Phenol-Formaldehyde Resin-Based Carbons for CO 2 Separation at Sub-Atmospheric Pressures

The challenge of developing effective separation and purification technologies that leave much smaller energy footprints is greater for carbon dioxide (CO2) than for other gases. In addition to its involvement in climate change, CO2 is present as an impurity in biogas and bio-hydrogen (biological production by dark fermentation), in post-combustion processes (flue gas, CO2-N2) and many other gas streams. Selected phenol-formaldehyde resin-based activated carbons prepared in our laboratory have been evaluated under static conditions (adsorption isotherms) as potential adsorbents for CO2 separation at sub-atmospheric pressures, i.e., in post-combustion processes or from biogas and bio-hydrogen streams. CO2, H2, N2, and CH4 adsorption isotherms at 25  ̋C and up to 100 kPa were obtained using a volumetric equipment and were correlated by applying the Sips model. Adsorption equilibrium was then predicted for multicomponent gas mixtures by extending the multicomponent Sips model and the Ideal Adsorbed Solution Theory (IAST) in conjunction with the Sips model. The CO2 uptakes of the resin-derived carbons from CO2-CH4, CO2-H2, and CO2-N2 at atmospheric pressure were greater than those of the reference commercial carbon (Calgon BPL). The performance of the resin-derived carbons in terms of equilibrium of adsorption seems therefore relevant to CO2 separation in post-combustion (flue gas, CO2-N2) and in hydrogen fermentation (CO2-H2, CO2-CH4).


Introduction
The sustainable production of energy is currently a topic of extensive research with the aim of producing low carbon footprint processes and mitigating the CO 2 impact [1].As a sustainable and clean energy source with minimal or zero use of hydrocarbons, hydrogen is a promising alternative to fossil fuels [2].Hydrogen can be generated by thermochemical, electrochemical or microbial fermentation processes.Biological methods are preferable to chemical methods because they offer the possibility of using sunlight, CO 2 and organic wastes as substrates for environmentally benign conversions under moderate conditions [3].The biological methods for generating H 2 include light-dependent methods, such as direct and indirect biophotolysis and photo fermentation; and methods not dependent on light, such as the dark fermentation process and bioelectrochemical systems (BES).Hydrogen production through dark fermentation has advantages over the other processes because it does not require the input of external energy and it offers the possibility of rapid scalability owing to its similarity to the well-known anaerobic digestion process [4].In addition, bio-hydrogen production from anaerobic fermentation is linked to bio-methane generation since the process develops in two main stages.In the first stage acidogenic bacteria break down substrates into primarily H 2 , acetic acid, and CO 2 , and in the second stage methanogenic bacteria convert acetic acid, H 2 , and CO 2 to methane gas.The two reactions can be separated, at least partially, in distinct bioreactors placed in series.Both streams must be further purified to obtain bio-hydrogen and bio-methane with a high calorific value, appropriate for industrial applications [5].Concentrations of H 2 of up to 30-70 vol% on average and of up to 45-80 vol% in the case of CH 4 on average can be achieved but the presence of CO 2 in both streams (20-70 vol%) is a nuisance and needs to be removed for further utilization of H 2 and CH 4 [6].
On the other hand, conventional energy production from fossil fuels is one of the main sources of anthropogenic CO 2 .The separation of CO 2 from flue gas (post-combustion CO 2 capture), is very challenging given that it is at near atmospheric pressure and CO 2 only represents between 4 to 15 vol%, depending on the fuel used, and if dry or wet basis conditions are considered.However, the conditions required for CO 2 transport, storage or subsequent use as a chemical make a concentration step necessary to reach the set target of ca.95 vol%.
Different technologies have been evaluated to separate CO 2 under sub-atmospheric pressure and particular emphasis has been paid in recent years to post-combustion CO 2 capture due to increasing concerns about global warming and climate change.Adsorption with low temperature solid sorbents has the potential to reduce the energy penalty associated with the separation of CO 2 at sub-atmospheric pressures, not only under post-combustion capture conditions (CO 2 /N 2 separation) but also for bio-hydrogen (CO 2 /H 2 separation) and bio-methane production (CO 2 /CH 4 separation) [7,8].However, the success of these approaches depends on the development of adsorbents with a high selectivity, sufficient adsorption capacity and easy regeneration.Carbon adsorbents fulfil all these requirements: they have a significant adsorption capacity at atmospheric pressure and the necessary characteristics for the separation of CO 2 at sub-atmospheric pressures including hydrophobicity, low cost and low intensity in terms of the amount of energy required for regeneration.
The distinction between activated or porous carbons and carbon molecular sieves has not been clearly defined.Whereas most of the pores in carbon molecular sieves are in the molecular size range, activated carbons may also have very small pores.The main difference is that activated carbons separate molecules through differences in their adsorption equilibrium whereas carbon molecular sieves provide molecular separations based on rate of adsorption, allowing the separation of molecules on the basis of their size, rather than on the differences in adsorption capacity [9,10].
The use of polymeric precursors to produce activated carbons allows the incorporation of custom tailored features (e.g., pore size, conformation, etc.) along with other material properties to meet the required specifications.Phenol-formaldehyde resin-derived microporous activated carbons have been previously studied in our laboratory [6,11,12].They can be produced in a wide variety of physical forms, at a low cost and with a close control of porosity.More importantly, all these features are accompanied by a very low level of impurities and good physical strength, key parameter in the design of an adsorption process [13,14].
In this work, the performance of phenol-formaldehyde resin-based activated carbons prepared in our laboratory to separate CO 2 at sub-atmospheric pressures has been evaluated in a fundamental study of the equilibrium of adsorption of CO 2 , N 2 , H 2 and CH 4 .A preliminary CO 2 uptake screening test has been carried out to discard the samples with less than 2 mol¨kg ´1 of CO 2 adsorbed at atmospheric pressure.Adsorption models are very useful as they can predict the behaviour of the equilibrium of adsorption over a wide range of temperatures and pressures.In order to predict multicomponent adsorption from binary CO 2 -CH 4 , CO 2 -H 2 , and CO 2 -N 2 mixtures, the extended multicomponent Sips equation and the Ideal Adsorbed Solution Theory (IAST) in conjunction with the Sips model have been used and the results have been compared.Both equations deliver different conclusions regarding the heterogeneity of the adsorbate-adsorbent system.Additionally, a commercial activated carbon (Calgon BPL) was evaluated under the same operating conditions as a reference carbon adsorbent.

Materials and Method
Porous carbons can be prepared from a wide range of carbon-containing materials including coal, lignin, wood, peat and synthetic and natural polymers.Carbonisation and activation of these materials under appropriate conditions yield carbons with a rather uniform pore structure consisting of micropores whose size is similar to that of the adsorbed molecules.For instance, low-density materials can be prepared by carbonisation of polymeric compounds pretreated by various procedures, including modification with inorganic additives [15].In particular, carbon sorbents with exactly the prescribed structure have been prepared using NaCl [16] and silicon [17] additives.

Synthesis of Carbon Precursors
Phenol-formaldehyde (PF) resins were used in this work to produce carbon-based microporous materials.Synthesis was conducted following two different routes, acid (hydrochloric acid, 37 wt% HCl solution) and basic (sodium hydroxide, NaOH) catalysis for the Novolac and the Resol resins, respectively.Details on the synthesis of the PF resins can be found elsewhere [18].Carbon precursors were prepared from the aforementioned resins, and potassium chloride (KCl) was incorporated as inorganic additive.One set of materials was impregnated with a saturated KCl solution at ambient temperature (set a) while another was boiled in a saturated KCl solution (set b).Another carbon precursor was prepared by mixing PF resin with an agricultural by-product, olive stones (OS), at a proportion of 20:80 wt% of PF to OS.A curing agent, hexamethylenetetramine (hexa) was added to PF at a hexa ratio of 7:2 wt%.Table 1 summarizes the materials and conditions for the production of the PF resin-derived carbon precursors.

Production of Microporous Carbons
The prepared carbon precursors were first carbonised and then activated with CO 2 to develop their microporous structure, preferably in the narrow microporosity domain (pore sizes of less than 1 nm) since CO 2 adsorption at sub-atmospheric pressures is known to focus on the narrow micropores [15,19,20].
Carbonisation was conducted in a tubular furnace under an inert atmosphere (50 mL¨min

´1
of N 2 ).Two different temperature programs were selected for PF-KCl; the two precursors of set a were subjected to a one-step carbonisation procedure at 600 ˝C for 1.5 h while for set b, a three-step slow carbonisation treatment at 200 (1 h), 600 (0.5 h) and 1000 ˝C (0.5 h) was carried out.The PF-OS composite was carbonised at 1000 ˝C (0.2 h) by slowly heating from ambient temperature at 4 ˝C¨min ´1.
Activation with carbon dioxide favours the development of microporosity [21].The largest increase in porosity is produced in the early stages of the activation process.Burn off (i.e., degree of activation) increases the widening of existing micropores but external burning of the particle outweighs the creation of new porosity, resulting in a net destruction of porosity, especially above 40%-50% burn off [22].Control of the activation parameters (temperature and burn off degree) is crucial for tailoring the micropore size distribution.Previous works carried out in our research group have demonstrated the relationship between the volume of narrow micropores of less than 0.7 nm and CO 2 uptake at atmospheric pressure [20].Response surface methodology was performed to obtain the optimum conditions of activation with CO 2 that maximise CO 2 adsorption at atmospheric pressure for each precursor (details can be found in [18]).Activation with CO 2 was conducted in a tubular furnace with a CO 2 flowrate of 10 mL¨min ´1.activation with CO 2 steps.Yields of char production during carbonisation were around 40% for PF-KCl precursors independently of the carbonisation temperature selected or type of PF resin (acid, No, or basic, Re), and slightly lower for PF-OS due to the high volatile matter content of the biomass: olive stones.Higher activation temperatures were required for the No1KCl than for the ReKCl precursors and even higher ones for No2OS.The burn off degrees ranged between 10 and 50%, the two limits of the experimental region tested, for the ReKCl precursors while intermediate values were found to be optimal for the No1KCl and No2OS precursors.It should be noted that for precursors No1KClb and No2OS the burn off was not statistically significant, according to the response surface methodology.Consequently, the lowest burn off to yield the highest experimental CO 2 uptake was selected.For the sense of clarity and simplicity the activated samples will be denoted hereafter as follows: RKa-A71 (ReKCla activated carbon), RKb-A75 (ReKClb activated carbon), NKa-A82 (No1KCla activated carbon), NKb-A82 (No1KClb activated carbon) and NOS-A94 (No2OS activated carbon).
, where m c is the mass of char produced and m i is the mass of raw precursor; ** Burn off or degree of activation is estimated as burn off (%) = (m c ´ma ) ˆ100/m c , where m c is the mass of char and m a is the mass of activated sample produced.

Chemical and Textural Characterisation
The elemental composition (carbon, hydrogen and oxygen contents) of the PF resins, the PF-KCl and PF-OS precursors and the corresponding chars and activated materials were determined using a LECO CHN-2000 analyzer.The acid/basic character of the carbon surfaces was evaluated by means of the Point of Zero Charge (pH PZC ), as determined by mass titration.The data are presented in Table 3.The synthesised resins, Re, No1 and No2, do not contain nitrogen and so it has not been included in the table.As expected for a carbon precursor the C contents in the initial resins are high (>70 wt%) and are enhanced during the subsequent steps of carbonisation and activation.The resultant activated materials present C contents well above 90 wt% at the expense of a reduction in the volatile matter content, here represented by the O and H contents.
There is a basification effect on the carbon surfaces as a consequence of the activation with CO 2 .This effect is particularly significant in the case of the activated carbons produced from the acid catalyzed resins (No1 and No2).Basicity might be ascribed to basic oxygen functionalities incorporated from the activating gas (CO 2 ) or to Lewis type basic sites associated to the carbon structure [11].
Textural characterisation of the samples mainly involved the evaluation of the microporosity (pore sizes < 2 nm), given the critical role of these pore sizes on the CO 2 adsorption capacity of the samples.The N 2 and CO 2 adsorption isotherms at ´196 and 0 ˝C, respectively (Figure 1a,b), were determined in a Micromeritics TriStar 3000 volumetric apparatus.Prior to any measurements, the samples were outgassed overnight at 100 ˝C under vacuum.The synthesised resins, Re, No1 and No2, do not contain nitrogen and so it has not been included in the table.As expected for a carbon precursor the C contents in the initial resins are high (>70 wt%) and are enhanced during the subsequent steps of carbonisation and activation.The resultant activated materials present C contents well above 90 wt% at the expense of a reduction in the volatile matter content, here represented by the O and H contents.
There is a basification effect on the carbon surfaces as a consequence of the activation with CO2.This effect is particularly significant in the case of the activated carbons produced from the acid catalyzed resins (No1 and No2).Basicity might be ascribed to basic oxygen functionalities incorporated from the activating gas (CO2) or to Lewis type basic sites associated to the carbon structure [11].
Textural characterisation of the samples mainly involved the evaluation of the microporosity (pore sizes < 2 nm), given the critical role of these pore sizes on the CO2 adsorption capacity of the samples.The N2 and CO2 adsorption isotherms at −196 and 0 °C, respectively (Figure 1a,b), were determined in a Micromeritics TriStar 3000 volumetric apparatus.Prior to any measurements, the samples were outgassed overnight at 100 °C under vacuum.The five tested activated carbons exhibited distinctive textural features, as can be observed in Figure 1a.RKa-A71 is the least developed in terms of total porosity but shows a type I isotherm, according to the IUPAC classification, characteristic of strictly microporous materials.RKb-A75 presents a wider microporosity, characterised by a more open knee at low relative pressures, and it also shows a hysteresis loop at relative pressures above 0.4, which suggests the presence of some mesoporosity in the sample.On the other hand, NKa-A82 and NKb-A82 display similar type I isotherms but with different volumes of adsorbed N 2 along the evaluated pressures.NOS-A94 is the sample that has the most extended textural development, particularly in the domain of microporosity.Regarding CO 2 adsorption at 0 ˝C (Figure 1b), the uptake of the activated carbons follows the order: NKa > NKb « NOS > RKa > RKb.RKa-A71 is the sample with the narrowest microporosity as reflected by the more pronounced curvature of the CO 2 isotherm.
The micropore volumes (W 0 ) and average micropore widths (L 0 ) were determined by applying the Dubinin-Radushkevich (DR) relation [23] and the Stoeckli-Ballerini relation [24] to these isotherms, respectively.This allowed the total microporosity and the narrow microporosity (pore sizes <1 nm) Energies 2016, 9, 189 6 of 17 to be assessed.The textural parameters estimated from the experimental N 2 and CO 2 isotherms are collected in Table 4.As expected, in agreement with the shape of the corresponding isotherms, most of the porosity in NKa-A82, NKb-A82 and NOS-A94 lies in the microporosity domain.To be more precise, NKb-A82 concentrates its microporosity in the narrow microporosity range, whereas NKa-A82 and, particularly, NOS-A94 have a wider microporosity.Samples RKa-A71 and RKb-A75 show similar narrow micropore volumes (W 0,CO2 ).The textural development of RKa-A71 is restricted to this narrow microporosity, whereas RKb-A75 also presents supermicropores (1-2 nm) and mesopores (2-50 nm) as can be inferred from the differences between V p , W 0,N2 and W 0,CO2 .Average micropore widths (L 0,N2 ) of around 1 nm for the NK and NOS based ACs and ca. 2 nm for the RKb-A75 sample were assessed.The narrow microporosity (L 0,CO2 ) fell within the 0.6-0.7 nm range.The route selected to synthesise the PF precursor compromised the textural development that could have been achieved for the activated carbon.In order to gain a better insight into the narrow microporosity, the pore size distributions in the range of 0.3-1 nm were estimated by means of the Density Functional Theory (DFT) for CO 2 adsorption onto slit pore carbons using Micromeritics' software (method: non-negative regularization, little smoothing).The plots are shown in Figure 2. The narrow micropore size distributions of the studied materials can be described as bimodal as they present two main peaks with characteristic pore sizes in the range of 0.55-0.65 and 0.8-0.9nm, respectively.The bimodal shape of the pore size distributions is a characteristic feature for many adsorbents possessing even a small amount of micropores.It is shown that this feature results from the similarity of the local adsorption isotherm in the range of the pore widths for which the gap between peaks (related to the primary and secondary micropore filling mechanism) exists [25].
Generally, the tested carbons show striking similarities in the pore size distributions.Sample The narrow micropore size distributions of the studied materials can be described as bimodal as they present two main peaks with characteristic pore sizes in the range of 0.55-0.65 and 0.8-0.9nm, respectively.The bimodal shape of the pore size distributions is a characteristic feature for many adsorbents possessing even a small amount of micropores.It is shown that this feature results from the similarity of the local adsorption isotherm in the range of the pore widths for which the gap between peaks (related to the primary and secondary micropore filling mechanism) exists [25].
Generally, the tested carbons show striking similarities in the pore size distributions.Sample RKa-A71 seems the exception as it shows a narrower micropore size distribution.The sizes of the narrow micropores in the materials are highly suitable for the separation of CO 2 at sub-atmospheric pressures [15,20].

CO 2 Uptake Screening
The CO 2 adsorption capacity of the produced carbons was first evaluated at sub-atmospheric pressures and room temperature.CO 2 adsorption isotherms at 25 ˝C and up to 101 kPa were determined in a Quantachrome Nova 4000 volumetric device.The samples were previously outgassed overnight at 100 ˝C under vacuum.A commercial activated carbon, Calgon BPL, was also tested for reference purposes [26].This is a Calgon Carbon granular activated carbon specifically designed for use in gas phase applications.The measured isotherms are plotted in Figure 3.The NK and NOS carbons showed substantial CO2 uptakes over the sub-atmospheric pressure range tested, with isotherms characterised by more pronounced slopes at pressures below 20 kPa.Maximum CO2 uptakes of 2.9, 2.4 and 2.3 mol•kg −1 were achieved at 101 kPa for samples NKa-A82, NKb-A82 and NOS-A94, respectively.The isotherms of the two NK samples nearly overlapped in the pressure range below 20 kPa, as might be expected from the similarities in the narrower microporosity of both samples.When the pressure approaches the atmospheric value, differences in the CO2 adsorption capacity appeared revealing the different microporosity features of the two NK activated carbons.The performance of carbon NOS shows striking similarities to that of NKb in agreement with the similarities in the narrow microporosity of both samples.The RK carbons showed similar performances to that of the commercial activated carbon over the tested pressure range with maximum CO2 uptakes of less than 2 mol•kg −1 at 101 kPa.Taking 2 mol•kg −1 as the screening value for selecting optimum CO2 adsorbents, RK carbons were discarded for further study.The NK and NOS carbons showed substantial CO 2 uptakes over the sub-atmospheric pressure range tested, with isotherms characterised by more pronounced slopes at pressures below 20 kPa.Maximum CO 2 uptakes of 2.9, 2.4 and 2.3 mol¨kg ´1 were achieved at 101 kPa for samples NKa-A82, NKb-A82 and NOS-A94, respectively.The isotherms of the two NK samples nearly overlapped in the pressure range below 20 kPa, as might be expected from the similarities in the narrower microporosity of both samples.When the pressure approaches the atmospheric value, differences in the CO 2 adsorption capacity appeared revealing the different microporosity features of the two NK activated carbons.The performance of carbon NOS shows striking similarities to that of NKb in agreement with the similarities in the narrow microporosity of both samples.The RK carbons showed similar performances to that of the commercial activated carbon over the tested pressure range with maximum CO 2 uptakes of less than 2 mol¨kg ´1 at 101 kPa.Taking 2 mol¨kg ´1 as the screening value for selecting optimum CO 2 adsorbents, RK carbons were discarded for further study.for the NK and NOS carbons were obtained using a Micromeritics TriStar 3000 volumetric equipment.BPL was also tested for comparison purposes.Detailed textural characteristics of this activated carbon can be found elsewhere [27].Prior to analysis the samples were outgassed overnight at 100 ˝C under vacuum.

Binary Adsorption from
Experimental data of the single component CO 2 , H 2 , CH 4 , and N 2 adsorption isotherms were fitted to the Sips equation, as follows: Sips equation: q " q s pbPq 1{n 1 `pbPq 1{n where q represents the concentration of the adsorbed species, q s the saturation capacity and P the pressure of the adsorptive.The parameters b, n and q s are temperature dependent; b usually takes the form of the adsorption affinity.The parameter n shows the heterogeneity of the system and its value is usually greater than unity; therefore, the larger the value of n, the more heterogeneous the system is.This empirical three-parameter equation has been widely used for fitting the isotherm data of different hydrocarbons on activated carbon.The Sips equation is believed to give a more accurate fit over a larger pressure regime than the standard Langmuir or Freundlich equations, and provides more accurate prediction of the quantity adsorbed at saturation than the Langmuir equation for heterogeneous adsorbents.However, it suffers from the same disadvantage as the Freundlich equation: it does not reduce to Henry's Law at low surface coverage [28].
Fitting of the model to the experimental data was conducted by means of the Solver Excel tool (Microsoft Office Excel 2010) departing from values of q s and n of 1 and b of 0. The goodness of the fit was evaluated on the basis of the minimum squared relative error (SRE) as given by the following expression: where q exp,i and q mod,i are the experimental and Sips-predicted adsorbed amounts of component i, respectively, and N is the number of experimental data points.The optimal parameters and squared relative errors from fitting the Sips model to the single-component data of CO 2 , H 2 , CH 4 , and N 2 at 25 ˝C are summarized in Table 5. Isotherm experimental data and fittings to the Sips model are shown in Figure 4.
The experimental adsorption data show that much more CO 2 is adsorbed than CH 4 and more significantly than N 2 and H 2 on the tested carbons.The differences in CO 2 , CH 4 and N 2 uptake may be explained by the larger quadrupole moment of CO 2 that produces a strong attraction towards the adsorbent surface resulting in a greater uptake.The high level of polarizability of CO 2 and CH 4 can create a momentary shift in its neutral electrostatic field but this attraction force is much weaker than the quadrupole moment [29].In contrast, N 2 molecules are nonpolar and smaller, compared with CH 4 molecules.For this reason, the differences in CO 2 and N 2 uptake are greater than the differences in CO 2 and CH 4 uptake.Since the narrow micropores allow the strongest interaction between the carbonaceous solid and the hydrogen molecule, it is to be expected that this fraction of the porous volume will make a major contribution to the hydrogen adsorption capacity of the materials.Although hydrogen should only interact through induced polarization, surface chemistry may influence hydrogen adsorption on carbonaceous surfaces, particularly at sub-atmospheric pressures [30,31].By comparing the quantities adsorbed by the phenol-formaldehyde carbons in Figure 4 it can be seen that NKa-A82 is the sample with the greatest CO2, CH4, N2 and H2 uptakes over the sub-atmospheric pressure range tested.Moreover, the adsorption capacities of the three PF carbons are greater than that of the reference carbon, BPL.In terms of CO2 adsorption, the performance at pressures below 20 kPa is quite similar for the NK and NOS carbons and it is only at higher pressures where NKa-A82 stands out.CH4 adsorption isotherms show differentiated uptakes for the three PF carbons that follow the order NKa > NOS > NKb.All three samples present relevant microporosity; in sample NKb narrow micropores (<1 nm) are mainly encountered, whereas for NKa and NOS microporosity >1 nm is also present, in agreement with the textural parameters estimated from the DR relation (see Table 4).In this scenario selectivity effects related to the kinetic diameters of the two gas molecules (3.30Å for CO2 and 3.80 Å for CH4) [29] may play a role in the change in the CO2 and CH4 adsorption trends of the three PF carbons.N2 and H2 adsorption is characterised by linear isotherms that reveal the unspecific nature of the adsorbate-adsorbent interaction [32].
The pure component CO2, H2, CH4, and N2 adsorption isotherms fitted to the Sips model (Equation ( 1)) are represented by the continuous lines in Figure 4.The saturation capacities (qs) and the parameter n have been fitted to the adsorption data for the four gas species independently (Table 5).
The Sips model reproduces the adsorption of CO2, CH4, and N2 with good accuracy, with By comparing the quantities adsorbed by the phenol-formaldehyde carbons in Figure 4 it can be seen that NKa-A82 is the sample with the greatest CO 2 , CH 4 , N 2 and H 2 uptakes over the sub-atmospheric pressure range tested.Moreover, the adsorption capacities of the three PF carbons are greater than that of the reference carbon, BPL.In terms of CO 2 adsorption, the performance at pressures below 20 kPa is quite similar for the NK and NOS carbons and it is only at higher pressures where NKa-A82 stands out.CH 4 adsorption isotherms show differentiated uptakes for the three PF carbons that follow the order NKa > NOS > NKb.All three samples present relevant microporosity; in sample NKb narrow micropores (<1 nm) are mainly encountered, whereas for NKa and NOS microporosity >1 nm is also present, in agreement with the textural parameters estimated from the DR relation (see Table 4).In this scenario selectivity effects related to the kinetic diameters of the two gas molecules (3.30Å for CO 2 and 3.80 Å for CH 4 ) [29] may play a role in the change in the CO 2 and CH 4 adsorption trends of the three PF carbons.N 2 and H 2 adsorption is characterised by linear isotherms that reveal the unspecific nature of the adsorbate-adsorbent interaction [32].
The pure component CO 2 , H 2 , CH 4 , and N 2 adsorption isotherms fitted to the Sips model (Equation ( 1)) are represented by the continuous lines in Figure 4.The saturation capacities (q s ) and the parameter n have been fitted to the adsorption data for the four gas species independently (Table 5).
The Sips model reproduces the adsorption of CO 2 , CH 4 , and N 2 with good accuracy, with substantial deviations for the adsorption of H 2 .It should be noted that the experimental H 2 adsorption data at sub-atmospheric pressures and ambient temperature are subject to greater uncertainty due to the significantly lower uptakes of H 2 under these conditions.The values of q s and b follow the trend CO 2 > CH 4 > N 2 >> H 2 , as might be expected from the experimental data where the capacity and, consequently, the affinity of the carbons to adsorb CO 2 and CH 4 is one and two orders of magnitude greater than that of N 2 and H 2 , respectively.The parameter n takes values close to unity for CO 2 and CH 4 while for N 2 takes values of unity, suggesting that heterogeneity plays a minor role in these systems.The uneven fitting of the H 2 isotherms for the studied carbons can be mainly ascribed to uncertainty of the experimental data.Sample NOS is where greatest deviation from unity in the values of n is found for the adsorption of CO 2 , CH 4 and H 2 .

Multicomponent Adsorption Prediction
In order to predict multicomponent adsorption from binary CO 2 -H 2 , CO 2 -CH 4 , and CO 2 -N 2 mixtures, the fitting of the single component adsorption data to the Sips model represented by Equation ( 1) was rerun to account for the interaction between components in each binary mixture.Given that CO 2 is the strongest adsorbate, the fitting was conducted keeping q s constant (the value of q s estimated from the fitting of single component CO 2 adsorption isotherm for each sample) and adjusting the b and n values to minimize the relative error for the pairs CO 2 -H 2 , CO 2 -CH 4 , and CO 2 -N 2 , respectively.The values of the parameters estimated from these fittings are collected in Table 6.The fitted parameters follow the same trend observed in the previous independent Sips fittings: the n values are close to unity and the b values follow the order CO 2 > CH 4 > N 2 >> H 2 .When mixed the affinity, as represented by the parameter b, increases for the strong adsorbate (CO 2 ) when compared to the pure component CO 2 adsorption data independent fitting.Likewise, the weaker adsorbate shows a substantial decrease in affinity particularly in the CO 2 -H 2 and CO 2 -N 2 systems.
In this way, use of the parameters from the fitting of pure component data pairs guarantees the thermodynamic consistency of the resulting analytical expression of the multicomponent Sips model.Using the same analogy for extending the single-component Langmuir equation to that for multicomponent adsorption, the following equation is obtained for the multicomponent Sips model [33]: `bj y j P ˘1{n where i and j stand for the components in the binary mixture, y is the mole fraction of the corresponding component in the gas phase, and N is the number of components in the gas mixture, i.e., 2. However, this equation only corresponds to a specific case of surface energetic heterogeneity.For normal activated carbons in which the energy sites are highly correlated, the Ideal Adsorbed Solution Theory (IAST) should be used.Application of the IAST with the concept of hypothetical pure-component pressure results in the following equation [34]: It can be seen that Equations ( 3) and ( 4) deliver different expressions to reproduce the multicomponent Sips model on the basis of different assumptions regarding the heterogeneity of the adsorbate-adsorbent system.Nevertheless, both equations were used in the present study to predict the binary adsorption equilibrium for CO 2 -H 2 , CO 2 -CH 4 , and CO 2 -N 2 systems and the results are discussed and compared.The parameter values used for such multicomponent adsorption predictions were those previously obtained from the combined fitting of the pure component adsorption data of the pairs of gases in each mixture as shown in Table 6.
The predictions of the binary gas adsorption equilibria from the multicomponent Sips model represented by Equations ( 3) and ( 4) and from the parameters included in Table 6 are depicted in Figures 5-7.Multicomponent predictions were assessed under the following temperature and pressure conditions: 25 ˝C and 100 kPa.
Energies 2016, 9, 189 12 of 18 where i and j stand for the components in the binary mixture, y is the mole fraction of the corresponding component in the gas phase, and N is the number of components in the gas mixture, i.e., 2. However, this equation only corresponds to a specific case of surface energetic heterogeneity.For normal activated carbons in which the energy sites are highly correlated, the Ideal Adsorbed Solution Theory (IAST) should be used.Application of the IAST with the concept of hypothetical pure-component pressure results in the following equation [34]: It can be seen that Equations ( 3) and ( 4) deliver different expressions to reproduce the multicomponent Sips model on the basis of different assumptions regarding the heterogeneity of the adsorbate-adsorbent system.Nevertheless, both equations were used in the present study to predict the binary adsorption equilibrium for CO2-H2, CO2-CH4, and CO2-N2 systems and the results are discussed and compared.The parameter values used for such multicomponent adsorption predictions were those previously obtained from the combined fitting of the pure component adsorption data of the pairs of gases in each mixture as shown in Table 6.
The predictions of the binary gas adsorption equilibria from the multicomponent Sips model represented by Equations ( 3) and ( 4) and from the parameters included in Table 6 are depicted in Figures 5-7.Multicomponent predictions were assessed under the following temperature and pressure conditions: 25 °C and 100 kPa.
Globally, the predicted multicomponent adsorption isotherms show a reduction in the uptakes of the four components when mixed in binary CO2-H2, CO2-CH4 or CO2-N2 mixtures.However, while the CO2 uptake when mixed in a 1:1 molar ratio is reduced to 60%, 70% and 75% (average values for the four evaluated carbons in the CO2-CH4, CO2-N2 and CO2-H2 binary mixtures, respectively) of the pure gas CO2 adsorption at 25 °C and 100 kPa, the H2, N2 and CH4 uptakes drastically drop down to around 30-35% of those corresponding to pure gas adsorption.This suggests that the presence of another component in the mixture influences the adsorption of CO2 to a lesser extent.It is apparent that when n (Table 6) approaches unity the values of the numerator and the denominator of Equations ( 3) and ( 4) tend to match each other and both Equations ( 3) and (4) give similar predictions.This suggests that there is little heterogeneity in the systems that could influence the adsorption of the binary mixtures onto the evaluated carbons.The CO2-H2 system is where greater deviations between the two predictions are observed, particularly for the H2 uptake.It should be noted that at sub-atmospheric pressures and room temperature experimental H2 adsorption is characterised by extremely low uptakes.In addition, the affinity of the carbons towards H2 adsorption is significantly lower than that to CO2.Consequently, binary adsorption prediction for the CO2-H2 system is subject to greater uncertainty.Moreover, predicted CO2 adsorption in the CO2-H2 binary mixtures nearly matches pure component CO2 adsorption at similar partial pressures suggesting that H2 adsorption in these mixtures can be considered as negligible.This is in agreement with previous results from the research team [6,35].
The CO2 uptake at yj = 0 (where j stands for H2, N2 and CH4, respectively) is slightly overestimated for the CO2-H2 and CO2-N2 systems compared to the pure component CO2 adsorption data.This may be attributed to the different affinity of the adsorbent towards CO2 and H2 or N2.
In the case of CO2-CH4 (Figure 6) and CO2-N2 (Figure 7) the predictions of the two Equations ( 3) and (4) seem consistent.The values of n (Table 6) are close to unity for the CO2-N2 system and thus Equations 3 and 4 deliver similar predictions.For the phenolic resin-biomass composite derived carbon, NOS-A94, Equation (3) predicts slightly greater CH4 uptakes (+0.15 mol•kg −1 ) than Equation Globally, the predicted multicomponent adsorption isotherms show a reduction in the uptakes of the four components when mixed in binary CO 2 -H 2 , CO 2 -CH 4 or CO 2 -N 2 mixtures.However, while the CO 2 uptake when mixed in a 1:1 molar ratio is reduced to 60%, 70% and 75% (average values for the four evaluated carbons in the CO 2 -CH 4 , CO 2 -N 2 and CO 2 -H 2 binary mixtures, respectively) of the pure gas CO 2 adsorption at 25 ˝C and 100 kPa, the H 2 , N 2 and CH 4 uptakes drastically drop down to around 30-35% of those corresponding to pure gas adsorption.This suggests that the presence of another component in the mixture influences the adsorption of CO 2 to a lesser extent.
It is apparent that when n (Table 6) approaches unity the values of the numerator and the denominator of Equations ( 3) and (4) tend to match each other and both Equations (3) and (4) give similar predictions.This suggests that there is little heterogeneity in the systems that could influence the adsorption of the binary mixtures onto the evaluated carbons.The CO 2 -H 2 system is where greater deviations between the two predictions are observed, particularly for the H 2 uptake.It should be noted that at sub-atmospheric pressures and room temperature experimental H 2 adsorption is characterised by extremely low uptakes.In addition, the affinity of the carbons towards H 2 adsorption is significantly lower than that to CO 2 .Consequently, binary adsorption prediction for the CO 2 -H 2 system is subject to greater uncertainty.Moreover, predicted CO 2 adsorption in the CO 2 -H 2 binary mixtures nearly matches pure component CO 2 adsorption at similar partial pressures suggesting that H 2 adsorption in Energies 2016, 9, 189 14 of 17 these mixtures can be considered as negligible.This is in agreement with previous results from the research team [6,35].
The CO 2 uptake at y j = 0 (where j stands for H 2 , N 2 and CH 4 , respectively) is slightly overestimated for the CO 2 -H 2 and CO 2 -N 2 systems compared to the pure component CO 2 adsorption data.This may be attributed to the different affinity of the adsorbent towards CO 2 and H 2 or N 2 .
In the case of CO 2 -CH 4 (Figure 6) and CO 2 -N 2 (Figure 7) the predictions of the two Equations ( 3) and (4) seem consistent.The values of n (Table 6) are close to unity for the CO 2 -N 2 system and thus Equations 3 and 4 deliver similar predictions.For the phenolic resin-biomass composite derived carbon, NOS-A94, Equation (3) predicts slightly greater CH 4 uptakes (+0.15 mol¨kg ´1) than Equation ( 4) for molar fractions of methane (y CH4 ) in the binary mixture between 0.3 and 0.6.Both CO 2 and CH 4 show specific interaction with the carbon surface, as reflected by the shape of the isotherms (type I, according to the IUPAC classification).However, despite the preferential adsorption of CO 2 over CH 4 , competition between both adsorbates exists.The significantly higher critical temperature of CO 2 in comparison with CH 4 makes carbon dioxide more likely to behave as a condensable steam than as a supercritical gas, making it less volatile and increasing its chances of adsorption.Moreover, CO 2 presents a higher polarizability which may enhance attractive forces with the surface and a permanent quadrupole, leading to stronger interactions with any solid surface.
The simplified extended Sips model (Equation ( 3)) shows limitations bearing in mind the assumptions needed to extend the single component Sips equation to the multicomponent one.However, the observed deviations between the multicomponent predictions represented by Equations ( 3) and ( 4) are small and therefore, both could be applied to predict the adsorption of CO 2 , CH 4 , and N 2 on the evaluated carbons in binary CO 2 -CH 4 , and CO 2 -N 2 mixtures.The H 2 uptakes predicted for the CO 2 -H 2 systems should be handled with care given the uncertainty of the experimental H 2 adsorption data under sub-atmospheric pressures and room temperature.H 2 adsorption can be regarded as negligible in the CO 2 -H 2 systems.Moreover, data on the performance of the phenolic resin-derived carbon for CO 2 -CH 4 adsorption were also experimentally obtained in a lab scale fixed-bed adsorption unit.Details can be found elsewhere [6].The CO 2 and CH 4 uptakes assessed at 120 kPa and 25 ˝C for a 1:1 CO 2 :CH 4 binary mixture are in good agreement with the multicomponent predictions at 100 kPa and 25 ˝C presented herein; for instance, the predicted CO 2 uptake on carbon NKa-A82 for a 1:1 CO 2 :CH 4 mixture at 120 kPa is 1.90 mol¨kg ´1 in agreement with 2.03 mol¨kg ´1 estimated experimentally.

Selectivity to CO 2 Separation
The selectivity of the prepared carbons to separate CO 2 from CO 2 -H 2 , CO 2 -N 2 and CO 2 -CH 4 mixtures at ambient temperature and sub-atmospheric pressures was evaluated on the basis of the multicomponent adsorption predictions.The following expression was used: where q 1 stands for the CO 2 uptake of the carbon from the binary mixture and q 2 represents the H 2 , N 2 and CH 4 uptakes, respectively.y 1 and y 2 are the corresponding molar fractions of the gas component in the binary mixtures.From the IAST-Sips multicomponent adsorption model represented by Equation ( 4), the following equation can be inferred to account for the selectivity to separate CO 2 from binary mixtures: where b 1 and b 2 stand for the affinity constants of CO 2 and H 2 , N 2 and CH 4 , respectively.According to Equation ( 6) the selectivity to separate CO 2 from binary mixtures is independent of the partial pressures of the components in the binary mixture.Table 7 summarizes the selectivities of the carbons as estimated from Equation ( 6  The selectivity values follow the order CO 2 -H 2 >> CO 2 -N 2 > CO 2 -CH 4 indicating that the separation of CO 2 from CO 2 -H 2 mixtures at sub-atmospheric pressures and ambient temperature is favoured.BPL shows the greatest selectivity values to separate CO 2 from CO 2 -H 2 and CO 2 -N 2 binary mixtures whereas the phenolic resin-derived carbon NKb-A82 presents the highest selectivity for CO 2 to be separated from CO 2 -CH 4 mixtures.Nevertheless, selectivity values for the four evaluated carbons are in the same order of magnitude for each mixture and the values are particularly close in the case of CO 2 -N 2 and CO 2 -CH 4 separation. The selectivity value, as estimated from Equation ( 6), could serve as a rough sorbent selection parameter.However, for a more precise evaluation the working capacities (differences between the gas uptakes of both components under adsorption and regeneration conditions) and the heat required for the regeneration of the adsorbent would also need to be taken into account [36].

Conclusions
Phenolic resin-derived carbons were prepared and evaluated for CO 2 adsorption at sub-atmospheric pressures.Single component adsorption isotherms of CO 2 , H 2 , N 2 and CH 4 were measured at 25 ˝C and up to 100 kPa and fitted to the Sips model.Binary adsorption from CO 2 -H 2 , CO 2 -N 2 and CO 2 -CH 4 mixtures was then predicted by applying the extended multicomponent Sips model and the Ideal Adsorbed Solution Theory (IAST) in conjunction with the Sips model.Both equations showed similar predictions for the adsorption of CO 2 , CH 4 and N 2 on the evaluated carbons in the binary mixtures.The adsorption of H 2 at the conditions evaluated can be considered negligible.Both Sips multicomponent equations might predict binary adsorption in the studied systems.This is a significant advantage from the viewpoint of computational modelling requirements in adsorption process design.
In terms of CO 2 uptake, the performance of the acid resin-derived carbons in separating CO 2 from CO 2 -CH 4 , CO 2 -H 2 , and CO 2 -N 2 at atmospheric pressure was superior to that of a reference commercial carbon (Calgon BPL) and an even higher selectivity towards CO 2 was found in the separation of CO 2 -CH 4 .

Figure 1 .
Figure 1.N 2 adsorption isotherms at ´196 ˝C (a) and CO 2 adsorption isotherms at 0 ˝C (b) for the activated carbons tested (bold symbols represent adsorption and empty symbols desorption).

Energies 2016, 9 , 189 7 of 18 Figure 2 .
Figure 2. Micropore size distributions from the CO2 adsorption isotherms at 0 °C by means of the DFT slit pore carbon model.

Figure 2 .
Figure 2. Micropore size distributions from the CO 2 adsorption isotherms at 0 ˝C by means of the DFT slit pore carbon model.

Figure 3 .
Figure 3. CO 2 adsorption isotherms at 25 ˝C and sub-atmospheric pressures for the studied carbons.

2 Figure 4 .
Figure 4. CO 2 , CH 4 (a); H 2 (b) and N 2 (c) adsorption isotherms at 25 ˝C on samples NKa-A82, NKb-A82, NOS-A94 and BPL.Fitting of the single component adsorption data to the Sips model is represented by the solid lines.

Table 1 .
Departing materials and conditions for the production of PF resin-derived carbon precursors.
* F/P: formaldehyde to phenol molar ratio; ** K/R: potassium chloride to resin weight ratio.
Table 2 summarises the conditions of the carbonisation and

Table 2 .
Conditions of carbonisation and activation with CO 2 for each precursor.
* Char yield has been estimated as yield

Table 4 .
Textural parameters evaluated from the N 2 and CO 2 adsorption isotherms at ´196 and 0 ˝C, respectively.

Table 5 .
Optimal parameters of the single-component CO 2 , CH 4 , H 2 , and N 2 adsorption data fitting to the Sips model.

Table 6 .
Optimal parameters of the single-component CO 2 , H 2 , CH 4 , and N 2 adsorption data fitting to the Sips model for multicomponent prediction.

Table 7 .
Selectivities of the carbons to separate CO 2 from CO 2 -H 2 , CO 2 -N 2 and CO 2 -CH 4 binary mixtures.