Structure, Stability, and Infrared Spectrum of Capped Carbon Cones: A

Article pubs.acs.org/JPCC

Structure, Stability, and Infrared Spectrum of Capped Carbon Cones: A DFTB Study Hélio F. Dos Santos,*,† Leonardo A. De Souza,‡ Wagner B. De Almeida,‡,§ and Thomas Heine∥ †

NEQC: Núcleo de Estudos em Química Computacional, Departamento de Química, ICE, Universidade Federal de Juiz de Fora, Campus Universitário Martelos, 36036-330, Juiz de fora, MG, Brasil ‡ LQC-MM: Laboratório de Química Computacional e Modelagem Molecular, Departamento de Química, ICEx, Universidade Federal de Minas Gerais, Campus Pampulha, 31270-901, Belo Horizonte, MG, Brasil § Departamento de Química Inorgânica, Instituto de Química, Universidade Federal Fluminense, Campus do Valonguinho, Centro, Niterói, RJ, 24020-141, Brasil ∥ School of Engineering and Science, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Deutschland S Supporting Information *

ABSTRACT: Capped carbon cones, known as carbon nanohorns (CNHs), are currently considered to be promising drug carrier agents. To explore the drug-carrying ability and other properties for practical use, the chemistry of production, functionalization, and characteristics of CNHs must be elucidated. To this end, molecular modeling can complement the experimental results by providing the molecular properties for single idealized molecules. In the present study, distinct structures for CNHs are proposed, and their equilibrium geometries, stability, and infrared spectrum are discussed. In addition to the opening angle of the cone, the topology of the tips was also changed, giving rise to 12 distinct geometries, which were analyzed by using the density functional-based tight binding approach (DFTB).

1. INTRODUCTION Since the first published studies examining the production and characterization of carbon nanotubes (CNTs),1−5 the research in this field has been intensified, contributing to the growth of the field of carbon-based nanoscience and nanotechnology. As a result of the large quantity of knowledge obtained and the development of powerful techniques, the production, chemical modification and characterization of CNTs and their derivatives can currently enable the planning of applications beyond academic problems. Carbon nanocones, also known as carbon nanohorns (CNHs), were identified by Iijima et al.6 in 1999 as a product of CO2 laser ablation of carbon at room temperature and without the presence of metal catalysts. Transmission electron microscopy (TEM) images revealed that such nanostructures are observed in the form of nearly spherical aggregates with diameters of approximately 80 nm, containing thousands of molecules spatially arranged in a quaternary dahlia-like structure6 (Figure 1a). Recently, the literature has reported several studies related to the synthesis, characterization, and functionalization of this new class of carbon nanostructures.7−24 The single CNH molecular unit is structurally organized as a capped cone section with an average diameter and length of approximately 3 and 40 nm, respectively, and an opening angle of the cone of approximately 20°8 (Figure 1b). The larger diameter and shorter length relative to the CNTs make CNHs a special class of carbon molecules with potential applications in the field of drug adsorption and delivery.7,25−30 The CNHs have many advantages over CNTs, such as low © XXXX American Chemical Society

Figure 1. (a) Dahlia-like structure of CNH aggregate. (b) Molecular model of a capped cone section with indication of the observed dimension.

toxicity, high purity, better solubility when oxidized and suitable diameter that is able to accommodate small clusters of most drugs.30−34 Ajima and co-workers28−30 evaluated the anticancer effect of cisplatin (cDDPt) incorporated inside oxidized singlewalled CNHs (CNHox) exhibiting significant in vitro and in vivo antineoplastic activity. The high biological response was Received: July 14, 2014 Revised: September 27, 2014

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dx.doi.org/10.1021/jp5070209 | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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Figure 2. General procedure used to construct the CNH structures. The structure named 4d (C356H30) with four pentagons on the tip (highlighted in green) is used as model.

compounds considered. In these papers, standard quantummechanical methods were used for relatively small molecules of less than 120 carbon atoms. More recently, Hawelek et al.40 investigated the topological defects on CNHs surface using pulsed neutron diffraction (PND) and molecular dynamics (MD) simulation. From the pulsed neutron diffraction pattern, the structure factor was obtained and converted to the pair correlation function (PCF), which was further compared to the predicted PCF for real-size models, including topological defects randomly distributed over the entire surface. Reactivepotential MD was conducted for the models, and the PCF was calculated from the structure factor. The author concluded that the experimental PCF is better reproduced when the Stone− Wales (SW)41 defects are included in the model, even though mono- and divacancies also play a minor role. The SW topological defect can be created on the tube surface by rotating the C−C bond of two adjacent hexagons of 90°, resulting in two pentagons and two heptagons conjugated in a 5−7−7−5 arrangement.42 The predominance of SW defects was also described in the recent study by Burgos et al.,42 who evaluated the role of the catalyst on the defect formation on the SWNT growth using reactive MD. They concluded that SW defects are always created, regardless of the shape of the catalyst nanoparticle. Our group43 recently reported some structures of the inclusion complexes formed by cDDPt and CNH, as predicted from standard DFT calculations. The global minimum was formed with the cDDPt placed close to the bottom of the CNH. Looking over the current stage of the chemistry of CNHs, a molecular description of the structure and properties is still desired to tune the physicochemical characteristics of the CNHs and to improve their applications. In the present work, the structures of the carbon capped cones are addressed by considering all five possible cone angles (112.9°, 83.6°, 60.0°, 38.9°, and 19.2°) and the distinct topologies for the capped moiety resulting in 12 distinct structures containing a number of carbon atoms ranging from 310 to 402. In addition to the structures, the relative stability is discussed and the infrared (IR) spectrum assignments are presented, as predicted from a density-functional theory based tight-binding approach.

attributed to the accumulation of the inclusion complex cDDPt@CNHox at the tumor tissue, which keeps the drug concentration high near the tumor cell.30 Insights on the drug releasing mechanism were also provided by removing the oxygen-containing groups from the opened windows. This process led to a substantial enhancement of the amount of the drug released: from 15% to 70%. More recently, Nakamura et al.25 conducted a study of the application of prednisolone, an anti-inflammatory steroid, adsorbed onto CNHox in mice with collagen-induced arthritis. Over 2−5 h, the drug was released, and its local concentration in the tarsus (the upper region of the animal’s paw) of mice was dependent on the size and amount of holes in the surface of the CNHox. As a result, the authors observed a regression of the disease compared to the control methods adopted in their experiments. The theoretical studies addressing the structure and properties of CNHs remain scarce. The first paper appeared in 2000, authored by Berber et al.,35 who used a simple parametrized linear combination of atomic orbitals (LCAO). The authors considered six structures containing five pentagons on the tip at different relative positions (topologies). All these structures exhibit an opening angle of the cone equal to 19.2°, corresponding to the average observed value6,7 (see Figure 1b). They found that the structures with all pentagons at the conical shoulder are slightly more stable than those with one pentagon at the apex. In addition, the average CC bond lengths (dCC) were determined to be in the range of 1.41−1.42 Å in the tubular region and 1.43−1.44 Å at the pentagonal sites on the tip. The pentagonal-hexagonal adjacencies on the tip exhibited a slightly shorter dCC of approximately 1.39 Å. Amano and Muramatsu36 reported the X-ray spectra predicted by the discrete variational (DV)-Xα method for the series of CNHs containing one to five pentagons on the capped moiety. A single symmetric topology was used for each CNH, and the geometries were optimized using the classical molecular mechanics approach. Most of the results were discussed based on the density of states (DOS) of the pentagonal rings, which was observed to be similar for all species, regardless of the relative arrangement of pentagons on the hexagonal carbon network. These results suggest that the electronic properties (including reactivity) of CNHs near and on the tip should be determined by the local structure. Gotzias et al.37 described a study of H2 adsorption onto CNHs using a classical Grand Canonical Monte Carlo simulation. Very large molecules (up to 2056 atoms) were used, and the results indicated that the H2 interaction near the tip is significantly enhanced compared to the interaction near a graphene sheet. Some other early papers discussed the structure and molecular properties of functionalized CNHs,38,39 where the focus of the studies are on the structure and stability of the hybrid

2. COMPUTATIONAL DETAILS Starting from a flat graphene sheet, the cone shape can be idealized by cutting sectors of angle 60° (called disclination angle, ϕ) and connecting the resulting edges. The procedure used to build the initial guess of CNH structures is represented in Figure 2 for the derivative 4d (see Table 1). A graphene sheet is chosen with desired size, ∼22 Å for 4d (Figure 2a), and the topology of the tip is specified by the number of pentagons (n) and their relative positions (n = 4 for B



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Table 1. Geometrical Parameters and Molecular Formulas of the CNHs Studieda 1a 2a 2b 3a 3b 4a 4b 4c 4d 5a 5b 5c

C400H50 C314H36 C310H36 C370H38 C402H38 C352H30 C354H30 C354H30 C356H30 C360H24 C372H24 C368H24

C1 C2v C2 Cs C1 C2 C2v Cs Cs C1 C1 C1

n

ϕ (°)

θ (°)

NCC

NCH

1 2 2 3 3 4 4 4 4 5 5 5

60 120 120 180 180 240 240 240 240 300 300 300

112.9 83.6 83.6 60.0 60.0 38.9 38.9 38.9 38.9 19.2 19.2 19.2

399 313 309 369 401 351 353 353 355 359 371 367

50 36 36 38 38 30 30 30 30 24 24 24

A(ν) = cl

∑ i=1

⎡ 2ω ⎤ 1 ⎢A i i ⎥ ⎣ π 4(ν − νi)2 + ωi2 ⎦

(2)

The final absorbance was converted to relative transmittance (in %) for comparative analysis of the band spectra. The DFTB calculations were performed using the deMonNano54 code.

3. RESULTS AND DISCUSSION Structure and Stability of CNHs. The molecular formulas of the compounds studied in the present work are presented in Table 1. Although the point group was specified, all of the geometries were optimized without any symmetry constraint. The final DFTB geometries are depicted in Figure 3, showing the front and side views. The pentagon rings are highlighted in green, indicating the distinct topologies of the tips. The overall structural parameters are summarized in Table 2, including the average diameter (da), maximum diameter (dm), length of the wall (lw), and the number of carbon layers. These values represent the average over the set of structures within each

The symbols n, ϕ, and θ stand by the number of pentagons on the tip, disclination angle, and cone angle, respectively. The NCC and NCH abbreviations refer to the number of carbon−carbon and carbon−hydrogen bonds. a

structure 4d). The sectors are cut by deleting atoms within the area defined by the disclination angle (Figure 2b). The number of sectors defines the number of pentagons (n) on the tip, which assumes integer values from 1 to 5. Next, the carbon atoms on the opposite edges of each sector are connected by single bonds (Figure 2c) and the resulting geometry optimized using any method available (e.g., molecular mechanics). The flat graphene disk obtained (Figure 2d) is then submitted to a short molecular dynamic simulation (e.g., 100 ps at 300 K in vacuum) yielding the cone shape of CNH represented in Figure 2e, which is further used as initial guess for geometry optimization at higher level of theory. The molecular formulas of the structures proposed are given in Table 1, in addition to the total disclination angle (ϕ), the opening angle of the cone (θ; eq 1) and the numbers of CC (NCC) and CH (NCH) bonds. The structures are named according to the number of pentagons on the tip (1, 2, ...) and topologies (a, b, ...). ⎛ n⎞ θ = 2 sin−1⎜1 − ⎟ ∴ n = 1 − 5 ⎝ 6⎠

(1)

Note that the number of hydrogen atoms included at the opened rim of the cone is the same within each set of molecules, namely, for each n, as well as the number of carbon atoms and their arrangement on the first layer of the opened side of the cone; this process was implemented to minimize the effect of edges atoms on the calculated properties. The geometries proposed according to the procedure represented in Figure 2 were optimized at the DFTB level.44−47 We have chosen the standard DFTB treatment for superior computational stability and performance. This is justified by a large number of applications on carbon systems where this approach was found to yield excellent results (see, e.g., refs 48−52). The infrared (IR) spectra were then calculated at the same level of theory. For such large molecules, with only carbon and hydrogen atoms, a great number of vibrational frequencies are found on narrow regions; therefore, to simplify the infrared assignments and make them of more practical use, the calculated wavenumbers (νi in cm−1) and intensities (Ai in cm mol−1) were fitted as a sum of Lorentizian functions (eq 2), setting the parameters ωi = 20 cm−1 for all modes and cl = 1 × 10−9 mol cm−2.53

Figure 3. DFTB optimized geometries of the CNHs studied. The pentagon’s rings (highlighted in green) show the different topologies of the tips. C



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5b, with the former being closer to the observed value (∼30 Å). These results suggest that the real tip should be close to the size proposed here, with the pentagons observed to be set apart from one another to avoid pentagon−pentagon adjacencies, as represented by structure 5a. This type of arrangement is reasonable, considering that minimization of pentagon adjacency is the major factor favoring relative stability, as shown for the fullerene’s isomers48 and discussed further in this paper. The analysis of the local structure was also accomplished by considering the CC bond lengths. Scheme 1 shows the main building blocks of the defective regions (tips) giving rise to the distinct topologies. The values included are the average bond lengths measured over the set of molecules proposed here. The equilibrium bond length for the pentagonal sites (side of pentagon) was 1.43−1.44 Å, and for the CC bond connecting the two pentagons (Scheme 1a−c) or the pentagon−hexagon (Scheme 1b−d), the corresponding values range from 1.38 to 1.40 Å. Very short bonds ( 2a (0.37); 3a (0.00) > 3b (2.01); 4a (0.00) > 4c (0.17) > 4d (0.23) > 4b (0.29); 5a (0.00) > 5c (0.38) > 5b (0.57). By carefully examining Figure 3 and Scheme 1, the stability order within the distinct series is mainly driven by the number of pentagon-pentagon bonds, which do not exist for the forms 2b, 3a, 4a, 5a, and 5c found as the most stable structures.

Table 2. DFTB Structural Parameters for Each Series of CNHsa n

#layers

da (Å)

dm (Å)

lw (Å)

1 2 3 4 5

8 8 8 11 12

20.6 16.2 19.7 14.5 12.7

32.4 26.0 25.9 21.0 15.3

18.5 17.5 19.0 21.9 24.3

a All values are averages over the set of structures proposed for each n. The number of carbon layer (#layers), average diameter (da), maximum diameter (dm), and length of the wall (lw) are included.

series defined by n and do not depend strongly on the topology of the tip. For the sake of illustration, the measured DFTB parameters for molecules with n = 4 are spread over the following ranges: 14.3−14.9 Å (da), 20.6−21.7 Å (dm), and 21.3−22.6 Å (lw). The average diameter (da) was taken from the carbon layer at half of the height, namely, layer 4 for n = 1−3 and layer 5 for n = 4−5, which are very close to the actual values considering all the layers. Note that the molecules studied here are very small compared to the observed ones, which have average diameter and length of approximately 30 and 400 Å, respectively6,7 (see also Figure 1b). For the most common structure observed experimentally with n = 5,6,7 our molecular models proposed have average values of da = 12.4 Å and lw = 24.3 Å. To extrapolate these values for larger CNHs, the length of the wall (lw) was plotted against the maximum diameter (dm) for the structures 5a and 5b as shown in Figure 4.

Figure 4. Correlation between the length of the wall (lw) and the maximum diameter (dm) for structures 5a and 5c, which are often observed experimentally. The equations inset represent the fitting curves (dashed lines) for both structures.

A perfect fitting can be obtained by using a first-order exponential growth, and then these relationships can be used to predict the dm as a function of the size of CNHs and to calculate the average diameter. For the topology 5a, we found dm = 32 Å for lw = 400 Å (actual length of CNHs), and for structure 5b, the larger CNH is predicted to be slightly narrower, with dm ∼ 27 Å, due mostly to the more compact arrangement of the pentagons on the tip. The average diameters estimated analytically from the function given in Figure 4 were 29.2 Å for structure 5a and 24.9 Å for structure D



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Scheme 1. Distinct Connectivity Found on the CNH Tipsa

a

The values are the average distance over all CC bonds of the same type (in Å).

As a general observation, the spectral region between 4000 and 2000 cm−1 exhibited one absorption band close to 3085 cm−1, regardless of the number of pentagons, which is assigned to CH stretching of the edges; therefore, the important region to be discussed is in the range of 2000 to 500 cm−1. The IR main transitions and assignments are summarized in Table 3, and the following features can be related with the distinct structures: (i) the most stable structures within each series, namely, 2b, 3a, 4a, and 5a, exhibit more intense IR transitions, except 3a; therefore, these can be likely identified; (ii) absorption bands at frequencies higher than 1800 cm−1 indicate two consecutive pentagons; (iii) topologies with no consecutive pentagons can be characterized by slightly more intense bands at 1730−1780 cm−1; (iii) longitudinal and radial vibrations of the tubular moiety are found at 1560−1700 cm−1; (iv) in the 1230−1000 cm−1 region, the intense bands are mainly due to the in-plane CH deformation; (v) the overall IR profile must be analyzed besides the specific bands, which is affected by the cone shape and might guide in the analysis of CNH mixtures.56 Finally, we claim the data reported in the present study should help the experimentalist to assign the structure of this highly complex class of molecules in addition to providing molecular models for further theoretical works studying CNHs.

Figure 5. Normalized DFTB energy (ET/NCC) as a function of the opening angle of the cone (θ) for all CNHs studied and graphene.

Therefore, as established for fullerenes,48 our results suggest that the so-called “pentagon connections” is a major factor in the relative stability of CNHs. Infrared Spectra of CNHs. The infrared (IR) spectrum is not commonly used for carbon nanostructures, primarily due to the high symmetry of the molecules, which results in low intensity transitions. In this case, instead of IR spectroscopy, Raman spectroscopy is preferable.55 Nevertheless, when defects are inserted in the molecule, for example, in the production of CNHs, most of CC modes become IR active and might aid to elucidate the overall geometries and local defects. The analysis performed here aims to assign fingerprint bands for single molecules that might be utilized as reference in the experimental works for the overall characterization of the CNHs as well as to gain insight on the local structures or topologies of the defects. The discussion of the IR spectra is focused on the different topologies within each series of molecules defined by the number of pentagons (n), as represented in Figures S1 and S2 (Supporting Information). Figures S1 and S2 promptly allow the identification of fingerprints bands, though for some species the band intensities are significantly small. The normal modes vector representation for the main absorption bands are represented in Figures S3− S6 (Supporting Information), in addition to the detailed discussion and band assignments.

4. CONCLUSIONS In this paper, the density-functional-based tight-binding method (DFTB) was used to study distinct molecular models for carbon nanohorns (CNHs). The molecules differed by the cone angle, ranging from 19.2 to 112.9°, as well as the number of pentagons on the capped moiety, ranging from 1 to 5. In addition, several topologies defining the relative position of pentagonal and hexagonal sites were proposed, leading to 12 structures. For our largest molecule (n = 5), the length of wall (lw) was 24.3 Å, and the average diameter was equal to (da) 12.4 Å; these values are quite different from the actual sizes, which are approximately 400 and 30 Å, respectively. To evaluate the size-consistency of our model, the relationship between lw and the maximum diameter (dm) was determined, reveling a first-order exponential growth. This function was then used to estimate the average diameter for a CNH with lw = 400 Å, resulting in da = 29.2 Å, in perfect agreement to the experiment (da = 30 Å). This result indicates that our model can be extended up to the actual size by keeping the same tip in the same topology. The analysis of the local structure in the defective region was also performed. The results indicated E



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Table 3. Vibrational Frequencies (in cm−1) and Assignments for the CNHs Studied; The Stretching (ν) and In-Plane Deformation (δ) Modes are Assigneda 2a

2b

1825, ν(C5−C5) 1777, 1738, 1681, ν(CC) tubular moiety 1488, 1455, ν(CC) tubular moiety + δ(CH) open rim 1208, δ(CH) open rim 3a

1755, ν(CC) tubular moiety 1690, 1647, 1596, ν(CC) tubular moiety 1480, 1440, ν(CC) tubular moiety + δ(CH) open rim 1202, δ(CH) open rim 3b

assignments was made. In general, the overall profile of the spectra is quite distinct for the forms studied, even within a single series. Thus, this spectral assignment can be used by an experimentalist to characterize the topology of the CNHs. Specifically, the presence of pentagon−pentagon links can be clearly identified by the presence of absorption bands at approximately 1820 cm−1.

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S Supporting Information *

Figures S1 and S2 represent the calculated IR spectra in the band form, and Figures S3−S6 show the vector representation of the main normal modes used to assign the IR spectra of CNHs. This material is available free of charge via the Internet at http://pubs.acs.org.

1773, ν(CC) tip 1781, ν(C5−C5) + ν(CC) tip 1679, ν(CC) tubular moiety + ν(CC) tip 1736, 1668 ν(CC) tubular moiety 1517, 1458, ν(CC) tip 1397, ν(CC) tubular moiety + ν(CC) tip 1268, ν(CC) tubular moiety + + δ(CH) open rim δ(CH) open rim 4a 4b

1705, 1662, ν(CC) tubular moiety + ν(CC) tip 1596, 1564, ν(CC) tubular moiety + ν(CC) tip 1226, 1115, 1054, ν(CC) tubular moiety + ν(CC) tip + δ(CH) open rim 986, 686, ν(CC) tubular moiety + ν(CC) tip + δ(CH) open rim 4c

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*E-mail: [email protected]. Phone: 55 32 2102 3310. Fax: 55 32 2102 3314. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS L.A.D.S., W.B.D.A., and H.F.D.S. would like to thank CNPq and FAPEMIG (PRONEX APQ-04730-10) for providing support to this studied. H.F.D.S. is grateful to CAPES/ DAAD/PROBRAL 338/10 for providing resources during the stay in Bremen, Germany.

791, ν(CC) tubular moiety + ν(CC) and δ(CH) open rim 4d

1743, ν(C5−C6) 1654, ν(CC) tubular moiety 1577, ν(CC) tubular moiety + ν(CC) tip

1345, ν(CC) tubular moiety + ν(CC) tip

AUTHOR INFORMATION

Corresponding Author

1868, ν(C5−C5) 1759, ν(CC) tubular moiety 1660, ν(CC) tubular moiety + ν(CC) tip 1554, ν(CC) tubular moiety + ν(CC) tip

1897, ν(C5−C5) 1835, 1819, ν(C5−C5) + ν(CC) tip 1766, ν(CC) tubular moiety 1771, ν(CC) tubular moiety 1642, ν(CC) tubular moiety + ν(CC) 1641, ν(CC) tubular moiety + ν(CC) tip tip 1550, ν(CC) tubular moiety + ν(CC) 1536, ν(CC) tubular moiety + ν(CC) tip tip 805, ν(CC) tubular moiety + ν(CC) 809, ν(CC) tubular moiety + ν(CC) and δ(CH) open rim and δ(CH) open rim 5a 5b 5c 1732, ν(C5−C6) 1655, ν(C5−C6)

ASSOCIATED CONTENT

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REFERENCES

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1759, ν(C5−C6) 1669, ν(CC) tubular moiety + ν(CC) tip 1413, 1367, ν(CC) tubular moiety + ν(CC) tip

1303, ν(CC) tubular 1319, ν(CC) tubular moiety + δ(CH) open moiety + δ(CH) open rim rim 756, ν(CC) tubular moiety + ν(CC) tip a

C5 and C6 stand by pentagon and hexagon rings, respectively. The calculated normal modes are represented in the Figures S3−S6 of the Supporting Information.

shorter CC bonds (1.38−1.40 Å) for pentagon−pentagon and pentagon−hexagon sites and on average 1.42 ± 0.01 Å for the tubular region, in agreement with previous ab initio data. Regarding the stability of the distinct CNHs forms, the total energy per number of carbon bonds was used as benchmark to establish the stability order within each series of molecules according the values of n. The results indicated that the number of pentagon−pentagon bonds on the tip is the main factor responsible for the spread over the distinct topologies, with those structures avoiding pentagonal adjacencies being more stable. Finally, the IR spectra were calculated, and an attempt at F



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