E. Belorizky

Physical properties of solid polymer electrolyte PEO(LiTFSI) complexes

The physical properties of the ionic conductor, obtained by dissolution of lithium trifluoromethanesulphonylimide in polyethylene oxide, (PEO)nLi+((CF3SO2)2N)- have been investigated for several values of n. The phase diagram has been established from both DSC and NMR techniques. The diffusion coefficients of 7Li and 19F containing Species, determined by the pulsed magnetic field gradient (PMFG) technique, are interpreted as the measures of the cationic and anionic transport numbers, which are concentration dependent, and t+ reaches a value close to 0.3. This study is complemented by a systematic analysis of the behaviour of the 7Li relaxation time T1 versus temperature and concentration which is correlated to the glass temperature Tg.

NMR study of spectral densities over a large frequency range for intermolecular relaxation in liquids: Pair correlation effects

In order to study the dynamic effects of pair correlation functions on intermolecular translational relaxation in liquids, we have measured the relaxation times T1 of the protons in neopentane in the presence of di‐t‐butylnitroxide free radicals with concentrations varying up to 6.5×1020 paramagnetic centers × cm−3. Under these conditions, the dominant relaxation mechanism for the resonating protons arises from their interactions with the electronic spins of the free radicals. NMR experiments were performed between 2.2 and 250 MHz and these allowed us to obtain information about the behavior of the relevant spectral densities over a very wide range of frequencies 0<ωSτ≲50, where ωS is the electronic resonance frequency of the radical and where τ is the translational correlation time. It is shown that a model in which the effects of eccentricity of the spins are included and where the translational motion of the molecules is described by a Smoluchowski diffusion equation, (i.e., taking into account their i...

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.

Effects of eccentricity on nuclear magnetic relaxation by intermolecular dipole–dipole interactions: 13C relaxation of neopentane

In order to study the eccentricity effects on the nuclear magnetic relaxation by intermolecular dipole–dipole interactions, we measured the relaxation times T1 of the center and off‐center 13C nuclei in neopentane C(CH3)4. To eliminate a competition between several relaxation machanisms, mainly with the protons, di‐t‐butylnitroxide free radicals were included with concentrations varying up to 5.6×1020 paramagnetic centers × cm−3. Under these conditions, the dominant relaxation mechanism for the resonating 13C nuclei spins arises from their interactions with the electronic spins of the free radicals. A difference of 15% between the relaxation times of the central 13C and of the off‐center carbons is observed. These results are partially interpreted by using the spectral densities j2(ω) resulting from translational and rotational motions as established in our previous work. It is shown that pair correlation effects must also be taken into account to improve the fit with the experimental data.

Various aspects of dynamical properties of high and low molecular weight PPO-LITFSI polymer electrolytes obtained by NMR techniques

Abstract Complementary NMR studies on PPO n (LiTFSI) polymer electrolytes are reported. An improved sequence for measuring the diffusion constants of proton and lithium nuclei is presented, allowing the determination of the transport number of these systems. Our descriptive model, involving the coexistence of entangled and non-entangled parts of the high weight polymer chains, is supported by the various results concerning the relaxation times and the 1 H diffusion constants.

Monte Carlo calculation of the intermolecular dipolar spin relaxation in a liquid solution

The time correlation function characteristic of the intermolecular dipolar spin relaxation in a liquid solution is calculated by a Monte Carlo diffusive simulation. The validity of the Monte Carlo method for modeling molecular dynamics is examined referring to the careful analysis by Hilhorst and Deutch of the Monte Carlo work on polymer kinetics of Verdier et al. The Monte Carlo estimates of the time correlation function are compared with those obtained by analytical solutions of translational diffusion equations. The normalized solutions of the Smoluchowski diffusion equation, including the effects of the nonuniform radial molecular distribution, are appropriate for describing the relative random walks of two given molecules in the liquid.

Determination of relative diffusion constants in a non-viscous liquid solution by nuclear spin relaxation

The frequency dependence of the intermolecular relaxation rate, 1/T 1, of the protons of neopentane in a liquid solution containing di-t-butylnitroxide free radicals is analysed at low frequency. This allows a direct determination of the relative diffusion constant of the two kinds of molecules around room temperature from which it is possible to deduce the absolute diffusion constant of the free radicals.

An efficient diagonalization method for fitting the exchange constants in a spin cluster from susceptibility data: Application to a pentacopper(II) complex

We describe a simple method for diagonalizing the isotropic exchange hamiltonian of a cluster of N spins in the most general case where all the exchange constants are different. The technique which is based on the rotation invariance of the system, leads to a reduction of the total hamiltonian matrix to submatrices of the lowest possible order and represents a considerable decrease of the computational work with respect to usual methods. Simple analytical expressions of the magnetization and magnetic susceptiblity are provided. As an example, the exchange constants of a pentacopper(II) complex are fitted from susceptibility data.

Frequency dependence of the effects of eccentricity on nuclear magnetic relaxation in liquids. 13C relaxation of neopentane due to free radicals

Abstract Measurements of the relaxation time T 1 of the central and of the four equivalent off center 13 C nuclei in neopentane, C(CH 3 ) 4 , were performed in solutions containing di- tert -butyl nitroxide free radicals. In such systems, the intermolecular dipole magnetic interaction with the electronic spins of the free radicals is the only efficient relaxation mechanism for the resonating 13 C nuclei. The difference between the relaxation times of the central and of the off-center carbons was measured at three different resonance frequencies (15, 25, and 63 MHz) at T = 303 K. It is shown that spin exchange has a negligible effect and the results are interpreted using the spectral densities resulting from the molecular translational and rotational motions as we established previously. It is shown that the effects of eccentricity cannot be explained with a uniform equilibrium distribution of the interacting molecules. It is essential to take into account pair correlation effects and the translational diffusive motion of the molecules must be described by a Smoluchowski equation. Good agreement with experiment is then obtained for the relaxation times and the effects of eccentricity.