The local molecular motion of $cis$-polybutadiene, a typical polymeric material exhibiting a glass transition ($T_{\mathrm{g}}=168\mathrm{K}$), is investigated by the spin relaxation of muonated radicals, where the relaxation is induced by the fluctuation of hyperfine (HF) fields exerted from an unpaired electron to a nearby muon and surrounding protons. The relaxation rate $1/T_{\mu }$ measured under various longitudinal magnetic fields is analyzed using the recently developed theory of spin relaxation to consider the coexistence of quasistatic and fluctuating HF fields, where the fluctuation frequency for the latter $\nu$ is evaluated over a temperature $T$ range of 5–320 K. The obtained $\nu \left(T\right)$ is found to be well reproduced by the Arrhenius relation, and the activation energy and preexponential factor are in good agreement with those for the “elemental process” revealed by quasielastic neutron scattering and attributed to a fluctuation across three carbon-carbon bonds. This result demonstrates that muonated-radical spin relaxation is a promising approach for direct access to local molecular motions in the subnanosecond range and for their detailed modeling at the atomic scale.

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• Glass transition
• Polymer behavior
• Polymer glasses
• Density functional theory
• Muon spin relaxation & rotation
• Quantum chemistry methods