Pentagonal Network Research Articles

The multiplicative degree-Kirchhoff index and complexity of a class of linear networks

<abstract><p>In this paper, we focus on the strong product of the pentagonal networks. Let $ R_{n} $ be a pentagonal network composed of $ 2n $ pentagons and $ n $ quadrilaterals. Let $ P_{n}^{2} $ denote the graph formed by the strong product of $ R_{n} $ and its copy $ R_{n}^{\prime} $. By utilizing the decomposition theorem of the normalized Laplacian characteristics polynomial, we characterize the explicit formula of the multiplicative degree-Kirchhoff index completely. Moreover, the complexity of $ P_{n}^{2} $ is determined.</p></abstract>

Analyzing the normalized Laplacian spectrum and spanning tree of the cross of the derivative of linear networks

<abstract><p>In this paper, we focus on the strong product of the pentagonal networks. Let $ R_{n} $ be a hexagonal network composed of $ 2n $ pentagons and $ n $ quadrilaterals. Let $ P_{n}^{2} $ denote the graph formed by the strong product of $ R_{n} $ and its copy $ R_{n}^{\prime} $. By utilizing the decomposition theorem of the normalized Laplacian characteristics polynomial, we characterize the explicit formula of the multiplicative degree-Kirchhoff index completely. Moreover, the complexity of $ P_{n}^{2} $ is determined.</p></abstract>

Quasicrystalline Antimony Thin Films

AbstractThe growth of antimony (Sb) thin films on the fivefold surface of icosahedral Ag−In−Yb quasicrystal has been studied by scanning tunneling microscopy (STM) and x‐ray photoelectron spectroscopy (XPS). At low coverage, the deposited Sb yields a network of pentagons of different sizes and heights. These Sb pentagons can be mapped by a pentagonal tiling of the substrate and thus exhibit quasicrystalline long‐range order. Subsequent deposition of Sb yields a disordered film. XPS observations of the growth mode are consistent with the STM results.

Anisotropic Thermoelectric Materials: Pentagonal PtM2 (M = S, Se, Te).

We here report a new pentagonal network structure of the PtM2 (M = S, Se, Te) monolayers with the P21/c (no. 14) space group. The electronic structure and thermoelectric properties of the pentagonal PtM2 monolayers are calculated through the VASP and BoltzTraP codes. We verify their dynamic and thermodynamic stabilities by calculating their phonon spectra and simulating ab initio molecular dynamics. It is found that the new material belongs to the medium-wide indirect band gap semiconductors from the PBE and HSE06 methods. At 300 K, the lattice thermal conductivities (Kl) of the pentagonal PtTe2 in the x and y directions are the smallest among these three materials, being 1.77 and 5.17 W/m K, respectively. The anisotropic zT values (2.60/1.14) in the x/y direction of the pentagonal PtTe2 at 300 K are much greater than those of the pentagonal PtSe2 (1.75/0.82) and the pentagonal PtS2 (0.58/0.16) at 300 K. Importantly, the p-type pentagonal PtTe2 also has excellent thermoelectric properties at 600 K, with a zT value of 5.03 in the x direction, indicating that the p-type pentagonal PtTe2 has a good application potential in the thermoelectric field.

Retraction: Pentadiamond: A Hard Carbon Allotrope of a Pentagonal Network of sp^{2} and sp^{3} C Atoms [Phys. Rev. Lett. 125, 016001 (2020)

Retraction of DOI: 10.1103/PhysRevLett.125.016001.

Pentadiamond: A Hard Carbon Allotrope of a Pentagonal Network of sp^{2} and sp^{3} C Atoms.

A pentagonal covalent network consisting of sp^{2} and sp^{3} C atoms has been investigated based on the density functional theory. Our theoretical investigations clarified that the pentagonal covalent network is a metastable three-dimensional carbon allotrope with the Fm3[over ¯]m space group possessing remarkable mechanical properties: relatively high bulk modulus of 381GPa together with a negative Poisson's ratio of -0.241. Accordingly, the pentagonal covalent network possesses extremely high Young's and shear moduli of 1691 and 1113GPa, respectively, surpassing those of the diamond. The electronic structure of the pentagonal network is a semiconductor with an indirect band gap of 2.52eV between L and X points for valence and conduction band edges, respectively, with the relatively small carrier masses.

Spectral analysis for weighted iterated pentagonal graphs and its applications

Deterministic weighted networks have been widely used to model real-world complex systems. In this paper, we study the weighted iterated pentagonal networks. From the construction of the network, we derive recursive relations of all eigenvalues and their multiplicities of its normalized Laplacian matrix from the two successive generations of the weighted iterated pentagonal networks. As applications of spectra of the normalized Laplacian matrix, we study the Kemeny’s constant, the multiplicative degree-Kirchhoff index, and the number of weighted spanning trees and derive their exact closed-form expressions for the weighted iterated pentagonal networks.

Dimer Physics in the Frustrated Cairo Pentagonal Antiferromagnet Bi_{2}Fe_{4}O_{9}.

The research field of magnetic frustration is dominated by triangle-based lattices but exotic phenomena can also be observed in pentagonal networks. A peculiar noncollinear magnetic order is indeed known to be stabilized in Bi_{2}Fe_{4}O_{9} materializing a Cairo pentagonal lattice. We present the spin wave excitations in the magnetically ordered state, obtained by inelastic neutron scattering. They reveal an unconventional excited state related to local precession of pairs of spins. The magnetic excitations are then modeled to determine the superexchange interactions for which the frustration is indeed at the origin of the spin arrangement. This analysis unveils a hierarchy in the interactions, leading to a paramagnetic state (close to the Néel temperature) constituted of strongly coupled dimers separated by much less correlated spins. This produces two types of response to an applied magnetic field associated with the two nonequivalent Fe sites, as observed in the magnetization distributions obtained using polarized neutrons.

A unique pentagonal network structure of the NiS2 monolayer with high stability and a tunable bandgap.

Two dimensional atomic crystals with pentagonal building blocks have attracted extensive interest in recent years for their fundamental significance and potential applications in nanoscale devices. Here, with the help of ab initio calculations based on density functional theory, we report a unique pentagonal structured NiS2 monolayer in P4[combining macron]21m symmetry, named P-NiS2. Its dynamic stability has been confirmed by phonon mode analysis. Molecular dynamics simulations and total-energy calculations show that this new P-NiS2 has robust thermal stability and energetically more stable than all other reported NiS2 monolayer structures. Electronic band structure calculations show that it is a semiconductor with an indirect band gap of 1.94 eV. Furthermore, we find that small strain triggers a transition from the indirect to direct band gap for this P-NiS2, suggesting its great potential for applications based on strain-engineering techniques.

Toward obtaining 2D and 3D and 1D PtPN with pentagonal pattern

We apply an alloying strategy to single-layer PtN$_2$ and PtP$_2$, aiming to obtain a single-layer Pt-P-N alloy with a relatively low formation energy with reference to its bulk structure. We perform structure search based on a cluster-expansion method and predict single-layer and bulk PtPN consisting of pentagonal networks. The formation energy of single-layer PtPN is significantly lower in comparison with that of single-layer PtP$_2$. The predicted bulk structure of PtPN adopts a structure that is similar to the pyrite structure. We also find that single-layer pentagonal PtPN, unlike PtN$_2$ and PtP$_2$, exhibits a sizable, direct PBE band gap of 0.84 eV. Furthermore, the band gap of single-layer pentagonal PtPN calculated with the hybrid density functional theory is 1.60 eV, which is within visible light spectrum and promising for optoelectronics applications. In addition to predicting PtPN in the 2D and 3D forms, we study the flexural rigidity and electronic structure of PtPN in the nanotube form. We find that single-layer PtPN has similar flexural rigidity to that of single-layer carbon and boron nitride nanosheets and that the band gaps of PtPN nanotubes depend on their radii. Our work shed light on obtaining an isolated 2D planar, pentagonal PtPN nanosheet from its 3D counterpart and on obtaining 1D nanotubes with tunable bandgaps.

Hydrogen Desorption from Pentagraphane

Thermally activated hydrogen desorption from pentagraphane is studied by atomistic computer simulation. Pentagraphane is a recently predicted quasi-two-dimensional hydrocarbon compound that represents a pentagraphene single layer, in which both sides are covered with hydrogen and the C–C bonds form a network of adjacent pentagons, whereas the hexagons characteristic of carbon nanostructures are lacking. The effect of hydrogen desorption on the electronic structure, phonon density of states, and Young’s modulus are studied. The temperature dependence of the characteristic desorption time is determined by the molecular-dynamics method.

Десорбция водорода из пентаграфана

AbstractThermally activated hydrogen desorption from pentagraphane is studied by atomistic computer simulation. Pentagraphane is a recently predicted quasi-two-dimensional hydrocarbon compound that represents a pentagraphene single layer, in which both sides are covered with hydrogen and the C–C bonds form a network of adjacent pentagons, whereas the hexagons characteristic of carbon nanostructures are lacking. The effect of hydrogen desorption on the electronic structure, phonon density of states, and Young’s modulus are studied. The temperature dependence of the characteristic desorption time is determined by the molecular-dynamics method.

Mechanical Properties of Penta-Graphene Nanotubes

Penta-graphene is the name given to a novel puckered monolayer of carbon atoms tightly packed into an inerratic pentagonal network, theoretically, which exhibits excellent thermal and mechanical stability and can be rolled into penta-graphene nanotubes (PGNTs). Herein, we perform the first simulation study of mechanical properties of PGNTs under uniaxial tension. In addition to comparable mechanical properties with that of carbon nanotubes (CNT), it is found that PGNTs possess promising extensibility with typical plastic behavior due to the irreversible pentagon-to-polygon structural transformation and the hexagon carbon ring becomes the dominating structural motif after the transformation. The plastic characteristic of PGNTs is inherent with strain-rate and tube-diameter independences. Moreover, within ultimate temperature (T<1100 K), tensile deformed PGNTs manifest similar phase transition with an approximate transition ratio from pentagon to hexagon. The intrinsic insight provides a fundamental understanding of mechanic properties of PGNTs, which should open up a novel perspective for the design of plastic carbon-based nanomaterials.

Heptagons in Aromatics: From Monocyclic to Polycyclic.

Heptagons in Aromatics: From Monocyclic to Polycyclic.

An In Vitro Assessment of the Cerebral Hemodynamics Through Three Patient Specific Circle of Willis Geometries

The Circle of Willis (CoW) is a complex pentagonal network comprised of fourteen cerebral vessels located at the base of the brain. The collateral flow feature within the circle of Willis allows the ability to maintain cerebral perfusion of the brain. Unfortunately, this collateral flow feature can create undesirable flow impact locations due to anatomical variations within the CoW. The interaction between hemodynamic forces and the arterial wall are believed to be involved in the formation of cerebral aneurysms, especially at irregular geometries such as tortuous segments, bends, and bifurcations. The highest propensity of aneurysm formation is known to form at the anterior communicating artery (AcoA) and at the junctions of the internal carotid and posterior communicating arteries (PcoAs). Controversy still remains as to the existence of blood flow paths through the communicating arteries for a normal CoW. This paper experimentally describes the hemodynamic conditions through three thin walled patient specific models of a complete CoW based on medical images. These models were manufactured by a horizontal dip spin coating method and positioned within a custom made cerebral testing system that simulated symmetrical physiological afferent flow conditions through the internal carotid and vertebral arteries. The dip spin coating procedure produced excellent dimensional accuracy. There was an average of less than 4% variation in diameters and wall thicknesses throughout all manufactured CoW models. Our cerebral test facility demonstrated excellent cycle to cycle repeatability, with variations of less than 2% and 1% for the time and cycle averaged flow rates, respectively. The peak systolic flow rates had less than a 4% variation. Our flow visualizations showed four independent flow sources originating from all four inlet arteries impacting at and crossing the AcoA with bidirectional cross flows. The flow paths entering the left and right vertebral arteries dissipated throughout the CoW vasculature from the posterior to anterior sides, exiting through all efferent vessels. Two of the models had five flow impact locations, while the third model had an additional two impact locations within the posterior circulation caused by an additional bidirectional cross flows along the PcoAs during the accelerating and part of the decelerating phases. For a complete CoW, bidirectional cross flows exist within the AcoA and geometrical variations within the CoW geometry can either promote uni- or bidirectional cross flows along the PcoAs.

High-resolution structure of a plasmid-encoded dihydrofolate reductase: pentagonal network of water molecules in theD2-symmetric active site

R67 plasmid-encoded dihydrofolate reductase (R67 DHFR) is an NADPH-dependent homotetrameric enzyme that catalyzes the reduction of dihydrofolate to tetrahydrofolate. The amino-acid sequence and molecular architecture of R67 DHFR and its inhibitory properties toward folate analogues are different from those of chromosomal DHFR. Here, the crystal structure of R67 DHFR refined using 1.1 A resolution data is presented. Blocked full-matrix least-squares refinement without restraints resulted in a final R factor of 11.4%. The anisotropic atomic displacement parameters analyzed by Rosenfield matrices and translation-libration-screw validation suggested four quasi-rigid domains. A total of ten Calpha-H...O hydrogen bonds were identified between the beta-strands. There is reasonable structural evidence that His62 is not protonated in the tetramer, which is in accord with previous pH-profile studies. The side chain of Gln67 that protrudes into the active site exhibits dual conformation, a feature noticed for the first time owing to the availability of atomic resolution data. The R67 DHFR active site is unique: it has D2 symmetry and is a large active site with a pentagonal network of water molecules and exposure of backbone atoms to solvent; the central pore is favorable for planar ring-stacking interactions. The geometrical shape, overall symmetry, local asymmetry and waters appear to dominate the binding of ligands, catalysis and inhibition.

ELECTRONIC STRUCTURE OF Si20 FULLERENE AND SOLID Si20

The electronic structure of the dodecahedral Si 20 fullerene obtained in the density-functional theory is discussed. In addition, the Si 46 lattice, which is known to be the real geometry of the Si atoms when crystallized with metal atoms, is pointed out to be essentially solid Si 20, and its geometrical and electronic properties are also discussed. The novel pentagonal bond network in these materials is found to have strong influence on their electronic structure. In the case of Na 2 Ba 6 Si 46, which is the ideal phase of superconducting-doped solid Si 20, the high Fermi-level density of states due to the hybridization between the Ba states and the Si 46 conduction-band states is considered to be important for the observed superconductivity.

Electronic structure of Si46 and Na2Ba6Si46.

We study solids of ${\mathrm{Si}}_{20}$ fullerenes, ${\mathrm{Si}}_{46}$ and ${\mathrm{Na}}_{2}$${\mathrm{Ba}}_{6}$${\mathrm{Si}}_{46}$, in the framework of density-functional theory. The electronic structure of ${\mathrm{Si}}_{46}$ is remarkably different from that of the diamond Si lattice due to its pentagonal network. The valence-band top becomes deeper, resulting in a narrow valence-band width and a wide fundamental gap. Also, another gap appears within the valence bands. In the Na- and Ba-codoped phase, Ba states show strong hybridization with ${\mathrm{Si}}_{46}$ states giving a very high Fermi-level density of states, which should be of essential importance for the superconductivity observed in ${\mathrm{Na}}_{\mathit{x}}$${\mathrm{Ba}}_{\mathit{y}}$${\mathrm{Si}}_{46}$.

Dynamical simulations of diffraction contrast images of straight dislocations in icosahedral quasicrystals

A structural model of the orthorhombic approximant Al3Co of the Al-Co decagonal quasicrystal has been derived from the monoclinic approximant Al13Co4 by high-resolution electron microscopy. In the [010] projected image, the bright image points correspond to the Co-atom pentagonal networks in these two phases, but the tessellation of pentagons in them is different. The structure of Al3Co can be obtained by introducing repeated (100) faults at the unit-cell level in Al13Co4. There are 78 Al and 24 Co atom sites (some Al sites are only partially occupied) in a unit cell (a = 1.446 nm, b = 0.8156 nm and c = 1.236 nm) satisfying the symmetry of the Pnmn space group. This structure is also akin to that of the orthorhombic Al3Mn which has similar a and c parameters.

A structural model of the orthorhombic Al3Co derived from the monoclinic Al13Co4by high-resolution electron microscopy

Abstract A structural model of the orthorhombic approximant Al3Co of the Al-Co decagonal quasicrystal has been derived from the monoclinic approximant Al13Co4 by high-resolution electron microscopy. In the [010] projected image, the bright image points correspond to the Co-atom pentagonal networks in these two phases, but the tessellation of pentagons in them is different. The structure of Al3Co can be obtained by introducing repeated (100) faults at the unit-cell level in Al13Co4. There are 78 Al and 24 Co atom sites (some A1 sites are only partially occupied) in a unit cell (a= 1.446 nm, b = 0.8156 nm and c= 1.236 nm) satisfying the symmetry of the Pnmn space group. This structure is also akin to that of the orthorhombic Al3Mn which has similar a and c parameters.