Measurement of ultrasonic exposure with radiation force and thermal methods

It is the purpose of this paper to discuss briefly the factors that influence the interaction of the ultrasonic field and medium being irradiated, and to collect together the various techniques that have been suggested for measuring energetic parameters of the ultrasonic field. The calorimetric and radiation force methods are then discussed in more detail. The former is discussed as a technique whose capabilities have not been fully exploited while the latter demands attention both because of its simplicity and its controversial theoretical basis. Areas in which further work is needed are indicated in the summary and conclusion. It is hoped that the paper will be of practical use to workers in the field.     

Self-trapped nonlinear matter waves in periodic potentials

We demonstrate that the recent observation of nonlinear self-trapping of matter waves in one-dimensional optical lattices [Th. Anker, Phys. Rev. Lett. 94, 020403 (2005)10.1103/PhysRevLett.94.020403] can be associated with a novel type of broad nonlinear state existing in the gaps of the matter-wave band-gap spectrum. We find these self-trapped localized modes in one-, two-, and three-dimensional periodic potentials, and demonstrate that such novel gap states can be generated experimentally in any dimension.     

X-ray studies of the structure of thermotropic copolyesters

This paper describes x-ray analysis of the structure of a group of wholly aromatic thermotropic liquid crystalline copolyesters, focusing on two systems: condensation copolymers of 4-hydroxy-benzoic acid (HBA) and 2-hydroxy–6-naphthoic acid; and of HBA, 2,6-dihydroxy-naphthalene, and terephthalic acid. The fiber diagrams of these copolymers contain a series of aperiodic meridional maxima that shift in position with the monomer ratio. We have shown that these characteristics are predicted by a structure consisting of an array of chains of completely random monomer sequence. The positions of the maxima are predicted by a simple model in which the monomers are represented by points, separated from their neighbors by the appropriate monomer lengths. Use of atomic models for the monomers leads to prediction of both the positions and the intensities of the maxima. Calculations for nonrandom sequence distribution show that all but minimal blockiness can be ruled out. From the breath of the meridional maximum at d = 2.1 Å it is possible to estimate the correlation or persistence length for the stiff chain conformation in the solid state.     

Riffs on the infinite ping-pong ball conundrum

This article presents a novel re-conceptualisation to a well-known problem – The Ping-Pong Ball Conundrum. We introduce a variant of this super-task by considering it through the lens of ‘measuring infinity’ – a conceptualisation of infinity that extrapolates measuring properties of numbers, rather than cardinal properties. This approach is consistent with a nonstandard analysis approach to infinite numbers, and gives credence to the intuitive (but otherwise normatively incorrect) resolution. We explore the mathematical motivation and consequences of this variant, as well as offer further ‘riffs’ on the infinite ball problem for consideration.     

Synthesis, NMR characterisation and X-ray structures of mixed chalcogenido PNP ligands containing tellurium: crystal structures of SeiPr2PNP(H)iPr2 and [NaN(EPiPr2)2]infinity (E = Se, Te)

Reaction of HN(PiPr2)2 with one equivalent of selenium in hexane at room temperature yields the monoselenide as the P-H tautomer Se=PiPr2-N=P(H)iPr2 (2b). Deprotonation of 2b with n butyllithium in the presence of TMEDA at -78 degrees C followed by addition of tellurium produces the air-sensitive, mixed chalcogenido complex [(TMEDA)Li(SePiPr2)(TePiPr2)N] (8Li) in >97% purity after recrystallisation. Similarly, deprotonation of Te=PiPr2-N=P(H)iPr2 (2c), followed by addition of sulfur, gives the sulfur analogue [(TMEDA)Li(SPiPr2)(TePiPr2)N] (7Li) in >99% purity. The symmetrical complexes [(TMEDA)Li(SePiPr2)2N] (4Li) and [(TMEDA)Li(TePiPr2)2N] (5Li) are produced by similar methods. Compounds 2b, 4Li, 5Li, 7Li and 8Li were characterised in solution by multinuclear (1H, 31P, 77Se and 125Te) NMR spectroscopy and their solid-state structures were determined by X-ray crystallography. The X-ray crystal structures of the polymeric chains [NaN(EPiPr2)2]infinity (4Na, E = Se and 5Na, E = Te) are also reported.     

Coordination chemistry of a new P,Te-centred ligand: synthesis, NMR spectra and X-ray structures of M(TePPri2NPPri2)2 (M = Zn, Cd, Hg)

The lithiation of the monotelluride TePPri2NP(H)Pri2 (2) with BunLi at -78 degrees C results in the formation of the reagent [LiTePPri2NPPri2] (5), which was characterized by 31P NMR spectroscopy but not isolated due to disproportionation upon solvent removal. Salt metathesis reactions of 5, generated in situ, with group 12 metal chlorides produce the complexes M(TePPri2NPPri2)2 (6, M = Zn; 7, M = Cd; 8, M = Hg), which were characterized by single crystal X-ray diffraction, multinuclear NMR spectroscopy and thermal analyses. The X-ray structures reveal distorted tetrahedral structures with two P,Te-chelating anionic ligands [TePPri2NPPri2](-). The 31P NMR spectra exhibit second order behaviour that arises from an AA'XX' spin system; the spectra were simulated to determine the 31P, 31P spin-spin coupling constants.     

Experimental and theoretical investigations of the redox behavior of the heterodichalcogenido ligands [(EP(i)Pr2)(TeP(i)Pr2)N](-) (E = S, Se): cyclic cations and acyclic dichalcogenide dimers

The two-electron oxidation of the lithium salts of the heterodichalcogenidoimidodiphosphinate anions [(EP (i)Pr 2)(TeP (i)Pr 2)N] (-) ( 1a, E = S; 1b, E = Se) with iodine yields cyclic cations [(EP (i)Pr 2)(TeP (i)Pr 2)N] (+) as their iodide salts [(SP (i)Pr 2)(TeP (i)Pr 2)N]I ( 2a) and [(SeP (i)Pr 2)(TeP (i)Pr 2)N]I ( 2b). The five-membered rings in 2a and 2b both display an elongated E-Te bond as a consequence of an interaction between tellurium and the iodide anion. One-electron reduction of 2a and 2b with cobaltocene produces the neutral dimers (EP (i)Pr 2NP (i)Pr 2Te-) 2 ( 3a, E = S; 3b, E = Se), which are connected exclusively through a Te-Te bond. Two-electron reduction of 2a and 2b with 2 equiv of cobaltocene regenerates the corresponding dichalcogenidoimidodiphosphinate anions as ion-separated cobaltocenium salts Cp 2Co[(EP (i)Pr 2)(TeP (i)Pr 2)N] ( 4a, E = S; 4b, E = Se). The ditellurido analogue Cp 2Co[(TeP (i)Pr 2) 2N] ( 4c) has been prepared in the same manner for comparison. Density functional theory calculations reveal that the preferential interaction of the iodide anion with tellurium is determined by the polarization of the lowest unoccupied molecular orbital [sigma*(E-Te)] of the cations in 2a and 2b toward tellurium and that the formation of the dimers 3a and 3b with a central Te-Te linkage is energetically more favorable than the structural isomers with either E-Te or E-E bonds. Compounds 2a, 2b, 3a, 3b, 4a, 4b, and 4c have been characterized in solution by multinuclear NMR spectroscopy and in the solid state by X-ray crystallography.