One- and two-electron reduction of triarylborane-based helical donor–acceptor compounds

One-electron chemical reduction of 10-(dimesitylboryl)-N,N-di-p-tolylbenzo[c]phenanthrene-4-amine (3-B(Mes)₂-[4]helix-9-N(p-Tol)₂) 1 and 13-(dimesitylboryl)-N,N-di-p-tolyldibenzo[c,g]phenanthrene-8-amine (3-B(Mes)₂-[5]helix-12-N(p-Tol)₂) 2 gives rise to monoanions with extensive delocalization over the annulated helicene rings and the boron p_z orbital. Two-electron chemical reduction of 1 and 2 produces open-shell biradicaloid dianions with temperature-dependent population of the triplet states due to small singlet-triplet gaps. These results have been confirmed by single-crystal X-ray diffraction, EPR and UV/vis-NIR spectroscopy, and DFT calculations.

Stepwise chemical reduction of D–π–A triarylborane-based helicenes gives the corresponding monoanions and dianions with delocalized unpaired electrons. The structures were confirmed by single crystal X-ray diffraction.     

Optimal estimates for lower and upper bounds of approximation errors in the p-version of the finite element method in two dimensions

Dedicated to Prof. O. Widlund on the occasion of his 60th birthday Correspondence to: B. Guo Summary. This paper will analyze the lower and upper error bounds of the finite element solution of the p-version for linear elliptic problems in polygonal domains. The optimal rate of convergence is rigorously proved based on the sharp estimates of lower and upper bounds of the approximation error.     

Hard-sphere radial distribution function again

A theoretically based closed-form analytical equation for the radial distribution function, g(r), of a fluid of hard spheres is presented and used to obtain an accurate analytic representation. The method makes use of an analytic expression for the short- and long-range behaviors of g(r), both obtained from the Percus-Yevick equation, in combination with the thermodynamic consistency constraint. Physical arguments then leave only three parameters in the equation of g(r) that are to be solved numerically, whereas all remaining ones are taken from the analytical solution of the Percus-Yevick equation.     

Thermodynamic Study of Cadmium Chloride in Aqueous Mixtures of 2-Butanol from Potential Difference Measurements

The standard molal potential differences (E_m∘) have been determined for the cell: CdHg_x(two phase) | CdCl₂(m), H₂O(1 − w), 2-butanol (w) | AgCl(s) | Ag(s) in aqueous mixtures of low mass fraction of 2-butanol (w_2-butanol = 0.05, 0.10, and 0.15) by using the literature data for the stability constants of the chlorocadmium complexes and the present potentiometric data for this cell at five temperatures from (293.15 to 313.15) K and at 10 molalities of CdCl₂ from (0.002 to 0.02) mol-kg⁻¹. The resulting values of E∘_m have been used to calculate the standard thermodynamic quantities (Δ_rG^∘, Δ_rH^∘, and Δ_rS^∘) for the cell reaction, the stoichiometric mean molal activity coefficients (γ_±) of CdCl₂, and the standard thermodynamic functions for CdCl₂ transfer (Δ_t G∘, Δ_t H∘, and Δ_t S∘) from water to the examined aqueous mixtures of 2-butanol. The values obtained have been compared with the analogous literature data for aqueous mixtures of 2-butanone; standard thermodynamic quantities for transfer of CdCl₂ and HBr from water to mixtures containing the same mass fraction of 2-butanol have also been compared. For both electrolytes, these quantities show analogous trends with the alcohol content. This transfer process is nonspontaneous and endothermic. Enthalpy and entropy are evidently influenced by structural changes.     

Acid-base equilibria in nonpolar media. 2.(1) Self-consistent basicity scale in THF solution ranging from 2-methoxypyridine to EtP(1)(pyrr) phosphazene

Relative ion-pair basicities Delta(pK)(ip) of 25 substituted aryl and alkyl iminophosphoranes (phosphazenes) and 20 other N-bases (various pyridines, amines, amidines) have been measured in THF medium using the UV-Vis and/or (13)C NMR methods. The Delta(pK)(ip) values were corrected for ion pairing using the Fuoss equation to obtain relative ionic basicities Delta(pK)(alpha). Based on the measurements, a basicity scale ranging from 2-methoxypyridine to EtP(1)(pyrr) and having a total span over 18 pK units has been created. The scale has been anchored to the pK(alpha) value of triethylamine (pK(alpha) = 12.5). The results are compared to pK(a) values in various other solvents and in the gas phase. The pK(alpha) values give better correlations than the pK(ip) values, thus indirectly validating the procedure of correction for ion pairing. The predictability of the basicity together with suitable spectral properties in the UV range make the phenylphosphazenes convenient neutral indicators in the high basicity range where the choice of neutral indicators is very limited.     

On a class of order pick strategies in paternosters

We study the travel time needed to pick n items in a paternoster, operating under the m-step strategy. This means that the paternoster chooses the shortest route among the ones that change direction at most once, and after collecting at most m items. For random pick positions, we find the distribution and moments of the travel time, provided n>2m. It appears that, already for m=2, the m-step strategy is very close to optimal, and better than the nearest item heuristic.     

Locally restricted colorings

We consider the following problem: given suitable integers χ and p, what is the smallest value ρ such that, for any graph G with chromatic number χ and any vertex coloring of G with at most χ+p colors, there is a vertex v such that at least χ different colors occur within distance ρ of v? Let ρ(χ,p) be this value; we show in particular that ρ(χ,p)?⌈p/2⌉+1 for all χ,p. We give the exact value of ρ when p=0 or χ?3, and (χ,p)=(4,1) or (4,2).     

Hybrid magnetic transistor

We report the development of a hybrid semiconductor-metal-semiconductor permeable-base transistor in vertical architecture. This transistor has a p-type silicon collector, a thin tin layer as base and a magnetoresistive conjugated polymer, poly(9,9-dioctyl-1,4-fluorenylenevinylene), as emitter material. The transistor transport characteristics are dependent on the applied magnetic field and the base transport factor for positive charge carriers is nearly ideal, independently of the magnetic field in the investigated range.     

Simple analysis of a fluid queue driven by an M/M/1 queue

In this note we consider the fluid queue driven by anM/M/1 queue as analysed by Virtamo and Norros [Queueing Systems 16 (1994) 373–386]. We show that the stationary buffer content in this model can be easily analysed by looking at embedded time points. This approach gives the stationary buffer content distribution in terms of the modified Bessel function of the first kind of order one. By using a suitable integral representation for this Bessel function we show that our results coincide with the ones of Virtamo and Norros.