Electronic relaxation of paramagnetic metal ions and NMR relaxivity in solution: critical analysis of various approaches and application to a Gd(III)-based contrast agent

The time correlation functions (TCFs) G(alphaalpha(t)[triple bond](Salpha(t)Salpha(0)) (alpha = x,y,z) of the electronic spin components of a complexed paramagnetic metal ion give information about the time fluctuations of its zero-field splitting (ZFS) Hamiltonian due to the random dynamics of the coordination polyhedron. These TCFs reflect the electronic spin relaxation which plays an essential role in the inner- and outer-sphere paramagnetic relaxation enhancements of the various nuclear spins in solution. When a static ZFS Hamiltonian is allowed by symmetry, its modulation by the random rotational motion of the complex has a great influence on the TCFs. We discuss several attempts to describe this mechanism and show that subtle mathematical pitfalls should be avoided in order to obtain a theoretical framework, within which reliable adjustable parameters can be fitted through the interpretation of nuclear-magnetic relaxation dispersion experimental results. We underline the advantage of the numerical simulation of the TCFs, which avoids the above difficulties and allows one to include the effect of the transient ZFS for all the relative magnitudes of the various terms in the electron-spin Hamiltonian and arbitrary correlation times. This method is applied for various values of the magnetic field taken to be along the z direction. At low field, contrary to previous theoretical expectations, if the transient ZFS has negligible influence, the longitudinal TCF GII(t) [triple bond] G(zz)(t) has a monoexponential decay with an electronic relaxation time T1e different from 1/(2D(r)), D(r) being the rotational diffusion coefficient of the complex. At intermediate and high field, the simulation results show that GII (t) still has a monoexponential decay with a characteristic time T1e, which is surprisingly well approximated by a simple analytical expression derived from the Redfield perturbation approximation of the time-independent Zeeman Hamiltonian, even in the case of a strong ZFS where this approximation is expected to fail. These results are illustrated for spins S = 1, 3/2, and 5/2 in axial and rhombic symmetries. Finally, the simulation method is applied to the reinterpretation of the water-proton relaxivity profile due to P760-Gd(III), an efficient blood pool contrast agent for magnetic-resonance imaging.     

Multiple solutions of boundary value problems: an elementary approach via the shooting method

In this paper we derive the existence of multiple solutions for boundary value problems of the type $$u\prime \prime + f\left( {t,u} \right) = 0,u\left( 0 \right) = 0,u\left( \pi \right) = 0$$ , in terms of the behaviour of the ratiof(t,u)/u nearu=0 and near infinity. The nonlinear termf is assumed to be locally Lipschitz inu, so that the shooting method can be used. (AMS Subject Classification: 34B15).     

Volumes of activation for dissociation of pentacyanoferrates(II) through pressure and salt effects on reactivity

Summary Dependences of rate constants on pressure (up to 1 kbar) and on added salt concentration (up to 6.0 mol dm^–3 LiNO₃, NaNO₃, NaCl, Na₂SO₄ or KNO₃) have been established for dissociative substitution of pentacyanoferrates(II), [Fe(CN)₅L]^3– with L = 4-cyanopyridine, 4,4-bipyridyl, 4-phenylpyridine and 4-t-butylpyridine. Activation volumes derived directly from pressure effects, and indirectly from salt effects via surface tension dependences and derived surfaces of activation, are reported, compared and discussed.     

Preparation of USY zeolite VOx supported catalysts from V(AcAc)3 and NH4VO3. Catalytic properties for the dehydrogenation of n-butane in oxygen-free atmosphere

The preparation of different samples of vanadia supported on ultrastable zeolite (VO(x)/USY) is discussed. The samples were prepared in order to obtain highly dispersed V-species, avoiding the formation of crystalline vanadia and the destruction of the zeolite framework. Two methods were employed for preparing VO(x)/USY samples: an organic route using V(AcAc)3 and an inorganic route using NH4VO3. The characterization of the samples was performed with XRD, TPR, NH3-TPD, and N2 isotherms. From these results it is concluded that when VO(x) is supported on the surface of USY from acidic aqueous solution of ammonium metavanadate, the destruction of the zeolite framework is accomplished. For higher pH values in the impregnating solution, undesired V2O5 is formed on the USY surface. On the other hand, VO(x)/USY prepared from the organic precursor shows no destruction of the USY structure. In addition, highly dispersed VO(x) are formed, though for relatively high V loadings (6%) an obstruction of the zeolite windows takes place. The samples are tested as catalysts for gas phase dehydrogenation of n-butane to olefins. The catalysts prepared from NH4VO3 are almost inactive for the reaction. On the other hand, both samples prepared from V(AcAc)3 present initial conversion levels in the 8-12% range. However, the selectivity depends on the V loading, the catalysts with 6% loading being the most selective (75%). The catalytic patterns of the samples (activity and selectivity) are in agreement with the physicochemical features of the VO(x)/USY surface.     

Solid solubility of Ge,Si, and Mg in Fe2O3 and photoelectric behavior

Solid solutions of GeO₂ in Fe₂O₃ were prepared by mechanically mixing the solids and firing at 1000°C in air, and from a gel obtained by the addition of an alcohol solution of germanium ethoxide to iron dissolved in HNO₃. The dried gel was then heated at 1000°C. The solubility limit is 5 mole% GeO₂, Fe_1.95Ge_0.05O₃. Similar procedures were used to prepare solid solutions with Si and the solubility limit is greater than 4 mole% SiO₂. Firing of mixtures or gels of Fe₂O₃ containing Mg produces a spinel phase even at the lowest detectable concentrations. The resistivity of pressed pellets of Fe_2?xGe_xO₃ varies from about 10⁶ ohm-cm for x = 0 to about 10^?1 ohm-cm for x = 0.05. The photoassisted electrolysis of water at Ge-doped Fe₂O₃ electrodes is demonstrated. The $\text{Fe}{}_2\text{O}{}_3\text{(Ge)}\text{0.7 M}\text{Fe(CN)}{}^{\mathrm{4?}}{}_6\text{,}\text{0.05 M}\text{Fe(CN)}{}^{\mathrm{3?}}{}_6\text{Pt}$ photoelectrochemical cell showed a 0.29-V open-circuit voltage, 1.2-mA/cm² short-circuit current, 0.31 fill factor, and 0.06% power efficiency.