Amorphous Porous Carbon

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Aligned Carbon Nanotubes/Amorphous Porous Carbon Nanocomposite: A Molecular Simulation Study Kisung Chae, and Liping Huang J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 10 Mar 2015 Downloaded from http://pubs.acs.org on March 11, 2015

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The Journal of Physical Chemistry

Aligned Carbon Nanotubes/Amorphous Porous Carbon Nanocomposite: A Molecular Simulation Study Kisung Chae and Liping Huang* Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, United States *

Email: [email protected]

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ABSTRACT A nanocasting method in molecular dynamics (MD) simulation was developed to mimetically synthesize nanocomposites that contain aligned carbon nanotubes (CNTs) as fillers in an amorphous porous carbon (a-PC) matrix. Structural features of aligned CNTs/aPC nanocomposites such as the crystallinity of the CNT and the matrix as well as the interfacial bond density between these two components can be controlled by the synthesis parameters, for instant, (i) the interaction strength between a template and carbon atoms, and (ii) the quench rate used in the mimetic nanocasting process. Our study shows that properties such as Young’s modulus and buckling resistance of aligned CNTs/a-PC nanocomposites can be tuned via the mimetic synthesis process. These mimetic models allow us to quantify the relationship between the structure and properties of aligned CNTs/a-PC nanocomposites, and to identify the optimal synthesis parameters for desired structure and properties.

Keywords: Mimetic synthesis, carbon nanotube, porous carbon, nanocomposite, structureproperty relation


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1. INTRODUCTION Composites using carbon nanotubes (CNTs) as fillers have been extensively investigated due to the superior mechanical properties of CNTs, including high stiffness and high strength1. However, realization of the full potential of CNT-reinforced composites has been hindered by difficulties in achieving a high degree of dispersion of CNTs in the matrix, primarily due to CNTs’ high affinity for one another (i.e., their tendency to aggregate in bundles and agglomerates) and their rather weak interaction with the matrix. Great efforts have been made by many groups to rectify these issues. For example, functionalization has been proved to enhance the interfacial bonding and dispersion of CNTs. Lee et al.2 fabricated various multi-walled CNT/polystyrene (MWCNT/PS) nanocomposites, and showed that functionalization yields better dispersion and enhanced mechanical properties such as hardness and Young’s modulus. Wang et al.3 reported enhanced stiffness and tensile strength of epoxy resin by addition of MWCNTs functionalized with ionic liquids. However, it should be noted that nanocomposites containing functionalized CNTs (f-CNTs) are usually synthesized by in situ polymerization, so that there is not much control in the arrangement of CNTs in the matrix. Irradiation is another method often used to improve the properties of nanocomposites by increasing covalent crosslink density. Enhanced mechanical properties by irradiation have been reported in various carbon nanostructures such as CNT bundles4, MWCNTs1,5 and bilayer graphene sheets6. More examples can be found in review papers7,8 and references therein. It should be noted, however, that care must be taken to optimize the balance between defect concentration and crosslink density due to the destructive nature of irradiation. After intensive investigations, some general rules have



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been found in terms of irradiation energy and dosage9. Unfortunately, the irradiation method suffers from the shallow penetration depth. It was reported that even for a thin bundle composed of 19 single-walled CNTs (SWCNTs), inner CNTs were barely affected while a significant damage occurred on outer CNTs4. On the other hand, template-based fabrication is a useful way to generate CNT-reinforced nanocomposites in a controlled manner. First of all, CNTs are well-aligned with each other by the template. Moreover, the structure of CNT arrays can be controlled by various factors such as temperature, catalyst, and source concentration10–12. In addition, this method yields more uniform structure compared to the irradiation method. It is also advantageous that the fabricated composite can be scaled with the dimension of the template. For instance, Li et al.13 fabricated highly ordered CNT arrays by pyrolysis of acetylene on cobalt within hexagonal close-packed nanochannels in an anodized alumina template with channel diameter ranging from 10 to 350 nm, with length up to 100 µm. Other mesoporous inorganic templates including MCM4114 and SBA-1515 have also been used for the CNT array fabrication. Chemical vapor deposition (CVD) is another widely used technique to generate aligned CNTs/carbon nanocomposites, in which vertically aligned CNTs are coated with high density amorphous carbon16–18. Studies so far have shown that it is difficult to control the dispersion of CNTs and their interfacial bonding with the matrix. It would be even more challenging to quantify them and their effects on the properties of CNT-reinforced nanocomposites in experiments. To this end, atomistic simulations such as molecular dynamics (MD) can play an important role in improving the design of CNT-reinforced nanocomposites, by illustrating the


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structure-properties relation at the atomic scale. Furthermore, a systematic study can be performed much more easily in simulations to establish the relations among synthesis conditions, structures and properties, as sample preparation and mechanical tests are timeconsuming and costly in experiments. However, most of existing models of CNT-reinforced nanocomposites are handmade. For example, Fyta et al.19 prepared the matrix first and then dug out a cylindrical volume from the simulation box, followed by insertion of a pristine CNT. The intrinsic structural features in nanocomposite evolved during the synthesis process are not captured in such models. On one hand, covalent interfacial bonds are not considered, which makes the reinforcement effect negligible19–21. On the other hand, perfect CNTs are usually used, even though various amounts of defects exist in real materials. These deficiencies in CNT-reinforced nanocomposite models seriously limit the power of atomistic simulations in understanding their synthesis-structure-properties relations. Recently, we developed a model template-based nanocasting method in MD simulations22 that can be used to mimetically synthesize aligned CNTs/amorphous porous carbon (a-PC) nanocomposites with tunable structure by controlling synthesis parameters such as template-carbon interaction strength (εt) and quench rate (qr). The mimetic nanocasting procedure follows the same steps as in experiments – pre-synthesis of template, infiltration of source material, pyrolysis, and removal of the template. The mimetically synthesized CNTs inherently have some defects and interfacial bonds with the matrix, which can be controlled by the synthesis conditions. In this study, we will use these mimetic models to quantify the relationship between the structure and mechanical properties of aligned CNTs/a-PC nanocomposites, and to identify the optimum synthesis



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parameters for desired structure and properties such as high stiffness and high buckling resistance under compressive loading. A complete feedback loop among synthesis, structure and properties will speed up the development and application of aligned CNTs/a-PC nanocomposites in many fields of technological importance.

2. COMPUTATAIL DETAILS 2.1. Sample Preparation Aligned CNTs/a-PC nanocomposites were generated by using the mimetic nanocasting method as described in our earlier work22. Briefly, during the quench molecular dynamics (QMD) process23,24, carbon atoms interact with a cylindrical template to form the CNT first, then to form the a-PC matrix in the region not occupied by the template. Interaction among carbon atoms was described by the reaction state summation (RSS) force field for carbon24, and the 11-5 Lennard-Jones (LJ) potential was used to describe the interaction between the cylindrical template and each carbon atom, by following the work of Cheng25. After the quenching process, any remaining singlet carbons were removed from the system, and then the as-quenched sample underwent a stress relaxation in the NPT (constant number of atoms, constant pressure and constant temperature) ensemble. Each of the simulation box dimensions was independently varied according to the individual normal stress, i.e., σxx, σyy and σzz, which were set to zero. In all cases, temperature and pressure were controlled via the Nosé-Hoover scheme26,27, and numerical integration of each atom’s trajectory was performed using the velocity Verlet algorithm28. To get better statistics, five parallel


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samples were generated under each condition. Synthesis parameters, such as the lateral CNT spacing (LCNT), the template-carbon interaction strength (εt) and the quench rate (qr) of the QMD process, were varied to obtain samples with different structural features. qr of 1 corresponds to 29.2 K/ps as in our previous study22, and different factors of it (qr×29.2 K/ps) were used to vary the cooling rate during the QMD process. Most of the samples were generated with qr of 1 in this study, unless otherwise specified. Lateral box sizes (Lx and Ly) of 4, 5 and 6 nm were used to change LCNT, and the simulation box dimension along the CNT axis (Lz) was fixed at 8 nm in all cases. Periodic boundary conditions were applied in all three directions of the orthogonal simulation box, making the aspect ratio of the CNT infinite. The template radius (rt) was chosen as 1 nm throughout the paper, giving rise to CNT with a diameter of 2 nm. As the number of carbon atoms consisting of CNT (NCNT) significantly varies due to synthesis conditions22, especially due to εt, we fine-tuned the initial carbon density (ρ0) before quenching to make the final matrix density (ρmatrix) constant for samples generated under different conditions. The ρmatrix is defined as

ρ matrix =

N total − N CNT , Vtotal − VCNT

(1)

where Ntotal is the total number of carbon atoms in the system. Vtotal and VCNT are volumes of the simulation box and the CNT formed during the QMD process, respectively. Here the VCNT is calculated as a cylinder with a radius of rt+0.5×rCC, where rt and rCC are the

template radius and the covalent bond length of carbon (1.42 Å), respectively. As a result,



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all the samples have ρmatrix of ~0.71 g/cm3 with sufficiently small deviation. On the other hand, the density of the whole system (Ntotal/Vtotal) varies with the synthesis conditions such as LCNT and εt. For example, samples generated with LCNT of 4, 5 and 6 nm have densities in the range of 0.82–0.88, 0.77–0.81 and 0.76–0.78 g/cm3, respectively. In each case, the density increases with the increase of εt.

2.2. Structure Characterization To understand the structure-properties relation in aligned CNTs/a-PC nanocomposites, we quantitatively measured the following structural features: crystallinity of the CNT (XCNT) and the matrix (Xmatrix), as well as area density of interfacial bonds between these two components (nbonds). Quality of graphitic structure is quantitatively assessed by crystallinity (X) defined as

X = 2×

N hex , NC

(2)

where Nhex and NC are the numbers of hexagons (6-membered rings) and constituting carbon atoms of the structure, respectively. For a perfect graphitic structure such as CNT and graphene, X would be 1 since each hexagon is composed of two carbon atoms in an ideal honeycomb structure. XCNT and Xmatrix were calculated according to the above equation within volumes of interest, i.e., in and outside of VCNT, respectively. We also calculated nbonds as a measure of the structural integrity, which is essential for load transfer between the CNT and the matrix. Any two atoms connecting the CNT and the 8 ACS Paragon Plus Environment

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matrix are considered to form an interfacial bond: one on the CNT and the other one in the matrix. nbonds is calculated by the number of bonds divided by the surface area of the CNT formed during the QMD process.

2.3. Calculation of Mechanical Properties Uniaxial compression tests were performed on as-prepared samples after the stress relaxation as described in Section 2.1. This was done by shrinking the box dimension along the CNT axis (z-axis) with a constant strain rate of 2.83 ns-1, while keeping the lateral directions stress-free (i.e., σxx=σyy=0). Young’s modulus (ENC) in the axial direction of the nanocomposite was calculated by taking the slope of a fitted line of the linear region of the stress-strain curve (up to 1% strain). We also investigated the load transferability between the CNT and the matrix in nanocomposites by measuring the potential energy change (∆PE) due to deformation at a compressive strain of 2% where most of the samples deviate from the linear elastic deformation. We differentiated the ∆PE in the CNT and in the matrix so that the behavior of each component can be seen individually. Furthermore, the relationship between the structure and buckling resistance of aligned CNTs/a-PC nanocomposites was studied, in comparison with that of a pristine CNT array.

3. RESULTS AND DISCUSSION 3.1. Structural Features



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Figure 1 shows a mimetically synthesized aligned CNTs/a-PC nanocomposite, in which the CNTs in a square array are embedded in the a-PC matrix. It can be seen that the space between CNTs is filled with the a-PC, similar to the densified aligned CNTs studied in experiments29. Moreover, there are some covalent bonds between the CNT and the matrix depicted as green balls in Figure 1. This is in stark contrast to previously reported computational models30–33, in which no interfacial bonds are formed and only van der Waals interaction is allowed between the CNT and the matrix. Our nanocomposite models are more realistic in that the CNTs contain tunable defect concentration originated from synthesis and that the CNT and the matrix are covalently bonded as in experiments34.


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Figure 1. Snapshot of a mimetically synthesized aligned CNTs/a-PC nanocomposite. Carbon atoms in the CNT and in the matrix region are drawn as red and grey balls, respectively. Green balls indicate the atoms making the interfacial bonds between the CNT and the matrix. The cutoff for C-C bonds is 1.8 Å. This sample was generated by the synthesis parameters of LCNT=4 nm, εt=2.0 eV, ρ0=1.07 g/cm3 and qr=1 (29.2 K/ps).



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Figure 2. Correlation between XCNT and nbonds. Symbols and colors vary with LCNT and εt, respectively, as indicated by the legend and the color bar. Inset shows the atomic configurations of nanocomposites synthesized with εt=1 eV and εt=5 eV, respectively.


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CNT crystallinity (XCNT) and interfacial bond density (nbonds) are highly correlated as seen in Figure 2; these two properties are inversely proportional to each other, indicating that interfacial bonds form by making defects on the CNT wall.

Figure 2 also shows that

XCNT increases as the template-carbon interaction (εt) increases, with the increment getting

smaller with higher εt. Note that the lateral CNT spacing (LCNT) has little effect on these properties, so it can be used as one of the parameters to tune the matrix density (ρmatrix) without affecting other structural features. As detailed in our previous study22, the εt in our model is relevant to the various combinations of template material and carbon source14,15,35,36, while the qr reflects processing conditions such as synthesis temperature and heat treatment in experiment37,38. Therefore, different structural features of aligned CNTs/a-PC nanocomposites can be independently controlled by varying proper synthesis conditions. We demonstrate this by showing an example below. We first performed the mimetic nanocasting procedure to an intermediate temperature that is low enough to form the CNT yet too high to form the a-PC matrix. Then, the process was continued to room temperature by using various qr values. Potential energies (PEs) during the cooling process are shown in Figure 3. For high enough εt (e.g., 3 eV or higher), there are two drops in the PE during the synthesis process, corresponding to the formation of the CNT and the a-PC matrix, respectively. The intermediate temperature can be chosen from the plateau between the two drops. The final PE varies with qr, indicating that the graphitic morphology of the a-PC matrix is different. In other words, the fraction of sp2 carbon is increased as a slower qr is used, consistent with the previous study39. As a result, XCNT and nbonds are invariant

regardless of qr; however, Xmatrix significantly decreases with increasing qr as seen in Figures 4 and 5. This shows that Xmatrix can be controlled independent of XCNT. 13 ACS Paragon Plus Environment


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Figure 3. Potential energy (PE) variation of the system during the quench process: samples are quenched with the same rate of qr=1 down to T*=0.9125 eV/kB, and then to room temperature at various rates indicated in legends. LCNT and εt are 5 nm and 4 eV, respectively.


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Figure 4. Structure characterization of nanocomposites as a function of qr: (a) crystallinity of the CNT (XCNT ) and the matrix (Xmatrix), and (b) interfacial bond density (nbonds). Each data point is averaged over 5 parallel samples. All the samples were generated with LCNT of 5 nm and εt of 4 eV.



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Figure 5. Snapshots of aligned CNTs/a-PC nanocomposites generated with different qr: (a) 0.5, (b) 1, (c) 2 and (d) 4. Color-coding is same as in Figure 1. In this case, LCNT of 5 nm and εt of 4 eV were used.

3.2. Mechanical Properties Young’s moduli of the nanocomposites (ENC) with various LCNT and εt are shown in Figure 6. Overall, the moduli are higher for samples with smaller LCNT. This is mainly due to the increase in the CNT volume fraction (19.6%, 12.6% and 8.7% for LCNT of 4, 5 and 6 nm, respectively) since other structural features such as XCNT and nbonds remain unaffected by LCNT as seen in Figure 2. For all LCNT studied in this work, εt has a larger effect on ENC in

the low value range than in the high value range. For example, for LCNT of 4 nm, ENC increases with εt up to 3 eV, then becomes more or less constant with further increase of εt. At low εt, ENC increases mainly due to the increased XCNT with increasing εt. At high εt, improvement in XCNT become marginal while nbonds continuously decreases with εt, so it has 16 ACS Paragon Plus Environment

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a less influence on ENC. Our results indicate that defects on CNT, if the concentration is small, would not severely deteriorate the structural robustness of the aligned CNTs/a-PC nanocomposite. This is consistent with previous MD results that effects of small defects such as vacancy and Stone-Wales defects on the elastic properties of the CNT are not significant unless the concentration is very high40.

Figure 6. Young’s modulus of aligned CNTs/a-PC nanocomposites (ENC) as a function of the interaction strength (εt). Each data point is averaged over 5 parallel samples. All samples are generated with qr of 1.



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Figure 7 shows potential energy changes (∆PE) for the CNT and the matrix between deformed (2% strain) and as-relaxed samples as a function of LCNT and εt. It appears that there is little influence of LCNT on ∆PE. On the other hand, ∆PE varies significantly with εt. For all εt values considered in this study, ∆PE for the CNT is positive and monotonously increasing with εt, indicating that the CNT takes up more external load as εt increases. On the other hand, the ∆PE for the matrix is positive for low εt, but becomes zero and then negative as εt increases. This indicates that the contribution of the matrix to the load carrying capability of the nanocomposite becomes smaller as εt increases, and even relaxes during compression in samples synthesized with high εt. This can be attributed to the decrease of nbonds with increasing εt as shown in Figure 2, reducing the load transferability from the CNT to the matrix.


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Figure 7. Change in potential energy (∆PE) between deformed (2% strain) and as-relaxed samples as a function of the interaction strength (εt) for different LCNT: 4 (■), 5 (●) and 6 nm (▴). Filled and empty symbols correspond to the CNT and the matrix, respectively.

Figure 8a shows that ENC decreases with increasing qr, clearly indicating that the Young’s modulus of the aligned CNTs/a-PC nanocomposite can be further tuned by varying the structure of the matrix. This is because a slower quench rate would lead to larger graphitic fragments in the matrix and better alignment to the CNT as seen in Figure 5. As a result, the matrix can contribute better in carrying the external load for the following 19 ACS Paragon Plus Environment


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reasons. The ordered graphitic layer around the CNT can have a similar effect as the multilayer formation, which was shown to enhance the compressive stiffness and strength of CNT foam (CNT arrays exposed to a post-growth chemical vapor deposition treatment)18. Furthermore, the increased graphitization is expected to improve the stiffness of the matrix itself (see Figure 8b), consistent with previous observations in densified aligned carbon nanotube films17.

Figure 8. Young’s moduli as a function of quench rates (qr). (a) CNT/a-PC nanocomposite. Each data point is averaged over 5 parallel samples. All the samples were generated with LCNT of 5 nm and εt of 4 eV. (b) Direct-quenched a-PC. Each data point is averaged over 5

parallel samples in three directions (x-, y- and z-axis). Density of the direct-quenched samples is chosen as 0.8 g/cm3, close to that of CNT/a-PC nanocomposites.


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Figure 9 shows stress-strain curves of the nanocomposites up to a strain of 0.2, in comparison with a pristine CNT array without a microporous matrix. The CNT array shows a higher Young’s modulus (212.35 GPa) compared to all of the nanocomposites studied here. However, it is prone to buckle at a small strain (0.02), and then the stress drops precipitously. On the other hand, all of the nanocomposites do not show such a large drop in stress even at higher strain levels. The stress actually keeps increasing with strain, indicating that the matrix helps support the CNT and prevents the nanocomposite from buckling. Therefore, aligned CNTs/a-PC nanocomposites are more robust against buckling compared to the pristine CNT arrays. Figure 9 also shows that the compressive strength of the nanocomposites changes with the εt used during the synthesis process. The compressive strength initially increases with εt between 1 and 2 eV, then decreases with increasing εt and gradually levels off. This is in line with the previous discussions that an optimum defect concentration is needed for the best performance of aligned CNTs/a-PC nanocomposites. In other words, while too low εt (e.g., 1 eV) makes the sample too soft, too high εt (e.g., 5 eV) would undermine the load transferability between the CNT and the matrix. Under the synthesis conditions we used (qr of 1 and ρmatrix of ~0.71 g/cm3), it seems that εt ranging from 2 to 3 eV gives a good balance between stiffness and buckling resistance of aligned CNTs/a-PC nanocomposites.



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Figure 9. Stress-strain curves of CNT and nanocomposites (NC) synthesized with different εt values, in comparison with that of a pristine CNT array. The curves for NCs are averaged

over 5 parallel samples, and LCNT of 4 nm was used in all cases.

Snapshots of selected samples at various strains are shown in Figure 10. Two samples with different structural features (XCNT, nbonds) were chosen - sample A (0.82, 0.037 Å-2) and sample B (0.96, 0.008 Å-2). That is to say, sample A has more defects on the CNT and higher interfacial bond density compared to sample B. Sample A and sample B were made with εt of 3 and 5 eV, respectively, while the rest of the synthesis conditions were kept the


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same for both samples (qr of 1 and LCNT of 4 nm). Prior to any deformation (snapshots at 0 strain in Figure 10), for CNTs in the nanocomposites, it can be seen that atoms adjacent to defects have higher potential energies compared to those in defect-free regions. Upon compression to 0.05 strains, the defect-free regions corrugate a little bit, making wrinkles connecting the defect sites. By doing so, most of the defect-free regions can remain undeformed. Upon further compression up to 0.15 strains, sample A and B behave quite differently. In sample B, high energy regions, where defects originally resided, experience the most deformation. On the other hand, the deformation is much more uniform throughout the CNT in sample A. This is the reason that the axis of the CNT in sample A is less deviated from the original axis compared to that in the sample B. In both cases, the deformation of the CNT is quite different from that of the pristine CNT array as seen in Figure 10c, where the deformation is concentrated at a localized region indicated by the high potential energy, making the system very unstable. This clearly shows that the interfacial bonds play a critical role in transferring the load from the CNT to the matrix and reducing the buckling propensity of aligned CNTs/a-PC nanocomposites.



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Figure 10. Snapshots of CNTs under compression in (a) sample A, (b) sample B and (c) CNT array with the strain value indicated at the bottom of each pane. Each carbon atom is color-coded by its potential energy accordingly to the color bar on the lower right corner. Atoms in the matrix are not shown for clarity. In all cases, LCNT is 4 nm and qr is 1.

4. CONCLUSION


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Using molecular dynamics simulations, we performed a systematic study on the mimetic synthesis, structural characterization and mechanical properties of aligned CNTs/a-PC nanocomposites. Our results showed that structural features such as the crystallinity of the CNT and the matrix in the nanocomposite as well as the interfacial bond density between these two components can be controlled by synthesis parameters: such as the interaction strength between the template and carbon atoms, and the quench rate used during the mimetic nanocasting process. Moreover, independent tuning of the structural features of the CNT and the matrix can be accomplished by varying synthesis conditions. We also showed that the mechanical properties of aligned CNTs/a-PC nanocomposites such as Young’s modulus and buckling resistance can be controlled via the above mentioned structural features. These mimetic models can be utilized to explore the synthesis-structure-properties relations for multi-functional applications of aligned CNTs/a-PC nanocomposites to take advantage of their extraordinary mechanical, thermal and electrical properties.

AUTHOR INFORMATION Corresponding Author *E-mail [email protected] (L.H.). Notes The authors declare no competing financial interest

ACKNOWLEDGMENTS This work is supported by NSF under Grant No.: CHE-1012719. Molecular dynamics



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simulations were performed using LAMMPS41 on supercomputers in the Center for Computational Innovations (CCI) at RPI.

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Table of Content Graphic


Page 32 of 43

z

LC

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45


NT

Page 33 of 43

y

x

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

XCN T

1.0 Journal of Physical ChemistryPage 34 of 43 The

0.9

εt

0.8

0.7 0.6

εt

εt

0.5 0.4 ACS Paragon Plus Environment 0.00 0.02 0.04 0.06 0.08 0.10

0.12

nbonds −2

1 Journal of Physical Chemistry Page 35 of 43 The 1 2 3 4 5 6 7 8 9 10 11 12 13

PE (eV/Atom)

0 -1

qr=0.5 qr=1.0 qr=2.0 qr=4.0

-2 -3 -4 -5 -6 -7ACS Paragon Plus Environment 1.8 1.5 1.2 0.9 0.6 0.3 0.0 Temperature (eV/kB )

Page 36 of 43

XCN T Xmatrix

nbonds −2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20



qr

(a) 0.5 Page 37 of 43

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(b) 1

(c) 2



(d) 4

1 2 3 4 5 6 7 8 9 10 11 12 13

EN C

The Journal of Physical Chemistry Page 38 of 43


εt

Page 39 of 43 The Journal of Physical Chemistry

ΔP E (eV/atom)

0.01 1 2 3 4 5 6 7 8 9 10 11 12 13

0.00

-0.01

4 nm 5 nm 6 nm


1

2

3

εt (eV)

4

5


1 2 3 4 5 6 7 8 9 10 11 12 13

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$

ACS Paragon qr Plus !"#Environment qr !"#

The Page 41 of 43 Journal of Physical Chemistry

1 2 3 4 5 6 7 8 9 10 11


(a) sample A


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(b) sample B

(c) SWCNT

-6.5

-7.0


-7.5

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Amorphous Porous Carbon

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