Molecular Modeling and Adsorption Properties of Ordered Silica

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Molecular Modeling and Adsorption Properties of Ordered Silica Templated CMK Mesoporous Carbons Surendra Kumar Jain, Roland J-M. Pellenq, Keith E. Gubbins, and Xuan Peng Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b04169 • Publication Date (Web): 06 Feb 2017 Downloaded from http://pubs.acs.org on February 11, 2017

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Molecular Modeling and Adsorption Properties of Ordered Silica Templated CMK Mesoporous Carbons Surendra Kumar Jain1, Roland J-M. Pellenq2,3,4, Keith E. Gubbins5 and Xuan Peng6* 1

Department of Chemical Engineering, SDMCET, Dharwad, India Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA 3 2 the MIT / CNRS /Aix-Marseille University joint laboratory, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA 4 Centre Interdisciplinaire des Nanosciences de Marseille, CNRS and Aix-Marseille Université, Campus de Luminy, Marseille, 13288 Cedex 09, France 5 Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh 27695, USA 6 College of Information Science and Technology, Beijing University of Chemical Technology, Beijing 100029, P. R. China 2

Abstract Realistic molecular models of silica-templated CMK-1, CMK-3 and CMK-5 carbon materials have been developed by using carbon rods and carbon pipes that were obtained by adsorbing carbon in a model MCM-41 pore. The interactions between the carbon atoms with the silica matrix were described using the PN-Traz potential, and the interaction between the carbon atoms was calculated by the Reactive Empirical Bond Order (REBO) potential. The carbon rods and pipes with different thickness were obtained by changing the silica-carbon interaction strength, the temperature and the chemical potential of carbon vapor adsorption. These equilibrium structures were further used to obtain the atomic models of CMK-1, CMK-3 and CMK-5 materials using the same symmetry as found in TEM pictures. These models are further refined and made more realistic by adding interconnections between the carbon rods and carbon pipes. We calculated the geometric pore size distribution of the different models of CMK-5 and found that the presence of interconnections results in some new features in the pore size distribution. Argon adsorption properties were investigated using GCMC simulations to characterize these materials at 77K. We found that the presence of interconnections results greatly improves the agreement with available experimental data by shifting capillary condensation to lower pressures. Adding interconnections also induce smoother adsorption/condensation isotherms while desorption/evaporationcurves show a sharp jump. These features reflex the complexity of the nano-voids in CMKs in terms of their pore morphology and topology.

* Corresponding author. E-mail: [email protected] and [email protected] (X. Peng)

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1. Introduction Microporous carbons (with pore size < 2nm) are widely used in industry in membrane technologies, gas separation, water purification, catalysis etc. [1] due to their large surface activity [2] that comes from the large amount of carbon atoms at the vicinity of the surface. However, it is very difficult to control the pore morphology and topology of the classically used activated carbons during their preparation process [3]. In many applications, such as adsorption of large hydrocarbons, carbons with mesopores of defined dimensions are desirable [4]. There are many techniques for obtaining mesoporous carbons [3], but most do not provide the well-ordered pores and uniform pore size. Some carbons such as fullerenes and single-wall nanotubes (SWNTs) exhibit periodic structures [5-6] with voids potentially accessible to some adsorbate molecules. However, the periodically arranged fullerenes and SWNTs are held together via weak van der Waals interactions [5-6] and thus cannot be considered as systems with permanent ordered porosity. Recently, nanocasting using highly ordered mesoporous materials (like silica) has made it possible to prepare novel mesostructured materials [7]. Ryoo et al. have shown that highly ordered mesoporous carbons can be obtained by templating highly ordered silica materials [8]. This template synthesis to obtain mesoporous carbons is interesting because it provides precise control of the porous structure of the final material. The structures of the carbons prepared in this way can be tailored by selecting the appropriate templating material [9]. These carbon materials offer mechanical and thermal stability, high pore volume, electrical conductivity and useful surface properties, and applications include adsorption of large molecules, catalysts in fuel cells and capacitor electrodes [3-4, 10-13]. In the preparation of templated mesoporous carbons, a porous material (also named template) is filled with carbon by means of various routes (liquid or gas). The resulting host/carbon materials are then chemically treated to selectively remove the template, which results in a carbon replica of the original template used [7]. The schematic for the synthesis mechanism is shown in Figure 1. impregnation of carbon precursor

Carbonization

Carbon – Silica

Silica template

template removal

Mesoporous carbon

Figure 1: Schematic for the synthesis of templated mesoporous carbon


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A three dimensional (3-D) pore structure makes the nanomaterials interconnect with each other, and after removal of the templates, the nanomaterials can completely maintain topologies of the templates to achieve interesting replica mesostructures. Highly ordered mesoporous carbons were first synthesized by Ryoo et al. [8] using cubic mesoporous silica MCM-48 as the template and sucrose as the carbon source. These carbons were named CMK-1. The replication process was carried out by impregnating the MCM-48 pores with the aqueous solution of sucrose and H2SO4. The silica template after the impregnation was heated to a temperature of 1173 K under vacuum during which sucrose was converted to carbon. The silica framework was then removed by treating with NaOH and ethanol to obtain CMK-1. Transmission electron microscopy (TEM) pictures confirmed the periodic nature of CMK-1. However, the authors found out from the X-ray diffraction (XRD) patterns obtained during the framework removal that CMK-1 was not a perfect replica of MCM-48. Rather, it underwent systematic transformation to a new ordered structure. This was also confirmed by comparing the pore diameter of the CMK1 with that of the pore wall thickness of the silica material that revealed that the pore diameter of CMK-1 was approximately twice that of the pore wall thickness of the silica material. Moreover, the atomically disordered nature of the CMK-1 framework was also confirmed by Raman Spectroscopy. Ryoo and coworkers [14] also reported the first synthesis of ordered mesoporous carbon (OMC) that retained the symmetry of the silica template. These mesoporous carbons were named CMK-3 and were obtained by templating SBA-15. Unlike CMK-1, the ordered structure of CMK-3 was found to be exactly an inverse replica of SBA-15, without any structural transformation. TEM pictures revealed that CMK-3 carbon is made up of two dimensional (2-D) hexagonally ordered carbon rods. From Raman Spectroscopy the authors found that the pore walls of CMK-3 are constructed by disordered carbon networks similar to activated carbons. The authors also used MCM-41 as a template and found that it yielded disordered high-surface area microporous carbon. SBA-15 and MCM-41 both exhibit 2-D hexagonally ordered structure of approximately cylindrical one dimensional pores. However, the templating procedure shed light on the fact that the mesopore channels in SBA-15 are indeed connected by micropores or narrow mesopores, whereas MCM-41 contains only unconnected mesopore channels [15]. Upon templating, carbon can impregnate the micropores and narrow mesopores to form small connections between the carbon rods formed in the main mesopore channels of SBA-15. These connections hold the carbon structure together upon the removal of the template. In the case of MCM-41, carbon infiltration leads to the formation of carbon rods that are not connected to each other and thus the carbon structure falls apart upon removing the template. Thus, the application of a template with a three dimensional interconnected channel system is crucial in the synthesis of periodic carbon frameworks [15]. Many carbon replicas of different ordered mesoporous silica have since been reported [16-23] and carbon inverse replication has also been widely accepted as a reliable method for assessing pore connectivity [14,17,24-26]. Templated synthesis of ordered carbons can be done via volume-templated or surface-templated carbons [27]. In the first case, the entire void space of the template is infiltrated with carbon, whereas in the second case, carbon is introduced as a film on the pore surface of the template. CMK1 [8,28] and CMK-3 [14-15] are examples of volume templated carbons. CMK-5 carbon 3 ACS Paragon Plus Environment

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[25] that consists of 2-D hexagonally ordered carbon pipes is the only surface templated OMC reported so far. CMK-5 was first synthesized using furfuryl alcohol as a carbon precursor and SBA-15 as a template [25]. Surface templating was achieved through the control of the amount of the carbon precursor and other synthesis conditions and resulted in pipe like carbons. The occurrence of surface roughness and corrugation on the internal surface of carbon pipes was also confirmed from experiments [27]. Thus, CMK-5 consists of a network of nanopipes which are connected by carbon interconnections and has two main types of porosity (i) mesopores inside the nanopipes, (ii) mesopores between the nanopipes [29]. The outside diameter of carbon pipes in CMK-5 is controlled by the choice of a template of SBA-15 with suitable pore diameter. The inside diameter of carbon pipes in CMK-5 and subsequently the wall thickness is controlled by controlling the amount of precursor infiltrated and polymerization conditions [25, 27]. Apart from the experimental studies, very few simulation studies have been attempted to model these materials and thus to understand the adsorption behavior in these carbon replicas. The most difficult part of the simulation studies is to obtain a carbon model that realistically describes the pore geometry and pore morphology in these carbon replicas. In recent experimental studies [30-31], it has been shown that the pores of the carbon replicas have the shape of the walls of SBA-15 template and it was also demonstrated using argon adsorption at 77 K that there is an appreciable roughness or corrugation of the internal surface of the carbon pipes. It means that classical gas adsorption/desorption models considering cylindrical pores cannot be applied for these materials. Thus, more realistic models are needed to understand the adsorption behavior in these materials. In a previous work [32], a rod-aligned slit like pore (RSP) model was used to study the adsorption of nitrogen and supercritical methane in CMK-1. This model is similar to the slit pore model; the only difference is that instead of the infinite graphite walls, the authors used carbon rods placed side by side and adsorption takes place in the region between the two layers of carbon rods. The carbon rods are made up of coaxial cylinders of graphene sheet. The largest diameter of the carbon rod, which corresponds to the number of coaxial cylinders, depends on the pore width of MCM-48. The authors noted that the RSP model was not realistic enough to describe the detailed adsorption mechanism of nitrogen on CMK-1 in a quantitative way. Recently, Peng et al [33] have published a model for CMK-5 materials. They built CMK-5 models by decorating carbon nanopipes on a hexagonal lattice. The authors used the geometric model from Solovyov et al to characterize the hexagonal structure of CMK-5 adsorbent. The structural parameters of CMK-5 were obtained by fitting the N2 adsorption parameters. The authors noted that their models did not have interconnections between their carbon pipes and that the interconnections will affect the adsorption behavior. To take into account the presence of interconnections, these authors increased the external diameter of the carbon pipe De to accommodate more carbon materials. For their simulations the authors have used a nanopipe wall thickness that are lower than the experimentally reported value of 1.6 g/cm3 in the literature. The authors then studied the adsorption of hydrogen in these materials. In this study, pseudo mimetic procedures are used to produce CMK-1, CMK-3 and CMK-5 like models. The surface roughness is incorporated by adsorbing carbon, from the gas phase, to the MCM-41 silica template. Finally, the effect of interconnections, present in real CMK materials, is taken into account by adding random interconnections 4 ACS Paragon Plus Environment

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to CMK-3 and CMK-5 models. Pseudo mimetic methods are used to build atomistic models for CMK-3 and CMK-5 type carbons and the adsorption properties of these carbons are explored using molecular simulation. Starting with a MCM-41 pore (silica template), carbon adsorption inside the silica template is simulated by adsorbing carbon from the gas phase in the MCM-41 pore using Grand Canonical Monte Carlo (GCMC) simulations. Simulation of carbon adsorption from vapor phase into the pores of a template has been used before by Roussel et al. [34,35] to obtain carbon replica of zeolites. They used a tight binding framework to model the interaction between the carbon atoms. However, the tight binding method is computationally expensive and is impractical to obtain models for mesoporous carbons involving thousands of carbon atoms. Reactive Empirical Bond Order (REBO) potential [36] is used to model the carbon-carbon interactions. This allows us to simulate thousands of carbon atoms within the computing limits. Carbon rods are obtained by adsorbing carbon, using GCMC simulations, in the total pore volume of the MCM-41 pore and carbon pipes are obtained by adsorbing carbon as a film on the pore surface of MCM-41. These carbon rods and carbon pipes are then used to build molecular models of CMK-1, CMK-3 and CMK-5 materials. A schematic showing the simulation methodology is shown in the supporting information (see Figure S1). Adsorption of argon is then studied in the CMK models at 77K, using GCMC simulations. 2. Simulation Methodology 2.1 The MCM-41 Silica Pore Model Starting with a block of cristoballite, we carve out a cylinder to make a MCM-41 silica pore, similar to what introduced by Pellenq et. al. [37]. The silicon atoms that are not in a tetrahedral environment are then removed as also any non bonded oxygen atoms. This method ensures that the silicon atoms do not have any dangling bonds and oxygen atoms have atleast one bond with a silicon atom. A hydrogen atom is then added to the oxygen atoms having one bond. This ensures the electroneutrality of the system. The silicon, oxygen and hydrogen atoms are then displaced randomly to mimic the amorphous nature of the MCM-41 silica surface. The resulting MCM-41 amorphous structure is then relaxed in the NVT ensemble at a high temperature [38]. The MCM-41 pore model used here has a diameter of 28 Angstrom and a pore length of 106.95 Angstrom.

2.2. The carbon-silica potential energy The interaction between adsorbate (the carbon atoms) with the silica matrix is assumed to be weak and in the physisorption energy range. The interaction energy was calculated using the PN-TrAZ potential, a simplified version of the original PN-type potential function as reported for adsorption of rare gases and nitrogen in silicalite-1 [39]. The PNTrAZ potential function is based on the usual partition of the adsorption intermolecular energy restricted to two body terms only: for a neutral species, it includes a dispersion interaction term, a repulsive short range contribution and an induction term. In the PN-


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TrAZ model, the adsorption energy ( u i ) of a carbon atom at a position i in the simulation box, is given by :

 −b r 5 C2n,ij  1 ij ij u = ∑  Aij e − ∑ f2 n 2n  − α i E i2 rij  2  j∈{O,Si,H }  n=3 i

(1)

Where rij is the distance between the matrix species j and the position i of the adsorbed carbon atom, f2n are so-called damping functions that depend on interspecies distance and on a repulsive parameter (see below) and finally Ei is the electric field created at adsorbate position i due to the inorganic species; all other symbols are physical parameters that depend on electronic properties of interacting species only.The choice of this particular model to describe the carbon/adsorbent interaction was motivated by the good degree of parameter transferability. The sum runs over all (j) atomic sites in the matrix that are oxygen, silicon and hydrogen atoms. The first term in the sum is a BornMayer term representing a two-body form of the short-range repulsive energy due to finite compressibility of electron clouds when approaching the adsorbate at a very short distance from the pore surface. There is one such term per pair of interacting species. The repulsive parameters (Aij and bij) are obtained from the 4th Bhöm and Ahlrich mixing rule for like-atoms pairs [40]. The second term in the above equation is a multipolar expansion series of the dispersion interaction in the spirit of the quantum mechanical perturbation theory applied to intermolecular forces. It has been shown that two (and three) body dispersion C2n coefficients for isolated or in-condensed phase species can be obtained from the knowledge of the dipole polarizability and the effective number of polarizable electrons, Neff, of all interacting species which are closely related to partial charges that can be obtained from ab initio calculations [41]. The f2n terms in the above equation are damping functions of the form:

 kj m  ( b rij ) .e−bkjrij f2 n = 1− ∑  m!  m=0   2n

(2)

The role of these damping functions is to avoid divergence of the dispersion interaction at short distance where the wave functions of the two species overlap (i.e. when the interacting species are at contact). They allow taking into account the possible electronic exchange that has a non-zero probability at short distance even for two close shell structures. For each pair of interacting species, they are parameterized with the single bkj repulsive parameter. The damped dispersion multipolar expansion can be seen as a convenient way to make the perturbation theory valid at short inter-atomic separations. The last term in equation 2 is the induction interaction as written in the context of the quantum mechanical perturbation theory applied to intermolecular forces. It represents an attractive energy arising from the coupling of the polarisable electronic cloud of the adsorbate atom of polarizability αi at position i with the electric field Ei induced by the 6 ACS Paragon Plus Environment

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charges carried by framework species (O, Si and H) that result from the bonding process within the inorganic matrix itself. In the case of a carbon atom interacting with SBA-15, one has to parameterize three different adsorbate/adsorbent-species potentials; all atomic parameters and potential coefficients are given in Table 1 and 2. In the PNTraz description, the (Muliiken atomic partial) charges on the atoms of the silica substrate (O, Si, H) induce an electrical field in the pore that couples with the dipole polaraizability of an adsorbate species. Here the adsorbed species is C(sp2). The polarisation also called induction energy (always attractive) is the last term in eq 1 contributes to 15% of the Csp2 adsorption energy. The rest is due to dispersion (attractive) and Pauli repulsion interactions. Table 1: PN-TrAZ physical parameters for Csp2 and SBA-15 species [a0=0.529177Å, 1Eh=3.1578 105 K]:

SBA-15

Csp2 Species

from ref

Si

O

H

[42]

from [ref 39]

from [ref 39]

from [ref 39]

0.0

+2

-1

+0.5

Aii (Eh)

35.681

6163

1543

1.338

bii (a0-1)

1.681

2.395

2.190

1.995

α (a03) (polarizability)

12.80

2.360

8.030

3.920

2.764

1.520

4.656

0.324

q (e)

Neff(effective

number

of

polarizable electrons)

Table 2: Csp2-SBA-15-species dispersion and repulsion PN-TrAZ parameters:

Silica species

Cij6(Eha06)

Cij8(Eha08)

Cij10(Eha010)

Aij(Eh)

bij (a0-1)

O

44.49

1214

27167

234.68

1.902

Si

13.33

298.0

-

468.95

1.976

H

13.37

348.1

-

6.912

1.825

Minimal image convention is adopted to calculate all interactions. In order to save computing time, the Csp2/substrate interactions have been calculated in advance and saved on a grid. This is possible since the substrate is kept rigid in this study. The grid mesh has been chosen close to 1 Å. None of these parameters in Table 2 were fitted (C6, C8, C10, A, b). They were obtained according to the PNTraZ model for interatomic non-bonded) interactions from the Mulliken charge, dipole polarisability and Paulli repulsion coefficients of each species (Table 1). As such the proposed CMK structures are predictions assuming that there is no chemical reaction involved between the carbon phase and the substrate. 7 ACS Paragon Plus Environment

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The potential parameters for GCMC simulation of carbon atoms with silica have been taken from Pellenq et. al. [39, 42]. The potential parameters for GCMC simulation of argon with carbon have been taken from Jain et al. [50] The argon-carbon parameters have been shown to predict the argon adsorption in porous carbon models very well.

2.3. The carbon-carbon potential energy The interaction between the carbon atoms is calculated using the REBO potential of Brenner [36]. The energy between two carbon atoms i and j is calculated using R A (3) ij ij ij ij ij ij

U = V (r ) + b V (r )

where VijR is a pair repulsive and VijA is a pair attractive term and bij is a bond order term, which weights the attractive part of the potential with respect to the repulsive part. The bond order term is a many body term, which depends on the local environment of atoms i and j. REBO potential is short ranged. However, the local chemistry is captured very well by REBO potential. REBO potential has been successfully used to build molecular models of disordered microporous carbons, by Jain et al [43] The authors noted that the local chemistry (bond lengths, bond angles, rings) are reproduced well in the models using the REBO potential. The AIREBO potential (which adds long range interactions to the REBO potential) could have been used in the current work. However, it is computationally expensive and we are mostly concerned with generating models that capture the mechanism of adsorption occurring in those models. 2.4. Simulation Technique GCMC simulations of carbon atoms (from vapor phase) are performed in the MCM-41 pore model. Periodic boundary conditions are used only in the pore axis (X-axis) direction. To speed up the simulation, the simulation box is first divided into a 100X100X100 grid and the interaction energy between the adsorbent (MCM-41 pore) and adsorbate atoms (carbon) is calculated at each grid point. Then during the GCMC simulations the energy is calculated using a trilinear interpolation of the energy grid. We start with many carbon dimers located near the pore wall and gradually increase the chemical potential till we obtain carbon pipes and rods. It must be stressed here that we are not mimicking the experimental synthesis procedure to obtain CMK models. In experiments, a carbon precursor (e.g. furfuryl alcohol or sucrose etc.) is impregnated into the silica pore and then carbonized to obtain the CMK materials. However, we are not simulating the synthesis procedure, as we are interested in the final CMK structures. By doing carbon adsorption in a silica pore we get carbon structures that resemble the real CMK materials. The interaction energy between silica-carbon is weak and in the physisorption range. However, the carbon-carbon energy involves covalent bond and is therefore much high in magnitude. Thus we were not able to wet the silica walls with carbon atoms to get carbon pipes. We obtain carbon rods where the carbon atoms completely fill the silica pore. To obtain carbon pipes, silica-carbon interaction energy was increased by multiplying with a 8 ACS Paragon Plus Environment

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fixed integer (value = 50). Thus, we were able to wet the silica pore with the modified energy and get carbon pipes. It is known from experiment that some carbon precursor (like sucrose) completely fill the pores of silica template, whereas other precursors (like furfuryl alcohol, which adsorb better than sucrose on the silica walls) produce a film on the silica pore [23,27]. Thus, increasing the silica-carbon interaction energy may be thought as adsorbing furfuryl alcohol which leads to better adsorption on the silica pore surface. Since Monte carlo simulations were used to obtain carbon rods and pipes, these carbon structures are equilibrium structures which are in a thermodynamically stable or metastable state. The final carbon rods and carbon pipes thus obtained capture the surface roughness and disordered nature of the real CMK structures [12,25,23]. A schematic showing the simulation methodology is shown in supporting information (see Figure S1). It is possible that there may be some hetero-atom present in the CMK materials. However, their effect will be negligible on argon adsorption. The effect will be prominent on adsorption of polar molecules. Experimentally there is not much data on the heteroatom content. We have developed molecular models of CMK-5 materials with attached functional groups. A future study will report the influence of functional groups on adsorption of polar molecules like carbon dioxide.

2.5. Molecular models for CMK-1, CMK-3 and CMK-5 carbons Carbon rods and carbon pipes of different diameters and wall thickness were obtained by changing the carbon-silica (fluid-wall) interaction energy, temperature and the chemical potential. After the carbon adsorption in the MCM-41 pore, the silica template is removed and the resultant carbon structure (rods and pipes) is relaxed in the NVT ensemble using Monte Carlo simulations. Periodic boundary conditions were used only in the pore axis direction. These carbon rods and carbon pipes were relaxed as free standing structures and undergo minor changes upon relaxation, due to the removal of the silica template, but remain intact and do not collapse. It was found that these carbon rods and carbon pipes obtained are not smooth and are disordered at the local level. Moreover, the outer and inner pore surfaces (in case of carbon pipes) are rough and corrugated. These carbon rods and carbon pipes were then used to build simple molecular models for CMK1, CMK-3 and CMK-5. The TEM pictures of CMK materials reveal that (i) CMK-1 is made up of a high alignment of carbon rods placed side by side arranged in a cubic symmetry [8,15], (ii) CMK-3 is made up of carbon rods arranged in a hexagonal symmetry [12] and (iii) CMK-5 is made up of carbon pipes arranged in a hexagonal symmetry [23,25]. Following the TEM images, simple models of these CMK materials were built by using the carbon rods and pipes obtained by doing carbon adsorption in a MCM-41 pore. We arranged a) the carbon rods in a cubic lattice to obtain a model of CMK-1 b) the carbon rods in a hexagonal lattice to obtain a model of CMK-3 and c) the carbon pipes in a hexagonal lattice to obtain a model of CMK-5 (see Figure 2).


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Figure 2: Molecular models for (a) CMK-1 (b) CMK-3 and (c) CMK-5 The unit cell used for GCMC simulation is a rectangular box for all the three CMK models. The models shown above have been replicated 9 times and are shown for visualization.

In our case, using different lattice parameters therefore controls the pore size of the CMK models. It is known from experiments that the carbon rods in CMK-3 and carbon pipes in CMK-5 are not isolated; rather they are interconnected by small carbon connections [44,48]. These interconnections between carbon rods and carbon pipes are essential to keep the ordered structure of CMK-3 and CMK-5 intact. These interconnections are believed to be formed by the infiltration of the carbon precursor and subsequent carbonization in the micropores or narrow mesopores of SBA-15 that connect the main mesoporous channels. We must emphasize one more point here. The density of CMK models is given in Table S1 of supporting information. The diameters as well as wall thickness of carbon rods and carbon pipes used in this study are smaller than what is inferred experimentally. The main reason for this is that the MCM-41 pore, used as our silica template, has a small pore diameter i.e. 2.8 nm. Thus, the carbon rods and carbon pipes obtained by doing a carbon adsorption in this pore are smaller compared to what found in experiments. We could have used a bigger MCM-41 pore diameter. However, the REBO potential used here is computationally expensive. CMK models with bigger rod and pipe diameter are being developed in our laboratory and will be presented in a future study. Our models however capture the main features of pore geometry and pore connectivity present in the real materials. Moreover, the carbon rods and carbon pipes used here also contain the surface roughness and surface corrugation present in the real CMK materials. Nevertheless, our models can give some insight into the adsorption phenomenon occurring in these materials although qualitatively. From a fundamental point of view, it is also interesting to study adsorption in these pore geometries that differ from a regular


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slit or cylindrical pore geometry. Here, we developed models for a lattice spacing of 14 Angstrom for our CMK-3 and CMK-5 models. Random interconnections were further added to the free-standing CMK-3 and CMK-5 models of 14 Angstrom lattice spacing. The size and number of interconnections is not known from the experiments as it is very difficult to characterize these interconnections. We randomly added 4, 6 and 8 interconnections to our CMK-3 and CMK-5 models. It should be noted that the size and number of interconnections could be varied in our models. The interconnections are not exactly cylindrical and the approximate diameter is from 8 to 12 Angstrom. Molecular models of the CMK-3 and CMK-5 materials with interconnections are shown in Figure 3.

Figure 3: Molecular models of CMK-3 and CMK-5 with interconnections.

It is possible that there may be some carbon pipes (in CMK-5 materials) or carbon rods (in CMK-3 and CMK-1 materials) of different diameter due to the different amount of carbon precursor being impregnated in the pores of real SBA-15 materials. Our carbon pipes and rods used in the CMK models are of the same diameter. This will have an impact on adsorption. However, to a first approximation our models capture the adsorption phenomena in the CMK models. We have developed CMK-5 models that have pipes of different diameters (unpublished work). Our new models will be able to capture the effect of such defects on adsorption. The density data for our CMK models are given in Table S1 of supporting information. Density data for the experimental CMK samples are not available. However, there is information available for the diameter of carbon rods and carbon pipes of CMK samples from experiment. The diameter of carbon rods in one of the CMK-1 materials is roughly 3.164 nm [32]. The external diameter of carbon nanopipes is about 5.8nm and the internal diameter is about 4.4nm [44]. However, it must be stressed that the diameters of carbon rods and carbon pipes is dependent on the pores of the silica material used as a template. Thus it is possible to obtain carbon rods and pipes with smaller diameters using a silica template with smaller pores. In our CMK models, the carbon rods and carbon pipes are of smaller diameter than the experimental ones. A smaller MCM-41 pore (2.8 nm) was used as the REBO potential used here is very computationally expensive. Thus the carbon rods used here have roughly diameter of 2.8nm and the outer diameter of carbon pipes is roughly 2.8nm. This difference in the diameters and thickness of carbon pipes and carbon rods between the models and experiments is one of the reasons for the discrepancy in the 11 ACS Paragon Plus Environment

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results. Nevertheless, our models capture the pore morphology and pore topology present in real CMK materials. We are developing CMK models with larger diameters and then we will have better comparison with experiments. Pore size distribution (PSD) was computed for the CMK-5 models (with and without interconnections), using the method of Bhattacharya and Gubbins [49], to measure the effect of interconnections on the pore size distribution. This is shown in Figure 4. It was found that the interconnections indeed break the porosity present between the carbon tubes (inter tube pores). This can be seen from Figure 4, where some features appear in the PSDs of CMK-5 models with interconnections in the 10-12 Å range which are absent in the CMK-5 models without interconnections. The peak at 8 Å refers to the pore inside the pipes and the peak at 13.5 Å refers to the inter tube porosity. Argon adsorption was then studied in the CMK-1, CMK-3 and CMK-5 models with and without interconnections (using GCMC simulations) and compared with experiments. The interaction parameters between carbon and argon atoms have been take from Jain et al [50]. A big enough simulation box was used and the statistical errors in GCMC simulations are expected to be minimum. The uncertainty on the final results, including the ensemble averages of the number of adsorbate molecules in the box and the total potential energy, is estimated to be less than 2%.

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Figure 4: Pore size distribution of CMK-5 models with and without interconnections.

3. Simulation of Argon adsorption in CMK-1 models Argon adsorption at 77K was studied in two CMK-1 models with varying pore sizes. Both Ar and N2 adsorption are used to characterize porous materials. Argon adsorption has been used here as the potential parameters for argon have been successfully used to predict isosteric heat for porous carbons [50]. In these CMK-1 models, the carbon rods are placed side by side in the horizontal (Z-) direction and the pore size is considered in the vertical (Y-) direction. This pore size refers to the distance between the outer surfaces of two carbon rods placed vertically (Y- direction). In our model, we found the carbon 12 ACS Paragon Plus Environment

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atom that has the maximum radial distance (rmax) from the axis ofthe carbon rod. We then placed another carbon rod with its axis at a distance d (d = 2×rmax +pore size) from the initial carbon rod in the vertical (Y-) direction. Argon adsorption was studied for two CMK-1 models of pore size 7.64 Å and 12.64 Å. This pore size was taken from the work of Ohkubo et al [32] from their RSP model for CMK-1. The X-axis is the rod axis direction. An orthorhombic unit cell was used as the simulation box for adsorption. The simulation boxlengths for the CMK-1 model of 7.64 Å pore size is: 106.95 Å × 38.3124 Å × 30.6725 Å and for 12.64Å pore size is: 106.95 Å × 43.3124 Å × 30.6725 Å. Periodic boundary conditions and minimum image conventions were used in all directions. A cut off radius of 4σ for the carbon-argon (for calculating the adsorbate-adsorbent energy grid) and argon-argon interaction was used for both 7.64 Å and 12.64 Å CMK-1 models. Argon adsorption isotherms for the CMK-1 models at 77 K are shown in Figure 5. The amount adsorbed at each relative pressure was normalized with respect to the total amount of adsorbate molecules when the pore was completely filled. From Figure 5, we see that there is a steep rise in the amount adsorbed at low pressure in both the CMK-1 models, as seen in microporous solids. This steep rise is due to the adsorption in the groove between two carbon rods placed horizontally (Z- direction) and at some high adsorption sites on the surface of carbon rods owing to the presence of surface roughness. Also both the models show a hysteresis loop, which is a characteristic of mesoporous materials and some super microporous solids [24,45], when capillary condensation occurs. The capillary condensation pressure moves to higher pressure (P/P0 = 0.5) for 12.64 Å pore as compared to (P/P0 = 0.2) for 7.64 Å as expected. The hysteresis loop widens upon increasing the pore size. Also, the jump, during the capillary condensation, for the 12.64 Å pore model is relatively larger than that of 7.64 Å pore model. Upon comparing with the RSP model [see Figure S2 in supporting information, 32], it was found that the isotherms obtained from our models are qualitatively similar to those obtained from the RSP model. However, the isotherms obtained from the RSP model do not show the pronounced jump that we see in our models (especially for the 12.64 Å pore model). This might be because they use a much higher rod diameter (3.164 nm [32]) compared to our case (2.2 nm). The higher rod diameterin RSP model leads to a higher density of carbon atoms as compared to the carbon rods used in our models. This will result in a higher fluid-wall interaction, which suppresses the capillary condensation pressure as well as the jump in the isotherm. Upon comparing with the experimental isotherm [see Figure S2, 32] (the experimental isotherm reported in ref 32 is obtained for N2 adsorption), it was found that the low pressure behavior is captured well by our model. The narrow pore space of the CMK-1 is important for adsorption at low pressure which is captured well by our CMK models, which confirms that REBO potential is able to reproduce the correct structure of narrow pores. Upon further increasing the pressure, there is a smooth rise in the adsorption behavior in the experimental isotherm till P/P0 = 0.35, although the slope is not as steep as at very low pressure. At P/P0 = 0.35 the slope in the experimental isotherm increases until P/P0 = 4.0 and then decreases and slowly flattens out. In our 12.64 Å pore model, a smooth increase in the adsorption isotherm from P/P0 = 0.05 to P/P0 = 0.45 is seen, though the slope is less as compared to that of experiments. However, at P/P0 = 0.5 a jump in the adsorption isotherm is seen, which is due to the capillary condensation, and 13 ACS Paragon Plus Environment

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then the isotherm flattens out. Analyzing the desorption branch, a wide hysteresis loop is seen in the CMK-1 models, whereas the experimental isotherm shows a small hint of hysteresis and is not as pronounced as in the models. The difference in hysteresis arises from the separate mechanisms for desorption in experiments and in simulations. In experiments, the adsorbed phase is in contact with a bulk gas phase whereas in simulations, due to the use of periodic boundary condition, there is no interface with the bulk gas phase. Hence, in simulations desorption occurs via nucleation of gas bubbles (cavitation) leading to a different behavior as compared to the experiments ([46] and references therein). We have performed GCMC simulations of argon in our models. But the behavior of argon and nitrogen will be similar on adsorption. The discrepancy between the experimental and simulated isotherms may be because of the difference in the carbon rod diameter. The carbon rods we are using (2.2 nm) are smaller in diameter as compared to the carbon rods present in the experimental sample (4-6 nm [24]). The reason for the small rod diameter used is due to the small pore diameter of MCM-41 (2.8nm) used in this work, which determines the diameter of the carbon rod. Thus, calculating the isotherms with larger rod diameters will give better agreement with the experiments [8]. The pore size as determined from BJH for the experimental sample was 3 nm where as we are using a pore size of 1.264 nm, following the work of Ohkubo et al [32]. Upon analyzing the simulated adsorption isotherm of CMK-1 models with different pore size, it is found that increase in pore size leads to a wider hysteresis loop, and the capillary condensation step moves to higher pressure. Increasing the rod diameter in our models will give a better agreement with experiment. It should be noted that the experimental CMK-1 sample may contain a wide pore size distribution and defects in some rods due to the partial filling of pores with carbon [47]. In our case, the pore size is very uniform and all the carbon rods are the same. Nonetheless, our model is able to qualitatively capture the adsorption phenomena occurringin the real materials. Figure 6 gives insight into the pore filling mechanism in the CMK-1 7.64 Å model. We found that at low pressure (P/P0 = 0.005) adsorption occurs in the groove between two carbon rods place horizontally and also at some selective high energy sites on carbon rods. On increasing the pressure (P/P0 = 0.05) adsorption occurs at the outer surfaceof the carbon rods where a film of argon is formed. On further increasing the pressure the film thickness on the carbon rods increases and also liquid bridges are formed between carbon rods placed vertically (P/P0 = 0.15). This leads to the formation of a gas liquid interface in the main cavity that coexists with the liquid bridges. These gas like regions shrink slightly as pressure is increased and at P/P0 = 0.2 capillary condensation occurs. Henceforth, there is a very little increase in the amount adsorbed with increasing pressure. The adsorption mechanism for the 12.64 Å pore model is slightly different. As in the 7.64 Å pore model, at low pressure, the fluid molecules are adsorbed in the groove between the carbon rods and also at selective high energy sites on the carbon rods. However, as the pressure is increased, a film of fluid begins to develop around the carbon rods. The thicknessof the fluid film increases as the pressure increases until it becomes unstable and capillary condensation occurs at P/P0 = 0.5. Thus, there is no formation of liquid bridges as was found for the 7.64 Å pore model.


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Figure 5: Argon adsorption isotherms at 77 K in CMK-1 models.

We also calculated the isosteric heat of adsorption in CMK-1 models from the fluctuation theorem (see Supporting information, Figure S3). The total isosteric heat is larger for model with 7.64 Å than for 12.64 Å pore model. This is expected as the confinement effect is more for 7.64 Å model. We also show the fluid-fluid and fluid-wall contribution to the total isosteric heat for 7.64 Å model. As, can be seen the fluid-fluid contribution increases monotonically and fluid-wall contribution decreases monotonically for all the pressures. This is typical of mesoporous and super microporous materials.

Figure 6: Pore filling mechanism in 7.64 Å pore model. (a) P/P0 = 0.005, (b) P/P0 = 0.05, (c) P/P0 =0.15 and (d) P/P0 = 0.2


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4. Simulation of Argon adsorption in CMK-5 models Argon adsorption at 77K was studied in the CMK-5 models using GCMC simulations. In Figure 7, adsorption isotherms in our CMK-5 models are shown, that can be compared with experiments [25,28] for some CMK-5 samples. From the adsorption isotherms of CMK-5 models, we see that there is a steep rise in the adsorbed amount at very low pressure. This is due to the adsorption in the interior of the carbon pipes (near the inner surface), which acts as high energy sites and at some selective high energy sites on the outer surface. On further increasing the pressure most of the adsorption occurs in the inside of the carbon pipes (this is because the confinement effect felt by the fluid molecules is more in the interior of the pipes) and the interior space gets filled. On further increasing the pressure, we see a jump (of different size) in the amount adsorbed for all the models, at different relative pressures. This jump is typical of mesoporous solids and some super microporous solids [22, 45] and is due to the capillary condensation of adsorbate in the pore. The capillary condensation occurs at a higher relative pressure for the CMK-5 model without interconnections and moves to lower relative pressures for the CMK-5 models with interconnections. From Figure 7, we see that the adsorption isotherm for the CMK-5 model with 8 interconnections is smoother compared to the other models. The experimental isotherms [25,28] on the other hand are much smoother. It should be pointed out that we are interested in qualitative comparison with experiments. The reason being the pore size and wall thickness of carbon pipes are smaller in our models compared to that of the samples used in the experiments. We can obtain models having similar pore size and wall thickness as that of the samples used in experiments if we use a MCM-41 model with a larger pore, which however is computationally more expensive. Then it is possible to do quantitative comparisons. However, the pore shape and pore connectivity in our models is similar to that of the experimental samples and thus the adsorption behavior (the adsorption isotherms) can be compared qualitatively. Moreover, the real CMK-5 materials (i) can exhibit a wide pore size distribution, (ii) may have some defective pipes due to partial filling of some of the porosity of the silica template with carbon (iii) have interconnections between the carbon pipes. These will lead to smoother adsorption isotherms. In our models however, we use the same carbon pipe and decorate on a hexagonal lattice. Thus all the carbon pipes are the same and also the distance between the carbon pipes is the same. This leads to uniform pores in our models. We do however incorporate the interconnections in our models and we see that the incorporation of the interconnections indeed leads to smoother isotherm (the jump is much smaller) as compared to that of the CMK-5 models without interconnections. This shows that the presence of interconnections reduces the mesoporosity and leads to significantly different pore size distribution. This was also seen from our pore size distribution calculations (Figure 4).


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Figure 7: Adsorption and desorption branches of the isotherm for CMK-5 models. The lines noted “No-conn”, “Conn-4”, “Conn-6” and “Conn-8” correspond to the adsorption branch for the CMK-5 model with no interconnections, 4 interconnections, 6 interconnections and 8 interconnections. Similarly, the lines noted “No-conn-D”, “Conn-D-4”, “Conn-D-6” and “Conn-D-8” correspond to the desorption branch for the CMK-5 model with no interconnections, 4 interconnections, 6 interconnections and 8 interconnections.

The visualization of the fluid inside the CMK-5 models at different pressures (shown in Figure 8) gives information about the adsorption mechanism in these materials. Initially the porosity inside the carbon tubes is filled where the confinement effect is large. On further increasing the pressure, fluid forms a thin film around the carbon pipes and the porosity inside the carbon pipes is completely filled. On increasing pressure, the space between the interconnections that are spaced not too far gets filled. The fluid forms a meniscus between the interconnections that are separated farther. On further increasing the pressure the larger pores between the interconnections gets filled and on further increasing the pressure the total porosity is filled with fluids.


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Figure 8: Snapshots showing the filling mechanism in the CMK-5 models increasing pressure.

We also calculated the isosteric heats of adsorption for the CMK-5 models (see supporting information Figure S4. Shown are the total and the fluid-fluid and fluid-wall contribution to the isosteric heats of adsorption). As can be seen (see supporting information Figure S4), the total isosteric heat has a minima i.e. it decreases initially and then increases. The fluid-wall portion of the isosteric heat decreases monotonously and the fluid-fluid portion increases monotonously. This is typical of mesoporous solids that exhibit capillary condensation. We also calculated the isosteric heat of the CMK-5 model with interconnections and the fluid-fluid and fluid-wall contribution for CMK-5 model with 8 interconnections. The overall shape is similar to the isosteric heat of CMK-5 model without interconnections (not shown here). There is a jump in the isoteric heat for model without interconnections at coverage close to 0.4. However, the isosteric heat with interconnections shows a smoother curve with jump at loading equal to 0.75. We also calculated the desorption branch of the adsorption isotherm which is shown in Figure 7. It was found that the desorption branch is almost the same for all the models 18 ACS Paragon Plus Environment

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and that they show a sharp jump at almost the same pressure. Though the adsorption branch of the model with 8 interconnections was a little smoother compared to the other models, the desorption branch exhibits the same characteristic as the other models. 5. Simulation of Argon adsorption in CMK-3 models GCMC argon adsorption isotherms in CMK-3 models are shown in Figure 9. From the adsorption isotherm, it can be seen that there is a steep rise initially in the isotherm. This is due to the presence of high energy sites on the outer wall of CMK-3 models due to surface roughness. This can be seen in Figure 10 presenting the pore filling mechanism. The fluid molecules initially make a film around the CMK-3 available surface. On further increasing the pressure we see a jump in the adsorption isotherms for all the CMK-3 models, which is typical of mesoporous solids and some super microporous solids. The capillary condensation occurs at a higher relative pressure for the CMK-3 model without interconnections and moves to lower relative pressures for the CMK-3 models with interconnections. We do not see a smoother isotherm for CMK-3 models with 8 interconnections as compared with CMK-5 model with interconnections. However, the pore shape and pore connectivity in our models is similar to that of the experimental samples and thus the adsorption behavior (the adsorption isotherms) can be compared qualitatively. The experimental adsorption isotherm [14] is very smooth and exhibit a smaller hysteresis loop as compared with that of CMK-5 samples. This is because CMK5 has 2 kinds of porosity and the wall thickness is smaller as compared to CMK-3 models. We also calculated the desorption isotherm for CMK-3 models without interconnections and CMK-3 models with interconnections (Figure 9). All the models exhibit hysteresis. However, the hysteresis loop is smaller than that seen for CMK-5 models. This is attributed to the wall thickness for CMK-3, which is higher compared to CMK-5 models.


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Figure 9: Adsorption and desorption branches of the isotherm for CMK-3 models.

The visualization of the fluid inside the CMK-3 models at different pressures (Figure 10) gives information about the adsorption phenomenon in these materials. Initially the fluid forms a thin film around the carbon rods. On increasing pressure, the space between the interconnections that are spaced not too far gets filled. On further increasing the pressure the larger pores between the interconnections gets filled and on further increasing the pressure the total porosity is filled with fluids. We also calculated the isosteric heat of adsorption for CMK-3 models with and without interconnections (we show only isosteric heat of adsorption for CMK-3 model with 8 interconnections in supporting information Figure S5). The isosteric heat of adsorption shows similar shape for CMK-3 models with and without interconnections. The isosteric heat at low coverage is larger for CMK-3 models (~24 KJ/mol) as compared to CMK-5 models (~15 KJ/mol). This is due to the adsorption of a few argon atoms in the central part of the rods (see Figure 10). Also, we see a lot more features in CMK-5 models with interconnections as compared to CMK-3 models with interconnections. We think that by increasing the size and number of interconnections in CMK-3 models we can get better comparison with experiments.


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Figure 10: Pore filling mechanism in the CMK-3 models upon increasing pressure.


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6. Conclusions Molecular models for CMK-1, CMK-3 and CMK-5 materials have been developed using carbon rods and carbon pipes, that were obtained by adsorbing carbon in a model MCM41 pore. It was found that the carbon rods and pipes of different thickness can be obtained by changing the silica-carbon strength, the temperature and the chemical potential at which carbon vapor is adsorbed. These carbon rods and pipes are equilibrium structures in a thermodynamically stable or metastable state, since they are obtained using Monte Carlo simulations. These carbon rods and carbon pipes are then used to obtain simple molecular models for CMK-1, CMK-3 and CMK-5 using the same symmetry as found in TEM pictures. However, it is widely believed that the carbon rods in CMK-3 and carbon pipes in CMK-5 are connected by small carbon interconnections. To mimic the real CMK-3 and CMK-5 materials in a more realistic way, random interconnections were added between these carbon pipes and carbon rods. These interconnections are present in the real materials and are a necessity to hold the carbon pipes and carbon rods together. From a fundamental point of view these models are very interesting, since they exhibit pore geometries different from a regular slit or cylindrical pore. The calculated geometric pore size distributions show that the presence of interconnections reveal some extra features in the 10-12 Angstrom pore size range which are absent in the CMK-5 model without interconnections. Argon adsorption isotherms calculated for the CMK-5 and CMK-3 models show capillary condensation as in mesoporous solids. It was found that adding the interconnections result in a somewhat smoother adsorption isotherm, as is revealed by the isotherm of 8 interconnections in CMK-5 models. However, the desorption branch still exhibits sharp jump during evaporation for all the CMK-5 and CMK-3 models. The real CMK materials can exhibit a wide pore size distribution and may also have some defective rods and pipes due to the partial filling of some of the porosity of the silica template with carbon. In our models, the pores as well as the carbon rods and carbon pipes are the same. We have developed CMK-5 models with different pipe diameters. A future study will aim at the effect of these defect on adsorption phenomena. For the CMK-5 models, it was found that the inner porosity of the carbon pipes is in the micropore range in our models, due to the use of carbon pipes having a smaller inner diameter as compared to the experimental ones. Thus, the adsorption in the inside of the carbon pipes do not contribute to the adsorption behavior after P/P0 = 0.025 and only the space between the carbon pipes contribute to the adsorption beyond P/P0 = 0.025. Hence, the capillary condensation is governed only by the porosity between the carbon pipes. However, it is found from the experiments that both the inside of the carbon pipe as well as the space between the carbon pipes are in the mesopore range and contribute to capillary condensation. Thus, increasing the inside diameter of the carbon pipe will give better agreement with the experiments. Nonetheless, our work provides insight into the adsorption properties and pore filling mechanism (from the snapshots at different relative pressure) of the pore geometriesfound in CMK materials. Acknowledgments RJMP thanks the support of the ICoME2 Labex (ANR-11-LABX-0053) and the AM*IDEX projects (ANR-11-IDEX-0001-02) funded by the French program 22 ACS Paragon Plus Environment

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"Investissementsd’Avenir" and managed by the ANR, the French national research agency and the support of the (ANR-13-BS08-0004-01) “Genesis”program. XP thanks the support of the National Natural Science Foundation of China (No. 21676006) and “Chemical Grid Project” of BUCT. References (1) (2) (3) (4)

(5) (6)

(7) (8) (9)

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Molecular Modeling and Adsorption Properties of Ordered Silica

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