Spectral diffusion of electron spin polarization in glasses doped with radicals for DNP

Spectral diffusion of electron spin polarization plays a key part in dynamic nuclear polarization (DNP). It determines the distribution of polarization across the electron spin resonance (ESR) line and consequently the polarization that is available for transfer to the nuclear spins. Various authors have studied it experimentally by means of electron-electron double resonance (ELDOR) and proposed and used macroscopic models to interpret these experiments. However, microscopic models predicting the rate of spectral diffusion are scarce. The present article is an attempt to fill this gap. It derives a spectral diffusion equation from first principles and uses Monte Carlo simulations to determine the parameters in this equation. The derivation given here builds on an observation made in a previous article on nuclear dipolar relaxation: spectral diffusion is also spatial diffusion and the random distribution of spins in space limits the former. This can be modelled assuming that rapid flip-flop transitions between a spin and its nearest neighbour do not contribute to diffusion of polarization across the ESR spectrum. The present article presents predictions of the spectral diffusion constant and shows that this limitation may lower the spectral diffusion constant by several orders of magnitude. As a check the constant is determined from first principles for a sample containing 40 mM TEMPOL. Including the limitation then results in a value that is close to that obtained from an analysis of previously reported ELDOR experiments.