Structural Modeling of Dahlia-Type Single-Walled Carbon Nanohorn

Article pubs.acs.org/JPCA

Structural Modeling of Dahlia-Type Single-Walled Carbon Nanohorn Aggregates by Molecular Dynamics L. Hawelek,*,†,‡ A. Brodka,‡ John C. Dore,§ Alex C. Hannon,∥ S. Iijima,⊥ M. Yudasaka,# T. Ohba,∇ K. Kaneko,○ and A. Burian‡ †

Institute of Non-Ferrous Metals, ulica Sowinskiego 5, 44-100 Gliwice, Poland A. Chelkowski Institute of Physics, University of Silesia, ulica Uniwersytecka 4, 40-007 Katowice, Poland § School of Physical Sciences, University of Kent, Canterbury CT2 7NH, United Kingdom ∥ Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, United Kingdom ⊥ Department of Physics, Meijo University, Nagoya 468-8522, Japan # National Institute of Advanced Industrial Science and Technology, Central 5, Tsukuba 305-8565, Japan ∇ Graduate School of Science, Chiba University, Yayoi 1-33, Inage, Chiba 263-8522, Japan ○ Exotic Nanocarbon Research Center, Shinshu University, Wakasato 4-17-1, Nagano 380-8553, Japan ‡

ABSTRACT: The structure of dahlia-type single-walled carbon nanohorn aggregates has been modeled by classical molecular dynamics simulations, and the validity of the model has been verified by neutron diffraction. Computer-generated models consisted of an outer part formed from single-walled carbon nanohorns with diameters of 20−50 Å and a length of 400 Å and an inner turbostratic graphite-like core with a diameter of 130 Å. The diffracted intensity and the pair correlation function computed for such a constructed model are in good agreement with the neutron diffraction experimental data. The proposed turbostratic inner core explains the occurrence of the additional (002) and (004) graphitic peaks in the diffraction pattern of the studied sample and provides information about the interior structure of the dahlia-type aggregates.

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SWCNHs was studied.10 It was found that the topological defects produced by the Stone−Thrower−Wales mechanism11,12 are randomly distributed in the hexagonal network of the SWCNHs with larger diameters. These findings are in agreement with the results of surface-enhanced Raman scattering and 13C NMR spectroscopy studies.13,14 Recently, the presence of a graphite-like interior in SWCNH aggregates was revealed using 13C NMR spectroscopy and HRTEM.14,15 These findings prompted us to consider a larger model of SWCNH aggregate consisting of the SWCNHs and the graphitic core inside the aggregate. In the present work, the whole diffraction pattern, including the (002) and (004) peaks, recorded for dahlia-type SWCNH aggregates is analyzed. For such aggregates, the pulsed neutron diffraction data are interpreted using classical molecular dynamics to optimize the energy of the system.

INTRODUCTION Single-walled carbon nanohorns (SWCNHs) belong to a class of carbon nanomaterials consisting of single-walled carbon nanotubes terminated with cone caps. Such nanocarbon materials can assemble to form roughly spherical dahlia-like aggregates.1 The dahlia-type SWCNH aggregates that are produced by CO2 laser ablation of a graphitic rod have spherical forms with diameters of about 800 Å. The hornshaped tips of individual SWCNHs have cone angles of about 20°. Their average diameters are 10−20 Å at the horn part and 20−50 Å in the tubule-body part.2 In the as-grown dahlia-type SWCNHs produced by laser ablation, more or less defective graphitic particles of micrometer size have been found by highresolution transmission electron microscopy (HRTEM) observations, thermogravimetric analysis, X-ray diffraction, and Raman studies.3 These particles can be efficiently removed from the SWCNHs using gravitational sedimentation. 4 SWCNHs have several potential applications strictly related to their porous structure in the form of enclosed nanoscale spaces, as described in many previous works.5−9 In our previous studies of SWCNHs by pulsed neutron diffraction and molecular dynamics, the graphitic contribution to the total diffraction pattern in the form of (002)- and (004)type peaks was removed, and only the structure of the pure © 2013 American Chemical Society

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EXPERIMENTAL SECTION The sample of SWCNHs investigated in the present work was produced by the CO2 laser ablation of a 50-mm-long graphite target rod with a diameter of 30 mm without any catalytic metal Received: January 23, 2013 Published: August 26, 2013 9057

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chemical bonding between carbon atomswas used. The Lennard−Jones potential with parameters optimized for interlayer interactions19 was used to account for bonding between atoms lying in the neighboring sheets. To keep the temperature of the system constant, the Berendsen algorithm was implemented.20 The Newtonian equations of motions were solved using the four-value predictor−corrector method21 with a time step of 0.2 fs. Each simulation run consisted of 105 time steps, so that the simulation length was 20 ps. The last set of atomic positions was used to calculate the structure factor as follows

inclusions. The preparation procedure is described in detail elsewhere.1 The sample was purified using gravitational sedimentation, which was previously reported as an efficient method of purifying SWCNHs from graphitic particles.4 Neutron diffraction experiments were carried out at the Rutherford Appleton Laboratory using the GEM (General Materials) diffractometer16 on the ISIS pulsed neutron source up to a maximum scattering vector of Qmax = 30 Å−1 [Q = 4π (sin θ)/λ, where 2θ is the scattering angle and λ is the wavelength]. The measured intensity was corrected and normalized using the data processing procedure of ref 17, yielding the I(Q) function. Then, the structure factor, S(Q) = I(Q)/b2, was determined dividing the intensity by the square of the scattering length of carbon, b. Converting the structure factor S(Q) by the sine Fourier transform, one obtains the pair correlation function (PCF) Q max 2 PCF = Q [S(Q ) − 1] sin(Qr ) π 0 sin(πQ /Q max ) dQ πQ /Q max

S(Q ) = 1 +

1 N

N

∑ i,j=1 i≠j

sin(Qrij) Qrij

(2)

where rij denotes the distance between the ith and jth atoms. A small-angle contribution due to the Debye volume scattering was removed.22 Then, the theoretical PCFs were calculated according to eq 1. To determine which model, A or B, correctly describes the atomic arrangement in the core of the SWCNH aggregates, the structure factors were computed for both models and are compared with the experimental data in Figure 1. From an

∫

(1)

where the last term in the integral of this equation is the Lorch modification function, which reduces effects arising from the finite value of the upper limit on Q.

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MODELING Structural models considered in the present work were computer-generated starting from sets of Cartesian atomic coordinates. The proposed models consisted of two parts, an inner part defined as the core of the aggregate and an outer part built from the SWCNHs. Two models differing in the degree of core ordering, denoted as A and B, were considered. Both models consisted of the same outer part composed of 18 pure SWNCHs with chiralities of (17,13), (19,18), and (28,16) and six defected carbon nanohorns (41,33) with randomly distributed Stone−Thrower−Wales defects in the cylindrical part of the nanotube. Each carbon nanohorn was generated in two steps according the mechanism used and precisely described in our previous article.10 All generated SWCNHs were attached to the core and radiated from it. The total number of carbon atoms in the outer part of the aggregate structure was 365514. Two spherical atomic arrangements of the core were constructed. The first one (model A) was based on the perfect graphite structure of the core with a diameter of 130 Å and an interlayer spacing of 3.35 Å. In the second model (model B), the turbostratic structure was assumed in which the −ABAB− stacking sequence typical for the graphite structure was lost and the layers were arranged without spatial correlation along the z axis. The turbostratic structure was generated from a perfect graphitic arrangement in which the individual layers were randomly shifted in directions parallel to the layer planes by 0−0.5 Å. The average interlayer distance was 3.43 Å. Additionally, each layer was rotated by an angle randomly chosen from the range of 0−60° around the axis perpendicular to the layers and passing the center of the layer. The total number of carbon atoms in the core of each aggregate structure was 128299. To obtain stable atomic configurations, the constructed models were relaxed during molecular dynamics calculations at 300 K to account for thermal vibrations. The Tersoff-type potentialthe reactive empirical bond order (REBO2) potential18 that takes into account many-body effects and

Figure 1. Comparison of the experimental and theoretical structure factors for models A and B.

inspection of Figure 1, it can be seen that the experimental structure factor is well reproduced in the whole range of the scattering vector Q by model B, in which the turbostratic disorder was generated in the graphite-like core. In the case of the model A, the sharp diffraction peaks typical for graphite can be clearly seen, in apparent disagreement with the experimental structure factor. These conclusions are reinforced by the comparison of the PCFs for the two models shown in Figure 2. The PCF calculated for model A exhibits sharper peaks with greater amplitudes and generally more structure that extends up to 30 Å and clearly differs from the experimental data in peak positions and amplitudes. On the other hand, the theoretical PCF of model B fits the experimental data very well in the whole range of radial distances. In the present work, the surface part of the model consisted of individual nanohorns with four different chiralities, six from each chirality, which is consistent with our previous studies10 and provides average information about the nanohorn part. It is essential to note that the present diffraction data do not allow for the precise determination of the SWCNH chiralities, providing only average information 9058

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Figure 2. Comparison of the experimental and theoretical pair correlation functions for models A and B.

Figure 4. Comparison of the theoretical structure factors for the graphitic core and the SWCNHs.

about the structure of the investigated object. The diffraction method can be regarded as a global probe of the SWCNH aggregate structure that characterizes the aggregates as a whole. From inspection of Figures 1 and 2, it can be clearly seen that the two-component model with the interior turbostratic graphite-like core precisely reproduces all of the structural features of the experimental data in both reciprocal and real space. The relaxed models of the dahlia-type SWCNH aggregate and the interior core structure are displayed in panels a and b, respectively, of Figure 3.

Figure 5. Comparison of the theoretical pair correlation functions for the graphitic core and the SWCNHs. The turbostratic contribution is described by a saw-like function.

in the core. The atomic proportion of the turbostratic core is about 26% and is lower than the value of about 67% suggested previously.14 Moreover, the PCF of the core is superimposed on a saw-like function computed according to ref 23 that is typical for the turbostratic structure. It is important to point out that the presence of turbostratic carbon outside the SWCNH aggregates would give a feature similar to that of the model B inner core. In model B, the outer nanohorn part and the inner core contribute to the total diffraction pattern practically independently because there are no spatial correlations between them or any such correlations are very weak. Taking into account that the sample was purified from graphitic contaminations not belonging to the SWCNHs, as described above, the presence of the (002) and (004) peaks can be explained by the formation of the turbostratic core.

Figure 3. Relaxed models of (a) dahlia-type SWCNH aggregate and (b) inner graphite-like core.

In Figures 4 and 5, the structure factors and PCFs, respectively, of the SWCNHs and the turbostartic core are shown separately. These two parts of the model contribute to the total structure factor and the PCF in proportions related to their atomic fractions. From the displayed plots, one can see that the contribution from the core exhibits sharp peaks at about 1.8 and 3.6 Å−1 that can be attributed to the (002) and (004) graphitic reflections. These peaks dominate the diffraction pattern of the core. Their presence can be related to the poorly ordered graphite-like structure of the initial carbon droplet that cannot be transformed into the final tubule structure. It is noteworthy that the general (hkl) graphitic peaks are not present in the diffraction pattern of the core. The PCF of the core exhibits peaks that are due to spatial correlations within a single graphitic layer but have apparently lower amplitudes because of the significantly smaller atomic content

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SUMMARY AND CONCLUSIONS The pulsed neutron diffraction technique used together with REBO2-based molecular dynamics simulations has proven to be an efficient tool for characterizing the atomic-scale structure of complex carbon nanosystems such as SWCNH aggregates. In this work, the joint use of these methods provided detailed structural information and built up a model that reconstructed all features of the experimental data on dahlia-type single-walled carbon nanohorn aggregates in both reciprocal and real space. 9059

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A comparison of the experimental data with model-based computer simulations showed that a highly ordered graphite core does not exist in such nanostructures. The results presented herein clearly show that dahlia-type SWCNH aggregates consist of two structural components. The inner graphite-like core structure of the proposed model reconstructs well the most intense (002) and (004) diffraction lines arising from interlayer turbostratic correlations. The outer part is built from 24 radially aligned SWCNHs with various diameters and degrees of order. The atomic ratio of the surface nanohorn part to the interior turbostratic graphite-like part is approximately 3:1. It is essential to note that the applied approach is able to discriminate the two models and clearly suggests that the generated configuration is present in the investigated material. It is important to point out that very good agreement with the experimental data was achieved by the calculated results obtained using model B, which match each other to a very high degree in both reciprocal and real space, owing to the careful modeling procedure. Additional structural information that has been deduced from the complementary methods such as high-resolution transmission electron microscopy, surfaceenhanced Raman spectroscopy, and nuclear magnetic resonance and electron spin resonance spectroscopies simplified the modeling. High-resolution transmission electron microscopy observations allowed the geometrical parameters of the singlewalled carbon nanohorns, such as the diameter and length, to be fixed.1,24 High-resolution transmission electron microscopy studies of the SWCNHs cut by a focused ion beam revealed that their interior comprises single-layered graphene sheets instead of nanohorns, suggesting the nucleation of nanohorns on the surface of such nanoparticles.15 The presence of topological defects in the form of nonhexagonal carbon rings (i.e., pentagons and heptagons) was confirmed by surfaceenhanced Raman spectroscopy.13 The results obtained using nuclear magnetic resonance and electron spin resonance spectroscopies showed that a graphite-like core structure14 or a fairly conducting disordered structure25 is present in the interior of dahlia-like particles. Therefore, the modeling procedure presented here, based on complementary data sets, leads to a reduction of the free parameters of the model to the size of the graphitic core and very good agreement with the experimental data. The atomistic view of the SWCNH aggregates presented in Figure 3 is the basis of simulations that agree with the experimental data to a large extent. The similarity of the atomic arrangement within the core and in the turbostratic structure was reported in the Supporting Information of ref 15 (Figure S5), in which a transmission electron microscopy image of the cut SWCNH aggregates containing graphitic nanoparticles is shown. Concerning the uniqueness of this model, it is important to note that the individual nanohorns with different diameters were attached to the core without geometrical correlations. In this sense, the model presented in Figure 3 is not unique because a different arrangement of the generated SWCNHs would lead to a similar diffraction pattern and, consequently, to practically the same PCF.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +48 32 2380-281. Fax: +48 32 2316-933. E-mail: [email protected], [email protected]. Notes

The authors declare no competing financial interest. 9060

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