Integrating factors and conservation laws for nonconservative dynamical systems

A general approach to the construction of conservation laws for classical nonconservative dynamical systems is presented. The conservation laws are constructed by finding corresponding integrating factors for the equations of motion. Necessary conditions for existence of the conservation laws are studied in detail. A connection between an a priori known conservation law and the corresponding integrating factors is established. The theory is applied to two particular problems.     

First Stabilization of 14‐Electron Rhodium(I) Complexes by Hemichelation

Hemichelation is emerging as a new mode of coordination where non‐covalent interactions crucially contribute to the cohesion of electron‐unsaturated organometallic complexes. This study discloses an unprecedented demonstration of this concept to a Group 9 metal, that is, Rh^I. The syntheses of new 14‐electron Rh^I complexes were achieved by choosing the anti‐[(η⁶:η⁶‐fluorenyl){Cr(CO)₃}₂] anion as the ambiphilic hemichelating ligand, which was treated with [{Rh(nbd)Cl}₂] (nbd=norbornadiene) and [{Rh(CO)₂Cl}₂]. The new T‐shaped Rh^I hemichelates were characterized by analytical and structural methods. Investigations using the methods of the DFT and electron‐density topology analysis (NCI region analysis, QTAIM theory) confirmed the closed‐shell, non‐covalent and attractive characters of the interaction between the Rh^I center and the proximal Cr(CO)₃ moiety. This study shows that, by appropriate tuning of the electronic properties of the ambiphilic ligand, truly coordination‐unsaturated Rh^I complexes can be synthesized in a manageable form.     

Control of Ostwald ripening by using surfactants with high surface modulus

We describe results from systematic measurements of the rate of bubble Ostwald ripening in foams with air volume fraction of 90%. Several surfactant systems, with high and low surface modulus, were used to clarify the effect of the surfactant adsorption layer on the gas permeability across the foam films. In one series of experiments, glycerol was added to the foaming solutions to clarify how changes in the composition of the aqueous phase affect the rate of bubble coarsening. The experimental results are interpreted by a new theoretical model, which allowed us to determine the overall gas permeability of the foam films in the systems studied, and to decompose the film permeability into contributions coming from the surfactant adsorption layers and from the aqueous core of the films. For verification of the theoretical model, the gas permeability determined from the experiments with bulk foams are compared with values, determined in an independent set of measurements with the diminishing bubble method (single bubble attached at large air-water interface) and reasonably good agreement between the results obtained by the two methods is found. The analysis of the experimental data showed that the rate of bubble Ostwald ripening in the studied foams depends on (1) type of used surfactant-surfactants with high surface modulus lead to much slower rate of Ostwald ripening, which is explained by the reduced gas permeability of the adsorption layers in these systems; (2) presence of glycerol which reduces the gas solubility and diffusivity in the aqueous core of the foam film (without affecting the permeability of the adsorption layers), thus also leading to slower Ostwald ripening. Direct measurements showed that the foam films in the studied systems had very similar thicknesses, thus ruling out the possible explanation that the observed differences in the Ostwald ripening are due to different film thicknesses. Experiments with the Langmuir trough were used to demonstrate that the possible differences in the surface tensions of the shrinking and expanding bubbles in a given foam are too small to strongly affect the rate of Ostwald ripening in the specific systems studied here, despite the fact that some of the surfactant solutions have rather high surface modulus. The main reason for the latter observation is that the rate of surface deformation of the coarsening bubbles is extremely low, on the order of 10(-4) s(-1), so that the relaxation of the surface tension (though also slow for the high surface modulus systems) is still able to reduce the surface tension variations down to several mN/m. Thus, we conclude that the main reason for the reduced rate of bubble Ostwald ripening in the systems with high surface modulus is the low solubility and diffusivity of the gas molecules in the respective condensed adsorption layers (which have solid rather than fluid molecular packing).     

Beck's rod with shear,compressibility and pulsating force

In-plane motion of an elastic rod, subjected to a compressive follower force is analyzed. Equations of motions are derived for the case when deformations are not small. It is assumed that the compressive force has a periodic component, so that a parametric instability is possible. The stability bound is estimated analytically and determined numerically. In deriving the differential equations of motion a generalized constitutive equation taking into account compressibility of the rod axis and the influence of shear stresses is used.     

Cycloruthenated complexes as homogeneous catalysts for atom-transfer radical additions

Various cycloruthenated complexes were used as homogeneous catalysts for the atom-transfer radical addition of polyhalogenated compounds to several olefinic substrates. Yields obtained through conventional or microwave heating could reach high values (up to 98% with CBrCl₃ and 88% with CCl₄).     

The Affinity of Some Lewis Bases for Hexafluoroisopropanol as a Reference Lewis Acid: An ITC/DFT Study

To figure out the possible role of 1,1,1,3,3,3-hexafluoropropan-2-ol (HFIP) as well as to provide reference thermochemical data in solution, the formation of Lewis acid-base complexes between HFIP (Lewis acid) and a series of 8 different Lewis bases (3 sulfoxides, 3 Nsp² pyridine derivatives, 1 aromatic amine, 1 cyclic aliphatic ether) was examined by isothermal titration calorimetry (ITC) experiments and static density functional theory augmented with Dispersion (DFT−D) calculations. Measured ITC association enthalpy values (ΔH_a) lie between −9.3 and −14 kcal mol⁻¹. Computations including a PCM implicit solvation model produced similar exothermicity of association of all studied systems compared to the ITC data with ΔH_a values ranging from −8.5 to −12.7 kcal mol⁻¹. An additional set of calculations combining implicit and explicit solvation by chlorobenzene of the reactants, pointed out the relatively low interference of the solvent with the HFIP-base complexation: its main effect is to slightly enhance the Gibbs energy of the HFIP-Lewis base association. It is speculated that the interactions of bulk HFIP with Lewis bases therefore may significantly intervene in catalytic processes not only via the dynamic microstructuring of the medium but also more explicitly by affecting bonds’ polarization at the Lewis bases.     

The Stereospecific Ligand Exchange at a Pseudo‐Benzylic T‐4 Iridium Centre in Planar‐Chiral Cycloiridium (η6‐Arene)tricarbonylchromium Complexes

The stereospecificity of ligand exchange at the Ir^III centre of a cycloiridium arenetricarbonylchromium complex has been established experimentally by various analytical methods as well as by X‐ray diffraction structural analysis and computational investigations. Two new cases of phenyl and methyl iridium(III) complexes have been prepared by reaction of ( , )‐chlorido{2‐[(tricarbonyl)(η⁶‐phenylene‐κC^1′)chromium(0)]pyridine‐κN}(pentamethylcyclopentadienyl)iridium(III) with PhMgBr and MeMgBr. The determining influence of electrostatic repulsion has been established by means of density functional theory at the Becke–Perdew/TZP(ZORA) level by using, among other means, energy partitioning analysis. It is also shown that the Cr(CO)₃ fragment is likely to ease the ionic cleavage of the Ir? Cl bond in chlorido cycloiridium tricarbonylchromium complexes in a way similar to that already established for the solvolysis of benzyl halide complexes, that is, through a direct interaction of the Cr⁰ centre with the cationic Ir^III centre.     

Vibrationally averaged spin densities on muons and protons in the hydroxyl and ethyl radicals

The observations of the residual isotope effect for muonated radicals are discussed using calculations on the hydroxyl and ethyl radicals. The origins are partly due to the non-linear increase of the hyperfine coupling constants with increase in bond length, although a significant contribution comes from the anharmonicity of the molecular vibrations.     

Selective oxidation of poly(4-methylstyrene)

A range of new functional copolymers bearing aldehyde and carboxylic acid groups have been prepared by functionalization of poly(4-methylstyrene). These polymers have molecular weights from 2,000 to 16,500 and contain up to 20% aldehyde and up to 90% carboxylic acid groups. The reaction proceeds by selective catalytic oxidations with molecular oxygen or air in acetic acid/organic cosolvent mixtures in presence of cobalt acetate and sodium bromide or hydrogen bromide. The effects of reaction temperature, catalyst, co-solvents and oxygen partial pressure on the reaction are described. © 1995 John Wiley & Sons, Inc.