Entire large solutions of semilinear equations involving the fractional Laplacian

We investigate the existence and nonexistence of positive entire large solutions of a class of semilinear equations involving the fractional Laplacian. Sharp lower and upper bounds of the minimal solution, if it exists, are also given.     

Attraction behaviour of Anagrus nilaparvatae to remote lemongrass (Cymbopogon distans) oil and its volatile compounds

Utilisation of Anagrus nilaparvatae is a promising and effective method for planthoppers manipulation. Twenty-seven components of remote lemongrass (Cymbopogon distans) oil were identified by GC/MS and nine volatiles were selected for behavioural experiments. In this study, we noted that the remote lemongrass oil was attractive to female A. nilaparvatae at concentrations of 0.1 and 1 mg/L. α-Pinene, β-pinene, eucalyptol, carveol and D-carvone attracted female wasps in the dose-dependent bioassays. Blend 1 (a mixture of eucalyptol, D-carvone, carveol, α-pinene, and β-pinene with ratios of remote lemongrass oil volatiles of 625:80:11:5:3) attracted female wasps at 10 mg/L, while blend 2 (a mixture of the same five volatiles at the same loading ratio) attracted them at 0.1 and 1 mg/L. These results suggested that plant essential oils could be attractants for natural enemies to control pests. The ratios of volatiles in the mixtures affect the attractiveness of the synthetic mixtures.     

Crystallographic and microstructural aspects of the superconductor YBa2Cu3O7-y —an overview

Crystal structures and structural inhomogeneities observed in YBa₂Cu₃O_7-y are reviewed. It is brought out that a proper understanding of the nature of the structural inhomogeneities is essential for exploiting the technological potential of this material. The need for an adequate characterization of specimens used for experiments is emphasized. Practical implications of the ferroelastic nature of the material are discussed.     

Synthesis and investigation of dual pH‐ and temperature‐responsive behaviour of poly[2‐(dimethylamino)ethyl methacrylate]‐grafted gold nanoparticles

Gold nanoparticles (AuNPs) were synthesized by reduction of chloroauric acid (HAuCl₄) aqueous solution with hydrazine monohydrate. The AuNPs were immediately treated with cysteamine to obtain amine‐functionalized nanoparticles (Au‐NH₂). The reaction of Au‐NH₂ with epichlorohydrin and subsequent treatment with sodium hydroxide gave epoxidized AuNPs (Au‐EP). Then, thiol‐capped AuNPs (Au‐SH) were synthesized by reaction of Au‐EP with cysteamine. A ‘grafting to’ approach was utilized to graft bromine‐terminated poly(N ,N ′‐dimethylaminoethyl methacrylate), synthesized via aqueous atom transfer radical polymerization, with various molecular weights (6280, 25 800, 64 200 and 87 600 g mol⁻¹) onto Au‐SH to obtain Au‐P1, Au‐P2, Au‐P3 and Au‐P4 samples, respectively. All samples were exposed to temperature and pH variations, and Z‐average diameter was monitored using dynamic light scattering. According to the results, polymer‐grafted nanoparticles collapsed at lower temperatures with increasing solution pH for all molecular weight ranges due to deprotonation of tertiary amine groups. However, higher molecular weight polymers were more sensitive to pH variation especially in alkaline media. Also, a high degree of agglomeration was observed for Au‐P4 nanoparticles in alkaline media on increasing the temperature to 55 and 65 °C.     

Behaviour of ‘free-standing’ hollow Au nanocages at finite temperatures: a BOMD study

Finite-temperature behaviour of a hollow golden cage (HGC) plays a crucialrole in its potential applications as a catalyst, drug delivery agent, contrasting agent and so on. This physico-chemical property of HGCs is not well understood so far. In that context, Born–Oppenheimer molecular dynamics (BOMD) simulations are performed on a well-known ‘free-standing’ HGC. The cluster considered in this study is the ground state Au₁₈ cluster (a cage with a diameter of about >5.5 Å). The results thus obtained are compared with the BOMD simulation results reported earlier on Au₃₂ icosahedron cage, a conformation with a diameter of nearly. The sphericity of both the clusters is studied using a shape deformation parameter as a function of time and temperature. These results are supplemented by radial distribution function at various temperatures. The observations and analysis of results indicate that, both the clusters retain an HGC conformation from 300 to 400 K, admitting structural fluxionality by the Au₁₈ cluster. Remarkably, the Au₁₈ cluster is able to maintain its hollowness and sphericity up to a high temperature of 1000 K. Underlying structural and electronic properties influencing the individualistic behaviour of cages are highlighted. Composition of the frontier molecular orbitals and the charge distribution play a crucial role in the finite-temperature behaviour of the Au cages. The conclusions are supplemented by supporting calculations on another degenerate ground state Au₁₈ hollow cage and a well-known pyramidal Au₁₈ cage at 300 and 400 K.     

Dispersion production by semi-continuous radical vinyl acetate emulsion polymerization with silane co-monomer and characterization of final products

Vinyl acetate radical emulsion polymerization in water with GF51 silane co-monomer was performed by semi continuous way. The GF51 impacts on dispersion rheology as well on films and bonding strength properties were determined. It should be stated that even low quantities of GF51 (up to 6% from VAc) determined high viscosity of dispersions. The GF51 modified films have low water absorption and high affinity to glass. Molecular mass and thermal properties of GF51 modified polymers were determined accordingly.     

New chiral liquid crystal monomers and cholesteric polyacrylates: synthesis and characterisation

The synthesis of new chiral monomers (M₁ ?M₃ ) based on menthol and the corresponding polyacrylates (P₁ ?P₃ ) is described. The chemical structures, formula and phase behaviour of the obtained monomers and polymers were characterised with FT-IR, ¹H-NMR, elemental analyses, differential scanning calorimetry (DSC), polarising optical microscopy (POM) and X-ray diffraction (XRD). The effect of the mesogenic core rigidity, spacer length and menthyl steric effect on the phase behaviour of M₁ ?M₃ and P₁ ?P₃ is discussed. The expected mesophase of the compounds based on menthol can be obtained by inserting a flexible spacer between the mesogenic core and the terminal groups. For the chiral monomers and polyacrylates, their corresponding melting temperature (T _m), glass transition temperature (T _g) and clearing temperature (T _i) increased with an increase of the mesogenic core rigidity; while the T _m, T _g and T _i decreased with increasing the spacer length. M₁ and P₁ showed no mesophase, while M₂ and M₃ all revealed a SmC* and cholesteric phases. P₂ and P₃ only showed a cholesteric phase.     

Effect of chiral isosorbide groups on mesomorphic properties of side-chain liquid-crystalline polysiloxanes

Chiral side-chain liquid-crystalline (LC) polysiloxanes containing isosorbide groups were graft copolymerised with poly(methylhydrogeno)siloxane, a chiral LC monomer 6-(4-methoxy-benzoyloxy)-hexahydro-furo[3,2-b]furan-3-yl 4'-(4-undec-10-enoyloxy-benzoyloxy)-biphenyl-4-yl adipate and a nematic LC monomer 4'-(4-methoxy-benzoyloxy)-biphenyl-4-yl 4-(2-undec-10-enoyloxy-ethoxy)-benzoate. The chemical structures and LC properties of the monomers and polymers were characterised by use of various experimental techniques including Fourier transform infrared spectroscopy (FTIR), ¹H-nuclear magnetic resonance (NMR), element analyses (EA), differential scanning calorimetry (DSC), polarised optical microscopy (POM) and X-ray diffraction (XRD). All the chiral LC polymers showed LC properties with very wide mesophase temperature ranges and the chiral component in the LC polymer systems lead to the appearance of a cholesteric phase. The polymers bearing most chiral LC monomer component showed smectic phases by reason of regular structures in the polymer systems. With the increase of another nematic LC monomer in the polymers, the regular polymer structures were destroyed because of different chemical structures between the two kinds of LC monomers, leading to the disappearance of the smectic arrangement.     

Mesophase behaviour of laterally di-fluoro-substituted four-ring compounds

Four new groups of the di-fluoro-substituted 4-(2′-(or 3′)-fluoro phenylazo)-2-(or 3-) fluoro phenyl-4″-alkoxyphenylazo benzoates (In–IVn) were prepared and investigated for their mesophase behaviour. An alkoxy group of variable chain length (n = 6, 10 and 14 carbons) is attached to the terminal phenylazo benzoate moiety, and two lateral fluoro substituents are attached individually with different orientations to the other two adjacent rings. The molecular structures of the prepared compounds were confirmed by Fourier transform infrared spectroscopy and ¹H NMR spectroscopy. The study aims to investigate the steric effect of the spatial orientation and relative positions of the two lateral fluorine atoms on the mesomorphic properties in their pure states. The mesophase behaviour was investigated via differential scanning calorimetry and mesophases were identified by polarised light microscopy. The investigation shows that these compounds exhibit high enantiotropic mesophases (SmC and N) and broad mesophase temperature range. The type and stability of the mesophase depends on the length of the terminal alkoxy chain and the position the two fluoro substituents. A comparison between these investigated compounds with their corresponding three-ring analogues was discussed.     

The effect of ethanol on the phase behaviour and micro-rheology of liquid crystals

The effect of ethanol on the phase behaviour and micro-rheology of lyotropic liquid crystals (LC) has been studied using a binary mixture of monoglyceride (MG) and aqueous ethanol. The phase behaviour study reveals the structural modulation of surfactant aggregates with increasing ethanol concentration, namely a bicontinuous cubic phase (Ia3d) transitions to the lamellar phase (L_α), at a fixed MG concentration. This behaviour is explained by considering the critical packing parameter (CPP) of the surfactant molecule. Because ethanol dehydrates the surfactant head group (a _s), the CPP values increase (decreasing a _s) and thus the formation of larger CPP aggregates is favoured (i.e., the Ia3d–L_α transition occurs). Cross-polarised images and X-ray scattering data support this conclusion. The structural modulation of the LC has further been investigated using a diffusing wave spectroscopy technique. The correlation and relaxation times, determined from the intersection point at short and long time scales of the mean square displacement (MSD), decrease with increasing concentrations of ethanol, indicating structural modulation of the LC. The micro-viscoelastic moduli (G′ and G′′) derived from the Laplace transformation of the MSD decrease with increasing ethanol concentrations, due to the LC modulation. The thermal effects on the micro-rheology of the LC have also been studied.