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Carbon Molecular Sieves: Reconstruction of Atomistic Structural Models with Experimental Constraints Piotr Kowalczyk,*,† Artur P. Terzyk,‡ Piotr A. Gauden,‡ Sylwester Furmaniak,‡ Marek Wiśniewski,‡ Andrzej Burian,§ Lukasz Hawelek,∥ Katsumi Kaneko,⊥ and Alexander V. Neimark# †

Nanochemistry Research Institute, Department of Chemistry, Curtin University of Technology, P.O. Box U1987, Perth, 6845 Western Australia, Australia ‡ Department of Chemistry, Physicochemistry of Carbon Materials Research Group, Nicolaus Copernicus University, Gagarin St. 7, 87-100 Torun, Poland § A. Chelkowski Institute of Physics, University of Silesia, Ulica Uniwersytecka 4, 40-007 Katowice, Poland ∥ Institute of Non-Ferrous Metals, ul. Sowinskiego 5, 44-100 Gliwice, Poland ⊥ Center for Energy and Environmental Science, Shinshu University, 4-17-1 Wakasato, Nagano 380-8553, Japan # Department of Chemical and Biochemical Engineering, Rutgers, The State University of New Jersey, 98 Brett Road, Piscataway, New Jersey 08854-8058, United States S Supporting Information *

ABSTRACT: We propose a novel methodology for developing experimentally informed structural models of disordered carbon molecular sieves. The hybrid reverse Monte Carlo simulation method coupled with wide-angle X-ray scattering experiments is used for constructing an atomistic level model of a representative sample of carbon molecular sieve film (CMS-F) synthesized in our laboratory. We found that CMS-F possesses a disordered matrix enriched with bended carbon chains and various carbon clusters as opposed to the turbostratic carbon or graphite-like microcrystals. The pore structure of CMS-F has a defected lamellar morphology of one-dimensional periodicity with narrow (∼0.4 nm) micropores. The model is applied to study adsorption properties of CMS-F with respect to adsorbates of practical interest, such as N2, H2, CO, and C6H6. Special attention is paid to the phase transformations in the course of adsorption. In particular, we show theoretically and confirm experimentally that nitrogen solidifies within CMS-F pores at 77 K upon adsorption of 5 mmol/g, and its further adsorption is associated with the adsorbed phase compression induced by strong surface forces.

I. INTRODUCTION Carbon molecular sieves (CMSs) represent a special class of carbonaceous nanoporous materials with remarkable separation properties.1−12 High thermal stability, resistance to aggressive acid environments, hydrophobicity, and the ability to control the internal nanopore structure during synthesis make CMSs competitive to more traditional crystalline inorganic oxide molecular sieves (such as zeolites, silicas, and others) and metal−organic frameworks.1 As recently pointed out by Mueller et al.,13 CMSs are expected to play an important role in the development of novel energy-efficient membranes for separation of gas mixtures composed of light particles (e.g., CH4, CO2, H2, He, N2, O2, H2S, SO2, Ar, etc.). From the point of view of adsorption selectivity, CMSs are comparable to the crystalline molecular sieves.1,2 Despite numerous studies directed toward establishing their internal structure, a full atomistic structural model of CMS that would be consistent with scattering, pycnometry, and porosimetry experiments has not been presented yet. It has © 2014 American Chemical Society

long been suggested that CMSs possess narrow carbon micropores within the molecular size range ∼0.4−0.7 nm embedded in a carbon matrix.1,2 The carbon surface around micropores is heavily disordered rather than crystalline.8,14,15 However, little is known about bonding configurations of carbon atoms at the pore walls. Therefore, it is not surprising that the standard slit-shaped pore model16−19 (including its variations that qualitatively account for the pore wall heterogeneity8,20−23) still serves as a basic structural model for studies of gas adsorption and separation by CMS membranes. Here, we present a novel three-stage approach to reconstructing the atomistic structural model of CMS from a set of distinct experimental measurements. The proposed threestage method implies sequential incorporation of the Received: April 14, 2014 Revised: May 22, 2014 Published: May 22, 2014 12996

dx.doi.org/10.1021/jp503628m | J. Phys. Chem. C 2014, 118, 12996−13007

The Journal of Physical Chemistry C

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experimental information into the atomistic structural model. The first stage involves reconstruction of the nonporous disordered carbon matrix of CMS from the wide-angle X-ray scattering (WAXS) experiment corresponding to the scattering from the porous sample. In the second stage the target porosity in the nonporous carbon matrix is introduced by an in silico burnoff process. The third stage involves the adjustment of the atomistic structural model with target porosity to secure target radial distribution functions. The foundations of the proposed three-stage method with experimental and simulation details are described in section II. We start with the basic idea of the method, followed by the details of the reconstruction of a representative sample of carbon molecular sieve film (CMS-F) synthesized and experimentally characterized in our laboratory. Detailed discussion is devoted to the experimental methods, to which the proposed model was applied: He pycnometry, N2 adsorption at 77 K, C6H6 adsorption at 313 K, and CO/H2 equimolar mixture separation at 293 K. The molecular models used for simulation of these systems are presented as well. In section III, we present our results with special attention to the predictions of CMS-F adsorption properties. Final conclusions are given in section IV.

II. THEORETICAL BACKGROUND, EXPERIMENTAL, AND SIMULATION DETAILS II.1. Methodology: Atomistic Structural Model of CMS and Its Validation. The goal of this work is to establish the atomistic structural model of CMS (i.e., two-phase material consisting of a disordered carbon matrix with embedded nanoscale pores) informed by the experimental measurements (including: wide-angle X-ray scattering (WAXS), He pycnometry, and N2 porosimetry measurements). In the current study we selected the sample of carbonaceous film as model CMS material designated as CMS-F (see Figure 1). Note that disordered CMSs are obtained from various precursors (i.e., woods, coals, coconut shells, peach stones, and others) that are consisting of different constituent biopolymers (e.g., cellulose, hemicellulose, lignin, etc.).1 In great contrast, the CMS-F sample shown in Figure 1 was synthesized from pure liquid cellulose. In previous studies24,25 we showed the pore size distribution function (PSD) computed from a N2 adsorption isotherm measured at 77 K, and conventional nonlocal density functional theory (NLDFT) is very homogeneous. Furthermore, we showed that CMS-F is free from any other larger pores, such as mesopores and macropores.24 As such, this sample seems to be an ideal candidate for the fundamental study devoted to reconstruction of the atomistic structural model of disordered two-phase materials. Theoretically, the atomistic structural model of CMS can be directly generated by using the Hybrid Reverse Monte Carlo (HRMC) simulation method, supplemented with experimental constraints and static penalty function for high-energetic structures of carbon atoms.26−32 Although this approach seems to be straightforward, we found that this optimization method generated an unphysical structural model of CMS-F. HRMC-reconstructed atomistic replicas of CMS-F were found fully consistent with the wide-angle X-ray scattering data. However, these replicas did not reveal any open porosity available for guest molecules in apparent contradiction to the porosimetry and calorimetric measurements clearly showing that CMS-F readily adsorbs N2 gas at 77 K and C6H6 vapor at 313 K.24 This result is not surprising because the standard HRMC simulation method inherently favors highly disordered

Figure 1. Studied carbonaceous film (∼10−20 μm thick) produced from pure liquid cellulose by sequential oxidation and activation processes.

carbon structures spanning the entire simulation box. In fact, as we show below, the correlation length determined from WAXS is ∼0.9−1.0 nm. Thus, CMS-F consists of ordered domains of ∼0.9−1.0 nm separated by highly disordered regions. To put this information into the HRMC reconstruction processes, one has to introduce some additional constraints to form the ordered and disordered regions during the HRMC reconstruction process. However, we found that this process is ambiguous and too complex to be implemented. The proposed three-stage method implies sequential incorporation of the experimental information into the atomistic structural model. The first stage involves reconstruction of the nonporous disordered carbon matrix of CMS from the WAXS experiment corresponding to the scattering from the porous sample. Here, we use the HRMC simulation method with a realistic many-body intermolecular potential for the calculation of interactions between carbon atoms (i.e., an environment-dependent interatomic potential for carbon developed by Marks et al.33). Thus, constructed nonporous structure serves as the first approximation. On the second stage, we create micropores in the obtained nonporous matrix by mimicking the burnoff process. Next, we relax the porous replicas of CMS-F by using the same HRMC method to match the experimental WAXS radial distribution function. It is worth noting that the relaxation of the structural model is a necessary step because the burnoff of micropores affects the radial distribution function. A series of atomistic replicas of CMS-F are then probed by modeling N2 adsorption at 77 K using the grand canonical 12997



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Monte Carlo (GCMC) simulation method. Theoretical N2 adsorption isotherms are compared with the experimental ones to select the most representative replica. The apparent surface area is computed from the variation of the surface area of N2adsorbed film by the method of Pfeifer et al.34 In addition, we use the atomistic structural model of CMS-F to study the thermodynamics of C6H6 vapor adsorption at 313 K as well as the adsorptive separation of the CO/H2 equimolar mixture at 293 K. Investigations of these adsorption processes allow us to explore the transferability of the reconstructed structural atomistic model of CMS-F to different adsorption systems. II.2. Wide-Angle X-ray Scattering Measurements. Wide-angle X-ray scattering measurements were performed at ambient temperature on a Rigaku-Denki D/MAX RAPID II-R diffractometer equipped with a rotating anode Ag Kα tube (λ = 0.5608 Å), an incident beam (002) graphite monochromator, and an image plate in the Debye−Scherrer geometry as a twodimensional detector.35−37 The pixel size was 100 μm × 100 μm. The investigated sample was placed inside a glass capillary (1.5 mm in diameter and 0.01 mm wall thickness), and measurements were carried out for the sample in the capillary and for the empty capillary, with the intensity for the empty capillary then subtracted. The beam width at the sample was 0.3 mm. The recorded two-dimensional diffraction patterns were integrated over the azimuthal angle to obtain one-dimensional intensity data expressed as a function of the scattering vector Q using suitable software. The scattering vector is defined as Q = 4π sin θ/λ, where 2θ is the scattering angle and λ is the wavelength. The intensity was then corrected for polarization and absorption and normalized using the data processing procedure developed for high-energy X-rays. The structure factor S(Q) = I(Q)/f 2 was then determined using the procedure developed for high-energy X-rays and adapted for the Debye−Scherrer cylindrical geometry.35−37 I(Q) is the corrected intensity normalized to electron units, and f indicates the atomic scattering factor of carbon. The intensity data were then converted to a real space representation in the form of the radial distribution function (RDF) via the sine Fourier transform according to35−37

ρc =

Xc (1/ρHe ) + VMP

(2)

where Xc is the weight percent of carbon in the CMS-F sample; ρc is the true density of the studied carbon sample; and VMP is the micropore volume. Note that eq 2 includes only the void space of micropores. The micropore volume was estimated to be 0.192 cm3/g by integrating over pore size distribution that was calculated from the N2 adsorption isotherm measured at 77 K using Tarazona’s nonlocal density functional theory (NDFT).24 The value of the true density of 1.66 g/cm3 was measured by He pycnometry (AccuPyc II 1340 Pycnometer) at 296 K. Finally, Xc of 0.97 was determined from the elemental analysis of the investigated carbon sample. Carbon density used to reconstruct the atomistic structural model of CMS-F was 1.22 g/cm 3 , which is slightly higher than 1.05 g/cm 3 corresponding to BPL activated carbon.30 As expected, carbon density of the studied porous CMS-F sample is significantly lower than the density of the carbon matrix, ρ0. The number of carbon atoms that need to be removed from the nonporous disordered carbon matrix corresponds to a density of 0.87 g/ cm3 (i.e., ρ0 − ρc). The N2 isotherm was measured at 77 K using the ASAP 2010 MicroPore System (Micromeritics, USA). Before measurement the CMS-F sample was desorbed in vacuum at 383 K for 3 h. The porosity of the studied CMS-F has been carefully characterized in our previous works.24,25 II.4. Hybrid Reverse Monte Carlo Simulation. We used the HRMC simulation method and the experimental radial distribution function (RDF) obtained from WAXS to reconstruct the three-dimensional atomistic structural model of nonporous (first stage) and porous (third stage) CMS-F samples. At fixed temperature T, we performed Monte Carlo simulation in a canonical ensemble with the transition probability to go from configuration o to n given by38,39 acc(o → n) = min{1, exp[−Δχ 2 /2]exp[−β ΔU ]}

(3)

where β = (kBT)−1 denotes inverse temperature; ΔU = U(n) − U(o) is the difference in potential energy, Δχ = χ(n) − χ(o); and χ is given by38,39 M

1 g (r ) = 1 + 2π 2ρ0 r

∫0

Q max

χ=

Q [S(Q ) − 1]sin(Qr )dr

2 (r j ) ∑ [gth(rj) − gexp(rj)]2 /σexp j−1

(1)

(4)

Here, M is the number of experimental data points; σ(r) is the standard deviations of experimental WAXS data; and g(r) denotes experimental (subscript “exp”) and theoretical (subscript “th”) RDF. Theoretical RDF is computed on the fly during the HRMC simulation run from the following expression31

Note that ρ0 represents the true density nonporous carbon matrix in the studied CMS-F sample. It is not a directly measurable property for any disordered porous materials. However, it can be easily extracted from the WAXS scattering data. For our CMS-F sample ρ0 = 2.09 g/cm3. Thus, in the studied CMS-F sample the nanoscale pores are formed between disordered carbon fragments with densities similar to graphite1 (i.e., 2.09−2.23 g/cm3). However, this result does not imply that the structure of the disordered carbon matrix in CMS-F is graphitic-like. II.3. He Pycnometry and N 2 Porosimetry. The reconstruction of the atomistic structural model of porous CMS-F is an ill-posed inverse problem. Therefore, the experimental constraints are essential for the selection of the most representative atomistic structural model from the infinite number of possible replicas. Because the CMS-F sample is strictly microporous, we estimated the carbon density from the following relation30,32

g th (r ) =

dNrV 4πr 2Ndr

(5)

where dNr is the number of carbon atoms in the shell of thickness dr; N denotes total number of carbon atoms; and V is the volume of the simulation box. II.5. CMS Atomistic Structural Model. II.5.1. HRMC Nonporous Structural Model with Target RDF. Knowing the experimental RDF and ρ0 we can reconstruct the atomistic structural model of the nonporous disordered carbon matrix of the investigated CMS-F. As previously,31 we used the HRMC algorithm implemented by Snook and co-workers.38,39 We start from the random initial configuration of 6706 carbon atoms in 12998



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the HRMC algorithm is used. However, the temperature quench program is modified. As previously, we use three stages in the HRMC temperature quench with a linear temperature ramp. On stage 1, all carbon atoms are heated to 800 K, which prevents melting of the CMS-F porous structure. Next, the temperature is continuously decreased to 600 K. On stage 2, the temperature is dropped from 600 to 400 K. Finally, in stage 3, the temperature is further decreased to 300 K. As previously, we collect RDF and the structure factor from 106 HRMC steps at 300 K. II.6. Simulated N2 Adsorption Isotherm, Enthalpy, and Entropy: Apparent Surface Area and Pore Volume Distribution. Adsorption isotherms of N2 at 77 K in HRMC-generated porous replicas of CMS-F were simulated by the GCMC method.41,42 N2 molecules and carbon atoms were modeled by single-site Lennard-Jones quasispherical particles.43 The fluid−fluid and solid−fluid parameters were taken from the work of Ravikovitch et al.44 These parameters correctly reproduce the bulk properties of N2 (including: vapor−liquid coexistence, liquid−vapor surface tension, and equation of state).44 Moreover, in the current work, we show that the N2 adsorption isotherm simulated on the HRMC reconstructed surface of Madagascar graphite at 77 K agreed well with the experimental N2 isotherm measured on Sterling highly graphitized carbon black45 (see Figures 1S and 2S in the Supporting Information). Thus, we are confident that the effective solid−fluid parameters and the algorithm used for the calculations of the apparent surface area are correctly implemented. A cubic simulation box of 4 nm × 4 nm × 4 nm with periodic boundary conditions for both fluid−fluid and solid−fluid interactions in x, y, and z directions was used in GCMC simulation41,42 (note that the size of the simulation box is ∼4 times larger than the correlation length determined from WAXS experiment). All interactions were truncated at 1.8 nm. At each state point along the adsorption isotherm, the simulations were equilibrated using at least 3 × 107 Monte Carlo steps. Statistics were then collected over at least 5 × 107 additional Monte Carlo steps. We used the final configuration from the previous adsorption point as a starting configuration for the simulation of the next one. For N2 at 77 K, the bulk phase in equilibrium with the N2 adsorbed in CMS-F was assumed to be ideal gas, and the difference between the absolute and Gibbs excess adsorption was neglected. The absolute value of adsorption per unit of mass was computed from41

a periodic cubic simulation cell of side length of 4 nm (i.e., 2.09 g/cm3). We assume the error of σ(r) = 0.05 in eq 4 for each experimental point on RDF. A previous HRMC temperature quench program was applied,31 i.e., three stages with a linear temperature ramp. In stage 1, all carbon atoms were heated to 5000 K. Next, the temperature was continuously decreased to 800 K. In stage 2, the temperature was dropped from 800 to 500 K. Finally, in stage 3, the temperature was further decreased to 300 K. For temperature quench, we used a total of 108 HRMC steps, and each step consisted of attempting displacement of a carbon atom. An additional 106 HRMC steps at 300 K were performed to compute the theoretical RDF and structure factor. The displacement step was accepted following the transition probability given by eq 3. II.5.2. In Silico Burnoff Process. Stereo high-resolution transmission electron microscopy (S-HRTEM) can provide the three-dimensional vision of pore structure with the resolution of about 1 nm.40 However, this and other experimental techniques do not provide direct observation of the size and topology of micropores embedded in a disordered carbon matrix. Therefore, we propose to mimic the physical process of pore formation. Previous calorimetric investigations24 showed that C6H6 solidifies in micropores of CMS-F at 313 K, indicating strong localization and restricting rotations of benzene rings in micropores. Therefore, we expect that adsorbed C 6 H 6 molecules lie flat with the plane of the ring parallel to the micropore walls. Theoretical description of the N2 adsorption isotherm at 77 K showed that micropore sizes in CMS-F are comparable with the size of the N2 molecule (i.e., 0.3615 nm).24 Collecting all these facts, we conclude that the lamellar morphology of micropores is a good representation of the collected experimental and theoretical results. Our heuristic algorithm for the in silico burnoff of micropores in the nonporous disordered carbon matrix is implemented as follows. First we specify the lamellar thickness (pore wall thickness), χ, and the interlamellar space (micropore size), Δ. These parameters define the micropore regions in the nonporous disordered carbon matrix. Next we compute the potential energy for each carbon atom by using EDIP potential.33 Then, from the regions of micropores (i.e., Δ) we select and extract the carbon atom with the highest potential energy. The process is continued until the carbon density of 1.22 g/cm3 is achieved. We would like to note that the proposed heuristic algorithm of the introduction of micropores into a nonporous matrix is not unique. One can use other algorithms, e.g., percolation, diffusion-limited aggregation, etc. The advantage of our algorithm is the fact that this in silico burnoff process does not increases the energy of the porous replica of CMS-F as compared to the parental nonporous disordered carbon matrix. As we show later, the most probable structural atomistic models of CMS-F are free from any unphysical high-energetic carbon atoms or fragments. II.5.3. HRMC Adjustment of the Structural Model. As we noted in section II.1, the assumption that the RDFs corresponding to nonporous and porous CMS-F samples are the same is an initial approximation. This bias is removed by relaxation of the porous replica of CMS-F generated from in silico burnoff of micropores in the additional HRMC simulation run. A reconstructed porous replica consisting of 3915 carbon atoms is placed in a periodic cubic simulation cell of side length of 4 nm (i.e., 1.22 g/cm3). The same setup for

nabs =

⟨N ⟩ NC·mC

(6)

where ⟨...⟩ is the ensemble average; N is the number of N2 molecules; NC is the total number of carbon atoms in the simulation box; and mC denotes the molar mass of the carbon atom. The isosteric heat of adsorption was computed from the fluctuation theory41 qst = RT +

⟨U ⟩⟨N ⟩ − ⟨UN ⟩ ⟨N 2⟩ − ⟨N ⟩2

(7)

where U is the configuration energy of the system; T is the temperature; and R denotes the universal gas constant. 12999



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(12,6) Lennard-Jones parameters were determined using the Lorentz−Berthelot mixing rule.42 A cubic simulation box of 4 nm × 4 nm × 4 nm with imposed periodic boundary conditions for both fluid−fluid and solid−fluid interactions in x, y, and z directions was used in our rotational-bias GCMC simulation experiments.9 All interactions were truncated at 1.85 nm. At each state point along the mixture adsorption isotherm, the simulations were equilibrated using at least 2 × 106 rotationalbias MC steps. Statistics were then collected over at least 8 × 106 additional rotational-bias MC steps. We used the final configuration from the previous adsorption point as a starting configuration for the simulation of the next one. Gibbs excess isotherms, the isosteric heat of mixture adsorption, and equilibrium selectivity of CO over H2 were computed from well-known relations.41 Other simulations details and validation of used force fields are documented in our previous work.58

To characterize the ordering of N2 molecules in micropores we computed the differential entropy of adsorption from the following expression46−48 Sdiff = Sg −

⎛ p⎞ − R ln⎜⎜ ⎟⎟ + R T ⎝ p0 ⎠

qdiff

(8)

where Sg is the molar entropy of the N2 gas at 77.3 K; qdiff = qst − RT is the differential enthalpy of N2 adsorption; and p and p0 are the equilibrium and saturated vapor pressures, respectively (see Hill et al.48 and Garbacz et al.46 for more details). The distribution of pore sizes in the atomistic structural model of CMS-F has been computed from the method of Bhattacharya and Gubbins.49 The pore size distribution is defined as the statistical distribution of the pore radius of the largest sphere that can be fitted inside a pore of a given point (see ref 49 for more details). The apparent surface area of the atomistic structural model of CMS-F is computed from the variation of the surface area of N2 adsorbed film by the method of Pfeifer et al.34 For comparison, we computed the apparent surface area from the experimental N2 adsorption isotherm at 77 K by using the Brunauer−Emmett−Teller (BET) method,50 the modified BET method of Rouquerol and co-workers,51 and the NLDFT method implemented by Kowalczyk et al.25 All computational details were described in our previous works.24,25 II.7. Adsorption of Organics: Benzene at 313 K. As a characteristic practical example we attempted to predict the thermodynamics of C6H6 adsorption from an atomistic structural model of CMS-F. C6H6 adsorption is essential for many technological problems, including adsorptive separation52 and purification of fluid mixtures from organics.53 We simulated C6H6 vapor adsorption in the atomistic structural model of CMS-F at 313 K by using the hyper parallel tempering Monte Carlo method (HPTMC).54 We used a six-site molecular model for the representation of C6H6 molecules. The six-site anisotropic united-atom (AUA) force field for C6H6 has been described in our previous work.54 For carbon atoms, we used (12,6) Lennard-Jones parameters from Steele,55 e.g., σss = 0.34 nm and εss/kB = 28 K. The cross-term (12,6) Lennard-Jones parameters were determined using the Lorentz−Berthelot mixing rule.42 The isotherm, enthalpy, and entropy of C6H6 adsorbed in CMS at 313 K were computed from eqs 6−8. All other simulations details were described previously.54 The C6H6 adsorption isotherm on an oxidized sample of CMS-F at 313 K was measured using a volumetric apparatus with Baratron pressure transducers (MKS Instruments, Germany). The measurement of the enthalpy of C 6 H6 adsorption, using a Tian-Calvet microcalorimeter, was described in detail previously.24 II.8. Adsorptive Separation: CO/H2 Equimolar Mixture at 293 K. The adsorptive separation efficiency of CMS-F can be computed using the rotational-bias GCMC simulation implemented for binary mixtures.9 In the current work, we selected CO/H2 (dry syngas) as the model equimolar binary mixture and operating conditions close to those corresponding to adsorptive industrial separations (i.e., 293 K and total pressures of equimolar mixture up to 10 MPa).52 Both H2 and CO molecules were represented by the fully atomistic rigid molecular model.9 For H2 we used the five-site molecular model of Belof et al.,56 whereas for CO we used the three-site molecular model of Stoll et al.57 For carbon atoms, we used (12,6) Lennard-Jones parameters from Steele.55 All cross-term

III. RESULTS AND DISCUSSION The structure factor, RDF, and neighbor distributions of the most representative atomistic structural model of porous CMSF, shown in Figure 2 (dashed lines), are in good agreement with the target functions measured from WAXS experiment

Figure 2. Structure factors (upper panel), radial distribution functions (middle panel), and neighbor distributions of the CMS-F sample obtained from the WAXS experiment (solid lines) and the atomistic structural model (dashed lines). 13000



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micrographite like crystallites), bended or flat graphene sheets, fullerene fragments, and triply periodic minimal carbon surfaces. Previous in situ Fourier Transform Infrared Spectroscopy (FT-IR) measurements of Zawadzki et al.60−62 showed that the CMS-F sample is transparent to infrared light. This experimental observation indicates that the disordered carbon matrix in CMS-F does not contain any larger graphitic-like fragments (i.e., sp2-hybridized carbons) that are able to absorb infrared light waves. Because carbon clusters and carbon chains are not supposed to be the infrared absorbers (note that benzene liquid is transparent to infrared light), we concluded that the reconstructed atomistic replica of CMS-F is in qualitative agreement with in situ FT-IR measurements.60−62 Moreover, we concluded that our theoretical atomistic structural model is in agreement with well-known experimental observations, which emphasize the relation between the structure of the carbonaceous porous materials and the used precursor.1 Pore size distributions computed from the structural atomistic model of CMS-F and Tarazona’s nonlocal density functional theory (NLDFT) implemented for the slit-shaped pore model25 are compared in Figure 4. The slit-shaped carbon pore model generates a remarkable narrow and sharp pore size distribution with a pore size of ∼0.55 nm. As shown in Figure 4 and a movie (jp503628m_si_002.mpg) in the Supporting Information, the atomistic replica of CMS-F has a defected

(solid lines). The structural features of the experimental RDF are observed up to about 0.9−1.0 nm suggesting a high degree of disorder of the investigated material. It is important to point out that this limit should be regarded as the correlation length beyond which there are no spatial correlations between atomic positions. Therefore, the WAXS data are sensitive to ordering within the range of ∼3σss (σss is the collision diameter of the carbon atom). The most representative atomistic structural model of CMS-F correctly reproduces the number of peaks and their positions on both experimental RDF and structure factor. We notice, however, that the intensity of the first and second peak on the theoretical RDF is somewhat higher than that extracted from WAXS experiment. The opposite trend is found for structure factor. Observed differences in peak intensities may result from the overprediction of the experimental value of skeleton density or finite size effects in HRMC simulations. From one side, He atoms can be adsorbed in very narrow carbon ultramicropores even at 296 K. From the other side, the finite size of the simulation box may stabilize the ordering of carbon atoms around the pore walls. A full understanding of the observed differences needs further experimental and theoretical collaborative research. The atomistic structure of the reconstructed structural model of the CMS-F sample is mainly composed of various carbon clusters (see Figure 3). Among them, bended linear carbon

Figure 3. Simulated transmission electron microscopy (TEM) images (left panels) and atomistic snapshots (right panels) of the structural model of disordered carbonaceous film. Note the presence of bended linear sp-hybridized carbon chains.

chains are clearly visible (i.e., carbon chains consisting of sphybridized carbons displayed in Figure 3). It is very tempting to make speculations that observed carbon chains are reminiscent of cellulose chains used as precursor material in the CMS-F synthesis. Moreover, Hawelek et al.59 have recently found similar chain-like structures in commercially available CXV activated carbon produced from powdered wood-based carbon. However, direct measurements of electronic bonding states are necessary to evaluate the content of sp-hybridized carbons in the CMS-F sample. Further inspection of the atomistic structure of the reconstructed structural replica of CMS-F reveals the lack of turbostratic graphitic fragments (i.e.,

Figure 4. Pore size distributions of the CMS-F sample computed from the atomistic structural model (upper panel) and Tarazona’s nonlocal density functional theory implemented for the slit-shaped pore model25 (bottom panel). 13001



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and experimental N2 isotherm at 77 K is useful for the selection of the pressure range for correct interpretation of the equilibrium porosimetry measurements. Further microscopic insight into the N2 adsorption mechanism can be provided by snapshots of equilibrium configurations collected from the GCMC simulation (see jp503628m_si_003.mpg and jp503628m_si_004.mpg movies in the Supporting Information). Due to strong confinement, N2 molecules at adsorbed phases are tightly squeezed together. There is a notable local order induced by the tendency of N2 molecules to stay together and pack into hexagonal solid-like layers. We may rapidly obtain the differential entropy of N2 adsorbed phases from eq 8. Indeed, the differential entropy of adsorbed N2 dropped very quickly with pore loading. Around ∼5 mmol/g, the computed differential entropy of adsorbed N2 is comparable to the entropy of solid N2 (see Figure 5). Moreover, the differential entropy of N2 adsorbed in narrow micropores is further reduced due to the compression of adsorbed phases induced by the strong surface forces. In a rough way of speaking, the CMS-F with adsorbed N2 molecules can be treated as a mixture of two solids. In situ X-ray diffraction studies by Kaneko and co-workers64−66 clearly showed solid-like packing of adsorbed molecules (e.g., alcohols, water, and others) in narrow carbon micropores. There is, therefore, little doubt that the assumption of the liquid state of N2 adsorbed in narrow carbon micropores is questionable. Therefore, the application of standard theories of gas adsorption with the liquid state of adsorbed fluid (i.e., theory of micropore filling, Gurvitvh rule, Kelvin-type relations, BET method, and others) for a description of the porosimetry data measured for CMS materials should be done with caution. The apparent surface area of CMS-F computed from the experimentally consistent atomistic replica of 1052 m2/g (see bottom panel in Figure 6) is higher than that computed from the conventional Tarazona’s weighted NLDFT method,25 705 m2/g. The standard BET surface area is only 447 m2/g, whereas the “equivalent” BET surface area computed from the method proposed by Rouquerol and co-workers is 606 m2/g (see upper and middle panels in Figure 6). Not surprisingly, the microscopic approaches predict higher values of the apparent surface area as compared to phenomenological BET theories. They account for more atomistic details of the internal pore surface. The remaining key question is why the current method gives higher apparent surface area as compared to the conventional NLDFT approach? The answer to this question is straightforward. In conventional NLDFT calculations the micropore walls are modeled as structureless flat graphitic surfaces. Within the framework of the proposed methodology, the structure of solid atoms around micropores is disordered (i.e., structurally and energetically heterogonous). It seems clear that the disordered nature of the carbon matrix induces the roughness of the solid surface (i.e., corrugated surface) surrounding the pore walls that is further probed by N2 molecules. The corrugated surface area is always larger than the flat one. It is interesting to note that BET and the surface area computed from the atomistic structural model defined some boundaries for the apparent surface areas computed from other phenomenological and statistical mechanics theories. Figure 7 presents the comparison between the theoretical and experimental adsorption isotherm, enthalpy, and entropy of C6H6 adsorbed in studied CMS-F at 313 K.24 Here, we would like to point out that the presented experimental measurements correspond to the adsorption of C6H6 on an oxidized sample of

lamellar morphology with one-dimensional periodicity. We found that very narrow pores (∼0.4 ± 0.1 nm wide, as shown in Figure 4) are embedded in a heavily disordered carbon matrix. The homogeneity of pore size distribution computed from the NLDFT method results from the simplicity of the used slitshaped carbon pore model. A small shift of the average pore size (by ∼0.15 nm) to higher values can be explained by neglecting the roughness of the pore walls in the standard slitshaped carbon pore model. Figure 5 shows the compassion between experimental and simulated N2 isotherms at 77 K. The agreement between the

Figure 5. Comparison between the experimental (crosses in upper panel) and theoretical N2 adsorption isotherms (circles in upper panel) at 77 K. The isosteric enthalpy (middle panel) and differential entropy (bottom panel) of N2 adsorbed in the CMS-F sample. The entropies of gas (Sgas), liquid (Sliquid), and solid (Ssolid) N2 are, respectively: 151.9, 79.133, and 57.03 J/mol/K.68

theoretical and experimental N2 adsorption isotherm at 77 K is excellent over 4 orders of magnitude in relative pressures. At very low pressures (∼10−6 p/p0), the experimental isotherm shows unphysical behavior. We argue that adsorption measurements at very low values of relative pressures are out of thermodynamic equilibrium. This is due to the well-known problem of slow diffusion of N2 molecules from the gas phase to the narrow micropores at 77 K.63 In strict contrast, a theoretical adsorption isotherm simulated at very low relative pressures is smooth. The amount of adsorbed N2 increases gradually as the relative pressure of N2 gas is increased. Thus, we concluded that direct comparison of the simulated (i.e., adsorption points measured at thermodynamic equilibrium) 13002



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Figure 7. Comparison between the experimental (crosses in upper panel) and theoretical C6H6 adsorption isotherm (open circles in upper panel) at 313 K.24 The experimental and simulated isosteric enthalpies (middle panel) and differential entropies (lower panel) of C6H6 adsorbed in carbonaceous film. The entropies of gas (Sgas), liquid (Sliquid), and solid (Ssolid) C6H6 are, respectively: 273.08, 179.89, and 136.5 J/mol/K.24 Figure 6. Apparent surface area of the CMS-F sample computed from the BET method (upper panel) and the modified BET method of Rouquerol and co-workers (middle panel). Lower panel shows the variation of the apparent surface with the thickness of N2 film (i.e., dr) covering the carbon skeleton of the structural atomistic model.

C6H6 adsorption enthalpy can only be explained by the specific interactions between aromatic π-electrons and surface functional groups.47 Interestingly, the experimental value of the C6H6 entropy measured at zero coverage corresponds to the solid-like entropy of C6H6 at 313 K (∼125 J/mol/K).24 Thus, C6H6 molecules are solidified in oxidized CMS-F at either zero or finite pore loadings. In strict contrast, the theoretical entropy of C6H6 adsorbed in an unoxidized CMS-F replica approaches the solid-like value at 1.5 mmol/g. For higher densities of C6H6 in micropores, the theoretical and experimental thermodynamic functions are in good agreement (see Figure 7). It is simply because the surface functional groups are saturated at higher C6H6 pore loadings. Therefore, we concluded that the surface chemistry of carbon cannot be neglected in a theoretical description of organic adsorption at low pressures of coexisting vapors. Theoretical studies of mixture gas adsorption and separation by disordered CMS materials are of great importance for an atomistic-level understanding of the relation between the porous structure and separation efficiency. Direct simulation of H2/CO binary mixture gas adsorption on a CMS-F replica gives us some insight into this fundamental problem. From the comparison between the experimental and theoretical benzene

CMS-F.24 The specific interactions between surface functional groups and aromatic π-electrons may change the values of studied thermodynamic functions. Surprisingly, the adsorption isotherm of C6H6 simulated on the unoxidized CMS-F replica is in good quantitative agreement with the experimental measurements (see jp503628m_si_004.mpg movie in Supporting Information and upper panel in Figure 7). We noticed that the theoretical C6H6 isotherm is slightly shifted to higher values of pressures. It is not surprising because in our atomistic structural model of CMS-F the specific interactions between aromatic π-electrons and surface functional groups were neglected. Variation of theoretical and experimental enthalpy and entropy highlights the observed differences (see middle and bottom panels in Figure 7). The theoretical enthalpy of C6H6 adsorbed in an unoxidized CMS-F replica is only ∼54− 60 kJ/mol at either zero or finite pore loadings. The experimental value of C6H6 enthalpy measured at zero coverage of ∼82 kJ/mol decreases with pore loadings. High values of 13003



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Concluding the current work, we would like to point out that the presented atomistic structural model is the first microscopic model of CMS materials that is consistent with WAXS, He pycnometry, and N2 porosimetry measurements. Atomistic structural details of the CMS-F replica coupled with molecular simulations give deep insight into the thermodynamics of studied adsorbate−adsorbent systems. The most interesting results concern the solidification of adsorbed molecules induced by strong surface forces generated from disordered carbon pore walls either at cryogenic (N2 at 77 K) or ambient (C6H6 at 313 K) temperatures. This finding has important implications for the correct description of porosimetry measurements by phenomenological theories of adsorption. The apparent surface area computed directly from the most representative replica of CMS-F is underpredicted by phenomenological BET approaches and the conventional NLDFT method. This result highlights the important role of carbon−carbon bonding close to the pore walls. Finally, we show that maximum equilibrium selectivity of CO over H2 of the order of ∼6 can only be achieved for total equimolar H2/CO mixture pressures lower than ∼10−3 MPa. Higher pressures of the H2/CO binary mixture will induce the H2 coadsorption that inevitably lowers the adsorptive separation efficiency. The extension of the current methodology for the analysis of the structural and surface heterogeneities (i.e., pore size distribution, apparent surface area, surface chemistry, etc.) of other disordered nanoporous carbonaceous materials will be the subject of our future works.

isotherm at 313 K we found that CMS-F has no kinetic restrictions near ambient temperatures. Thus, we can predict the equilibrium composition of the adsorbed H2/CO mixture directly from the rotational-bias GCMC simulation experiments. As would be expected, CO molecules are preferentially adsorbed from the H2/CO equimolar binary mixture on CMSF at 293 K (see upper panel in Figure 8). However, two

IV. CONCLUSIONS We presented a novel three-stage approach devoted to reconstruction of the atomistic structural model of disordered CMS materials (i.e., two-phase ill-defined materials). The most representative replica of CMS material is constructed by sequential incorporation of the experimental information into the atomistic structural model. First, we reconstruct the nonporous disordered carbon matrix of CMS (first phase in CMS) by combining the experimental RDF measured for the porous CMS sample and the HRMC simulation method. On the second stage, we introduce micropores (second phase in CMS) into the nonporous matrix by an in silico burnoff process. The final stage involves the adjustment of the atomistic structural model with target porosity to secure target RDF. From our study, we found that the structure of the disordered matrix of the studied CMS-F sample is enriched with bended carbon chains (sp-hybridized carbons) and various carbon clusters as opposed to turbostratic graphite or graphite-like microcrystals. The porous structure of CMS-F has a defected lamellar morphology with one-dimensional periodicity. Narrow carbon micropores (∼0.4 ± 0.1 nm wide) with the total surface area of 1052 m2/g possess highly disordered pore walls. The suggested atomistic structural model is the first microscopic model of CMS materials that is consistent with WAXS, He pycnometry, and N2 porosimetry measurements. Atomistic structural details of the CMS-F replica coupled with molecular simulations give deep insight into the thermodynamics of studied adsorbate−adsorbent systems. The constructed atomistic model was applied to study adsorption properties of CMS-F with respect to adsorbates of practical interest, such as N2, H2, CO, and C6H6. We found that the size of micropores has a profound effect on the phase transformations in the course of adsorption. The most interesting results concern the solidification of adsorbed molecules induced

Figure 8. Adsorptive separation of the H2/CO equimolar mixture simulated in an atomistic structural model of the CMS-F sample at 293 K. Upper panel shows the adsorption isotherms. Total (qtotal) and solid−fluid contribution to the total isosteric enthalpy (qsolid−fluid) of H2/CO mixture adsorption are displayed in the middle panel. The lower panel presents the equilibrium selectivity of CO over H2 computed from the rotational-bias GCMC method.9

important features immediately appear. First, the maximum equilibrium selectivity of CO over H2 is of the order of ∼6 when the total equimolar H2/CO mixture pressures are lower than ∼10−3 MPa. H2 molecules start to coadsorb at higher equimolar mixture pressures that result in a fast decrease of the equilibrium selectivity (see bottom panel in Figure 8). Second, the heat released during the H2/CO binary mixture adsorption at 293 K is dominated by the solid−fluid contribution up to a total equimolar mixture pressure of ∼0.5 MPa (see middle panel in Figure 8). Therefore, we concluded that the enhanced solid−fluid potential in narrow carbon micropores with disordered pore walls governs the physical adsorption and separation of the H2/CO mixture near ambient temperature. 13004



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program.69 This material is available free of charge via the Internet at http://pubs.acs.org.

by strong surface forces generated from disordered carbon pore walls at either cryogenic (N2 at 77 K) or ambient (C6H6 at 313 K) temperatures. Nitrogen solidifies within CMS-F pores at 77 K upon adsorption of 5 mmol/g, and its further adsorption is associated with the adsorbed phase compression induced by strong surface forces. This effect has important implications for the correct interpretation of the porosimetry measurements by phenomenological theories of adsorption. Solidification of C6H6 adsorbed in CMS-F pores at 313 K is theoretically predicted for higher vapor pressures. Interestingly, the porosimetry and calorimetry measurements of C6H6 vapor adsorption on oxidized CMS-F at 313 K showed that adsorbed C6H6 solidifies at either infinite dilution or finite pore loadings. Observed discrepancies are explained by the specific interactions between surface functional groups and aromatic π-electrons that are neglected in the atomistic structural model of CMS-F. The atomistic model can be used for the surface area and pore size characterization. The apparent surface area computed directly from the most representative replica of CMS-F is underpredicted by more common BET and NLDFT methods, although it might be better assessed with the QSDFT or 2DNLDFT method.20−23 This discrepancy highlights an important role of carbon−carbon bonding at the pore walls that may lead to the increase of the pore surface area due to the surface roughness. As an example of a practical application, we considered separation of CO/H2 mixtures at 293 K and predicted that maximum equilibrium selectivity of CO over H2 of the order of ∼6 can only be achieved for equimolar H2/CO mixtures at the pressures lower than ∼10−3 MPa. Higher pressures of the H2/ CO mixture induce H2 coadsorption that inevitably lowers the adsorptive separation efficiency. The proposed reconstruction technique can be recommended for building atomistic models of disordered activated carbons of different origin. Moreover, the proposed methodology can be further improved by the incorporation of additional experimental constraints into reconstruction of the atomistic structural model. Recently new powerful scanning transmission electron microscopy (STEM) was applied to elucidate the defective graphene-like wall structure of activated carbons.67 A hybrid reverse Monte Carlo simulation study for both X-ray scattering and STEM data should give a more realistic structure model of highly disordered carbonaceous materials such as carbon molecular sieves and activated carbons. Extension of this methodology for analyses of structural and surface heterogeneities (i.e., pore size distribution, apparent surface area, surface chemistry, etc.) will be the subject of our future works.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +61 8 9266 7800. E-mail: [email protected]. au. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS P.K. acknowledges partial support by the Office of Research & Development, Curtin University, Grant CRF10084. P.K. acknowledges partial support by the Japanese Society for Promotion of Science (short-term JSPS Invitation Fellowship). K.K. was supported by Exotic Nanocarbons, Japan Regional Innovation Strategy Program by the Excellence, JST. A.V.N. acknowledges partial support from the Rutgers NSF ERC “Structured Organic Particulate Systems”. A.P.T., P.A.G., S.F., and M.W. acknowledge the use of the computer cluster at Poznań Supercomputing and Networking Centre (Poznań, Poland) as well as the Information and Communication Technology Centre of the Nicolaus Copernicus University (Toruń, Poland). S.F. gratefully acknowledges financial support from Iuventus Plus Grant No. IP2012034872 from the Polish Ministry of Science and Higher Education. The authors thank Professor Leslie Glasser (Curtin University) for fruitful comments and suggestions. The authors gratefully acknowledge eng. Jãzef Nitka (general manager, SYL&ANT, Poland) for the pycnometry measurement. This work is dedicated to Professor Ian Snook (RMIT University) for his seminal contributions to the statistical mechanics of soft and condensed matter systems.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

Reconstruction of the atomistic surface of Madagascar graphite (Hybrid Reverse Monte Carlo/wide-angle X-ray scattering data) is presented in Figure 1S. Figure 2S presents the comparison between experimental (graphitized Sterling FT carbon black) and theoretical (grand canonical Monte Carlo, nonlocal density functional theory) N2 adsorption isotherms at 77 K. Movies show the snapshots of the atomistic structural model of the CMS-F sample (jp503628m_si_002.mpg) with adsorbed N2 at 77 K (jp503628m_si_003.mpg) and C6H6 at 313 K (jp503628m_si_004.mpg). It should be noted that Figure 3 and all movies were created using the VMD 13005



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