A tilted rotatory frame method for the measurement of nuclear spin diffusion coefficients in solids doped with paramagnetic centers: Mn-Doped CaF2

Abstract

Nuclear magnetic resonance (NMR) experiments recording the recovery of the magnetization of the nuclei in one phase, fo[lowing the excitation of the nuclei in the other phase, is a cIassical way of studying blends inhomogeneous at the nanometer scale. Interpretation of the time recovery in terms of the spatial dimension requires knowledge of the two-phase spin diffusion coefficients D o. A new method of measurement of D O is proposed on the basis of variable angle-tilted rotatory frame relaxation in homogeneous samples doped with paramagnetic centers. The choice of the tilt angle allows one to finely balance the direct relaxation by the paramagnetic center and the spin diffusion. The shape of the relaxation is analyzed with the solution for the diffusion-limited regime M(t)/M(O) = exp[-(r2t) la -rlt ] and D O then calculated from rl, r 2 and the concentration of paramagnetic centers. Conditions where reliable results can be obtained both theoretically and numerically ate explored. The method has been implemented and applied to polycrystalline Mn-doped CaF 2 leading to D O = 540+60 nmVs, in agreement with existing values on this model compound.

Measurement of Spin Diffusion Coefficients in Glassy Polymers: Failure of a Simple Scaling Law

“…The value derived from the spin diffusion experiments on block copolymers, [4,5] D PS % 800 nm 2 Á s À1 , is reasonably close to the value we have obtained with our method on Mn 2þ -doped poly(4-vinyl pyridine) of very comparable structure, D P4VP ¼ 500 nm 2 Á s À1 . [21] These difficulties are removed in PSd 5 , both because the natural T 1r is much longer at room temperature, and the Measurement of Spin Diffusion Coefficients in Glassy Polymers: Failure of a Simple Scaling Law Table 2. Fits of the tilted rotating frame relaxation to the Goesele Equation (3) and calculated values for b u and D.…”

“…Our method has been first tested on CaF 2, [21] a cubic crystal where D is known from calculations and measurements. The grating method of measurement which was used in undoped CaF 2 [24] requires the extremely high magnetic field gradients developed for NMR imaging.…”

“…[21,22] Magnetization spin lock at an angle u was obtained by a frequency jump of the radiofrequency field. [32] Its amplitude must therefore stay stable over several hundred milliseconds spin lock durations.…”

“…Relaxation measurements were carried out at 59 MHz on a homebuilt instrument 21, 22. Magnetization spin lock at an angle θ was obtained by a frequency jump of the radiofrequency field 32.…”

“…One observes in general a fast diffusion regime for relaxation in the laboratory frame ( T 1 scale), and a slow diffusion regime in the rotating frame ( T 1 ρ scale). The principle of our method,21, 22 which follows a 1997 suggestion of Goldman and coworkers,23 is to record relaxation in a tilted rotating frame, where the angle of tilt θ can be selected to reach the diffusion controlled limit.…”