Nanostructures Cluster Models in Solution: Extension to C, BC2N, and BN Fullerenes, Tubes, and Cones

Introduction

Nanoparticles (NPs) interest arose from the shape-dependent physical properties of nanoscale materials (Faraday, 1857; Murphy et al. 2010). Single-wall C-nanocones (SWNCs) were used to study the nucleation/growth of curved C-nanostructures (NSs) suggesting pentagon role. When a pentagonal defect is introduced into an C_graphite sheet (C_graphene) via extraction of a 60º sector from the piece a cone leaf is formed. The presence of pentagons in an SWNC apex is analogue of single-wall C-nanotube (SWNT) tip topology. Balaban et al. (1994), Klein (2002) and Klein and Balaban (2006) analyzed the eight classes of positive-curvature graphitic nanocones, and Klein (1992), Misra et al. (2009ab), Balaban & Klein (2009) and Klein & Balaban (2011) examined the Clar theory for conjugated C-NSs. The SWNT ends predicted electronic states related to topological defects in C_graphite lattice (Tamura & Tsukada, 1995). Kim et al. (1999) observed resonant peaks in the density of states in SWNTs and Carroll et al. (1997), in multiple-wall C-nanotubes (MWNTs).

Krishnan et al. (1997) observed SWNCs with discrete opening angles θ of ca. 19, 39, 60, 85 and 113º in C-sample generated by hydrocarbon pyrolysis. Observation was explained by a cone wall model composed of wrapped C_graphene sheets, where geometrical requirement for seamless connection naturally accounted for semi-discrete character and absolute angles θ. Total disclinations are multiples of 60º corresponding to number (P ≥ 0) of pentagons in SWNC apices. Considering C_graphene-sheet symmetry and Euler theorem five SWNC types are obtained from continuous C_graphene sheet matching to P = 1–5. Angle results θ = sin(θ/2) = 1 – P/6, leading to flat discs and caped SWNTs corresponding to P = 0, 6, respectively; most abundant SWNC with P = 5 (θ ≈ 19º) is single-wall C-nanohorn (SWNH). Several configurations exist for given SWNC angle depending on pentagon arrangement. According to isolated pentagon rule (IPR) configurations containing isolated pentagons lead to isomers that are more stable than those including grouped ones (Kroto, 1987); Han & Jaffe (1998) derived another rules from ab initio calculations. Covalent SWNCs functionalization with NH₄⁺ improved solubility (Tagmatarchis et al., 2006), which was achieved by skeleton (Cioffi et al., 2006, 2007; Pagona et al., 2007b)/cone-end (Pagona et al., 2006a) functionalization and supramolecular π–π stacking interactions (Pagona et al., 2006b, 2007a; Zhu et al., 2003) with pyrenes/porphyrins. An MNDO calculation of BN substitutions in C₆₀ showed that analogous one gave B₃₀N₃₀ (Xia et al., 1992). Atom substitution in C_diamond by alternating B/N atoms provided BN-cubic (Silaghi-Dumitrescu et al., 1993). BN-hexagonal (h) resembles C_graphite since it consists of fused planar six-membered B₃N₃ rings; however, interlayer B–N interactions exist. Hamilton et al. (1993, 1995) and Loiseau et al. (1996) visualized BN nanotubes. Rubio et al. (1994) proposed BN-h. Bourgeois et al. (1999, 2000) and Terauchi et al. (2000) observed BN nanocones, and Mota et al. (2003) and Machado et al. (2003abc, 2004, 2005) calculated them; most abundant ones presented 240/300º disclinations. Thesing et al. (2006) computed BN/AlN nanotube junction. Calculations of BC₂N tubules (Miyamoto et al., 1994) and C_graphite-like onion/nanotube production using layered materials [e.g., WS₂ (Tenne et al., 1992), MoS₂ (Margulis et al., 1993), BC₂N, BC₃ (Weng-Sieh et al., 1995), BN (Chopra et al., 1995)] allowed structures with oxidation resistance and low thermal/electronic conductivities. The NSs of pyrolytically grown B_xC_yN_z were studied: concentration profiles along/across tubes revealed that B, C and N are separated into C/BN domains; compound provides materials that are useful as robust nanocomposites (NCs) and semiconductor devices enhanced towards oxidation (Kohler-Redlich et al., 1999; Madden, 2009; Terrones et al., 1996). Kallus et al. (2010) examined dense periodic packings (Betke & Henk, 2000; Chen et al., 2010) of tetrahedra and Baker & Kudrolli (2010), those of Platonic solids.