Figure 1. Energy‐level diagrams (|m _S m _I>), transitions (ω _i), and relaxation rates W _i associated with an SI spin system. (a) The relaxation rates are given for dipolar coupling (W _I (nuclear), W ₀ (zero quantum), and W ₂ (double quantum)) and scalar coupling (W ^S ₀ (zero quantum)). (b) The Overhauser effect is achieved by applying saturating microwaves to the allowed EPR transitions (ω _e), while observing the NMR transitions (ω _n). In this example we assume that pure scalar relaxation is the dominant relaxation mechanism. (c and d) Solid‐effect, where W _S is the electron spin relaxation rate and ω _± are the forbidden transitions. The gray spheres represent the population probabilities (p ₁, p ₂, p ₃, p ₄) at the steady state without the application of microwaves (a) and with microwaves (b–d).

Figure 2. Dependence of the coupling factor ξ on the product of electron Larmor frequency and correlation time. Shown are cases of pure rotational and translational diffusion with dipolar coupling (solid lines), and of scalar coupling for various β values (dashed lines). The vertical lines correspond to experimental conditions of 9.8/0.3 and 260 GHz/10 T for a correlation time of 20 ps.

Figure 3. Energy‐level diagram (|m _S1  m _S2 m _I>) associated with a three‐spin SSI spin system (S, I = 1/2). Strong mixing between levels 4> and 5> occurs if the energy difference matches the nuclear Zeeman splitting.

Figure 4. Energy distribution of populations (n(E)) between electronic spin state manifolds m _Z = 1/2 and m _Z =− 1/2, separated by energy ħω _e. The width of each state (ħδ) is determined by electron–electron dipolar broadening. (a) Thermal equilibrium T _L = T _D = T _Z. (b) Application of off‐resonant microwave radiation at ω < ω _e “cools” the dipolar bath 0 < T _D < T _Z. (c) Application of off‐resonant microwave radiation at ω > ω _e “heats” the dipolar bath to a negative spin temperature 0 < |T _D| < T _Z, T _D < 0.

Figure 5. Setups for DNP at high magnetic fields.

Figure 6. DNP enhancement and EPR lineshape of 10 mM ‐TEMPOL in water at room temperature as a function of the external magnetic field.