Translational Diffusion Constants and Intermolecular Relaxation in Paramagnetic Solutions with Hyperfine Coupling on the Electronic Site

Abstract

We investigate the NMR relaxation of solvent nuclei in non viscous paramagnetic solutions, in the case where the electronic spin of the paramagnetic species is submitted to an internal hyperfine field H hyp . General expressions of the intermolecular longitudinal relaxation rates 1/T 1 are provided, and three distinct regimes corresponding to an applied external field lower, larger and much larger than H hyp appear, with three distinct linear laws for the relaxation rate 1/T 1 vs ν I 1/2 , where ν I is the nuclear resonance frequency. From each of these laws and mainly the third one, it is possible to derive the relative diffusion constant of the paramagnetic and solvent molecules without any model assumption for solutions with a rather high radical concentration of 10 -1 mol L -1 . This is illustrated for a triglyme solution with new stable 15 NTMIOD free radicals at various concentrations. For this solution, T 1 measurements were performed at ν I ) 244 MHz, then at low and intermediate frequencies by the field cycling technique and finally in the Earth's magnetic field. From these results and from measurements of the solvent molecule diffusion constant by the pulsed magnetic field gradient technique, a determination of the diffusion constant of the free radicals is obtained which is compared with that obtained from a direct ESR measurement at low concentration. These data are used for the interpretation of the frequency and temperature dependence of the relaxation rates in this solution.

Chemical analysis by ultrahigh-resolution nuclear magnetic resonance in the Earth’s magnetic field

“…NMR has been performed in the Earth's field in order to measure the 1 H− 31 P and 1 H− 14 N J-coupling constants 7,8 . Self-diffusion and relaxation-time measurements [9][10][11] , proton magnetic resonance imaging 11 (MRI), the detection of groundwater reservoirs 12 (>1 m 3 ) and the determination of water diffusion in the pores of the Antarctic shelf ice 13 were achieved by Earth's field NMR. Heteronuclear J-coupling constants have been measured with a spectral resolution of about 1 Hz in the micro-and nanotesla regime [14][15][16] by using SQUID sensors 17,18 .…”

Roto-translational diffusion of biaxial probes in uniaxial liquid crystal phases

“…The theory should be useful in the planning of experiments particularly sensitive to roto-translational effects such as those involving diffusion studied by optical, 12 neutron scattering, 14 and magnetic resonance techniques. 13,35,36 Another application should be in allowing the proper determination of rotational and translational diffusion tensor components for molecules of arbitrary shape dissolved in smectics by employing in the analysis of experi-mental data 9,37 this more general theory instead of one purely based on rotational motions such as that in Ref. 5.…”

Translational diffusion in paramagnetic liquids by 1H NMR relaxometry: Nitroxide radicals in solution

“…The proton spin relaxation is, however, affected by the hyperfine coupling between the electron and nitrogen spins. [21][22][23][24][25] The isotropic part of this coupling modifies the energy levels of the electron spin, while the anisotropic part (modulated by rotational dynamics of the paramagnetic molecule) leads to electron spin relaxation. In consequence, a description of the PRE effect caused by nitroxide radicals, valid for an arbitrary resonance frequency has proven to be a challenge.…”

“…In consequence, a description of the PRE effect caused by nitroxide radicals, valid for an arbitrary resonance frequency has proven to be a challenge. First the problem has been solved for 15 N-containing radicals 22 (as 15 N nuclei possess spin 1/2, the description is less complicated than for the 14 N case with the nitrogen spin 1); recently we have formulated a theory of PRE for 14 N-containing radicals in solution. 25 22 have been combined, in the same work, with the properties of the translational spectral density with the purpose to link the translational diffusion coefficient with the dependence (in fact, dependencies in this case-we shall explain this in the theory section) of the 1 H spin-lattice relaxation dispersion, in analogy to the case of diamagnetic liquids.…”

“…First the problem has been solved for 15 N-containing radicals 22 (as 15 N nuclei possess spin 1/2, the description is less complicated than for the 14 N case with the nitrogen spin 1); recently we have formulated a theory of PRE for 14 N-containing radicals in solution. 25 22 have been combined, in the same work, with the properties of the translational spectral density with the purpose to link the translational diffusion coefficient with the dependence (in fact, dependencies in this case-we shall explain this in the theory section) of the 1 H spin-lattice relaxation dispersion, in analogy to the case of diamagnetic liquids. [12][13][14][15] As 14 N spin probes are much more frequently used than 15 N radicals, in the present paper we extend this approach to the case of 14 N. We wish to stress that this is possible only on the basis of the recently developed description of PRE effects caused by 14 N-radicals.…”