Effect of Confinement on the Translational Diffusivity of Small Dye Molecules in Thin Polystyrene Films and Its Connection to <i>T</i> _g -Confinement and Fragility-Confinement Effects

Using fluorescence, we study the impact of nanoscale confinement on the translational diffusivity (<i>D</i>) of trace levels of a small-molecule dye, 9,10-bis(phenylethynyl)anthracene (BPEA), in supported polystyrene (PS) films via Förster resonance energy transfer (FRET). Reductions in BPEA diffusivity are observed in films thinner than ∼200 nm, with <i>D</i> decreasing by 80-90% in 100 nm-thick films compared to bulk. The activation energy of BPEA diffusivity increases from ∼210 kJ/mol in bulk films to ∼370 kJ/mol in 130 nm-thick films. BPEA exhibits a greater diffusivity-confinement effect than a larger dye, decacyclene, in terms of the length scale at which the effects of confinement become evident and the percentage reduction in diffusivity. For both BPEA and decacyclene, the diffusivity-confinement effect in supported PS films occurs at a length scale much larger than that for the glass transition temperature (<i>T</i>_g)-confinement effect and somewhat larger than that for the fragility-confinement effect. This difference in confinement-effect length scales can be rationalized as follows: small-molecule dye diffusivity relates predominantly to short times in the α-relaxation distribution, whereas <i>T</i>_g relates to long times in the α-relaxation distribution, and fragility reflects the overall breadth of this relaxation time distribution. If confinement results in a narrower relaxation time distribution in PS films with the short-time relaxations being shifted to longer times and the longest-time relaxation regimes being shifted to shorter times, then <i>T</i>_g, diffusivity, and fragility all decrease at sufficient levels of confinement. If the narrowing with confinement begins with the shortest relaxation time regimes, then fragility and small-molecule dye diffusivity are influenced by confinement at larger length scales than <i>T</i>_g.