Scholarly article on topic 'In silico designed microporous carbons'

In silico designed microporous carbons Academic research paper on "Nano-technology"

CC BY
0
0
Share paper
Academic journal
Carbon
OECD Field of science
Keywords
{}

Abstract of research paper on Nano-technology, author of scientific article — Aleksandra Gonciaruk, Flor R. Siperstein

Abstract This work presents a computational study on the packing of three-dimensional carbon nanostructures and their effect on gas adsorption properties. We show that it is possible to obtain intrinsically microporous materials without specifying structural properties such as surface area or pore size distribution by packing individual graphene platelets connected at a contortion site. The resulting structures can potentially represent disordered carbons and provide understanding of the relationship between pore structure and adsorption performance. The calculated CO2/CH4 selectivity of these materials at the zero coverage selectivity can be as high as 25, whilst at low finite pressures (0.05bar) is between 6 and 10, which is comparable with what is expected for most carbons. We compare the results to the ones obtained from a simple slit pore model and highlight the importance of pore morphological complexity to adsorption of industrially important gases.

Academic research paper on topic "In silico designed microporous carbons"

Available at www.sciencedirect.com

ScienceDirect

journal homepage: www.elsevier.com/locate/carbon

In silico designed microporous carbons

Aleksandra Gonciaruk, Flor R. Siperstein *

School of Chemical Engineering and Analytical Science, The University of Manchester, M13 9PL, United Kingdom

CrossMark

ARTICLE INFO

ABSTRACT

Article history:

Received 21 November 2014 Accepted 27 February 2015 Available online 5 March 2015

This work presents a computational study on the packing of three-dimensional carbon nanostructures and their effect on gas adsorption properties. We show that it is possible to obtain intrinsically microporous materials without specifying structural properties such as surface area or pore size distribution by packing individual graphene platelets connected at a contortion site. The resulting structures can potentially represent disordered carbons and provide understanding of the relationship between pore structure and adsorption performance. The calculated CO2/CH4 selectivity of these materials at the zero coverage selectivity can be as high as 25, whilst at low finite pressures (0.05 bar) is between 6 and 10, which is comparable with what is expected for most carbons. We compare the results to the ones obtained from a simple slit pore model and highlight the importance of pore morphological complexity to adsorption of industrially important gases. © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY

license (http://creativecommons.org/licenses/by/4.0/).

1. Introduction

Activated carbons have been used for thousands of years but an accurate microscopic description of their structure is still a mystery. Controlling their properties is a balance between art and science. Much research has been done in understanding the roles of the precursors and activating procedures, and the use of molecular simulation and reconstruction techniques has provided some insight into the fundamental properties of these materials.

The use of predesigned carbonaceous structures in the synthesis of these materials has been proposed by Mullen's group using an aromatic ring at the centre of the molecule or a tetrahedral carbon with graphene-like arms [1]. The materials proposed by Mullen have a flexible core which is expected to lead to non-porous structures. An alternative is to use a rigid core, similar to the one used in Organic Molecules of Intrinsic Microporosity [2] or Polymers of Intrinsic Microporosity [3] to create an inherently micropor-ous structure. In this work we aim to predict the properties

of in silico designed porous carbons using a systematic approach. The carbons are constructed using a well-established methodology to pack molecules that form amorphous materials [4]. The carbonaceous molecules contain a central unit that will be named core, and graphene-like arms that will provide the environment for adsorption. The molecules are designed to allow us assessing the role of core centre as well as the size and shape of the arms. Although the materials shown have not been synthesised to the best of our knowledge, the virtual structures obtained are expected to serve as a starting point to understand the connectivity between twisted and defective carbon sheets, the effect of edges, and packing abilities based on the precursors.

Molecular models of carbons have been studied since the pioneering work of Steele, and the derivation of the 10-4-3 potential for slit pores [5]. The slit pore model has served to characterise porous carbons by inversion of the adsorption isotherms to obtain the pore size distribution. Currently Density Functional Theory (DFT) models to obtain pore size distribution are common practice in most laboratories [6,7].

* Corresponding author.

E-mail addresses: aleksandra.gonciaruk@postgad.manchester.ac.uk (A. Gonciaruk), flor.siperstein@manchester.ac.uk (F.R. Siperstein). http://dx.doi.org/10.10167j.carbon.2015.02.073 0008-6223/© 2015 The Authors. Published by Elsevier Ltd.

This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Nevertheless, the slit pore model cannot capture all the properties of activated carbon which possesses great structural and chemical complexity. Significant efforts have been made to construct realistic models of porous carbons. The most physically sound approach is mimetic method that imitates experimental synthesis process. This is achieved using quench molecular dynamic [8,9] where gas or liquid carbon atoms are rapidly cooled simultaneously forming bonds resulting in connected amorphous structures or using canonical ensemble Monte Carlo simulation which evolves amorphous polymer to a disordered sp2 hybridized carbon by reforming bonds [10]. Another computationally expensive approach is reverse Monte Carlo (RMC) techniques that also reconstructs realistic disordered porous carbons structures by fitting experimental diffraction data of real materials [8,11-16]. Although these methods provide reasonable model structures for a specific material, it is difficult to generalise the information obtained from the simulations to a broader class of materials. Using well-defined building blocks or periodic structures as part of the model material complements the knowledge gained from very specific models. The amorphous structure of nanoporous carbons can also be represented by fullerenes, bundles of carbon nanotubes or a foam-like hypothetical C168 Schwarzite for surface morphology, for adsorption and diffusion studies [17-19]. A alternative approach that has gained significant attention consists in packing of idealized structures: structureless platelets [20,21], atomistically described platelets [22], the construction of virtual porous carbons [23]. Carbon models formed by unconnected building blocks lack some of the features that make an amorphous carbon self-standing material thus the method requires density, surface area and/or pore size distribution input data. We are particularly interested in exploring the latter approach of individual fragment packing but we introduce connectivity between them to obtain free standing material without the need of structural data.

This work follows on the idea of packing individual molecules to describe a carbonaceous material, but we do not explicitly specify the porosity (surface area or density of the material), which is necessary when using simple molecules like coronene [22]. The equilibrium structure of coronene would not be a porous carbon, but stacks of molecules packed together. We are able to obtain porous structures without imposing a predefined surface area as a result of having rigid contortion sites as part of the designed molecules. Although real carbon materials may not be equilibrium structures as prepared, ageing of the materials is expected to move them towards an equilibrium structure, therefore understanding the differences between materials with connected and unconnected graphene platelets can help understanding ageing of these materials.

This paper assess properties of carbonaceous materials obtained from packing pre-designed three-dimensional (3D) molecules and compares them with the carbon model proposed by Sarkisov group [22]. We test the validity of using a simple slit pore model with the calculated pore size distribution on the model material to predict the CO2 and CH4 adsorption at low pressures, which highlights the importance of platelet edges and various pore shapes observed in different materials.

2. Methodology

2.1. Preparation of carbon materials

Models were constructed and graphical displays generated using Material Studio software (Accelrys Inc.). Graphene arms were created in planar form by connecting six-membered carbon rings. The arms were then connected through two different centres inspired by triptycene ([2.2.2]propellane, hereinafter trip) and cyclotricatechylene (hereinafter CTC) (Fig. 1). The spherical structure of trip possesses rigid threefold symmetry that keeps graphene arms separated in 3 dimensions, whilst CTC centre is very flexible, thus allows for greater freedom for intramolecular graphene arms to form a single stack. Graphene arms were created connecting six membered aromatic carbon rings. The edge carbon atoms of the graphene were saturated by connecting hydrogens. Four different arms were constructed (Fig. 2): small (S), medium (M), large (L) arms of disk shape and medium size ribbon-like arm (M-ribbon). The carbon models as well as carbon dioxide and methane are described fully atomistically. Interactions between atoms are described using the Dreiding forcefield [24] for packing. This forcefield has been used previously to model structurally and chemically similar materials known as Organic Molecules of Intrinsic Microporosity [25], porous aromatic frameworks [26]. Five different materials were obtained by connecting arms and cores: S-trip, M-trip, L-trip, M-CTC and M-trip-ribbon.

2.2. Compression methodologies

The structures were packed in a low density box of 60 nm3 with periodic boundary conditions. The number of molecules varied between the systems to achieve a target density 0.49 g cm~3. Three simulation boxes were constructed for each of five model carbon structures obtain averaged results. The systems were then compressed using different packing procedures. The first packing method is based on the 21 step compression and decompression scheme described in Larsen et al. work [4]. We used slightly modified procedure to speed up the packing process, where all the NVT steps at 300 K were half as long as what was proposed initially [4]. Another method involves more rapid and less drastic compression pressure. The scheme is provided in Table 1. Molecules have more freedom to move at the first stage, where temperature is kept at 600 K and initial large volume is constrained. After this extended step system is cooled down and compressed

Fig. 1 - Centres of model carbons.

Fig. 2 - Disk shape arms of S - small, M - medium and L - large sizes and ribbon-like arm of M- medium size, and coronene molecule.

Table 1 - Molecular dynamic compression schemes.

Scheme 1 Scheme 2

Step Conditions Duration (ps) Step Conditions Duration (ps)

1, 2 NVT 600 K, 300 K 50, 50 1 NVT 600 K 200

3 NPT 1000 bar, 300 K 50 2 NVT 300 K 50

4, 5 NVT 600 K, 300 K 50, 50 3 NPT 1 bar, 300 K 50

6 NPT 30,000 bar, 300 K 50 4 NVT 600 K 50

7, 8 NVT 600 K, 300 K 50, 50 5 NVT 300 K 50

9 NPT 50,000 bar, 300 K 50 6 NPT1000 bar, 300 K 50

10, 11 NVT 600 K, 300 K 50, 50 7 NVT 600 K 50

12 NPT 25,000 bar, 300 K 5 8 NVT 300 K 50

13, 14 NVT 600 K, 300 K 5, 5 9 NPT 1 bar, 300 K 100

15 NPT 5000 bar, 300 K 5

16, 17 NVT 600 K, 300 K 5, 5

18 NPT 500 bar, 300 K 5

19, 20 NVT 600 K, 300 K 5, 5

21 NPT 1 bar, 300 K 800

to maximum of 1000 bar pressure following decompression to 1 bar.

In order to assess importance of the core, graphene arms were packed into boxes without connecting them through the core. In this way, it is expected to obtain denser systems, since movement of unconnected arms are not constrained by the core.

2.3. Slit pore

We created a slit pore model (Fig. 3) to test if the simpler model can predict the same CO2 and CH4 adsorption as in the system of model carbons. In the slit pore model adsorption occurs on the basal plane of graphene eliminating possibility of adsorption at the edges. Crystal structure of graphite was imported from pre-existing file stored in Material Studio database. The structure is a stack of two infinite graphene sheets (Fig. 3) confined in the periodic boundary box. The size of the superlattice was expanded parallel to graphene sheets to obtain sheets of 306 rings. The separation between two stacks was varied from 0.4 A to 20.1 A to represent the range of pores observed in the model carbons. The Dreiding force field was also used to describe interactions between the atoms.

Additionally, a material where the pores are formed by the edges in the model carbons was constructed. We denote this

Fig. 3 - Slit pore simulation box with pore size of 0.34 nm. Carbon atoms are shown in black. A single layer of adsorbed carbon dioxide is also shown. (A colour version of this figure can be viewed online.)

material as an "edge pore''. The edge pore was modelled as a two stacks of 6 infinite graphene sheet separated by a distance of 3.4 A, the edges of the carbon sheets were capped by hydrogen atoms (Fig. 4).

2.4. Structural characterisation

The models were characterised and compared in terms of density, accessible nitrogen surface area, helium volume and pore size distribution (PSD). Geometric nitrogen surface area is defined by a line that the centre of a probe draws

Fig. 4 - Edge pore simulation box. Pore carbon atoms are shown in black and hydrogen atoms are shown in white. Adsorbed CO2 molecules with carbon (grey) and oxygen (red) atoms are also shown. (A colour version of this figure can be viewed online.)

whilst rolling along the van der Waals surface of adsorbent. A nitrogen molecule (kinetic diameter 3.68 A) [27] is chosen for calculating the surface area, because it is the usual probe used in BET experiments. A helium (He) atom with a kinetic diameter of 2.6 A [28] is used for the pore volume calculation which is provided in supporting information along with surface area accessible to CO2 and CH4. Volume is also defined by the boundary that probe's centre can access which is considered to be appropriate approach to study porous solids in the context of adsorption [29].

Poreblazer [30] was used to generate geometric PSD. The tested pore is divided into bins. A point is placed in a bin and the largest possible sphere that can be placed at that point without overlapping with other adsorbent atoms is recorded as the pore size for that volume. The cumulative pore volume function V(d) is generated representing the volume that can be occupied by a probe of diameter d or smaller. The PSD function dV(d)/dd can be obtained differentiating V(d).

Radial distribution functions (RDFs) have also been calculated for carbon atoms of the developed structures (C-C RDF). An RDF is the measure of probability finding two atoms at a given spherical distance. The function is commonly given the g(r) symbol. Both experimental and calculated RDFs for carbon atoms are available in the literature and the comparison will shed light onto realism of the obtained structures.

A graphical method was used to understand the shape of the pores around adsorbed molecules. In a given structure, atoms were selected within radial distance of 11A from a CO2 molecule. The range from 4 to 11A was divided into 8 bins. The colour to each bin was selected from rainbow spectrum. Atoms that fall within each bin were assigned specific colour: the closest atoms were coloured warmest colour (red) and atoms that are at a 10-11 A distance were coloured coolest colour (dark blue).

2.5. Adsorption of gases

The computational results were obtained using the aforementioned Material Studio software. The Henry task in Sorption module was used for gas adsorption simulation

which employs Metropolis Grand Canonical Monte Carlo (GCMC) method [31]. Henry constant was calculated at 298 K. Adsorption of CO2 and CH4 were calculated at 298 K and 0.05 bar after 1 x 106 equilibration and 9 x 106 production steps which include exchange, rotation, translation and regrowth types. The heat of adsorption was obtained from GCMC simulations at fixed 0.05 bar pressure. A three-site model was used for the CO2 molecule where two oxygen and carbon atoms are explicitly modelled, and a five-site model was used for methane, where all atoms are modelled explicitly. The Lennard Jones parameters and charges for each atom are available in the Supporting information (Table S1).

Adsorption of CO2 and CH4 in the model carbons as predicted by the slit pore model was calculated on the basis of the model carbon pore size distribution determined using Poreblazer and CO2 and CH4 adsorption at 0.05 bar and 298 K in slit pores. The amount of gas adsorbed N at temperature T and pressure P is obtained using the adsorption equation:

N(P, T) = P,T)f(wi)(wi - Wi_a)

where p is the gas loading in slit pore model of width w, f is pore size distribution as determined by Poreblazer.

Radial distribution functions (RDF, g(r)) were calculated between CO2 molecules and aromatic carbon atoms and hydrogen atoms positioned at arm edges in order to investigate the composition of the pore surface and understand how this affects adsorption of gas molecules.

3. Results

3.1. Structural properties

Packed model carbons retain microporosity. The rigid 3D structures prevent molecules from packing efficiently leaving free interconnected voids. Model carbons have varying nitrogen surface area ranging from 175 to 500 m2 g-1 (Fig. 5). Although these values are small compared to typical activated carbon, one should keep in mind that the porosity in the materials modelled in this work is a result of the inability to pack efficiently the selected building units. No experimental information, such as the material's density, porosity or XRD was used. The S-trip having smallest arms have the lowest surface area whilst the rest model carbons have very similar surface area. M-CTC system have slightly smaller surface area most likely due to less rigid core which allows two of the three arms to overlay in some cases. This is consistent with the work of Abbot et al. [32] where they determined direct relationship between core rigidity and surface area. Nevertheless the difference between the surface area of M-CTC and M-trip is small. This suggests that packing of the model carbons is governed by the size of the arm rather than its core structure. However a rigid core keeps arms apart preventing structures from packing efficiently. In all of the cases model carbons have significantly higher surface area comparing to that of coronene and larger platelets which are not connected through the core. In this case, smaller arms create denser structures as the surface area increases with

_ 500 -■ □ Model

™ carbons

£ 400

g ; □ Model

10 ■ carbon arms

8 300 -■

Fig. 5 - Nitrogen surface area of packed model carbons (filled bars) and unconnected graphene platelets (stripped bars). (A colour version of this figure can be viewed online.)

the increase of the arm. Although it was shown in previous studies that bulkier groups lead to increased porosity [32,33], in our case, the trend is not clear. S-trip which has smallest arms also has lowest surface area but M-trip and L-trip create very similar surface area. Presumably, due to planar shape larger arms sense stronger attraction and layering of the arms is more evident. Shape of the arm does not influence differences as ribbon-like and disk arms have very similar surface area. Differences between the packing schemes are shown in Supporting Information (Fig. S2).

Coronene form up to 12 molecule stacks in a unit cell leaving a negligible amount of space between the stack edges as small coronene move more freely and interact with other molecules. The stacks do not seem to align in any particular direction over the time of simulation. A slower equilibration and lower temperatures could favour the crystallisation of coronene. Boxes containing only graphene arms of different size and shapes as the ones shown in Fig. 2 also form stacks. The stacks formed are significantly smaller than those observed with coronene. The materials formed exclusively by graphene arms can reach significant surface areas, but always smaller than the model carbon with same arm size connected to a rigid core.

Fig. 6 shows radial distribution function between carbon atoms in model carbons. All model carbons produced almost identical functions with the distinctive peaks at 1.45 and 2.45 A corresponding to first and second carbon-carbon neighbours in graphene lattice. The two peaks in the range from 3.75 to 4.25 A correspond to interlayer distance between two graphene arms and/or distance between two further carbon atoms within the same graphene sheet. The local ordering decreased rapidly with no prominent features at distances larger than 8 A. The function is in good agreement with those calculated for structures generated using computational methods [8-10] and those obtained for real disordered carbon materials [8,9,12,34-36] maintaining all the distinctive features which indicates disordered nature of the model carbons. However RDF peaks of model carbons obtained in this work are better resolved than RDFs obtained

1 \j\__A a ~ _ M-CTC

1 - .M-trip-ribbon

l 1—' 1 A * L-trip

H IA A A ~ . M-trip .

L _ S-,ri"

0 2 4 6 8 10

Distance, A

Fig. 6 - Averaged radial distribution functions between carbon atoms in model carbons (the values are offset by 10 for clarity).

for highly disordered carbon materials. In our work almost all carbon atoms are locally ordered forming fragments of gra-phene sheets compared to real disordered carbons where defective five and seven membered rings are observed, generating a significant disordered at short distances. Therefore, it is not surprising that our structure resembles carbon of lesser degree of activation (which is less disordered), where the third peak at about 3A is well resolved [35,36]. It is worth noting that the RDF is not an absolute measure of structure's realism. As discussed in Palmer and Gubbin's work [8] two structurally distinctive materials can produce identical RDFs. They further explain that the validity of a structure cannot be determined by an RDF, as materials with an "unphysical morphology'' can lead to the same RDF as realistic materials. Therefore the analysis of a model structure RDF should always be accompanied by complementary information.

The pore size distribution (PSD) of all compressed model carbons is very similar (Fig. 7). All PSDs have similar shape with a significant fraction of the pores smaller than 2 A; the volume of pores decreases rapidly between sizes of about 2 and 10 A. All PSDs exhibit tailing towards wider pores. All model carbons possess a high concentration of large pores (>10 A) except S-trip. In disordered materials one must be careful when interpreting the features observed at the largest scale that the simulation box can accommodate, as finite size effects can play an important role.

Average pore sizes for these materials can be obtained from the pore size distribution. Average pore size increases with the increase of arm size ranging from 0.31 nm for S-trip to 0.61 nm for L-trip with M-trip having the middle 0.56 nm average pore size. M-trip-ribbon also have intermediate pore size of 0.54. M-CTC has slightly smaller average pore of 0.49 nm, and coronene have the smallest 0.19 nm pores.

PSD obtained for model carbons studied in this work has a slightly different shape compared to PSD of experimental carbon materials as well as those generated computationally [8,22,34,37]. PSD peaks of model carbons is shifted to smaller pore sizes and does not capture mesoporous region that is often present in disordered carbons. This can be attributed to smaller pore volume created by these structures in general

Fig. 7 - Pore size distribution in packed model carbons and coronene. (A colour version of this figure can be viewed online.)

(see Supporting Information Table S2 and Fig. S4). The high concentration of pores smaller than 0.5 nm can be the result of tiny pores created between the layers of graphene arms. Larger volume can be created by manipulating the packing procedure or extracting the snapshot of desired structure from the range of frameworks created during packing. Great diversity of model carbons might be created by selecting different core structures that could connect not three but four or more graphene arms of different shapes and sizes thus creating variety of structures tailored to reproduce experimental materials. Furthermore, introduction of graphene sheet imperfections, such as missing carbon atoms, 5-membered carbon rings or carboxylic groups, may produce greater disorder of the structure by increasing interlayer distance.

3.2. Adsorption selectivity and capacity

Model carbons have higher selectivity towards CO2 over CH4 and it can reach up to 23 (Fig. 8). The selectivity does not appear to depend on the structure of the molecule used to create the carbon structure. S-trip has the highest selectivity of all carbon materials modelled, then the selectivity decreases with the increase of arm size. M-trip-ribbon have very similar selectivity compared with other model carbons connected through trip core. The selectivity is distinctly lower for coro-nene and M-CTC. This trend is expected following the work of Tan and Gubbins [38] who showed that a maximum in selectivity is expected at a specific pore size. Nevertheless, the small selectivity showed in M-CTC is not explained by the trend observed in simple systems, suggesting that caution should be taken when extrapolating properties between families of materials with different cores. Coronene seems to be as selective as some model carbons, however this result should be considered with care. Coronene have a very confined space which is less geometrically restricted for smaller linear CO2 molecule comparing to larger CH4. However the inner free volume of the real material most likely would not be accessible.

Fig. 8 - The CO2/CH4 selectivity in packed model carbons and coronene as calculated from Henry task at 298 K. (A colour version of this figure can be viewed online.)

The two methods used to determine the selectivity led to slightly different results. Selectivity calculated from constant 0.05 bar pressure adsorption simulation is more than twice smaller than that obtained from Henry constant simulation (Fig. 9), except for coronene which selectivity is almost the same regardless of the method used. When compared to selectivity calculated form Henry task, the trend itself does not change amongst model carbons. The exception only is M-CTC which becomes the most selective whereas selectivity calculated from Henry task is the lowest amongst model carbons. Even when a pressure of 0.05 bar was considered sufficiently low to be in the Henry's law regime, the differences obtained suggest that the Henry's law is not observed at this pressure. It is possible that a small amount of high energy sites exist in these materials, which would be completely fully occupied even at low pressures.

Although there is always the temptation to use simple models to predict the behaviour of complex materials, the

¡Mill

Fig. 9 - The CO2/CH4 selectivity in packed model carbons and coronene as calculated from loading at 0.05 bar fixed pressure and 298 K temperature. (A colour version of this figure can be viewed online.)

use of the slit pore model may not be appropriate for all the materials shown in this work. We calculated the adsorption of CO2 and CH4 in a collection of slit pores, and used the geometric pore size distribution to determine the total amount adsorbed in a material composed exclusively of slit pores that has the same PSD as the model carbons generated with complex molecules. Fig. 10 shows that the amount adsorbed of both CO2 and CH4 cannot be predicted by simple slit pore model. Even with wide error bars, the agreement is beyond them in some of the cases. Almost all of the model carbons except M-CTC adsorb more CO2 and CH4 than the slit simple pore. Even when for some materials, such as M-trip, L-trip and M-CTC there is good agreement, in other cases the discrepancies go beyond the error bars. Carbons with a trip centre adsorb more CO2 and CH4 than what the slit pore model predicts, suggesting the existence of more favourable adsorption sites than a simple slit geometry, which can be highly confined spaces created by three or more platelets (Fig. 11A). M-CTC shows lowest gas loadings than those predicted by the slit pore model. This suggests that there are weaker interactions between M-CTC and gas molecules than in a slit geometry. This is most likely due to a sufficient amount of pores created by the edges of arms or combination of edges and arm surface (Fig. 11B-D). Nevertheless M-trip,

Fig. 11 - Schematic representation of possible arm positions. (A colour version of this figure can be viewed online.)

L-trip and M-CTC materials could be represented by the slit pore model. This suggest that in materials where the platelets are sufficiently large, the slit pore model is still a good approximation, as most of the pore volume will be formed by slits, and the contribution of edges or other pore shapes will be negligible (or compensate one with the other).

The results shown in Fig. 10 are expanded in Fig. 12 where each point represents one simulation box, so there are 6 points (three boxes per packing scheme) for every model carbon structure. It is clear that systems with measureable different properties are obtained even if the same packing method is used (Fig. 13). In general, the 21-step method produces boxes that have a higher density than the method where compression is capped to 1000 bar. Nevertheless, the translation of higher density to higher or lower amount adsorbed is not evident, as the pore structure plays an important role. Systems where the predicted amount adsorbed is smaller than the calculated form GCMC simulations have a He accessible pore volume below 0.06 cm3 g_1 (see Supporting Information Table S2 and Fig. S4). The selectivity is not sensitive to the compression method used, but in all cases the selectivity calculated for model carbons is higher than the predicted one from the slit pore model (Supporting Information, Fig. S3).

The points above the straight line indicate that model carbons have more complex pore morphology and stronger energetics than the slit pore model. The importance of including pores of other geometries such as triangular and rectangular is discussed in the literature [39-41]. Such diversity of structures is important to describe accurately the material's PSD and high heats of adsorption observed experimentally. The materials obtained in this work spontaneously create a variety of pore shapes by simply specifying the structure of the building units.

Adsorption of CH4 in model carbons versus its loading in slit pore have a different trend to what was observed for CO2; most of the points are below the straight line except for S-trip which retains more favourable adsorption compared to the slit pore.

Fig. 14 shows two radial distribution functions between CO2 and aromatic carbons (C) or edge hydrogens (H) of the

Fig. 10 - CO2 (A) and CH4 (B) loading calculated directly in model carbons versus loading predicted by slit pore model at 0.05 bar pressure (diamond - S-trip, triangle - M-trip, square - L-trip, closed circle - M-CTC and open circle - M-trip-ribbon). (A colour version of this figure can be viewed online.)

Fig. 12 - CO2 (A) and CH4 (B) loading calculated in model carbons versus predicted loading by the slit pore model at 0.05 bar pressure. (A colour version of this figure can be viewed online.)

Fig. 13 - CO2 loading in model carbons generated using scheme 1 (A) and scheme 2 (B) versus predicted loadings in slit pore model at 0.05 bar pressure. (A colour version of this figure can be viewed online.)

model carbons. In all of the cases peaks of hydrogen are more intense than peaks of aromatic carbons in the range between 3.75 and 6.25 A. This is explained by the fact that there are less hydrogen atoms than aromatic carbons in systems thus the normalisation factor enhances the value of the CO2-H RDF first peak. To qualitatively assess the amount of pores formed by edges we compared the ratio of the first peak in the CO2-H RDF to the first peak in the CO2-C RDF (Fig. 15). This comparison shows that L-trip and M-CTC materials form pores where arm edges play an important role in comparison to other materials. In all cases, the contribution of the edges is small compared to the contribution of the slits, given the dramatic difference between the values calculate for disordered model materials and pore formed exclusively by edges. Nevertheless, the difference in structures explains the variation in the applicability of the slit pore model.

We propose that a measure of the edge contribution to the pore structure is a ratio of the H/C peak in a model carbon to the H/C peak in an edge pore. This ratio is zero for an infinite slit and 1 for an edge pore. Using this criterion, the amount of pores formed by edges of platelets will range from 8% to 11.5% in the studied model carbons.

Quantifying the contribution of more energetically favourable pore shapes compared to a perfect slit is difficult, given the diversity in pore structures and the difficulty in

systematically identifying them. Representative examples of different kind of pores created in model carbons are shown in Fig. 16.

4. Conclusions

In this work we presented the simple approach for representing carbonaceous materials with complex pore geometry. It is possible to pack individual molecules that does not rely on input of structural properties such as porosity, surface area or density which is otherwise necessary when using simple molecules like coronene. By connecting flat graphene like platelets through rigid contortion sites we were able to obtain porous structures without imposing restrictions to structural properties of the resulting material. Packed 3-dimentional structures created moderate sizes of free volume and showed CO2/CH4 selectivity comparable to most carbons. The pore volumes obtained are significantly smaller than most activated carbons, but we expect that constructing building blocks that pack inefficiently one can create more open structures where small stacks of graphene layers are still observed but with pore volumes comparable to typical activated carbons. Alternatively, it is possible to mix different building blocks which will extend the diversity of materials obtained.

Fig. 14 - Radial distribution functions between CO2 and edge hydrogens (A) and between CO2 and aromatic carbons (B). (A colour version of this figure can be viewed online.)

Fig. 15 - Ratio between maximum peak values of CO2-H RDF and CO2-aromatic C RDF within 3.25-6.25 A radial distance. (A colour version of this figure can be viewed online.)

We also found that rigid cores, such as triptycene, lead to materials with a more open structure than flexible cores that allow the arms to form stacks. The choice of the molecule's arms size allows tuning material's properties such as surface area. Some similarities can be found when using building blocks to create organic molecules of intrinsic microporosity [32].

The porous structured created with the methods used contains pores of different sizes and shapes, some formed by the building unit's platelets, whilst others by edges. We showed

Fig. 16 - Examples of pores created in model carbons: (A) pore of type A created by L-trip, (B) pore of type D created in S-trip and (C) pore of type C created in M-CTC. For pore types see Fig. 11. (A colour version of this figure can be viewed online.)

that when the contribution of pores formed by edges of the platelets is small, predictions using a simple slit pore model are expected to be accurate, but one must be careful in using a simple slit pore model if the edge effects are significant. We propose a simple method for quantifying the contribution of edge effects using the information obtained from a RDF.

It is well known that amorphous carbons are complex structures and the shapes of the building blocks used in this work represent some of the possible structures that can be found in a real material, nevertheless, it is far from comprehensive. Using the tools presented in this work, further analysis can be carried out to assess the effect of defects and functional groups in amorphous carbon materials.

Acknowledgements

This work was supported by EPSRC Grant EP/K016946/1. A.G. is grateful for the postdoctoral scholarship from the School of Chemical Engineering and Analytical Science at the University of Manchester.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.carbon. 2015.02.073.

REFERENCES

[1] Simpson CD, Mattersteig G, Martin K, Gherghel L, Bauer RE, Rader HJ, et al. Nanosized molecular propellers by cyclodehydrogenation of polyphenylene dendrimers. J Am Chem Soc 2004;126(10):3139-47.

[2] Abbott LJ, McDermott AG, Del Regno A, Taylor RGD, Bezzu CG, Msayib KJ, et al. Characterizing the structure of organic molecules of intrinsic microporosity by molecular simulations and X-ray scattering. J Phys Chem B 2012;117(1):355-64.

[3] McKeown NB, Budd PM. Exploitation of intrinsic microporosity in polymer-based materials. Macromolecules 2010;43(12):5163-76.

[4] Larsen GS, Lin P, Hart KE, Colina CM. Molecular simulations of PIM-1-like polymers of intrinsic microporosity. Macromolecules 2011;44(17):6944-51.

[5] Steele WA. The physical interaction of gases with crystalline solids: I. Gas-solid energies and properties of isolated adsorbed atoms. Surf Sci 1973;36(1):317-52.

[6] El-Merraoui M, Aoshima M, Kaneko K. Micropore size distribution of activated carbon fiber using the density functional theory and other methods. Langmuir 2000;16(9):4300-4.

[7] Landers J, Gor GY, Neimark AV. Density functional theory methods for characterization of porous materials. Colloids Surf A 2013;437:3-32.

[8] Palmer JC, Gubbins KE. Atomistic models for disordered nanoporous carbons using reactive force fields. Microporous Mesoporous Mater 2012;154:24-37.

[9] Shi Y. A mimetic porous carbon model by quench molecular dynamics simulation. J Chem Phys 2008;128(23).

[10] Kumar A, Lobo RF, Wagner NJ. Porous amorphous carbon models from periodic Gaussian chains of amorphous polymers. Carbon 2005;43(15):3099-111.

[11] Bock H, Gubbins KE, Pikunic J. Chapter five - models of porous carbons. In: Bottani EJ, Tascon JMD, editors. Adsorption by carbons. Amsterdam: Elsevier; 2008. p. 103-32.

[12] O'Malley B, Snook I, McCulloch D. Reverse Monte Carlo analysis of the structure of glassy carbon using electron-microscopy data. Phys Rev B 1998;57(22):14148-57.

[13] Opletal G, Petersen T, O'Malley B, Snook I, McCulloch DG, Marks NA, et al. Hybrid approach for generating realistic amorphous carbon structure using metropolis and reverse Monte Carlo. Mol Simul 2002;28(10-11):927-38. 2002/10/01.

[14] Farmahini AH, Opletal G, Bhatia SK. Structural modelling of silicon carbide-derived nanoporous carbon by hybrid reverse Monte Carlo simulation. J Phys Chem C 2003;117(27):14081-94. 2013/07/11.

[15] Thomson KT, Gubbins KE. Modeling structural morphology of microporous carbons by reverse Monte Carlo. Langmuir 2000;16(13):5761-73. 2000/06/01.

[16] Pikunic J, Pellenq RJM, Thomson KT, Rouzaud JN, Levitz P, Gubbins KE. Improved molecular models for porous carbons. In: Yasuhiro Iwasawa NO, Hironobu K, editors. Studies in surface science and catalysis. Elsevier; 2001. p. 647-52.

[17] Arora G, Sandler SI. Nanoporous carbon membranes for separation of nitrogen and oxygen: insight from molecular simulations. Fluid Phase Equilib 2007;259(1):3-8.

[18] Klauda JB, Jiang J, Sandler SI. An ab initio study on the effect of carbon surface curvature and ring structure on

N2(O2)-carbon intermolecular potentials. J Phys Chem B 2004;108(28):9842-51. 2004/07/01.

[19] Kumar KV, Müller EA, Rodriguez-Reinoso F. Effect of pore morphology on the adsorption of methane/hydrogen mixtures on carbon micropores. J Phys Chem C 2012;116(21):11820-9. 2012/05/31.

[20] Segarra EI, Glandt ED. Model microporous carbons: microstructure, surface polarity and gas adsorption. Chem Eng Sci 1994;49(17):2953-65.

[21] Liu JC, Monson PA. Monte Carlo simulation study of water adsorption in activated carbon. Ind Eng Chem Res 2006;45(16):5649-56.

[22] Di Biase E, Sarkisov L. Systematic development of predictive molecular models of high surface area activated carbons for adsorption applications. Carbon 2013;64:262-80.

[23] Biggs MJ, Buts A. Virtual porous carbons: what they are and what they can be used for. Mol Simul 2006;32(7):

579-93.

[24] Mayo SL, Olafson BD, Goddard WA. DREIDING: a generic force field for molecular simulations. J Phys Chem 1990;94:8897-909.

[25] Regno AD, Siperstein FR. Comparison of generic force fields for packing of concave molecules. Mol Phys 2004;112(17):2241-8. 2014/09/02.

[26] Fraccarollo A, Canti L, Marchese L, Cossi M. Monte Carlo modeling of carbon dioxide adsorption in porous aromatic frameworks. Langmuir 2014;30(14):4147-56. 2014/04/15.

[27] Hirschfelder CF, Curtiss CF, Bird RB. Molecular theory of gases and liquids. New York: Wiley; 1954.

[28] Breck D. Zeolite molecular sieves: structure chemistry and use. New York: Wiley; 1974.

[29] Düren T, Millange F, Fdrey G, Walton KS, Snurr RO. Calculating geometric surface areas as a characterization tool for metal-organic frameworks. J Phys Chem C 2007;111(42):15350-6. 2007/10/01.

[30] Sarkisov L, Harrison A. Computational structure characterisation tools in application to ordered and disordered porous materials. Mol Simul 2011;37(15):1248-57.

[31] Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E. Equation of state calculations by fast computing machines. J Chem Phys 1953;21:1087.

[32] Abbott LJ, McKeown NB, Colina CM. Design principles for microporous organic solids from predictive computational screening. J Mater Chem A 2013;1(38):11950-60.

[33] Tozawa T, Jones JTA, Swamy SI, Jiang S, Adams DJ, Shakespeare S, et al. Porous organic cages. Nat Mater 2009;8(12):973-8.

[34] Palmer JC, Brennan JK, Hurley MM, Balboa A, Gubbins KE. Detailed structural models for activated carbons from molecular simulation. Carbon 2009;47(12):2904-13.

[35] Hawelek L, Brodka A, Dore JC, Honkimaki V, Burian A. Fullerene-like structure of activated carbons. Diam Relat Mater 2008;17(7-10):1633-8.

[36] Burian A, Ratuszna A, Dore JC. Radial distribution function analysis of the structure of activated carbons. Carbon 1998;36(11):1613-21.

[37] Industrial Fluid Properties Simulation Collective. 8th Challenge. 2014 [cited; Available from: <http:// fluidproperties.org/8th-benchmarks>.

[38] Tan Z, Gubbins KE. Selective adsorption of simple mixtures in slit pores: a model of methane-ethane mixtures in carbon. J Phys Chem 1992;96(2):845-54.

[39] Soares Maia D, de Oliveira JCA, Toso J, Sapag K, Lopez R, Azevedo DS, et al. Characterization of the PSD of activated carbons from peach stones for separation of combustion gas mixtures. Adsorption 2011;17(5):853-61. 2011/10/01.

[40] Kaskel S, Llewellyn P, Rodriguez-Reinoso F, Seaton NA. Mixed geometry characterization of activated carbons PSD. In: Characterisation of porous solids VIII: Proceedings of the 8th international symposium on the characterisation of porous solids: the royal society of chemistry 2009: p. 211-7.

[41] Azevedo DCS, Rios RB, Lopez RH, Torres AEB, Cavalcante CL, Toso JP, et al. Characterization of PSD of activated carbons by using slit and triangular pore geometries. Appl Surf Sci 2010;256(17):5191-7.