How a Solid Catalyst Determines the Chirality of the Single-Wall

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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials

How a Solid Catalyst Determines the Chirality of the Single-wall Carbon Nanotube Grown On It Xiao Wang, and Feng Ding J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.9b00207 • Publication Date (Web): 31 Jan 2019 Downloaded from http://pubs.acs.org on February 4, 2019

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The Journal of Physical Chemistry Letters

How a Solid Catalyst Determines the Chirality of the Single-Wall Carbon Nanotube Grown on It Xiao Wang, † Feng Ding*,†,‡

†

Center for Multidimensional Carbon Materials, Institute for Basic Science, Ulsan 44919, South

Korea

‡

School of Materials Science and Engineering, Ulsan National Institute of Science and

Technology, Ulsan 44919, South Korea

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]

ABSTRACT Although the growth of single-wall carbon nanotubes (SWCNTs) with a chirality selectivity up to 90 % has been successfully achieved using solid catalysts (Yang, F. et al. Nature, 2014, 510, 522; Zhang, S. et al. Nature, 2017, 543, 234, etc.), the underlying mechanism that governs the chirality selection is far from clear. Here we propose a mechanism to understand how a solid catalyst particle determines the structure of the SWCNT grown on it. The mechanism has to satisfy three criteria: (i) thermodynamic selection of SWCNTs that possess a structural symmetry the same as that of the catalyst surface; (ii) kinetic elimination of the achiral

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SWCNTs with extremely low growth rates; (iii) rough control over the catalyst particle size leads to SWCNTs with only one or a few dominant chiralities. Besides the deep understanding on the mechanisms of experimentally synthesized (12, 6) and (8, 4) SWCNTs, the preference growth of other SWCNTs of the (2n, n) family, such as the (10, 5) or (6, 3) SWCNTs, by using catalyst surface with a five- or three-fold symmetry is predicted. Such a simple three-criteria mechanism deepens our understanding of the selective growth of SWCNTs and provides a guideline for catalyst design for controlled SWCNT synthesis.

TOC GRAPHICS

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KEYWORDS carbon nanotube, chemical vapor deposition, chirality control, epitaxy A single-wall carbon nanotube (SWCNT), can be regarded as a rolled-up single layer graphene and the rolling vector, (n, m),1

uniquely determines the structure of the SWCNT and,

consequently, all its properties. Since its discovery,2-3 because of its fascinating properties4-7 and various potential applications,8 the SWCNT has been deemed to be one of the most promising materials for the future.9-12 For many of the potential applications, such as CNT-based devices and sensors, chirality-selective SWCNTs or SWCNTs with uniform properties are highly


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desired. Therefore, in the past 20 years, tremendous experimental13-37 and theoretical effort38-49 has been dedicated to understanding the mechanism of SWCNT growth, aimed at synthesizing SWCNTs with desired chirality. Among the three main means of SWCNT synthesis,50-51 chemical vapor deposition16 (CVD) is the most promising method to achieve this goal because of its controllability and the potential of it being scaled up for mass production, in comparison with the arc discharge and laser ablation methods. In 2006, Reich and coworkers proposed that SWCNTs grown on a solid catalyst may inherit the structural characteristics of the catalyst surface.52 Later, Xu and coworkers demonstrated the role of the last pentagon in the SWCNT chirality determination during the growth and concluded that an anisotropic solid catalyst may allow chirality-selective growth by biasing the location of the last pentagon insertion during SWCNT nucleation.53 These theoretical results are supported by experiment in that nearly all chirality-selective SWCNTs grown with conventional catalysts (e.g., Fe, Co, Ni) have been conducted at relatively low growth temperatures (mostly < 800 °C),16-18, 54 which are required to maintain the crystallinity of the catalyst particle. In recent experiments, to use this advantage of solid catalysts, high-melting-point transition metals, such as Mo, W, Rh, or their alloys have been chosen for the controllable synthesis of SWCNTs at relatively higher temperatures (up to 1000 °C).14-15, 55 In 2014, Yang and coworkers successfully synthesized SWCNT samples with an abundance of up to ~ 92 % (12, 6) SWCNTs using W6Co7 as the catalyst.14 Recently, Zhang and coworkers designed new solid catalysts, Mo2C and WC nanoparticles, and successfully synthesized (12, 6) and (8, 4) SWCNT arrays, respectively.15 All these intriguing results validate the strategy of using a high-melting-point catalyst for SWCNT chirality-selective growth. In both studies, mimicking the central idea of epitaxial growth, a structural match between the SWCNT and the


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catalyst surface is considered the key factor that governs chirality control. Although the structural match partially explains the preferential growth of (12, 6) and (8, 4) SWCNTs, it doesn’t exclude the growth of other SWCNTs that may also match the substrate well, such as (12, 0), (18, 0), (9, 9), (8, 8), (16, 0), (12, 4), etc. Therefore, other factors must be considered in order to obtain a complete picture of SWCNT selective growth on a solid catalyst surface. Here, we proposed a mechanism of SWCNT selective growth from a solid catalyst particle that considers three criteria: (i) the thermodynamic control governed by the symmetry match between the SWCNT and the catalyst surface; (ii) kinetic control governed by the number of active sites at the SWCNT-catalyst interface and (iii) diameter control governed by the size of the catalyst particles. According to this mechanism, only one or very few types of SWCNTs can be synthesized in large populations. Specifically, our model shows that the experimentally synthesized (12, 6) or (8, 4) SWCNTs are the smallest chiral SWCNTs with a six- or four-fold rotational symmetry and, therefore, fitting a catalyst surface with six- or four-fold symmetry, and their synthesis can be easily achieved by a rough control over the size distribution of the catalyst particles. Based on this theoretical model, we have also predicted the routes for synthesizing other types of SWCNTs, such as (10, 5), (6, 3), by catalyst design. Therefore, it is expected to be a standard model to guide chirality-selective SWCNT synthesis using solid catalysts. It is known that the structural match between a SWCNT and a surface of a catalyst particle determines the stability of the SWCNT-catalyst interface and therefore the abundance of the nucleated SWCNTs with a lower interfacial formation energy. Here we first discuss the determination of the structural match between a SWCNT and a catalyst. As a rolled-up graphene, the spiral symmetry of a SWCNT is different from the translational symmetry of a normal crystal.56 Here we consider the rotational symmetry of a SWCNT. Generally, a SWCNT whose


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chiral index can be written as (p × i, p × j) or p × (i, j) has a p-fold rotational symmetry. As shown later, the percentage of SWCNTs with p-fold rotational symmetry in the SWCNT triangular chiral map is proportional to 1/p2. For example, only ~ 1/36 of the SWCNTs have a six-fold rotational symmetry. Considering a SWCNT with a p-fold rotational symmetry attached to a catalyst surface with q-fold symmetry, the structural match between the SWCNT and the catalyst surface requires p = q, which can result in a strong binding between the SWCNT and the catalyst surface and therefore a low formation energy of the SWCNT-catalyst interface. With the above criterion of symmetry control, the recently reported SWCNT selective growth can be easily understood. The great enrichment of (12, 6) = 6 × (2, 1) SWCNTs is due to a match between the six-fold rotational symmetry (Figure S1) of the (12, 6) SWCNT and the near sixfold symmetry of the Mo2C (0 0 1) or W6Co7 (0 0 12) surfaces.14-15 Similarly, the abundance of (8, 4) = 4 × (2, 1) SWCNTs is also due to the symmetry match between the SWCNT and the WC (1 0 0) surface.15 In Figure 1a, we present the formation energies of two series of SWCNTs (see Supporting information for more details). Throughout our calculations, the SWCNT segment model was used to calculate the interfacial formation energy. Although a cap is the embryo of a SWCNT, previous calculations clearly proved that it displays no chirality bias. This indicates that the interfacial formation energy plays an important role in SWCNT selection only after the SWCNT becomes reasonably large, which is in agreement with our model of calculation. It can be clearly seen that the formation energy of a (12, 6) SWCNT on Mo2C (0 0 1) surfaces, or an (8, 4) SWCNT on WC (1 0 0) surface corresponds to a deep local minimum in each series, which validates the symmetry control criterion for chirality-selective SWCNT growth. Detailed analysis proves that, compared to SWCNTs with different symmetries from that of the catalyst


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surface, the one with the same symmetry binds to the catalyst surface stronger because the carbon atoms at an open end of the SWCNT can be more properly anchored to the catalyst surface. Figure 1c shows the atomic configuration of the interface of four optimized SWCNTs on the WC (1 0 0) surface. It can be clearly seen that there are only two types of carbon atoms at the (12, 0) SWCNT edges (colored in red and blue) and three types at the (8, 4) SWCNT edges (colored in red, yellow and blue, respectively). In comparison, the (7, 5) or (6, 6) SWCNTs do not have a four-fold symmetry and could not match the four-fold WC (1 0 0) surface well and each edge atom binds to the substrate differently. Fewer types of carbon atoms allow better relaxation of the interfacial structure and stable binding between the SWCNT and the substrate.

Figure 1. Symmetry-dependent SWCNT-catalyst interfacial formation energy. (a) The formation energies two series of SWCNTs (b) on two different catalyst surfaces, (8, 4) series SWCNTs on WC (1 0 0) and (12, 6) series SWCNTs on Mo2C (0 0 1), as functions of the SWCNTs’ chiral angle. Each series of SWCNTs in (a) have very similar diameters but different chiral angles, from zigzag (0 degree) to armchair (30 degree). (c) The optimized structure of (12, 0), (8, 4), (7, 5) and (6, 6) SWCNTs on a WC (1 0 0) surface and (d) the corresponding W-C bond length distributions and the corresponding Gaussian fits (red curves).


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As shown in Figure 1d, the W-C bond length distributions between the SWCNTs and the WC (1 0 0) surface shows a distinct difference between the four SWCNTs. The (8, 4) or (12, 0) one has a narrower W-C bond length distribution, which implies that nearly each edge atom of the SWCNT can be optimized to a proper position of the WC surface to form strong W-C covalent bonds with the substrate. In contrast, the wider bond length distribution for (7, 5) or (6, 6) SWCNTs implies that some of the W-C bond lengths are far from the equilibrium distance and confirms therefore the formation of the interface is less stable. The analyses of SWCNT on Mo2C (1 1 1) surface show the similar results (Figure S2-S3). From Figure 1a, we can see that the formation energy of a (12, 6) or (8, 4) SWCNT corresponds to a local minimum in each series but not always the global minimum of the energy profile. For example, the formation energies of (9, 9)-Mo2C and (12, 0)-WC are lower than those of (12, 6)-Mo2C and (8, 4)-WC. The lower formation energy of a (9, 9) SWCNT on Mo2C or a (12, 0) SWCNT on WC is expected because their three- or four-fold symmetry also matches the corresponding catalyst surface well. To understand why the most abundant SWCNTs are not achiral ones, we must take the kinetics of SWCNT growth into account. As demonstrated in previous studies, an achiral SWCNT may bind to the catalyst surface tightly but it is very difficult to add more carbon atoms into the tube wall because of the lack of active sites at the SWCNT-catalyst interface.48 In contrast, a chiral SWCNT always has some active kink sites at the SWCNT-catalyst interface and therefore its growth rate can be orders of magnitude faster than an achiral one.47-48 To include the kinetics in the chirality-selective SWCNT growth, as an example, we calculated the formation energy variations during the growth of three SWCNTs, the (12, 0), (8, 4) and (6, 6) SWCNTs, on the WC (1 0 0) surface and the calculated energy profiles are shown in Figure 2a


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(see Supporting information for more details). It has been proved that the formation energy difference between two SWCNTs is similar to the activation barrier difference, and thus can be used to estimate the relative growth rates of various SWCNTs with different chiralities.39, 48, 57 It is found that a full cycle of (12, 0) SWCNT growth requires the addition of 12 hexagons to the SWCNT-catalyst interface and the threshold step is the addition of the first hexagon (Figure S5) with a very high formation energy of 3.61 eV. In contrast, the full growth cycle of a (6, 6) SWCNT includes the addition of six hexagons and the addition of the third hexagon is the threshold step which has a formation energy of 1.15 eV (Figure S6). The growth of the chiral (8, 4) SWCNT has a periodicity of four steps, each step only increases the formation energy a very small amount due to its kinked structure (Figure S4) and the formation energy of the threshold step is 0.54 eV only. This calculation validates the model of kink-mediated SWCNT/graphene growth on solid catalyst surfaces and unambiguously proves that the growth rate of the chiral (8, 4) SWCNT is orders of magnitude faster than those of the achiral ones.48 Similarly, we can see the variation of the stability of each SWCNT-catalyst interface during the addition of carbon atoms from the metal-C bond length distribution. Figure 2e and S7 shows the W-C bond length distributions of a (6, 6) SWCNT on the WC (1 0 0) surface during a growth cycle. Before carbon addition, the edge of a (6, 6) SWCNT is flat and the W-C bond lengths is distributed in a narrow range. During the adding of carbon atoms, the high symmetry of the interface was broken and the W-C bond varies at a wide range. At the range of 2.18 Å - 2.30 Å, the number of W-C bonds is 17 at the 0th step, while in each intermediate step of the growth cycle, either longer or shorter W-C bonds appear and the number of W-C bonds in the medium bond length range reduces. The appearance of the longer or shorter W-C bonds implies that the W-C interaction could not be well optimized because of the geometrical confinement. At the


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third step, the W-C bonds distribution is the widest and the number of W-C bonds ranging from 2.12 to 2.24 Å is only 7, which is the fewest among all the steps. Therefore, the third step is the threshold step with the highest formation energy. After a full cycle of growth, the flat open end of the SWCNT was restored and the SWCNT-catalyst interface is in a high stable configuration again. Similar analysis can be applied to the growth of (12, 0) SWCNT as shown in Figure 2c and S8.

Figure 2. The growth of three different SWCNTs on a WC (1 0 0) surface. The interfacial formation energy evolution during a repeated cycle of growth as a function of the number of added carbon atoms is shown in (a) and the corresponding structures of the threshold steps during the growth of each tube is shown in (b). (c-e) The W-C bond length distributions and corresponding Gaussian fits (red curves) in each configuration during the growth of (12, 0), (8, 4) and (6, 6) SWCNTs on WC (1 0 0) surface, in which the number of added hexagons in each shown in each panel.

In sharp contrast to the achiral SWCNTs, during the growth of the (8, 4) SWCNTs, each carbon addition only leads to a very small variation of the W-C bond length distribution, which


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means the SWCNT-catalyst configuration variation is minor in compare with those of (12, 0) and (6, 6) (Figure 2d) and, therefore, the formation energy variation during the carbon addition to the (8, 4) SWCNT is much smaller than those of the achiral SWCNTs.

As demonstrated in previous studies, the population of a specific SWCNT in the final product can be roughly estimated as:48 P = N × R,

(1)

in which N and R are the nucleation density and growth rate of the SWCNT, respectively. Figure 3 shows the predicted relative abundance of the SWCNTs on the WC (1 0 0) surface. The calculated relative percentage of (8, 4) SWCNTs is 98.1 % (see Supporting Information for more details). In contrast, the population of the (12, 0) SWCNTs which has an even lower formation energy than the (8, 4) SWCNTs is only 1.8 % because of its extremely slow growth rate.

Figure 3. The relative abundance of the chosen SWCNTs with similar diameters on a WC (1 0 0) surface according to Eq. (1).

The above thermodynamic and kinetic study clearly show that the synthesis of chiralityselective SWCNTs using solid catalysts is possible and that the chiral SWCNTs whose structures


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match the symmetry of the catalyst surface are the most likely ones to be selected. Although the above two-step screening greatly reduces the number of different SWCNTs selected, there are still many possible chiral SWCNTs in the chiral map (Figure 4). In order to synthesize SWCNTs with only one specific chirality, a proper control of the size of the catalyst surface is necessary.

Figure 4. The three-criteria mechanism of SWCNT’s selective growth from a solid catalyst surface with four(a) and six- (b) fold symmetries.

Here we introduce the final step of the three in the growth mechanism—the catalyst size control. As shown in Figure 4a, in the diameter range of d < 1.66 nm, there are a total of 154 SWCNT types in the triangular chirality map, of which 14 have the four-fold symmetry although most are achiral. After the kinetic control, the number of chiral SWCNTs with four-fold


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symmetry is reduced to 5, they are (8, 4), (12, 4), (12, 8), (16, 4) and (16, 8). It can be clearly seen that the (8, 4) SWCNT, which was successfully synthesized recently, is the smallest chiral SWCNT with four-fold symmetry. If we roughly control the size of the catalyst to be less than the diameter of a (12, 4) SWCNT, the (8, 4) SWCNT will be the only dominant type in the SWCNT sample.


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Figure 5. The three-criteria growth mechanism of SWCNT from a solid catalyst. The screening chiralities with two-, three-, five- and six-fold symmetry shown in b)-e), respectively.

With the mechanism shown in Figure 4a, we have successfully explained why the (8, 4) SWCNT is the only dominant type in the SWCNT samples synthesized by using WC as the catalyst. Figure 4b shows the selection evolution of SWCNTs with the six-fold symmetry. The exact same analysis showed that the (12, 6) SWCNT is the smallest chiral one with a six-fold symmetry and, therefore, can be easily synthesized from a catalyst surface with a six-fold symmetry. Besides the experimentally synthesized (8, 4) and (12, 6) SWCNTs, we can apply same analysis to predict the selective SWCNTs growth on catalyst surfaces with different symmetry (Figure S9-S11). For a catalyst surface with a two- or three-fold symmetry, the smallest chiral SWCNT is (4, 2) or (6, 3), (Figure 5). The (4, 2) SWCNT has a diameter of only 0.41 nm and its very high curvature makes its synthesis by CVD very difficult.58 However, the (6, 3) SWCNT has a diameter is ~ 0.62 nm and is among the SWCNTs that were synthesized by the CVD method. In the case of using a quasicrystal59-60 or multiple twinned particles as the catalysts,61-62 we may be able to grow SWCNTs with a five-fold symmetry and the smallest chiral one is (10, 5) (Figure 5). Apart from these smallest chiral SWCNTs with two-, three-, four-, five-, six-fold symmetries which belongs to the category of p × (2, 1) (p = 2, 3, 4, 5, 6), with proper control of the catalyst size we may be able to synthesize other categories of SWCNTs (Figure 4 and 5). For a catalyst surface with two-, three-, four-, five- or six-fold symmetry, the second smallest chiral SWCNTs with same symmetries are respectively (6, 2), (9, 3), (12, 4), (15, 5) and (18, 6), which belong to the family of p × (3, 1) (p = 2, 3, 4, 5, 6). If we can control the size of the catalyst surface to be in


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the ranges 0.6-0.7, 0.9-1.0, 1.2-1.4, 1.4-1.7 or 1.7-2.1 nm, these large diameter SWCNTs, such as those belonging to the family p × (3, 2) cannot be synthesized and the smaller ones, which belong to the family p × (2, 1), have a relatively larger curvature energy and therefore might not be dominating. A summary of the analysis is shown in Table 1, in which the families of p × (2, 1) and p × (3, 1) SWCNTs and the required sizes of the catalyst surface are shown.

Table 1. The two smallest chosen chiralities and the corresponding required sizes of the catalyst surface for different symmetries.

Fold of Symmetry 2

3

4

5

6

Chirality (n, m)

Catalyst Size / nm

(4, 2)

(0.41, 0.56)

(6, 2)

(0.56, 0.68)

(6, 3)

(0.62, 0.85)

(9, 3)

(0.85, 1.02)

(8, 4)

(0.83, 1.13)

(12, 4)

(1.13, 1.36)

(10, 5)

(1.04, 1.41)

(15, 5)

(1.41, 1.71)

(12, 6)

(1.24, 1.69)

(18, 6)

(1.69, 2.05)

It is important to note that SWCNTs of the p × (3, 1) and p × (3, 2) families are the two dominant species besides the p × (2, 1) family in chirality-controlled experiments. Although the dominant species of SWCNTs synthesized without hydrogen belong to the p × (2, 1) family,


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many SWCNTs belonging to the p × (3, 1) and p × (3, 2) families are synthesized in the presence of hydrogen.15,

63

Although the mechanism of the chirality change is still not clear, the

dominance of the p × (i, j) SWCNTs grown from solid catalysts is unambiguous. Besides, due to the lack of exact SWCNT-catalyst interface structure, some experimental results of chiralityselective SWCNT growth cannot be explained with the criteria proposed in this study. Such as the dominating growth of (16, 0) or (14, 4) by using the W-Co alloy at different experimental conditions. Therefore, deeper theoretical and experimental investigations on the chiralityselective SWCNT growth is very necessary. In conclusion, we have shown the atomic mechanism of the growth of SWCNTs with a specific chirality. The selection of a single chirality can be achieved by three control steps. The dominance of the (8, 4) and (12, 6) SWCNTs in previous experiments was well explained by using this three-criteria mechanism. The enrichment of SWCNTs of other chiralities, such as those belong to the family of (3n, n) and other member of the family of (2n, n), such as (10, 5) and (6, 3) are predicted. The mechanism of SWCNT’s selective growth on a solid catalyst agrees well with most previous experimental observations and could be used to guide the catalyst design for chirality controlled SWCNT growth.

ASSOCIATED CONTENT The detailed computational modeling and the numerical analysis on the chirality distribution are shown in the first part. The crystalline structures of WC (1 0 0) and Mo2C (0 0 1) are shown in Figure S1. Optimized structure of (12, 6) and (13, 5) SWCNTs Mo2C (0 0 1) and the corresponding W-C bond length distribution are presented in Figure S2 and S3. The optimized


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structures of (8, 4), (12, 0) and (6, 6) SWCNTs when adding carbon atoms on the edges are presented in Figure S4-S6. The W-C bond length distribution of (6, 6) and (12, 0) when adding carbon atoms on the SWCNT-metal interface are shown in Figure S7-S8. The mechanism of chirality-selective SWCNT growth with two-, three-, five-fold symmetry are presented in Figure S9-S11. AUTHOR INFORMATION Notes The authors declare no competing financial interests. ACKNOWLEDGMENT The research is financially supported by the support of the Institute for Basic Science (IBSR019-D1) of Korea. REFERENCES (1) Hamada, N.; Sawada, S.-i.; Oshiyama, A. New one-dimensional conductors: graphitic microtubules. Phys. Rev. Lett. 1992, 68, 1579-1581. (2) Bethune, D.; Klang, C.; De Vries, M.; Gorman, G.; Savoy, R.; Vazquez, J.; Beyers, R. Cobalt-catalysed growth of carbon nanotubes with single-atomic-layer walls. Nature 1993, 363, 605-607. (3) Iijima, S.; Ichihashi, T. Single-shell carbon nanotubes of 1-nm diameter. Nature 1993, 363, 603-605. (4) Treacy, M. J.; Ebbesen, T.; Gibson, J. Exceptionally high Young's modulus observed for individual carbon nanotubes. Nature 1996, 381, 678-680.


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How a Solid Catalyst Determines the Chirality of the Single-Wall

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