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

The spectrum of the electron spin–spin interactions largely determines the mechanism that governs dynamic nuclear polarization (DNP). A narrow spectrum favors 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 spin–spin 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.