The influence of boundary layer on the growth kinetics of carbon nanotube forests

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The influence of boundary layer on the growth kinetics of carbon nanotube forests Jaegeun Lee a, Eugene Oh a, Teawon Kim a, Jeong-Hoon Sa a, Sung-Hyun Lee a, Junbeom Park a, Dustin Moon a, In Seok Kang a, Myung Jong Kim b, Seung Min Kim c, Kun-Hong Lee a,* a Department of Chemical Engineering, Pohang University of Science & Technology, 77 Cheongam-Ro, Nam-Gu, Pohang, Gyeongbuk 790-784, South Korea b Soft Innovative Materials Research Center, Korea Institute of Science and Technology, Eunha-ri San 101, Bongdong-eup, Wanju-gun, Jeollabuk-do 565-905, South Korea c Carbon Convergence Materials Research Center, Korea Institute of Science and Technology, Eunha-ri San 101, Bongdong-eup, Wanju-gun, Jeollabuk-do 565-905, South Korea

A R T I C L E I N F O

A B S T R A C T

Article history:

The growth of carbon nanotube (CNT) forests has been limited to the centimeter scale due

Received 12 January 2015

to insufficient understanding of their growth kinetics. To investigate the growth kinetics of

Accepted 22 May 2015

CNT forests, we characterized the mass transport phenomena arising during CNT forest. We formulated the hypothesis that such growth is mass transport limited and proposed a model describing this mass transport. According to our model, the effects of diffusion boundary layers on the growth rate are significant. The initial growth rate is expected to increase with the velocity of the bulk gas flow as the boundary layer thickness decreases. To test this prediction, CNT forests were grown at various total gas flow rates in the range 170–1700 sccm, which correspond to flow velocities in the range 0.79–to 7.9 cm/s. The initial growth rate was found to increase from 1.4 mm/h to 3.5 mm/h as the total flow rate increases from 170 sccm to 1700 sccm. Thus there is a clear inverse proportionality between the initial growth rate and the thickness of the diffusion boundary layer, which confirms that the growth of CNT forests is mass transport limited. These results provide new insight into the growth kinetics of CNT forests.  2015 Elsevier Ltd. All rights reserved.

1.

Introduction

The chemical vapor deposition (CVD) method for the growth of carbon nanotubes (CNTs) on a substrate is now a familiar technique in the field of CNT research. Particularly, when CNTs are grown with high areal number density, they stand on the substrate forming a vertically aligned structure known

* Corresponding author: Fax: +82 54 279 8298. E-mail address: [email protected] (K.-H. Lee). http://dx.doi.org/10.1016/j.carbon.2015.05.080 0008-6223/ 2015 Elsevier Ltd. All rights reserved.

as a CNT forest. The CNTs in a CNT forest have a high degree of alignment with few impurities and their growth is more controllable than with other growth techniques. Thus, CNT forests have a variety of potential applications such as field emitters [1], super-capacitor electrodes [2], membranes [3] and strong fibers [4,5], and are of particular interest as model systems.

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There have been steady needs to grow tall CNT forests because many applications of CNT forest require long CNTs; for example, in fiber applications the tensile strength increases as the component CNTs become longer [6]. The height of CNT forest have shown a gradual advance from the millimeter scale to the centimeter scale [7–10], up to about 2 cm [11]. In principle, however, CNTs can grow much longer. To date, the longest CNTs ever reported are 55 cm in length (without forming a forest structure) [12]. In this case, the CNTs grew according to the so called ‘‘kite mechanism’’ in which the catalysts float like kites while producing the CNTs [13]; remarkably, their growth rate is as high as 5000 lm/min. Looking back at the history of carbon research, the growth of vapor grown carbon fibers (VGCFs), which contain a CNT-like structure along their axes, is particularly noteworthy. Such fibers were produced on a centimeter scale within a few minutes with growth rates as high as 2100 lm/min [14], 30000 lm/min [15], and even 150000 lm/min [16] from metal catalysts floating in the vapor phase. In contrast, the growth rates of CNT forests are less than 100 lm/min. The marked difference between the growth rates of the two systems is illustrated in Fig. 1. Why is the growth of CNTs in forest structures so slow even though individual CNTs can grow much faster? Previous research into the growth of CNT forests has mostly focused on increasing the growth lifetime. As a result, catalyst lifetimes have been extended to as long as 10 hours,

but the reported growth rates are so low that several tens of hours would be required to grow a centimeter-scale CNT forest with the reported growth rates, as shown in Table S1. Significant increases in the heights of CNT forests are not likely to be achieved by merely extending the growth lifetimes. Nevertheless, the growth rates of CNT forests have not received much research attention. The understanding of the growth kinetics of CNT forests is so undeveloped that even the rate limiting step of their growth remains unclear. The purpose of this study was to investigate the growth kinetics of CNT forests and to identify the rate limiting step of their growth. Here, we made a hypothesis that the growth is mass transport limited, because the reactant molecules travel a considerable distance to the catalysts at the bottom of CNT forests, so the growth of CNTs in CNT forests is much slower than in a floating catalyst system. A model describing this mass transport was developed and tested experimentally. According to this model, the effects of the diffusion boundary layer on the growth rate are significant; the importance of this factor has not previously been recognized. By correlating the initial growth rate and boundary layer thickness, we verified that the growth of CNT forests is mass transport limited. An as-grown 1.8 cm tall CNT forest was characterized with SEM, TEM, and Raman analysis, and its component CNTs were found to be uniform and of fine quality despite the long growth time.

2.

Fig. 1 – Comparison of the growth of CNTs in the forest and floating catalyst system. (A color version of this figure can be viewed online.)

Experimental

A silicon wafer was used as the substrate for the growth of the centimeter-tall CNT forests. The substrate was first coated with a 10 nm thick aluminum oxide film by performing atomic layer deposition, and then coated with a 1 nm thick Fe thin film by using e-beam evaporation. The substrate was cut into small pieces with dimensions of about 0.2 cm · 1 cm. CNT forests were synthesized on each piece by using conventional thermal CVD (Lindberg/Blue M) with a quartz tube reactor. The inner diameter of the tube was 21.4 mm and its length was 50 cm. The catalyst-coated substrate was loaded into the tube reactor. The substrate was located 12 cm downstream from the middle of the tube reactor. Then the reactor was heated to 820 C over 15 min with flowing Ar gas. During the ramping process, H2 gas was supplied together with Ar when the temperature passed through 725 C. When the temperature reached 820 C, a gaseous mixture of Ar, H2, C2H4, and ethanol vapor with Ar carrier gas was introduced and the synthesis was carried out. C2H4 was used as the carbon source and ethanol was used to enhance the growth and prolongs the catalyst lifetime since it decomposes into active carbon species and H2O [8]. The volumetric ratio was Ar:H2:C2H4 = 5:10:2. The heater was turned off after the reaction and the substrate was removed after it had cooled to below 200 C under an Ar gas flow. The morphologies of the vertically aligned CNT forests were examined by performing field-emission scanning electron microscopy (FE-SEM, JEOL JMS-7400F) and scanning transmission electron microscopy (STEM, JEOL JEM-2200FS with an energy-dispersive X-ray spectrometer).

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Results and discussion

There are two key steps in the CVD growth of a CNT forest: mass transport of reactants from the bulk fluid to the catalyst, and chemical reaction on the catalyst surface. When the mass transport is slower than the surface reaction, the concentration of the reactants at the reaction site becomes insufficient. Thus, the mass transport rate determines the overall growth rate. In contrast, when the surface reaction is slower than the mass transport, the concentration of the reactant is sufficient and the surface reaction rate determines the overall growth rate. The slower of these two steps determines the overall growth rate: that is, the growth is either reaction limited or mass transport limited. A standard method for determining the rate limiting step of a process is to create an Arrhenius plot [17]. An Arrhenius plot is generated by plotting the logarithm of the kinetic constant of the process against inverse temperature. At low temperatures in the system under consideration, the surface reaction is much slower than mass transport, and thus this reaction is the rate limiting step and the overall growth rate is proportional to exp (EA/kT). As the temperature rises, the chemical reaction becomes faster than mass transport, and growth becomes mass transport limited. The overall growth rate in the mass transport limited regime is proportional to T3/2. Thus, a change in the slope of the Arrhenius plot is expected, which enables the identification of the rate limiting step. However, this method is not suitable for the study of the kinetics of CNT forest growth. In this system, the catalyst particles can maintain their shape and population only in a narrow range of temperatures. The mobility of the catalyst metal atoms depends on temperature, so the size and areal number density of the catalyst particles are strongly affected by the temperature. Thus, outside this narrow temperature range, the diameter and number density of the CNTs vary significantly. For this reason, it is improper to compare the growth rates at two significantly different temperatures, and it is not practical to obtain a meaningful Arrhenius plot over a sufficiently broad temperature range. Instead, in this study, we formulated the hypothesis that the growth is mass transport limited at the temperatures of interest, and constructed a model of this mass transport for experimental testing. Two consideration form the foundation of this hypothesis. First, the catalysts remain on the substrate during growth, i.e., growth occurs in the bottom growth mode, so the gaseous carbon source is required travel a long distance. Second, the reported growth rates of CNT forests are much lower than for floating catalyst systems: as mentioned above, the growth rates in floating catalyst systems are as high as 5000 lm/min [13], whereas those of forest structures are less than 100 lm/min. Of course, different growth condition and lack of mechanical constraint in the floating catalyst system may contribute to higher growth rate [18]. Nevertheless, the enormous discrepancy in growth rate suggests that the full potential of catalysts to produce CNTs is not exploited in CNT forest growth. The proposed model for the mass transport of the gaseous carbon sources to the catalysts is illustrated in Fig. 2a. The gas molecules diffuse through two regions before they arrive

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at the catalysts: the diffusion boundary layer and the CNT forest. First, they should diffuse through a diffusion boundary layer. When a bulk flow passes by a solid object, a layer develops in the vicinity of the object where the effects of viscosity are significant, known as a boundary layer [19]. With regards to mass transport, the concentration in the boundary layer is different from the bulk concentration and so forms what is known as a diffusion boundary layer. During the growth of a CNT forest, a diffusion boundary layer develops above the CNT forest. In fact, there are several papers addressing the diffusion issue in the growth of CNT forests [10,20,21], Xiang et al. presented a diffusion model during the CNT forest growth and qualitatively evaluated the degree of diffusion limit of feedstock [20]. Based on the model, the critical lengths from which CNT forests begin to suffer strong diffusion resistance was predicted. Yasuda et al. and Zhong et al. improved the diffusion flux by using shower head [10] and patterned catalyst, [21] respectively. However, the diffusion boundary layer concept has not been employed despite its importance in transport phenomena. After diffusing through the diffusion boundary layer, the gas molecules encounter the CNT forest. They travel from the top of the CNT forest to the bottom where the catalysts are present. The mass transport from the side of the CNT

Fig. 2 – (a) A schematic representation of the proposed diffusion model for mass transport in the growth of CNT forests and (b) the calculated diffusion fluxes for the corresponding diffusions under our growth conditions for a total flow rate of 170 sccm. (A color version of this figure can be viewed online.)

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forest was considered to be negligible compared to the mass transport parallel to CNTs, so it was neglected for simplicity. The structure of a CNT forest is complex, but can be approximated as a cylindrical porous structure (Fig. S2). It is then necessary to determine whether the diffusion through the CNT forest proceeds via continuum diffusion or Knudsen diffusion. Knudsen diffusion is a means of diffusion that occurs when the characteristic length of a system is comparable to or smaller than the mean free path of the particles. The diffusion mechanism can be determined by the Knudsen number, Kn = k/L, provides information about the diffusion mechanism; k is the mean free path and L is the characteristic length. When Kn  1, diffusion occurs via the continuum mechanism and when Kn  1, diffusion occurs via the Knudsen mechanism [22]. The mean free path was calculated with the following expression, kB T k ¼ pffiffiffi 2 2pd p where kB is the Boltzmann constant, T is the temperature, d is the diameter of the molecule, and p is the pressure. In this system, the mean free path is approximately 200 nm. In this system, the characteristic length is the diameter of

hypothetical cylindrical pore, which is about 40 nm from Fig. S1. Therefore, the Knudsen number is 5, which is in the transition regime between continuum diffusion and Knudsen diffusion. In our model, diffusion through the CNT forest was assumed to occur via Knudsen diffusion. In the mass transport limited situation, the growth rate of the CNT forest should be proportional to the mass flux of the carbon source. Thus, it is necessary to calculate the mass diffusion flux under various conditions. To understand each step of the diffusion process, the diffusion fluxes for the two steps were calculated separately: (1) diffusion through the boundary layer, (2) diffusion through the CNT forest. Then, the overall diffusion flux, taking into account both steps, was calculated. The diffusion fluxes for the growth condition of a centimeter-tall CNT forest with a total flow rate of 170 sccm are plotted in Fig. 2b as a function of the CNT forest height. First, the diffusion through the diffusion boundary layer occurs via the continuum mechanism. The diffusion flux arising in continuum diffusion is given by J = D$n, where n is the molecular density and D is the diffusion coefficient. Here, the diffusion coefficient of ethylene at 800 C is 1.5217 cm2/s [23], and $n = DC/d is calculated in the Supporting Information for a total flow rate of 170 sccm. The diffusion flux through the

Fig. 3 – (a) Calculated thickness of the diffusion boundary layer, (b) a schematic representation of the boundary layer for two different flow velocities, (c) diffusion flux through the diffusion boundary layer as a function of the gas flow rate, and (d) the overall diffusion fluxes as functions of the CNT forest height for various gas flow rates. (A color version of this figure can be viewed online.)

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diffusion boundary layer is constant because the thickness of the boundary layer does not change during a growth. Second, the diffusion through the CNT forest from top to bottom was calculated. This diffusion occurs via the Knudsen mechanism, for which the diffusion flux is given by JK = DK$n, where DK is the Knudsen diffusion coefficient [24]. The Knudsen diffusion coefficient was calculated with the equation [24]  1=2 2 8RT DK;capillary ¼ rcapillary 3 pm where R is the gas constant, T is the temperature, mi is the molecular weight, and rcapillary is the radius of the capillary. The Knudsen diffusion flux through a CNT forest decreases as the height of the CNT forest increases. Finally, the overall diffusion describes the actual situation of CNT forest is growth, so includes the diffusion through the boundary layer followed by diffusion through the CNT forest. The overall diffusion flux is obtained with a mass balance equation. In the steady state, the diffusion flux from A to B must be balanced by that from B to C. JAB ¼ JBC D

CA  CB CB  CC ¼ DK d H

d is the thickness of diffusion boundary layer and H is the height of CNT forest. According to the assumption that the growth is diffusion limited, CC  0. Thus, solving the above equation with respect to CB, CB ¼

HDCA dDK þ HD

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) Joverall ¼ DK

CB DDK CA ¼ H dDK þ HD

Since the growth rate should be proportional to the overall diffusion flux, it is worth examining the equation for the overall diffusion flux in detail. During the initial stage of the growth, H  d, and the overall diffusion flux equation is reduced to Joverall = DCA/d, and after the CNT forest has become tall, H  d, the equation is reduced to Joverall = DKCA/H. As the CNT forest grows, the overall diffusion flux develops a shape that is similar to that of the Knudsen diffusion flux. The increase in H is inevitable, so it is difficult to enhance the overall diffusion flux during the later stages of growth. In the initial stage, however, there is a room to improve the overall diffusion flux. Since the diffusion boundary layer thickness, d, is independent of H, it is possible to increase the overall diffusion flux during the initial stage by decreasing the thickness of the boundary layer. Then, how can the thickness of the diffusion boundary layer be controlled? The thickness of a diffusion boundary pffiffiffiffiffiffiffiffiffiffiffiffiffiffi layer is given by d  2 Dx=u0, where x is the distance from the start of the boundary layer and u0 is the velocity of the bulk flow [19]. Thus, the thickness of the boundary layer can be controlled by varying the bulk flow velocity (Fig. 3a). The effect of varying the bulk flow velocity on the diffusion flux is shown in Fig. 3b. If the flow velocity increases, the boundary layer will be thinned, and the diffusion flux in boundary layer will be higher (Fig. 3c). As a result, the overall diffusion flux will increase as the bulk flow velocity increases, especially during the initial stage of the growth (Fig. 3d). Thus, the initial growth rate should be proportional to the square root of the bulk flow velocity:

Fig. 4 – Photographs at various stages of the growth of an 18-mm-tall CNT forest in a tube. (A color version of this figure can be viewed online.)

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Initial growth rate / Joverall / 1=d /

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pffiffiffiffiffi u0

By using this relationship, it is possible to test the hypothesis that CNT forest growth is mass transport limited by observing the initial growth rates of CNT forests at various flow velocities. If the growth of a CNT forest is mass transport limited, the initial growth rate should be proportional to the square root of the bulk flow velocity, u0. On the other hand, if the growth is not mass transport limited, the initial growth rate will have a different dependence on the bulk flow velocity. To investigate the relationship between the bulk flow velocity and the initial growth rate, CNT forests were grown at various total gas flow rates, and their growth rates were observed. The growth of each forest was monitored with a webcam to obtain its growth curve, as shown in Fig. 4, which presents photographs at various stages of the growth of an 18-mm-tall CNT forest in a tube reactor. Fig. 5a shows the growth curves rates during the initial two hours of growth of CNT forests grown at various flow. Note that the growth rates increase gradually as the flow rate increases. To assess the proportionality, the initial growth rate is plotted as a function of the square root of the flow velocity in Fig. 5b, where the initial growth rate was defined for the initial two hours. The proportionality between the initial growth rate and the square root of the flow velocity is clear, which supports the hypothesis that CNT forest growth is mass transport limited. To test the universality of this observation, the growth rate was also obtained under another growth conditions described in [25]. The noticeable differences between those conditions and the conditions employed in this study are in the carbon source (C2H2) and the growth temperature, which was 670 C. Fig. 5c plots the initial growth rate obtained in this system as a function of the square root of the flow velocity. Here, the initial growth rate was defined for the initial 3 min, which is much shorter than in Fig. 5b because of the much shorter growth lifetime. Once again, it is evident that the initial growth rate is proportional to the square root of the bulk flow velocity. Thus, the growth of both CNT forests was found to be mass transport limited. Here, it is necessary to discuss about the effects of change in gas velocity other than diffusion boundary layer thickness. First, the change in gas flow velocity affects the thermal decomposition of carbon precursor gas. Previous studies revealed the importance of this issue. Preheating of the incoming gases decoupled the substrate temperature from gas heating temperature, which enabled the growth of CNT forests from the catalyst-coated substrate located at lower temperatures [26,27]. It was also reported that increase of gas dwell time resulted in higher growth rate of CNT forests [28]. From these studies, it was revealed that as the carbon sources are thermally decomposed better, the growth of CNT forest is fostered. In our experimental results, however, the opposite trend was observed. When the gas flow velocity decreased, the growth rate also decreased in spite of better thermal decomposition of carbon precursor. The only way to explain this contradictory results is from the viewpoint of mass transport. In our residence time regime (10 s), which was much longer than those in the abovementioned papers (0.1 s [26,27], 1 s [28]), the thermal decomposition is so

sufficient that the mass transport rate limits the growth rate of CNTs. Therefore, it would be reasonable to understand that there are two competing factors regarding the gas flow velocity: thermal decomposition of carbon source gas and mass transport to catalysts. When the residence time is short, the gas flow velocity significantly affects the thermal decomposition of carbon source gas. In this case, slower velocity is beneficial for achieving higher growth rate. However, when the

Fig. 5 – (a) Growth curves of CNT forests grown with various gas flow rates, and the initial growth rates of CNT forests as functions of the square root of the flow velocity grown under (b) the conditions to produce a centimeter-tall CNT forest and (c) the conditions in Ref. [25]. (A color version of this figure can be viewed online.)

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Fig. 6 – Reported growth rates of CNTs with respect to diffusion boundary layer thickness. Red squares: growth with the ‘‘kite mechanism’’, where catalysts produce CNTs as they float like kites [29–31]. Pink triangle: growth of vapor grown carbon fiber (VGCF) [14]. Black circles: growth of CNT forests [9,32,33]. Blue stars: growth of CNT forests in this study. (A color version of this figure can be viewed online.) residence time is sufficiently long, the growth of CNTs becomes less sensitive to thermal decomposition, and more largely affected by mass transport to catalysts. Our residence time was relatively so long that the thermal decomposition of the gas is expected to be enough. In fact, beyond the maximum velocity reported in this work, the growth rate decreased with gas velocity, which is in accordance with the Ref. [28]. Second, removal of byproducts from the forest is also affected by the flow velocity. Since no significant pressure drop is expected from the chemical reactions near or on the catalyst surface, the mass transport within a CNT forest

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structure is driven mainly by diffusion. The byproducts will diffuse out due to concentration gradient and this will be more effective with thinner boundary layer. When the catalysts in a CNT synthesis are floating rather than remaining on the substrate, the mass transport to the catalysts is different. In this case, the boundary layers are very thin because they are formed on nano-scale catalyst particles not on a macro-scale substrate. In addition, the gas molecules do not need to pass through an additional diffusion barrier such as a CNT forest. Thus, it is more likely that CNT growth in a floating catalyst system is reaction limited rather than mass transport limited. In Fig. 6, growth rates of CNTs in representative studies are plotted as a function of the diffusion boundary layer thickness. The thicknesses of the diffusion boundary layers were calculated based on the experimental conditions mentioned in each reference and are listed in Table S2 in the Supporting Information. Growth in the floating catalyst systems is much faster and involves much thinner boundary layers than growth in CNT forest structures, where the catalysts are in contact with macroscale substrates. As the thickness of the boundary layer decreases, the diffusion flux becomes higher and moves the system out of the mass transport limited regime towards the chemical reaction limited regime. Thus, if CNT forests can be grown in a tip growth mode, their growth rates can be greatly increased. A photograph of the 1.8 cm tall CNT forest is shown in Fig. 7a. The CNT forest has a rectangular structure with uniform height. Raman, SEM, and TEM analyses were conducted at the four locations of the CNT forest along its height as marked in Fig. 7a. In the Raman spectra of these locations, the IG/ID ratio gradually decreases as we move from the bottom of the forest to the top (Fig. 7b). This trend arises because the growth of the CNT forest occurs in the bottom growth mode; the top of the forest has experienced a longer period

Fig. 7 – Characterization of the as-grown CNT forest. (a) Photograph of the CNT forest, (b) Raman spectra, and (c–f) SEM and (g–j) TEM images obtained at the positions marked in (a). (A color version of this figure can be viewed online.)

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of amorphous carbon deposition than the bottom of the forest [8]. The degree of amorphous carbon deposition is not sufficient for it to be detected in the microscopy images. In the SEM and TEM images, it can be seen that clean CNTs have grown from the bottom to the top with diameters ranging from 10 to 13 nm (Fig. 7c–j).

4.

Conclusion

In this study, the mass transport during the growth of a centimeter-tall CNT forest was studied. Under the hypothesis that the growth is mass transport limited, a mass transport model was proposed for this system. In our model, the mass flux is affected by the thickness of the boundary layer, particularly during the initial growth stage. Experimentally, the thickness of the boundary layer was controlled by varying the bulk flow velocity. A clear positive relationship between the initial growth rate and the square root of the gas flow velocity was observed, which demonstrates that the growth of this CNT forest is mass transport limited. It is expected that the growth rate of such CNT forests can be increased to produce still taller forests by further decreasing the thickness of the boundary layer. In addition, we suggest that if CNT forests can be grown in the ‘‘tip growth’’ mode, growth will be freed from the mass transport limit, and thus their growth rates will be much improved.

Acknowledgements The present study was supported by a Korea Science and Engineering Foundation (KOSEF) grant funded by the Korean government (MEST) (Grant No. 2014-003266). We also acknowledge the Research Institute of Industrial Science & Technology for financial support. Finally, we thank Cheong Ho Lee for graphical assistance.

Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.carbon. 2015.05.080.

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