On a dynamical system related to fluid mechanics

We introduce a dynamical system strictly related to fluid mechanics and similar to the classical N point vortex system. In the first part we analyze the qualitative behavior of the time evolution and in particular we show the properties of collapse and chaoticity. In the second part of the paper we investigate the relation of the dynamical system with a system of N concentrated large enough smoke rings in an incompressible and inviscid fluid, with axial symmetry and without swirl. We prove the rigorous connection between the two models at time zero for any N. The extension of the same result to any time is obtained only for a smoke ring alone, while for the general case it is just a matter of conjecture. Received June 1998; Revised November 1998     

A global condition for periodic Duffing-like equations

We study Duffing-like equations of the type ,with periodic. We prove that if the stable and unstable manifolds to the origin do not coincide, then the system exhibits positive topological entropy.

     

NHCs as Neutral Donors towards Polyphosphorus Complexes

The first adducts of NHCs (=N-heterocyclic carbenes) with aromatic polyphosphorus complexes are reported. The reactions of [Cp*Fe(η⁵-P₅)] ( 1 ) (Cp*=pentamethyl-cyclopentadienyl) with IMe (=1,3,4,5-tetramethylimidazolin-2-ylidene), IMes (=1,3-bis(2,4,6-trimethylphenyl)-imidazolin-2-ylidene) and IDipp (=1,3-bis(2,6-diisopropylphenyl)-imidazolin-2-ylidene) led to the corresponding neutral adducts which can be isolated in the solid state. However, in solution, they quickly undergo a dissociative equilibrium between the adduct and 1 including the corresponding NHC. The equilibrium is influenced by the bulkiness of the NHC. [Cp′′Ta(CO)₂(η⁴-P₄)] (Cp′′=1,3-di-tert-butylcyclopentadienyl) reacts with IMe under P atom abstraction to give an unprecedented cyclo-P₃-containing anionic tantalum complex. DFT calculations shed light onto the energetics of the reaction pathways.     

Photoinduced conformational switch of enantiopure azobenzenes controlled by a sulfoxide

Two series of enantiopure azobenzenes with a p-tolylsulfoxide at the ortho or meta position with respect to the azo group, have been regioselectively synthesized. Both can act as enantiopure molecular switches showing different structural features owing to the presence of the stereogenic sulfur. The photoisomerization process, studied by UV-vis, circular dichroism (CD), NMR, and chiral HPLC evidenced a double role of the sulfoxide. A transfer of chirality from the sulfoxide to the azo system was observed by CD in both cis and trans-isomers of the meta sulfinyl derivatives 3, whereas this perturbation was evident for the ortho sulfinyl series 7 only in the cis isomer. The NMR study evidenced that the s-cis rigid conformation of the bisaromatic sulfoxide was fixing a different orientation of the overall system in each series both in the trans and cis isomers, by forcing a final U-shaped structure in cis-3 and an S-shaped structure in cis-7. Very different values of specific optical rotations were measured in both trans and cis isomers, also reflecting the existence of distinct chiral entities in the photostationary states. The easy and reversible changes occurring between different conformational states could find applications in the photocontrol of several molecular switches.     

Aluminosilicate surfaces as promoters for peptide bond formation: an assessment of Bernal's hypothesis by ab initio methods

The role in prebiotic chemistry that Br?nsted and Lewis sites, both present at the surface of common aluminosilicates, may have played in favoring the peptide bond formation has been addressed by ab initio methods within a cluster approach. B3LYP/6-31+G(d,p) free energy potential energy surfaces have been fully characterized for the model reaction glycine + NH3 --> 2-NH2 acetamide (mimicking the true 2 Gly --> GlyGly one) occurring on (i) a Lewis site, (ii) a Br?nsted site, and (iii) a combined action of Lewis/Br?nsted sites. Compared to the gas-phase (gp) activation free energy of 50 kcal/mol, the Lewis site alone reduces the gp barrier to 41 kcal/mol, whereas the activation by the Br?nsted site dramatically reduces the barrier to about 18 kcal/mol. Nevertheless, formation of the prereactant complex in this latter case will rarely occur, since water will easily displace the glycine molecule interacting with the Br?nsted site. However, if a realistic feldspar surface with neighboring Br?nsted and Lewis sites is considered, the proper prereactant complex is highly stabilized by a simultaneous interaction with the Lewis and the Br?nsted sites, in such a way that the Lewis site strongly attaches the glycine molecule to the surface whereas the Br?nsted site efficiently catalyzes the condensation reaction, showing that the interplay between Lewis/Br?nsted sites is an important issue. The free energy barrier computed for the realistic feldspar surface model is 26 kcal/mol. The role of dispersive interactions on the free energy barrier and the stabilization of the final product, not accounted for by the B3LYP functional, have been estimated and shown to be substantial. Speculations about further elongation of the formed dipeptide have been put forward on the basis of the relatively strong interaction energy of the formed GlyGly dipeptide with the aluminosilicate surface.     

Electrochemical and EPR studies of the corannulene ruthenium(II) sandwich complex [(eta6-C6Me6)Ru(eta6-C20H10)](SbF6)(2)

The dication [(eta6-C6Me6)Ru(eta6-C20H10)]2+ in propylene carbonate solution exhibits a sequence of reduction processes that is either metal-centered [Ru(II)/Ru(I)/Ru(0)] or ligand-centered. The marginally stable Ru(I) monocation [(eta6-C6Me6)Ru(eta6-C20H10)]+ has been characterized by EPR spectroscopy. The electrochemistry of C20H10 and EPR features of its stable monoanion [C20H10]- have also been revisited.     

Recovering the Crooks equation for dynamical systems in the isothermal-isobaric ensemble: a strategy based on the equations of motion

The Crooks equation [Eq. (10) in J. Stat. Phys. 90, 1481 (1998)] relates the work done on a system during a nonequilibrium transformation to the free energy difference between the final and the initial state of the transformation. Recently, the authors have derived the Crooks equation for systems in the canonical ensemble thermostatted by the Nose-Hoover or Nose-Hoover chain method [P. Procacci et al., J. Chem. Phys. 125, 164101 (2006)]. That proof is essentially based on the fluctuation theorem by Evans and Searles [Adv. Phys. 51, 1529 (2002)] and on the equations of motion. Following an analogous approach, the authors derive here the Crooks equation in the context of molecular dynamics simulations of systems in the isothermal-isobaric (NPT) ensemble, whose dynamics is regulated by the Martyna-Tobias-Klein algorithm [J. Chem. Phys. 101, 4177 (1994)]. Their present derivation of the Crooks equation correlates to the demonstration of the Jarzynski identity for NPT systems recently proposed by Cuendet [J. Chem. Phys. 125, 144109 (2006)].     

Viscoelasticity and Stokes-Einstein relation in repulsive and attractive colloidal glasses

We report a numerical investigation of the viscoelastic behavior in models for steric repulsive and short-ranged attractive colloidal suspensions, along different paths in the attraction strength vs packing fraction plane. More specifically, we study the behavior of the viscosity (and its frequency dependence) on approaching the repulsive glass, the attractive glass, and in the reentrant region where viscosity shows a nonmonotonic behavior on increasing attraction strength. On approaching the glass lines, the increase of the viscosity is consistent with a power-law divergence with the same exponent and critical packing fraction previously obtained for the divergence of the density fluctuations. Based on mode-coupling calculations, we associate the increase of the viscosity with specific contributions from different length scales. We also show that the results are independent of the microscopic dynamics by comparing Newtonian and Brownian simulations for the same model. Finally, we evaluate the Stokes-Einstein relation approaching both glass transitions, finding a clear breakdown which is particularly strong for the case of the attractive glass.     

(1,2,3,4,7-Pentamethylindenyl)rhodium complexes with arene ligands

The reaction of (η⁵-C₉H₂Me₅)Rh(1,5-C₈H₁₂) (1) with I₂ gives the iodide complex [(η⁵-C₉H₂Me₅)RhI₂]₂ (2). The solvate complex [(η⁵- C₉H₂Me₅)Rh(MeNO₂)₃]²⁺ (generated in situ by treatment of 2 with Ag⁺ in nitromethane) reacts with benzene and its derivatives giving the dicationic arene complexes [(η⁵-₉H₂Me₅)Rh(arene)]²⁺ [arene = C₆H₆ (3a), C₆Me₆ (3b), C₆H₅OMe (3c)]. Similar reaction with the borole sandwich compound CpRh(η⁵-C₄H₄BPh) results in the arene-type complex [CpRh(μ-η⁵:η⁶-C₄H₄BPh)Rh(η⁵-C₉H₂Me₅)]²⁺ (4). Treatment of 2 with CpTl in acetonitrile affords cation [(η⁵-C₉H₂Me₅)RhCp]⁺ (5). The structure of [3c](BF₄)₂ was determined by X-ray diffraction. The electrochemical behaviour of complexes prepared was studied. The rhodium-benzene bonding in series of the related complexes [(ring)Rh(C₆H₆)]²⁺ (ring = Cp, Cp^∗, C₉H₇, C₉H₂Me₅) was analyzed using energy and charge decomposition schemes.     

Chemical semi-IPN hydrogels for the removal of adhesives from canvas paintings

Semi-interpenetrating (IPN) poly (2-hydroxyethyl methacrylate)/polyvinylpyrrolidone hydrogels were synthesized and used for the removal of adhesives from the back of canvas paintings. The high water retention capability and the specific mechanical properties of these gels allow the safe cleaning of water-sensitive artifacts using water-based detergent systems. The cleaning action is limited to the contact area and layer-by-layer removal is achieved while avoiding water spreading and absorption within water-sensitive substrates, which could lead, for example, to paint detachment. The use of these chemical gels also avoids leaving residues over the treated surface because the gel network is formed by covalent bonds that provide high mechanical strength. In this contribution, the physicochemical characterization of semi-IPN chemical hydrogels is reported. The successful application of an o/w microemulsion confined in the hydrogel for the removal of adhesives from linen canvas is also illustrated.