Recasting the wobbling-in-a-cone model for the rotational anisotropy of phenylselenocyanate in poly(methyl methacrylate): Effect of internal bond rotation and polymer segmental motion

The rotational anisotropy of a molecule in a constrained environment is modeled by wobbling-in-a-cone (WIAC) motion, which describes the angular space sampled by the molecule. Recent polarization-selective IR pump-probe measurements have applied this model to phenylselenocyanate in amorphous polymers, aiming to probe the surrounding free volume. A faster rotational timescale was hypothesized to reflect the angular space within the static voids of the polymer matrix, while a slower timescale relates to constraint release by the polymer backbones. To better quantify the contributions of internal bond rotation and polymer segmental motion, we conduct molecular dynamics simulations on two phenylselenocyanate variants with different internal rotational barriers, as well as on p-chlorobenzonitrile, which lacks such internal rotational freedom, within a polymer matrix. Our analyses reveal that the faster (∼10 ps) component of the cyano group's anisotropy decay arises from concurrent angular sampling due to internal bond rotation and WIAC motion. Conversely, polymer segmental motion was found to have a minimal influence on the slow (∼200 ps) anisotropy component. Based on these findings, we refine the WIAC model to better link rotational diffusion with the distinct free volume elements accessed by the probe molecule. This revised model allows the quantification of free volume elements associated with both internal bond rotation and wobbling motion within the polymer cage.