On the Nitroxide Quasi‐Equilibrium in the Alkoxyamine‐Mediated Radical Polymerization of Styrene

Summary: The range of validity of two popular versions of the nitroxide quasi‐equilibrium (NQE) approximation used in the theory of kinetics of alkoxyamine mediated styrene polymerization, are systematically tested by simulation comparing the approximate and exact solutions of the equations describing the system. The validity of the different versions of the NQE approximation is analyzed in terms of the relative magnitude of (dN/dt)/(dP/dt). The approximation with a rigorous NQE, k_c[P][N] = k_d[P N], where P, N and P N are living, nitroxide radicals and dormant species respectively, with kinetic constants k_c and k_d, is found valid only for small values of the equilibrium constant K (10⁻¹¹–10⁻¹² mol · L⁻¹) and its validity is found to depend strongly of the value of K. On the other hand, the relaxed NQE approximation of Fischer and Fukuda, k_c[P][N] = k_d[P N]₀ was found to be remarkably good up to values of K around 10⁻⁸ mol · L⁻¹. This upper bound is numerically found to be 2–3 orders of magnitude smaller than the theoretical one given by Fischer. The relaxed NQE is a better one due to the fact that it never completely neglects dN/dt. It is found that the difference between these approximations lies essentially in the number of significant figures taken for the approximation; still this subtle difference results in dramatic changes in the predicted course of the reaction. Some results confirm previous findings, but a deeper understanding of the physico‐chemical phenomena and their mathematical representation and another viewpoint of the theory is offered. Additionally, experiments and simulations indicate that polymerization rate data alone are not reliable to estimate the value of K, as recently suggested.

Validity of the rigorous nitroxide quasi‐equilibrium assumption as a function of the nitroxide equilibrium constant.     

Hemilabile MIC^N ligands allow oxidant-free Au(i)/Au(iii) arylation-lactonization of γ-alkenoic acids

Oxidant-free Au-catalyzed reactions are emerging as a new synthetic tool for innovative organic transformations. Oxidant-free Au-catalyzed reactions are emerging as a new synthetic tool for innovative organic transformations. Still, a deeper mechanistic understanding is needed for a rational design of these processes. Here we describe the synthesis of two Au(i) complexes bearing bidentated hemilabile MIC^N ligands, [Au^I(MIC^N)Cl], and their ability to stabilize square-planar Au(iii) species (MIC = mesoionic carbene). The presence of the hemilabile N-ligand contributed to stabilize the ensuing Au(iii) species acting as a five-membered ring chelate upon its coordination to the metal center. The Au(iii) complexes can be obtained either by using external oxidants or, alternatively, by means of feasible oxidative addition with strained biphenylene C_sp²–C_sp² bonds as well as with aryl iodides. Based on the fundamental knowledge gained on the redox properties on these Au(i)/Au(iii) systems, we successfully develop a novel Au(i)-catalytic procedure for the synthesis of γ-substituted γ-butyrolactones through the arylation-lactonization reaction of the corresponding γ-alkenoic acid. The oxidative addition of the aryl iodide, which in turn is allowed by the hemilabile nature of the MIC^N ligand, is an essential step for this transformation.

A novel hemilabile MIC^N ligand-based Au(i)-catalytic procedure for the synthesis of γ-substituted γ-butyrolactones through the arylation-lactonization reaction of the corresponding γ-alkenoic acid is presented.     

Regularized bridge-type estimation with multiple penalties

Annals of the Institute of Statistical Mathematics - The aim of this paper is to introduce an adaptive penalized estimator for identifying the true reduced parametric model under the sparsity...     

Krichever Maps,Faà di Bruno Polynomials,and Cohomology in KP Theory

We study the geometrical meaning of the Faà di Bruno polynomials in the context of KP theory. They provide a basis in a subspace W of the universal Grassmannian associated to the KP hierarchy. When W comes from geometrical data via the Krichever map, the Faà di Bruno recursion relation turns out to be the cocycle condition for (the Welters hypercohomology group describing) the deformations of the dynamical line bundle on the spectral curve together with the meromorphic sections which give rise to the Krichever map. Starting from this, one sees that the whole KP hierarchy has a similar cohomological meaning.     

On the statistical solutions of the two-dimensional,periodic Euler equation

We investigate the problem to define statistical solutions for the two-dimensional, periodic Euler Equation and prove a theorem of global existence and uniqueness for a regularized version. Moreover, we deduce the existence of the Euler flow in a weak form.     

New nickel(II) chloride-morpholine complexes

The compounds [NiCl₂(Morph)₃(H₂O)₂] and [NiCl₂(Morph)₃] have been prepared by treating NiCl₂·6H₂O with morpholine (Mo     

Di-μ-hydroxo complexes of palladium(II) with α-diimines

The binuclear hydroxo α-diiminate palladium complexes [Pd2(R′N=CR-CR=NR′)2(μ-OH)2][ClO4]2 (R=H, R′= C6H4Me-o or C6H4Me-p; R=Me, R′=Ph, C6H4Me-o or C6H4Me-p) have been prepared by reacting the corresponding chloro complexes with AgClO4 in Me2CO–H2O. The hydroxo complexes react with the protic electrophiles ethanoic acid, acetylacetone and8-hydroxoquinoline to give the corresponding acetylacetonate, acetate and 8-hydroxiquinolinate complexes. This revised version was published online in June 2006 with corrections to the Cover Date.     

Chemical reactions of cycloalkanespirohydantoins. Part 2. Synthesis of new 4-hydroxyimidazolidinone N3-substituted from cycloalkanespirohydantoins

N₃-Substituted hydantoins have been to undergo lithium aluminum hydride reduction (THF, room temperature, 5 hours) to give 4-hydroxy-2-imidazolidinones in good yields.     

A preliminary study on the migration mechanism of heavy metals into the vadose zone of soils of a dismissed industrial site

Within the framework of the site assessment of a dismantled steel-making plant area contaminated by Electric Arc Furnace dust (EAF dust), the actual migration of Cr, Cu, As, Cd, Pb, Zn and Ni (contaminants) from an industrial waste layer towards the vadose zone of the underlying soil has been evaluated. The crystalline phases and contaminant abundance of samples of the industrial waste layer and the surrounding soils were analysed, while the release of contaminants was evaluated by leaching tests. Results indicate the migration of pollutants from the industrial waste layer into the subsurface soil, but the high leachability of soil hides its real degree of contamination, with the consequent possibility of underestimating the hazardous characteristics of the actual situation.