Synthesis and Photocatalytic Properties of Titanium-Porphyrinic Aerogels

We present novel titanium-porphyrinic gels (TPGs) and titanium-porphyrinic aerogels (TPAs), in which porphyrinic ligand tetrakis(4-carboxyphenyl)porphyrin is coordinated to Ti-oxo clusters. These hierarchically porous TPAs, with micro-, meso-, and macropores and reactant-concentration-dependent Brunauer-Emmett-Teller surface areas of 407–738 m² g⁻¹, are prepared by CO₂ critical point drying of TPGs. Although the Ti⁴⁺ → Ti³⁺ photoreduction of TPAs is less efficient than that of crystalline microporous Ti-porphyrinic framework DGIST-1, prompt diffusion of O₂ and spin-trapping agents into the TPA pores causes the rapid generation of reactive oxygen species (ROS), as observed by EPR spectroscopy. When used as an ROS scavenger, large 1,3-diphenylisobenzofuran is degraded by the best-performing TPA 10 times faster than by DGIST-1, suggesting that the accessibility of molecules (reactants) to pores (reactive centers) strongly influences photocatalytic activity.     

A hierarchically consistent,iterative sequence transformation

Recently, the author proposed a new nonlinear sequence transformation, the iterative transformation, which was shown to provide excellent results in several applications (Homeier [15]). In the present contribution, this sequence transformation is derived by a hierarchically consistent iteration of some basic transformation. Hierarchical consistency is proposed as an approach to control the well-known problem that the basic transformation can be generalized in many ways. Properties of the transformation are studied. It is of similar generality as the well-knownE algorithm (Brezinski [3], Håvie [18]). It is shown that the transformation can be implemented quite easily. In addition to the defining representation, there are alternative algorithms for its computation based on generalized differences. The kernel of the transformation is derived. The expression for the kernel is relatively compact and does not depend on any lower-order transforms. It is shown that several important other sequence transformations can be computed in an economical way using the transformation.Communicated by C. Brezinski     

Conductance distributions in random resistor networks. Self-averaging and disorder lengths

The self-averaging properties of the conductanceg are explored in random resistor networks (RRN) with a broad distribution of bond strengthsP(g)g ^–1. The RRN problem is cast in terms of simple combinations of random variables on hierarchical lattices. Distributions of equivalent conductances are estimated numerically on hierarchical lattices as a function of sizeL and the distribution tail strength parameter . For networks above the percolation threshold, convergence to a Gaussian basin is always the case, except in the limit 0. Adisorder length _D is identified, beyond which the system is effectively homogeneous. This length scale diverges as _Dµ^–v ( is the regular percolation correlation length exponent) when the microscopic distribution of conductors is exponentially wide (0). This implies that exactly the same critical behavior can be induced by geometrical disorder and by strong bond disorder with the bond occupation probabilityp. We find that only lattices at the percolation threshold have renormalized probability distributions in aLevy-like basin. At the percolation threshold the disorder length diverges at a critical tail strength µ_c as µ–^–z withz3.2±0.1, a new exponent.Critical path analysis is used in a generalized form to give the macroscopic conductance in the case of lattices abovep _c.     

Computation of hierarchical renormalization-group fixed points and their ε-expansions

We compute hierarchical renormalization-group fixed points as solutions to an algebraic equation for the coupling constants. This method does not rely on an iteration of renormalization-group transformations and therefore avoids the problem of fine tuning. We solve truncated versions of the fixed-point equation numerically for different values of the dimension parameter in the range 2<d<4 and different orders of truncations. The method is well suited even for multicritical fixed points with any number of unstable directions. Precise numerical data are presented for the first three nontrivial fixed points and their critical indices. We also develop an -expansion for the hierarchical models using computer algebra. The numerical results are compared with the -expansion.     

Modelling matrix damage and fibre–matrix interfacial decohesion in composite laminates via a multi-fibre multi-layer representative volume element (MRVE)

A three-dimensional multi-fibre multi-layer micromechanical finite element model was developed for the prediction of mechanical behaviour and damage response of composite laminates. Material response and micro-scale damage mechanism of cross-ply, [0/90]_ns, and angle-ply, [±45]_ns, glass-fibre/epoxy laminates were captured using multi-scale modelling via computational micromechanics. The framework of the homogenization theory for periodic media was used for the analysis of the proposed ‘multi-fibre multi-layer representative volume element’ (M²RVE). Each layer in M²RVE was represented by a unit cube with multiple randomly distributed, but longitudinally aligned, fibres of equal diameter and with a volume fraction corresponding to that of each lamina (equal in the present case). Periodic boundary conditions were applied to all the faces of the M²RVE. The non-homogeneous stress–strain fields within the M²RVE were related to the average stresses and strains by using Gauss’ theorem in conjunction with the Hill–Mandal strain energy equivalence principle. The global material response predicted by the M²RVE was found to be in good agreement with experimental results for both laminates. The model was used to study effect of matrix friction angle and cohesive strength of the fibre–matrix interface on the global material response. In addition, the M²RVE was also used to predict initiation and propagation of fibre–matrix interfacial decohesion and propagation at every point in the laminae.     

Well‐defined Sb2S3 nanostructures: citric acid‐assisted synthesis,electrochemical hydrogen storage properties

Well‐defined (three‐dimensional) 3‐D dandelion‐like Sb₂S₃ nanostructures consisted of numerous nanorods have been achieved via a facile citric acid‐assisted solvothermal process. The as‐prepared products were characterized by X‐ray diffraction (XRD), field‐emission scanning electron microscopy (FESEM), transmission electron microscopy (TEM) and high‐resolution TEM (HRTEM), respectively. The influence factors of the formation of the hierarchical Sb₂S₃ nanostructures are discussed in details based on FESEM characterizations. By simply controlling the quantity of citric acid, the nucleation and growth process can be readily tuned, which brings the different morphologies and nanostructures of the final products. On the basis of a series of contrastive experiments, the aggregation‐based process and anisotropic growth mechanism are reasonably proposed to understand the formation mechanism of Sb₂S₃ hierarchical architectures with distinctive morphologies including nanorods, and dandelion‐like nanostructures. Charge‐discharge curves of the obtained Sb₂S₃ nanostructures were measured to investigate their electrochemical hydrogen storage behaviors. It revealed that the morphology played a key role on the hydrogen storage capacity of Sb₂S₃ nanostructure. The dandelion‐like Sb₂S₃ nanostructures exhibited higher hydrogen storage capacity (108 mAh g⁻¹) than that of Sb₂S₃ nanorods (95 mAh g⁻¹) at room temperature.     

Evolution of hierarchical‐structured CaCO3 in binary mixed solvent

Calcium carbonate with hierarchical structure was synthesized in water/organic compound binary soluvent by a chemical solution process within CaCl₂/NaCO₃ reaction system. Acetone, isopropanol, glycol, tetrahydrofuran were selected as the organic compound. Evolution of the hierarchical structure of CaCO₃ was investigated. The as‐prepared products were characterized by X‐ray diffraction (XRD) and scanning electron microscopy (SEM). CaCO₃ aggregations with spicate hierarchical structure were obtained with a high volume fraction of the organic solvent. Aspect ratio of the hierarchical structure increases to the highest when the volume fraction was 50%. Solvent with low dielectric constant was conducive to the oriented aggregation of the CaCO₃ grains.     

Large‐Scale Production of Hierarchical TiO2 Nanorod Spheres for Photocatalytic Elimination of Contaminants and Killing Bacteria

We report a facile non‐hydrothermal method for the large‐scale production of hierarchical TiO₂ nanorod spheres for the photocatalytic elimination of contaminants and killing bacteria. Crescent Ti/RF spheres were prepared by deliberately adding titanium trichloride (TiCl₃) to the reaction of resorcinol (R) and formaldehyde (F) in an open reactor under heating and stirring. The hierarchical TiO₂ nanorod spheres were obtained by calcining the crescent Ti/RF spheres in a furnace in air to burn off the RF spheres. This method has many merits, such as large‐scale production, good crystallisation of TiO₂, and good reproducibility, all of which are difficult to realise by conventional hydrothermal methods. The calcination temperature plays a significant role in influencing the morphology, crystallisation, porosity, Brunauer–Emmett–Teller (BET) specific surface area, and hierarchy of the TiO₂ nanorod spheres, thus resulting in different photocatalytic performances under UV light and solar light irradiation. The experimental results have demonstrated that the hierarchical TiO₂ nanorod spheres obtained after calcination of the crescent Ti/RF spheres at different temperatures displayed similar photocatalytic activities under irradiation with UV light. We attribute this to a balance of opposing effects of the investigated factors. A higher calcination temperature leads to greater light absorption capability of the TiO₂ nanorod spheres, thus resulting in higher photocatalytic antibacterial activity under solar light irradiation. It is also interesting to note that the hierarchical TiO₂ nanorod spheres displayed intrinsic antibacterial activity in the absence of light irradiation, apparently because their sharp outward spikes can easily pierce and penetrate the walls of bacteria. In this study, the sharpest hierarchical TiO₂ nanorod spheres were obtained after calcination at 500 °C, and these exhibited the highest antibacterial activity without light irradiation. A higher calcination temperature proved detrimental to the sharpness of the TiO₂ nanorods, thus reducing their intrinsic antibacterial activity.     

Covalent Assembly of Hierarchical Particles by Efficient Coupling of β‐Diketones and Benzyl Chloride

A coupling reaction is performed between polymeric nanoparticles and microparticles via the nucleophilic substitution of pendent β‐diketone groups with benzyl chloride. The coupling reaction results in the formation of hierarchical particles, through the nanoparticles being covalently linked onto the microparticles. The coupling reaction is tracked by TEM and SEM, and the formation of covalent C–C bonds through the coupling reaction between the polymeric nanoparticles and microparticles is confirmed by solid‐state ¹³C CP‐MAS NMR spectroscopy and XPS. The proposed coupling reaction between the nanoparticles and the microparticles is believed to be a promising strategy in particle‐surface modification.