A Note on Partitions into Distinct Parts and Odd Parts

Bousquet-Mélou and Eriksson showed that the number of partitions of n into distinct parts whose alternating sum is k is equal to the number of partitions of n into k odd parts, which is a refinement of a well-known result by Euler. We give a different graphical interpretation of the bijection by Sylvester on partitions into distinct parts and partitions into odd parts, and show that the bijection implies the above statement.     

Structural Dependence of the Selectivity of Fluorescent Chemosensors to Mg2+ from Alkali Earth Metal Ions

A series of novel 2,2′‐bipyridylene‐containing conjugated polymers are synthesized through the Wittig reaction. Some of these polymers show a highly selective affinity toward Mg²⁺ in a mixture of alkaline earth metal ions, which is different from the 2,2′‐bipyridylene‐containing poly(phenylene vinylene) derivatives reported previously. This is the first case to demonstrate that some materials show a selectivity toward Mg²⁺. The structures of the polymers may play a crucial role for this selectivity.     

Contributions of the nanovoid structure to the kinetics of moisture transport in epoxy resins

Absorbed moisture can degrade the physical properties of an epoxy resin, jeopardizing the performance of an epoxy‐based component. Although specific water–epoxy interactions are known to be very important in determining transport behavior, the role of network topology is not clear. In this article, a series of epoxies in which the topology is systematically varied (and the polarity held constant) is used to explore how topology influences the kinetics of moisture transport. The topology is quantified via the positron annihilation lifetime spectroscopy technique in terms of the size and volume fraction of electron density heterogeneities 5–6 Å in diameter, a dimension comparable to the 3‐Å kinetic diameter of a water molecule. Surprisingly, the volume fraction of such nanopores does not affect the diffusion coefficient (D) of water in any of the resins studied. For temperatures at and below 35 °C, there is a mild exponential dependence of D on the average nanopore size observed. Otherwise, the kinetics of moisture transport do not appear to depend on the nanopores. However, the initial flux of moisture into the epoxy does appear to correlate with the intrinsic hole volume fraction. That this correlation persists only in the initial stages of absorption is partially understood in terms of the ability of the water to alter the nanopore structure; only in the initial stages of uptake are the nanopores, as quantified in the dry state, relevant to transport. The role of specific epoxy–water interactions are also discussed in terms of transport kinetics. The lack of a correlation between the topology and transport suggests that polar interactions, and not topology, provide the rate‐limiting step of transport. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 776–791, 2000     

Determination of propagation rate coefficients for an α‐substituted acrylic ester: Pulsed laser polymerization of dimethyl itaconate

Pulsed laser polymerization experiments have been performed on the bulk polymerization of dimethyl itaconate over the temperature range 20–50 °C. The activation energy and frequency factor were calculated as 24.9 kJ/mol⁻¹ and 2.15 × 10⁵ L/mol⁻¹s⁻¹, respectively. The activation energy is comparable with the methacrylate series of monomers. The frequency factor is relatively small and reflects steric hindrance in the transition state caused by the bulky 1,1, disubstitution in the monomer (and consequently the radical). The Mark–Houwink–Kuhn–Sakurada constants were also determined for poly(dimethyl itaconate) in tetrahydrofuran, these are reported as 46 × 10⁻⁵ dL/g (K) and 0.51 (α). The influence of penultimate units (γ‐substituents) on homopropagation reactions is discussed particularly for polymerizations leading to significant 1,3 interactions in the resultant polymer. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 2192–2200, 2000     

An investigation of the thermal and thermo‐oxidative degradation of polybenzoxazines with a reactive functional group

The thermal behavior of a series of polybenzoxazines based on 3‐aminophenylacetylene has been investigated. The effect of reactive amine on the thermal cleavage of the Mannich base is examined under both inert and oxidative environments. It has been shown that the thermal stability of polybenzoxazines is substantially improved by the reactive amine. Various biphenols are found to have insignificant effect on the thermal stability of this series of polybenzoxazines. These nitrogen containing phenolic resins are nonflammable polymers. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 647–659, 1999     

Mechanistic study on the thermal decomposition of polybenzoxazines: Effects of aliphatic amines

The thermal degradation of a series of polybenzoxazines based on bisphenol A and various aliphatic amines has been studied. Using the hyphenated techniques of thermogravimetric analysis-Fourier transform infrared spectroscopy (TGA-FTIR), and gas chromatography-mass spectrometry (GC-MS), the mechanisms of thermal decomposition have been proposed. It is also proposed that the Mannich base in polybenzoxazines plays a significant role in the thermal degradation of polybenzoxazines. The contribution of hydrogen bonding to the degradation mechanism of the Mannich base has been examined. The proposed mechanisms have also been supported through the thermal degradation study of benzoxazine model dimers. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1935–1946, 1998     

Superlattice-based Plasmonic Catalysis: Concentrating Light at the Nanoscale to Drive Efficient Nitrogen-to-Ammonia Fixation at Ambient Conditions

Plasmonic catalysis promises green ammonia synthesis but is limited by the need for co-catalysts and poor performances due to weak electromagnetic field enhancement. Here, we use two-dimensional plasmonic superlattices with dense electromagnetic hotspots to boost ambient nitrogen-to-ammonia photoconversion without needing co-catalyst. By organizing Ag octahedra into a square superlattice to concentrate light, the ammonia formation is enhanced by ≈15-fold and 4-fold over hexagonal superlattice and disorganized array, respectively. Our unique catalyst achieves superior ammonia formation rate and apparent quantum yield up to ≈15-fold and ≈10³-fold, respectively, better than traditional designs. Mechanistic investigations reveal the abundance of intense plasmonic hotspots is crucial to promote hot electron generation and transfer for nitrogen reduction. Our work offers valuable insights to design electromagnetically hot plasmonic catalysts for diverse chemical and energy applications.