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Search results for: x-ray diffractometry
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The Reactivity of Phosphanylphosphinidene Complexes of Transition Metals Toward Terminal Dihaloalkanes
PublicationThe reactivities of phosphanylphosphinidene complexes [(DippN)2W(Cl)(η2-P−PtBu2)]− (1), [(pTol3P)2Pt(η2- P=PtBu2)] (2), and [(dppe)Pt(η2-P=PtBu2)] (3) toward dihaloalkanes and methyl iodide were investigated. The reactions of the anionic tungsten complex (1) with stochiometric Br(CH2)nBr (n = 3, 4, 6) led to the formation of neutral complexes with a tBu2PP(CH2)3Br ligand or neutral dinuclear complexes with unusual tetradentate...
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Highly selective impedimetric determination of Haemophilus influenzae protein D using maze-like boron-doped carbon nanowall electrodes
PublicationThis study reports a novel impedimetric immunosensor for protein D detection in purified and bacterial (Haemophilus influenzae, Hi) samples. The detection was based on antigen recognition by anti-protein D antibodies (apD) immobilised at the maze-like boron-doped carbon nanowall electrodes (B:CNW). The B:CNW electrodes were synthesised, and their surface was characterised by scanning electron microscopy (SEM) and X-ray photoelectron...
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Ultrasensitive electrochemical determination of the cancer biomarker protein sPD-L1 based on a BMS-8-modified gold electrode
PublicationThis work describes the modification of a gold electrode with the BMS-8 compound that interacts with the Programmed Death-Ligand 1 (PD-L1), an immune checkpoint protein. The results show that we can confirm the presence of the sPD-L1 in the concentration range of 10−18 to 10−8 M using electrochemical impedance spectroscopy (EIS) with a limit of detection (LOD) of 1.87 × 10−14 M for PD-L1 (S/N = 3.3) and at a concentration of 10−14...
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Multi-Technique Investigation of Grave Robes from 17th and 18th Century Crypts Using Combined Spectroscopic, Spectrometric Techniques, and New-Generation Sequencing
PublicationThe textile fragments of the funeral clothes found in the 17th and 18th century crypts were subjected to spectroscopic, spectrometric, and microbial investigation. The next-generation sequencing enabled DNA identification of microorganisms at the genus and in five cases to the species level. The soft hydrofluoric acid extraction method was optimized to isolate different classes of dyes from samples that had direct contact with...
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Cu( II ) ions removal from wastewater using starch nanoparticles ( SNPs ): An Eco‐sustainable approach
PublicationThe complex structured starch particles were reduced to the nanoscale size range through hydrolysis utilizing low concentration acid assisted with ultrasound irradiation. The synthesized starch nanoparticles (SNPs) were characterized by TEM, FTIR, and XRD techniques. The synthesized SNPs possessed surface activated entities, as many cationic functional groups were confirmed through the FTIR spectrum. Also, these SNPs were effectively...
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Locally sculptured modification of the electrochemical response of conductive poly(lactic acid) 3D prints by femtosecond laser processing
PublicationThis manuscript presents an approach to sculpture high electrochemical activity of the 3D printed electrodes with poly(lactic acid) (PLA) matrix and carbon black (CB) filler by femtosecond laser (FSL) ablation. CB-PLA utility for electrochemical applications depends on a surface modification aiming to remove the PLA and uncover the conductive CB. We have discussed how laser pulse energy is critical for such an activation process....
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The phenomenon of increasing capacitance induced by 1T/2H-MoS2 surface modification with Pt particles – Influence on composition and energy storage mechanism
PublicationIn this paper, several approaches to the synthesis of molybdenum-based electrode materials for supercapacitors are presented, including anodization, hydrothermal process and annealing. For the material prepared via anodization of a molybdenum plate, followed by a hydrothermal process in thiourea aqueous solution, a thorough study of the Pt-surface modification through repetitive cycling in 1 M sulfuric acid with Pt acting as a...
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Effect of processing parameters on the cyclic behaviour of aluminium friction stir welded to spark plasma sintered aluminium matrix composites with bimodal micro-and nano-sized reinforcing alumina particles
PublicationUnderstanding the cyclic behaviour of Alumina reinforced Aluminium composites (Al-A2O3) was of critical importance, for their further application in the different industrial sectors. The present study is focussing on the cyclic behaviour of the Al-Alumina nanocomposite produced through the combination of spark plasma sintering (SPS) method and friction stir welding (FSW). The added Alumina with total content of 10% is the combination...
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The role of electrolysis and enzymatic hydrolysis treatment in the enhancement of the electrochemical properties of 3D-printed carbon black/poly(lactic acid) structures
PublicationAdditive manufacturing, also known as 3D printing, is beginning to play an unprecedented role in developing many applications for industrial or personalized products. The conductive composite structures require additional treatment to achieve an electroactive surface useful for electrochemical devices. In this paper, the surfaces of carbon black/poly(lactic acid) CB-PLA printouts were activated by electrolysis or enzymatic digestion...
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On the origin of surface imposed anisotropic growth of salicylic and acetylsalicylic acids crystals during droplet evaporation
PublicationIn this paper droplet evaporative crystallization of salicylic acid (SA) and acetylsalicylic acid (ASA) crystals on different surfaces, such as glass, polyvinyl alcohol (PVA), and paraffin was studied. The obtained crystals were analyzed using powder X-ray diffraction (PXRD) technique. In order to better understand the effect of the surface on evaporative crystallization, crystals deposited on glass were scraped off. Moreover,...
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Optical properties of polyazomethine with oxygen atom in the backbon
PublicationPurpose: The aim of this paper is to show results of optical measurement performed on poly –(1-(4-methylenephenoxy-1)phenylene-4-methylene-1.4-phenylnenitrylomethylene) (PPI2) polyazomethine thinfilms and to compare with poly - (1.4-phenylenemethylenenitrilo-1.4 phenylenenitrilomethylene) (PPI).Design/methodology/approach: Influence of oxygen atom in the polymer chain on optical properties ofpolyazomethine was investigated....
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Physicochemical Properties and Application of Silica-Doped Biochar Composites as Efficient Sorbents of Copper from Tap Water
PublicationThis article concerns research on new sorption materials based on silica-doped activated carbon. A two-stage synthesis involved pyrolysis of plant material impregnated in a water glass solution , followed by hydrothermal activation of the pyrolysate in KOH solution. The resulting composite can be used as a sorbent in drinking water filters. The proposed method of synthesis enables the design of materials with a surface area...
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Insight into the microstructural and durability characteristics of 3D printed concrete: Cast versus printed specimens
PublicationThis study presents the comparison of microstructural and durability characteristics of 3D printed concrete (3DPC) depending on its production method (printing or casting). Printed samples with different numbers of layers, as well as a cast specimen with an identical mix composition, were produced and compared, with their microstructural pore and solid characteristics quantitatively and qualitatively investigated. For this purpose,...
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Classification of submandibular salivary stones based on ultrastructural studies
PublicationIntroduction: Sialolithiasis remains a clinical problem with unclear etiopathogenesis, lack of prevention methods, and only surgical treatment. Materials and methods: An ultrastructure examination of submandibular sialoliths obtained from patients with chronic sialolithiasis was conducted using a scanning electron microscope and X-ray photoelectron...
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Size-Controlled Synthesis of Pt Particles on TiO2 Surface: Physicochemical Characteristic and Photocatalytic Activity
PublicationDifferent TiO2 photocatalysts, i.e., commercial samples (ST‐01 and P25 with minority of rutile phase), nanotubes, well‐crystallized faceted particles of decahedral shape and mesoporous spheres, were used as supports for deposition of Pt nanoparticles (NPs). Size‐controlled Pt NPs embedded in TiO2 were successfully prepared by microemulsion and wet‐impregnation methods. Obtained photocatalysts were characterized using XRD, TEM,...
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Iridium 5d -electron driven superconductivity in ThIr3
PublicationA polycrystalline sample of superconducting ThI r 3 was obtained by arc-melting Th and Ir metals. Powder x-ray diffraction revealed that the compound crystalizes in a rhombohedral crystal structure (R-3m, s.g. #166) with the lattice parameters: a = 5.3394 ( 1 ) Å and c = 26.4228 ( 8 ) Å . Normal and superconducting states were studied by magnetic susceptibility, electrical resistivity, and heat capacity measurements. The results...
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Titania Nanofiber Scaffolds with Enhanced Biointegration Activity—Preliminary In Vitro Studies
PublicationThe increasing need for novel bone replacement materials has been driving numerous studies on modifying their surface to stimulate osteogenic cells expansion and to accelerate bone tissue regeneration. The goal of the presented study was to optimize the production of titania-based bioactive materials with high porosity and defined nanostructure, which supports the cell viability and growth. We have chosen to our experiments TiO2...
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Application of micellar electrokinetic chromatography for detection of silver nanoparticles released from wound dressing
PublicationThe recent emergence of nanotechnology has provided a new therapeutic modality in case of silver nanoparticles. Dressings containing silver form the basis for the treatment of burns and wounds, either acute or chronic ones. The aim of the study was to examine silver release from the different wound dressings: commercially available (Atrauman Ag, Aqua- cel Ag) and experimental (FKDP-AgNPs) using MEKC. In order to characterize prepared keratin...
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Syntheses and Structures of Transition Metal Complexes with Phosphanylphosphinidene Chalcogenide Ligands
PublicationThe reactivity of the phosphanylphosphinidene complex [(DippN)2W(Cl)(η2-P-PtBu2)]− (1) toward chalcogens (Ch = Se, S) was studied. Reactions of stoichiometric amounts of 1 with chalcogens in DME yielded monomeric tungsten complexes with phosphanylphosphinidene chalcogenide ligands of the formula tBu2P−P−Ch (Ch = Se (in 2) and S (in 5)), which can be regarded as products of the addition of a chalcogen atom to a P=W bond in starting...
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Mechanism of Reduced Sintering Temperature of Al2O3–ZrO2 Nanocomposites Obtained by Microwave Hydrothermal Synthesis
PublicationA novel method to obtain Al2O3–ZrO2 nanocomposites is presented. It consists of the co-precipitation step of boehmite (AlO(OH)) and ZrO2, followed by microwave hydrothermal treatment at 270 ◦ C and 60 MPa, and by calcination at 600 ◦ C. Using this method, we obtained two nanocomposites: Al2O3–20 wt % ZrO2 and Al2O3–40 wt % ZrO2. Nanocomposites were characterized by Fourier transformed infrared spectroscopy, Raman spectroscopy,...
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Novel nitrogen precursors for electrochemically driven doping of titania nanotubes exhibiting enhanced photoactivity
PublicationNitrogen doped titania nanotubes were successfully sensitized by electrochemical method, i.e. as-anodized titania was immersed in different amine (diethyleneamine-DETA, triethyleneamine-TEA, ethylenediamine-EDA) and urea (U) solution and a constant potential was applied. The highly ordered morphology of fabricated N-TiO2 was investigated by using scanning electron microscopy. Spectroscopic techniques, i.e. UV-Vis spectroscopy,...
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Microstructure and corrosion behaviour of carbon steel and ferritic and austenitic stainless steels in NaCl solutions and the effect of p-nitrophenyl phosphate disodium salt
PublicationThe microstructure and corrosion behavior of carbon steel (CSA516) and ferritic (SS410) and austenitic (SS304L) stainless steels were studied and compared. Corrosion tests were carried out in 0.5 M NaCl solutions. Rates of corrosion were monitored based on weight loss, Tafel extrapolation and linear polarization resistance (LPR) methods. Rates of corrosion were ranked following the order: CSA516 >> SS410 > SS304L. The impact of...
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Synthesis and photoelectrochemical behaviour of hydrogenated titania nanotubes modified with conducting polymer infiltrated by redox active network
PublicationIn this work, we show preparation of ordered inorganic-organic composite electrode material where hydrogenated titania nanotubes H-TiO2 with tubularly developed surface modified with poly(3,4-ethylenedioxythiophene) matrix permeated by Prussian Blue (PB) inorganic redox network in order to reach highly photoactive heterojunction. The polymer deposition was realized via two subsequent processes covering: i) potentiostatic polymerization...
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Structural motifs in the Cu(II), Mn(II) and Zn(II) complexes based on N,N,N-donor dipodal or N,N,N,N-donor tripodal ligands obtained in situ: Synthesis, crystal structures and xanthine oxidase inhibition properties
PublicationA series of four novel transition metal complexes, [Cu(NCS)2L1] (1), [Mn(NCS)2L1] (2) where L1 = bis(1-(3,5-dimethylpyrazolyl)methyl)amine, [Mn(NCS)2L2] (3) and [Zn(NCS)L2]2[Zn(NCS)4] (4) where L2 = tris(1-(3,5-dimethylpyrazolyl)methyl)amine, has been obtained in situ by a one-step, one-pot synthetic path starting from 1-hydroxymethyl-3,5-dimethylpyrazole (L). The isolated complexes were fully characterised by elemental analysis,...
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Chemical-Assisted Mechanical Lapping of Thin Boron-Doped Diamond Films: A Fast Route Toward High Electrochemical Performance for Sensing Devices
PublicationThere is an urgent need for an effective and economically viable increase in electrochemical performance of boron-doped diamond (BDD) electrodes that are used in sensing and electrocatalytic applications. Specifically, one must take into consideration the electrode heterogeneity due to nonhomogenous boron-dopant distribution and the removal of sp2 carbon impurities saturating the electrode, without interference in material integrity....
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Chiral and achiral crystals, charge-assisted hydrogen-bond patterns and self-organization of selected solid diaminium thiosulfates
PublicationAbstract A series of diaminium thiosulfates, derivatives of diamines: NH2CH2CH(CH3)NH2 (1) and NH2(CH2)nNH2, n = 3-6 (2-5 respectively)and thiosulfuric acid were prepared and their structures determined by crystal X-ray diffraction analysis. Compounds 1, 2 and 4 turned out to be hydrates. The crystal structure of 1,2-proylenediaminium thiosulfate is chiral and exhibits spontaneous resolution. Crystals for both enantiomers...
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Composite Materials Based on Polymer-Derived SiCN Ceramic and Disordered Hard Carbons as Anodes for Lithium-Ion Batteries
PublicationNew composite materials based on polymer-derived SiCN ceramics and hard carbons were studied in view of its application as anodes for lithium-ion batteries. Two kinds of composites were prepared by pyrolysis of the preceramic polysilazane (HTT1800, Clariant) at 1000 °C in Ar atmosphere mixed with hard carbons derived from potato starch (HC_PS) or with a hard carbon precursor, namely potato starch (PS), denoted as HTT/HC_PS and...
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Fabrication and characterization of composite TiO2 nanotubes/ boron-doped diamond electrodes towards enhanced supercapacitors
PublicationThe composite TiO2 nanotubes / boron-doped diamond electrodes were deposited using Microwave Plasma Enhanced Chemical Vapor Deposition resulting in the improved electrochemical performance. This composite electrode can deliver high specific capacitance of 7.46 mF cm‐− 2 comparing to boron-doped diamond (BDD) deposited onto flat Ti plate (0.11 mF cm‐− 2).The morphology and composition of composite electrode were characterized...
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Cadmium complex possessing simultaneously silanethiolato- and dithiocarbamato-ligands. A novel single-source precursor of cadmium sulfide
PublicationThermal decomposition of suitable coordination compounds may be used as efficient route for fabrication of semiconducting layers. A new potential CdS precursor—a cadmium complex with all-sulfur Cd-coordination sphere [Cd{l-SSi(OBut)3}(S2CNC4H8)]2 (1) —has been prepared and its properties are investigated. The complex was obtained in the reaction between dimeric bis(tri-tert-butoxysilanethiolato) cadmium(II) [Cd{SSi(OBut)3}2]2 and...
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Study of the formation of calcareous deposits on cathodically protected steel in Baltic sea water
PublicationPurpose – The purpose of this paper is to investigate whether the sedimentation of calcareous deposits occurs on cathodically protected steel in Baltic sea water. Design/methodology/approach – Steel electrodes were cathodically polarized in natural Baltic sea water at potential þ0.150 V vs Zn electrode in potentiostatic mode. During exposure chronoamperometric measurements were carried out. After the exposure, the electrode’s surface...
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Electrochemical cobalt oxidation in chloride media
PublicationThe green transition, despite recent advances in cobalt-free battery technologies, is still highly dependent on the availability of critical cobalt-based materials. Consequently, there has been increasing interest towards the development of new methods that maximize critical metals recovery from industrial hydrometallurgical solutions. In the current study, direct anodic oxidation of cobalt species from cobalt chloride solutions...
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Mechanical Properties of Additively Manufactured Polymeric Materials—PLA and PETG—For Biomechanical Applications
PublicationThe study presented herein concerns the mechanical properties of two common polymers for potential biomedical applications, PLA and PETG, processed through fused filament fabrication (FFF)—Material Extrusion (ME). For the uniaxial tension tests carried out, two printing orientations—XY (Horizontal, H) and YZ (Vertical, V)—were considered according to the general principles for part positioning, coordinates, and orientation typically...
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Enhancing colloidal stability of nanodiamond via surface modification with dendritic molecules for optical sensing in physiological environments
PublicationPre-treatment of diamond surface in low-temperature plasma for oxygenation and in acids for carboxylation was hypothesized to promote the branching density of the hyperbranched glycidol polymer. This was expected to increase the homogeneity of the branching level and suppress interactions with proteins. As a result, composite nanodiamonds with reduced hydrodynamic diameters that are maintained in physiological environments were...
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Effect of the ex situ physical and in situ chemical modification of bacterial nanocellulose on mechanical properties in the context of its potential applications in heart valve design
PublicationBacterial nanocellulose (BNC) is a promising material for heart valve prostheses. However, its low strength properties limit its applicability in cardiovascular surgery. To overcome these limitations, the mechanical properties of BNC can be improved through modifications. The aim of the research was to investigate the extent to which the mechanical properties of BNC can be altered by modifying its structure during its production...
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Structure and water uptake in BaLnCo2O6−δ (Ln =La, Pr, Nd, Sm, Gd, Tb and Dy)
PublicationThe structure of BaLnCo2O6-δ (Ln =La, Pr, Nd, Sm, Gd, Tb and Dy) was studied by the means of synchrotron radiation powder X-ray diffraction, neutron powder diffraction and Transmission Electron Microscopy (TEM), while water uptake properties were analysed with the use of thermogravimetry (TG) and water adsorption isotherms. The structure refinement revealed that the dominant phase in all compositions was orthorhombic with an ordering...
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Effect of Aromatic System Expansion on Crystal Structures of 1,2,5-Thia- and 1,2,5-Selenadiazoles and Their Quaternary Salts: Synthesis, Structure, and Spectroscopic Properties
PublicationRational manipulation of secondary bonding interactions is a crucial factor in the construction of new chalcogenadiazole-based materials. This article reports detailed experimental studies on phenanthro[9,10-c][1,2,5]chalcogenadiazolium and 2,1,3-benzochalcogenadiazolium salts and their precursors. The compounds were synthesized, characterized employing NMR and UV-Vis spectroscopy. TD-DFT calculations were also performed. The influence...
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Polaronic and Mott insulating phase of layered magnetic vanadium trihalide VCl3
PublicationTwo-dimensional (2D) van der Waals (vdW) magnetic 3d-transition metal trihalides are a new class of functional materials showing exotic physical properties useful for spintronic and memory storage applications. In this article, we report the synthesis and electromagnetic characterization of single-crystalline vanadium trichloride, VCl 3 , a novel 2D layered vdW Mott insulator, which has a rhombohedral structure (R3, No. 148) at...
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High-Temperature Oxidation of Heavy Boron-Doped Diamond Electrodes: Microstructural and Electrochemical Performance Modification
PublicationIn this work, we reveal in detail the effects of high-temperature treatment in air at 600 °C on the microstructure as well as the physico-chemical and electrochemical properties of boron-doped diamond (BDD) electrodes. The thermal treatment of freshly grown BDD electrodes was applied, resulting in permanent structural modifications of surface depending on the exposure time. High temperature affects material corrosion, inducing...
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Temperature distribution of supercapacitors prepared by various technologies
PublicationSupercapacitors, also known by different names such as electrostatic double-layer capacitors (EDLCs) or ultra-capacitors, are electrical storage devices still in development. These devices require fast and reliable methods of assessing their state-of-health. Thermographic imaging is a method which can be applied with this aim due to its popularity, and the high negative impact of overheating on a supercapacitor’s parameters. Moreover,...
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BODIPY‐Perylene Charge Transfer Compounds; Sensitizers for Triplet‐Triplet Annihilation Up‐conversion
PublicationBODIPY heterochromophores, asymmetrically substituted with perylene and/or iodine at the 2 and 6 positions were prepared and investigated as sensitizers for triplet-triplet annihilation up conversion (TTA-UC). Single-crystal X-ray crystallographic analyses show that the torsion angle between BODIPY and perylene units lie between 73.54 and 74.51, though they are not orthogonal. Both compounds show intense, charge transfer absorption...
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Influence of Surface-Modified Montmorillonite Clays on the Properties of Elastomeric Thin Layer Nanocomposites
PublicationIn recent years, polyurethane nanocomposites have attracted more attention due to the massive demand for materials with increasingly exceptional mechanical, optical, electrical, and thermal properties. As nanofillers have a high surface area, the interaction between the nanofiller and the polymer matrix is an essential issue for these materials. The main aim of this study is to validate the impact of the montmorillonite nanofiller...
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Fabrication of the cross-linked PVA/TiO2/C nanocomposite membrane for alkaline direct methanol fuel cells
PublicationA crosslinked Poly(vinyl alcohol) based composite membrane was developed through a phase inversion process for use in alkaline direct methanol fuel cells (ADMFCs). The titanium dioxide (TiO2) and carbon nanoparticles (NPs) have been incorporated into the PVA polymer matrix to improve the mechanical and thermal properties. The membrane samples were further modified with maleic acid, a carboxylic acid acting as the cross-linker,...
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Modeling and optimization of chemical-treated torrefaction of wheat straw to improve energy density by response surface methodology
PublicationToday, torrefaction is important technique for extending the potential of biomass for improvement of energy density. The independent variables investigated for torrefaction study were temperature, retention time, acid concentration, and particle size. The experiment was designed by central composite design (CCD) method using design expert (version 11). The three dependent variables were higher heating value (HHV), energy enhancement...
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Bovine Serum Albumin – Hydroxyapatite Nanoflowers as Potential Local Drug Delivery System of Ciprofloxacin
PublicationIntroduction: Hybrid nanoflowers are structures consisting of organic (enzymes, proteins, nucleic acids) and inorganic components (mostly metal phosphates) with a flower-like hierarchical structure. Novel hybrid nanoflowers based on bovine serum albumin (BSA) and hydroxyapatite (HA) were obtained and characterized. Study on BSA-HA nanoflowers as potential drug delivery system is reported for the first time. Methods: Embedding ciprofloxacin...
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Magnetism and structure of Li_xCoO2 and comparison to Na_xCoO2
PublicationW pracy dyskutowane są właściwości magnetyczne i strukturalne Li_xCoO2 dla 0.5< x< 1.0. Jon Co +4 znajduje się w stanie wysokospinowym w Li_xCoO2 dla zawartości litu od 0.94 do 1.00 i w stanie niskospinowym dla x od 0.50 do 0.78.
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Structure and superconductivity of VN-SiO2 films obtained by thermal nitridation of sol-gel derived coatings
PublicationPraca prezentuje wyniki badań strukturalnych oraz właściwości nadprzewodzących cienkich warstw xVN-(100-x)SiO2, gdzie x = 90, 80, 70, 60 mol%. Warstwy zostały wykonane metodą termicznego azotowania z użyciem amoniaku cienkich warstw tlenkowych otrzymanych metodą zol-żel. Badania struktury przeprowadzono metodami XRD oraz XPS, natomiast właściwości nadprzewodzące badano metodą MMMA. Właściwości nadprzewodzące warstw zależą zarówno...
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The convex domination subdivision number of a graph
PublicationLet G = (V;E) be a simple graph. A set D\subset V is a dominating set of G if every vertex in V - D has at least one neighbor in D. The distance d_G(u, v) between two vertices u and v is the length of a shortest (u, v)-path in G. An (u, v)-path of length d_G(u; v) is called an (u, v)-geodesic. A set X\subset V is convex in G if vertices from all (a, b)-geodesics belong to X for any two vertices a, b \in X. A set X is a convex dominating...
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Dokładność skal ekwiwalentności a indyferencja stochastyczna
PublicationW pracy dowodzimy twierdzenia, które wiąże założenie dokładności skal ekwiwalentności (ESE) z symetrycznym czynnikiem dominacji stochastycznej pierwszego rzędu. Dokładniej, niech X i Y będą rozkładami wydatków, odpowiednio, analizowanej grupy gospodarstw domowych i grupy gospodarstw odniesienia. Niech Z oznacza rozkład X skorygowany za pomocą pewnej skali ekwiwalentności. Jeśli spełnione jest założenie ESE, to Z jest stochastyczne...
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Global defensive sets in graphs
PublicationIn the paper we study a new problem of finding a minimum global defensive set in a graph which is a generalization of the global alliance problem. For a given graph G and a subset S of a vertex set of G, we define for every subset X of S the predicate SEC ( X ) = true if and only if | N [ X ] ∩ S | ≥ | N [ X ] \ S | holds, where N [ X ] is a closed neighbourhood of X in graph G. A set S is a defensive alliance if and only if for...
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Two families of infinitely many homoclinics for singular strong force Hamiltonian systems
PublicationWe are concerned with a planar autonomous Hamiltonian system with a potential possessing a single well of infinite depth at a point X and a unique strict global maximum 0 at a point A. Under a strong force condition around the singularity X, via minimization of an action integral and using a shadowing chain lemma together with simple geometrical arguments, we prove the existence of infinitely many geometrically distinct homoclinic...