Analysis of Avoided Level Crossing Muon Spin Resonance Spectra of Muoniated Radicals in Anisotropic Environments: Estimation of Muon Dipolar Hyperfine Parameters for Lorentzian-like Δ1 Resonances

Abstract

Avoided level crossing muon spin resonance (ALC-μSR) is used to characterize muoniated free radicals. These radicals are used as probes of the local environment and reorientational motion of specific components in complex systems. The parameter that provides information about the anisotropic motion is the motionally-averaged muon dipolar-hyperfine coupling constant (Dμ‖). The ALC-μSR spectra of muoniated radicals in anisotropic environments frequently have Lorentzian-like Δ1 resonances, which makes it challenging to extract Dμ‖. In this paper, we derive a means to estimate|Dμ‖| from ALC-μSR spectra with Lorentzian-like resonances by measuring the amplitude, width, and position of the Δ1 resonance and the amplitude, width, and position of a Δ0 resonance. Numerical simulations were used to test this relationship for radicals with a wide range of muon and proton hyperfine parameters. We use this methodology to determine |Dμ‖| for the Mu adducts of the cosurfactant 2-phenylethanol in C12E4 bilayers. From this we determined the amplitude of the anisotropic reorientational motion of the cosurfactant.