On the Modified Crystalline Stefan Problem with Singular Data

We study the behavior of solutions of the modified Stefan problem in the plane for polygonal interfaces. We are particularly interested in a solution near a singularity of either the loss of a facet or the breaking of a facet. We establish precise regularity results if a facet disappears. We use them to establish the existence of a weak solution with singular data, i.e., when some of the zero-crystalline-curvature facets have zero length.     

Oxygen incorporation in polyethylene implanted with 150 keV Sb+ ions

Samples of polyethylene (PE) loaded with carbon black up to 8 wt.% and implanted with 150 keV Sb⁺ ions to the doses from 2×10¹³–2×10¹⁵ cm^–2 were studied using standard Rutherford Back Scattering (RBS) technique. On the PE samples implanted to the doses above 2×10¹⁴ cm^–2, a considerable surface carbonization is observed. The measured parameters of the Sb depth profile are compared with theoretical TRIM estimations. The projected range is by 25% lower than the theoretical one and the range straggling is about twice of that predicted. The differences are explained by stepwise polymer degradation during the ion bombardment. Strong oxidation of the ion implanted polymers is also observed. The oxygen depth profiles from the sample surface up to the depth comparable with Sb⁺ ion range evolve from nearly uniform one for low ion doses to highly non-uniform one for doses above 1×10¹⁵ cm^–2. The total oxygen content in the sample surface layer 300 nm thick reaches a maximum for the doses of (1–2)×10¹⁴ cm^–2.On leave from Belorussian State University, 220050 Minsk, Belarus.The authors thank the member of electrostatic accelerator group at INP for help during RBS measurements. The work was partly (V.H. and J.K.) supported by the Internal Grant Agency of the Academy of Sciences of Czech Republic under the grant No. 14805 and by the Internal Grant Agency of the Ministry of Education of Czech Republic under the grant No. 1002 (V.., V.R., V.H. and J.K.). In the final stage, the work was also supported by the Grant Agency of Czech Republic under the grant No. 202/93/0121.     

DOSY NMR as a tool for predicting optimal conditions for hydrogel formation: The case of a hyperbranched polyglycidol cross‐linked with boronic acids

This article demonstrates the utility of DOSY NMR for the determination of the optimal conditions for the efficient covalent, reversible cross‐linking of macromolecules in water for hydrogel formation. The studied model system was hyperbranched polyglycidol (HbPGL) containing numerous diol groups in peripheral regions and two types of boronic acids, that is, B(OH)₄^? and benzene‐1,4‐boronic diacid, as cross‐linking agents. Diffusion coefficient changes of a polymer in solution, under the influence of various concentrations of cross‐linking agent and pH, which influences the equilibrium of the reaction between boronic acids and diols, were recorded. These data are consistent with the rheological properties, namely the G′_max(ω) of hydrogels prepared under analogous conditions, from more concentrated solutions of HbPGL. This approach appears to be promising as it facilitates avoiding the loss of a large amount of polymer that is necessary for the elaboration of appropriate conditions for network formation in aqueous media. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2171–2178     

Zinc Imine Polyhedral Oligomeric Silsesquioxane as a Quattro-Site Catalyst for the Synthesis of Cyclic Carbonates from Epoxides and Low-Pressure CO2

In the present research, the synthesis, spectroscopic characterization, and structural investigations of a unique Zn^II complex of imine-functionalized polyhedral oligomeric silsesquioxane (POSS) is designed, and hereby described, as a catalyst for the synthesis of cyclic carbonates from epoxides and CO₂. The uncommon features of the designed catalytic system is the elimination of the need for a high pressure of CO₂ and the significant shortening of reaction times commonly associated with such difficult transformations like that of styrene oxide to styrene carbonate. Our studies have shown that imine-POSS is able to chelate metal ions like Zn^II to form a unique coordination complex. The silsesquioxane core and the hindrance of the side arms (their steric effect) influence the construction process of the homoleptic Zn₄@POSS-1 complex. The compound was characterized in solution by NMR (¹H, ¹³C, ²⁹Si), ESI-MS, UV/Vis spectroscopy and in the solid state by thermogravimetric/differential thermal analysis (TG-DTA), elemental analysis, diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS), cross-polarization magic angle spinning (CP MAS) NMR (¹³C, ²⁹Si) spectroscopy, and X-ray crystallography.     

Fine singularity analysis of solutions to the Laplace equation

We present here a fine singularity analysis of solutions to the Laplace equation in special polygonal domains in the plane. We assume piecewise constant Neumann data on one component of the boundary. Our motivation is to study the so‐called Berg effect, which is explained in the introduction. Copyright © 2014 John Wiley & Sons, Ltd.     

Synthesis of activated carbon foams with high specific surface area using polyurethane elastomer templates for effective removal of methylene blue

Carbon foams have gained significant attention due to their tuneable properties that enable a wide range of applications including catalysis, energy storage and wastewater treatment. Novel synthesis pathways enable novel applications via yielding complex, hierarchical material structure. In this work, activated carbon foams (ACFs) were produced from waste polyurethane elastomer templates using different synthesis pathways, including a novel one-step method. Uniquely, the produced foams exhibited complex structure and contained carbon microspheres. The ACFs were synthesized by impregnating the elastomers in an acidified sucrose solution followed by direct activation using CO₂ at 1000 ℃. Different pyrolysis and activation conditions were investigated. The ACFs were characterized by a high specific surface area (S_BET) of 2172 m²/g and an enhanced pore volume of 1.08 cm³/g. Computer tomography and morphological studies revealed an inhomogeneous porous structure and the presence of numerous carbon spheres of varying sizes embedded in the porous network of the three-dimensional carbon foam. X-ray diffraction (XRD) and Raman spectroscopy indicated that the obtained carbon foam was amorphous and of turbostratic structure. Moreover, the activation process enhanced the surface of the carbon foam, making it more hydrophilic via altering pore size distribution and introducing oxygen functional groups. In equilibrium, the adsorption of methylene blue on ACF followed the Langmuir isotherm model with a maximum adsorption capacity of 592 mg/g. Based on these results, the produced ACFs have potential applications as adsorbents, catalyst support and electrode material in energy storage systems.     

Keratin Scaffolds Containing Casomorphin Stimulate Macrophage Infiltration and Accelerate Full-Thickness Cutaneous Wound Healing in Diabetic Mice

Impaired wound healing is a major medical challenge, especially in diabetics. Over the centuries, the main goal of tissue engineering and regenerative medicine has been to invent biomaterials that accelerate the wound healing process. In this context, keratin-derived biomaterial is a promising candidate due to its biocompatibility and biodegradability. In this study, we evaluated an insoluble fraction of keratin containing casomorphin as a wound dressing in a full-thickness surgical skin wound model in mice (n = 20) with iatrogenically induced diabetes. Casomorphin, an opioid peptide with analgesic properties, was incorporated into keratin and shown to be slowly released from the dressing. An in vitro study showed that keratin-casomorphin dressing is biocompatible, non-toxic, and supports cell growth. In vivo experiments demonstrated that keratin-casomorphin dressing significantly (p < 0.05) accelerates the whole process of skin wound healing to the its final stage. Wounds covered with keratin-casomorphin dressing underwent reepithelization faster, ending up with a thicker epidermis than control wounds, as confirmed by histopathological and immunohistochemical examinations. This investigated dressing stimulated macrophages infiltration, which favors tissue remodeling and regeneration, unlike in the control wounds in which neutrophils predominated. Additionally, in dressed wounds, the number of microhemorrhages was significantly decreased (p < 0.05) as compared with control wounds. The dressing was naturally incorporated into regenerating tissue during the wound healing process. Applied keratin dressing favored reconstruction of more regular skin structure and assured better cosmetic outcome in terms of scar formation and appearance. Our results have shown that insoluble keratin wound dressing containing casomorphin supports skin wound healing in diabetic mice.     

How to Obtain the Maximum Properties Flexibility of 3D Printed Ketoprofen Tablets Using Only One Drug-Loaded Filament?

The flexibility of dose and dosage forms makes 3D printing a very interesting tool for personalized medicine, with fused deposition modeling being the most promising and intensively developed method. In our research, we analyzed how various types of disintegrants and drug loading in poly(vinyl alcohol)-based filaments affect their mechanical properties and printability. We also assessed the effect of drug dosage and tablet spatial structure on the dissolution profiles. Given that the development of a method that allows the production of dosage forms with different properties from a single drug-loaded filament is desirable, we developed a method of printing ketoprofen tablets with different dose and dissolution profiles from a single feedstock filament. We optimized the filament preparation by hot-melt extrusion and characterized them. Then, we printed single, bi-, and tri-layer tablets varying with dose, infill density, internal structure, and composition. We analyzed the reproducibility of a spatial structure, phase, and degree of molecular order of ketoprofen in the tablets, and the dissolution profiles. We have printed tablets with immediate- and sustained-release characteristics using one drug-loaded filament, which demonstrates that a single filament can serve as a versatile source for the manufacturing of tablets exhibiting various release characteristics.