Far infrared study of molecular reorientation in some alkoxyazoxybenzenes

Abstract

Far infrared spectra in the frequency range 20 to 200 cm^?1 for the 4,4δ-di-n-alkoxyazoxybenzene homologous series are presented for the isotropic and nematic phases and for 0.1 M solution in benzene. In addition some partially deuteriated samples were studied. The spectra consist generally of two broad bands. By comparison of the spectra for different deuteriated compounds it is possible to interpret the higher frequency band as being connected with the intramolecular torsional vibration of the end groups. The band at lower frequencies we associate with the Poley absorption of librating molecules. The confined rotator model calculations performed for this band, for all compounds studied, give the rotational correlation time which is in good agreement with the correlation times as derived from quasi-elastic neutron scattering experiments.     

Power laws in zero-range processes on random networks

We study statistical properties of a zero-range process (ZRP) on random networks.We derive an analytic expression for the distribution of particles (also called node occupation distribution)in the steady state of the ZRP in the ensemble of uncorrelated random graphs. We analyze the dependence of this distribution on the node-degree distribution.In particular, we show that when the degree distribution is tuned properly, one can obtainscale-free fluctuations in the distribution of particles.Such fluctuations lead to a power law in the distribution of particles, just like in the ZRP with the hopping rate u(m) = 1+b/mon homogeneous graphs.     

Critical influence of the alkane length in surface and liquid-crystalline properties of perfluorodecyl-n-alkanes

Differential scanning calorimetry (DSC) measurements together with texture observation with polarizing microscope revealed the presence of a smectic phase for shorter homologues. Film forming properties of all the perfluorodecyl-n-alkanes synthesized here at the air-water interface were thoroughly investigated. Nearly all the compounds investigated were found to be capable of Langmuir monolayer formation when spread at the water-air interface, apart from semifluorinated alkanes (SFA) containing short hydrogenated moiety (n < 10), which partially dissolve in the water subphase. The investigated homologous series of SFA can be divided into four groups, regarding their liquid-crystalline and surface properties. The first group includes molecules with n = 6-10, which form smectic phases in the bulk and do not form stable monolayers at the free water surface. SFA containing 11 or 12 hydrogenated carbons belong to the second group, forming smectic phases at elevated temperatures, which transform into 3D ordering upon cooling. These molecules are found to form Langmuir monolayers of intermediate stability. The remaining groups contain perfluorodecylalkanes with n > 12, which differ in their calorimetric properties; however, both form very stable films on the water surface and do not exhibit liquid-crystalline properties.     

Effect of additives on properties of vanadia-based catalysts for oxidative dehydrogenation of propane: Experimental and quantum chemical studies

Effect of additives (A) comprising main group elements (K, P) and transition metals (Ni, Cr, Mo) to VO_x/SiO₂ catalysts on their catalytic behavior in oxidative dehydrogenation (ODH) of propane are studied. The experimental findings are compared with results of quantum chemical calculations performed for a model O=V---O---V^* cluster in which V^* atom is replaced by an atom of A. The selectivities to propene found in experiments change on introducing the additives, decreasing in the sequence VK(64)>VCr(38)>VMo=VNi(32)>VP(28)V0(27). Quantum chemical calculations indicate the change in the electron density on the atoms of the active O=V---O groups for the clusters with the additives’ atoms. The extent of the electron transfer from A towards the active group (the increase in the centre basicity) follows the sequence of the decreasing selectivity to propene, confirming the role of acid–base properties in controlling the selectivity in ODH of propane. Results of calculations show also an exceptional behavior of the potassium (the most effective additive for the increase in the selectivity in experiments); in contrast to all other additivies, K transfers electrons towards both V and O atoms in the active group, and does not form a definite O---K bond, but is rather “adsorbed” on the cluster.     

Phosphorus-31 spin-lattice NMR relaxation in bone apatite and its mineral standards

Phosphorus-31 spin-lattice relaxation, both in the laboratory (B(0)=4.7 T) and rotating frame (B(1)=2.2 mT), was studied in the following samples: mineral of whole human bone (samples B1-B6), apatite prepared from bone (BHA), natural brushite (BRU), synthetic hydroxyapatite hydrated (HAh) and calcined (HAc), and synthetic carbonatoapatite of type B (CHA-B) with 9 wt% of CO(3)(2-). The T(1)(P) relaxation time was determined directly using the saturation recovery technique, while the T(1 rho)(P) relaxation time was measured via (1)H-->(31)P CP by incrementing the (31)P spin-lock. In order to avoid an effect of magic-angle spinning (MAS) on CP and relaxation, the experiments were carried out on static samples. The (31)P spin-lattice relaxation was discussed for trabecular and cortical bone tissue from adult subjects in comparison to the synthetic mineral standards. None of the reference materials has matched accurately the relaxation behaviour of the bone mineral. The most striking differences between the examined substances were observed for T(1)(P), which for human bone was sample dependent and appeared in the range 55-100 s, while for HAh, HAc, and CHA-B was 7.2, 10.0, and 25.8 s, respectively. Possible reasons of so large relaxation diversity were discussed. It has been suggested that T(1)(P) of apatites is to some extent dependent on the concentration of the structural hydroxyl groups, and this in turn is controlled by the material crystallinity. It was also found that T(1)(P) decreased on hydration by ca. 30%. For T(1rho)(P), both its magnitude and dependence on the CP contact time gave useful structural information. The dehydrated samples (HAc and BHA) had long T(1 rho)(P) over 250 ms. Those, which contained water, either structural (BRU) or adsorbed on the crystal surface (HAh, CHA-B, and B1-B6), had shorter T(1 rho)(P) below 120 ms. It was concluded that the effect of water on T(1 rho)(P) is much more pronounced than on T(1)(P). The interpretation has involved P-OH groups and adsorbed water, which cover the apatite crystal surface.     

Balls-in-boxes condensation on networks

We discuss two different regimes of condensate formation in zero-range processes on networks: on a q-regular network, where the condensate is formed as a result of a spontaneous symmetry breaking, and on an irregular network, where the symmetry of the partition function is explicitly broken. In the latter case we consider a minimal irregularity of the q-regular network introduced by a single Q node with degree Q>q. The statics and dynamics of the condensation depend on the parameter alpha=ln Q/q, which controls the exponential falloff of the distribution of particles on regular nodes and the typical time scale for melting of the condensate on the Q node, which increases exponentially with the system size N. This behavior is different than that on a q-regular network, where alpha=0 and where the condensation results from the spontaneous symmetry breaking of the partition function, which is invariant under a permutation of particle occupation numbers on the q nodes of the network. In this case the typical time scale for condensate melting is known to increase typically as a power of the system size.     

A non-smooth three critical points theorem with applications in differential inclusions

We extend a recent result of Ricceri concerning the existence of three critical points of certain non-smooth functionals. Two applications are given, both in the theory of differential inclusions; the first one concerns a non-homogeneous Neumann boundary value problem, the second one treats a quasilinear elliptic inclusion problem in the whole \mathbb R^N{\mathbb R^N}.