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Molecular Modeling of Microporous Structures of Carbide-Derived Carbon Based Supercapacitors Sabine Schweizer, Robert Meissner, Marc Amkreutz, Karsten Thiel, Peter Schiffels, Johannes Landwehr, Bastian J.M. Etzold, and Jörg-Rüdiger Hill J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b12774 • Publication Date (Web): 16 Mar 2017 Downloaded from http://pubs.acs.org on March 20, 2017

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The Journal of Physical Chemistry

Molecular Modeling of Microporous Structures of Carbide-Derived Carbon Based Supercapacitors Sabine Schweizer,† Robert Meißner,‡ Marc Amkreutz,‡ Karsten Thiel,‡ Peter Schiffels,‡ Johannes Landwehr,¶ Bastian J. M. Etzold,¶ and Jörg-Rüdiger Hill∗,† †Scienomics GmbH, B¨ urgermeister-Wegele-Straße 12, 86167 Augsburg, Germany ‡Fraunhofer-Institut f¨ ur Fertigungstechnik und Angewandte Materialforschung IFAM Klebtechnik und Oberfl¨ achen -, Wiener Straße 12, 28359 Bremen, Germany ¶Ernst-Berl-Institut f¨ ur Technische und Makromolekulare Chemie, Technische Universit¨ at Darmstadt, Alarich-Weiss-Straße 8, 64287 Darmstadt, Germany E-mail: [email protected] Phone: + 49 (0) 821 450 165 60. Fax: + 49 (0) 821 450 165 62 Abstract Microporous carbide-derived carbons are an important structural class for various technological applications. We present two possible strategies based on molecular dynamics simulations for modeling microporous amorphous carbon. In addition, we have investigated the influence of the precursor structure and simulation parameters on the porosity of the final model structure. We observed a minor influence of the precursor structure on the porosity and found that the structural properties such as pore size and hybridization in the modeled carbon structures agree well with experimental findings. Moreover, CO2 adsorption isotherms have been simulated using Monte Carlo simulations for comparsion with experimental data. In this context, we have also considered partially oxidized carbon structures for which an increased uptake of CO2 was observed.

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Introduction Microporous materials play an important role in a broad variety of industrial applications. They are used, for example, as catalysts, 1 in fuel cells, 2 for hydrogen storage, 3 or in adsorption processes. 4,5 An exceedingly interesting class of microporous materials are carbidederived carbons (CDCs), since their structure and porosity can be tuned through the choice of carbide precursor and experimental conditions. 6 CDCs are usually synthesized by chlorination of metal or metalloid carbides at elevated temperatures. Commonly used precursors are TiC or SiC from which the metal is extracted while the carbon matrix rearranges in a microporous, amorphous structure with primarily sp2 -hybridized carbon. 7 Due to their unique properties, CDCs have gained special attention for various technological applications such as adsorption processes, gas storage, and especially in the field of electrochemical energy storage. 8 Much efforts have been spent on the development and characterization of CDC-based materials using both experimental and computational approaches, see e.g. references. 7,9–12 Rational design of CDCs, influencing material properties through chemical functionalization, or increasing the energy density in CDC-based supercapacitors are, however, challenging tasks. 13 In order to overcome the limitations of existing systems, a fundamental understanding of the structural features of the porous material and molecular processes is essential. In the last decades, computational methods have been proven highly useful for revealing critical insights at the atomistic level. Molecular modeling can provide structural information and realistic model structures when experimental methods are not able to show the necessary details. This is often of vital importance, because many properties are governed by the structure. In particular, amorphous systems are difficult to characterize only based on experiments and molecular modeling can efficiently complement experimentation. In literature, Monte Carlo(MC)-based methods have been discussed for modeling microporous carbon. 12,14–17 As it has been pointed out, 7,11 these approaches are capable to produce reasonable structural models, but they usually rely on input from experimental data which 2


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is limiting the predictive capabilities. A pure computational approach had been suggested by Shi 11 who proposed a pseudo-mimetic molecular dynamics-based method which has also been successfully applied by Palmer et al. 7 Though this method allows to generate realistic model structures, the influence of the carbide precursor is not directly taken into account in the simulations. However, it is known from experiment, that the precursor does play a role. 18 The aim of the present work is to compare two different computational approaches for modeling morphological realistic microporous carbon structures and to study how the initial structure influences the porosity. Furthermore, we investigate the influence of chemical functionalization of the carbon skeleton on the adsorption properties. For the first approach, we start from a carbid precursor (SiC) and follow a pseudo mimetic approach using quenched molecular dynamics (QMD) in a similar way as described in Refs. 7,11,19 The second approach starts from a pure platelet like carbon system and uses bond-order based potentials 20–22 for modeling microporous carbon. The computed structures are thoroughly characterized with regards to pore size, pore and ring size distribution as well as hybridization. For additional comparison with experimental data, CO2 adsorption isotherms were calculated based on the modeled structures using Monte Carlo methods. In order to study how functionalization of the carbon skeleton affects the adsorption properties, we have generated microporous carbon structures functionalized with oxygen and simulated adsorption isotherms in dependence of the oxygen content. The remaining part of the paper is organized as follows: In the next two sections, the simulation system and methods used to model the structures and to calculate adsorption isotherms are described and experimental details are provided. Afterwards, the results of the molecular dynamics simulations are presented and discussed. Then, the Monte Carlo simulations of the adsorption isotherms are shown and compared with experimental results. Finally, the conclusion is presented in the last section.

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Computational Details The first approach applies QMD starting from a carbide precursor, while the second approach uses molecular dynamics (MD) together with bond-order based force fields on a platelet model.

Pseudo mimetic approach using quenched molecular dynamics The crystal structure of SiC was used as initial structure. The unit cell of the SiC polytype 4H-SiC was built taking the cell parameters from Melinon. 23 A 20x20x6 supercell containing 19,200 atoms and with cell lengths of a=b=61.6 ˚ A and c=60.4 ˚ A was created to ensure a sufficiently large periodic cell for modeling a microporous, amorphous carbon skeleton. This structure was then subjected to various molecular dynamics (MD) simulations using the SiC Tersoff potential, 24 where we basically followed a recently published scheme 19 for modeling microporous structures. SiC had to be used as starting point for the QMD simulations since there does not exist a suitable potential for TiC, which was used in the experimental characterization of the CDCs. Since the metal is removed during the preparation of the amorphous carbon the results should be comparable. First, a 50 ps MD simulation in the NVT ensemble was performed at room temperature for obtaining a decent starting structure followed by a 200 ps NPT equilibration at 2500 K. Then, the system was quenched to room temperature using a rate constant of 2.2 · 1012 K/s (this corresponds to 1 ns simulation time) in the NPT ensemble. Afterwards, all Si atoms were removed and a 200 ps MD simulation in the NVT ensemble at room temperature was carried out for the remaining pure carbon skeleton. Additional sets of simulations were performed to evaluate the stability of the modeled porous structure and to look into how (i) the starting structure, i.e. the SiC polytype, (ii) the cell size and (iii) simulation parameters, such as temperature and quench rate, influence the final porous structure. Details about all simulation protocols can be found in the Supplemental Information. For comparison with

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experimental data, the final structurs were analyzed with respect to pore size, pore size distribution, density, and ring distribution of connected carbon atoms. Moreover, CO2 adsorption isotherms were computed using MC simulations in the GibbsNPT ensemble. In addition to the pure carbon skeleton, partially oxidized carbon structures were generated to investigate the impact of oxygen functionalities on the adsorption properties. For this purpose, oxygen was added randomly to potential sites, i.e. sp2 hybridized carbon atoms, to a certain percentage (2% and 5%) using the script functionality of the MAPS platform 25 after removing all non-bonded carbon atoms. Force field parameters for the carbon backbone were taken from literature 26 and the Harris and Yung model 27 was used for CO2 . The CO2 simulation box was generated containing 600 molecules at an initial density of ρ = 0.002 g/cm3 . MC calculations consisting of 107 moves were carried out at 273 K in the NPT ensemble to equilibrate the CO2 gas box at various pressures starting from a MD structure, which was pre-equilibrated over 500 ps in the NPT ensemble at 273 K and the respective pressure. Production runs in the Gibbs-NPT ensemble consisted of 106 moves. For the partially oxidized structures, ketone parameters were taken from the OPLS-AA force field. 28 For building and manipulating structures, setting-up and analyzing simulations Scienomics MAPS software platform 25 was used. Zeo++ 29,30 was used for determining the pore size and pore size distribution, respectively, and the Python script polypy 31 was used for analyzing the ring distribution. MD simulations were performed using the software package LAMMPS. 32 MC calculations were carried out using the software package Towhee. 33 Further details on the simulations can be found in the Supporting Information.

Platelet model approach using bond-order potentials A platelet model was used as second approach to preserve the microcrystalline structure evident in real CDCs as discussed in the previous chapter. A variant of the platelet model 34 was generated using the following approach: (i) VMD 35 and its Nanotube Builder extension 5



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are used to create a stack of graphene sheets which is saved with the TopoTools extension in a LAMMPS data format. (ii) To account for the estimated graphitic cluster length obtained from Raman spectroscopy 36 , La , pairs of round shaped graphene sheets are carved out with random diameters ranging between 10.0 and 20.0 ˚ A from the previous structure using the functionality of the LAMMPS package. A variable diameter of the platelets is chosen to account for the heterogeneity of the graphitic regions in amorphous carbons. Similar to the approach of Terzyk 37 only complete hexagonal rings are allowed to avoid unphysical behavior when a reactive force field is used later on. (iii) A random platelet structure is then obtained by defining pairs of graphene sheets as individual rigid bodies, assuming a soft potential between them. The resulting structure is coupled to a heat bath at 300 K using a Nosé-Hoover NVT thermostat. (iv) A high degree of disorder of the platelets was generated in a first step by allowing the platelets to move almost freely in a periodically repeated simulation domain by increasing the size of the central box in the periodic simulation. (v) Afterwards, the central box was again shrunk to a size where the density of the particles corresponds to the value found by Liu, 38 ρ = 0.88 g/cm3 . The resulting initial structure using this approach is shown in Fig. 1.

Experimental methods To characterize CDCs the experimental techniques described in the following have been used. EELS and Raman spectroscopy represent highly useful methods in this context. 18 Information obtained from these techniques has been used for modelling amorphous carbon using the platelet model approach.

TiC Isotherms Amorphous carbon structures were synthesized by selective etching of titanium carbide with chlorine at temperatures ranging from 500 ◦ C to 1000 ◦ C. Depending on the etching tem-

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Table 1: Texture analysis of TiC-CDC synthesized at 500 ◦ C, 800 ◦ C or 1000 ◦ C. For each material the specific surface area and the pore volume based on the QSDFT method for slit pores at equilibrium are listed. Additionally, the calculated mean pore diameter and the BET surface are given. Data was acquired by isotherm nitrogen adsorption using the instrument Autosorb-1P by Quantachrome Instruments. Material

TiC-CDC-500 TiC-CDC-800 TiC-CDC-1000

Specific surface area (BET, N2 ) SSABET [m2 g–1 ] 1280 1520 1340

Specific surface area (QSDFT, N2 ) SSAQSDFT [m2 g–1 ] 1680 1720 1740

Pore Volume (QSDFT, N2 ) VQSDFT [cm3 g–1 ] 0.55 0.62 0.72

Calculated mean pore diameter dcalc [˚ A] 6.5 7.2 8.3

perature the process yielded microporous carbons with specific surface areas (SSA) ranging from 1680 m2 g–1 to 1740 m2 g–1 and pore volumes (V) of 0.55 cm3 g–1 to 0.72 cm3 g–1 , respectively. The data presented in Fig. 2 is based on high resolution nitrogen sorption analysis at 77 K using the instrument Autosorb-1P by Quantachrome Instruments. Data evaluation of the recorded isotherms was based on the quenched solid density functional theory (QSDFT) method assuming equilibrium condition and slit pores. The average pore diameter dcalc of the synthesized carbons was calculated from the ratio 2 · V/SSA. According to this method, CDC was synthesized that exhibited an average pore diameter of 6.5 ˚ A, 7.2 ˚ A or 8.3 ˚ A. The material texture properties obtained by nitrogen isotherms are summarized in Table 1. Corresponding data for CO2 adsorption is provided in the Supporting Information.

Electron Energy Loss Spectroscopy The sp2 and sp3 content of amorphous carbons can be derived using electron energy loss spectroscopy (EELS). Here, the size of the peaks describing the transition to the π∗ state in the K-edge absorption spectrum are relevant for the sp2 content 18,39–41 . Core loss spectra of the investigated CDCs have been obtained using a FEI Tecnai F20 (Hillsboro, USA) in scanning mode (STEM) equipped with a Gatan GIF2001 image filter (Pleasanton, USA). The energy resolution measured at the zero-loss peak was around 1 eV. A core loss spectrum

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Table 2: sp2 and sp3 contents derived from the EELS spectra analysis of the CDCs.

sp2 / (%) sp3 / (%)

T (◦ C) 500 800 1000 69 87 89 31 13 11

of a CDC produced at a chlorination temperature of 800 ◦ C with corresponding fits is shown in Fig. 3. Peak 1 (P1 ) and Peak 2 (P2 ) are related to the transition to the π∗ state while Peak 3 (P3 ) is related to the σ∗ state. According to Ref. 41 the ratio of the integral of P1 and P2 to the total integral of the three functions for a material is given by

Rmat =

Area(P1 + P2 ) , Area(P1 + P2 + P3 )

(1)

This ratio has to be normalized using a reference material with 100% sp2 hybridization to obtain the sp2 content of the material investigated sp2 =

Rmat . Rref

(2)

In this case, graphite with Rref = 0.28 has been used as reference. The sp2 and sp3 contents derived from the EELS spectra analysis of our CDCs assuming a negligible sp contribution are summarized in Table 2. Our results show a sp2 hybridization of ∼90% for CDCs produced at 800 ◦ C and 1000 ◦ C. This is in good agreement with the results of Urbonaite et al. 18 for TiC-derived CDCs with the same synthesis temperatures. Urbonaite et al. 18 investigated CDCs produced at chlorination temperatures from 700 ◦ C to 1200 ◦ C and found a more or less constant sp2 content of around 90% for those. In contrast to that, an increase of sp3 hybridization to 31% has been found for CDCs produced at 500 ◦ C. With the sp3 content known, it is possible to calculate the density of the CDCs without pores assuming a linear relationship between the sp3 fraction and the density according to

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Table 3: Densities and mass densities derived from the EELS spectra analysis of the CDCs and the volume of micropores determined by CO2 adsorption.

Density / (g/cm3 ) Mass density / (g/cm3 )

T (◦ C) 500 800 1000 2.35 2.10 2.07 1.1 1.0 1.2

the formula 18,40 ρ [g/cm3 ] = 1.92 + 1.37 · (sp3 fraction) ,

(3)

The densities derived from the sp3 contents of the CDCs are given in Table 3. Again, these results are in good agreement with the ones of Urbonaite et al. 18 for synthesis temperatures of 700 ◦ C to 1200 ◦ C who obtained densities of ∼2.1 g/cm3 . In the case of 500 ◦ C, a higher density was found presumably due to the higher sp3 content. In addition to the calculation of the density without taking into account the pore volumes, the mass density of the CDCs including the pore volume can be derived from the bulk plasmon position since this is proportional to the valence electron density 18 . The mass density can be calculated using ρ [g/cm3 ]

MC m ∗ ε 0 2 = Ep , 4NA¯h2 e2

(4)

with MC being the carbon molar mass, NA the Avogadro number, e the electron charge, ¯h Planck’s constant, ε0 the vacuum dielectric function, and m∗ the effective electron mass, defined as 0.87 m and m being the free electron mass. The mass densities derived from the position of the plasmon peak of the CDCs are included in Table 3. These results differ from the ones of Urbonaite et al. 18 . They found that the position of the bulk plasmon peaks does not vary with synthesis temperature and that all the calculated mass densities of the samples are ∼1.5 g/cm3 . We calculated considerably lower mass densities for all synthesis temperatures used to produce the CDCs studied here. However, they are also almost constant independently of the synthesis temperature. Since the density decreases with increasing synthesis temperature, but the pore volume increases (cf. Tab. 1) there must

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be two effects counteracting each other. If one would assume, that the volume occupied by the carbon atoms is constant, the decrease in density would mean that the pore volume should also decrease. However, we know that the amount of sp3 hybridized carbon atoms also decreases with increasing synthesis temperature (cf. Tab. 2). sp3 hybridized carbon atoms are packed more closely than sp2 hybridized ones (the density of diamond is higher than the density of graphite). We assume thus that the increasing amount of sp2 hybridized carbon atoms means that the volume occupied by the carbon atoms is not constant and the pore volume also increases with increasing synthesis temperature.

Raman Spectroscopy As quoted in Ferrari and Robertson 40 , the sp2 and sp3 content of amorphous carbons can also be deduced from the D- and G-peak properties of the Raman spectra in a qualitative manner. Raman spectra of the CDCs produced at several chlorination temperatures of the TiC source material are shown in Fig. 4. If not stated otherwise, we refer to Raman data at 532 nm. In order to allow a thorough evaluation of the spectra, D- and G-peaks have to be approximated by a fit of either Gaussian or Lorentzian shape. As proposed by Ferrari and Robertson 40 a fit to a combination of a Lorentzian for the D and a Breit-Wigner-Fano (BWF) peak, I(ω) =

2(ω0 –ω) 2 I0 1 + QΓ 2(ω0 –ω) 2 1+ Γ

,

(5)

which reduces to a Lorentzian for Q–1 → 0, for the G-peak is preferred over the fitting to either pure Gaussians or Lorentzians. Here, I0 is the peak intensity at peak position ω0 , Γ the full width at half maximum and Q–1 the BWF coupling coefficient. Furthermore, a linear background was subtracted from the spectra. The graphitic cluster size, La , is obtained from the relation between the D- and G-peak

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Table 4: Summary of the results from the Raman spectroscopy analysis of the CDCs. TemR perature in degrees refers to the chlorination temperature, CABOT Black Pearls 2000 are abbreviated as CBP and FWHM stands for Full Width at Half Maximum of the respective D- or G-peak. ID /IG 500 ◦ C 800 ◦ C 1000 ◦ C CBP

0.90 1.03 1.05 1.07

FWHMD (nm) 257.1 175.4 119.1 132.5

FWHMG (nm) 111.9 97.4 91.5 84.4

ωD max (s–1 ) 1343 1334 1337 1332

ωG max (s–1 ) 1586 1589 1592 1588

La (nm) 1.20 1.29 1.30 1.31

according to 40 , ID = C′ (λ) · L2a , IG

(6)

R and summarized in Table 4 for the CDCs and a reference material (CABOT Black Pearls

2000). C′ (λ) is a wavelength dependent parameter which can be estimated according to Urbonaite et al. 42 : C′ (λ) ≈

C0 + λC1 , L3a

(7)

with C0 = –12.6 nm, C1 = 0.033 and La = 2 nm. According to Urbonaite et al. 42 and our sp3 estimates from EELS it can be assumed that our CDCs are in Stage 2 of the Ferrari and Robertson 40 definition making it necessary to use eq. (6). It has to be considered in Table 4 that in an asymmetric BWF line the maximum intensity is not at ω0 as it would be in a symmetric Lorentzian line. Instead it is shifted depending on the sign of the asymmetry factor Q in eq. (5) to the left or right of ω0 . Thus, for a BWF line shape ωmax is at

ωmax = ω0 +

Γ . 2Q

(8)

Since the hybridization of the carbon atoms is more or less constant for chlorination temperatures over 800 ◦ C a decrease in the FWHMs is accompanied by a reduced deviation of the graphitic regions from ideality (ideal means: equal C-C bond lengths and bond angles

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of 120◦ ) 18,40,42,43 . The change in the ID /IG ratio is usually related to an amorphization or graphitization 36,40,42,44 in terms of a change in the sp2 /sp3 ratio. As expected in this temperature regime, 42 the Raman analysis shows only slight differences between the three CDC materials. Similarly, very small crystallite sizes result, showing the turbostratic nature of the carbons. Even if none of the materials can be seen to be in an highly ordered state, the pronounced higher FWHM for the CDC prepared at 500 ◦ C is an indicator for a slightly more unordered structure compared to the other ones 36,40,44 .

Results and discussion In the following, we will present the results of the structural characterization of the modeled microporous carbon skeletons and then discuss the simulated adsorption isotherms, first for the QMD approach and then for the platelet approach.

QMD-based modeling of the carbon skeleton For clarity it must be noted that the QMD-based modeling is used to obtain a porous carbon structure from a SiC, while removing the Si. This is inspired by the real CDC synthesis method. The resulting carbon structures are used later on to represent carbons materials with similar experimental obtained properties. Thus, a SiC-QMD derived carbon is used in this work to represent a TiC-CDC material. In a similar manner, Zhang et al. have successfully performed computational studies on TiC-CDC material based on SiC-derived structures. 45 Over 200 polymorphs of silicon carbide are known. 4H-SiC belongs to the technological most important ones and is used in our work as initial structure for modeling CDC-like structures. 4H means that 4H-SiC has a hexagonal structure and a stacking sequence consisting of four layers ABCB. Other major polytypes are 6H-SiC, which is also hexagonal and has a stacking sequence ABCACB, and 3C-SiC, which is a cubic polytype with the sequence ABC.

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The structures of these polytypes are depicted in Fig. 5. To obtain a microporous carbon structure, SiC was equilibrated at elevated temperatures, quenched to room temperature, and again equilibrated at room temperature after removing all Si atoms to allow for pore formation during the last step. The final structure was analyzed with respect to density, pore size, and pore size distribution. The apparent density of the final structure of the carbon skeleton is 1.0 g/cm3 and the diameter of the largest included sphere (also denoted as maximum pore size in the following) is 9.7 ˚ A. The apparent density obtained agrees well with the mass density from the EELS measurements (cf. Tab. 3). The pore size distribution is shown in Fig. 6 and ranges between 3.2 ˚ A and 9.8 ˚ A. To rule out possible artifacts, the last simulation step was performed 5 times to provide some statistical analysis of the pore size. The average maximum pore size of the final structure is 9.3 ˚ A with a standard deviation of 0.4 ˚ A which demonstrates that the suggested workflow is able to provide microporous structures in a reproducible way. Overall, the results agree well with the experimentally observed pore sizes (cf. Tab. 1) and literature data. 6 It is known from literature that pore sizes measured for SiC are very similar to those of TiC at 1000 ◦ C. 46 Influence of the polytype As noted above, there exist two other polytypes, which are of technological importance. It is therefore interesting to investigate, if and how the initial structure of the polytype influences the final porous structure. For this reason, simulations were performed for both 6H-SiC and 3C-SiC-based models as well. The density in both structures was the same as found for the carbon model based on 4H-SiC. The maximum pore size in the 6H-SiC-based structure converged towards a similar value (9.6 ˚ A) as obtained for the 4H-SiC-based model, while the maximum pore size in the 3C-SiC-based structure is with 9.0 ˚ A slightly reduced. The pore size evolution over the simulation time in the three polytypes is illustrated in Fig. 7. The results suggest that the structure of the SiC polytype affects the pore formation only

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slightly. However, since especially 4H-SiC and 6H-SiC are structurally closely related, huge differences in the porosity cannot be expected. Nevertheless, some influence on the pore size is observed for polytypes crystallizing in different crystal systems. Stability of the modeled porous structure To evaluate the stability of the porous carbon skeleton, the microporous structures were equilibrated over longer time spans and in the isothermal-isobaric ensemble. (a) First, we performed a MD simulation over additional 800 ps to check if the pore size is indeed converged after 200 ps. After 1 ns NVT simulation the pore size did not change significantly indicating that 200 ps indeed suffice for converging the structure regarding the porosity. (b) Furthermore, the carbon skeleton was equilibrated in the NPT ensemble to allow volume relaxation after NVT equilibration. Relaxation at room conditions using a NPT ensemble should yield results closer to experimental conditions. Since we are dealing with porous systems, using the NPT ensemble can cause physically unrealistic densities. However, the structure did not collapse during NPT equilibration, as one might have expected, and the volume decreased only slightly under NPT conditions. The maximum pore size after 1 ns simulation in the NPT ensemble was reduced by 0.6 ˚ A. (c) Finally, the system was equilibrated over longer simulation times in both the NVT and NPT ensemble. A 10 ns MD simulation in the NVT ensemble was carried out followed by 30 ns in the NPT ensemble. The maximum pore size varies during NVT and NPT equilibration between 9.5 ˚ A and 8.7 ˚ A. The final value after 30 ns NPT simulation is 8.9 ˚ A. The density increased during equilibration in the NPT ensemble from 0.98 to 1.10 g/cm3 . Results from (b) and (c) show that there is no drastic change neither in cell parameters nor in the maximum pore size corroborating that the simulation protocol described above allows to generate stable microporous structures.

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Influence of system size on the pore size In order to study the influence of the cell size on the maximum pore size, we increased the cell size and built a 2x2x2 supercell. Due to the larger system size, the system was allowed to equilibrate over longer time spans. After 5 ns NVT simulation, the maximum pore size increased somewhat by about 2 ˚ A to 11.4 ˚ A compared to the original cell. The supercell was then equilibrated for 10 ns in the NPT ensemble with a final maximum pore size of 9.7 ˚ A. Thus, despite doubling the system size in each spatial direction, the maximum pore size diameter basically remained the same. The density of the converged NPT structure is 1.1 g/cm3 which is in line with the results obtained for the original cell size. The fact that the maximum pore size diameter is not affected to a large extent upon increasing the cell size shows that the initial system size is sufficiently large for modeling the porosity which validates the simulation strategy pursued. Influence of simulation parameters The simulation protocol was systematically varied to test the influence of (a) temperature, (b) quench rate, and (c) presence of metal/metalloid atoms on the pore size. (a) In a separate set of simulations, the structure was heated to only 500 K instead of 2500 K for studying the impact of temperature. The quench rate was kept the same as in the initial workflow. With this approach, the maximum pore size is slightly reduced by about 0.5 ˚ A compared to the reference setup. This trend is also observed experimentally where chlorination at lower temperatures goes in line with smaller pore sizes. (b) Increasing the quench rate from 2.2 · 1012 to 1.1 · 1013 K/s had no impact on the maximum pore size diameter. This finding is different to the results obtained by Shi 11 and Palmer 7 who both observed a dependence of the pore size on the chosen quench rate. Possible reasons can be attributed to differently chosen initial and final temperatures and the use of different force field potentials. (c) In another set of simulations, Si atoms were removed right from the beginning to analyze how the presence of metal atoms affects the pore formation and if this procedure allows to tune the 15



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porosity of the final model structure. From a computational point of view, this approach is also interesting, because it provides insights into the transferability of the force field potential which could be used on other carbide precursors that contain metals or elements other than Si and C. A justification for this procedure is that the final structure may not depend on the metal partner itself, but only on the carbon skeleton. For this set of simulations, all MD simulations were performed in the NVT ensemble. When starting from the pure carbon backbone of SiC, the maximum pore size diameter becomes larger and increases by about 3 ˚ A to 12.7 ˚ A. Finally, a 200 ps run in the NPT ensemble was performed to evaluate the stability of the pores obtained with the modified set-up. After NPT equilibration the maximum pore size has slightly reduced to 11.3 ˚ A. For analyzing the temperature effect on structures without metal atoms, a second set of simulations was performed during which the structure was heated to only 500 K. In this case, the final pore size is reduced by about 3 ˚ A to 9.8 ˚ A, which is larger compared to the original set-up. Though purely pseudo-experimental, it seems to be possible to tune the pore size to a certain extent with the modified simulation protocol. Hybridization and ring size distribution Apart from the pore size analysis, the structures were analyzed with respect to the bonding situation within the porous framework to gain information about the hybridization of the carbon atoms and thus about the degree of graphitization. For analyzing the hybridization, the coordination number of each carbon atom was determined by counting the number of bond partners, while taking the local geometry into account. This means that carbon atoms either with three bond partners or with two bond partners enclosing an angle of 120 ±20 ◦ were considered as sp2 -hybridized. Carbon atoms with four bond partners or with three bond partners and a deviation of 10◦ or more from planarity were counted as sp3 -hybridized. The analysis showed that the hybridization depends on the simulation setup: For those setups, in which Si atoms have been removed after the quenching step (setup (A), (B), (C), cf.

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Supplemental Information), around 84% of the carbon atoms have been determined to be sp2 -hybridized, while the remaining 16% are sp3 -hybridized. The amount of sp3 -hybridized carbon atoms increases significantly, when Si is removed in the initial simulation box and the simulation protocol is applied to the pure carbon backbone. In this case, we also observed a dependence on the temperature to which the structures were heated before quenching. When heating to a higher temperature (2500 K), about 54% of carbon atoms are sp2 -hybridized and 46% are sp3 -hybridized, whereas, when equilibrating the model at a lower temperature (500 K), the final structure contains 79% sp2 -hybridized and only 21% sp3 -hybridized carbon. This trend is opposite to what has been observed in experiment, but in experiment the metal atoms are removed during the heating. Therefore, the simulation protocol used here does not reflect the experimental conditions. Equilibrating the simulation box in an NPT ensemble gives final structures with 75% sp2 -hybridization and 25% sp3 -hybridization. The same trend has been observed for the 2x2x2 supercells. Results for 6H-SiC- and 3C-SiC-based models are similar to the values obtained for the 4H-SiC-based structures suggesting that the SiC polymorph has no significant influence on the hybridization. The sp2 content of the latter (∼84%) is in good agreement with results of Urbonaite et al. 18 who found a relative sp2 content in CDCs between 83-98% based on experimental EELS studies. The detailed analysis of the coordination number for the different simulation setups is provided in the Supporting Information. The ring size analysis indicates the presence of five-, six-, and seven-membered rings. The majority of the identified rings (57-67%) are six-membered rings. A significant amount of seven-membered rings (32-39 % of all rings) has been detected, while only a minor fraction (6% at most) of five-membered rings was found. When varying the simulation parameters, the total number of rings is in the same range for the different setups, except again when all silicon atoms were removed from the beginning and the system was heated to the higher temperature (setup (D), cf. Supplemental Information). In this case, there are almost twice as much rings found, however with a similar distribution. Additional details on the ring size

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analysis can be found in the Supporting Information.

Structural properties of the platelet model It has been shown by Liu et al. 38 that the platelet model yields a good agreement to ethane and methane adsorption isotherms. With further modification of the pure carbon platelets with oxygen on the edges of the platelets it was even possible to predict correctly the experimentally observed water adsorption isotherm by means of simulations. 16 The previously generated structure served as input for a further thermalization at various temperatures ranging from 500-1500 ◦ C using bond-order based force fields. To account for the heterogeneity of the CDCs regarding their sp2 -/sp3 -hybridization, hexagonal/pentagonal ring ratios and amorphous/crystalline structure ranging from highly porous to fully dense, the platelet structure in Fig. 1 has been thermalized for several nanoseconds at temperatures the CDCs have been produced. The platelet diameter is chosen according to the graphitic cluster size found from Raman spectroscopy (cf. eq. 6 and tab. 4). Angle distributions, ring distributions, hybridization and the amount of bonded neighbors of the carbon atoms for different bond-order based force fields are evaluated: ReaxFF with the parametrizations of Chenoweth et al. 21 and Mattson et al. 22 as well as the LCBOP potential proposed by Los et al. 20 Hybridization and ring size distribution The main drawback of the ReaxFF variants is the prediction of an unphysically high amount of 3-fold rings of up to 40 rings per 1000 atoms using the Chenoweth et al. 21 and 343 rings per 1000 atoms using the Mattsson et al. 22 parameterization. Most controversial, the amount of 3-fold rings increases with higher simulation temperatures. Furthermore, structures generated with Chenoweth et al. 21 or Mattsson et al. 22 parameterization show a relative high amount of carbon atoms which have only two neighbors and are not incorporated into a 6-fold ring: 10%, 18% and 20% at 500, 1000 and 1500 ◦ C, respectively, for the Chenoweth 18


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et al. 21 parameterization and 18% at 800 ◦ C for the Mattsson et al. 22 parameterization. Approximately 76%, 62% and 54% of the carbon atoms are sp2 -hybridized and 12%, 20% and 26% are sp3 -hybridized when using the Chenoweth et al. 21 parameterization and simulation temperatures of 500, 1000 and 1500 ◦ C, respectively. While for the Mattsson et al. 22 parameterization 6% are sp2 -hybridized and 61% are sp3 -hybridized. Again, we counted as sp3 -hybridized atoms all atoms which have an out-of-plane angle of more than 10◦ . It should be noted that high out-of-plane angles of more than 40◦ occur mainly in systems where a 3fold ring is involved. In contrast, simulations employing the LCBOP potential and the same production routine show no 3-fold ring defects, a nearly complete incorporation of carbon atoms into 6-fold rings and fewer sp3 -hybridized carbon atoms are found. The amount of sp3 -hybridized carbon atoms increases with increasing temperature until it reaches a plateau at 29% for 3000 ◦ C as indicated in Fig. 8. Thus, as long as realistic structures should be represented it is crucial to use an accurate force field which represents experimental findings. However, if the pore size and its distribution are of utmost interest, it could be sufficient to represent only those correctly in the model. A recent overview of the capabilities of different force fields to describe amorphous carbons can be found in Ref. 47 Pore size distributions Pore size distributions for the amorphous carbons using the platelet approach and the LCBOP potential at various temperatures are illustrated in Fig. 9. The distribution of pores corresponds well with experimental results, where higher synthesis temperatures yield mesoporous CDCs 48 and lower temperatures yield microporous CDCs.

Calculation of adsorption isotherms In order to further validate the structures modeled, adsorption isotherms were computed for comparison with experimental data. CO2 adsorption isotherms were simulated for amorphous carbon structures prepared with both methods shown above. 19



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First, we will present the results for the SiC-based models. The elemental analysis of the carbons used showed that they contain between 2% and 5% of oxygen. Adsorption isotherms were therefore computed for both pure and partially oxidized carbon skeletons for analyzing how the adsorption properties are influenced by the presence of oxygen. Simulations were performed for 0%, 2%, and 5% oxygen in the carbon skeleton. Oxygen atoms were added in the respective percentage as C=O groups to potentially sp2 hybridized carbons (details are provided in the Computational Details section and the Supporting Information). Fig. 10 shows the results of the simulations (straight lines). The simulations indicate that the amount of adsorbed CO2 increases with an increasing percentage of oxygen. This can be attributed to a polarization of the carbon skeleton upon introducing the functional groups. The CO2 uptake in the pure carbon framework (0% oxygen) is throughout smaller compared to the experimental finding, while for the 5% oxygen model a larger specific volume of adsorbed CO2 is found. The best agreement with experimental measurements is obtained for the model containing 2% oxygen. An exemplary structure of carbon with 2% oxygen and adsorbed CO2 is shown in Fig. 11. At smaller relative pressures a slightly higher specific volume and at higher pressures a slightly smaller specific volume than in experiment is found, but the curve shape is overall in quite good agreement. Next, we will discuss the results for the platelet model. CO2 adsorption isotherms were calculated for a platelet model equilibrated at 1200 ◦ C and containing 0% and 2% oxygen, respectively. The results are illustrated in Fig. 10 (dashed lines). At small relative pressures, a higher uptake of CO2 is found compared to the experimental data and the corresponding QMD-based models, while at a high relative pressure a smaller specific volume has been obtained. This behavior is similar to the one observed for the QMD-derived models, but is distinctly more pronounced leading to a curvature which looks flatter than the experimental one. Regarding the influence of the oxygen content, the trend is similar as observed for the QMD-based models and a high oxygen content goes in line with a higher specific volume of adsorbed CO2 . The impact of the partial oxidation of the carbon skeleton is, however, 20


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somewhat smaller compared to the QMD-based model. Overall, the QMD-based model containing 2% oxygen shows the best agreement with the experimental data and the slope of the isotherm also fits nicely.

Conclusion Two different approaches for modeling CDC based microporous carbon have been presented. The modeled structures have been thoroughly characterized with respect to structural features, especially their porosity, and the results agree well with experimental data. In the spirit of a pseudo-mimetic approach, we used quenched molecular dynamics to model microporous carbon starting from a SiC precursor. Within this approach, we have also studied to what extent different polytypes of the carbide precursor affect the porosity of the carbon skeleton and indeed observed some differences in the pore size for different crystalline systems. Simulations in the NPT ensemble over longer time spans confirmed that stable microporous structures can be modeled using the suggested approach. The analysis of the hybridization in the final structures agrees well with experimental data and confirms the validity of the model structures. Furthermore, simulations of adsorptions isotherms have shown that functionalization of the carbon backbone with carbonyl groups influences adsorption properties. The best agreement with experimental data has been found for a partially oxidized carbon skeleton containing 2% oxygen. Our second approach to model amorphous porous carbon aimed at preserving the microcystallinity found in real structures by starting from a pure platelet like model and imposing constraints known from experiment such as the graphitic cluster length or density. The sp3 to sp2 ratio can be adjusted via the temperature of the thermalization as demonstrated in Fig. 8. Our results suggest that neither ReaxFF with the parameterization of Chenoweth 21 nor the parameterization of Mattson 22 reproduces realistic amorphous carbons since the formation of energetically unfavourable 3-fold rings is overrated using these force fields. However, if

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only the porous structure is important, approaches using ReaxFF give reasonable estimates. In general, both approaches used create morphologically realistic molecular models of amorphous carbon. It has been shown that both theoretical approaches are able to model experimentally produced CDCs. However, the two different approaches offer different ways in which experimental results are incorporated into the models. They allow, depending on which features should be considered, e.g., the graphitization or pore size distribution, an easy-to-adjust parameter. The pore sizes can to some degree be influenced by the simulation protocol. In particular, we have been able to show that the pore sizes can be tuned by running the simulations at different temperatures such as in experiment. A comparison with experimental data has demonstrated that the structures generated with both approaches have the same properties as CDCs sythesized in the laboratory. The models built can be used to further study effects of this important structural class.

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Figures

Figure 1: Random platelet structure consisting of 25868 carbon atoms created with our approach.

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(a)

(b) Figure 2: High resolution nitrogen sorption analysis of titanium carbide derived carbon (TiCCDC) using the instrument Autosorb-1P by Quantachrome Instruments after degassing the samples in vacuum for 12h at 250 ◦ C. The carbons were synthesized by selective etching of titanium carbide with chlorine at temperatures ranging from 500 ◦ C to 1000 ◦ C. Figure (a) presents the adsorbed volume of nitrogen at standard conditions as a function of the partial pressure and figure (b) shows the differential pore volume as a function of the pore size.

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Figure 11: Porous carbon obtained from setup (A) with 2% oxygen and adsorbed CO2 at a relative pressure of 0.0282. Color code: red - carbon backbone, green - C=O groups, blue CO2 .

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Acknowledgement The AktivCAPs project which forms the basis of this paper has been funded by the German Federal Ministery of Education and Research under grant no. 03SF0430. The responsibility for the contents of this paper lies with the authors. S. S. thanks Dr. Andreas Bick at Scienomics for helpful discussions.

Supporting Information Available Details of the various simulation set-ups within the QMD approach and the MC calculations and results of the maximum pore size analysis, density and cell parameters, ring size and coordination number analysis are provided in the supporting information. This material is available free of charge via the Internet at http://pubs.acs.org/.

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