Metal-containing triarylboron compounds for optoelectronic applications

Triarylboranes have recently emerged as a powerful new class of electron acceptors with great potential as optoelectronic materials. The empty p(z) orbital on the boron centre promotes strong charge-transfer transitions, leading to highly luminescent compounds with colors spanning the entire visible spectrum. Due to intense research efforts over the past decade, many examples now exist of organic molecules based on this structural motif. Only recently, however, have transition metal-containing triarylboranes been closely investigated. These compounds are capable of bright luminescence from a triplet excited state, and have been developed as efficient emissive materials for organic light-emitting diodes (OLEDs) as a result. In addition, their long-lived phosphorescence gives these materials potential as highly selective chemical sensors for small anions using time-gated detection, eliminating interference from background fluorescence. The research of the past several years has now led to a better understanding of the impact of the triarylboron group on the photophysical properties of metal complexes, which we expect will provide many opportunities for research into this class of functional phosphorescent materials.     

Every Large Point Set contains Many Collinear Points or an Empty Pentagon

We prove the following generalised empty pentagon theorem for every integer ℓ ≥ 2, every sufficiently large set of points in the plane contains ℓ collinear points or an empty pentagon. As an application, we settle the next open case of the “big line or big clique” conjecture of Kára, Pór, and Wood [Discrete Comput. Geom. 34(3):497–506, 2005].     

Mechanically induced scission and subsequent thermal remending of perfluorocyclobutane polymers

Perfluorocyclobutane (PFCB) polymer solutions were subjected to pulsed ultrasound, leading to mechanically induced chain scission and molecular weight degradation. (19)F NMR revealed that the new, mechanically generated end groups are trifluorovinyl ethers formed by cycloreversion of the PFCB groups, a process that differs from thermal degradation pathways. One consequence of the mechanochemical process is that the trifluorovinyl ether end groups can be remended simply by subjecting the polymer solution to the original polymerization conditions, that is, heating to >150 °C. Stereochemical changes in the PFCBs, in combination with radical trapping experiments, indicate that PFCB scission proceeds via a stepwise mechanism with a 1,4-diradical intermediate, offering a potential mechanism for localized functionalization and cross-linking in regions of high stress.     

Hybrid density functional theory band structure engineering in hematite

We present a hybrid density functional theory (DFT) study of doping effects in α-Fe(2)O(3), hematite. Standard DFT underestimates the band gap by roughly 75% and incorrectly identifies hematite as a Mott-Hubbard insulator. Hybrid DFT accurately predicts the proper structural, magnetic, and electronic properties of hematite and, unlike the DFT+U method, does not contain d-electron specific empirical parameters. We find that using a screened functional that smoothly transitions from 12% exact exchange at short ranges to standard DFT at long range accurately reproduces the experimental band gap and other material properties. We then show that the antiferromagnetic symmetry in the pure α-Fe(2)O(3) crystal is broken by all dopants and that the ligand field theory correctly predicts local magnetic moments on the dopants. We characterize the resulting band gaps for hematite doped by transition metals and the p-block post-transition metals. The specific case of Pd doping is investigated in order to correlate calculated doping energies and optical properties with experimentally observed photocatalytic behavior.     

A Differential Harnack Inequality for the Newell-Whitehead-Segel Equation

This paper will develop a Li-Yau-Hamilton type differential Harnack estimate for positive solutions to the Newell-Whitehead-Segel equation on R^n.We then use our LYH-differential Harnack inequality to prove several properties about positive solutions to the equation,including deriving a classical Harnack inequality and characterizing standing solutions and traveling wave solutions.     

Single-molecule transistors: Electron transfer in the solid state

Single-molecule transistors (SMTs) incorporating individual small molecules are unique tools for examining the fundamental physics and chemistry of electronic transport in molecular systems at the single nanometer scale. We describe the fabrication and characterization of such devices, and the synthesis and surface attachment chemistry of novel transition metal complexes that have been incorporated into such SMTs. We present gate-modulated inelastic electron tunneling vibrational spectroscopy of single molecules, strong Kondo physics (T_K ∼ 75 K) as evidence of excellent molecule/electrode electronic coupling, and a demonstration that covalent attachment chemistry can produce SMTs that survive repeated thermal cycling to room temperature. We conclude with a look ahead at the prospects for these nanoscale systems.     

Proper-Time Classical Electrodynamics

We construct a generalization of Maxwell's equations associated with the proper-time of the source which accounts for radiation reaction without any assumptions concerning the nature of the source. The theory leads to a new invariance group, related to the Lorentz group, which leaves the proper-time of the source fixed for all observers.     

Canonical Proper-Time Formulation of Relativistic Particle Dynamics. II

Our purpose in this paper is to provide theframework for a generalization of classical mechanicsand electrodynamics, including Maxwell's theory, whichis simple, technically correct, and requires noadditional work for the quantum case. We first show thatthere are two other definitions of proper-time, eachhaving equal status with the Minkowski definition. Weuse the first definition, called the proper-velocity definition, to construct a transformationtheory which fixes the proper-time of a given physicalsystem for all observers. This leads to a new invariancegroup and a generalization of Maxwell's equations left covariant under the action of this group.The second definition, called the canonical variablesdefinition, has the unique property that it isindependent of the number of particles. This definition leads to a general theory of directlyinteracting relativistic particles. We obtain theLorentz force for one particle (using its proper-time),and the Lorentz force for the total system (using theglobal proper-time). Use of the global proper-time tocompute the force on one particle gives the Lorentzforce plus a dissipative term corresponding to thereaction of this particle back on the cause of itsacceleration (Newton's third law). The wave equation derivedfrom Maxwell's equations has an additional term, firstorder in the proper-time. This term arisesinstantaneously with acceleration. This shows explicitly that the longsought origin of radiationreaction is inertial resistance to changes in particlemotion. The field equations carry intrinsic informationabout the velocity and acceleration of the particles in the system. It follows that our theory isnot invariant under time reversal, so that the existenceof radiation introduces an arrow for the (proper-time ofthe) system.     

On graphical partitions and planarity

Chvátal gave a necessary condition for a partition to have a planar realization. It is of interest to find: (i) partitions which satisfy the condition of the theorem but have no planar realization, and also (ii) partitions which satisfy the condition and have only planar realizations. We give a list of all such partitions with 6, 7, 8 and 9 elements. We also give an algorithm for generating all graphs with a given partition, an algorithm for generating all subcompositions of a given composition and some general classes of partitions which have planar realizations only and some which have non-planar realizations only.