Electron spin relaxation due to small-angle motion: Theory for the canonical orientations and application to hierarchic cage dynamics in ionomers

Abstract

Analytical expressions for transverse electron spin relaxation induced by small angle motion were derived for the first time within an anisotropic model for rotational diffusion by using an approximation of the spin Hamiltonian and its variation during reorientation that is valid close to the canonical orientations. The dependence of the decay of the stimulated echo on such motion was studied by extensive Monte Carlo simulations and regimes were identified in which the time constant of this decay is related to parameters of the anisotropic diffusion model by simple equations. For testing these theoretical findings and obtaining insight into hierarchical cage dynamics in soft matter, high-field electron paramagnetic resonance (EPR) measurements were performed at a frequency of 94 GHz where the canonical orientations for nitroxide spin labels are well resolved. A combination of continuous wave EPR, saturation recovery measurements, and measurements of the decay of primary and stimulated electron spin echoes was employed to cover time scales from a few picoseconds up to several microseconds. Ionic spin probes attached by electrostatic interactions to the surface of ionic clusters in ionomers were used as a model system in which slow cage reorientation can be studied in the glass transition region of the polymer (0.64<T/Tg<1.05). Three hierarchical reorientation processes of the spin probe were observed on different time scales. The spin probe undergoes fast intramolecular libration on the time scale of a few picoseconds, it experiences a local rearrangement of the cage on the time scale of hundreds of nanoseconds and it performs cooperative reorientation coupled to the structural relaxation of the glassy matrix over time scales comparable to or longer than several microseconds in the glass transition region.