Driving Organic Nanocrystals Dissolution Through Electrochemistry

We have recently discussed how organic nanocrystal dissolution appears in different morphologies and the role of the solution pH in the crystal detriment process. We also highlighted the role of the local molecular chemistry in porphyrin nanocrystals having comparable structures: in water-based acid solutions, protonation of free-base porphyrin molecules is the driving force for crystal dissolution, whereas metal (Zn^II) porphyrin nanocrystals remain unperturbed. However, all porphyrin types, having an electron rich π-structure, can be electrochemically oxidized. In this scenario, a key question is: does electrochemistry represent a viable strategy to drive the dissolution of both free-base and metal porphyrin nanocrystals? In this work, by exploiting electrochemical atomic force microscopy (EC-AFM), we monitor in situ and in real time the dissolution of both free-base and metal porphyrin nanocrystals, as soon as molecules reach the oxidation potential, showing different regimes according to the applied EC potential.     

Schröndiger Type and Relaxed Dirichlet Problems for the Subelliptic p-Laplacian

We study at first the solutions of a Schrödinger type problem relative to the subelliptic p-Laplacian: we prove, for potentials that are in the Kato space, an Harnack inequality on enough small intrinsic balls; the continuity of the solutions to the homogeneous Dirichlet problem follows from some estimates in the proof of the Harnack inequality. In the second part of the paper we study a relaxed Dirichlet problem for the subelliptic p-Laplacian and we prove a Wiener type criterion for the regularity of a point (with respect to our problem).     

Metal-induced assembling/disassembling of fluorescent naphthalenediimide derivatives signalled by excimer emission

The new quadridentate bischelating ligands 2 and 3 display in solution the typical absorption and emission properties expected for naphthalenediimide derivatives. Spectrophotometric studies show that systems 2 and 3 interact with Zn(II), Cd(II) and Cu(I) in CHCl3 or MeCN according to an apparent 1:1 stoichiometry. Molecular modelling, ESI-MS and 1H NMR experiments indicate that the complex species formed in the presence of stoichiometric amounts of metal ion are nonhelical [2 + 2] adducts. The metal-induced self-assembling process is signalled by an intense excimer-type emission caused by the intramolecular interaction of two naphthalenediimide subunits that face each other in the [2 + 2] adduct, as shown by molecular modelling studies. In the presence of excess metal ion, a disassembling process takes place, leading to a dinuclear complex with a 2:1 metal/ligand stoichiometry, in which the intramolecular excimer is no longer allowed to form because the interaction between the naphthalenediimide subunits has been lost. Thus, the overall metal-induced assembling/disassembling process is signalled by the appearance and disappearance of the excimer band in the emission spectrum.     

Nonlinear susceptibility measurements in a supercooled liquid close to Tg: Growth of the correlation length and possible critical behavior

The existence of a growing correlation length associated with the strong increase of relaxation times of glass-formers close to the glass transition is still a major open question in glass physics. It has been recently proposed that the ac nonlinear susceptibility of a supercooled liquid close to the glass transition temperature T_g would be a probe of dynamical correlations. As for spin glasses, where the nonlinear susceptibility diverges at the transition, this quantity is tailored to reveal the possible “hidden” critical behavior of the glass transition. We have developed a high sensitivity experimental device to measure the nonlinear dielectric susceptibility of an insulating material at finite frequency. It measures the third harmonics of the current flowing out of a capacitor with the supercooled liquid as the dielectric layer. It is based on a bridge with two capacitors, and reaches a sensitivity better than 10^− 7 (ratio of third to first harmonics). Our first results on supercooled glycerol are presented. They clearly reveal the growing of the correlations close to the glass transition.     

Stability results for Mountain Pass and Linking type solutions of semilinear problems involving Dirichlet forms

Some stability results for Mountain Pass and Linking type solutions of semilinear problems involving a very general class of Dirichlet forms are stated. The non linear terms are supposed to have a suitable superlinear growth and the family of Dirichlet forms is required to be dominated from below and from above by a fixed diffusion type form. Some concrete examples are also given.     

Asymptotic behavior for an almost periodic,strongly dissipative wave equation

This paper deals with asymptotic behavior for (weak) solutions of the equation $\text{u}{}_{\mathrm{tt}}\text{? Δu + β(u}{}_{\mathrm{t}}\text{) ? ?(t, x)}$, on $\text{R}$⁺ × Ω; u(t, x) = 0, on $\text{R}$⁺ × ?Ω. If $\text{?∈L∞(R}{}^{\mathrm{+}}\text{,L}{}^2\text{(Ω))}$ and β is coercive, we prove that the solutions are bounded in the energy space, under weaker assumptions than those used by G. Prouse in a previous work. If in addition $\text{?}{}_{\mathrm{t}}\text{∈S}{}^2\text{(R}{}^{\mathrm{+}}\text{,L}{}^2\text{(Ω))}$ and ? is srongly almost-periodic, we prove for strongly monotone β that all solutions are asymptotically almost-periodic in the energy space. The assumptions made on β are much less restrictive than those made by G. Prouse: mainly, we allow β to be multivalued, and in the one-dimensional case β need not be defined everywhere.