Role of information theoretic uncertainty relations in quantum theory

Uncertainty relations based on information theory for both discrete and continuous distribution functions are briefly reviewed. We extend these results to account for (differential) Rényi entropy and its related entropy power. This allows us to find a new class of information-theoretic uncertainty relations (ITURs). The potency of such uncertainty relations in quantum mechanics is illustrated with a simple two-energy-level model where they outperform both the usual Robertson–Schrödinger uncertainty relation and Shannon entropy based uncertainty relation. In the continuous case the ensuing entropy power uncertainty relations are discussed in the context of heavy tailed wave functions and Schrödinger cat states. Again, improvement over both the Robertson–Schrödinger uncertainty principle and Shannon ITUR is demonstrated in these cases. Further salient issues such as the proof of a generalized entropy power inequality and a geometric picture of information-theoretic uncertainty relations are also discussed.     

Experimental survey of the kinetics of acene Diels–Alder reactions

Second‐order rate constants were gathered for solution Diels–Alder reactions of substituted and unsubstituted acenes, with the intention of ascertaining ideal diene–dienophile combinations. Particular focus was placed on the larger ring systems namely tetracene, pentacene, and rubrene. The rate constants between the acenes ranged roughly six orders of magnitude, from the slowest reacting diene, rubrene, to the fastest diene, pentacene. The utilized dienophiles covered a large range of reactivity from 2,3‐dichloromaleic anhydride to tetracyanoethylene. To aid in the interpretation of acene reactivity, constants were compared to the extensive body of Diels–Alder literature with well‐studied dienes such as anthracene and trans‐1‐methoxy‐1,3‐butadiene serving as points of reference. Complex reaction kinetics for the addition of MeTAD and rubrene was found: initial fast consumption generated an intermediate, followed by dramatically slower product formation. The kinetic data creates a foundation for the analysis of prior and future reactions between organic semiconductor acene materials with volatized dienophiles, a surface functionalization technique for enhancing these electronic materials. Copyright © 2015 John Wiley & Sons, Ltd.     

Optical and electronic properties of air-stable organoboron compounds with strongly electron-accepting bis(fluoromesityl)boryl groups

Three compounds with phenyl (1), 4-tert-butylphenyl (2) and 4-N,N-diphenylaminophenyl (3) groups attached to bis(fluoromesityl)boryl ((FMes)₂B) through B–C bonds have been prepared. The restricted rotation about the B–C bonds of boron-bonded aryl rings in solution has been studied by variable-temperature ¹⁹F NMR spectroscopy, and through-space F–F coupling has been observed for 3 at low temperature. Steric congestion inhibits binding of 1 by Lewis bases DABCO and tBu₃P and the activation of H₂ in their presence. Photophysical and electrochemical studies have been carried out on 2, 3, and an analogue of 3 containing a bis(mesityl)boryl ((Mes)₂B) group, namely 4. Both 2 and 3 show bright emission in nonpolar solvents and in the solid-state, very strong electron-accepting ability as measured by cyclic voltammetry, and good air-stability. In addition, 2 displayed unusually long-lived emission (τ = 2.47 s) in 2-MeTHF at 77 K. The much stronger acceptor strength of (FMes)₂B than (Mes)₂B leads to significantly red-shifted emission in solution and the solid state, stronger emission solvatochromism, and significantly lower reduction potentials. Theoretical calculations confirm that 2 and 3 tend to form highly twisted excited states with good conjugation between one FMes group and the boron atom, which correlate well with their blue-shifted solid-state emissions and low k _r values in solution.     

Impacts of gold nanoparticle charge and ligand type on surface binding and toxicity to Gram-negative and Gram-positive bacteria

Although nanomaterials facilitate significant technological advancement in our society, their potential impacts on the environment are yet to be fully understood. In this study, two environmentally relevant bacteria, Shewanella oneidensis and Bacillus subtilis, have been used as model organisms to elucidate the molecular interactions between these bacterial classes and Au nanoparticles (AuNPs) with well-controlled and well-characterized surface chemistries: anionic 3-mercaptopropionic acid (MPA), cationic 3-mercaptopropylamine (MPNH₂), and the cationic polyelectrolyte poly(allylamine hydrochloride) (PAH). The data demonstrate that cationic, especially polyelectrolyte-wrapped AuNPs, were more toxic to both the Gram-negative and Gram-positive bacteria. The levels of toxicity observed were closely related to the percentage of cells with AuNPs associated with the cell surface as measured in situ using flow cytometry. The NP concentration-dependent binding profiles were drastically different for the two bacteria strains, suggesting the critical role of bacterial cell surface chemistry in determining nanoparticle association, and thereby, biological impact.     

A rod-airfoil experiment as a benchmark for broadband noise modeling

A low Mach number rod-airfoil experiment is shown to be a good benchmark for numerical and theoretical broadband noise modeling. The benchmarking approach is applied to a sound computation from a 2D unsteady-Reynolds-averaged Navier–Stokes (U-RANS) flow field, where 3D effects are partially compensated for by a spanwise statistical model and by a 3D large eddy simulation. The experiment was conducted in the large anechoic wind tunnel of the Ecole Centrale de Lyon. Measurements taken included particle image velocity (PIV) around the airfoil, single hot wire, wall pressure coherence, and far field pressure. These measurements highlight the strong 3D effects responsible for spectral broadening around the rod vortex shedding frequency in the subcritical regime, and the dominance of the noise generated around the airfoil leading edge. The benchmarking approach is illustrated by two examples:

Use of 3-(4-hydroxyphenyl)propionic acid as electron donating compound in a potentiometric aflatoxin M1-immunosensor

We developed a potentiometric aflatoxin M₁-immunosensor which utilizes 3-(4-hydroxyphenyl)propionic acid (p-HPPA) as electron donating compound for horseradish peroxidase (HRP; EC 1.11.1.7). The assay system consists of a polypyrrole-surface-working electrode coated with a polyclonal anti-M₁ antibody (pAb-AFM₁), a Ag/AgCl reference electrode and a HRP-aflatoxin B₁ conjugate (HRP-AFB₁ conjugate).To optimize the potentiometric measuring system p-HPPA as well as related compounds serving as electron donating compounds were compared. Also the influence of different buffer systems, varying pH and substrate concentrations on signal intensity was investigated. Our results suggest that reaction conditions that favor the formation of Pummerer's type ketones lead to an increase in signal intensity rather than formation of fluorescent dye. Comparison with commercial ready-to-use HRP electron donating compounds such as 2,2′-azino-bis(3-ethylbenzothiazoline-6-sulfonic acid) diammonium salt (ABTS), o-phenylenediamine (OPD) or 3,3′,5,5′-tetramethylbenzidine (TMB) showed that only 34%, 77% and 49% of the signal intensity of p-HPPA were reached, respectively.The optimized assay had a detection limit of 40 pg mL⁻¹ and allowed detection of 500 pg mL⁻¹ (FDA action limit) aflatoxin M₁ (AFM₁) in pasteurized milk and UHT-milk containing 0.3-3.8% fat within 10 min without any sample treatment. The working range was between 250 and 2000 pg mL⁻¹ AFM₁.     

Role of entropy in the stability of cobalt titanates

The standard molar Gibbs free energy of formation of Co₂TiO₄, CoTiO₃, and CoTi₂O₅ as a function of temperature over an extended range (900 to 1675) K was measured using solid-state electrochemical cells incorporating yttria-stabilized zirconia as the electrolyte, with CoO as reference electrode and appropriate working electrodes. For the formation of the three compounds from their component oxides CoO with rock-salt and TiO₂ with rutile structure, the Gibbs free energy changes are given by:$\begin{array}{cc}\hfill & {\mathrm{\Delta }}_{\text{f}}{G}_{(\text{ox})}^{°}({\text{Co}}_2{\text{TiO}}_4)\pm 104/(\text{J}·{\text{mol}}^{-1})=-18865-4.108(T/\text{K})\hfill \\ \hfill & {\mathrm{\Delta }}_{\text{f}}{G}_{(\text{ox})}^{°}({\text{CoTiO}}_3)\pm 56/(J·{\text{mol}}^{-1})=-19627+2.542(T/\text{K})\hfill \\ \hfill & {\mathrm{\Delta }}_{\text{f}}{G}_{(\text{ox})}^{°}({\text{CoTi}}_2{O}_5)\pm 52/(\text{J}·{\text{mol}}^{-1})=-6223-6.933(T/\text{K})\hfill \end{array}$Accurate values for enthalpy and entropy of formation were derived. The compounds Co₂TiO₄ with spinel structure and CoTi₂O₅ with pseudo-brookite structure were found to be entropy stabilized. The relatively high entropy of these compounds arises from the mixing of cations on specific crystallographic sites. The stoichiometry of CoTiO₃ was confirmed by inert gas fusion analysis for oxygen. Because of partial oxidation of cobalt in air, the composition corresponding to the compound Co₂TiO₄ falls inside a two-phase field containing the spinel solid solution Co₂TiO₄–Co₃O₄ and CoTiO₃. The spinel solid solution becomes progressively enriched in Co₃O₄ with decreasing temperature.     

Accessible silanol sites - beneficial for the RP-HPLC separation of constitutional and diastereomeric azaspirovesamicol isomers

Different RP-HPLC columns (phenyl, conventional ODS, cross-linked C(18) and special end-capped C(8) and C(18) phases) were used to investigate the separation of four basic ionizable isomers. Using ACN/20mM NH(4)OAc aq., a separation was observed exclusively on RP columns with higher silanol activity at unusual high ACN concentration, indicating cation-exchange as main retention mechanism. Using MeOH/20mM NH(4)OAc aq., another separation at low MeOH concentrations was observed on both, RP columns with higher as well as RP columns with lower silanol activity, which is mainly based on hydrophobic interactions. The isomers were also separated on a bare silica column at higher MeOH content using NH(4)OAc. Since cation-exchange governs this retention, the elution order was different compared to the RP phases. A strong retention on the silica column was observed in ACN, which could be attributed to partition processes as additional retention mechanism.