Reaction Between Bis(Dichlorophosphoryl)Imide and Hexamethyldisilazane

By reaction between bis(dichlorophosphoryl)imide and hexamethyldisilazane – with or without solvent – the authors obtain two phases. The solid phase is the ammonium salt of the bis(dichlorophosphoryl)imide which can be obtained, like many other metallic salts of this type, by the general reaction: . The salt is characterized by its I.R., and ³¹P, ¹H, and ¹⁴N N.M.R. spectra and by its hydrolysis reaction. The composition of the liquid phase changes according the experimental conditions. It seems that at first the main components are Cl₂(O)P? N?P(OSiMe₃)Cl₂ and Cl₂(Me₃SiO)P?N? PCl(OH)NSiMe₃. These compounds condense further to high polymers.     

Beitrag zur Chemie der Phosphor-Stickstoff-Verbindungen. Reaktion von Cl2(O)P?NH?P(O)Cl2 mit Tetrahydrofuran

Contribution to the Chemistry of Phosphorus-Nitrogen Compounds. Reaction of Cl₂(O)P? NH? P(O)Cl₂ with Tetrahydrofuran As well as many phosphorus compounds, the imidodiphosphoryl tetrachloride HN(P(O)Cl₂)₂ reacts with a large excess of tetrahydrofuran to give the polytetrahydrofuran. Otherwise, if we use smaller molecular ratios THF/HN(P(O)Cl₂)₂ (1/2 to 3) a polytetrahydrofuran with short chains and N(ω-hydroxypolytetramethylenoxy)imidodiphosphoryl tetrachloride R? N(P(O)Cl₂)₂; R = H(O(CH₂)₄)_n- are obtained at 22° or 30°C. The ¹H and ³¹P n.m.r. spectra show that oxonium ions are formed with progressive additions of THF to HN(POCl₂)₂/CCl₄ solution. Then two mechanisms have been considered by nucleophilic attack on carbon α of oxonium ion coming from: the free electronic dublett on oxygen of THF to give polytetrahydrofuran or (and) from the nitrogen of imido diphosphoryl tetra chloride anion ((Cl₂OP)₂N)^? to obtain N(ω-hydroxypolytetramethylenoxy)imidodiphosphoryl tetrachloride.     

Complexation properties of phosphonocarboxylic acids in aqueous solutions

The concentration formation constants of phosphonoacetic acid (PAA) complexes with the Ca²⁺ and Mg²⁺ ions were determined in aqueous solution at 25°C by potentiometric and coulometric titrations at different ionic strengths and were extrapolated to I=0 in order to obtain thermodynamic values of the formation constants. Complexes were formed by the completely deprotonated K _f (ML) and monoprotonated K _f (MHL) forms of the PAA anion. The respective values for the complexes are: log K _f (CaL)=4.68±0.03, log K _f (CaHL)=2.61±0.08; log K _f (MgL)=5.58±0.09, log K _f (MgHL)=3.0±0.3. The enthalpy and entropy of complexation for the deprotonated Ca²⁺ and Mg²⁺ PAA species, determined from the temperature dependence of the log K _f (ML), are: H⁰(Ca) =0.6±0.2 kcal-mol^–1, S⁰(Ca)=21.4±0.6 cal-mol^–1-K^–1, H⁰(Mg)=3.0±0.7 kcal-mol^–1, and S⁰(Mg)=35±2 cal-mol^–1-K^–1. It is seen there-fore, that the complexes are entropy stabilized but enthalpy destabilized. Formation constants were also determined for Ca²⁺ and Mg²⁺ complexes with PAA analogs, phosphonoformic and 3-phosphonopropionic acids and the complexation of PAA was also studied at a single ionic strength, with Na⁺, Ag⁺, Tl⁺, Sr²⁺, Ba²⁺, Cd²⁺, Cu²⁺, and Pb²⁺ ions.     

Flavonol based ruthenium acetylides as fluorescent chemosensors for lead ions

Flavonol based alkynyl ruthenium complexes devoted to the detection of metal traces in solution are described. The sensitivity of both absorption and emission properties of the 3-hydroxyflavone unit as a receptor for the metal cations, and of an alkynyl ruthenium moiety as an extended π-conjugated system, provides an efficient molecular sensor for rapid, sensitive and selective detection of lead(II) cations.     

Hydrodynamics of Brownian particles

When considering the hydrodynamics of Brownian particles, one is confronted to a difficult closure problem. One possibility to close the hierarchy of hydrodynamic equations is to consider a strong friction limit. This leads to the Smoluchowski equation that reduces to the ordinary diffusion equation in the absence of external forces. Unfortunately, this equation has infinite propagation speed leading to some difficulties. Another possibility is to make a Local Thermodynamic Equilibrium (L.T.E) assumption. This leads to the damped Euler equation with an isothermal equation of state. However, this approach is purely phenomenological. In this paper, we provide a preliminary discussion of the validity of the L.T.E assumption. To that purpose, we consider the case of free Brownian particles and harmonically bound Brownian particles for which exact analytical results can be obtained [S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943)]. For these systems, we find that the L.T.E. assumption is not unreasonable and that it can be improved by introducing a time dependent kinetic temperature T_kin(t)=γ(t)T instead of the bath temperature T. We also compare hydrodynamic equations and generalized diffusion equations with time dependent diffusion coefficients.     

Statistical mechanics of geophysical turbulence: application to jovian flows and Jupiter’s great red spot

We propose a parameterization of 2D geophysical turbulence in the form of a relaxation equation similar to a generalized Fokker–Planck equation [P.H. Chavanis, Phys. Rev. E 68 (2003) 036108]. This equation conserves circulation and energy and increases a generalized entropy functional determined by a prior vorticity distribution fixed by small-scale forcing [R. Ellis, K. Haven, B. Turkington, Nonlinearity 15 (2002) 239]. We discuss applications of this formalism to jovian atmosphere and Jupiter’s great red spot. We show that, in the limit of small Rossby radius where the interaction becomes short-range, our relaxation equation becomes similar to the Cahn–Hilliard equation describing phase ordering kinetics. This strengthens the analogy between the jet structure of the great red spot and a “domain wall”. Our relaxation equation can also serve as a numerical algorithm to construct arbitrary nonlinearly dynamically stable stationary solutions of the 2D Euler equation. These solutions can represent jets and vortices that emerge in 2D turbulent flows as a result of violent relaxation. Due to incomplete relaxation, the statistical prediction may fail and the system can settle on a stationary solution of the 2D Euler equation which is not the most mixed state. In that case, it can be useful to construct more general nonlinearly dynamically stable stationary solutions of the 2D Euler equation in an attempt to reproduce observed phenomena.     

A heuristic wave equation parameterizing BEC dark matter halos with a quantum core and an isothermal atmosphere

The European Physical Journal B - A two-cluster system with a bistable potential is constructed in one-dimensional channels. Using molecular dynamics and Monte Carlo methods, we study the...     

A stochastic Keller–Segel model of chemotaxis

We introduce stochastic models of chemotaxis generalizing the deterministic Keller–Segel model. These models include fluctuations which are important in systems with small particle numbers or close to a critical point. Following Dean’s approach, we derive the exact kinetic equation satisfied by the density distribution of cells. In the mean field limit where statistical correlations between cells are neglected, we recover the Keller–Segel model governing the smooth density field. We also consider hydrodynamic and kinetic models of chemotaxis that take into account the inertia of the particles and lead to a delay in the adjustment of the velocity of cells with the chemotactic gradient. We make the connection with the Cattaneo model of chemotaxis and the telegraph equation.