Atomistic modelling insight into the structure of lignite-based activated carbon and benzene sorption behavior

Abstract

Improved structure–property relationships for activated carbon were obtained by devising realistic, large-scale, structural models. Herein, an improved approach was employed to construct atomistic models of a lignite precursor of activated carbon, based on the high resolution transmission electron micrographs (HRTEM) of pyrolyzed lignite coal, in combination with experimental pore size distribution analysis of tailored lignite-based activated carbon. Benzene sorption was experimentally characterized at 303 and 318 K and resulted in 13–18% mass gain. To model the carbon structure and benzene sorption, we have devised two structures, including either micropores (4–20 Å) or micro/mesopores (4–40 Å). For the 303 K conditions, the predictions of the two models are consistent with experimental observations. For the micro/mesoporous model, benzene molecules sorbed in both micropores and mesopores, as the mesopores provide access to the internal part of the carbon structure, and benzene molecules would pass readily through these small mesopores to the final sorption sites in micropores of 14–18 Å in size. The most favored sorption energy was −37.45 kJ mol⁻¹, with a preferred rotation angle from 20–30°, and a second favored angle from 30–40° relative to the graphene surface. These benzene molecules were aggregated in T-shaped and parallel-displaced configurations, with a separation distance of 5.75 Å from the benzene centers of mass to the carbon surface in a monolayer state. The most favored position was found to be parallel to and between two carbon surfaces, especially close to 5- or 7-membered rings.

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1. Introduction

Activated carbon is an efficient material to remove toxic volatile organic compounds (VOCs) from air and effluent streams. Activated carbons can be tailored so as to improve their sorption of targeted VOCs by modifying their pore structure and surface chemistry. This tailoring protocol could be enhanced yet further by better understanding how the internal structure of activated carbon influences sorption behavior. Studies have been performed to elucidate how preparation, adsorption, and structural properties influence sorption behavior. Previous experimental tests have shown that activated carbon’s affinity for contaminants was regulated by pore size distribution, surface area, and surface chemistry.^1–5 Rangel-Mendez et al. and Nowack et al. employed thermal methane plus steam post-treatment on activated carbons to create a high pore volume and a more stable surface, which corresponded to higher 2-methylisoborneol (MIB) removal.^4,6 Redding et al. compared six granular activated carbons which exhibited a wide range of pore volumes, showing that both ultra-fine micropores and small diameter mesopores control methyl tert-butyl ether (MTBE) adsorption.⁷ Chen et al. determined that ammonia-tailoring resulted in activated carbons with more positive surface charge density at pH = 7.5, which enhanced adsorption capacity for perchlorate.⁸

In light of this extensive previous research, an improved understanding of the fundamental mechanisms concerning physical and chemical processes involved in sorptive behavior remains desirable. Molecular modelling can provide atomistic insight into carbon structure and sorption phenomena. Thus, various activated carbon porous models have been generated as a basis for the theoretical study of sorption behavior.^9,10 Gubbins et al. used Reverse Monte Carlo (RMC)-based techniques to accurately generate structural carbon models, while also capturing the morphological features observed in experimental TEM images.^11–15 Morphological and topological disorders were detected, and they are proposed to significantly affect the capillary condensation phenomenon of argon adsorption in silica nanopores.^16,17 Harris et al. examined the high resolution transmission electron micrography (HRTEM) of activated carbons, and proposed fullerene-like models which consist of discrete fragments of curved carbon sheets.^18–24 Using these models as a starting point, Terzyk et al. performed molecular dynamics simulations to mimic adsorption behavior.^25–27 They discerned that the simulated adsorption isotherms of CCl₄, C₆H₆ and noble gases (Ne to Xe) fit well the Dubinin-related empirical relationships that they derived from experimental data; and they linked this to the constructed models that simulate adsorption phenomena.

Overall, there are three types of carbon structural models that are most widely used for sorption studies: (a) the slit pore model, which is a simplification of the pore structure that facilitates the introduction of different pore widths,^27–31 (b) modelling of carbon nanotubes, which includes structural defects, functionality, pore length, pore connectivity and pore blocking effects; these enable a more accurate depiction of the complex features of carbon structures, ^17,32–36 and (c) recently, a proposed virtual porous carbon model that has exhibited the capability to present experimental characteristics of surface area, accessible pore volume and density, as well as the disordered nature of graphene sheets in orientation and curvature.^{12,15,37–47} The simulated adsorption isotherms of N₂ and Ar were used to extract pore size distributions, and then used for predicting organic compound adsorption.^{14,16,25,30,38,41} A number of studies have focused on the adsorption behavior of light gases and volatile organic compounds, for example CO₂, SO₂, H₂O, CH₄ and C₆H₆.^{12,27,28,32,36,37,39,40,43,47} Others have experimentally or fundamentally investigated the adsorption of organic compounds from water: benzene, phenol, paracetamol, etc.^{31,42,44,46,48,49} In this experimental and modelling work, the authors have particularly focused on how carbon surface chemistry and graphene layer curvature influenced sorption. Surface curvature was found to provide a strong adsorption energy for organic compounds in comparison to flat graphite surfaces.⁴⁹ When modelling the sorption of polycyclic aromatic hydrocarbons (PAH) onto single-walled carbon nanotubes, it was flat-oriented PAHs that sorbed more preferentially.³⁵

1.1 Objectives

The specific objectives are: (a) to employ HRTEM and interpretive techniques to characterize the graphene structure of lignite precursors of activated carbons; (b) adapt the team’s previous modelling techniques to a tailored lignite-based activated carbon that has been identified as “SuperDarco”;^4,6,10 (c) experimentally monitor the sorption of benzene onto activated carbon at temperatures of 303 and 318 K, and (d) perform sorption simulations on the constructed atomistic activated carbon models, combined with experimental results to explore the sorption behavior of benzene molecules in different pore structures.

Activated carbons are comprised mostly of graphene sheets that are arranged somewhat amorphously relative to one another, as revealed by X-ray diffraction and HRTEM observations.^{18–21,23,50–52} To obtain the HRTEM images of activated carbon is extremely challenging, since the apparent high porosity and disordered arrangement of graphene sheets make it difficult to extract structural features from the images. Therefore, the authors herein sought an improved approach for interpreting the HRTEM images of a pyrolyzed lignite coal, i.e. a precursor of lignite-based activated carbon; and then combined the extracted structural features (fringe length, orientation and stacking distribution) with the experimental pore size distribution of a tailored lignite-based activated carbon to construct an atomistic model. To elucidate the effect of pore structure and surface functionality on benzene sorption, two structures were considered in our 100 × 100 × 100 Å model volume. These included either solely micropores (4–20 Å) or micro/mesopores (4–40 Å). In each of these modelled cubes, we modelled the graphene sheets to be lined along their fringes with carboxyl, lactone, phenol, and carbonyl functional groups, so as to conform to elemental compositions. The work utilizes a highly effective construction protocol via Fringe3D⁵³ and Vol3D⁵⁴ Perl scripts (as discussed in our previous paper¹⁰) in combination with Materials Studio platform, aimed at exploring the behavior of benzene sorption (sorption sites, molecular movement, binding energy, etc.) based on sorption dynamics simulations.

Benzene represents a relatively simple structural surrogate amongst aromatic volatile organic compounds (VOCs), and it is also a common component of gasoline and exhaust gases from coal-fired power plants.^55,56 Thus, benzene was selected as a surrogate VOC to gain insight into the sorption behavior of not only benzene but of other aromatic VOCs of a similar structure. From a fundamental perspective, benzene sorption onto activated carbon occurs via an array of phenomena and mechanisms that are dictated by pore width and surface chemistry. Micropores are primarily responsible for adsorption at low concentrations (ppbv and ppmv), since the volume filling of pores can occur even at a low relative pressure.^57,58 Sorption in mesopores proceeds via the formation of multilayers of adsorbates followed by capillary condensation.⁵⁹ Indeed, a large specific area generally correlates a with higher sorption capacity, because with higher surface areas comes greater micropore volumes – where higher sorption energies occur. Furthermore, higher micropore and small mesopore volumes offer more sorption via the pore filling process.⁶⁰ Thus, activated carbons with highly micro/mesoporous structures have shown high affinity towards aromatic molecules and fast sorption kinetics, and have resulted in higher sorption capacity and less mass transfer resistance than solely microporous activated carbons.⁶¹ On atomistic silica surfaces and in cylindrical nanopores, a strong layering of benzene molecules was observed with a perceived preferential orientation that was nearly perpendicular to the pore surface when fully hydroxylated surfaces were considered, and a second preferential orientation of ∼50° when encountering a partially hydroxylated surface.^17,62 However, benzene adsorbed in the disordered porous carbon exhibited a liquid-like structure.⁶³

2. Experimental characterization and model input methodology

2.1 Experimental observations of lignite coal microstructure

Lignite coal samples provided by ADA Carbon Solutions, LLC. from northwest Louisiana were heat-treated under a nitrogen atmosphere at 800 °C for 20 min. A 200 kV field-emission TEM (FEI Titan3) was used to obtain high-resolution coal char micrographs where crystallite layers were recorded digitally and could be qualitatively interpreted (Fig. 1a). A semi-automated procedure in Adobe Photoshop was applied to extract parameters regarding fringe width, orientation angles and centroid coordinates (Fig. 1b). Fringes smaller than 3 Å were rejected, since they could be considered as noise and removed without loss of data.^54,64–67 Stack distribution was identified using a graphical user interface (GUI) developed in Matlab (Fig. 1c). We set parameters for midpoint distance (7.0 Å), perpendicular distance (4.0 Å) and angle difference (30°), while the program compared the information regarding the fringe length, coordinates, and orientation angle of one fringe relative to all other fringes. If all three of these conditions were met, fringe characterizations were identified as part of a multiple fringe stack. A final check was conducted to ensure that no fringe formed a part of more than one recognized stack.⁵⁴ The steps of HRTEM analysis coupled with Adobe Photoshop and Matlab are discussed in the ESI† (Section 1), and the extracted distribution of structural parameters, including the distributions of fringe width and orientations, are shown in Fig. 1 and 2. The lignite coal particles examined using TEM were placed in no particular orientation, so the original HRTEM images did not present bedding plane information.⁶⁸ To aid in the identification and quantification of fringe orientation, we assumed that the dominant orientation was aligned vertically, and fringes orientated within ∼10° bins were summed (data processed via Excel) (Fig. 2b). These characterizations were adapted as we next developed our computerized model of the 100 ų depiction of a tailored lignite-based activated carbon.

Fig. 1 (a) Original high-resolution transmission electron microscopy (HRTEM) images of pyrolyzed lignite coal, (b) the processed HRTEM images, and (c) stack identification where two-layer is colored red, three-layer is colored blue, four-layer is colored pink, and five or more layers is colored teal.

Fig. 2 Distribution of the (a) fringe length and (b) fringe orientation for pyrolyzed lignite coal.

2.2 Experimental characterization of lignite-based activated carbon

The lignite-based activated carbon used in this research was prepared by NORIT Americas, Inc. of eastern Texas, and is identified as “SuperDarco”. Prior to tests, the samples were crushed and sieved to 200 × 400 US mesh. Experimental characterization included mercury porosimetry, helium pycnometry, elemental analysis, pore size distribution (N₂), Brunauer–Emmett–Teller surface area, and elemental composition. Testing methods and results are presented in the ESI† (Section 2.). The volumetric composition of this lignite-based activated carbon and pore size distribution were shown in Fig. 3.

Fig. 3 (a) Composition of lignite-based activated carbon including pores and voids up to 490 000 Å with volume distribution (mL g⁻¹) as indicated, and (b) pore volume distribution calculated from nitrogen adsorption isotherms using a density functional theory (DFT) method.

For the modelling work here, as a simplification, the structure within the modelled 100 ų volume was taken to be comprised solely of carbonaceous solid or vacant pores, but no ash. The characterization of pore size distribution by HRTEM image analysis turns out a useful and powerful method, especially when applied in the small micropore region of <0.7 nm.⁶⁹ However, due to the amorphous structure of this lignite-based activated carbon, and limitations of HRTEM characterization technique, it is extremely difficult to obtain useful HRTEM images of activated carbon, and this limits characterization of the full range of the pore size distribution. Therefore, nitrogen adsorption analysis (using a Micromeritics 2020) was adopted, and the adsorption data was converted to an incremental pore volume distribution using Density Functional Theory (DFT) theory assuming a slit-shaped pore model, yielding the pore volumes shown in Fig. 3b. This tailored lignite-based activated carbon exhibited a peak in pore volume at 13 and 46 Å pore widths. To explore the effect of pore size on benzene sorption, the authors herein mimicked the micropore (and small mesopore) distributions shown in Fig. 3b when creating a 100 × 100 × 100 Å cube atomistic model of a “typical” volume within the activated carbon structure. In preparing these modelled cubes, we assumed two different structures: model 1, a microporous-only model which includes only micropores of 4–20 Å; and model 2, a micro/mesoporous model which including both micropores and small mesopores of 4–40 Å. The volumetric composition (in mL g⁻¹) of these two representative activated carbon cubes is summarized in Fig. 4. These could also be presented as relative volumetric compositions (in mL mL⁻¹), as presented later in Fig. 7.

Fig. 4 Modelling composition of a “typical” 100 × 100 × 100 Å lignite-based activated carbon with a volumetric distribution as indicated: (a) model 1, including only micropores (4–20 Å), and (b) model 2, including both micropores and mesopores (4–40 Å).

2.3 Experimental thermogravimetric sorption tests

Sorption tests on this lignite-based activated carbon used benzene, which is of major environmental and health concern when present in water and air streams, even at low concentrations. Moreover, benzene was used as a surrogate for a broader range of the aromatic VOCs that originate from gasoline and coal-burning operations. A certified benzene standard gas (Rising Gas, China) in a N₂ gas-based standard mixture was used, with a concentration of 10 331.6 × 10⁻⁶ mol mol⁻¹ (10 331 ppmv). Benzene sorption tests were conducted using a thermogravimetric analyzer (Mettler Toledo TGA/DSC 1, Switzerland), so as to characterize the sorption of benzene. Testing temperature was maintained 303 or 318 K. Initially, samples were degassed in the TGA with pure nitrogen at 393 K for 60 min. After cooling to the testing temperature, the inlet line was switched to a benzene gas stream, maintained at a 50 mL min⁻¹ volumetric flow rate. The TGA instrument monitored mass change with time until an equilibrium was reached, and this method yielded very precise benzene sorption values throughout the experimental protocol.

2.4 Atomistic model construction of lignite-based activated carbon

Fringe3D and Vol3D Perl scripts were used to generate a large-scale molecular model for lignite-based activated carbon based on the available structural data. This automated construction protocol was derived from our previously work.¹⁰ This tailored lignite-based activated carbon presented a normalized elemental composition of C₁₀₀H_17.57O_27.96N_0.41 (H/C = 0.18), in atomic proportions. As analyzed from the HRTEM images of lignite coal, the mean fringe length was 7.5 Å, which corresponds to ∼C₂₅H₁₃ (H/C = 0.52) in circular/parallelogram catenation. Thus, small graphite sheets nearby were considered to connect through C₅, C₇, or C₅/C₇ pairs to form larger fragments during the activation process,^70–72 as representatively depicted by the two structures in Fig. 5. Low-rank lignite coal is highly oxygenated, which creates a potential for cross-linking to occur through reactions involving oxygen-containing groups.^73,74 Therefore, carbon–oxygen–carbon cross links were gradually introduced via bonds until the total system conformed with the experimental atomic H/C ratio.^75–77 This process was accomplished by close contact examination between oxygen-related functionalities and nearby fragments using Materials Studio, and then manually creating bonds between them, as illustrated in Fig. 6 and the ESI† (Section 3.).

Fig. 5 Examples of small graphene sheets connected through C₅, C₇, or C₅/C₇ pairs, that form larger fragments during tailored activation.

Fig. 6 Cross-linked cluster generation example: randomly distributed graphene sheets showing potential bonding sites (left) and geometry-optimized cross-linked cluster (right). Atoms are represented by sticks: carbon, green; hydrogen, white; oxygen, red; nitrogen, blue.

The dimensions of the lignite-based activated carbon model were initially 100 × 100 × 100 Å, including pores up to 20 or 40 Å and stacks in a variety of width and orientations. The stack distribution was simplified to include 87% single layers, 10% double layers, and 3% triple layers, with a mean interlayer spacing of 3.5 Å, as derived from Matlab analysis. Functional groups were included by using a Perl script developed within Materials Studio, and the underlying principle was to select specific atoms with a random number generator and then replacing them with determined functionalities. The resulting models were geometry optimized in the Materials Studio Forcite module using a pcff force field and smart minimization algorithm at a maximum 500 iterations to retain local orientations and stacking. Here we calculated the solvent-accessible surface area and porosity using the “Atom Volume & Surface” module, which takes into account only the free volume that can be accessed from at least one of the six sides of the simulation box. As a part of this computer modelling, pore size distributions were computed using the Poreblazer 3.0.2 program.⁷⁷ In this computation, the authors used a probe radius of 1.82 Å, which corresponds to the kinetic radius of N₂.⁷⁸ This N₂ radius was also used in Micromeretics pore volume analyses.

2.5 Sorption simulation details

Simulation of benzene sorption was achieved through Metropolis Monte Carlo simulations in the Grand canonical ensemble, performed on the Materials Studio7.0 platform using the Sorption module. Fixed pressure simulations were processed by varying the number of benzene molecules in the framework to keep the fugacity of the sorbate components fixed. A specified 10⁴ step equilibration period was set to ensure that the simulation started from a reasonable low energy state, then a 10⁶ step production run was followed. During the sorption course, benzene molecules would change position, orientation and conformation to be adsorbed in the carbon system. Specifically, the conformation of benzene structures was limited in 5° rotation and 1 Å translation amplitude according to the Metropolis Monte Carlo method. The pcff force field was selected for the energy calculations, while electrostatic and van der Waals interactions was computed using Ewald & Group and atom based techniques, separately. Single molecule sorption simulations were also conducted to identify the preferential (i.e., lowest energy) sites using a simulated annealing method. This was achieved by repeatedly exploring the sorbate–sorbent system as the temperature slowly decreased using a canonical Monte Carlo sampling method. Herein, the authors addressed the effect of pore size distribution on sorption behavior, which was detected by determining the temperature at 303 or 318 K, and fugacity at 1.047 kPa. The benzene concentration used in experimental thermogravimetric sorption tests was 10 331.6 × 10⁻⁶ mol mol⁻¹, corresponding to relatively low pressure, so the authors considered that the value of fugacity was identical to the absolute pressure of benzene.⁷⁹ The pair correlation function G(r) concerning the separation distance of benzene molecules and carbon surface was calculated using the Forcite module with a cutoff of 20 Å and interval of 0.1571 Å⁻¹.

3. Results

3.1 Large scale atomistic representation of a lignite-based activated carbon

The large scale modelled representations of tailored lignite-based activated carbon characterized an arrangement of ∼33 000 atoms within a 100 × 100 × 100 Å cube, while allowing a high level of control over graphite sheet length, orientation, stack distribution and pore size. There were ∼77% fragments involved in cross-linked clusters, exhibiting a broad molecular mass distribution ranging from 1221 to 18 075 g mol⁻¹. Fig. 7 depicts the two models that were evaluated: model 1, the microporous model with pores in the range of 4–20 Å; and model 2, the micro/mesoporous model, with pores in the range of 4–40 Å. Fig. 7 presents these as a series of visualizations; first, Fig. 7a1 and b2 depict the graphene fragments, decorated with H and O and N heteroatoms, where oxygen and nitrogen are present in carboxyl, lactone, phenol, and carbonyl functional groups. Fig. 7a2 and b2 describe the solvent-accessible surfaces, which are coloured in blue. Pore volumes were calculated from these surfaces. Finally, Fig. 7a3 and b3 present three-dimensional slices throughout the simulation cube, so as to aid insight into internal porosity. The computed results for the model 1 and model 2 cubes are compared to experimental results in Table 1 and Fig. 8. As is shown, the experimental and modelled pore volumes match one another nicely, as do the elemental compositions. The calculated solvent-accessible surface areas for the two simulated models are 2202 and 2576 m² g⁻¹, separately. These simulated values greatly exceed the experimental N₂ adsorption BET value of 879 m² g⁻¹; this highlights the (well-known) limitations that are inherent to the N₂ adsorption protocol for accessing and truly documenting all the sheet surfaces of graphene.

Fig. 7 Large scale atomistic representation of lignite-based activated carbon composed of ∼33 000 atoms in a 100 × 100 × 100 Å cubic box. Model 1 includes only micropores (4–20 Å), and model 2 includes both micropores and mesopores (4–40 Å). (a1) and (b1) Simulated models containing heteroatoms, with carbon coloured green, hydrogen coloured white, oxygen coloured red, and nitrogen coloured blue. (a2) and (b2) Representation of solvent-accessible surface area by blue areas, and (a3) and (b3) depiction of two-dimensional slices ”cut” perpendicular to one another, so as to show the simulated pore volume that could be occupied by adsorbates (blue), and unoccupied (red).

Table 1 Main structural parameters of models compared with experimental characteristics

Characterization	Experimental value	Model 1	Model 2
a Model 1: including only micropores 4–20 Å.b Model 2: including micro/mesopores 4–40 Å.
Elemental composition		C22687H3861O6231N92	C18240H3094O5043N75
C (atomic%)	68.5%	69.0%	68.9%
H (atomic%)	12.0%	11.7%	11.7%
O (atomic%)	19.2%	19.0%	19.1%
N (atomic%)	0.3%	0.3%	0.3%
Porosity (nitrogen), mL mL^−1	0.39^a/0.48^b	0.37^a	0.47^b
Microporosity	0.39^a/0.33^b	0.37^a	0.32^b
Mesoporosity	0^a/0.15^b	0^a	0.15^b
Solvent-accessible surface area (m^2 g^−1)		2202	2576
System density (g cm^−3)		0.63	0.50
Helium density (g cm^−3)		0.79	0.60
Percentage of ring type
Five-membered ring (%)		8%	9%
Six-membered ring (%)		86%	84%
Seven-membered ring (%)		6%	7%
Initial number of fragments		170	135
Ratio of cross-linked clusters		0.77	0.74
Range of molecular mass (g mol^−1)		1374–14 982	1221–18 075

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Fig. 8 Cumulative pore volume distributions (ų Å⁻³) of atomistic models compared with experimental data. (a) Model 1, including only micropores of 4–20 Å and (b) model 2, including micro/mesopores of 4–40 Å.

3.2 Experimental results of benzene sorption

The experimental benzene sorption results are shown in Fig. 9. The tailored lignite-based activated carbon samples retained a linear mass increase for the first few minutes, indicating that all the benzene gas that entered the TGA chamber during this time was removed from the gas phase, and sorbed into the activated carbon. The slightly steeper initial slope at 318 K corresponds to its slightly faster mass transfer kinetics than at 303 K. As the sorption capacity became exhausted, the sample mass increased more gradually until it reached a pseudo-equilibrium state. Herein, when a 10 331 ppmv concentration of benzene in nitrogen was used, this tailored lignite-based activated carbon gained 18.31 mass% at 303 K; and it gained 13.60 mass% at 318 K. Generally, a longer breakthrough time results in a higher dynamic sorption capacity. The amount of benzene gas that was adsorbed decreased with increasing temperature, which indicates that the mechanism of physical sorption caused partitioning of the vapor between the gas and adsorbed phases.

Fig. 9 Mass gain of lignite-based activated carbon under 10 300 ppmv benzene under nitrogen at 303 and 318 K.

3.3 Simulation results

The fixed-pressure sorption simulations predicted benzene uptake for specific temperatures, as illustrated in Table 2. The pseudo-equilibrium mass gain at 303 K shows good agreement with experimental results of 18.31% mass gain. This matches closely to the “average” of 18.08% mass gain between the two models, thus suggesting the validity of this modelling approach. Of these two, the micro/mesoporous model 2 exhibited the greater mass gain, due to the inclusion of small mesopores. We note that at the higher temperature of 318 K, however, the simulated sorption was ∼22% greater than the experimental result. Specifically, the rise in temperature propels the diffusion of benzene molecules through the pore systems. As the modelling work was a simplification of activated carbons which exhibit more microporosity, thus the simulated models provided more sorption sites and the adsorption capacity was enhanced at a higher temperature. Also, this disparity may be related in part by noting that the 318 K temperature is approaching benzene’s boiling point of 353 K.

Table 2 Simulated sorption results for the constructed microporous model 1 and micro/mesoporous model 2

	Temperature (K)	Benzene loading number	Mass gain (%)	Average isosteric heat (kJ mol^−1)	Peak energy (−kJ mol^−1)
Model 1	303	817	16.91	44.56	38.70
	318	762	15.77	45.40	36.19
Model 2	303	738	18.97	43.45	37.45
	318	648	16.65	45.81	37.57

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Isosteric heat is a function of temperature and pressure at constant loading number, and is usually interpreted as the sum of adsorbate–adsorbate and adsorbate–adsorbent contributions. Decreased isosteric heat was observed in both models, however was associated with increased benzene sorption. As the adsorbate–adsorbate contribution is an increasing function of loading, this decrease is mainly due to the decreased adsorbate–adsorbent contributions in the micro/mesoporous systems that is determined by pore size. The simulated average isosteric heat of sorption was 44 kJ mol⁻¹ for the two models, agrees well with reported values in the literature for six kinds of activated carbons.⁸⁰ The simulated energy distributions exhibit a distinct peak centered at −37–39 kJ mol⁻¹. This position of peak had the largest number of available sorption sites. These peak values are similar to those measured for activated carbons by Heuchel and Jaroniec.⁸¹

4. Discussion

To further explore the process of benzene sorption and thus the sorption behavior, a close examination of sorption behavior was conducted at 303 K. The models revealed distinctions in where and how benzene sorbed, as is discussed below.

4.1 Changes of pore volume distribution

Comparison of the incremental pore volume distributions of pristine and benzene-loaded carbon models revealed the more favored pore range for benzene molecules to occupy, as shown in Fig. 10. In the microporous model 1, the most noticeable decrease in incremental pore volume was observed in the range from 14–18 Å, which contributes to 76% of the total pore volume loaded by benzene molecules. Pores of 9–11 Å constitute about 11% of the decreased volume. In the micro/mesoporous model 2, the decreased micro- and mesopore volumes were 89 386 and 46 159 ų, respectively, which demonstrates that micropores provide the major sorption site for benzene molecules to occupy. Benzene molecules were primarily loaded in pores of 15–16 Å, 19 Å, 28 Å, 30 Å and 39 Å in size. In both of these two models, the smallest pore size that benzene molecules could occupy was about 4.9–5.2 Å. It is interesting to notice that pore volume in the range of <6–7 Å after sorption simulations is greater than that of the pristine counterparts, indicating that benzene partially fills slightly larger pores to where the remaining vacant volume was smaller than 6 Å wide. In comparison, Lillo-Ródenas et al. found that low concentration benzene (200 ppmv) could sorb into ultra-microporous carbons, where pores <7 Å were the most important parameters affecting sorption performance.⁸² Moreno-Castilla et al. proposed that benzene sorption (741 ppmv) displays a good linear relationship with micropore sizes up to 10.5–11.0 Å.⁸³ The results herein show that benzene sorption (10 000 ppmv) is attributable to both larger micropores (14–18 Å) and small mesopores. This inconsistency might be due to the different concentrations of benzene. Therefore, the authors attempted to conclude that benzene sorption in activated carbon is size-dependent. At relatively low concentrations, smaller micropores exhibited a greater effect on benzene sorption, while with increased concentration, benzene loading was more profound in the presence of large micropores and small mesopores.

Fig. 10 Comparison of the incremental pore volume distribution (ų) of pristine and benzene-loaded carbon models. (a) Microporous model 1; and (b) micro/mesoporous model 2. Decreased pore volume was obtained by pristine incremental pore volumes minus loaded ones.

4.2 Exploration of favorable sorption site

Single molecule sorption was modelled via the “Sorption Locate” tool to identify the favored (i.e. low energy) sorption site. In this model, the benzene molecule would go through translations, rotations, and rejections until its position was “accepted” on the basis of the most favorable interaction energy. The location of a single adsorbed benzene molecule within the carbon structure is shown in Fig. 11. At 303 K, the benzene molecule was found to be adsorbed between two carbon surfaces, while at the higher temperature of 318 K, the most favored position was parallel to the carbon surfaces. The average separation distance was about 4.23 Å, and the benzene molecule was located near 5- or 7-membered rings on the carbon surface, due to the strong sorption energy provided by this curvature. Relative to subsequent tailoring strategies, we note that if more defects in structures could be created, their presence would improve the sorption capacity for VOCs with configurations like benzene.

Fig. 11 Simulated location of a single benzene molecule adsorbed inside the carbon structure.

4.3 Exploration of sorption process in micro/mesoporous model

To elucidate the process of benzene sorption, the authors observed the sorption behavior of the micro/mesoporous model 2 at 303 K. Distributions of the orientation angles of adsorbed benzene molecules and graphene sheets are shown in Fig. 12. To aid with identification, the authors assumed that the dominant orientation of graphene sheets was aligned vertically, and angles within ∼10° bins were summed (data processed via Excel). The angle distribution was similar during the sorption process, and benzene molecules were highly disordered. Herein, the authors gathered that benzene molecules prefer to form an angle of 40–50° to the carbon surface at the beginning of sorption. Whereas, approaching the pseudo-equilibrium state, a most favored orientation of 20–30°, and a second preferred angle of 30–40° was observed. This simulation indicates that benzene molecules could readily rotate within the structure during the sorption process so as to fit the optimal energy, and they tended to orient in a highly disordered manner.

Fig. 12 Distributions of the orientation angles of adsorbed benzene molecules and graphene sheets relative to a horizontal plane at four different values of fractional filling.

This simulation also models where and how the benzene molecules align themselves on the carbon surface. This alignment is characterized by positional pair correlation function G(r), where G(r) is the probability density of finding a benzene center separated by a given distance, r (Å) from a graphene’s carbon atoms, or from the graphene’s oxygen atoms. This function is given by

G(r) = 4πr²ρdr

where r is the separation distance, and ρ is the average number of molecules per unit volume in the system. Therefore, G(r) > 0 occurred when the minimum distance was found between the two sets, and the peak intensity of G(r) was associated with the largest number of r (Å), in other words the most favored separation distance. Fig. 13 shows the positional pair correlation function G(r), while taking into consideration the benzene centers of mass with respect to the carbon surface at four different values, which was helpful to illustrate the layering of adsorbates at the adsorbent surface during the sorption process.

Fig. 13 Simulated pair correlation function of (a) benzene centers of mass to the carbon atoms on the graphene surface; (b) benzene centers of mass to the oxygen atoms on the graphene surface; and (c) benzene centers of mass.

The G(r) functions of benzene centers of mass to carbon atoms on graphene surface are shown in Fig. 13a. At relatively low fillings (loading number of 318 benzene molecules), a smaller shoulder was found at 4.31 Å, corresponding to first layer sorption. The broad peak centered at 6.15 Å denotes second layer formation. In that a benzene molecule is about 4.7–5.0 Å long, from H tip to H tip, and the most favored angle of 40–50° at this state, it is inferred that benzene rings were aggregated in T-shaped configurations in this pseudo-bilayer sorption. When full pseudo-equilibrium sorption occurred, the main features of the distributions curves were a distinct peak located at 5.75 Å, indicating that monolayer sorption is dominant, and that sorption behavior was primarily regulated by van der Waals forces. Benzene molecules adsorbed at a smaller distance to oxygen atoms, as revealed in Fig. 13b, illustrate that the introduction of oxygen functionalities induced the polarity of carbon surface, which becomes more attractive to the adsorbate. When 463 benzene molecules adsorbed in the structure, a prominent shoulder is visible at 3.51 Å, and the most probable separation distance peaked at 5.75–6.68 Å. This implies that benzene molecules preferred to arrange adjacent to previously sorbed benzene molecules near oxygen-related functionalities, and presented a pseudo benzene-on-benzene stacking configuration. With increased fractional fillings, the minimum distance was decreased to 2.71 Å, corresponding to hydrogen bonding between benzene molecules and oxygen atoms, and benzene molecules adsorbed in a monolayer with a separation of 5.15 Å to the oxygen atoms when approaching the pseudo-equilibrium state. The center of benzene mass G(r) revealed the stacking configurations of benzene molecules. When approaching a full loading of benzene molecules, the minimum distance was at 3.89 Å, and distinct shoulders were found in the range of 5.1–6.9 Å (Fig. 13c). Taking into account the distribution of orientation angles of benzene molecules in Fig. 12, it can be inferred that benzene rings adsorbed on the carbon surface were aggregated in T-shaped and parallel-displaced configurations.⁸⁴

The incremental pore volume distributions during the sorption process are shown in Fig. 14. At a relatively low fractional filling of benzene (loading number of 318 benzene molecules), the decreased micro- and mesopore volumes were 27 861 and 39 268 ų, respectively, indicating that benzene molecules were primarily adsorbed in the mesopores. With yet more benzene loading, benzene molecules moved towards the micropores, as an obvious decrease in micropore volume was displayed, whereby the peaks at 14–18 Å gradually disappeared and the pore volume of mesopores slightly changed. This phenomenon proves that both micropores and mesopores work for sorption behavior, as mesopores provide access to the internal part of carbon structures, and benzene molecules would pass readily through these small mesopores to the final sorption sites in micropores.

Fig. 14 Comparison of incremental pore volume distributions (ų) of pristine and benzene-loaded carbon models with increasing loading number.

Thus, the simulations indicate that the most favorable configuration was of benzene molecules located at a separation distance of 5.75 Å between the benzene center and the carbon surface, and a rotation angle of 20–30° to the carbon surface with a binding energy of −37.45 kJ mol⁻¹. At this relatively low partial pressure of benzene (corresponding to 10 332 ppmv), the behavior of benzene molecule sorption into the atomistic structure of activated carbon could be summarized as follows: benzene molecules first adsorb near the oxygen-related functionalities on the graphene surface that are distributed throughout the carbon structure, with several preferential orientations to maximize the interaction energy. This mainly occurs in small mesopores with a preferential orientation of 40–50° to the pore surface. With yet more benzene loading, the benzene molecules attempted to find the optimum position where they could arrange adjacent to previously sorbed benzene molecules, and aggregated in T-shaped configurations in this pseudo-bilayer sorption. Then, with yet more benzene loading, these molecules moved through the mesopores to the micropores. At this level of loading, monolayer sorption was initially dominant, and the separation distance of benzene mass centers to carbon surface decreased as a manifestation of single-layer stacking. Finally, when approaching pseudo-equilibrium saturation, benzene molecules were presented in T-shaped and parallel-displaced configurations beyond the carbon surface with a separation distance of 5.75 Å and a most favored angle of 20–30° in a monolayer sorption. The benzene molecules filled out throughout the pore volumes, when all the spaces closer to the graphene surfaces had been exhausted. This filling process occurred preferentially in the corner of pores where adsorption energies from both sides could be manifested, with less occupation at the middle of pores. All benzene molecules were accepted into the atomistic structure at energetically optimal positions.

5. Conclusions

Construction of large-scale atomistic representations of activated carbon aids the exploration of structure–property relationships. Here, an automated construction protocol, based on HRTEM images and experimental data, in conjunction with Fringe3D and Vol3D Perl scripts, was applied to generate atomistic models for a lignite-based activated carbon identified as “SuperDarco”. Two carbon structures were constructed; one included only micropores (4–20 Å) while the other included both micro- and mesopores (4–40 Å). The simulated models were conducted on a large-scale of 100 × 100 × 100 Å in volume with ∼33 000 atoms, as well as in greater experimental conformity and structural diversity. Benzene sorption was simulated to explore the sorption behavior relative to pore size distribution and surface heteroatoms. The micro/mesoporous model showed greater sorption capacity, when compared to the microporous one under the same temperature conditions. Sorption behavior mainly occurred in larger micropores and small mesopores, and benzene molecules would pass through the mesopores to access the internal structure in activated carbons, where micropores in the range of 14–18 Å in size provide a significant proportion of the sorption sites – although other pore sizes were also important. Single molecule sorption simulations showed that the benzene molecule adsorbed parallel to, and between, two carbon surfaces, and located near 5- or 7-membered rings on the carbon surface. Fundamental insight regarding the simulated sorption behavior of benzene molecules into a micro/mesoporous atomistic structure as a function of loading number reveals that with relatively extensive loading, benzene molecules were presented in T-shaped and parallel-displaced configurations beyond the carbon surface with a separation distance of 5.75 Å in a monolayer sorption. These molecules preferred a major rotation angle of 20–30°, and a second preferred angle of 30–40°, with a sorption energy of −37.45 kJ mol⁻¹. The present work provides useful insight into the behavior of benzene sorption, and offer strategies for better tailoring activated carbons to adsorb benzene and other similar aromatic volatile organic carbons.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra07533a

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