Ends,tangles and critical vertex sets

We show that an arbitrary infinite graph G can be compactified by its ends plus its critical vertex sets, where a finite set X of vertices of an infinite graph is critical if its deletion leaves some infinitely many components each with neighbourhood precisely equal to X. We further provide a concrete separation system whose ?₀‐tangles are precisely the ends plus critical vertex sets. Our tangle compactification is a quotient of Diestel's (denoted by ), and both use tangles to compactify a graph in much the same way as the ends of a locally finite and connected graph compactify it in its Freudenthal compactification. Finally, generalising both Diestel's construction of and our construction of , we show that G can be compactified by every inverse limit of compactifications of the sets of components obtained by deleting a finite set of vertices. Diestel's is the finest such compactification, and our is the coarsest one. Both coincide if and only if all tangles are ends. This answers two questions of Diestel.     

Interaction between the end groups and the main chain of conjugated polymers by time-resolved EPR and fluorescence spectroscopy

ABSTRACT

Interaction between a zinc porphyrin (ZnPor) as the end-group and poly(9,9-di-n-octylfluorene-2,7-vinylene) (PFV) as the main chain in a porphyrin end-modified fluorescent conjugated polymer, ZnPFV, was studied by time-resolved electron paramagnetic resonance (EPR) and fluorescence spectroscopy. While fluorescence from the PFV part of ZnPFV showed a spectral profile almost identical to that of a PFV oligomer without end-modification, the emission spectrum of the ZnPor part exhibited a much broader profile compared to that of the reference zinc porphyrin monomer. Based on the analysis of lifetimes and quantum yields, it was found that radiative rate constant of the ZnPor part was enhanced by nearly three times. The observed unusual enhancement in the radiative rate constant was rationalised in terms of a partial π-conjugation between the end group and the main chain, as a result of co-planarisation in fluid solution. On the other hand, the time-resolved EPR spectrum of ZnPFV at 100?K basically showed a similar spectral pattern to that of the reference zinc porphyrin, but with significant differences in zero-field spitting parameters and initial population ratios. The π-system of the excited triplet state is deduced to deviate from D_4h symmetry in the end zinc porphyrin groups. The obtained results show that interaction of the porphyrin end group with the main chain of the polymer significantly influences the excited singlet state properties of the porphyrin, while its triplet state properties were affected to a lesser extent.     

Generic applications of 13C‐detected NMR diffusion to formulated systems with suppression of thermal convection induced by proton decoupling

Fast and effective structural/compositional analysis on formulated systems represents one of the major challenges encountered in analytical science. ¹³C‐detected diffusion represents a promising tool to tackle the aforementioned challenges, particularly in industry. Toward exploring the generic applications of ¹³C‐detected diffusion, thermal convection induced by ¹H decoupling has been identified as a key factor that resulted in significantly reduced resolution in the diffusion dimension. Optimization of experimental parameters and utilization of double‐stimulated echo‐based pulse sequence both can effectively suppress the thermal convection caused by the ¹H decoupling, the success of which allows robust and generic applications of ¹³C‐detected diffusion to systems from mixtures of small molecules, polymer blends, and copolymers to actual complex formulated systems. The method is particularly powerful in differentiating small molecules from polymers, polymer blends from copolymers, and end‐group analysis. Copyright © 2016 John Wiley & Sons, Ltd.     

Singly Periodic Solutions of the Allen-Cahn Equation and the Toda Lattice

The Allen-Cahn equation ? Δu = u ? u ³ in ?² has family of trivial singly periodic solutions that come from the one dimensional periodic solutions of the problem ?u″ =u ? u ³. In this paper we construct a non-trivial family of singly periodic solutions to the Allen-Cahn equation. Our construction relies on the connection between this equation and the infinite Toda lattice. We show that for each one-soliton solution to the infinite Toda lattice we can find a singly periodic solution to the Allen-Cahn equation, such that its level set is close to the scaled one-soliton. The solutions we construct are analogues of the family of Riemann minimal surfaces in ?³.     

Effect of barium titanate nanoparticles of different particle sizes on electro-optic and dielectric properties of ferroelectric liquid crystal

A comparative study of two different particle sizes of ferroelectric barium titanate (BaTiO₃) nanoparticles as a dopant on the molecular structure, spontaneous polarization and dielectric behavior of a pure ferroelectric liquid crystal 6F₆T have been studied. It has been found that there is a remarkable decrease in isotropic temperature of both doped samples as compared to the pure 6F₆T sample. The spontaneous polarization also decreases for both the doped samples and the reduction is more pronounced in case of the dopant with large particle size. The dielectric spectroscopy confirms the presence of soft mode as well as Goldstone mode and also shows the decrease in the value of dielectric permittivity ?' as a function of frequency for both doped samples. The improvised properties of liquid crystal host doped with BaTiO₃ nanoparticles mainly depend upon the synthesis method of nanoparticles and also upon the particle size of dopant.     

Nitroxide‐mediated Living Radical Polymerization of Styrene with Fluorescent Initiator

A fluorescence method was used for determination of marked chain ends in polystyrene samples prepared by 4‐substituted TEMPO type nitroxide‐mediated living free radical polymerization of styrene. 2,2,6,6‐Tetramethyl‐1‐(1‐phenylethoxy)‐piperidin‐4‐yl‐4‐pyren‐1‐ylbutanoate (PYNOR) was prepared and used as an unimolecular initiator bearing pyrene as a fluorescence mark on mediating nitroxide fragment. The bulk polymerization of styrene at 120°C, in the presence of new unimolecular initiator, was a typical nitroxide mediated living radical polymerization. For comparison, two different molar ratios of initiator and monomer (1∶400 and 1∶1000 initiator ‐ monomer [I:M]) were used for polymerization. When I:M=1∶400, the obtained polydispersity was 1.12 and maximum molecular weight 27,000 g/mol was obtained at 62% conversion. For ratio 1∶1000, slightly higher polydispersity was obtained ?1.26 and the molecular weight was 53,000 g/mol at 70% conversion. The content of the polystyrene chains bearing mediating nitroxide fragment was determined by fluorescence spectroscopy. The intensity of pyrene fluorescence decreased as the molar mass, and the conversion increased as well. The extent of the incorporation of chromophore at propagating chain end or “livingness” of polymerization decreased despite the fact that the polydispersity did not change. The extent of side reaction leading to broadening of polydispersity is suppressed due to the high viscosity of the system at higher conversion. A low extent of “livingness” will have a very negative effect on possible preparation of block copolymers.     

Elastomeric Properties of Polysiloxane Networks. Bimodal Elastomers that are Spatially Inhomogeneous and Others that are Very Broadly Multimodal

End‐linking poly(dimethylsiloxane) was used to prepare bimodal elastomers networks so as to have inhomogeneous nanostructures, and also to prepare others having very broadly multimodal chain‐length distributions. Macroscopic phase separation, probably high crosslink density clusters, was observed to occur in some of the bimodal networks. The mechanical properties in simple extension and in equilibrium swelling were measured. The bimodal elastomers that were not obviously inhomogeneous showed very good mechanical properties, but the macroscopically phase‐separated networks, and the broadly multimodal network were weak. Analysis of the Mooney‐Rivlin profiles suggests that the reinforcing mechanism could have a structural component in addition to that from the limited extensibilities of the short chains. The mechanical properties and the extents of swelling support the cluster conjecture, in accord with previous morphological studies on spatially‐inhomogeneous polysiloxane elastomers.     

X-ray diffraction and dielectric spectroscopy studies on a partially fluorinated ferroelectric liquid crystal from the family of terphenyl esters

The fluorinated compound, (S)-4′′-(6-perfluoropentanoyoxyhexyl-1-oxy)-2′,3′-difluoro-4-(1-methylheptyloxycarbonyl)-[1,1′:4′,1′′]-terphenyl, which exhibits antiferroelectric SmC_A*, ferroelectric SmC* and paraelectric SmA* phases, has been investigated by polarising optical microscopy, differential scanning calorimetry, X-ray diffraction and frequency-dependent dielectric spectroscopy methods. X-ray studies have revealed that the layer thickness remains almost constant in the SmA* phase but within the SmC* and SmC_A* phases it decreases with decreasing temperature, a step jump being observed only at the SmA*–SmC* transition. The tilt angle in the SmC_A* phase decreases from 22.2° to 19.5°, and in the SmC* phase it decreases from 18.8° to 5.5°. Spontaneous polarisation is found to be quite high and varies between 74.1 and 118.7 nC cm^?2. The variation in ε′ and ε′′ with temperature shows a discontinuous change at the transition temperatures. Goldstone mode relaxation is only observed in the ferroelectric and antiferroelectric phases and is found to be of the Cole–Cole type. The soft mode is observed on application of a bias field near the SmC*–SmA* transition. Neither the soft mode nor the anti-phase azimuthal angle fluctuation mode is observed in SmC_A*. Rotational viscosity decreases quite rapidly with temperature but in a different manner in the ferroelectric and antiferroelectric phases. Activation energy for this process is found to be 48.14 kJ mol^?1 in the SmC* phase.     

Preparation of Methyl 6‐O‐p‐Nitrobenzoyl‐β‐d‐Glucoside

Methyl 6‐O‐p‐nitrobenzoyl‐β‐d‐glucoside was synthesized by reacting methyl 4,6‐O‐p‐nitrobenzylidine‐β‐d‐glucoside with N‐bromosuccinimide (NBS). First, methyl β‐d‐glucoside was converted into methyl 4,6‐O‐p‐nitrobenzylidine‐β‐d‐glucoside with p‐nitrobenzaldehyde. Later, methyl 4,6‐O‐p‐nitrobenzylidine‐β‐d‐glucoside was opened oxidatively with NBS to give methyl 6‐O‐p‐nitrobenzoyl‐β‐d‐glucoside.     

Genotyping of exons 1 to 20 in Duchenne muscular dystrophy by universal multiplex PCR and short‐end capillary electrophoresis

One rapid CE method was established to diagnose Duchenne muscular dystrophy (DMD). DMD is a severe recessive inherited disorder frequently caused by gene deletions. Among them, exons 1–20 account for nearly 30% of occurrences. In this study, the universal multiplex PCR was used to enhance the fluorescently labeling efficiency, which was performed only by one universal fluorescent primer. After PCR, a short‐end injection CE (short‐end CE) speeded up the genotyping of the DMD gene. This method involved no extra purification, and was completed within 9 min. The CE conditions contained a polymer solution of 1.5% hydroxylethylcellulose in 1× TBE buffer at 6 kV for separation. This method was applied to test six DMD patients and one healthy male person. The results showed good agreement with those of multiplex ligation‐dependent probe amplification. This method can be applied for clinical diagnosis of DMD disease. Accurate diagnosis of the DMD gene is the best way to prevent the disease.