Molecular dynamics of $cis$-polybutadiene across glass transition revealed by muonated-radical spin relaxation

The local molecular motion of $cis$-polybutadiene, a typical polymeric material exhibiting a glass transition ($T_{\rm g}=168$ K), has been investigated by the spin relaxation of muonated radicals, where the relaxation is induced by the fluctuation of hyperfine (HF) fields exerted from unpaired electron to nearby muon and surrounding protons. The relaxation rate ($1/T_\mu$) measured under various longitudinal magnetic fields was analyzed by the recently developed theory of spin relaxation to consider the coexistence of quasistatic and fluctuating HF fields, where the fluctuation frequency for the latter ($\nu$) was evaluated over a temperature ($T$) range of 5--320 K. The obtained $\nu(T)$ is found to be well reproduced by the Arrhenius relation, and the activation energy and pre-exponential factor are in good agreement with those for the ``E-process'' revealed by quasielastic neutron scattering and attributed to a fluctuation across three CC bonds. This result demonstrates that muonated-radical spin relaxation is a promising approach for direct access to local molecular motions in the sub-nanosecond range and for their detailed modeling in the atomic scale.