Stochastic analysis of a thermoelastic problem in functionally graded plates with uncertain material properties

The statistics (i.e., mean and variance) of temperature and thermal stress are analytically obtained in functionally graded material (FGM) plates with uncertainties in the thermal conductivity and coefficient of linear thermal expansion. These FGM plates are assumed to have arbitrary nonhomogeneous thermal and mechanical properties through the entire thickness of plate and are subjected to deterministic convective heating. The stochastic temperature and thermal stress fields are analysed by assuming the FGM plate is multilayered with distinct, random thermal conductivity and coefficient of linear thermal expansion in each layer. Vodicka’s method, which is a type of integral transform method, and a perturbation method are employed to obtain the analytical solutions for the statistics. The autocorrelation coefficients of each random property and cross-correlation coefficients between different random properties are expressed in exponential function forms as a non-homogeneous Markov random field of discrete space. Numerical calculations are performed for FGM plates composed of partially stabilised zirconia (PSZ) and austenitic stainless steel (SUS304), which have the largest dispersion of the random properties at the place where the volume fractions of the two constituent materials are both 0.5. The effects of the spatial change in material composition, thermal boundary condition and correlation coefficients on the standard deviations of the temperature and thermal stress are discussed.     

Orientation and mechanical properties of laser‐induced photothermally drawn fibers composed of multiwalled carbon nanotubes and poly(ethylene terephthalate)

This study presents a novel photothermal drawing of poly(ethylene terephthalate) (PET)/multiwalled carbon nanotube (MWCNT) fibers. The photothermal drawing was carried out using the near infrared laser‐induced photothermal properties of MWCNTs. An uniform fiber surface was obtained from a continuous necking deformation of the undrawn fibers, particularly at a draw ratio of 4 and higher. The breaking stress and modulus of the photothermally drawn PET/MWCNT fibers were significantly enhanced, in comparison to those of hot drawn fibers at the same draw ratio. The enhanced mechanical properties were ascribed to the increased orientation of PET chains and MWCNTs as well as PET crystallinity due to photothermal drawing. In particular, a significantly higher degree of orientation of the MWCNTs along the fiber axis was obtained from photothermal drawing, as shown in polarized Raman spectra measurements. The photothermal drawing in this study has the potential to enhance the mechanical properties of fibers containing MWCNTs. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 603–609     

Asymptotic behavior of spreading fronts in the anisotropic Allen–Cahn equation on Rn

We consider the Cauchy problem for the anisotropic (unbalanced) Allen–Cahn equation on ${\mathbb{R}}^n$ with $n\ge 2$ and study the large time behavior of the solutions with spreading fronts. We show, under very mild assumptions on the initial data, that the solution develops a well-formed front whose position is closely approximated by the expanding Wulff shape for all large times. Such behavior can naturally be expected on a formal level and there are also some rigorous studies in the literature on related problems, but we will establish approximation results that are more refined than what has been known before. More precisely, the Hausdorff distance between the level set of the solution and the expanding Wulff shape remains uniformly bounded for all large times. Furthermore, each level set becomes a smooth hypersurface in finite time no matter how irregular the initial configuration may be, and the motion of this hypersurface is approximately subject to the anisotropic mean curvature flow $V_{\gamma }={\kappa }_{\gamma }+c$ with a small error margin. We also prove the eventual rigidity of the solution profile at the front, meaning that it converges locally to the traveling wave profile everywhere near the front as time goes to infinity. In proving this last result as well as the smoothness of the level surfaces, an anisotropic extension of the Liouville type theorem of Berestycki and Hamel (2007) for entire solutions of the Allen–Cahn equation plays a key role.     

α‐exomethylene lactone possessing acetal–ester linkage: Polymerization and postpolymerization modification for water‐soluble polymer

2,6‐Dimethyl‐5‐methylene‐1,3‐dioxa‐4‐one (DMDO), a cyclic acrylate possessing acetal–ester linkage, was obtained as a mixture of cis‐ and trans‐isomers (95:5) from Baylis–Hillman reaction of an aryl acrylate. The radical and anionic polymerizations of DMDO yielded the corresponding vinyl polymers without any side reactions such as cleavage of the acetal–ester linkage. The polymerization behaviors were significantly different from that of the acyclic acrylate, α‐(hydroxymethyl)acrylic acid, which was expected inactive against polymerization due to the steric hindrance around the vinylidene group by the α‐substituent. The acetal–ester linkage of the obtained polymer ( P1 ) was completely cleaved via acid hydrolysis to afford a water soluble polymer, P2 . © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 955–961     

A new cyano-substituted fluorescamine superior to its original form as a fluorescent probe for amino acid detection

Synthesis and spectral study of two new cyano-substituted fluorescamine as the fluorescent probes for amino acid detection have been carried out comparing with the original fluorescamine. Of the three compounds, the derivative with a cyano group at the meta-position on the 4-phenyl group was found to be superior to the original one in the reactivity toward some amino acids as well as the fluorescence intensity of the adducts. The fluorescent amino acid adducts were also applied to the peroxyoxalate chemiluminescence system as the fluorophores, in which the derivative described above was found to be more effective also in chemiluminescence than the original one.     

Preparation of graphene oxide-coated silk fibers through HBPAA [a molecular glue]-induced layer-by-layer self-assembly

Carbon nanomaterials recently gained extensive interests for their good application potential in composite nanomaterials because of their unique physicochemical properties. In this study, graphene oxide (GO)-coated silk fibers were fabricated through HBPAA-induced layer-by-layer (LbL) self-assembly technology. The closely adhered GOs coatings were achieved by circular incubation with solutions of hyperbranched poly (amidoamine) (HBPAA) and GOs, with HBPAA serving as the “molecular glue” that could bind single or mutilayered GOs to the surface of silk fibers. In the experiments, GOs nanosheets were synthesized by a modified Hummers method and were characterized by atomic force microscopy, transmission electron microscopy, X-ray diffraction and X-ray photoelectron spectroscopy. Our developed technology was able to tightly bind GOs to the silk surface and control their loading capacity. Owing to the positive charges and abundant amino end groups of HBPAA, GOs were found to be completely adsorbed onto silk surface. Therefore, their assembly would be green and controllable. The Fourier transform infrared (FTIR) spectroscopy, XPS, XRD, Thermogravimetric analyses (TGA) confirmed the attachment of HBPAA and GOs. Field mission scanning electron microscopy (FESEM) indicated that GOs closely spread on the surface of silk fibers without any self-folding though excessive stacking were observed in a small part of a silk surface with the increased density of GOs coatings. The developed LbL self-assembly technology may provide a controllable approach to coat GOs on the surface of biological fibers and graphene-based functional materials.     

Synthesis of Fluorescent Gelators and Direct Observation of Gelation with a Fluorescence Microscope

Fluorescein‐, benzothiazole‐, quinoline‐, stilbene‐, and carbazole‐containing fluorescent gelators have been synthesized by connecting gelation‐driving segments, including l ‐isoleucine, l ‐valine, l ‐phenylalanine, l ‐leucine residue, cyclo(l ‐asparaginyl‐l ‐phenylalanyl), and trans‐(1R,2R)‐diaminocyclohexane. The emission behaviors of the gelators were investigated, and their gelation abilities studied against 15 solvents. The minimum gel concentration, variable‐temperature spectroscopy, transmission electron microscopy, scanning electron microscopy, fluorescence microscopy (FM), and confocal laser scanning microscopy (CLSM) were used to characterize gelation. The intermolecular hydrogen bonding between the N?H and C=O of amide, van der Waals interactions and π–π stacking play important roles in gelation. The colors of emission are related to the fluorescence structures of gelators. Fibrous aggregates characterized by the color of their emission were observed by FM. 3D images are produced by the superposition of images captured by CLSM every 0.1 μm to a settled depth. The 3D images show that the large micrometer‐sized aggregates spread out three dimensionally. FM observations of mixed gelators are studied. In the case of gelation, two structurally related gelators with the same gelation‐driving segment lead to the gelators build up of the same aggregates through similar hydrogen‐bonding patterns. When two gelators with structurally different gelation‐driving segments induce gelation, the gelators build up each aggregate through individual hydrogen‐bonding patterns. A fluorescent reagent that was incorporated into the aggregates of gels through van der Waals interactions was developed. The addition of this fluorescent reagent enables the successful observation of nonfluorescent gelators’ aggregates by FM.