Monitoring electron spin fluctuations with paramagnetic relaxation enhancement

The Effect of Disorder on Endogenous MAS-DNP: Study of Silicate Glasses and Crystals

“…In principle a quadratic dependence is expected at low saturation efficiencies (assuming T 1 e ∝ T 2 e ), with a bend toward a weaker dependence approaching higher efficiencies. In an experimental study we actually found a linear relation within a range of almost 1 order of magnitude in τ 1e , which we attributed to this bending . From the experimentally determined differences in electron relaxation times in this study it is clear that they will contribute to the observed divergence in DNP enhancements among glass and crystalline samples.…”

“…This steep decrease was not observed when estimating electron relaxation from τ 1e via NMR relaxation. Also in previous studies we only observed a very moderate decrease of T 1e with concentration within this range. , A possible explanation for this pronounced trend could be that extrapolation of the relaxation data obtained at 10 K at Q-band frequencies is not representative of the behavior at 100 K and 9.4 T, as different relaxation mechanisms might be involved …”

“…In addition, we showed that for low concentration of dopant, τ 1e is a good measure of the electron relaxation time T 1e . The correlation time τ 1e is simply related to the nuclear relaxation times and the nuclear Larmor frequency ω n according to , τ 1 e = ( T 1 T 2 − 7 6 ) 6 4 ω n 2 Using this equation, we estimate τ 1e values using the nuclear relaxation times of 29 Si and 6 Li for all concentrations to be approximately 0.8 ± 0.2 μs in the glass and about 2.0 ± 0.5 μs in the crystal (see Table S9 and accompanying discussion in the Supporting Information). Thus, the crystal has about a factor of 2–3 times longer electron relaxation times.…”

“… R 1 , 2 = T 1 , 2 − 1 are the relaxation rates, with R 1 D Q ≈ R 1 e ( ω d ω n ) 2 and R 1 n ∝ ( ω d ) 2 T 1 e 1 + ( T 1 e ω n ) 2 , assuming that one can replace τ 1e by T 1e . A more detailed derivation of this relation was given in previous studies. , The important consequence is that enhancements benefit from longer electron relaxation times (both T 1e and T 2e ). In principle a quadratic dependence is expected at low saturation efficiencies (assuming T 1 e ∝ T 2 e ), with a bend toward a weaker dependence approaching higher efficiencies.…”

“…Since these transitions are formally forbidden, the effective nutation frequency ω̃ 1 will be scaled by the strength of the dipolar coupling divided by the nuclear Larmor frequency, ω̃ 1 ≈ ω 1 ω d ω n . Saturation of these transitions is generally not achieved in MIDNP and is therefore a major limiting factor of signal enhancement . The analytical expression for the saturation efficiency, assuming that the polarizing agent is at the same time the main source of relaxation, is related to T 1e and T 2e according to , Δ p D Q / Z Q = Δ p D Q / Z Q , e q 1 + ω̃ 1 2 [ R 2 e false( 2 R 1 D Q + 2 R 1 n false) ] − 1 where normalΔ p D Q / Z Q is the polarization of the irradiated (DQ or ZQ) transition. R 1 , 2 = …”