Characteristic size of molecular dynamics in polymers probed by dielectric probes of variable length

Recently we introduced a rigid-rod type chromophore, E-4,4′-N,N-dibutylamino-nitro-stilbene (DBANS), that acts as a dielectric and fluorescent probe, and enables the study of molecular dynamics in apolar polymers by dielectric relaxation spectroscopy (DRS). This work focuses on the effect of the probe size and concentration on the specific probe response. For this purpose, a series of probe molecules with core lengths (l) between 0.6 and 2 nm was used to ‘dope’ polystyrene at concentrations from 0.1 to 1.0 wt%. For all probes, a selective amplification of the intrinsic α-relaxation was found that was linear within the whole probe concentration range. Moreover, two clear size effects on the probe dynamics were revealed. At high temperatures, the probe relaxation time obeys τ ∝ l3, which confirmed rotational diffusion as the linking mechanism between the polymeric segmental dynamics and dielectric probe response. The shortest probe revealed an additional Arrhenius-type (β∗) relaxation that was attributed to large angular probe fluctuations involving discrete jumps. Its exclusive occurrence indicates a critical lower probe size (l∗ ∼ 0.6 nm) below which the dielectric probe acts also as a ‘free-volume probe’ as indicated by the pronounced anormality in the τβ∗(T)τβ∗(T) dependence. Finally, an attempt was made to relate probe concentration effects on the glass transition temperature (plasticizing effect) to the intrinsic length scale of cooperative dynamics ξ. Based on a simple model for local plasticization we have determined a lower bound for ξ in the order of 5 nm.