Adsorption of Carbon Dioxide, Methane, and Their Mixtures in Porous

24 Jan 2013 - adsorption at 77 K, Vsp has been calculated with a probe molecule having the size of a nitrogen molecule. The porous volumes Vsp are giv...
3 downloads 0 Views 2MB Size
Download PDF
Article pubs.acs.org/Langmuir

Adsorption of Carbon Dioxide, Methane, and Their Mixtures in Porous Carbons: Effect of Surface Chemistry, Water Content, and Pore Disorder Pierre Billemont,† Benoit Coasne,*,‡,§,∥ and Guy De Weireld*,† †

Service de Thermodynamique, Faculté Polytechnique, UMons, Université de Mons, 20 Place du Parc, 7000 Mons, Belgium Institut Charles Gerhardt Montpellier, CNRS (UMR 5253), ENSCM, Université Montpellier 2, 8 rue de l’Ecole Normale, 34096 Montpellier, France § Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge Massachusetts 02139-4307, United States ∥ 2, UMI 3466 CNRS-MIT, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307, United States ‡

S Supporting Information *

ABSTRACT: The adsorption of carbon dioxide, methane, and their mixtures in nanoporous carbons in the presence of water is studied using experiments and molecular simulations. Both the experimental and numerical samples contain polar groups that account for their partially hydrophilicity. For small amounts of adsorbed water, although the shape of the adsorption isotherms remain similar, both the molecular simulations and experiments show a slight decrease in the CO2 and CH4 adsorption amounts. For large amounts of adsorbed water, the experimental data suggest the formation of methane or carbon dioxide clathrates in agreement with previous work. In contrast, the molecular simulations do not account for the formation of such clathrates. Another important difference between the simulated and experimental data concerns the number of water molecules that desorb upon increasing the pressure of carbon dioxide and methane. Although the experimental data indicate that water remains adsorbed upon carbon dioxide and methane adsorption, the molecular simulations suggest that 40 to 75% of the initial amount of adsorbed water desorbs with carbon dioxide or methane pressure. Such discrepancies show that differences between the simulated and experimental samples are crucial to account for the rich phase behavior of confined water−gas systems. Our simulations for carbon dioxide−methane coadsorption in the presence of water suggest that the pore filling is not affected by the presence of water and that adsorbed solution theory can be applied for pressures as high as 15 MPa.

1. INTRODUCTION Ecological concerns have led to increasing research efforts in the field of carbon dioxide capture and storage (CCS).1,2 The main solutions being considered for CO2 storage are sequestration in geological media such as oil and gas reservoirs, deep saline formations, and unminable coal beds. The storage of supercritical carbon dioxide in coal beds has the advantage of provoking the liberation of methane that is naturally stored in these coal seams, which is referred to as enhanced coal bed methane (ECBM). Although ECBM is already extracted in Canada, Australia, China, and India, fundamental and practical aspects still need to be understood and developed in order to enhance the recovery process. Advanced knowledge is required to understand complex issues covering the sorption mechanism, storage capacity, diffusion, permeability, and swelling. As far as swelling is concerned, several experimental and simulation studies have addressed the coupling between the adsorption and volume strain of coal.3,4 Of particular interest, Brochard et al.5 have developed poromechanics constitutive equations that allow a description of the swelling or shrinkage of microporous © 2013 American Chemical Society

solids upon gas adsorption. Another important issue relevant to CO2 storage and CH4 recovery in coals concerns the effect of the presence of adsorbed water, which cannot be avoided owing to the partial hydrophilic nature of the samples.6,7 In addition to reducing the storage capacity of coals, the presence of such adsorbed water leads to new complex phenomena such as gas dissolution/solubilization8,9 and coal swelling, which strongly affect the diffusion and permeability properties of the sample. Although most adsorption and diffusion experiments have been performed on dry samples,10−14 several works have considered adsorption on moisture-equilibrated7,15−17 coals. In a recent study,17 we studied the adsorption of carbon dioxide and methane in the presence of water using experiments on an activated carbon and molecular simulations in slit-shaped nanopores. We found that water does not affect the pore-filling mechanism because the shape of the adsorption isotherm and Received: December 15, 2012 Revised: January 22, 2013 Published: January 24, 2013 3328

dx.doi.org/10.1021/la3048938 | Langmuir 2013, 29, 3328−3338

Langmuir

Article

applied to the sample volume V0sample. The excess adsorbed mass is then given by mexcess = Δm + V0sampleρgas(T, p). The second buoyancy correction is applied to the adsorbed phase to take into account the buoyancy effect on the adsorbed phase volume Vφs. The absolute adsorbed mass is then given by mabsolute = mexcess + Vφs(T, p) ρgas(T, p). The adsorbed phase volume Vφs is estimated according to the following method that has been proposed by Gensterblum et al.23 Excess sorption isotherms with respect to the free gas density exhibit a linear trend at high pressure in the density range of >250 kg/m3 for CO2 and >80 kg/m3 for CH4. The intercept of this extrapolated linear trend with the gas density axis (i.e., x axis) gives an accurate estimate of the density of the adsorbed phase and thus of the adsorbed phase volume. The gas phase density ρgas is determined using an appropriate equation of state (EOS). The helium density required to estimate V0sample is determined from a modified Benedict−Webb−Rubin EOS.24 The water vapor density is estimated using the data by Wagner and Pruss,25 and those for carbon dioxide and methane are estimated using the EOS by Span and Wagner26 and the EOS by Setzmann and Wagner,27 respectively. The setup, which has been described in detail by De Weireld et al.,28 allows measurements in the temperature range of 243−393 K and in the pressure range of 0−16 MPa. The pressure is measured from vacuum (10−3 Pa) up to 133.3 kPa with an MKS Baratron 621C pressure sensor and up to 16 MPa with a Tecsis series P3382 pressure sensor. The whole system is placed in a climate chamber that maintains the temperature at a constant value in order to avoid local condensation in the system. 2.1.2. Sample and Sample Preparation. The experimental sample, Filtrasorb 400 (F400), used in the present work has been described in detail in our previous study.17 F400 is an activated carbon of the Calgon Carbon Corporation, which was kindly supplied by Chemviron Carbon GmbH, Germany. The sample was dried at 473 K for 24 h prior to performing the experiments. Fine characterization of this sample, which has been performed in the present work, will be described in section 3. 2.1.3. Moisture Equilibration of the Samples. The method used to preadsorb water prior to CO2 or CH4 sorption measurements, which has been fully described in our previous paper,17 can be summarized as follows. A cylinder containing pure water is placed in the climate chamber. The temperature is maintained at the temperature at which the CO2 or CH4 adsorption experiment has to be measured (so that the pressure inside the adsorption cell is the saturating vapor pressure of water at the temperature of the experiment). The adsorption cell containing the sample is brought into contact with the cylinder containing water until the desired amount of preadsorbed water is reached. This preadsorbed amount, which corresponds to the mass gained by the sample upon moisture equilibration mads water, is adjusted by increasing or decreasing the water pressure in the sample cell. Once moisture-equilibrated samples have been obtained using the method described above, the cylinder containing pure water is isolated from the sample and CO2 or CH4 adsorption experiments are performed according to the classical procedure (i.e., a quantity of gas is introduced into the adsorption cell and the mass gained by the sample after equilibration has been reached is recorded as a function of the final pressure). Assuming that the amount of preadsorbed water remains constant during the experiment, the CO2 or CH4 adsorbed mass at a given pressure and temperature is determined by Δm = mmeasured(T, p) − (m0sample + mads water), with mmeasured(T, p) being the apparent mass measured at constant temperature T and pressure p. The latter assumption is supported by the fact that the mass sample after CO2 and CH4 adsorption/desorption cycles are carried out is close to the initial mass m0sample + mads water. mexcess and mabsolute are determined according to the same procedure described above for pure CO2 and CH4 adsorption experiments. The skeletal volume V0sample used to calculate the excess adsorbed amount is the same as that used under dry conditions. The influence of water on the density of the bulk phase is neglected because the partial pressure of water is negligible compared to the high CO2 or CH4 pressure. It should also be noted that no correction was made for the solubility of gas in preadsorbed

the pressure at which the maximum adsorbed amount of CH4 or CO2 is reached are nearly insensitive to the number of preadsorbed water molecules. Both the experimental and simulated data further showed a linear decrease in the adsorbed amounts of methane and carbon dioxide upon increasing the number of adsorbed water molecules. Although the molecular simulation and experiments were found to be in fair agreement, small discrepancies between the two sets of data were thought to be due to the structural differences between the simulated and experimental samples. In particular, the simple graphite nanopores considered in our previous molecular simulation work and its hydrophobic nature cannot represent the features of real porous carbons that exhibit morphological disorder and heterogeneous chemistry. To gain insight into the effect of morphological disorder and surface chemistry on adsorption in coals, we report in this Article experiments and molecular simulations on the adsorption of CO2 and CH4 in the presence of water in disordered porous carbons having partial hydrophilicity. Both the experiments and molecular simulations consist of determining adsorption isotherms at 318.15 K and isosteric heat of adsorption curves for pure CO2 and CH4 and for CO2/H2O and CH4/H2O mixtures in porous carbons. In addition, adsorption isotherms for CO2/CH4/H2O have been investigated by means of molecular simulation. Experiments are performed for a Filtrasorb 400 activated carbon. An activated carbon was selected as a first step toward considering real coal samples; it consists of a simpler system with a chemical composition and microporous structure comparable to those of natural coal. The molecular simulations consist of grand canonical Monte Carlo simulations for a disordered porous carbon18 that has been modified to include polar groups (hydroxyl groups) in order to make it partially hydrophilic and hence to account for the presence of preadsorbed water. We note that other molecular models of coal, which take into account of chemical heterogeneities, have been reported in the literature.19,20 The remainder of this Article is organized as follows. Section 2 presents the details of the experimental and molecular simulation techniques. Section 3 reports the characterization of porous carbons, the adsorption isotherms, and the isosteric heat of adsorption curves for CO2, CH4, and their mixture in the presence of water in nanoporous carbons. Both the experimental and molecular simulation data are discussed. Section 4 presents some concluding remarks and discusses what can be learned from the comparison between the experimental and simulation results.

2. EXPERIMENTAL AND MOLECULAR SIMULATION METHODS 2.1. Experimental Methods. 2.1.1. Description of the Apparatus. Adsorption isotherms were measured using an in-housebuilt apparatus around a marketed Rubotherm high-pressure magnetic suspension balance.21 The high-pressure part of the magnetic suspension balance is exposed to the sorptive, H2O, CO2, or CH4, at constant temperature and increasing pressure. The adsorbed amount is determined from the apparent mass change Δm = mmeasured(T, p) − m0sample of the sample recorded during this procedure, where m0sample is the original sample mass and mmeasured(T, p) the mass measured at constant temperature T and pressure p. This apparent sample mass change is corrected for two buoyancy effects. The first correction consists of taking into account the skeletal volume V0sample of the sample. V0sample is determined from a helium isotherm measurement in which helium is assumed to be nonadsorbing.22 The mass change during the helium measurement is thus due to only a buoyancy effect 3329

dx.doi.org/10.1021/la3048938 | Langmuir 2013, 29, 3328−3338

Langmuir

Article

0.1364 nm from the carbon atom and 0.096 nm from the hydrogen atom with a COH angle of 113°. The carbon and oxygen atoms are the center of a Lennard-Jones interaction potential with the interaction parameters reported in Tables S2 and S3 of the Supporting Information file. In our simulations, all of the carbon atoms are described as a Lennard-Jones sphere with the following parameters: σ = 0.34 nm and ε = 28 K.35 The interaction energy UAB between A and B (A and B represent the adsorbed molecule, group, or carbon atom) is given by

water so that the sorption capacities reported in this Article are slightly overestimated. 2.2. Molecular Simulation Methods. 2.2.1. Water, Carbon Dioxide, Methane, and Nitrogen Models. The single-point charge (SPC) model by Berendsen et al.29 was used for water because it reproduces the structure and thermodynamics of bulk liquid water at ambient temperature. In this model, water is represented as a rigid molecule; the hydrogen atoms are 0.100 nm away from the oxygen atom and the HOH angle is 109.47°. The oxygen atom is the center of a Lennard-Jones interaction potential with the interaction parameters reported in Table S1 of the Supporting Information file. In addition, the atoms in the water molecule carry the following partial charges: −0.82e for the oxygen and +0.41e for each of the hydrogen atoms. The rigid model by Harris and Yung was used in this work to describe the carbon dioxide molecule.30 The carbon−oxygen distance is 0.115 nm. Each of the three atoms is a Lennard-Jones site that also carries a partial charge. The interaction parameters, partial charges, and the geometry of the carbon dioxide molecule are shown in Table S1 of the Supporting Information file. In our simulations, the methane and nitrogen molecules are simply described as a single Lennard-Jones sphere with the parameters shown in Table S1 of the Supporting Information file. 2.2.2. Porous Carbons Models. Two models of porous carbons have been used in this work. The first model, CS1000A, which has been obtained by Jain et al. using a constrained reverse Monte Carlo method, mimics the structure of activated saccharose-based carbon obtained at 1000 °C (Figure 1a).18,31 Although this atomistic model

U

AB

=

∑∑ i

j

qiA qjB 4πε0rijAB

+

⎡⎛ AB ⎞12 σ AB⎢⎜ ij ⎟ qεij ⎢⎜ AB ⎟ r ⎣⎝ ij ⎠

⎛ σ AB ⎞6 ⎤ ij ⎥ − ⎜⎜ AB ⎟⎟ ⎥ r ⎝ ij ⎠ ⎦

(1)

where the two first symbols Σ indicate that the interaction is summed over sites i of A and sites j of B, respectively. The first term in eq 1 is the Coulombic interaction (qAi and qBj are the charges of sites i and j, rAB ij is the distance between the two sites, and ε0 is the dielectric permittivity of vacuum). The second terms in eq 1 are the repulsion/ AB dispersion interactions between the two sites with εAB ij and σij being the corresponding Lennard-Jones energy and size interaction parameters. The unlike atom Lennard-Jones interaction parameters in eq 1 have been determined using the Lorentz−Berthelot combining rules. It should be noted that there is no Lennard-Jones interaction with the H atoms and no electrostatic interaction with carbon atoms that are nonbonded to an H or O atom. The Coulombic interaction was computed using the Ewald summation technique.36 The parameters for the Ewald sum are α = 0.128 Å−1 and kmax = 7. 2.2.3. Grand Canonical Monte Carlo (GCMC). We performed GCMC simulations of nitrogen adsorption at 77 K (for characterization purposes) as well as carbon dioxide, methane, and water at 318.15 K in CS1000A and CS1000AF. In CS1000AF, we also performed GCMC simulations of carbon dioxide and methane adsorption in the presence of preadsorbed water (four quantities of preadsorbed water were considered). We also considered the coadsorption of carbon dioxide−methane mixtures with bulk compositions of 75−25, 50−50, and 25−75% in the presence of preadsorbed water (in this case, a single quantity of preadsorbed water has been selected). The GCMC technique is a stochastic method that simulates a system having a constant volume V (the pore with the adsorbed phase) in equilibrium with an infinite reservoir of molecules imposing its chemical potential μA on each species (A = CO2, CH4, H2O, and N2) at temperature T. The absolute adsorption/desorption isotherm is given by the ensemble average of each quantity of adsorbate molecule as a function of the fugacity fA of the reservoir (the latter are determined from the chemical potential μA). In the case of CO2, CH4, and CO2−CH4 mixture adsorption in the presence of preadsorbed water, we started from an initial configuration obtained along the water adsorption isotherm. Unlike our previous study,17 the number of adsorbed water molecules is not kept constant upon subsequent gas adsorption. Although the number and the position of carbon atoms in the porous carbon models are held constant, the −OH and −H groups are allowed to rotate around the carbon that carries them.

Figure 1. (a) Molecular configuration of a model of disordered porous carbon obtained by RMC.18 (b) The same model as in panel a after hydrogen and hydroxyl groups are added (this work). The sticks are C−C, C−H, and C−O bonds. Red and white spheres in the functionalized sample are the oxygen and hydrogen atoms, respectively. The models in panels a and b will be referred to as CS1000A and CS1000AF, respectively, throughout the Article. The size of the simulation box is 5 nm. captures the structural features of disordered porous carbons, it does not allow the study of water adsorption because it does not contain any oxygen-, sulfur-, or nitrogen-containing groups that are responsible for the partial hydrophilicity of porous carbons. To overcome this limitation, polar groups consisting of hydroxyl groups were added to the CS1000A model in order to induce partial hydrophilicity of the sample. Hydrogen atoms were also added to the sample in order to match the composition of the experimental active carbon CS1000A (molar ratios H/C = 0.091 and O/C = 0.087).32 This functionalized model, which is shown in Figure 1b, will be referred to as CS1000AF in what follows. Although the −OH and −H groups were randomly distributed on carbon atoms, it was ensured that the same carbon atom did not carry more than one group. After groups were added to the sample, the system was relaxed by means of Monte Carlo simulations in order to allow the −OH and −H groups to rotate around the carbon atom and find the most favorable configuration. The interaction parameters and partial charges of the groups have been taken from the OPLS all-atom force field.33 The bond parameters are from the AMBER all-atom force field.34 The bonds in the −COH (hydroxyl) groups are treated as rigid. The oxygen atom is located

3. RESULTS AND DISCUSSION 3.1. Characterization of the Experimental Sample and Numerical Models. Properties for the F400 carbon were reported in our previous study.17 The mass composition is about 90 wt % carbon, 6 wt % oxygen, and 0.2 wt % hydrogen. To characterize the sample further, nitrogen sorption at 77 K was performed using a volumetric adsorption apparatus (BELSORP-max, Bel Japan Inc.). Figure 2 shows the adsorption isotherm obtained for F400. The BET method37 applied to the data leads to a specific surface area of 1150 m2/g and a porous volume of 0.61 cm3/g. Figure 2 also shows the simulated nitrogen isotherms at 77 K for CS1000A and CS1000AF. At low relative pressures, the adsorbed amounts of 3330

dx.doi.org/10.1021/la3048938 | Langmuir 2013, 29, 3328−3338

Langmuir

Article

Figure 2. N2 adsorption isotherm at 77 K on porous carbons. The circles are experimental data for the Filtrasorb F400 activated carbon (closed and open symbols are the adsorption and desorption data, respectively). The closed and open triangles are the simulated N2 adsorption isotherms for CS1000A and CS1000AF, respectively. Adsorbed amounts are in mmol/g of sample. p0 is the bulk saturating vapor pressure for N2 at 77 K. The inset shows the same data plotted on a semilogarithmic scale.

Figure 3. Simulated pore size distribution of the CS1000A (closed triangles) and CS1000AF (open triangles) models and pore size distribution of the activated carbon (closed circles) determined by the MP method.39

CS1000A and CS1000AF using the method proposed by Gelb and Gubbins.40 In this method, the pore size distribution is obtained as follows: for a large number of mathematical points A selected randomly within the porous sample, we determine the largest sphere containing A without overlapping with any of the carbon atoms. The pore size distributions for CS1000A and that for CS1000AF show a mean value at about 1.1 nm. This value is in agreement with the value obtained by Coasne et al.41 The results in Figure 3 show that adding heteroatoms to the porous carbon affects the pore size distribution because N(H) for CS1000AF is lower than that for CS1000A for all probe sizes. To compare the porous volume given by the mathematical procedure above and that obtained from nitrogen adsorption at 77 K, Vsp has been calculated with a probe molecule having the size of a nitrogen molecule. The porous volumes Vsp are given in Table 1. The values obtained using the two methods are in fair agreement, although the mathematical procedure overestimates by 15% the porous volume obtained by nitrogen adsorption. 3.2. Effect of Surface Chemistry and Pore Disorder on CO2, CH4, and Water Adsorption. 3.2.1. Adsorption of Pure Carbon Dioxide and Methane. All carbon dioxide and methane adsorption measurements in this work were performed at 318.15 K because this temperature is relevant to enhanced coal bed methane (ECBM) recovery. Experimental excess sorption isotherms are given in Figure S1 of the Supporting Information file. The adsorbed-phase density used to obtain absolute sorption isotherms are 936 and 414 kg/m3 for CO 2 and CH 4 , respectively. Figure 4 shows the experimental absolute adsorption isotherms for carbon dioxide (a) and methane (b) at 318.15 K on activated carbon F400. Both adsorption isotherms, which exhibit reversible and continuous pore filling, are type I according to the IUPAC classification.42 The adsorbed amount increases rapidly with increasing pressure because of the very small pore sizes in F400 and then reaches a plateau as the pores get filled. At a pressure of 15 MPa, the adsorbed amount is 10 mmol/g for CO2 and 6 mmol/g for CH4. Figure 4 also shows the isosteric heat of adsorption Qst as a function of the absolute adsorbed amounts for CO2 and CH4 in activated carbon F400. The latter curve has been obtained using the isosteric method from four absolute adsorption isotherms measured at temperatures of between 288

nitrogen are larger for CS1000AF than for CS1000A, owing to enhanced interactions between the nitrogen molecules and the heteroatoms in CS1000AF. In contrast, at higher pressures, the adsorbed amount in CS1000A is slightly larger than that in CS1000AF because part of the pore volume in CS1000AF is not available for adsorption as a result of the presence of the heteroatoms. Those simulated adsorption isotherms have also been interpreted by means of the BET method; the resulting specific surface areas and pore volumes are given in Table 1. The calculated BET specific surface area (SBET) and pore volume (VP) for CS1000AF are respectively 12.1 and 15.3% lower than for CS1000A. Table 1. Specific Surface Areas (SBET) and Specific Pore Volumes (VP) Determined by the BET Method and Specific Pore Volume (Vsp) Determined by a Monte Carlo Procedure for Activated Carbon Sample F400 and Models CS1000A and CS1000AF porous carbons

SBET (m2/g)

Vp (cm3/g)

Vsp (cm3/g)

Filtrasorb 400 CS1000A CS1000AF

1150 1601 1408

0.61 0.747 0.632

0.867 0.717

For both CS1000A and CS1000AF samples, we also computed the pore volume using a Monte Carlo scheme that has been described previously in the literature.38 In this method, the porosity (φ) and specific pore volume (Vsp) are estimated by attempting to randomly insert a great number N of spheres of diameter δ within the porous carbon. Let Np be the number of spheres inserted in the pore voids (i.e., located at a distance greater than δ/2 from any carbon atom of the porous material (δ is about 0.36 nm for the nitrogen molecule)). The porosity is given simply by Np/N, and the porous volume is given by Vsp = φV, where V is the volume of the simulation box containing the porous material. The pore size distribution of the activated carbon, which has been determined using the MP method analysis,39 is given in Figure 3. The main pore sizes in the sample are 0.8, 1.3, and 1.5 nm. Figure 3 also shows the pore size distributions obtained for 3331

dx.doi.org/10.1021/la3048938 | Langmuir 2013, 29, 3328−3338

Langmuir

Article

Figure 4. (a) Experimental absolute adsorption isotherm for carbon dioxide at 318.15 K on the Filtrasorb F400 activated carbon. The inset shows the corresponding isosteric heat of adsorption as a function of the adsorbed amount of carbon dioxide. (b) Experimental absolute adsorption isotherm for methane at 318.15 K on the Filtrasorb F400 activated carbon. The inset shows the corresponding isosteric heat of adsorption as a function of the adsorbed amount of methane.

Figure 5. (a) Simulated adsorption isotherm for carbon dioxide at 318.15 K: CS1000A (closed triangles) and CS1000AF (open triangles). The inset shows the corresponding isosteric heat of adsorption as a function of the adsorbed amount of carbon dioxide. (b) Simulated adsorption isotherm for methane at 318.15 K: CS1000A (closed squares) and CS1000AF (open squares). The inset shows the corresponding isosteric heat of adsorption as a function of the adsorbed amount of methane.

adsorbed at a pressure of p = 15 MPa in CS1000AF. As in the case of the experimental adsorption isotherm, the simulated adsorption isotherms are of type I in the IUPAC classification.42 The adsorbed amount increases rapidly with increasing pressure because of the very small pore sizes in CS1000A and CS1000AF and then reaches a plateau as the pores get filled. The simulated adsorbed amounts are higher than the experimental value because of the fact that the simulated samples have a larger porosity than the experimental sample. The agreement between the experimental and simulated data could be improved by developing a new model by applying the RMC technique to the structural data corresponding to our experimental sample. For both CH4 and CO2, there is no significant difference between the shape of the adsorption isotherm for CS1000A and that for CS1000AF. The quantitative difference between the adsorbed amounts for these two samples is at most a few mmol/g because of the fact that the interactions of CO2 or CH4 with CS1000AF are stronger than with CS1000A. Henry’s constants for CO2 and CH4 in CS1000AF are larger than for CS1000A. Again, this difference can be explained by the fact that the interactions between CO2 or CH4 and the porous material are stronger in CS1000AF as a

and 333 K. In the isosteric method, Qst is estimated at a given adsorbed amount nads using the Clausius−Clapeyron equation: ⎛ ∂ ln P ⎞ ⎟ Q st(nads) = −ΔH = kBT 2⎜ ⎝ ∂T ⎠n

ads

(2)

At low pore filling (