Utilizing a defective MgO layer for engineering multifunctional Co-MOF hybrid materials with tailored leaf-like and polyhedral structures for optimal electrochemical and photocatalytic activities

The hybridization of metal-organic framework(MOF)with inorganic layers would lead to the discovery of novel hybrid materials that can provide a compelling strategy for enhancing its photocatalytic and electrochemical response.In the present study,a highly efficient multifunctional hybrid material was developed by exploiting the defective layer formed on AZ31 Mg alloy through plasma electrolytic oxidation(PEO)as a nucleation and growth site for Co-MOF.The concentrations of the organic linker 2-Methylimidazole(2,MIm)and cobalt nitrate as a source of Co^(2+) ions were varied to control the growth of the obtained Co-MOF.Lower concentrations of the 2,MIm ligand favored the formation of leaf-like MOF structures through an anisotropic,two-dimensional growth,while higher concentrations led to rapid,isotropic nucleation and the creation of polyhedral Co-MOF structures.The sample characterized by polyhedral Co-MOF structures exhibited superior electrochemical stability,with the lowest corrosion current density(3.11×10^(-9) A/cm^(2))and the highest top layer resistance(2.34×10^(6)Ωcm^(2)),and demonstrated outstanding photocatalytic efficiency,achieving a remarkable 99.98%degradation of methylene blue,an organic pollutant,in model wastewater.To assess the active adsorption sites of the Co-MOF,density functional theory(DFT)was utilized.This study explores the changes in morphologies of the coatings of Co-MOF with the change of solution concentration to form coatings with enhanced properties on the metallic substrate,which could establish the groundwork for the development of next-generation multifunctional frameworks with diverse applications.

Relationship between polyhedral structures formed by tangent planes of ellipsoidal particles and system sound velocity

Internal polyhedral structures of a granular system can be investigated using the Voronoi tessellations.This technique has gained increasing recognition in research of kinetic properties of granular flows.For systems with mono-sized spherical particles,Voronoi tessellations can be utilized,while radial Voronoi tessellations are necessary for analyzing systems with multi-sized spherical particles.However,research about polyhedral structures of non-spherical particle systems is limited.We utilize the discrete element method to simulate a system of ellipsoidal particles,defined by the equation(x a)2+(y1)2+(z 1/a)2=1,where a ranges from 1.1 to 2.0.The system is then dissected by using tangent planes at the contact points,and the geometric quantities of the resulting polyhedra in different shaped systems,such as surface area,volume,number of vertices,number of edges,and number of faces,are calculated.Meanwhile,the longitudinal and transverse wave velocities within the system are calculated with the time-of-flight method.The results demonstrate a strong correlation between the sound velocity of the system and the geometry of the dissected polyhedra.The sound velocity of the system increases with the increase in a,peaking at a=1.3,and then decreases as a continues to increase.The average volume,surface area,number of vertices,number of edges,and number of faces of the polyhedra decrease with the increase in sound velocity.That is,these quantities initially decrease with the increase in a,reaching minima at a=1.3,and then increase with further increase of a.The relationship between sound velocity and the geometric quantities of the dissected polyhedra can serve as a reference for acoustic material design.

Ratio of In-Sphere Volume to Polyhedron Volume of the Great Pyramid Compared to Selected Convex Polyhedral Solids

The architecture of the Great Pyramid at Giza is based on fascinating golden mean geometry. Recently the ratio of the in-sphere volume to the pyramid volume was calculated. One yields as result RV = π ⋅ φ5, where is the golden mean. It is important that the number φ5 is a fundamental constant of nature describing phase transition from microscopic to cosmic scale. In this contribution the relatively small volume ratio of the Great Pyramid was compared to that of selected convex polyhedral solids such as the Platonic solids respectively the face-rich truncated icosahedron (bucky ball) as one of Archimedes’ solids leading to effective filling of the polyhedron by its in-sphere and therefore the highest volume ratio of the selected examples. The smallest ratio was found for the Great Pyramid. A regression analysis delivers the highly reliable volume ratio relation , where nF represents the number of polyhedron faces and b approximates the silver mean. For less-symmetrical solids with a unique axis (tetragonal pyramids) the in-sphere can be replaced by a biaxial ellipsoid of maximum volume to adjust the RV relation more reliably.

Synthesis and Luminescent Property of Polycarbazole/Polyhedral Oligomeric Silsesquioxane Nanocomposites

Polyvinylcarbazole（PVK） composites containing organic-inorganic hybrid polyhedral oligomeric silse-squioxane（POSS） PVK-POSS were prepared by free radical polymerization. POSS monomers reacted with vinylcarbazole and were completely dispersed at molecular level in PVK matrix and PVK-POSS nanocomposites display higher glass transition temperature（Tg） in comparison with neat PVK. Optical properties of PVK/POSS nanocomposites were investigated by UV-spectrum and PL-spectrum and the results show that the PVK-POSS nanoparticles have a good interface effect and improve color purity effectively. The maximum absorption wavelength bathochromically shifts gradually with the increasing of the content of POSS. The luminescent intensity becomes higher and higher with the increase of POSS content, and reaches its maximum luminescent intensity when the POSS content is 3% （mass fraction）, while some POSS-rich nanoparticles are present in matrix when contents of POSS are beyond 5%.

Delay-dependent robust H_∞control of convex polyhedral uncertain fuzzy systems

The robust H∞ control problem for a class of uncertain Takagi-Sugeno fuzzy systems with timevarying state delays is studied. The uncertain parameters are supposed to reside in a polytope. Based on the delay-dependent Lyapunov functional method, a new delay-dependent robust H∞ fuzzy controller, which depends on the size of the delays and the derivative of the delays, is presented in term of linear matrix inequalities （LMIs）. For all admissible uncertainties and delays, the controller guarantees not only the asymptotic stability of the system but also the prescribed H∞ attenuation level. In addition, the effectiveness of the proposed design method is demonstrated by a numerical example.

Gregory Solid Construction for Polyhedral Volume Parameterization by Sparse Optimization

In isogeometric analysis,it is frequently required to handle the geometric models enclosed by four-sided or non-four-sided boundary patches,such as trimmed surfaces.In this paper,we develop a Gregory solid based method to parameterize those models.First,we extend the Gregory patch representation to the trivariate Gregory solid representation.Second,the trivariate Gregory solid representation is employed to interpolate the boundary patches of a geometric model,thus generating the polyhedral volume parametrization.To improve the regularity of the polyhedral volume parametrization,we formulate the construction of the trivariate Gregory solid as a sparse optimization problem,where the optimization objective function is a linear combination of some terms,including a sparse term aiming to reduce the negative Jacobian area of the Gregory solid.Then,the alternating direction method of multipliers(ADMM)is used to solve the sparse optimization problem.Lots of experimental examples illustrated in this paper demonstrate the effectiveness and efficiency of the developed method.

Study of Flame Retardation of Polycarbonate Modified by Polyhedral Oligomeric Silsesquioxane and Caged Bicyclic Phosphate

The flame-retarded polycarbonate（PC） has been made with octaphenyl polyhedral silsesquioxane（OPS） and/or caged bicyclic phosphate（Trimer）.Thermal gravimetric analysis（TGA）,Fourier-transform infrared（FTIR）,TGA-FTIR,limiting oxygen index（LOI）,and mechanical tests have been employed to characterize the modified PC.The additives of OPS and Trimer in PC have been proved to be effective flame-retardants because of the synergistic interaction between the elements of P and Si.The role of OPS and Trimer in PC degradation are different：OPS participates in the charring of PC,while Trimer makes PC degrade in advance.In addition,OPS and Trimer induced obvious differences in the mechanical properties of PC.

Synthesis and characterization of poly(methyl methacrylate-co-polyhedral oligomeric silsesquioxane)hybrid nanocomposites

A novel poly（methyl methacrylate-co-polyhedral oligomeric silsesquioxane） hybrid nanocomposite was synthesized by free radical polymerization and characterized by 1H NMR, 29Si NMR, and TGA technologies. Compared with PMMA homopolymer, the nanocomposite has better thermal stability.

Modeling calving process of glacier with dilated polyhedral discrete element method

Mass loss caused by glacier calving is one of the direct contributors to global sea level rise.Reliable calving laws are required for accurate modelling of ice sheet mass balance.Both continuous and discontinuous methods have been used for glacial calving simulations.In this study,the discrete element method(DEM)based on dilated polyhedral elements is introduced to simulate the calving process of a tidewater glacier.Dilated polyhedrons can be obtained from the Minkowski sum of a sphere and a core polyhedron.These elements can be utilized to generate a continuum ice material,where the interaction force between adjacent elements is modeled by constructing bonds at the joints of the common faces.A hybrid fracture model considering fracture energy is introduced.The viscous creep behavior of glaciers on long-term scales is not considered.By applying buoyancy and gravity to the modelled glacier,DEM results show that the calving process is caused by cracks which are initialized at the top of the glacier and spread to the bottom.The results demonstrate the feasibility of using the dilated polyhedral DEM method in glacier simulations,additionally allowing the fragment size of the breaking fragments to be counted.The relationship between crack propagation and internal stress in the glacier is analyzed during calving process.Through the analysis of the Mises stress and the normal stress between the elements,it is found that geometric changes caused by the glacier calving lead to the redistribution of the stress.The tensile stress between the elements is the main influencing factor of glacier ice failure.In addition,the element shape,glacier base friction and buoyancy are studied,the results show that the glacier model based on the dilated polyhedral DEM is sensitive to the above conditions.

Synthesis and Characterization of a New Titanium-silicate Material Containing Cage-like Polyhedral Oligosilsesquioxane

A new titanium-silicate material was synthesized with cubic cage-like tetramethylammonium octasilicate and TiCl4 ethanol solution as precursors. The product was characterized by FTIR, ^29Si NMR, UV-Vis, and XRD. Struc-tural and ingrediental analyses suggest that this material has a layered structure with cubic cage-like polyhedral oligo-silsesquioxane as building blocks and titanium as bridging atoms.

Fabrication of Layer-by-layer Films of Polyhedral Oligomeric Silsesquioxanes

Layer-by-layer (LBL) self-assembly method was used to fabricate siliceous ultrathin films by using polyhedral oligomeric silsesquioxanes as building blocks. Ammonium salt of octasilsesquioxane acid (OSi8) and poly(diallyldimethylammonium chloride) (PDDA) were alternately assembled onto CaF2 slide to form nanocomposite multilayers. Linear build-up of the LBL films was confirmed by UV-Vis spectroscopy. IR spectrum suggests existence of OSi8 and PDDA in the LBL films. Atomic force microscopic surface topography of the LBL films indicates the OSi8 covers the entire surface of the topmost layer and shows a granular morphology.

Polyhedral symmetry and quantum mechanics

A thorough study of regular and quasi-regular polyhedra shows that the symmetries of these polyhedra identically describe the quantization of orbital angular momentum, of spin, and of total angular momentum, a fact which permits one to assign quantum states at the vertices of these polyhedra assumed as the average particle positions. Furthermore, if the particles are fermions, their wave function is anti-symmetric and its maxima are identically the same as those of repulsive particles, e.g., on a sphere like the spherical shape of closed shells, which implies equilibrium of these particles having average positions at the aforementioned maxima. Such equilibria on a sphere are solely satisfied at the vertices of regular and quasi-regular polyhedra which can be associated with the most probable forms of shells both in Nuclear Physics and in Atomic Cluster Physics when the constituent atoms possess half integer spins. If the average sizes of the constituent particles are known, then the average sizes of the resulting shells become known as well. This association of Symmetry with Quantum Mechanics leads to many applications and excellent results.

A Geometric Method for Generating Discrete Trace Transition System of a Polyhedral Invariant Hybrid Automaton

Supervisory control and fault diagnosis of hybrid systems need to have complete information about the discrete states transitions of the underling system. From this point of view, the hybrid system should be abstracted to a Discrete Trace Transition System (DTTS) and represented by a discrete mode transition graph. In this paper an effective method is proposed for generating discrete mode transition graph of a hybrid system. This method can be used for a general class of industrial hybrid plants which are defined by Polyhedral Invariant Hybrid Automata (PIHA). In these automata there are no resetting maps, while invariant sets are defined by linear inequalities. Therefore, based on the continuity property of the state trajectories in a PIHA, the problem is reduced to finding possible transitions between all two adjacent discrete modes. In the presented method, the possibility and the direction of such transitions are detected only by computing the angle between the vector field and the normal vector of the switching surfaces. Thus, unlike the most other reachability methods, there is no need to solve differential equations and to do mapping computations. In addition, the proposed method, with some modifications can be applied for extracting Stochastic or Timed Discrete Trace Transition Systems.

An Interpolation-Free Cell-Centered Finite Volume Scheme for 3D Anisotropic Convection-Diffusion Equations on Arbitrary Polyhedral Meshes

Most existing cell-centered finite volume schemes need to introduce auxiliary unknowns in order to maintain the second-order accuracy when the mesh is distorted or the problem is discontinuous,so interpolation algorithms of auxiliary unknowns are required.Interpolation algorithms are not only difficult to construct,but also bring extra computation.In this paper,an interpolation-free cell-centered finite volume scheme is proposed for the heterogeneous and anisotropic convectiondiffusion problems on arbitrary polyhedral meshes.We propose a new interpolationfree discretization method for diffusion term,and two new second-order upwind algorithms for convection term.Most interestingly,the scheme can be adapted to any mesh topology and can handle any discontinuity strictly.Numerical experiments show that this new scheme is robust,possesses a small stencil,and has approximately secondorder accuracy for both diffusion-dominated and convection-dominated problems.

Architecture of Platonic and Archimedean polyhedral links

A new methodology for understanding the construction of polyhedral links has been developed on the basis of the Platonic and Archimedean solids by using our method of the ‘three-cross-curve and dou- ble-twist-line covering’. There are five classes of polyhedral links that can be explored: the tetrahedral and truncated tetrahedral links; the hexahedral and truncated hexahedral links; the dodecahedral and truncated dodecahedral links; the truncated octahedral and icosahedral links. Our results show that the tetrahedral and truncated tetrahedral links have T symmetry; the hexahedral and truncated hexahedral links, as well as the truncated octahedral links, O symmetry; the dodecahedral and truncated dodeca- hedral links, as well as the truncated icosahedral links, I symmetry, respectively. This study provides further insight into the molecular design, as well as theoretical characterization, of the DNA and protein catenanes.

Polymer solar cells with an inverted device configuration using polyhedral oligomeric silsesquioxane-[60]fullerene dyad as a novel electron acceptor

A polyhedral oligomeric silsesquioxane-[60]fullerene (POSS-C60) dyad was designed and used as a novel electron acceptor for bulk heterojunction (BHJ) polymer solar cells (PSCs) with an inverted device configuration. The studies of time-resolved photoinduced absorption of the pristine thin film of poly[(4,4'-bis(2-ethylhexyl)dithieno[3,2-b:2',3'-d]silole)-2,6-diyl-alt-(4,7-bis (2-thienyl)-2,1,3-benzothiadiazole)-5,5'-diyl] (SiPCPDTBT) and the composite thin film of SiPCPDTBT:POSS-C60 indicated efficient electron transfer from SiPCPDTBT to POSS-C60 with inhibited back-transfer. BHJ PSCs made by SiPCPDTBT mixed with POSS-C60 yielded the power conversion efficiencies (PCEs) of 1.50%. Under the same operational conditions, PCEs observed from BHJ PSCs made by SiPCPDTBT mixed with [6,6]-phenyl-C61-butyric acid methyl ester were 0.92%. These results demonstrated that POSS-C60 is a potentially good electron acceptor for inverted BHJ PSCs.

Ultrasmall Nanoparticle ROS Scavengers Based on Polyhedral Oligomeric Silsesquioxanes

Although tremendous efforts have been devoted to the structural and functional tailoring of natural polyphenol-functionalized nan oparticles,preparing ultrasmall sized(<6 nm)particles with precisely-defined structures has remained a grand challenge.In this work,we reported the preparation of ultra-small and precisely structured polyhedral oligomeric silsesquioxanes(POSS)-based polyphenol nanopartides(T8^-,T10^-,and T12^-GAPOSS)by accurately functionalizing the POSS surface with plant polyphenol gallic acid units via thiol-Michael"click"reactions.Those polyphenol nanoparticles exhibited strong free radical scavenging capacity,good biocompatibility and ability to resist cell oxidative damage,which dem on strated great potentials in inhibiting oxidative stress in duced pathologies.

A Polyhedral Theory on Graphs

This paper provides a polyhedral theory on graphs from which the criteria of Whit- ney and MacLane for the planarity of graphs are unified, and a brief proof of the Gauss crossing conjecture is obtained.

Effectiveness of an ocular adhesive polyhedral oligomeric silsesquioxane hybrid thermo-responsive FK506 hydrogel in a murine model of dry eye

Dry eye is a common ocular disease that results in discomfort and impaired vision,impacting an individual’s quality of life.A great number of drugs administered in eye drops to treat dry eye are poorly soluble in water and are rapidly eliminated from the ocular surface,which limits their therapeutic effects.Therefore,it is imperative to design a novel drug delivery system that not only improves the water solubility of the drug but also prolongs its retention time on the ocular surface.Herein,we develop a copolymer from mono-functional POSS,PEG,and PPG(MPOSS-PEG-PPG,MPEP)that exhibits temperature-sensitive sol-gel transition behavior.This thermo-responsive hydrogel improves the water solubility of FK506 and simultaneously provides a mucoadhesive,long-acting ocular delivery system.In addition,the FK506-loaded POSS hydrogel possesses good biocompatibility and significantly improves adhesion to the ocular surface.In comparison with other FK506 formulations and the PEG-PPG-FK506(F127-FK506)hydrogel,this novel MPOSS-PEG-PPG-FK506(MPEP-FK506)hydrogel is a more effective treatment of dry eye in the murine dry eye model.Therefore,delivery of FK506 in this POSS hydrogel has the potential to prolong drug retention time on the ocular surface,which will improve its therapeutic efficacy in the management of dry eye.

A novel method of determining the optimal polyhedral orientation for discrete global grid systems applicable to regionalscale areas of interest

The polyhedral discrete global grid system(DGGS)is a multi-resolution discrete earth reference model supporting the fusion and processing of multi-source geospatial information.The orientation of the polyhedron relative to the earth is one of its key design choices,used when constructing the grid system,as the efficiency of indexing will decrease if local areas of interest extend over multiple faces of the spherical polyhedron.To date,most research has focused on global-scale applications while almost no rigorous mathematical models have been established for determining orientation parameters.In this paper,we propose a method for determining the optimal polyhedral orientation of DGGSs for areas of interest on a regional scale.The proposed method avoids splitting local or regional target areas across multiple polyhedral faces.At the same time,it effectively handles geospatial data at a global scale because of the inherent characteristics of DGGSs.Results show that the orientation determined by this method successfully guarantees that target areas are located at the center of a single polyhedral face.The orientation process determined by this novel method reduces distortions and is more adaptable to different geographical areas,scales,and base polyhedrons than those employed by existing procedures.