations (S4) and (S5)) behaviors of the DSL model with merely the unary gas adsorption regression parameters listed in Table S3 (Supplementary Materials). No binary data were needed to forecast the dual adsorption equilibrium data. The predicted effects of the mole fraction of CO 2 in the adsorbed phase (x CO 2 ) on the gas-phase mole fraction of CO 2 (y CO 2 ) and selectivity of adsorbing CO 2 relative to CH 4 (S CO 2 ,CH 4 ) are illustrated in Figure 12.   Figure 13a shows that both 2 and 4 predicted by the PP behavior increase by either decreasing the temperature or by increasing the pressure. Moreover, it is observed from Figure 13b that the 2 , 4 predicted by the PP behavior increases by increasing the exposed pressure at 313 and 333 K, but remains constant at 293 K. The value of 2 , 4 increases when decreasing temperature, especially at low to moderate pressures. Figure 13c,d exposes the PN behavior relationship between 2 and pressure for an equimolar feed gas mixture of CO2 and CH4 at 293, 313 and 333 K. It is noticed that the 2 and 4 both increase with increasing pressure at all temperatures. The value of 2 increases by decreasing temperature, whereas that of 4 is almost independent of temperature. If the values of 2 of Figure 13a,b are compared to those of Figure  13c Figure 12a,b show the predicted relationships between x CO 2 and y CO 2 for the PP and PN behaviors, respectively, at various temperatures, and at both minimal and high pressures (0.1 MPa and 0.5 MPa, respectively). It is noticed that y CO 2 increases with increasing x CO 2 . However, Figure 12a exposes that the PP behavior always predicts higher x CO 2 than y CO 2 at all temperatures. Therefore, the PP predicts no azeotropic behavior between CO 2 and CH 4 gases at the full scale of temperature. At a high pressure (0.5 MPa), y CO 2 increases very slightly with increasing temperature. At any x CO 2 , the value of y CO 2 at 0.5 MPa is always higher than that at 0.1 MPa. It is observed from Figure 12b that at a low temperature (293 K), the PN behavior predicts no azeotropic conditions in the full range of x CO 2 with coinciding curves at both low and high pressures (0.1 and 0.5 MPa, respectively). Furthermore, at medium temperature (313 K), an azeotropic behavior is predicted at x CO 2 of~0.85 only at high pressure. Furthermore, at an elevated temperature (333 K), azeotropic behaviors are predicted at x CO 2 of~0.55 in states of both minimal and elevated pressures. At any x CO 2 , the value of y CO 2 corresponding to the PN behavior (Figure 12b) is higher than that corresponding to the PP behavior (Figure 12a). Figure 12c,d illustrate the predicted relationships between x CO 2 and S CO 2 ,CH 4 for the PP and PN behaviors, respectively, at different temperatures and at both low and high pressures (0.1 MPa and 0.5 MPa, respectively). It was observed from Figure 12c that the PP behavior predicts that, at a low temperature (293 K), S CO 2 ,CH 4 is constant at 3.25 and 2.33 in the cases of a low or a high pressure (0.1 and 0.5 MPa), respectively. Nonetheless, at higher temperatures (313 and 333 K), S CO 2 ,CH 4 increases when increasing x CO 2 , especially at 333 K when x CO 2 > 0.8. Moreover, S CO 2 ,CH 4 was higher at minimal pressure (0.1 MPa) than that at elevated pressure (0.5 MPa), and no azeotropes were predicted at both pressures. On the other hand, it can be seen from Figure 12d that the S CO 2 ,CH 4 predicted by the PN behavior at low temperature was constant at 1.5, regardless of x CO 2 or pressure. However, at higher temperatures (313 and 333 K), it decreases when increasing x CO 2 at both minimal and elevated pressures (0.1 and 0.5 MPa). At a moderate temperature (313 K), the value of S CO 2 ,CH 4 predicted at elevated pressure (0.5 MPa) is lower than that at minimal pressure (0.1 MPa) when x CO 2 >~0.65. Furthermore, at a high temperature (333 K), the value of S CO 2 ,CH 4 at elevated pressure (0.5 MPa) is lower than that at minimal pressure (0.1 MPa) when x CO 2 >~0.56. The azeotropic behavior appeared at x CO 2 of~0.85 at moderate temperature (313 K) and high P (0.5 MPa), and at x CO 2 of~0.55 at high temperature (333 K) for both pressures. The selectivity in both behaviors (i.e., PP and PN) is affected significantly by the structure adsorbents, adsorption capacity and temperature. Increasing surface area and pore volume (as presented in Table 1) enhance the adsorption capacity. This is due to an increase in the AC-RFA content in the mixed adsorbent, which makes its structure more amorphous. Furthermore, it is reported in the literature that an incompetence of MWCNTs persists for the adsorption or selectivity of gases [47][48][49], while activated carbons generally expose good adsorption capacities and selectivities of gases [50][51][52]. Therefore, adding AC-RFA to MWCNTs enhances the adsorption capacity and selectivity based on adsorption isotherms as preliminary data. It is to be noted that the recent data of only S50 are not enough to discuss the full range of MWCNTs to AC-RFA ratios and their effects on selectivity, specifically. Figure 13a-d illustrates the predicted relationship between pressure and adsorption performance (i.e., Figure 13a,c exposing n CO 2 and n CH 4 and Figure 13b,d exposing S CO 2 ,CH 4 ) for an equimolar gas mixture of CO 2 and CH 4 at different temperatures for the (a, b) PP and (c,d) PN behaviors. Figure 13a shows that both n CO 2 and n CH 4 predicted by the PP behavior increase by either decreasing the temperature or by increasing the pressure. Moreover, it is observed from Figure 13b that the S CO 2 ,CH 4 predicted by the PP behavior increases by increasing the exposed pressure at 313 and 333 K, but remains constant at 293 K. The value of S CO 2 ,CH 4 increases when decreasing temperature, especially at low to moderate pressures. Figure 13c,d exposes the PN behavior relationship between n CO 2 and pressure for an equimolar feed gas mixture of CO 2 and CH 4 at 293, 313 and 333 K. It is noticed that the n CO 2 and n CH 4 both increase with increasing pressure at all temperatures. The value of n CO 2 increases by decreasing temperature, whereas that of n CH 4 is almost independent of temperature. If the values of n CO 2 of Figure 13a,b are compared to those of Figure 13c,d, it can be seen that the PP and PN behaviors are around the same average value. The values of S CO 2 ,CH 4 at different temperatures increase very slightly by increasing the pressure at 313 and 333 K, and remain constant at 293 K. Further, S CO 2 ,CH 4 decreases with an increasing temperature. The impact of temperature and pressure on n CH 4 is very small and almost insignificant in the case of PN behavior, while it is observable in the case of PP behavior. Table 2 exposes a comparison of adsorption capacities of CO 2 and CH 4 on AC-RFA (this work) against some data reported in the literature. It can be observed that AC-RFA has a higher adsorption capacity than other adsorbents such as AC-coconut-shells, shale, AC-waste tea, etc. The adsorption capacity of AC-RFA towards CO 2 is lower than those on AC-commercial and AC-CCVD. Moreover, the adsorption capacity of AC-RFA towards CH 4 is lower than that of AC-hard coal, AC-CCVD, AC-xerogels, AC-Maxsorb II and AC-Clay-rich shale. Overall, it can be said that AC-RFA has a good adsorption capacity towards both CO 2 and CH 4 gases.  Table 2 exposes a comparison of adsorption capacities of CO2 and CH4 on AC-RFA (this work) against some data reported in the literature. It can be observed that AC-RFA has a higher adsorption capacity than other adsorbents such as AC-coconut-shells, shale, AC-waste tea, etc. The adsorption capacity of AC-RFA towards CO2 is lower than those on AC-commercial and AC-CCVD. Moreover, the adsorption capacity of AC-RFA towards CH4 is lower than that of AC-hard coal, AC-CCVD, ACxerogels, AC-Maxsorb II and AC-Clay-rich shale. Overall, it can be said that AC-RFA has a good adsorption capacity towards both CO2 and CH4 gases.

Conclusions
Resorcinol-formaldehyde aerogels and their subsequent activated carbons (AC-RFA) were prepared. Multiwall carbon nanotubes (MWCNTs) and AC-RFA were mixed together with various ratios. Samples were characterized by various devices. Adsorption/desorption isotherms of pure CO 2 and CH 4 gases on each sample were studied. The impact of temperature on the adsorption/desorption isotherms of gases was conducted on the sample of medium composition (S50). One of key findings of this study is that the carbonaceous adsorbent structure uniformity and its order have a significant influence on pore structure, adsorption capacity and adsorption selectivity towards gases. Moreover, the highest adsorption capacity for either CO 2 or CH 4 gases was for the sample that did not contain any MWCNTs; whereas adding AC-RFA to MWCNTs enhances their adsorption capacity. Furthermore, it can be deduced that the adsorption capacity of MWCNTs towards gases is relatively very low compared to AC-RFA.
The pure-component dual site Langmuir (DSL) isotherm model was applied to correlate the adsorption data onto S50 over the entire scale of pressure at various temperatures. Moreover, the extended DSL model was utilized for predicting the adsorption equilibrium of the binary gas mixture of CO 2 and CH 4 with perfect-positive (PP) and perfect-negative (PN) behaviors at various temperatures. The selectivity of adsorbing CO 2 from CO 2 /CH 4 gas mixtures was also investigated.
This study also indicated some key findings, such as the point that the adsorption of gases can follow either of the PP or PN behaviors; while the adsorption capacities are not significantly affected by the followed adsorption behavior (i.e., PP or PN behavior). Nonetheless, the adsorption selectivity is affected significantly, if the adsorption trend follows either of the PP or PN behaviors.
In the future, it is anticipated that further investigations will be carried out to improve the selectivity and adsorption capacity as well by studying different forms of carbon-carbon hybrid nanostructures. Different carbons such as SWCNTs, graphene oxides, reduced graphene oxides, graphite, etc., can be studied to evaluate their hybrid nanostructures. Furthermore, the interactions between these different carbon nanostructures shall be examined to track their mechanisms and potential applications for gas adsorption or otherwise in detail.