Asymptotic expansions of integrals of two Bessel functions via the generalized hypergeometric and Meijer functions

Asymptotic expansions of certain finite and infinite integrals involving products of two Bessel functions of the first kind are obtained by using the generalized hypergeometric and Meijer functions. The Bessel functions involved are of arbitrary (generally different) orders, but of the same argument containing a parameter which tends to infinity. These types of integrals arise in various contexts, including wave scattering and crystallography, and are of general mathematical interest being related to the Riemann—Liouville and Hankel integrals. The results complete the asymptotic expansions derived previously by two different methods — a straightforward approach and the Mellin-transform technique. These asymptotic expansions supply practical algorithms for computing the integrals. The leading terms explicitly provide valuable analytical insight into the high-frequency behavior of the solutions to the wave-scattering problems.     

Nonlinear dynamics of charged particles interacting with combined ac-dc electromagnetic fields

A nonlinear Lorenz model describing interactions between charged particles and combined ac-dc electromagnetic fields is studied for various combinations of frequencies, field strengths and relative angle (θ) between the ac and dc magnetic fields. Strong directional effects on the magnitude and location of resonant particle motion are observed when θ is varied and the regular resonance windows in the aligned field (θ = 0) and linear version of the model studied previously by Durney etaal., break up to form irregular and less well pronounced regions of large and small particle displacements when nonlinearities are taken into account. The length of time takne to achieve resonant behaviour also becomes larger and more variable when nonlinearities are present. The possible relevance of these effects to interactions between electromagnetic fields and biological media is briefly discussed.     

The effect of solvent upon molecularly thin rotaxane film formation

We have investigated variations in molecularly thin rotaxane films deposited by solvent evaporation, using atomic force microscopy (AFM). Small changes in rotaxane structure result in significant differences in film morphology. The addition of exo-pyridyl moietes to the rotaxane macrocycle results in uniform domains having orientations corresponding to the underlying substrate lattice, while a larger, less symmetric molecule results in a greater lattice mismatch and smaller domain sizes. We have measured differences in film heights both as a function of the solvent of deposition and as a function of surface coverage of rotaxanes. Based on these observations we describe how the use of solvents with higher hydrogen-bond basicity results in films which are more likely to favour sub-molecular motion.     

DSC study of charge-transfer complexes of polynuclear aromatic hydrocarbons with nitroaromatic acceptors

Charge-transfer, crystalline complexes of 1,3,5-trinitrobenzene (TNB), 2,4,7- trinitro-9-fluorenone (TNF). and 2,4,5,7-tetranitro-9-fluorenone (TENF) with eleven polynuclear aromatic hydrocarbons were compared for thermal stability, ΔH and ΔS of melting. Factors possibly influencing the above parameters are discussed.Melting does not induce separation of the components; these complexes can be repeatedly crystallized and melted without variation of the ΔH of melting, thereby indicating high thermal stability.With a few exceptions, melting temperatures of the complexes increase in the order TNB<TNF<TENF: so do ΔH and ΔS of melting. A number of crystal transitions were observed.     

Mössbauer effect of iodine at pressures to 30 GPa

We report the first high pressure¹²⁹I Mössbauer measurements with elemental iodine at pressures to 30 GPa. A 20 mg/cm^{2 129}I₂ absorber was mounted in a diamond anvil cell with an effective diameter of 0.21 mm. The source used was Mg₃ ^129mTeO₆. Experiments were performed mainly at 4 K and the pressure was monitored by the ruby fluorescence method. With increasing pressure we observe a gradual decrease in ¦e²qQ¦ and an increase in IS and values of the low pressure, molecular phase; at 16 GPa a new phase (HP1) is detected characterized by a change in sign of e²qQ and a smaller value of ¦e²qQ¦, and a substantial increase in . At 24 GPa a new phase (HP2) is formed that is characterized by a smaller value of . In general the population of the molecular phase decreases from 1.0 near 15 GPa to a value of 0.4 at 30 GPa. The fraction of the high pressure phase (HP1 + HP2) increases at the expense of the molecular phase and that of the HP2 at the expense of the HP1 phase. These observations are discussed in relation to the onset of a metallic phase near 16 GPa and recent x-ray diffraction studies.Work performed under the auspices of the U.S. Department of Energy.     

Interaction of aryldiazonium salts with some schiff-base complexes of cobalt and ruthenium

The interaction of aryldiazonium ions with some Schiff-base complexes of cobalt and ruthenium have been studied. With cobalt, one-electron oxidation of [Co(II)Salen] occurred; with [Co(I)Salen] the corresponding Co(III)-aryl complexes were isolated. In the case of ruthenium oxidation also occurs, [Ru(Salen)(CO)py] gave the corresponding monocation. The results, especially for ruthenium, are in contrast to the stabilisation of both nitrosyl and aryldiazonium adducts in analogous porphyrin complexes.     

Rh(II) and Rh(I) two-legged piano-stool complexes: structure,reactivity, and electronic properties

The ligand 1,4-bis[4-(diphenylphosphino)butyl]-2,3,5,6-tetramethylbenzene, 3, was used to synthesize a mononuclear Rh(II) complex [(eta(1):eta(6):eta(1)-1,4-bis[4-(diphenylphosphino)butyl]-2,3,5,6-tetramethylbenzene)Rh][PF(6)](2), 6+, in a two-legged piano-stool geometry. The structural and electronic properties of this novel complex including a single-crystal EPR analysis are reported. The complex can be cleanly interconverted with its Rh(I) form, allowing for a comparison of the structural properties and reactivity of both oxidation states. The Rh(I) form 6 reacts with CO, tert-butyl isocyanide, and acetonitrile to form a series of 15-membered mononuclear cyclophanes [(eta(1):eta(1)-1,4-bis[4-(diphenylphosphino)butyl]-2,3,5,6-tetramethylbenzene)Rh(CO)(3)][PF(6)] (8), [(eta(1):eta(1)-1,4-bis[4-(diphenylphosphino)butyl]-2,3,5,6-tetramethylbenzene)Rh(CNC(CH(3))(3))(2)][PF(6)] (10), and [(eta(1):eta(1)-1,4-bis[4-(diphenylphosphino)butyl]-2,3,5,6-tetramethylbenzene)Rh(CO)(CH(3)CN)][PF(6)] (11). The Rh(II) complex 6+ reacts with the same small molecules, but over shorter periods of time, to form the same Rh(I) products. In addition, a model two-legged piano-stool complex [(eta(1):eta(6):eta(1)-1,4-bis[3-(diphenylphosphino)propoxy]-2,3,5,6-tetramethylbenzene)Rh][B(C(6)F(5))(4)], 5, has been synthesized and characterized for comparison purposes. The solid-state structures of complexes 5, 6, 6+, and 11 are reported. Structure data for 5: triclinic; P(-)1; a = 10.1587(7) A; b = 11.5228(8) A; c = 17.2381(12) A; alpha = 96.4379(13) degrees; beta = 91.1870(12) degrees; gamma = 106.1470(13) degrees; Z = 2. 6: triclinic; P(-)1; a = 11.1934(5) A; b = 12.4807(6) A; c = 16.1771(7) A; alpha = 81.935(7) degrees; beta = 89.943(1) degrees; gamma = 78.292(1) degrees; Z = 2. 6+: monoclinic; P2(1)/n; a = 11.9371(18) A; b = 32.401(5) A; c = 12.782(2) A; beta = 102.890(3) degrees; Z = 4. 11: triclinic; P(-)1; a = 13.5476(7) A; b = 13.8306(7) A; c = 14.9948(8) A; alpha = 74.551(1) degrees; beta = 73.895(1) degrees; gamma = 66.046(1) degrees; Z = 2.