Honeycomb Network Research Articles

Designed layer assembly: a three-dimensional framework with 74% extra-framework volume by connection of infinite two-dimensional sheets.

A coordination polymer with 74% extra-framework volume is prepared by predictable linking of the honeycomb network to generate a framework-structured solid designed with two distinct connecting ligands.

A Honeycomb Network of a Paddlewheel-type Dirhodium Complex in Two Oxidation States and Pinning of the Oxidation States

Abstract The reaction of a mixture of [Rh2(acam)4(H2O)2] (Hacam = acetamide) and its radical cation salt with sodium chloride in an aqueous solution gave a mixed-valent 2-D honeycomb crystal of [{Rh2(acam)4}3(μ3-Cl)2]n·4nH2O. The oxidation states of the dirhodium units are pinned at each of the crystal sites by hydrogen bonding with solvate-water molecules.

Supramolecular synthesis of brick wall and honeycomb networks from the T-shaped molecule 5-nitrosalicylic acid

The T-geometry of O–H⋯O and C–H⋯O hydrogen bonding groups in the title molecule (5-NSA) form a brick wall network that is modularly expanded and transformed to chair cyclohexane and honeycomb architectures in molecular complexes with trans-1,4-dithiane-1,4-dioxide and dioxane. The variation in hydrogen bond synthons results in different examples of topologically related (6,3) nets.

Novel one-dimensional tubelike and two-dimensional polycatenated metal-organic frameworks.

Two novel metal-organic frameworks (MOFs) [Zn(TITMB)(OAc)](OH).8.5H(2)O (1) and [Ag(TITMB)N(3)].H(2)O (2) [TITMB = 1,3,5-tris(imidazol-1-ylmethyl)-2,4,6-trimethylbenzene, OAc = acetate anion] were synthesized and their structures were determined by X-ray crystallography. Complex 1 crystallizes in tetragonal space group P(-)4 with a = 23.2664(7) and c = 11.9890(3) A and Z = 8. 1 has a one-dimensional tubelike structure with large inner pore size of approximately 17 A. Complex 2 crystallizes in monoclinic space group C2 with a = 20.7193(10), b = 11.5677(8), and c = 12.2944(6) A, beta = 125.5770(10) degrees, and Z = 4. 2 consists of two-dimensional honeycomb networks that interpenetrate each other to generate a polycatenated structure. In these two complexes, both zinc(II) and silver(I) atoms are four-coordinated with the same tetrahedral coordination geometry. The topologies of 1 and 2 are predominated by the conformations of TITMB, which are cis, trans, trans in 1 and cis, cis, cis in 2, respectively.

Modeling of planar applicators for microwave thermotherapy

In order to improve the external applicators used for microwave thermotherapy controlled by microwave radiometry in medical applications, we propose specific planar applicators developed for heating: either annular ones to be used at the frequency equal to 915 MHz or in the shape of a horseshoe (short-circuited ring) for 434 MHz. The final goal of this paper is the realization of a honeycomb network for the treatment of larger areas and greater volumes.

Synthesis, structures and properties of two-dimensional honeycomb and stepwise networks from self-assembly of tripodal ligand 1,3,5-tris(imidazol-1-ylmethyl)-2,4,6-trimethylbenzene with metal saltsElectronic supplementary information (ESI) available: hydrogen bond network indicated by dashed lines in 2 (Fig. S1), coordination environment of Cd2B (minor component) (Fig. S2), FT-IR spectra of anion exchange (Fig. S3) and excitation and emission spectra of 2 (Fig. S4). See http://www.rsc.org/suppdata/dt/b2/b202138b/

Three new coordination networks, [Zn(L)2](ClO4)2 (1), [Mn(L)2](SO4)·16H2O (2) and [Cd3(L)2(SO4)4(H2O)2(CH3CH2OH)2][Cd(H2O)6]·2H2O (3) were obtained by self-assembly of the corresponding metal salts with 1,3,5-tris(imidazol-1-ylmethyl)-2,4,6-trimethylbenzene (L). Single crystal X-ray diffraction studies reveal that 1 and 2 have 2D honeycomb network structures in which each L ligand coordinates to three metal centers with the nitrogen atoms of imidazole group. When the ligand L reacts with CdSO4·2.7H2O, an interesting complex 3 with an unusual 2D stepwise structure involving the coordination of ethanol, water molecules, and sulfate anion, was obtained. Three distinct Cd centers reside in the complex 3. One of them binds to six water molecules to form a [Cd(H2O)6]2+ cation, and the other two are bridged by both L ligand and sulfate anion to give a 2D network. Furthermore, the complex 2 was found to have interesting properties of anion exchange and luminescence.

Spontaneous magnetization below 44 K in (benzo[1,2-d:4,5-d ′]bis[1,3,2]dithiazole) [formula omitted] driven by evaporation of crystal solvent

An organic/inorganic hybrid system, (benzo[1,2-d:4,5-d ′]bis[1,3,2]dithiazole (=BBDTA))·FeCl 4·CH 3COCH 3, is shown to exhibit a drastic change in magnetism after evaporation of the volatile crystal solvent, acetone. The solvated material, with a crystal structure consisting of ladder-like BBDTA and a honeycomb network of Fe(III)Cl 4, exhibits antiferromagnetic ordering at 6.3 K. Magnetic measurements and Mössbauer spectra suggest that the desolvated material includes a ferrimagnetic phase with T N =44.0 K.

Theory of superconducting transition of micro-hole lattices

The phase transition temperature and configurations of fluxoids in the superconducting honeycomb network are studied theoretically using the de Gennes–Alexander nodal equation. In the network with the periodic boundary condition, the transition temperature curve ( Φ– T c curve) shows a dip-structure at the points Φ/ Φ 0=1/3, 2/5, 3/7, 1/2, 4/7, 3/5, and 2/3 in the broad structure of Little–Parks oscillation. In the network with edge, the dip-structure in the Φ– T c curve is vanished. Fluxoid-patterns of the network are also discussed.

Comparison of phase boundaries between kagomé and honeycomb superconducting wire networks

We measure resistively the mean-field superconducting-normal phase boundaries of both kagome and honeycomb wire networks immersed in a transverse magnetic field. In addition to their agreement with theory about the overall shapes of phase diagrams, they show striking one-to-one correspondence between the cusps in the honeycomb and kagome phase boundaries. This correspondence is due to their geometric arrangements and agrees with Lin and Nori's recent calculation. We also find that for the frustrated honeycomb network at f=1/2, the current patterns in the superconducting phase differ between the low-temperature London regime and the higher-temperature Ginzburg-Landau regime near T_c.

De Haas-van Alphen effect in single crystal MgB2.

We report observations of quantum oscillations in single crystals of the high temperature superconductor MgB2. Three de Haas-van Alphen frequencies are clearly resolved. Comparison with band structure calculations strongly suggests that two of these come from a single warped Fermi surface tube along the c direction, and that the third arises from cylindrical sections of an in-plane honeycomb network. The measured values of the effective mass range from (0.44-0.68)m(e). By comparing these to calculated band masses, we find that the electron-phonon coupling strength lambda is a factor of approximately 3 larger for the c-axis tube orbits than for the in-plane network orbit, in accord with recent microscopic calculations.

2,4,6-Tris(4-nitrophenoxy)-1,3,5-triazine: a hexagonal host framework stabilised by the NO2-trimer supramolecular synthon.

The title molecule forms a honeycomb network of molecular and nitro-trimer synthons with guest species included in the hexagonal voids.

Synthesis and Crystal Structure of a New 2D Honeycomb‐like Cadmium (II) Complex with Tripodal Ligand

AbstractA new cadmium (II) coordination polymer, [Cd(TTTMB)2]‐(SO4) · 21H2O, where TTTMB =1,3, 5‐tris (imidazol‐1‐yl‐methyl)‐2,4,6‐trimethylbenzene, was obtained by self‐assembly of tripodal ligand TTTMB with CdSO4·2.7H2O in acetonitrile, and characterized by X‐ray crystallography. The crystal data belongs to monoclinic space group Cc with cell parameters a = 1.16891(4) nm, b=2.06671(6) nm, c = 2.48185(7) nm, β = 97.8560(10)°, R = 0.0487, wR = 0.1211. The results of structure analysis indicate that each TTTMB ligand coordinates three metal atoms and in turn each Cd(II) atom with octahedral coordination geometry connects six nitrogen atoms of imidazole group from six different TTTMB ligands to produce a 2D honeycomb network structure. There are a lot of water molecules linked by hydrogen bonds and occupied the channels formed intra‐ and inter‐sheets.

Electron density distribution in a single crystal ofMg1−xB2[x=0.045(5)]

The electron density distribution in ${\mathrm{Mg}}_{1\ensuremath{-}x}{\mathrm{B}}_{2}$ has been obtained by the precise x-ray structure analysis on high-quality single crystals. A slight deficiency $(x\ensuremath{\sim}0.04)$ of Mg has been observed. The obtained sectional Fourier map in the B plane shows the triangle-shaped electron distribution extended along the B-B bonds, which indicates the typical ${\mathrm{sp}}^{2}$ orbitals of the boron atom. Further, the difference Fourier maps clearly reveal the $\mathrm{B}\ensuremath{\sigma}{(sp}^{2})$ covalent bonds within the B plane and $\mathrm{B}\ensuremath{\pi}{(p}_{z})$ orbitals perpendicular to the B plane. Both \ensuremath{\sigma} and \ensuremath{\pi} bonds construct the two-dimensional honeycomb network of the B atoms along the (001) plane. In contrast, there is no covalency between the B and Mg atoms, indicating the ionic bonds between B and Mg layers.

HIGHER DIMENSIONAL HONEYCOMB NETWORKS

We define the higher dimensional honeycomb graphs as a generalization of hexagonal plane tessellation, and consider it as a multiprocessor interconnection network. A 3-D honeycomb mesh network with n nodes has degree 4 and diameter approximately 3.63n. The network cost, defined as the product of degree and diameter, is about 20 percents better for the 3-D honeycomb than for the 3-D mesh. We describe the addressing scheme, the routing and broadcasting algorithms for three-dimensional and higher dimensional honeycombs. Furthermore, a formula for the diameter of a higher dimensional honeycomb network of given size is determined.

Corrections to scaling for percolative conduction: Anomalous behavior at smallL

Recently Grassberger [Physica A 262, 251 (1999)] has shown that the correction to scaling for the conductance of a bond-percolation network on a square lattice is a nonmonotonic function of the linear lattice dimension with a minimum at $L=10,$ while this anomalous behavior is not present in the site-percolation networks. We perform a high-precision numerical study of the bond-percolation random-resistor networks on the square, triangular, and honeycomb lattices to further examine this result. We use the arithmetic, geometric, and harmonic means to obtain the conductance and find that the qualitative behavior does not change: it is not related to the shape of the conductance distribution for small system sizes. We show that the anomaly at small L is absent on the triangular and honeycomb networks. We suggest that the nonmonotonic behavior is an artifact of approximating the continuous system for which the theory is formulated by a discrete one that can be simulated on a computer. We show that by slightly changing the definition of the linear lattice size we can eliminate the minimum at small L without significantly affecting the large L limit.

Self-Assembled Honeycomb Networks of Gold Nanocrystals

Size-monodisperse 35 Å diameter, sterically stabilized gold nanocrystals self-assemble into hexagonal networks, or two-dimensional honeycombs, during drop casting of a dispersion onto a substrate under the appropriate conditions. By changing the nanocrystal concentration prior to deposition, the microscopic morphology of self-assembled nanocrystal structures can be tuned from rings at high concentrations to honeycombs at low concentrations. The temperature dependence of the surface tension of the gold nanocrystal dispersions was measured using a ring tensiometer and found to depend on the particle concentration, particle size, and distribution. The morphological transition from rings to honeycombs appears to occur due to a transition from diffusive to convective fluid flow during solvent evaporation, which results directly from the surface tension and thermal conductivity differences between the dispersions.

Bonding Nature in MgB2

The accurate charge density of MgB 2 was observed at room temperature (R.T.) and 15 K by the maximum entropy method (MEM)/Rietveld analysis using synchrotron radiation powder data. The obtained charge density clearly revealed the covalent bonding feature of boron forming the 2D honeycomb network in the basal plane, on the other hand, Mg is found to be in divalent state. A subtle but clear charge concentration was found on boron 2D sheets at 15 K, which should be related to superconductivity.

A New Macroporous Luminescent Hydrogel from Poly(allylamine)

The synthesis of a novel highly swelling, macroporous hydrogel from poly(allylamine) using 3-chloropentan-2,4-dione as a crosslinker is reported. The swelling of the hydrogel was sensitive to changes in pH, temperature, and the extent of crosslinking. The dry gel exhibited a regular honeycomb network with smooth macropores. The hydrogel was inherently luminescent, and so was a metal polychelate.

`Chicken-coop' network assembled by hydrogen bonds with bridging nitrate ions. Crystal structure of bis(4,4 ′-bipyridinium) diaquatetraisothiocyanatonickellate(II) dinitrate

The two-dimensional hydrogen-bonded honeycomb networks formulated as (4,4 ′-H 2bipy) 2[Ni(NCS) 4(H 2O) 2](NO 3) 2(4,4 ′-H 2bipy=4,4 ′-bipyridinium) with R 10 12(64) rings and ca. 24×20 Å internal dimensions are triply interwoven to generate two-dimensional `chicken-coop' sheets, featuring unusual hydrogen bonds involving the NO 3 − groups.

A unified formulation of honeycomb and diamond networks

Honeycomb and diamond networks have been proposed as alternatives to mesh and torus architectures for parallel processing. When wraparound links are included in honeycomb and diamond networks, the resulting structures can be viewed as having been derived via a systematic pruning scheme applied to the links of 2D and 3D tori, respectively. The removal of links, which is performed along a diagonal pruning direction, preserves the network's node-symmetry and diameter, while reducing its implementation complexity and VLSI layout area. In this paper, we prove that honeycomb and diamond networks are special subgraphs of complete 2D and 3D tori, respectively, and show this viewpoint to hold important implications for their physical layouts and routing schemes. Because pruning reduces the node degree without increasing the network diameter, the pruned networks have an advantage when the degree-diameter product is used as a figure of merit. Additionally, if the reduced node degree is used as an opportunity to increase the link bandwidths to equalize the costs of pruned and unpruned networks, a gain in communication performance may result.