Diffusion equation for the longitudinal spectral diffusion: the case of the RIDME experiment

Relaxation-induced dipolar modulation enhancement (RIDME) time trace shapes reveal linear scaling with the proton concentration in homogeneous glassy samples. We describe here an approximate diffusion equation-based analysis of such data, which uses only two fit parameters and allows for global data fitting with good accuracy. By construction, the approach should be transferable to other pulse EPR experiments with longitudinal mixing block(s) present. The two fit parameters appear to be sensitive to the type of the glassy matrix and can be thus used for sample characterisation. The estimates suggest that the presented technique should be sensitive to protons at distances up to 3 nm from the electron spin at a 90% matrix deuteration level. We propose that a structural method might be developed based on such an intermolecular hyperfine (ih-)RIDME technique, which would be useful, for instance, in structural biology or dynamic nuclear polarisation experiments.