Compositions of nanoparticles of cubic symmetry

The formulas for calculation of the number of particles in structures of cubic symmetry O _h are reported. The numbers of atoms in the shells of cubic symmetry are determined by four structurally invariant numbers and the “quantum number” of the order n of the group. The classification of the shells of cubic symmetry is presented, and eight classes of shells are revealed. A key role in this classification is played by basic shells; in the case of close-packed spheres, these basic shells are repeated every six layers. The sum of all coordination numbers of all atoms of subshells is 24. The possibility of the existence of new fullerenes and nanoparticles of elemental boron and its oxides is considered.     

Compositions and structures of nanoparticles of tetrahedral symmetry

The formulas for calculation of the composition of nanoparticles with symmetry group T _d are reported. The numbers of atoms in the shells of tetrahedral symmetry are determined by three structurally invariant numbers and the “quantum number” of the group order n. Four classes of all possible nanostructures with symmetry group T _d are revealed: C _{? + 12z} , where z = 0, 1, 2, ..., and C _? is C ₄, C ₆, C ₈, C ₁₀, or C ₁₄. The sum rule for the coordination numbers of the shell sites located on the axes of symmetry is obtained. The six-shell periodicity of the number of occupied sites located on the symmetry axes and in symmetry planes is revealed.     

Compositions of the shells of nanoparticles with pentagonal symmetry

A method of calculation of the number of atoms in the structure of nanoforms with pentagonal symmetry (fullerenes, nanoparticles, clusters) depending on the arrangement of atoms on the symmetry elements of the I _h group has been developed. The formulas for calculation of the number of particles in all possible shells, including multilayer ones, are reported. The numbers of atoms in the shells of pentagonal symmetry are determined by four structurally invariant numbers and the “quantum number” of the order n of the group. The classification of all possible atomic shells S _{? + 60z} (z = 0, 1, ...) is presented, and the constructions of the basic shells S _? (? = 12, 20, 30, 50, 60) are given. For each basic shell, the sum rule is met: the sum of the coordination numbers of the elements of subshells is equal to 60. In clusters with magic numbers, basic shells are periodically repeated. In addition to the known shells of nanostructures, the formulas of new structures that are expected to be stable—B₂₀O₃₀, B₆₀O₉₀ (B₂O₃), and B₉₀O ₁₃₀ ¹⁰⁺ (borate)—are reported for the first time. The same is valid for similar compounds of Group III elements.     

A bicontinuous mesophase geometry with hexagonal symmetry

We report that a specific realization of Schwarz's triply periodic hexagonal minimal surface is isotropic with respect to the Doi-Ohta interface tensor and simultaneously has minimal packing and stretching frustration similar to those of the commonly found cubic bicontinuous mesophases. This hexagonal surface, of symmetry P6(3)/mmc with a lattice ratio of c/a = 0.832, is therefore a likely candidate geometry for self-assembled lipid/surfactant or copolymer mesophases. Furthermore, both the peak position ratios in its powder diffraction pattern and the elastic moduli closely resemble those of the cubic bicontinuous phases. We therefore argue that a genuine possibility of experimental misidentification exists.     

Preparation and characterization of hexagonal close-packed Ni nanoparticles

Hexagonal close-packed Ni nanoparticles were synthesized using a heat-treating technique with the precursors prepared by the sol-gel method. The synthesis condition, structure, and morphology of the samples were characterized and analysed by thermogravimetric analysis (TG), differential thermal analysis (DTA), X-ray diffraction (XRD) and transmission electron microscopy (TEM). Results indicate that the hexagonal close packed Ni nanoparticles were synthesized at a heat-treating temperature of 300°C. The cell constants are calculated at a = 0.2652 nm and c = 0.4334 nm. The average grain size of the hexagonal close-packed Ni particles evaluated by Scherrer equation is about 12 nm. The phase transformation from a hexagonal close-packed Ni to a face-centered cubic Ni structure occurred when the heat-treating temperature was increased. __________ Translated from Chemical Journal of Chinese Universities, 2007, 28(7): 1232–1234 [译自: 高等学校化学学报]     

Dewetting self-assembly of nanoparticles into hexagonal array of nanorings

Nanoparticles self-assembled into ring-shaped aggregates that were arranged in a two-dimensional (2D) hexagonal pattern. This hierarchic pattern was prepared by casting a toluene solution composed of polystyrene (PS) and Ag nanoparticles (NP). Dewetting of the thin composite layer induced the mesoscopic hexagonal array of PS-NP droplets. Within each dried droplet (dot), Ag nanoparticles self-assembled into a spot- or a ring-shaped 2D superlattice alternatively depending on the size of the dot, which was controlled by the molecular weight of PS.     

Fivefold symmetry in superlattices of monolayer-protected gold nanoparticles

Three-dimensional (3D) superlattices of gold nanoparticles were prepared at an air/solution interface. The surface of the gold nanoparticles used is protected by N-acetylglutathione (NAG). Morphological studies revealed that the superlattices formed fivefold symmetric structures such as pentagonal rod, decahedron, and icosahedron, which were probably developed by multiple twinning. Moreover, high-resolution surface images of the superlattices in fivefold symmetry showed excellent ordered arrangements of nanoparticles with both close-packed and non-close-packed structures.     

Preparation of conjugated polymeric columns with a hexagonal symmetry from star-shaped supramolecular liquid crystals

New conjugated polymeric columns with a hexagonal symmetry were prepared via topochemical polymerisation of star-shaped supramolecular liquid crystals formed by hydrogen bonding between a phloroglucinol core and pyridine derivatives containing a diacetylenic group in the alkyl chain. The mesomorphic properties of the supramolecular monomer and its photopolymerisation behaviour were investigated. The supramolecular liquid crystal exhibited a rectangular columnar mesophase. Photopolymerisation of supramolecular monomer along the column axis in the liquid crystalline state provided well-ordered conjugated polydiacetylenic columns with a two-dimensional hexagonal symmetry. Fourier transform infrared and ultraviolet–visible spectroscopy affirmed that conjugated polydiacetylenes were produced by 1,4-polymerisation of the supramolecular monomer along the column axis. X-ray diffraction analysis showed that a two-dimensional columnar order in the supramolecular monomer was maintained after photopolymerisation, and that the resulting polydiacetylene had a hexagonal array of conjugated columns. Our controlled methodology provides a new route to conjugated polymeric columns with highly ordered structures by self-assembly and polymerisation of star-shaped supramolecular liquid crystals.     

Transition metal vinylidene complexes as supramolecular building blocks: nucleobase-mediated self-assembly of crystals with hexagonal symmetry

Reaction of the ruthenium half sandwich compound RuCl(eta(5)-C(5)H(5))(PPh(3))(2) with the uracil (Ur) substituted alkyne HC[triple bond, length as m-dash]CUr in the presence of halide scavengers NH(4)X (X = PF(6), BF(4), OTf) results in the formation of the vinylidene complexes [Ru([double bond, length as m-dash]C[double bond, length as m-dash]CHUr)(eta(5)-C(5)H(5))(PPh(3))(2)][X] which crystallize in the hexagonal space group P6(3)/m. The hexagonal symmetry inherent to the system is due to the formation of a hydrogen bonded array mediated by the two sets of donor-acceptor units on the uracil, resulting in the formation of a cyclic "rosette" containing six ruthenium cations. In solution the (1)H and (31)P{(1)H} NMR spectra of the vinylidene complexes are both concentration and temperature dependent, in accord with the presence of monomer-dimer equilibria in which the rate of rotation of the vinylidene group is fast on the NMR timescale in the monomeric species, but slow in the dimers. The isoelectronic molybdenum-containing vinylidene complex [Mo(eta(7)-C(7)H(7))(dppe)([double bond, length as m-dash]C[double bond, length as m-dash]CHUr)][BF(4)] (dppe = 1,2-bis(diphenylphosphino)ethane) has also been prepared, but forms symmetric dimers in the solid state.     

Comparison of the magnetic properties of metastable hexagonal close-packed Ni nanoparticles with those of the stable face-centered cubic Ni nanoparticles

We report the first magnetic study of pure and metastable hexagonal close-packed (hcp) Ni nanoparticles (sample 1). We also produced stable face-centered cubic (fcc) Ni nanoparticles, as mixtures with the hcp Ni nanoparticles (samples 2 and 3). We compared the magnetic properties of the hcp Ni nanoparticles with those of the fcc Ni nanoparticles by observing the evolution of magnetic properties from those of the hcp Ni nanoparticles to those of the fcc Ni nanoparticles as the number of fcc Ni nanoparticles increased from sample 1 to sample 3. The blocking temperature (T(B)) of the hcp Ni nanoparticles is approximately 12 K for particle diameters ranging between 8.5 and 18 nm, whereas those of the fcc Ni nanoparticles are 250 and 270 K for average particle diameters of 18 and 26 nm, respectively. The hcp Ni nanoparticles seem to be antiferromagnetic for T < T(B) and paramagnetic for T > T(B). This is very different from the fcc Ni nanoparticles, which are ferromagnetic for T < T(B) and superparamagnetic for T > T(B). This unusual magnetic state of the metastable hcp Ni nanoparticles is likely related to their increased bond distance (2.665 angstroms), compared to that (2.499 angstroms) of the stable fcc Ni nanoparticles.     

On the microstructure and symmetry of apparently hexagonal BaAl2O4

The P6₃ (a=2a_p, b=2b_p, c=c_p) crystal structure reported for BaAl₂O₄ at room temperature has been carefully re-investigated by a combined transmission electron microscopy and neutron powder diffraction study. It is shown that the poor fit of this P6₃ (a=2a_p, b=2b_p, c=c_p) structure model for BaAl₂O₄ to neutron powder diffraction data is primarily due to the failure to take into account coherent scattering between different domains related by enantiomorphic twinning of the P6₃22 parent sub-structure. Fast Fourier transformation of [0 0 1] lattice images from small localized real space regions (∼10 nm in diameter) are used to show that the P6₃ (a=2a_p, b=2b_p, c=c_p) crystal structure reported for BaAl₂O₄ is not correct on the local scale. The correct local symmetry of the very small nano-domains is most likely orthorhombic or monoclinic.     

Control of stripelike and hexagonal self-assembly of gold nanoparticles by the tuning of interactions between triphenylene ligands

We describe the self-assembly of gold nanoparticles (Au NPs) protected with newly synthesized discotic liquid crystalline molecules of hexaalkoxy-substituted triphenylene (TP) in mixed toluene/methanol solvent. The stripelike (i.e., 2D consisting of linear 1D in stripe) self-assembly is realized successfully by the aid of pi-pi stacking of TP ligand on Au NPs. The smaller Au NPs with TP (AuTP) or the longer alkyl chain between TP and the gold core provide more free spaces among TP moieties. These spaces allow easy insertion of TP on adjacent AuTPs to lead an interparticle pi-pi interaction to form the stripelike arrangement. The solvent hydrophilicity can also serve as a controlled index to tune arrangement among stripelike, hexagonal close packed (hcp), or disorder. We have changed the solvent hydrophilicity by changing the ratio of methanol to toluene, which affects the balance of solution of AuTP (in toluene) and deposition (in methanol). The larger space between TPs and appropriate solvent hydrophilicity realize stripelike self-assembly caused by a strong pi-pi interaction between TPs, which was characterized by TEM, as well as fluorescence, dynamic light scattering, and 1H NMR spectra.     

Self-assembled geometric liquid-crystalline nanoparticles imaged in three dimensions: hexosomes are not necessarily flat hexagonal prisms

Attempts to understand the complex 3D morphology of non-lamellar liquid-crystalline nanostructured particles, formed by the dispersion of a reversed hexagonal phase (hexosomes) and bicontinuous cubic phase (cubosomes) in water, have been limited by the lack of suitable 3D imaging techniques. Using cryo-field emission scanning electron microscopy, we show that whereas the structure of cubosomes generally reflects that anticipated from modeling approaches, hexosomes, which were previously proposed to be flat hexagonal prisms, in fact often possess a "spinning-top-like" structure, which is likely to influence their interactions with surfaces.     

NiCe bimetallic nanoparticles embedded in hexagonal mesoporous silica (HMS) for reverse water gas shift reaction

Reverse water gas shift (RWGS) reaction is a crucial process in CO₂ utilization. Herein, Ni- and NiCe-containing hexagonal mesoporous silica (Ni-HMS and NiCe-HMS) catalysts were synthesized using an in-situ one-pot method and applied for RWGS reaction. At certain reaction temperatures 500-750 °C, Ni-HMS samples displayed a higher selectivity to the preferable CO than that of conventionally impregnated Ni/HMS catalyst. This could be originated from the smaller NiO nanoparticles over Ni-HMS catalyst. NiCe-HMS exhibited higher activity compared to Ni-HMS. The catalysts were characterized by means of TEM, XPS, XRD, H₂-TPR, CO₂-TPD, EPR and N₂ adsorption-desortion technology. It was found that introduction of Ce created high concentration of oxygen vacancies, served as the active site for activating CO₂. Also, this work analyzed the effect of the H₂/CO₂ molar ratio on the best NiCe-HMS. When reaction gas H₂/CO₂ molar ratio was 4 significantly decreased the selectivity to CO at low temperature, but triggered a higher CO₂ conversion which is close to the equilibrium.     

Chemisorption-induced spin symmetry breaking in gold clusters and the onset of paramagnetism in capped gold nanoparticles

We present a simple model to describe the induction of magnetic behavior on gold clusters upon chemisorption of one organic molecule with different chemical linkers. In particular, we address the problem of stability of the lowest lying singlet and show that for some linkers there exists a spin symmetry-breaking that lowers the energy and leads to preferential spin density localization on the gold atoms neighboring the chemisorption site. The model is basically an adaptation of the Stoner model for itinerant electron ferromagnetism to finite clusters and it may have important implications for our understanding of surface magnetism in larger nanosystems and its relevance to electronic transport in electrode-molecule interfaces.     

Extremal hexagonal chains

Some extremal properties of the linear chainL _h ofh hexagons are pointed out. In the class of all hexagonal chains withh hexagons,L _h has minimumK,Z andx ₁ values, as well as maximum W and values;K = number of perfect matchings,Z = number of independent edge sets (Hosoya index),x ₁ = largest graph eigenvalue,W = Wiener index, = number of independent vertex sets (Merrifield-Simmons index). The extremality ofL _h with respect toZ, andx ₁ is demonstrated here for the first time.Dedicated to Frank Harary, teacher, inspirer and friend, pioneer, champion and proprietor of graph theory, on the occasion of his 70th birthday.