Effect of Confinement\non the Translational Diffusivity\nof Small Dye Molecules in Thin Polystyrene Films and Its Connection\nto <i>T</i><sub>g</sub>‑Confinement and Fragility-Confinement\nEffects

Using fluorescence, we study the impact of nanoscale\nconfinement\non the translational diffusivity (<i>D</i>) of trace levels\nof a small-molecule dye, 9,10-bis(phenylethynyl)anthracene (BPEA),\nin supported polystyrene (PS) films via Förster resonance energy\ntransfer (FRET). Reductions in BPEA diffusivity are observed in films\nthinner than ∼200 nm, with <i>D</i> decreasing by\n80–90% in 100 nm-thick films compared to bulk. The activation\nenergy of BPEA diffusivity increases from ∼210 kJ/mol in bulk\nfilms to ∼370 kJ/mol in 130 nm-thick films. BPEA exhibits a\ngreater diffusivity-confinement effect than a larger dye, decacyclene,\nin terms of the length scale at which the effects of confinement become\nevident and the percentage reduction in diffusivity. For both BPEA\nand decacyclene, the diffusivity-confinement effect in supported PS\nfilms occurs at a length scale much larger than that for the glass\ntransition temperature (<i>T</i><sub>g</sub>)-confinement\neffect and somewhat larger than that for the fragility-confinement\neffect. This difference in confinement-effect length scales can be\nrationalized as follows: small-molecule dye diffusivity relates predominantly\nto short times in the α-relaxation distribution, whereas <i>T</i><sub>g</sub> relates to long times in the α-relaxation\ndistribution, and fragility reflects the overall breadth of this relaxation\ntime distribution. If confinement results in a narrower relaxation\ntime distribution in PS films with the short-time relaxations being\nshifted to longer times and the longest-time relaxation regimes being\nshifted to shorter times, then <i>T</i><sub>g</sub>, diffusivity,\nand fragility all decrease at sufficient levels of confinement. If\nthe narrowing with confinement begins with the shortest relaxation\ntime regimes, then fragility and small-molecule dye diffusivity are\ninfluenced by confinement at larger length scales than <i>T</i><sub>g</sub>.