First order phase equilibrium for classical bodies

Summary In this note the Author gives a general and unified treatment of first order phase equilibria for classical bodies like those considered by Truesdell and Toupin in[3].The Author reaches a system of partial differential equations (generalized Clapeyron equations) the conditions of whose solution are shown always to be satisfied.In particular, the Author derives the equations governing the polarized phase equilibrium for a fluid.Besides the equations ruling the phase equilibrium for a two phase n-component fluid mixture are given and the equivalence with the statical Gibbs-Duhem relation is shown.

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Sommario In questa nota l'Autore presenta una trattazione generale ed unificata degli equilibri di fase del primo ordine per corpi classici come quelli definiti da Truesdell e Toupin in[3].L'Autore perviene ad un sistema di equazioni alle derivate parziali (equazioni di Clapeyron generalizzate) del quale si dimostra la integrabilità.In particolare, si deducono le equazioni che governano gli equilibri di fase polarizzati.Inoltre si ottengono le equazioni che regolano l'equilibrio di fase per una miscela fluida a n componenti; in questo caso si dimostra l'equivalenza delle equazioni con la relazione statica di Gibbs-Duhem.

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This work was supported by the Gruppo Nazionale per la Fisica Matematica of C.N.R.     

Hybrid gold-nanoparticle-cored conjugated thiophene dendrimers: synthesis, characterization, and energy-transfer studies

A series of hybrid Au-nanoparticle-dendrimer materials: nanoparticle-cored thiophene dendrimers (NCTDs) were synthesized, characterized, and investigated for their energy-transfer properties. These hybrid nanoparticles were obtained by the simultaneous and in situ reduction of gold(III) chloride and self-assembly of the thiol-containing thiophene dendritic ligands. The dendron ligands were radially attached to the gold nanoparticles and were analyzed by TEM, UV/Vis, (1)H NMR, and FTIR spectroscopies. The solution fluorescence of the attached thiophene dendrons are quenched progressively. Both alkyl-chain length and dendron size have significant influence on the energy-transfer efficiency, as well as on core sizes and size distribution of the Au nanoparticles. In spite of the phenomenon's dependence on nanoparticle size, the energy transfer generally follows the 1/d(2) distance dependence. Single NCTD nanoparticles were also adsorbed on highly ordered pyrolytic graphite (HOPG) and uniform aggregates were observed on mica flat substrates.     

A review of the determination of organic compounds in Bayer process liquors

Bayer process liquors present a difficult and complex matrix to the analytical chemist, and the history of the application of modern analytical techniques to this problem is a case study in innovation. All Bayer process liquors contain organic compounds, in amounts varying from traces to several grams per litre. The total organic carbon content of Bayer liquors may be less than 5 g/L up to as much as 40 g/L. The presence of these organic impurities is of concern to Bayer technologists because they can have significant impacts on the economics of the process and the quality of the product. This review examines the history and current state-of-the-art of the analysis of organics in Bayer process liquors, and provides guidance on the applicable techniques matched to a comprehensive list of the compounds most likely to be present.     

Non-oxo vanadium(IV) alkoxide chemistry: solid state structures, aggregation equilibria and thermochromic behaviour in solution

The reversible thermochromic behaviour of homoleptic [{V(OR)(4)}(n)] complexes in solution [R = Pr(i) (product I), Bu(s) (B(s)), Nep (N) and Cy (C)] is accounted for the existence of an aggregation equilibrium involving dimeric and monomeric species in which vanadium(iv) is respectively five- and four-coordinate. Bulky R groups such as Bu(t) and Pe(t) (tert-pentoxide) prevent aggregation and therefore give rise to exclusively mononuclear compounds (B(t) and P(t), respectively) that are not thermochromic. The complexes and their temperature-dependent interconversion were characterised by single crystal X-ray diffractometry, magnetic susceptibility measurements and electronic, FTIR and EPR spectroscopies in a wide temperature range. Equilibrium constants and enthalpy and entropy changes for the dimerization reactions have been determined and compared with literature data.     

A retelling of Newton’s work on Kepler’s Laws

This paper details an investigation into Kepler’s Laws. Newton’s technique for deducing an inverse-square law from Kepler’s Laws is given a modern presentation, with necessary background material included. Kepler’s Laws are then deduced from the assumption of an inverse-square law. This is done in a geometric style, inspired by Newton’s work. Finally, a problem involving planetary orbits is stated and solved using the earlier results of the paper.     

Templated synthesis of glycoluril hexamer and monofunctionalized cucurbit[6]uril derivatives

We report that the p-xylylenediammonium ion (11) acts as a template in the cucurbit[n]uril forming reaction that biases the reaction toward the production of methylene bridged glycoluril hexamer (6C) and bis-nor-seco-CB[10]. Hexamer 6C is readily available on the gram scale by a one step synthetic procedure that avoids chromatography. Hexamer 6C undergoes macrocylization with (substituted) phthalaldehydes 12, 14, 15, and 18-in 9 M H(2)SO(4) or concd HCl at room temperature to deliver monofunctionalized CB[6] derivatives 13, 16, 17, and 19-that are poised for further functionalization reactions. The kinetics of the macrocyclization reaction between hexamer and formaldehyde or phthalaldehyde depends on the presence and identity of ammonium ions as templates. p-Xylylenediammonium ion (11) which barely fits inside CB[6] sized cavities acts as a negative template which slows down transformation of 6C and paraformaldehyde into CB[6]. In contrast, 11 and hexanediammonium ion (20) act as a positive template that promotes the macrocyclization reaction between 6C and 12 to deliver (±)-21 as a key intermediate along the mechanistic pathway to CB[6] derivatives. Naphthalene-CB[6] derivative 19 which contains both fluorophore and ureidyl C═O metal-ion (e.g., Eu(3+)) binding sites forms the basis for a fluorescence turn-on assay for suitable ammonium ions (e.g., hexanediammonium ion and histamine).     

Diastereoselective total synthesis of (+)-13-stemarene by fourth generation methods: a formal total synthesis of (+)-18-deoxystemarin

The problem of constructing diastereoselectively the C/D ring system of stemarane diterpenes from a bicyclo[2.2.2]octane intermediate was solved resulting in very simple synthesis of (+)-13-stemarene 1. The obtaining of the latter represents also a formal synthesis of (+)-18-deoxystemarin 2. In the key step, the epimeric mixture 10, dissolved in toluene, was converted by the action of TsOH into (+)-stemar-13-en-15-one 28.     

Modular peripheral functionalization of thiophene dendrons and dendrimers

A series of thiophene dendrons and dendrimers with peripheral functional groups were designed and synthesized. Two methodologies using thiophene dendrons and dendrons as synthetic building blocks, namely, (1) periphery functionalization; (2) a combination of focal and periphery functionalization have been demonstrated.     

Measurements of the tip leakage vortex structures and turbulence in the meridional plane of an axial water-jet pump

Particle image velocimetry (PIV) measurements at varying resolutions focus on the flow structures in the tip region of a water-jet pump rotor, including the tip-clearance flow and the rollup process of a tip leakage vortex (TLV). Unobstructed views of these regions are facilitated by matching the optical refractive index of the transparent pump with that of the fluid. High-magnification data reveal the flow non-uniformities and associated turbulence within the tip gap. Instantaneous data and statistics of spatial distributions and strength of vortices in the rotor passage reveal that the leakage flow emerges as a wall jet with a shear layer containing a train of vortex filaments extending from the tip of the blade. These vortices are entrained into the TLV, but do not have time to merge. TLV breakdown in the aft part of the blade passage further fragments these structures, increasing their number and reducing their size. Analogy is made between the circumferential development of the TLV in the blade passage and that of the starting jet vortex ring rollup. Subject to several assumptions, these flows display similar trends, including conditions for TLV separation from the shear layer feeding vorticity into it.