One-, two- and three-photon spectroscopy of π-conjugated dendrimers: cooperative enhancement and coherent domains

We use wavelength tunable femtosecond pulses to measure intrinsic (simultaneous) two-photon absorption (2PA) and three-photon absorption (3PA) molecular cross section in two series of π-conjugated dendrimers built of identical 4,4′-bis(diphenylamino) stilbene (BDPAS) and 4,4′-bis(diphenylamino) distyrylbenzene (BDPADSB) repeat units. Record large 2PA cross sections, σ₂=10⁻⁴⁶ cm⁴ s are obtained for the largest second-generation BDPAS-based dendrimer, as well as zeroth-generation 4-arm BDPADSB-based dendrimer. In both series, maximum 2PA cross section increases nonlinearly with the number of π-electrons, whereas for higher generations this dependence turns to linear one. 3PA cross section also increases nonlinearly with the size of the system in the series of BDPAS-based molecules, amounting a record large value, σ₃=10⁻⁷⁹ cm⁶ s², for the largest, second-generation dendrimer. We interpret these results in terms of direct inter-branch conjugation, which facilitates cooperative enhancement of the nonlinear-optical response. We propose a simple model which allows us to determine the effective size of coherent domains (extent of conjugation), which, in turn, determines the optimum dendrimer size for most efficient nonlinear response.     

Symmetry and boundness of four-particle coulomb systems

The problem of boundness of a ⁺ b ⁺ c ⁻ d ⁻ four-particle Coulomb systems (quadrions) is studied versus the masses of the particles involved. Inequalities that make it possible to deduce that, if some reference quadrions form a bound state, the same is true for a large number of quadrions formed by particles having various masses were derived. A compendium of calculations for energies of reference systems that possess various symmetries [positronium molecules (e ⁺ e ⁺ e ⁻ e ⁻) and quadrions of the a ⁺ b ⁺ b ⁻ b ⁻, a ⁺ b ⁺ a ⁻ b ⁻, and a ⁺ a ⁺ b ⁻ c ⁻ types] is given, and groups of bound asymmetric quadrions corresponding to them are determined. An inequality for kinetic energies of particles that makes it possible to find out, by using asymmetric reference systems, whether specific quadrions are bound is obtained. It is shown that the boundness of many quadrions is ensured by the boundness of respective three-particle systems. The entire body of the present results permits proving that, of the total number of 406 quadrions containing electrons, muons, pions, kaons, protons, deuterons, and tritons and their antiparticles, 227 quadrions are bound.     

Geometric bounds of energy of many-particle quantum-mechanical systems

The energy bounds are constructed for the ground state of many-particle Coulomb and gravitational systems using the method of a model Schrödinger equation for a correlated exponential wave function. The method is based on geometric inequalities for average values of cosines of the angles of the triangles formed by triples of particles and does not require calculations of the wave functions. Two-sided energy bounds for an n-particle gravitational system are derived by using this method.     

The formation of oxide nanoparticles on the surface of natural clinoptilolite

Nanoparticles of NiO, ZnO and Cu₂O crystallize when the Ni-, Zn- and Cu-exchanged natural clinoptilolite, respectively, are dehydrated by heating in air at 550 °C. The dehydration of Mn-exchanged clinoptilolite does not lead to the crystallization of manganese oxide but affects the crystallinity of the host clinoptilolite lattice, which becomes amorphous. The NiO, ZnO and Cu₂O nanoparticles are found to be randomly dispersed in the clinoptilolite matrix. The particle size varies from 2 to 5 nm and exceeds the aperture of the clinoptilolite channel (approximately 0.4 nm), suggesting that the crystallization of the oxide phases takes place on the surfaces of clinoptilolite microcrystals.     

The behavior of a spherical bubble near a solid wall in a compressible liquid

Summary The behavior of a spherical bubble near a solid wall is analysed by considering the liquid compressibility. The equation of motion of the bubble with first order correction for the effects of liquid compressibility and solid wall is derived. The equation obtained here coincides with the known result in case of L or C . Further experimental study is made on the motion of bubbles produced by a spark discharge in water. The theoretical results are in good agreement with the experiments.

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Das Verhalten einer kugelförmigen Blase in einer kompressiblen Flüssigkeit in der Nähe einer festen Wand

Übersicht Bei Berücksichtigung der Flüssigkeitskompressibilität wird das Verhalten einer kugelförmigen Blase in der Nähe einer festen Wand analysiert. Die Gleichung der Bewegung der Blase wird mit der Korrektur erster Ordnung für den Einfluß der Flüssigkeitskompressibilität und der festen Wand angegeben. Aus der erhaltenen Gleichung wird für L oder C das bekannte Ergebnis hergeleitet. Darüber hinaus wird eine experimentelle Untersuchung der Blasenbewegung durchgeführt. Die Blase wird mit Hilfe von Funkendurchschlägen zwischen Elektroden in Wasser erzeugt. Die theoretischen Ergebnisse stimmen gut mit den Experimenten überein.