Exactness of SWKB for shape invariant potentials

The supersymmetry-based semiclassical method (SWKB) is known to produce exact spectra for conventional shape invariant potentials. In this paper we prove that this exactness follows from their additive shape invariance.     

End group polarity and block symmetry effects on cloud point and hydrodynamic diameter of thermoresponsive block copolymers

Thermoresponsive block copolymers are of interest for delivery vehicles in the body. Often an interior domain is designed for the active agent and the exterior domain provides stability in the bloodstream, and may carry a targeting ligand. There is still much to learn about how block sequence and chain end identity affect micelle structure, size, and cloud points. Here, hydrophilic oligo(ethylene glycol) methyl ether acrylate and more hydrophobic di(ethylene glycol) methyl ether methacrylate monomers were polymerized to give amphiphilic block copolymers with amphiphilic chain ends. The block sequence and chain end identity were both controlled by appropriate choice of RAFT chain transfer agents to study the effect of ‘matched’ and ‘mismatched’ chain end polarity with amphiphilic block sequence. The affect of matching or mismatching chain end polarity and block sequence was studied on the hydrodynamic diameter, cloud point, and temperature range of the chain collapse on linear di‐ and triblock copolymers and star diblock polymers. The affects of matching or mismatching chain end polarity were significant with linear diblock copolymers but more complex with triblock and star copolymers. Explanations of these results may help guide others in designing thermoresponsive block copolymers. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2838–2848     

Invariant discrete flows

In this paper, we investigate the evolution of joint invariants under invariant geometric flows using the theory of equivariant moving frames and the induced invariant discrete variational complex. For certain arc length preserving planar curve flows invariant under the special Euclidean group , the special linear group , and the semidirect group , we find that the induced evolution of the discrete curvature satisfies the differential‐difference mKdV, KdV, and Burgers' equations, respectively. These three equations are completely integrable, and we show that a recursion operator can be constructed by precomposing the characteristic operator of the curvature by a certain invariant difference operator. Finally, we derive the constraint for the integrability of the discrete curvature evolution to lift to the evolution of the discrete curve itself.     

Ligands Based on Phosphine-Stabilized Aluminum(I), Boron(I), and Carbon(0)

A systematic quantum chemical study of the bonding in d⁶-transition-metal complexes, containing phosphine-stabilized, main-group-element fragments, (R₃P)₂E, as ligands (E=AlH, BH, CH⁺, C), is reported. By using energy decomposition analysis, it is demonstrated that a strong M−E bond is accompanied by weak P−E bonds, and vice versa. Although the Al−M bond is, for example, found to be very strong, the weak Al−P bond suggests that the corresponding metal complexes will not be stable towards phosphine dissociation. The interaction energies for the boron(I)-based ligand are lower, but still higher than those for two-carbon-based ligands. For neutral ligands, electrostatic interactions are the dominating contributions to metal–ligand bonding, whereas for the cationic ligand a significant destabilization, with weak orbital and even weaker electrostatic metal–ligand interactions, is observed. Finally, for iron(II) complexes, it is demonstrated that different reactivity patterns are expected for the four donor groups: the experimentally observed reversible E−H reductive elimination of the borylene-based ligand (E=BH) exhibits significantly higher barriers for the protonated carbodiphosphorane (CDP) ligand (E=CH) and would proceed through different intermediates and transition states. For aluminum, such reaction pathways are not feasible (E=AlH). Moreover, it is demonstrated that the metal hydrido complexes with CDP ligands might not be stable towards reduction and isomerization to a protonated CDP ligand and a reduced metal center.     

Unprecedented Oxidative Addition and Metal‐Only Lewis Pair Chemistry of Antimony Trihalides

Reaction of the zero‐valent platinum complex [Pt(PCy₃)₂] with SbF₃ generates the cationic diplatinum stibenium complex [{(Cy₃P)₂Pt}₂(μ‐SbF₂)]⁺, the first unsupported metal‐only Lewis pair containing an antimony‐centered Lewis acid. In contrast, SbCl₃ undergoes oxidative addition to [Pt(PCy₃)₂], resulting in the dihalostibanyl complex trans‐[PtCl(SbCl₂)(PCy₃)₂], the first example of oxidative addition of an antimony–halide bond to a transition metal.     

New fabrication approach to develop a high birefringence photo-crosslinked film based on a sulfur-containing liquid crystalline molecule with large temperature dependence of birefringence

ABSTRACT

We present a new fabrication approach to achieve a high birefringence film by means of photopolymerization based on an alkylthio-containing rod-like liquid crystalline molecule exhibiting large temperature dependence of birefringence. We designed a new reactive mesogen having alkylthio linkages (BPM–S). It was found that BPM–S had a larger increment of birefringence with decreasing temperature, relative to commercially available alkoxy analog LC242. This result could be thought to be due to enhanced intermolecular attractive interaction for an alkylthio mesogen implied by the proximity of laterally neighboring molecules and cybotactic nematic tendency based on wide-angle X-ray measurement. The uniaxially-aligned photo-polymerized film for BPM–S showed higher birefringence than that for LC 242.