Electron Spin–Spin Interactions in DNP: Thermal Mixing vs. the Cross Effect

Abstract

The spectrum of the electron spin-spin interactions largely determines the mechanism that governs dynamic nuclear polarization (DNP). A narrow spectrum favours the solid effect (SE). A broader spectrum brings the cross effect (CE) into play-that is an exchange of electron Zeeman energy with the nuclear spins-and a very broad spectrum also thermal mixing (TM)-that is an exchange of electron spinspin interaction energy with the nuclear spins. A previous article described Monte Carlo simulations of the spectrum of these interactions for approximately spherical radicals in glasses and showed that this spectrum is best described by a Lorentzian that is smoothly cut-off by a broad Gaussian. That work also provided analytical approximations for the lower moments of the spectrum and the width of the Gaussian cut-off. Here we extend that work with the derivation of an analytical approximation for the width of the Lorentzian and use the result to determine the relative strengths of the energy flows due to the CE and TM as function of the diameter of the radicals, their concentration and the magnetic field.

Radical-induced Hetero-Nuclear Mixing and Low-field $^{13}$C Relaxation in Solid Pyruvic Acid

“…These findings support a recent derivation of the triple spin flip rate by Wenckebach. 16,17,22 The observed carbon relaxation is in qualitative agreement with our model, but we find that the direct 1 H- 13 C exchange is increased at low fields, and that relaxation at high fields is slower than predicted by the model. As we discuss below, the latter discrepancy may be accounted for by limited transfer across the diffusion barrier.…”

“…An expression for the left-hand side of equation ( 6) has been given by Wenckebach 17,30 , and the matrix elements therein have recently been evaluated explicitly 22 . As detailed in the Supplementary Material, Eq.…”

Radical-Induced Low-Field 1H Relaxation in Solid Pyruvic Acid Doped with Trityl-OX063

“…An expression for the left-hand side of eq has recently been given by Wenckebach. , As detailed in the SI, his expression may be rewritten using the high-temperature approximation, leading to the following expression for the TSF rate 1 τ NZ − normalI = C normalI C NZ μ 0 2 80 false( ℏ γ I γ S false) 2 N S r ba 3 · prefix∫ − ω 0 I ω 0 I normald normalΔ ∫ − ∞ ∞ normald ω h ( Δ , ω ) with the integrand h false( normalΔ , ω false) = g i false( ω false) g i false( ω − normalΔ false) ( ω 0 I 2 − Δ …”

Three mechanisms of room temperature dynamic nuclear polarization occur simultaneously in an ionic liquid

“…6,7 The other possible DNP effects, CE 8,9 and TM, 10,11 are associated with the presence of interactions between several electron spins with simultaneous coupling to a nuclear spin. 12 These effects also exhibit most of their efficiency in solids and at low temperatures. Additionally, high radical concentrations improve the efficiency of both CE and TM.…”

“…At the same time, different theoretical approaches separate them by type of energy flow involved in triple spins flips. 9,17,18 The effect of the radical size, magnetic field strength, as well as radicals concentration on the mixing of CE and TM was theoretically described using a unified approach, 12 showing dominating TM at a low field, corresponding to the X-band, with small radicals in the 15-60 mM concentration range.…”